liangzid/robench2025a_test_all_category_setq-bioSCP-s

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A: It combines ncRNA sequences across 47 different databases, resulting in a total of ∼similar-to\sim∼27 million RNA sequences (Supplementary Table 2, 3, 4).B: This dataset is a comprehensive collection of ncRNA sequences, representing all ncRNA types from a broad range of organismsC: The large-scale dataset used in the pre-training phase was collected from RNAcentral 47, the largest ncRNA dataset available to date	CBA	BCA	BCA	CAB	Selection 1
A: When subpopulations have different trait values, selection acts to create a non-uniform distribution of populations sizesB: This illustrates the essence of the general case (14), where the Shannon entropy is replaced by a weighted entropy [47].C: This equation describes the balance between variation in the trait between subpopulations and the entropy in the distribution of subpopulation sizes, when subpopulations are following SHM in the way we have described	ABC	ABC	ABC	BCA	Selection 4
A: In SO scenarios, one might simply assess the absolute difference between the fitness expected from training data and the fitness observed on new dataB: However, in MO scenarios, it is crucial to consider each solution’s contribution to the Pareto frontC: We introduce two novel metrics to measure this estimation error in MO CV setups.	ACB	ABC	CAB	BCA	Selection 2
A: Barbieri et al. [6] proposed an unsupervised, physics-informed DNN (IVIM-NET) with results comparable to Bayesian methods with further optimizations by Kaandorp et al. [24] (IVIM-NEToptimoptim{}_{\textrm{optim}}start_FLOATSUBSCRIPT optim end_FLOATSUBSCRIPT)B: Zhang et al. [42] used a multi-layer perceptron with an amortized Gaussian posterior to estimate the IVIM model parameters from fetal lung DWI data. Recently, Vasylechko et al. [37] used unsupervised convolutional neural networks (CNN) to improve the reliability of IVIM parameter estimates by leveraging spatial correlations in the data.C: In the past few years, state-of-the-art, DNN-based methods were introduced for IVIM parameter estimation. Bertleff et al. [8] demonstrated the ability of supervised DNN to predict the IVIM model parameters from low SNR DWI data	BAC	BCA	BAC	ACB	Selection 2
A: The advantages of the GNN architecture are well illustrated by the results for chignolin. A previous machine-learning study of chignolin identified two slow CVs, one for the folding-unfolding transition and one distinguishing competing folded states[63]. Our VAMPnets appear to recover these two CVs (Figures 3 and S3; results shown are with SubMixer), distinguishing folded and unfolded states with CV 1 and four folded states with CV 2B: CV 2 distinguishes the folded states by the configurations of Thr6 and Thr8 side chains, which can each occupy two rotamers, yielding four possible folded states. These side chain dynamics could not be detected by VAMPnets that take backbone internal coordinates as inputs, as is common, or even GNNs limited to backbone atoms (Bonati, Piccini, and Parrinello [63] included distances to side chain atoms and then manually curated the inputs).C: To understand the physical differences between the folded states, we plot CVs 1 and 2 as functions of the fraction of native contacts and the χ1subscript𝜒1\chi_{1}italic_χ start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT side chain dihedral of Thr6 or Thr8 (Figure 4). The fraction of native contacts clearly correlates with CV 1, consistent with earlier studies	BAC	CBA	CBA	ACB	Selection 4
A: [47] introduced two models inspired by the COVID-19 pandemic, incorporating elements of game theory, disease dynamics, human behaviour, and economics. A study by A. Rajeev et al. [55] delved into an evolutionary game theory model to examine individuals’ behavioural patterns and identify stable statesB: M. Alam et al. [2] emphasized the significance of implementing multiple provisions promptly to enhance disease containment efforts using game theory and human behaviour. H. Khazaei et al. [39] analyzed the SEIR epidemiological model alongside an individual behaviour response model, specifically exploring the dynamics of a game where the public’s compliance with social distancing measures is influenced by the state of disease and associated payoffs. C: During the COVID-19 outbreak, several distinct computational and mathematical models have been developed to investigate the significance of quarantine as a game-theoretic strategy and its impact on disease transmission as well as hospitalization rates [59, 47, 2, 39]. C. N. Ngonghala et al	CAB	BCA	ACB	CAB	Selection 2
A: Convergence of the chains was assessed using Rubin’s R𝑅Ritalic_R statistic [23]B: The analysis produced approximate samples from the posterior distribution of the parameter vector θ∗superscript𝜃∗\theta^{\ast}italic_θ start_POSTSUPERSCRIPT ∗ end_POSTSUPERSCRIPT (see Figure 4 below). C: The MCMC analysis was based on two chains of 3,000 iterations, with a burn-in period of 1,000 iterations	ABC	ABC	BAC	BCA	Selection 4
A: Other authors have studied biophysical network models of premotor neuronsB: The stationary distributions of the motor neurons were then used to infer synaptic polarities, i.e., whether a synapticC: Rakowski et al. (2013) and (2017) simulated the dynamics of a pre-motor and motor circuit	CAB	CAB	BCA	ACB	Selection 4
A: What might you do? If you start very early and have plenty of time, you might prefer to walk all the way. If you have very little time, you might need to run all the wayB: But if you had an intermediate amount of time, what might you do? Here, we perform this experiment for two long distances over 800 meters, and show that humans systematically use a mixture of walking and running when there is an intermediate amount of time. That is, we show that for such overground tasks, there is not a sharp gait transition speed below which walking is preferred and above which running is preferred. Having this mixture of walking and running instead of a sharp gait transition speed is energy optimal [1, 22, 23], and was earlier observed over short distance tasks in humans [1], so the primary experimental contribution of the current study is its demonstration over much longer distances. C: Imagine you need to travel on foot from your home to an important appointment a kilometer away at a particular time (Figure 1). Unlike on a treadmill, where the speed is constrained, in this overground experiment, you can change speed or change gait	ACB	BCA	CAB	ABC	Selection 2
A: Metabolic cost models developed from isolated muscles experiments in-vitro have generally been compared with whole body movement tasks such as walking and have not been compared in detail with in-vivo human isometric experiments designed explicitly to test those models [22, 23, 24, 25, 26, 27]B: Previous metabolic cost models have certain limitations in the prediction of metabolic cost for isometric tasksC: Most models are particularly deficient in predicting the cost of isometric force. For instance, the Umberger et al model [27] predicted roughly 7% of experimentally measured cost for an isomeric task involving tracking sinusoidal forces [28]. The models developed from in vivo human experiments have either no prediction for isometric tasks as they were derived with terms specific to non-isometric tasks [29, 30, 31], considered only force level changes but not time series changes [32, 8] or only time series changes but not force level changes [33, 28].	CAB	ABC	BAC	CAB	Selection 3
A: Figure 2: The pathogens distribution on nodes with different distances from the root node (values on titles)B: Initial parameters are as in Figure 1C: The x𝑥xitalic_x-axis is α𝛼\alphaitalic_α and the y𝑦yitalic_y-axis is the ratio of the number of nodes infected with each pathogen to the total number of infected nodes in this distance.	BAC	BAC	CAB	ABC	Selection 4
A: The black line is the least-squares fit to the red dataB: The curve is closely fitted by the simple power relationship, y=0.0506⁢x−0.822𝑦0.0506superscript𝑥0.822y=0.0506x^{-0.822}italic_y = 0.0506 italic_x start_POSTSUPERSCRIPT - 0.822 end_POSTSUPERSCRIPT.C: values	ABC	BAC	BCA	ABC	Selection 3
A: Second, there is a separation of mutational time scales: site complexity changes take place at a much lower rate than recognition site and target mutations (ν≪μmuch-less-than𝜈𝜇\nu\ll\muitalic_ν ≪ italic_μ). Third, because selection on the recognition function depends only the binding affinity phenotype Δ⁢GΔ𝐺\Delta Groman_Δ italic_G, the model does not introduce any explicit fitness benefit of sequence complexity. Nevertheless, complexity can emerge as a collateral of selection for function in a non-equilibrium dynamical pathway – an evolutionary ratchet. We will first characterize the complexity of stationary states in different parameter regimes of the evolutionary model, then derive specific dynamical pathways towards these states.B: Three model features turn out to be crucial for what follows. First, the sequence mutation dynamics does not introduce any bias towards higher complexityC: Clearly, the minimal evolutionary model is a broad approximation to the evolutionary dynamics of any specific receptor-target interface. The model neglects many details of actual molecular evolution processes that are not important for conclusions of this paper	ACB	BCA	CBA	BAC	Selection 3
A: For peak calling, MACS2 (v2.1.2) software was used with option --nomodel --nolambda --keep-dup all -p 0.01. ATAC-seq tracks were visualized using Integrative Genomics Viewer (IGV), and footprinting analysis was performed using HINT-ATAC (Li2019, ). Note that the paired-end output of the sequence was used to reconstruct the fragments, where paired two reads correspond to both ends of a fragment. B: ATAC-seq reads were aligned using BWA version 0.7.16a with default parameters. SAMtools was used to convert SAM files into compressed BAM files and sort the BAM files by chromosome coordinatesC: PICARD software (v1.119) (http://broadinstitute.github.io/picard/) was used to remove PCR duplicates using the MarkDuplicates options. Reads with mapping quality scores less than 30 were removed from the BAM files	BAC	BCA	CAB	ABC	Selection 3
A: A strong core-periphery structure implies the system has a set of dominant, highly interconnected basins of attraction (the core) where transitions are frequent and stableB: The peripheral basins of attraction are less frequently visited, with transitions mainly leading back to the coreC: This structure indicates that the system tends to remain within the core’s stable dynamics and only occasionally explores the less stable, transient states represented by the periphery. In contrast, in the syncopation condition, the average dwelling time and motif length decreased, betweenness centrality declined, and average shortest path length increased. This indicates that stronger coupling in syncopation enhances the stability of a larger set of states and distributes the probability flow more broadly, reducing the dominance of core nodes and creating a more distributed but less efficient flow.	BAC	BAC	CBA	ABC	Selection 4
A: 2023; Harini, Sekijima, and Gromiha 2024a), focusing on extracting structural features at the binding interface, such as energy and contact distance. Based on the extracted features, they developed structure-based machine-learning approaches for affinity prediction. However, these methods are highly dependent on feature engineering with limited generalization ability on new samples due to the limited development dataset size.B: However, their performance is often limited because the binding affinity is mainly determined by the binding interface structure (Deng et al. 2019). Other recent methods are structure-based (Hong et alC: Several computational methods have been proposed for protein-RNA binding affinity prediction, including sequence-based and structure-based methods. The sequence-based approaches process the protein and RNA sequence separately with different sequence encoders (Yang and Deng 2019a; Pandey et al. 2024), and subsequently model the interactions	CBA	CAB	BCA	BAC	Selection 1
A: Additionally, because our metric is lighter, faster and requires significantly fewer resources, it is efficient than previous metrics. We believe this work will empower researchers to train and test generative models more efficiently.B: Our metric has been shown to be monotonic with respect to various noise types found in histopathology, including noise, occlusion, and blurC: We developed a new evaluation metric based on normalizing flow and measures the L2 distances between real and generated features	ABC	CBA	CAB	ACB	Selection 2
A: Figure 1: Commuting network among Brazilian cities. The map displays the locations of Brazilian cities, which correspond to the network nodesB: Edge widths indicate the number of commuters between city pairs. In this visualization, edges are grouped based on their proximity using a kernel-based edge bundling algorithm [33]. The emerging structures of this network illustrate the complexity of inter-city interactions. Figure created using Matplotlib [34], GeoPandas [35], and NetworkX [36].C: Connections represent the flow of commuters between city pairs, irrespective of direction. Node sizes are proportional to the weighted total degree of the cities and are also color-coded accordingly	BCA	ACB	BAC	CAB	Selection 2
A: To address this issue, network embedding techniques can be employed [39]B: Shingo Tsuji successfully used a deep neural network (DNN) to embed a PIN into latent space, creating a framework for inferring Alzheimer’s disease targets [37]. Building on this, more advanced AI-powered embedding algorithms, such as those based on Random Walk, Graph Neural Networks (GNNs), and edge sampling, offer promising improvements for leveraging PIN data to identify druggable genes [19, 26, 41].C: Network embedding aims to maximally preserve a network’s information while reducing its dimensionality, facilitating higher resolution and better quality of network data [9]	CBA	ABC	ACB	ABC	Selection 3
A: Given the ability to treat design directly as the reverse problem for structural and functional prediction, developments in these categories should be closely linkedB: Advancements in structural prediction, most notably from Alphafold2, have yet to make its impact in protein designC: Proper evaluation methods will need to catch-up first however if future advancements are to be properly measured.	ABC	BAC	ABC	ABC	Selection 2
A: Unlike simpler PCA-based inference models, VNNs offer stability [11] and transferability guarantees [18], which ensure reproducibility of the inference outcomes by VNNs with high confidence. B: Theorem 1 in [11] established the equivalence between processing data samples with principal component analysis (PCA) transform and processing data samples with a coVariance filter 𝐇⁢(𝐂)𝐇𝐂{\mathbf{H}}({\mathbf{C}})bold_H ( bold_C )C: Hence, it can be concluded that input data is processed with VNNs, at least in part, by exploiting the eigenvectors of 𝐂𝐂{\mathbf{C}}bold_C	CAB	ACB	BCA	CBA	Selection 1
A: Relationships between living things and their natural environments are the only focus of ecological research. Ecological systems are developed by their interactions, which are important for population ecology. In nature, resources are frequently distributed extensively over the ecosystemB: Therefore, organisms are diffusive throughout the environment because they must locate food and survive. Since trophic interactions are greatly influenced by species movement, different spatial patterns in nature have evolved. Several studies have demonstrated that aquatic and terrestrial populations may form patterns [31, 32]C: Spatial patterns are shaped by many causes, including deterministic processes, species growth, mobility, stochastic processes, environmental changes, and more. Because species interact across habitats, patterns are common in the ecological system [33, 34]. Self-organized spatial patterns are the result of a deterministic process in interacting organisms. The spatio-temporal predator-prey model is given as follows:	CAB	ABC	BAC	CAB	Selection 2
A: This trend continued with the OOD Testing independent from pMT-unseen tetsing, where Fusion-pMT scored 0.6320, significantly higher than pMTnet’s 0.5744. In terms of accuracy (ACC), Fusion-pMT also showed superior performance. On the pMT-unseen tetsing, Fusion-pMT had an accuracy of 0.7092, while pMTnet had 0.6558. This pattern was evident in the OOD Testing as well, with Fusion-pMT scoring 0.6001 against pMTnet’s 0.5428.B: For instance, when evaluating the ROC AUC on the pMT-unseen tetsing, Fusion-pMT achieved a mean score of 0.7326 compared to pMTnet’s 0.7158C: Our Fusion-pMT consistently outperformed the pMTnet across various metrics and datasets shown in Figure 3	CBA	CAB	BAC	BAC	Selection 1
A: Täuber, and Mauro MobiliaB: The C++ code used to generate the data and the Python and Matlab codes to process and visualize the data within this work can be found at the Open Science Framework repository (Lluís Hernández-Navarro, Kenneth Distefano, Uwe CC: 2024.	BAC	ABC	CBA	ACB	Selection 1
A: Here, we discuss the functionality included in PENSA and demonstrate its usefulness on three real-world applications: We show how to describe the influence of local frustration on loop opening during the catalytic cycle of an oxidoreductase,Stelzl et alB: (2020) how to quantify the influence of force-field parameter changes on simulations of nucleic acids,Cruz-León et alC: (2021) and how to identify the effect of ionization on receptor proteins. The examples reproduce existing results, confirming the reliability of our approach, but also demonstrate additional new discoveries made possible by systematic comparison of molecular simulations.	CBA	BCA	ABC	CBA	Selection 3
A: In this way, we wished to see how the ERP component is regulated by the distinctiveness of the event and the selective listening mechanism. B: The motivation for this experimental design was to investigate the cognitive processing of speech eventsC: Going from paradigm 1 to 3, the experimental complexity was increased in terms of task difficulty and practicality	CAB	BAC	CBA	CBA	Selection 1
A: assembled structures or copied polymers. As a consequence, complex systems can achieve stereotyped reproducible behaviors, despite living in high-dimensional disordered state spaces, through simple non-equilibrium mechanisms that also provide speed benefits. B: Finally, resets have been shown to be a broadly relevant strategy for speeding up search in a broad range of contexts [40, 62, 60, 65, 63, 86]. Our work points out that in addition to saving time, reset mechanisms effectively reduce the entropy of paths used to reach a destination stateC: Such ‘canalization’ into a few paths can be seen as a non-equilibrium version of Waddington’s homeorhesis [87]. The reduction in trajectory entropy can show up as higher observable order in, e.g	BAC	CBA	CAB	CBA	Selection 3
A: This scale is instrumental in both clinical settings and research studies for monitoring the progression of the disease and assessing the impact of therapeutic interventions on cognitive function.B: A lower FVC value thus reflects a worse disease state for a fibrosis patient. In the evaluation of Alzheimer’s Disease, the ADAS-13 (Alzheimer’s Disease Assessment Scale-cognitive subscale with 13 items) serves as a pivotal metric for modeling cognitive impairmentC: An increase in the ADAS-13 scores is indicative of a deterioration in cognitive abilities, with higher scores corresponding to a more severe decline	BAC	BCA	ACB	CAB	Selection 4
A: Similarly, when the default FI (red triangles) was compared to leave-one-out NFPFP5 (cyan squares), the FI was superior. Both the NFPFP5 and FI typically out-performed chronological age, except for predicting weakness (deficit grip strength)B: Figure 1: The FI predicts future FPFP5 deficits better than NFPFP5. The FI that includes the FPFP5 performed the best (green upside-down triangles)C: Only NFPFP5 including all deficits (purple circles) performed comparably to the default FI. The AUC is the probability that a metric will correctly rank positive individuals as higher than negative individuals [31] (dotted line at 0.5 indicates a random guess). Leave-one-out excludes the outcome deficit from the predictor. Error bars are standard errors.	ABC	BAC	ABC	BCA	Selection 2
A: Our downstream performance on genomic benchmarks indicates the potential of METAGENE-1 as a general-purpose foundation modelB: We are continuing to actively explore this direction, through incorporating additional human reference genomes and multi-species genomic datasets in our metagenomic pretraining data.C: Our results also indicate that METAGENE-1 benefits from continual pretraining on a diverse mixture of data sources in addition to metagenomic data (at least for tasks similar to these genomic benchmarks)	BAC	ACB	CBA	BAC	Selection 2
A: We employ two age grouping strategiesB: This approach is motivated by its interpretability, as decade intervals are commonly used and easily understood, making the results accessible to a broad audience. The second grouping is based on research by [24], which identified key inflection points in aging at approximately 34,60, and 78 years. This strategy divides the age range into four segments: [0-34), [34-60), [60-78), and 78+, aligning with significant biological and proteomic changes that correspond to shifts in aging patterns.C: The first divides the age range into decade-sized intervals: [0−10),[10−20),[20−30),…,[90−100),[100+[0-10),[10-20),[20-30),\ldots,[90-100),[100+[ 0 - 10 ) , [ 10 - 20 ) , [ 20 - 30 ) , … , [ 90 - 100 ) , [ 100 +	ACB	CBA	CAB	BCA	Selection 1
A: We find the model learns a factorised representation (Fig. 1G) and maintains a similar level of sparseness compared to the discrete model (FigB: 1F). We also observe that both discrete and asynchronous models have very similar learning trajectories (FigC: 1D), reaching the same error at convergence. In contrast, the continuous model is more unstable and does not reach the same error.	CAB	CAB	ABC	BAC	Selection 3
A: We demonstrate the wide applicability of UniGuide by tackling a variety of geometry-constrained drug discovery tasksB: With performance either on par with or superior to tailored models, we conclude that UniGuide offers advantages beyond its unificationC: Firstly, while the novelty of conditional models often stems from the condition incorporation, our method redirects focus to advancing unconditional generation, which directly benefits multiple applications. Furthermore, this separation of model training and conditioning allows us to tackle tasks with minimal data, a common scenario in the biological domain.	CAB	CAB	BCA	ABC	Selection 4
A: Peptides have aroused great interest due to their potential as therapeutic agents (Wang et al., 2022)B: Here, we focus on peptide generation by diffusion models.C: Currently, there are several reviews (Wan et al., 2022; Ge et al., 2022; Goles et al., 2024) that summarize the application of generative models to peptides	CAB	ACB	ABC	CBA	Selection 2
A: Activation of GABAB receptors initiates a signaling cascade that can lead to the opening of potassium channels and inhibition of adenylate cyclase activity. This results in the slow and prolonged inhibitory effects of GABA, contributing to the overall inhibitory tone in the nervous system.B: GABAA receptors are ionotropic receptors that function as ligand-gated chloride channels. When GABA binds to these receptors, the channel opens, allowing chloride ions to enter the neuronC: This influx of chloride ions causes hyperpolarization of the neuronal membrane, making it less likely for the neuron to fire an action potential. GABAA receptors act quickly and are primarily responsible for the rapid inhibitory effects of GABA. In contrast, GABAB receptors are metabotropic receptors that are coupled to G-proteins	BCA	ABC	ACB	CAB	Selection 4
A: We compared our model to an end-to-end baseline derived from Shen et al. (2019) [11], aligned with our goals of spatially accurate reconstructions. B: While recent image reconstruction models, such as diffusion models, produce high-resolution outputs, our study prioritizes spatial accuracy and interpretability in an end-to-end frameworkC: Diffusion models, though effective in generating detailed images, have objectives distinct from ours, given their reliance on separate generative processes rather than latent representation learning	CAB	ABC	BAC	CBA	Selection 1
A: B: Noticed that all those are encoded in Branish and none of them has been assigned weight yetC: This function G takes the state as input, based on its knowledgement of the world, it will output a matrix of gist, which might be possible actions in IG and thoughts, answers, and questions in TG	BAC	ACB	BAC	CBA	Selection 4
A: By exploring its applications across multiple disciplines, we aimed to inspire further exploration and application of the FHN model in diverse scientific domains. B: In conclusion, we hope our review will serve as a guide for understanding and using the diverse dynamical behaviors offered by the FHN modelC: Throughout our analysis, stability analyses and bifurcation studies provided insights into the observed dynamics	CAB	CBA	CBA	ABC	Selection 1
A: On the other hand, phase shifts smaller than π𝜋\piitalic_π lead to connections with the preceding excited region, resulting in connective pulses that propagate in the same direction as the driving wave (Supp. Fig. S5B).B: Specifically, phase shifts greater than π𝜋\piitalic_π prompt the system to connect with the forthcoming excited region, producing connective pulses that travel opposite to the driving wave (Fig. 9)C: In another instance, narrowing the driving pulse strengthens the phase shifts. With optimal diffusion levels, the system can link with the nearest excited region, generating connective pulses	CBA	ACB	ABC	BAC	Selection 1
A: MPNN operates on a graph consisting of a set of vertices and edgesB: We follow Dauparas et alC: (2022); Ganea et al. (2022) and set as initial node features a positional encoding that reflects the residue’s ordering within the sequence, while for the edge features, we use a concatenation of pairwise distance features, relative orientation features and relative positional embeddings.	ABC	CAB	BCA	BCA	Selection 1
A: A future research direction is deriving the brain’s slow dynamics and learning mechanismsB: Promising results have emerged in simplified neuron models [12]. Transferring the approach to realistic neuron models creates a data-driven possibility to recover biological slow dynamics.C: Training many parameters over extended periods allows black-box models, such as neural networks representing protein networks, to act as homeostatic-control agents within cells	ACB	BCA	CBA	CBA	Selection 1
A: In extreme cases this mismatch in individual fitness and population viability can lead to evolutionary suicide, where viable populations adapt in a way that they can no longer persist (Parvinen, 2005; Ferriere and Legendre, 2013). Conversely, because of the interplay between evolutionary and ecological processes (such as fluctuation in host densities), parasites should evolve toward decreased virulence (Lenski and May, 1994). Moreover, co-infection of hosts (singly infected cells remain susceptible and can be infected again) (Alizon, 2013) can result in feedback loops between the rate at which susceptible individuals acquire a disease (the force of infection) and virulence: when double infections are common increased virulence is favored; however, increased pathogen virulence decreases the force of infection, favoring decreased virulence once more (van Baalen and Sabelis, 1995). B: Still, since selection acts first and foremost on the level of individuals, traits which produce more offspring should generally increase in frequency. This suggests tensions between selective pressures on individual phages and the viability of the phage population overallC: A natural expectation is that larger burst sizes would benefit the phage population. However, our analysis suggests that thereby phages also deplete their resources for further replication	CBA	BAC	BCA	ABC	Selection 1
A: An advantage, in contrast, is that DNA-based approaches are well suited for parallelization. These (dis)advantages are familiar from DNA computing in general.B: This can certainly not be said about DNA computers. Their computational speed depends on how fast the chemical reactions take place, which can be of the order of many minutesC: A further aspect to note here are the time scales involved here. Photonic neural networks (see the chapters by Kathy Lüdge/Lina Jaurigue and by Lennart Meyer/Rongyang Xu/Wolfram Pernice) have the attractive feature that they operate with the speed of light, i.e., they are extremely fast	CBA	BCA	ACB	BCA	Selection 1
A: (2023) developed a model using Bidirectional Encoder Representations from Transformers (BERT) contextual embeddings (Devlin et al., 2018) to predict MEG signals. In terms of decoding, one paper (Défossez et al., 2023) successfully reconstructed audio from MEG signals through contrastive learning which was based on aligning signals with the latent space generated by the wav2vec2 library (Baevski et al., 2020). These efforts demonstrate the potential of using MEG data to reconstruct the stimulus that has generated it.B: So far, research in brain encoding for speech and language processing has primarily used functional Magnetic Resonance Imaging (fMRI) (Huth et al., 2012; Antonello et al., 2023; Caucheteux et al., 2023). These studies have contributed to the development of both linear and nonlinear models that map stimuli to brain activity from fMRI signals. Previous work focused on e.gC: enhancements in network scaling and uncovering associations between brain activity and specific auditory and semantic processing tasks (Caucheteux and King, 2022). However, limitations in the temporal resolution of fMRI, which are particularly relevant in speech decoding due to the high-frequency content of the stimuli, have led researchers to explore MEG data collected during exposure to auditory stimuli. On the encoding side, Oota et al	ACB	CAB	CBA	BAC	Selection 2
A: In a homogeneous attractant environment, after a large number of runs and tumbles the net displacement of the cell is zero. But in presence of an attractant concentration gradient, runs in the favorable direction are extended and those in the opposite direction are shortened, giving rise to a chemotactic drift [27, 28, 29, 30, 31].B: In this work, we use reinforcement learning to study a model that has been motivated by the phenomenon of bacterial chemotaxis [15, 16, 17]. Certain bacteria like E.coli, S.typhimurium, B.subtilis are known to show chemotaxis where they can move along a chemical gradient in their environment [18, 19, 20]C: When these microorganisms experience concentration gradient of an attractant chemical in their surroundings, they show a tendency to migrate towards regions of higher attractant concentration [21, 22, 23, 24]. This migration happens via run-and-tumble motion, which is characterized by persistent movement along a particular direction (run), punctuated by abrupt change of direction (tumble) [25, 26]	CBA	BCA	BCA	CAB	Selection 4
A: Neural encoding models, particularly those designed to predict neural activity from naturalistic images, significantly enhance our understanding of how visual stimuli are processed and represented in the brainB: Such models are crucial for developing advanced visual neuroprosthetics aimed at simulating neural activity to possibly restore vision. Nevertheless, the application of these models must be undertaken with prudence, given the intricate nature of brain functionality and its interaction with the environment. C: These models, incorporating aspects of retinotopy, are pivotal in elucidating the complex relationship between external visual environments and their corresponding neural responses	BAC	CAB	CAB	ACB	Selection 4
A: Future research should be focused on further investigation and characterization of the differences in the results produced by traditional DGE and XAI techniques and their biological relevance, being the XAI techniques not limited to SHAP. Other interesting directions would include, introducing more data modalities, adding more features into the training data like RNA velocity and use of more sophisticated NN models.B: A subset of genes and altered pathways are only detected using the proposed XAI approach and are missed by a traditional differential expression method, which underestimates their potential contribution to the diseaseC: The use of NN models with XAI techniques offers a more detailed analysis of gene expression at single-cell resolution when compared with traditional techniques	CBA	CAB	ACB	ACB	Selection 1
A: Existing software tools that implement these corrections are PoPoolation (3, 4), poolfstat (5, 6), and npstat (2). These tools however lack usability, do not scale to contemporary large datasets, and do not support haplotype-corrected frequencies in low-coverage E&R experiments such as those from HAF-pipe or other HARP-based pipelines (7, 8). B: Typical population genetic statistics, such as measures of diversity (θ𝜃\thetaitalic_θ, Tajima’s D) and differentiation (FST), hence need to be adapted to correct for the induced biasesC: The pooling of a finite number of individuals from the population, as well as the finite number of reads being sequenced from each individual, introduce two levels of sampling noise in allele counts (2)	CBA	ACB	CAB	ABC	Selection 1
A: Additionally, techniques employing recurrent neural architectures have been employed for the sequential modeling of amino acids [35]. [36] introduced a novel approach that utilizes neural networks to emulate an energy landscape, facilitating the inference of protein foldsB: The groundbreaking AlphaFold algorithm [21, 37] has significantly raised the bar in terms of accuracy for protein structure prediction. It is important to highlight, however, that proteins are structurally simple, primarily linear molecules, which is in contrast to the complex and branched configurations often found in general molecules, including various ring structures. This structural disparity makes the direct application of protein-folding methodologies less suitable for the intricate task of predicting the conformation of general molecular structures. Hence, there is a compelling need for distinct modeling techniques that are tailored to address the unique challenges posed by non-protein molecular structures.C: The field of protein topology prediction has experienced rapid expansion, with a multitude of innovative methodologies emerging. These innovations encompass a range of approaches, including the use of flow-based models [34, 26], which effectively map the conformations of protein main chains	CBA	CAB	BAC	BCA	Selection 4
A: Thus we were able to obtain the exact solutions of the KPP equation which to the best of our knowledge were not known before. Additionally we obtain the exact analytical traveling wave solutions of the generalized Burgers–Huxley equation.B: (6)C: In this paper we will use the method of exclusion of the independent variable benguria ; rosu ; kogan3 ; kogan4 ; kogan5 , which allows to reduce the problem of integration of the second order ODE to the problem of integration of the first order ODE, to obtain the exact solutions of Eq	BAC	CBA	ACB	CAB	Selection 2
A: Stochasticity in ecological systems is typically categorized into two main types: demographic stochasticity and environmental stochasticity Lande et al. (2003)B: Demographic stochasticity arises from random variation in the reproductive success of individuals. For instance, each individual might have an equal probability of producing either zero or two offspringC: In contrast, environmental stochasticity affects entire populations in a correlated manner. For example, during favorable years, each individual may, on average, produces two offspring, whereas in unfavorable years, this average might drop to just one-half.	ABC	ACB	BAC	CBA	Selection 1
A: The curve catches also the rise in cases that began in mid-October.B: Since the gap between the curve and the data is smaller from July, we can deduce that a better monitoring policy is induced by the introduction of Green Pass obligation (notice that the Green Pass can also be granted if swabs are negative)C: In Figure 22 we show the trend of positive individuals in the GP case, and observe that it matches available data	ABC	BCA	CBA	BAC	Selection 3
A: There are three key steps in Dual-RAG-IF: 1) Mutation region identification: Mutation regions can be determined either manually or automatically. For manual design, the input must include a target 2D structure in dot-bracket notation defining with the target dual graph, along with a sequence that marks mutation regions by representing residues as ’N’B: Each candidate is evaluated by applying two 2D folding programs (such as NUPACK[24], IPknot[25], and PKNOTS[26]) capable of handling pseudoknots to verify the resulting fold, and a sequence is considered successful when both programs agree on the target fold. In our application, we use the NUPACK and IPknot packages. 3) Sequence optimization: The candidate sequences are ordered by minimal mutations, ensuring an optimal final design.C: For automatic design, we only need the target dual graph information, and the entire sequence is taken as the mutation region. 2) Candidate sequence generation: Candidate sequences with mutations are generated using a genetic algorithm	ABC	ACB	BCA	BCA	Selection 2
A: Fig. 3(a) shows the evolution of ΦΦ\Phiroman_Φ for (i) an initially uniform distribution for F𝐹Fitalic_F, and (ii) a distribution F𝐹Fitalic_F consisting of randomly placed Gaussian spherical clusters of equal standard deviation. The long–time states of ΦΦ\Phiroman_Φ for both (i) and (ii) show an significant increase over the static uniform RanGEF case, as previously computed in Fig. 2(d)B: To compare the cases (i) and (ii), we compute the angular average of RanGEF,C: Moreover, the long–time concentration profile of chromatin-bound RanGEF shows a sharply varying spatial profile within the nucleus, with a significant accumulation at the NE	ACB	ABC	ABC	CAB	Selection 1
A: Allosteric regulation is one of the most relevant transduction mechanisms at the molecular level [11, 35, 36]B: Ion binding in metal sensor proteins is a brilliant example of the exploitation of this multi-scale strategy, in which the affinity of the molecule to the DNA substrate is modulated through the control of the distal ion coordination site [2, 3].C: The system-wide modifications that one or few atoms, interacting in very local regions, induce on the whole protein make allostery an exquisitely multi-scale process, whose versatility and consequent ubiquity are paired by the complexity of its investigation	CBA	ABC	CBA	ACB	Selection 4
A: We let the drug effectiveness γ𝛾\gammaitalic_γ to be a free parameter instead of fixing itB: This allows for variability in how different patients respond to the drug, and provides a more accurate assessment of how close the initial total cancer cell population is to the carrying capacity, i.eC: how close x⁢(0)𝑥0x(0)italic_x ( 0 ) is to 1111.	CBA	CAB	BCA	ABC	Selection 4
A: In Fig. 4 and in Figs. S3-7 of the supplementary material calibration curves for all uncertainty measures across all molecules are shown for GPR with Coulomb as well as GPR with SOAP. In nearly all cases, the GPR standard deviation demonstrates much better global calibration, with notably lower miscalibration areas compared to the other two uncertainty measures. The only exception is GPR with Coulomb for benzene. Here, the calibration curve for the GPR standard deviation shows a relatively high miscalibration area, which exceeds that of the two sets uncertainty measure. B: In Fig. 3, calibration curves for all three uncertainty measures are shown. We exemplary show calibration curves of GPR with SOAP for rMD17 benzene and WS22 SMAC: The calibration curve for the GPR standard deviation is nearly diagonal and has a low miscalibration area, indicating relatively good calibration across the dataset. In contrast, the two sets and bootstrap uncertainty measures show much poorer calibration, with significantly higher miscalibration areas	BCA	ACB	ABC	CAB	Selection 4
A: Notably, XATGRN’s robust performance highlights its ability to handle the skewed degree challenge more effectively compared to DeepFGRN and DGCGRN. However, it is worth noting that in certain cases, such as the human COVID-19, breast cancer, and lung cancer datasets, the recall of XATGRN is slightly lower than that of DeepFGRN.B: These results demonstrate that XATGRN effectively captures the complex regulatory interactions within gene networks and accurately predicts both the presence and types of regulatory relationshipsC: Our XATGRN achieves the highest AUC, recall, F1-score, and precision across the DREAM5 network1 and all four E.coli datasets	ABC	BAC	ABC	CBA	Selection 4
A: The human induced pluripotent stem cell (hiPSC) line BIHi250-A (https://hpscreg.eu/cell-line/BIHi250-A) was cultivated in Essential 8 medium prepared according to the original recipe [60] and grown on Geltrex (Thermo, A1413302) coated tissue culture platesB: Media change was performed daily for six days with one double-feed on day 7C: Cells were passaged when confluency reached approximately 80%. Mouse embryonic fibroblasts (MEFs) immortalized by limited dilution were grown in tissue culture flasks and cultivated in DMEM/F-12 (Thermo, 11320033) supplemented with 5% FBS (PAN Biotech, P30-3030M) and passaged when a confluency of approximately 80% was reached. All cell cultures were kept at 37°C and 5% CO2.	ABC	ACB	ACB	ACB	Selection 1
A: MyESL took 5.255.255.255.25 minutes to read and pre-process input datasets and less than 1111 minute to build the ESL model and process result files. The peak memory usage for this analysis was 1.31.31.31.3 GB.B: We analyzed a fungus dataset containing amino acid sequence alignments of 1,23312331,2331 , 233 genes from 86868686 yeast species (Shen et al., 2016, 2017). We built an ESL model for a clade (44444444 species), where all species received a +11+1+ 1 label, while the remaining 42424242 species were assigned −11-1- 1C: The combined sequence alignments from all genes contained 609,013609013609,013609 , 013 sites, and the total number of bit columns was 4,105,44441054444,105,4444 , 105 , 444, distributed among 1,23312331,2331 , 233 groups. We used weighted class balance and set the position and group sparsity parameter values at 0.10.10.10.1 and 0.20.20.20.2, respectively	BCA	BAC	CBA	CAB	Selection 4
A: An estimated probability is counted as correct if it falls on the right side of 0.5. If we chose a single peer’s probability rating at random, the accuracy of our collective inferences about the claims would match the average accuracy of the peers: about 62% for the set of 1,200 general-knowledge claims in our online experiment (FigB: We first consider the accuracy achieved by simple methods for aggregating the judgments. The accuracy of an individual person or collective inference algorithm is defined as the rate of correct answersC: 2). Trusting a random peer does not benefit from the wisdom of the crowd.	BAC	ACB	CBA	CBA	Selection 1
A: While diffusion models have shown promising performance, they are not without limitations. Due to their iterative nature, requiring thousands of steps to generate outputs, diffusion models often suffer from inefficiencies in sampling. In the context of molecular conformation generation, some diffusion model variants have reduced the number of sampling steps from thousands to tens or even a single step, but this often comes at the expense of accuracy, leading to suboptimal results \parencitejing2022torsional, fan2023ec.B: Deep learning methods, on the other hand, enable atom-level research, eliminating the dependence on fixed templatesC: With the advancement and success of diffusion models in image generation \parenciterombach2022high, ramesh2022hierarchical, these approaches have also been adopted in chemistry \parencitehoogeboom2022equivariant, abramson2024accurate, song2024equivariant, including molecular conformation generation	BAC	CAB	BCA	CBA	Selection 2
A: This study begins with an introduction in Section I, followed by a review of related works in Section IIB: The background study is detailed in Section III, methodology is detailed in Section IV, results are analyzed in Section V, and limitations with future work are discussed in Section VIC: Finally, Section VII summarizes the study.	ACB	BAC	ABC	CBA	Selection 3
A: Additionally, learning discrete states independently becomes prohibitively costly when estimating dynamics for a population that contains multiple independent subgroups. In this scenario, SLDS learns distinct systems for each potential combination of dynamicsB: For example, switched systems often learn approximate dynamics which have discontinuities along the boundaries of the switches. This can be well suited to capturing sudden changes in dynamics, but may not accurately represent smooth transitions between dynamical modes. Approximating smooth transitions requires increasing the number of linear states available to capture intermediate stagesC: However, the number of possibilities grows exponentially as the number of subgroups and dynamical modes increases, rendering it combinatorially impractical. Moreover, this challenge is compounded during inference where the learned systems are rigid and cannot adapt to capture similar dynamics. Instead, SLDS must learn new distinct states to accurately represent subtle variations of similar dynamics. For a fixed number of parameters, dLDS improves the expressivity of the switching linear approach by offering a controlled way to flexibly modify and reuse learned linear regimes.	BAC	CAB	BCA	BCA	Selection 1
A: The family subsets have varying sizes in terms of interactions ( from 19K to 220K), number of proteins ( from 100 to 1K), and number of compounds (from 10K to 120K). B: These datasets include interactions belonging to different protein superfamilies, including membrane receptors, ion channels, transporters, transcription factors, epigenetic regulators, and enzymes with five subgroups (i.e., transferases, proteases, hydrolases, oxidoreductases, and other enzymes)C: ProtBENCH [37] contains protein family-specific bioactivity datasets	ACB	CBA	CAB	BCA	Selection 2
A: To overcome this limitation, we have introduced virtual adversarial training as a means to improve the model generalizability (see Method 4.6)B: Given the vast diversity of HLA and TCR repertoires, the experimentally validated bindings currently available are limited and even biased, posing a tough challenge of overfitting in the development of prediction modelC: Specifically, we apply adversarial perturbations to the sequence embeddings to generate virtual adversaries that aim to maximize the loss function. The adversarial training makes our model less sensitive to slight changes in input sequences, thereby significantly improves the performance (see Method 4.8).	ACB	BAC	CBA	ABC	Selection 2
A: By providing a simultaneous handle on the multiple timescales that govern behavior such as cruising and wandering, differential modulation of speed and egocentric direction preference, our approach sets the stage for dissecting the underlying brain circuits for navigation in a transparent vertebrate brain. Along with the serotoninergic modulation of motor activity mentioned previously, we can dissect how multiple brain regions function together to give rise to this hierarchy of timescales in behaviorB: The hindbrain oscillator, also called anterior rhombencephalic turning region has been identified as one brain region that confers a persistence of the left/right steering in the larval zebrafish (dunn2016brain, wolf2017sensorimotor). We hypothesize that the interplay of this region with the mesencephalic locomotor region (MLR, carbo2023mesencephalic), the nucleus of the medial longitudinal fasciculus (wang2014selective, berg2023brainstem), projecting onto the reticular formation (orger2008control, carbo2023mesencephalic) could explain the dynamics we uncoverC: In particular, the modulation of the MLR by dopamine released from posterior tuberculum (carbo2023mesencephalic) could explain the long-lived persistence of cruising behaviors. There is already some evidence for this in mice, where dopamine release has been associated with long time scale (seconds to minutes) persistence of motor sequences (markowitz2023spontaneous).	ACB	ABC	BCA	CBA	Selection 2
A: In the presence of the error signal, SGD in a single neuron model leads to a local plasticity rule, that could be plausibly implemented in a biological neuron, unlike in multi-layer networks (see Appendix C). Finally, it will be interesting to investigate the computational abilities of a neuron with non-linear dendrites in a purely unsupervised learning setting. B: In cerebellar Purkinje cells, this teaching signal could be implemented by the climbing fiber input, which has been shown to correlate with error in motor tasks. In cortical pyramidal cells, the presence of error signals is more speculativeC: Another important future direction concerns synaptic plasticity algorithms. Here, we have investigated a simple plasticity algorithm (SGD) in a standard supervised learning scenario, in which a teaching signal is available to the neuron	BAC	ACB	CBA	CAB	Selection 3
A: (c,d) Performance of neural network architectures across datasets. Bar plots indicate the mean test set performance (with error bars denoting the standard deviation), in comparison with the XGBoost baseline (dashed line: average performance, shaded area: standard deviation). Performance was quantified as balanced accuracy in classification (c), and as concordance index in regression (d).B: The similarity was quantified as the Tanimoto coefficient on extended connectivity fingerprints39, and the maximum similarity was reported. Different distributions can be observed in the classification (a) and regression (b) datasets, with the former containing more dissimilar molecules on averageC: Figure 2: Overview of dataset similarity and of model performance. (a,b) Distribution of test set similarities in comparison with training set molecules	ABC	CBA	CAB	ABC	Selection 2
A: Moreover,B: While this is obvious for directed networks and level-1 semi-directed networks, for higher-level semi-directed networks it takes some care to prove that the intuitive definition worksC: Reflecting the relative complexity of restricting a semi-directed network to a subset of its taxa, we show that this process is well-defined (see Section 4)	ACB	CBA	BAC	BAC	Selection 2
A: Notably, we observed that smaller initial gains can paradoxically hinder learning. This result is explained by our analysis of the Lyapunov exponent, which is crucial for the stability and information propagation within the network. We found that smaller initial gains resulted in larger deviations of the Lyapunov exponent from zero before training, indicating a greater challenge in achieving the balanced dynamical properties necessary for effective learningB: To address this challenge, we brought the gradient flossing method into the biologically plausible learning framework, leading to performance improvement for suboptimal initial weight magnitudes. Overall, these findings provide insights into how variations in initial connectivity may influence learning in neural circuits, offering predictions that can guide future experimental work. Additionally, these findings have practical implications for the design of neuromorphic chips, where optimizing initial weight configurations could enhance the efficiency and effectiveness of energy-efficient biologically plausible learning algorithms. C: This study highlights the role of initial weight magnitude in shaping the learning dynamics of biologically plausible rules, predicting its importance in neural circuit learning. While the influence of initial connectivity on learning has been extensively explored in the realm of backpropagation-based learning, our work is novel because it extends this inquiry to biologically plausible settings. Our findings demonstrate that, similar to backpropagation through time (BPTT), the choice of initial weight magnitude in e-prop — a biologically plausible learning rule — has a profound impact on learning performance	CAB	BCA	ABC	CBA	Selection 2
A: Pre-training set. 2,372,675 SMILES strings were obtained from ChEMBL v33 44B: SMILES strings longer than 80 tokens were dropped. The final set consisting of 1,584,858 molecules was randomly divided into training (n𝑛nitalic_n = 1,500,000), validation (n𝑛nitalic_n= 40,000), and test splits (n𝑛nitalic_n = 44,858).C: Salts were removed and molecules composed only of C, H, O, N, S, P, F, Cl, Br, I atoms were retained. The SMILES strings of the remaining compounds were sanitized, canonicalized, and the charge and sterochemistry annotations were removed	CBA	BCA	ACB	ABC	Selection 3
A: The primary limitation for both the semi- and fully-automated segmentation tracking methods is the accuracy of the segmentations, which can have downstream effects on length and width predictions for animalsB: In turbid water, the pectoral and caudal fins are occasionally left out of the segmentation, or the caudal lobe will be segmented separately from the rest of the body. In addition, obtaining precise biometrics from segmentation masks may be challenging in aerial videos where drone metadata isn’t available. Ultimately, the quality of the drone aerial imagery has a significant effect on the accuracy of detection and segmentation for any marine and terrestrial species (Ramos et al., 2022).C: When the shark is swimming near the seafloor in very shallow water, SAM 2 will occasionally segment the shadow of the shark along with the shark itself	CBA	CAB	BAC	ACB	Selection 4
A: To start using the SpinPath JavaScript tool, the user first selects a WSI and uploads it to the program. The OpenSeadragon.js package is then used to display the image in a viewer, allowing the user to move and zoom into the image as neededB: Using the GeoTiff.js and Transformers.js libraries to access the WSI data and implement the user’s selected model and feature extractor in JavaScript, respectively, The program then automatically handles patching, patch embedding, and aggregating results. The results and logits are then displayed to the user, and the user is given the option to download the patch coordinates and attention scores in the form of GeoJSON data.C: Once loaded, the user can then select regions for analysis using the Annotorious package. The user can then click the “Run Model Analysis” button to run their selected model on the annotated regions	CBA	BCA	ACB	BCA	Selection 3
A: However, in finite systems the absorbing configuration can always be achieved, even in the supercritical phase. To avoid this issue, we apply a quasi-stationary method to characterize the dynamics of the model. Specifically, we apply a reactivation method [28, 29] in which we perform a reinfection of one individual (randomly chosen) every time the dynamics reaches the absorbing configuration.B: In epidemic models, the absorbing state refers to the configuration without infected individualsC: If this state is reached, the dynamics stops	ABC	CBA	CAB	BAC	Selection 3
A: Since the cluster mass is the only parameter in our modeling, the spectrum of masses for the catalytic reactants should be sparse, so that catalysts are rareB: In many catalytic reactions, only a small subset of the reactants are catalyticC: Here we treat an extreme model where only monomers are catalytic. In Appendix A we briefly consider the model where clusters with ‘magic’ masses 2nsuperscript2𝑛2^{n}2 start_POSTSUPERSCRIPT italic_n end_POSTSUPERSCRIPT are catalytic.	CAB	ACB	BAC	CBA	Selection 3
A: By optimising over these convex sets with a given set of rate parameters, one can obtain upper and lower bounds on the moments. These bounds provide error guarantees for predicting moments, unlike approximation methods based on system size expansion or moment closure. Whether similar approaches could be utilised to provide error bounds for parameter inference has remained unexplored heretofore. B: In recent years, a few authors have obtained theoretically guaranteed bounds on the stationary moments (Kuntz et al., 2016; Sakurai and Hori, 2017; Ghusinga et al., 2017; Dowdy and Barton, 2018a, b; Sakurai and Hori, 2018a; Kuntz et al., 2019; Hori, 2020; Sakurai and Hori, 2022) and the transient moments (Dowdy and Barton, 2018b; Sakurai and Hori, 2018b; Holtorf and Barton, 2023) of stochastic reaction networksC: These approaches rely on convex optimisation of sets constrained by moment equations, a set of equations involving the moments and the reaction rate parameters, and positive semidefinite constraints on the moments	BCA	CBA	CAB	BAC	Selection 3
A: We emphasise that we have assumed that the probability of selecting a link connecting nodes in opposite states, σ𝜎\sigmaitalic_σ, is independent of the degree of the nodes which it connects. This is a shortcoming of the homogeneous pair approximationB: Extensions have been proposed, such as the heterogeneous pair approximation [34], which allows σ𝜎\sigmaitalic_σ to depend on degree. Similarly, we assume an infinite graphC: The stochastic pair approximation [45] accounts for finite-size corrections. However, here, we do not consider these extensions.	BCA	ABC	CAB	ACB	Selection 2
A: We achieve this balance by designing a novel GP kernel function that defines a smooth, locally linear prior on dynamics. While our main focus is on providing an alternative to the rSLDS, the gpSLDS also contributes a new prior which allows for more interpretable learning of dynamics and fixed points than standard priors in the GP-SDE framework (e.g., the RBF kernel). Our implementation of the gpSLDS is available at: https://github.com/lindermanlab/gpslds.B: The gpSLDS combines the modeling advantages of the GP-SDE with the structured flexbility of the rSLDSC: To address these limitations of the rSLDS, we propose a new class of models called the Gaussian Process Switching Linear Dynamical System (gpSLDS)	ABC	CBA	ABC	CAB	Selection 2
A: Participants diagnosed with NDs were categorized into aforementioned groups based on disease specific clinical diagnostic criteria diagnosis: B: These participants were either categorized as healthy (CTL) or diagnosed and treated for a ND by a subspecialist neurologist or geriatric psychiatrist from Johns Hopkins HospitalC: The authors of this study collected a dataset from 113 participants from a larger digital biomarker cohort, NeuroLogical Signals, which our group has previously reported [18, 19, 20, 21, 22, 23]	CAB	BCA	CBA	BCA	Selection 3
A: To the best of our knowledge, this is with the very recent exception of [4] the only known example of an explicit primal-dual algorithm in phylogeneticsB: [13]). We suspect that unpacking many of these integer linear programming formulations to study properties of the linear programming relaxations could be a very fruitful line of research. The recent duality-based 2-approximation algorithm for agreement forests [12] is a good example of this potential. C: This is interesting, since the polyhedral angle on phylogenetics problems dates back to at least 1992 [5] and integer linear programming has been used quite frequently in the field (see e.g	BAC	CBA	ACB	BCA	Selection 3
A: It is also assumedB: The infected cells produce new viruses at the rate m⁢dI𝑚subscript𝑑𝐼md_{I}italic_m italic_d start_POSTSUBSCRIPT italic_I end_POSTSUBSCRIPT during their life; and dVsubscript𝑑𝑉d_{V}italic_d start_POSTSUBSCRIPT italic_V end_POSTSUBSCRIPT is the death rate of new virions, where m𝑚mitalic_m is any positive integerC: of lytic effect	BCA	CAB	CAB	CBA	Selection 4
A: In Fig.3 an input at location 13 generates a set of values across a range of nearby nodesB: In Fig 3a, the recursion creates a symmetrical gradient. In Fig 3b, a reward node is connected to node 16, In Fig 3c, the de-inforcement function is activated, providing the impetus for the agent to choose the highest visible value (node 14). Note that node values are normalized so max = 1.C: Figure 3: Node values exhibit a gradient across a simple graph	ACB	CAB	ACB	BCA	Selection 4
A: This artificial category acts as a segmentation tool within the vast, undetermined space of potential arguments and predicates [52]. These arguments and predicates may align with existing human-like categories or form entirely novel “alien-like” categories that could represent statistical constructs [11] or “polysemic concepts” [14, 53] not directly relatable to human cognitive categories. B: Each synthetic category is created during the training phase by the neural network itselfC: In our epistemological framework, synthetic categories, much like human categories [74], are immanent cognitive constructs	BCA	ABC	CBA	ACB	Selection 3
A: Seasonal antigenic prediction, particularly for influenza A H3N2, has benefited from machine learning approaches that help forecast viral evolution, supporting timely vaccine updates [304]. Finally, phylogenetic analyses have identified optimal influenza virus candidates for seasonal vaccines, underscoring the significance of LLMs in guiding vaccine development against anticipated strains [316]. B: Additionally, antigenic prediction plays a crucial role in designing effective influenza vaccines, especially for rapidly evolving strains. Statistical analyses of antigenic similarity, such as those conducted for influenza A (H3N2), highlight the potential of machine learning models in mapping antigenic drift and optimizing strain selection for seasonal vaccines [313]C: Moreover, cellular correlates of protection identified through human influenza virus challenges have advanced our understanding of immune responses to oral vaccines, demonstrating the applicability of machine learning models in immune signature identification [314]. Blood inflammatory biomarkers have also been analyzed to differentiate COVID-19 from influenza cases, showcasing the predictive power of LLMs in clinical biomarker differentiation [315]	BAC	CAB	CBA	BCA	Selection 2
A: Due to its ubiquitous applications, collagen needs to be thermally stableB: Collagen is one of the most abundant proteins in animals and has numerous applications in the field of medicine 90C: Yu et al.51 have experimentally gathered the melting temperature of 633 different primary sequences of collagen to investigate their thermal stability. The higher the melting temperature, the greater the stability of collagen.	CAB	BAC	BCA	CAB	Selection 2
A: We are interested in what would happen if grazers and browsers are added into a purely competitive environment among plants and whether trees, grass, grazers, and browsers can coexist. Therefore, we focus on the co-existence steady state of four species (which is unique) in the proposed savanna system (1.1) and study related traveling wave solutions, which may provide important information about the transition dynamics between the co-existence state and other steady statesB: To obtain our results, we employ the upper-lower solution method widely used in related studies. However, due to the absence of linear reaction terms in our herbivore equations for G𝐺Gitalic_G and B𝐵Bitalic_B, the usual form of exponential functions for the lower solutions does not work in our case. To overcome this difficulty, we introduce Gaussian-like functions at one end of the real line domain and successfully find suitable lower solutions for our problem.C: We demonstrate the existence of two types of traveling waves, the waves transitioning from the extinction state to the co-existence state and the waves from a grass-vegetation state (where only grass and grazers exist) to the co-existence state. Our results indicate that under suitable conditions, the co-existence state of four species may be dominant or more stable compared to other steady states in the sense of wave dynamics	ABC	BCA	BAC	ACB	Selection 4
A: Transformer architectures excel at capturing global features from textual dataB: The Transformer encoder comprises two sub-layers: a multi-head attention layer and a fully-connected feed-forward layer. Each sub-layer is followed by a residual connection and layer normalization to normalize input values for all neurons in the same layer [27], as illustrated in Fig 1. C: Building on this capability, we leverage the attention mechanism of the Transformer to model global relationships within molecular structures	CAB	BCA	CAB	ACB	Selection 4
A: In this package, we integrate tools for protein structure downloading and processing, interface-fitted tetrahedral mesh generation, parameter assignment, and the output of mesh data files, electrostatic potential functions, and ionic concentration functions in formats compatible with visualization tools such as ParaViewB: To enable broad applications, we have implemented the NSMPB finite element iterative solver in Python and Fortran as a software packageC: The NSMPB package also seamlessly integrates the Fortran subroutines that we wrote to handle computationally intensive tasks. With these efforts, we have not only simplified the usage of the NSMPB package but also improved the performance of our NSMPB package.	ACB	BCA	BAC	CAB	Selection 3
A: These evaluation metrics are defined below in terms of true positive (TP), true negative (TN), false positive (FP), and false negative (FN) cases. B: We investigated a number of performance metrics to evaluate and compare our proposed method to existing onesC: These metrics are namely accuracy, precision, recall, f1-score [66], kappa score[67] , and AUC value in ROC analysis	ACB	CAB	BAC	ACB	Selection 2
A: Clinical Trial MatchingB: Many studies have focused on learning patient retrieval and enrollment information for predicting individual patient outcomes within clinical trials, rather than making overall predictions about trial success. Doctor2Vec [1] learns representations for medical providers from EHR data, and for trials from their descriptions and categorical information, in order to address data insufficiency issues such as trial recruitment in less populated countriesC: DeepEnroll [28] encodes enrollment criteria and patient records into a shared latent space for matching inference. COMPOSE [7] encodes structured patient records into multiple levels based on medical ontology and used the eligibility criteria embedding as queries to enable dynamic patient-trial matching. In contrast, our work focuses on predicting the clinical trial outcome directly based on drug molecules, target diseases, and eligibility criteria.	ABC	BAC	BAC	CBA	Selection 1
A: In particular, the notations in [64] will be used. It is convenient to recall the following definitions (from [64]), B: Owing to the large size of the 2-group behavior model (making the computation of the eigenvalues of its Jacobian evaluated at the respective DFE less tractable mathematically), the linearization approach will be combined with some results related to the properties of Metzler matrices [62, 63]C: The stability of the three non-trivial DFE of the 2-group behavior model (G1DFE, G2DFE, and G3DFE) will be analyzed using standard linearization	CAB	CBA	ACB	CAB	Selection 2
A: The methods of both Zou and Zhang, (2015) and Castoe et al., (2009) require that the foreground lineages share the same amino acid. However, there are cases where replicated changes in protein function arise from different amino acids at the same site (Zhen et al., , 2012; Mohammadi et al., , 2022). One approach to address this is to relax the requirement for each foreground lineage to have evolved the same amino acid. For example, this can be achieved running the above two methods multiple times for different subsets of the foreground lineagesB: However this approach is computationally intensive for studies with a large number of foreground lineages (Fukushima and Pollock, , 2023). Chabrol et al., (2018) developed a model that inherently accommodates situations where some foreground species have different amino acids. Their approach steps away from explicit ancestral sequence reconstruction and instead uses a Continuous Time Markov Model of sequence evolution to determine the likelihood of replicated amino acid transitions occurring in the phylogeny branches leading to the foreground lineages. The ConDor workflow (Morel et al., (2024), available as a web-based tool) can also facilitate some foreground lineages not sharing a particular amino acid by allowing the user to specify a minimum number of lineages required to share the same amino acid substitutionC: Their approach was designed to account for potential uncertainty in phenotypic classification, which can be common in viral studies. The Profile Change with One Change (PCOC) method (Rey et al., , 2018) takes a different approach to modeling variation in the amino acids of the foreground lineages by identifying sites where the foreground lineages have a different amino acid preference (e.g. a preference for a hydrophobic versus hydrophilic amino-acid) compared to the background lineages. While the other approaches focus solely on the most common amino acid in the foreground lineages, PCOC uses all the amino acids in the foreground lineage to determine changes in amino acid profile. Additionally, both the “PC” and “OC” components of the model can be used independently, allowing for analysis of a range of amino acid replication scenarios.	BAC	ABC	CAB	CAB	Selection 2
A: While it is true that between minutes 5 and 6 more than one ant reaches the barrier, the process would then be mediated by multiple ants seeking information, retaining it, and triggering a cascadeB: From the moment this effective ant reaches the barrier, it remains activated and triggers a panic avalanche among its nestmates. C: This, along with the finite nature of information retention, leads us to conclude that a more simplified mechanism explaining the shift in the CM can be understood as a single “effective ant” representing several informed ants	ACB	CBA	CAB	CBA	Selection 1
A: To this end, we recruited three raters to annotate Chapter 9 of Harry Potter across the two domainsB: Furthermore, we examined whether domain-specific fine-tuning would specifically bolster the model’s capability in predicting MEG responses associated with words from that domain, as compared to words outside that domainC: We release these annotations as a resource for the dataset to facilitate further analysis. Details on the annotation process can be found in Appendix H. Examples of each phenomenon within the Harry Potter text can be found in Appendix I.	BAC	ABC	ACB	BCA	Selection 1
A: This NEM method to study games in the thermodynamic limit, is applicable to any two-player two-strategy game, both cooperative like Public Goods game or non-cooperative like Hawk-Dove game or Prisoner’s dilemma game, since we are making an exact mapping to the spin-1/2 Ising model via Nash equilibriumB: In fact in a recent work, our group has worked on the Nash equilibrium mapping in the context of the vaccination game, in the thermodynamic limit, see Ref. [19]. C: Thus be it the battle of sexes(BoS) or, game of chicken or, Volunteer’s dilemma, or the vaccination game, all these games can be understood in the thermodynamic limit via the Nash equilibrium mapping	CBA	ABC	BCA	ACB	Selection 4
A: (2022; 2024), the authors proposed models to identify time delays between cross-regional brain interactions, overcoming the challenge of distinguishing indirect, concurrent, and bi-directional interactions in two or more populationsB: However, their model focuses on analyzing sessions individually and is not intended to uncover the full underlying set of transition matrices, but rather to recognize meaningful time delays that can imply interactions. Other models addressed multi-regional interactions through a communication subspace Semedo et al. (2019) using dimensionality reduction, or by Generalized Linear Models (GLMs), with either Poisson (Yates et al., 2017) or Gaussian (Yates et al., 2017) statisticsC: In Gokcen et al	ACB	ACB	BAC	BCA	Selection 4
A: Hence, the population is considered to be composed of cell sub-populations in two different states: up-regulated and down-regulated bacteria, namely motile m𝑚mitalic_m and static s𝑠sitalic_s, respectively, and the concentration of autoinducers is given by q𝑞qitalic_q. As autoinducers are produced by both sub-populations at a rate r𝑟ritalic_r (see [38]), and the bacteria can either switch or remain in their category, we assume that: B: When a bacterium responds to an external stimulus by increasing the amount of a cellular component, the process is up-regulated, and it is down-regulated otherwise. To put it another way, the dynamics of the bacteria are regulated by both, autoinducers as well as growth of the bacteria population itselfC: In order to capture the key qualitative ingredients of QS mechanisms in bacteria, we follow a simplified approach. In so doing, we assume that the autoinducers bind to receptors that enhance the expression of a particular gene, and its production also directly depends on the bacteria population (e. g. [25])	CBA	BCA	BAC	BCA	Selection 1
A: However, a regime configuration based on a more natural classification of traits, i.e., shape of the antlers, results in an MGPM that is more plausible in explaining the process that generated observed data.B: We showed how an MGPM with multiple regimes does not necessarily result in a better fit to the observed data than using a single process on the whole treeC: We illustrate how our method can be used to test several evolutionary hypotheses in a real world setting	ABC	BAC	BCA	CBA	Selection 4
A: Regarding PI feature, SHTE has a higher mean pitch interval (2.512.512.512.51) with more variability (STD 1.011.011.011.01), indicating a wider range of interval sizesB: The generated data has a mean interval of 2.332.332.332.33 with a smaller standard deviation (0.320.320.320.32), indicating it varies less than SHTE but more than Bach. The KLD values for PI are 0.110.110.110.11 (SHTE) and 0.040.040.040.04 (Bach), showing that the generated data’s pitch interval distribution aligns better with Bach. The overlap areas are 0.550.550.550.55 with SHTE and 0.710.710.710.71 with Bach, again indicating that the generated data’s intervals are closer to those in Bach. C: Bach has a lower mean interval (1.921.921.921.92) and less variation, suggesting smoother transitions between notes	CAB	ACB	CAB	ABC	Selection 2

**A**: It combines ncRNA sequences across 47 different databases, resulting in a total of ∼similar-to\sim∼27 million RNA sequences (Supplementary Table 2, 3, 4).**B**: This dataset is a comprehensive collection of ncRNA sequences, representing all ncRNA types from a broad range of organisms**C**: The large-scale dataset used in the pre-training phase was collected from RNAcentral 47, the largest ncRNA dataset available to date

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**A**: When subpopulations have different trait values, selection acts to create a non-uniform distribution of populations sizes**B**: This illustrates the essence of the general case (14), where the Shannon entropy is replaced by a weighted entropy [47].**C**: This equation describes the balance between variation in the trait between subpopulations and the entropy in the distribution of subpopulation sizes, when subpopulations are following SHM in the way we have described

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**A**: In SO scenarios, one might simply assess the absolute difference between the fitness expected from training data and the fitness observed on new data**B**: However, in MO scenarios, it is crucial to consider each solution’s contribution to the Pareto front**C**: We introduce two novel metrics to measure this estimation error in MO CV setups.

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**A**: Barbieri et al. [6] proposed an unsupervised, physics-informed DNN (IVIM-NET) with results comparable to Bayesian methods with further optimizations by Kaandorp et al. [24] (IVIM-NEToptimoptim{}_{\textrm{optim}}start_FLOATSUBSCRIPT optim end_FLOATSUBSCRIPT)**B**: Zhang et al. [42] used a multi-layer perceptron with an amortized Gaussian posterior to estimate the IVIM model parameters from fetal lung DWI data. Recently, Vasylechko et al. [37] used unsupervised convolutional neural networks (CNN) to improve the reliability of IVIM parameter estimates by leveraging spatial correlations in the data.**C**: In the past few years, state-of-the-art, DNN-based methods were introduced for IVIM parameter estimation. Bertleff et al. [8] demonstrated the ability of supervised DNN to predict the IVIM model parameters from low SNR DWI data

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**A**: The advantages of the GNN architecture are well illustrated by the results for chignolin. A previous machine-learning study of chignolin identified two slow CVs, one for the folding-unfolding transition and one distinguishing competing folded states[63]. Our VAMPnets appear to recover these two CVs (Figures 3 and S3; results shown are with SubMixer), distinguishing folded and unfolded states with CV 1 and four folded states with CV 2**B**: CV 2 distinguishes the folded states by the configurations of Thr6 and Thr8 side chains, which can each occupy two rotamers, yielding four possible folded states. These side chain dynamics could not be detected by VAMPnets that take backbone internal coordinates as inputs, as is common, or even GNNs limited to backbone atoms (Bonati, Piccini, and Parrinello [63] included distances to side chain atoms and then manually curated the inputs).**C**: To understand the physical differences between the folded states, we plot CVs 1 and 2 as functions of the fraction of native contacts and the χ1subscript𝜒1\chi_{1}italic_χ start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT side chain dihedral of Thr6 or Thr8 (Figure 4). The fraction of native contacts clearly correlates with CV 1, consistent with earlier studies

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**A**: [47] introduced two models inspired by the COVID-19 pandemic, incorporating elements of game theory, disease dynamics, human behaviour, and economics. A study by A. Rajeev et al. [55] delved into an evolutionary game theory model to examine individuals’ behavioural patterns and identify stable states**B**: M. Alam et al. [2] emphasized the significance of implementing multiple provisions promptly to enhance disease containment efforts using game theory and human behaviour. H. Khazaei et al. [39] analyzed the SEIR epidemiological model alongside an individual behaviour response model, specifically exploring the dynamics of a game where the public’s compliance with social distancing measures is influenced by the state of disease and associated payoffs. **C**: During the COVID-19 outbreak, several distinct computational and mathematical models have been developed to investigate the significance of quarantine as a game-theoretic strategy and its impact on disease transmission as well as hospitalization rates [59, 47, 2, 39]. C. N. Ngonghala et al

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**A**: Convergence of the chains was assessed using Rubin’s R𝑅Ritalic_R statistic [23]**B**: The analysis produced approximate samples from the posterior distribution of the parameter vector θ∗superscript𝜃∗\theta^{\ast}italic_θ start_POSTSUPERSCRIPT ∗ end_POSTSUPERSCRIPT (see Figure 4 below). **C**: The MCMC analysis was based on two chains of 3,000 iterations, with a burn-in period of 1,000 iterations

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**A**: Other authors have studied biophysical network models of premotor neurons**B**: The stationary distributions of the motor neurons were then used to infer synaptic polarities, i.e., whether a synaptic**C**: Rakowski et al. (2013) and (2017) simulated the dynamics of a pre-motor and motor circuit

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**A**: What might you do? If you start very early and have plenty of time, you might prefer to walk all the way. If you have very little time, you might need to run all the way**B**: But if you had an intermediate amount of time, what might you do? Here, we perform this experiment for two long distances over 800 meters, and show that humans systematically use a mixture of walking and running when there is an intermediate amount of time. That is, we show that for such overground tasks, there is not a sharp gait transition speed below which walking is preferred and above which running is preferred. Having this mixture of walking and running instead of a sharp gait transition speed is energy optimal [1, 22, 23], and was earlier observed over short distance tasks in humans [1], so the primary experimental contribution of the current study is its demonstration over much longer distances. **C**: Imagine you need to travel on foot from your home to an important appointment a kilometer away at a particular time (Figure 1). Unlike on a treadmill, where the speed is constrained, in this overground experiment, you can change speed or change gait

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**A**: Metabolic cost models developed from isolated muscles experiments in-vitro have generally been compared with whole body movement tasks such as walking and have not been compared in detail with in-vivo human isometric experiments designed explicitly to test those models [22, 23, 24, 25, 26, 27]**B**: Previous metabolic cost models have certain limitations in the prediction of metabolic cost for isometric tasks**C**: Most models are particularly deficient in predicting the cost of isometric force. For instance, the Umberger et al model [27] predicted roughly 7% of experimentally measured cost for an isomeric task involving tracking sinusoidal forces [28]. The models developed from in vivo human experiments have either no prediction for isometric tasks as they were derived with terms specific to non-isometric tasks [29, 30, 31], considered only force level changes but not time series changes [32, 8] or only time series changes but not force level changes [33, 28].

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**A**: Figure 2: The pathogens distribution on nodes with different distances from the root node (values on titles)**B**: Initial parameters are as in Figure 1**C**: The x𝑥xitalic_x-axis is α𝛼\alphaitalic_α and the y𝑦yitalic_y-axis is the ratio of the number of nodes infected with each pathogen to the total number of infected nodes in this distance.

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**A**: The black line is the least-squares fit to the red data**B**: The curve is closely fitted by the simple power relationship, y=0.0506⁢x−0.822𝑦0.0506superscript𝑥0.822y=0.0506x^{-0.822}italic_y = 0.0506 italic_x start_POSTSUPERSCRIPT - 0.822 end_POSTSUPERSCRIPT.**C**: values

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**A**: Second, there is a separation of mutational time scales: site complexity changes take place at a much lower rate than recognition site and target mutations (ν≪μmuch-less-than𝜈𝜇\nu\ll\muitalic_ν ≪ italic_μ). Third, because selection on the recognition function depends only the binding affinity phenotype Δ⁢GΔ𝐺\Delta Groman_Δ italic_G, the model does not introduce any explicit fitness benefit of sequence complexity. Nevertheless, complexity can emerge as a collateral of selection for function in a non-equilibrium dynamical pathway – an evolutionary ratchet. We will first characterize the complexity of stationary states in different parameter regimes of the evolutionary model, then derive specific dynamical pathways towards these states.**B**: Three model features turn out to be crucial for what follows. First, the sequence mutation dynamics does not introduce any bias towards higher complexity**C**: Clearly, the minimal evolutionary model is a broad approximation to the evolutionary dynamics of any specific receptor-target interface. The model neglects many details of actual molecular evolution processes that are not important for conclusions of this paper

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**A**: For peak calling, MACS2 (v2.1.2) software was used with option --nomodel --nolambda --keep-dup all -p 0.01. ATAC-seq tracks were visualized using Integrative Genomics Viewer (IGV), and footprinting analysis was performed using HINT-ATAC (Li2019, ). Note that the paired-end output of the sequence was used to reconstruct the fragments, where paired two reads correspond to both ends of a fragment. **B**: ATAC-seq reads were aligned using BWA version 0.7.16a with default parameters. SAMtools was used to convert SAM files into compressed BAM files and sort the BAM files by chromosome coordinates**C**: PICARD software (v1.119) (http://broadinstitute.github.io/picard/) was used to remove PCR duplicates using the MarkDuplicates options. Reads with mapping quality scores less than 30 were removed from the BAM files

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**A**: A strong core-periphery structure implies the system has a set of dominant, highly interconnected basins of attraction (the core) where transitions are frequent and stable**B**: The peripheral basins of attraction are less frequently visited, with transitions mainly leading back to the core**C**: This structure indicates that the system tends to remain within the core’s stable dynamics and only occasionally explores the less stable, transient states represented by the periphery. In contrast, in the syncopation condition, the average dwelling time and motif length decreased, betweenness centrality declined, and average shortest path length increased. This indicates that stronger coupling in syncopation enhances the stability of a larger set of states and distributes the probability flow more broadly, reducing the dominance of core nodes and creating a more distributed but less efficient flow.

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**A**: 2023; Harini, Sekijima, and Gromiha 2024a), focusing on extracting structural features at the binding interface, such as energy and contact distance. Based on the extracted features, they developed structure-based machine-learning approaches for affinity prediction. However, these methods are highly dependent on feature engineering with limited generalization ability on new samples due to the limited development dataset size.**B**: However, their performance is often limited because the binding affinity is mainly determined by the binding interface structure (Deng et al. 2019). Other recent methods are structure-based (Hong et al**C**: Several computational methods have been proposed for protein-RNA binding affinity prediction, including sequence-based and structure-based methods. The sequence-based approaches process the protein and RNA sequence separately with different sequence encoders (Yang and Deng 2019a; Pandey et al. 2024), and subsequently model the interactions

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**A**: Additionally, because our metric is lighter, faster and requires significantly fewer resources, it is efficient than previous metrics. We believe this work will empower researchers to train and test generative models more efficiently.**B**: Our metric has been shown to be monotonic with respect to various noise types found in histopathology, including noise, occlusion, and blur**C**: We developed a new evaluation metric based on normalizing flow and measures the L2 distances between real and generated features

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**A**: Figure 1: Commuting network among Brazilian cities. The map displays the locations of Brazilian cities, which correspond to the network nodes**B**: Edge widths indicate the number of commuters between city pairs. In this visualization, edges are grouped based on their proximity using a kernel-based edge bundling algorithm [33]. The emerging structures of this network illustrate the complexity of inter-city interactions. Figure created using Matplotlib [34], GeoPandas [35], and NetworkX [36].**C**: Connections represent the flow of commuters between city pairs, irrespective of direction. Node sizes are proportional to the weighted total degree of the cities and are also color-coded accordingly

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**A**: To address this issue, network embedding techniques can be employed [39]**B**: Shingo Tsuji successfully used a deep neural network (DNN) to embed a PIN into latent space, creating a framework for inferring Alzheimer’s disease targets [37]. Building on this, more advanced AI-powered embedding algorithms, such as those based on Random Walk, Graph Neural Networks (GNNs), and edge sampling, offer promising improvements for leveraging PIN data to identify druggable genes [19, 26, 41].**C**: Network embedding aims to maximally preserve a network’s information while reducing its dimensionality, facilitating higher resolution and better quality of network data [9]

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**A**: Given the ability to treat design directly as the reverse problem for structural and functional prediction, developments in these categories should be closely linked**B**: Advancements in structural prediction, most notably from Alphafold2, have yet to make its impact in protein design**C**: Proper evaluation methods will need to catch-up first however if future advancements are to be properly measured.

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Selection 2

**A**: Unlike simpler PCA-based inference models, VNNs offer stability [11] and transferability guarantees [18], which ensure reproducibility of the inference outcomes by VNNs with high confidence. **B**: Theorem 1 in [11] established the equivalence between processing data samples with principal component analysis (PCA) transform and processing data samples with a coVariance filter 𝐇⁢(𝐂)𝐇𝐂{\mathbf{H}}({\mathbf{C}})bold_H ( bold_C )**C**: Hence, it can be concluded that input data is processed with VNNs, at least in part, by exploiting the eigenvectors of 𝐂𝐂{\mathbf{C}}bold_C

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Selection 1

**A**: Relationships between living things and their natural environments are the only focus of ecological research. Ecological systems are developed by their interactions, which are important for population ecology. In nature, resources are frequently distributed extensively over the ecosystem**B**: Therefore, organisms are diffusive throughout the environment because they must locate food and survive. Since trophic interactions are greatly influenced by species movement, different spatial patterns in nature have evolved. Several studies have demonstrated that aquatic and terrestrial populations may form patterns [31, 32]**C**: Spatial patterns are shaped by many causes, including deterministic processes, species growth, mobility, stochastic processes, environmental changes, and more. Because species interact across habitats, patterns are common in the ecological system [33, 34]. Self-organized spatial patterns are the result of a deterministic process in interacting organisms. The spatio-temporal predator-prey model is given as follows:

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**A**: This trend continued with the OOD Testing independent from pMT-unseen tetsing, where Fusion-pMT scored 0.6320, significantly higher than pMTnet’s 0.5744. In terms of accuracy (ACC), Fusion-pMT also showed superior performance. On the pMT-unseen tetsing, Fusion-pMT had an accuracy of 0.7092, while pMTnet had 0.6558. This pattern was evident in the OOD Testing as well, with Fusion-pMT scoring 0.6001 against pMTnet’s 0.5428.**B**: For instance, when evaluating the ROC AUC on the pMT-unseen tetsing, Fusion-pMT achieved a mean score of 0.7326 compared to pMTnet’s 0.7158**C**: Our Fusion-pMT consistently outperformed the pMTnet across various metrics and datasets shown in Figure 3

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**A**: Täuber, and Mauro Mobilia**B**: The C++ code used to generate the data and the Python and Matlab codes to process and visualize the data within this work can be found at the Open Science Framework repository (Lluís Hernández-Navarro, Kenneth Distefano, Uwe C**C**: 2024.

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**A**: Here, we discuss the functionality included in PENSA and demonstrate its usefulness on three real-world applications: We show how to describe the influence of local frustration on loop opening during the catalytic cycle of an oxidoreductase,Stelzl et al**B**: (2020) how to quantify the influence of force-field parameter changes on simulations of nucleic acids,Cruz-León et al**C**: (2021) and how to identify the effect of ionization on receptor proteins. The examples reproduce existing results, confirming the reliability of our approach, but also demonstrate additional new discoveries made possible by systematic comparison of molecular simulations.

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**A**: In this way, we wished to see how the ERP component is regulated by the distinctiveness of the event and the selective listening mechanism. **B**: The motivation for this experimental design was to investigate the cognitive processing of speech events**C**: Going from paradigm 1 to 3, the experimental complexity was increased in terms of task difficulty and practicality

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**A**: assembled structures or copied polymers. As a consequence, complex systems can achieve stereotyped reproducible behaviors, despite living in high-dimensional disordered state spaces, through simple non-equilibrium mechanisms that also provide speed benefits. **B**: Finally, resets have been shown to be a broadly relevant strategy for speeding up search in a broad range of contexts [40, 62, 60, 65, 63, 86]. Our work points out that in addition to saving time, reset mechanisms effectively reduce the entropy of paths used to reach a destination state**C**: Such ‘canalization’ into a few paths can be seen as a non-equilibrium version of Waddington’s homeorhesis [87]. The reduction in trajectory entropy can show up as higher observable order in, e.g

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**A**: This scale is instrumental in both clinical settings and research studies for monitoring the progression of the disease and assessing the impact of therapeutic interventions on cognitive function.**B**: A lower FVC value thus reflects a worse disease state for a fibrosis patient. In the evaluation of Alzheimer’s Disease, the ADAS-13 (Alzheimer’s Disease Assessment Scale-cognitive subscale with 13 items) serves as a pivotal metric for modeling cognitive impairment**C**: An increase in the ADAS-13 scores is indicative of a deterioration in cognitive abilities, with higher scores corresponding to a more severe decline

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**A**: Similarly, when the default FI (red triangles) was compared to leave-one-out NFPFP5 (cyan squares), the FI was superior. Both the NFPFP5 and FI typically out-performed chronological age, except for predicting weakness (deficit grip strength)**B**: Figure 1: The FI predicts future FPFP5 deficits better than NFPFP5. The FI that includes the FPFP5 performed the best (green upside-down triangles)**C**: Only NFPFP5 including all deficits (purple circles) performed comparably to the default FI. The AUC is the probability that a metric will correctly rank positive individuals as higher than negative individuals [31] (dotted line at 0.5 indicates a random guess). Leave-one-out excludes the outcome deficit from the predictor. Error bars are standard errors.

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**A**: Our downstream performance on genomic benchmarks indicates the potential of METAGENE-1 as a general-purpose foundation model**B**: We are continuing to actively explore this direction, through incorporating additional human reference genomes and multi-species genomic datasets in our metagenomic pretraining data.**C**: Our results also indicate that METAGENE-1 benefits from continual pretraining on a diverse mixture of data sources in addition to metagenomic data (at least for tasks similar to these genomic benchmarks)

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**A**: We employ two age grouping strategies**B**: This approach is motivated by its interpretability, as decade intervals are commonly used and easily understood, making the results accessible to a broad audience. The second grouping is based on research by [24], which identified key inflection points in aging at approximately 34,60, and 78 years. This strategy divides the age range into four segments: [0-34), [34-60), [60-78), and 78+, aligning with significant biological and proteomic changes that correspond to shifts in aging patterns.**C**: The first divides the age range into decade-sized intervals: [0−10),[10−20),[20−30),…,[90−100),[100+[0-10),[10-20),[20-30),\ldots,[90-100),[100+[ 0 - 10 ) , [ 10 - 20 ) , [ 20 - 30 ) , … , [ 90 - 100 ) , [ 100 +

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**A**: We find the model learns a factorised representation (Fig. 1G) and maintains a similar level of sparseness compared to the discrete model (Fig**B**: 1F). We also observe that both discrete and asynchronous models have very similar learning trajectories (Fig**C**: 1D), reaching the same error at convergence. In contrast, the continuous model is more unstable and does not reach the same error.

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**A**: We demonstrate the wide applicability of UniGuide by tackling a variety of geometry-constrained drug discovery tasks**B**: With performance either on par with or superior to tailored models, we conclude that UniGuide offers advantages beyond its unification**C**: Firstly, while the novelty of conditional models often stems from the condition incorporation, our method redirects focus to advancing unconditional generation, which directly benefits multiple applications. Furthermore, this separation of model training and conditioning allows us to tackle tasks with minimal data, a common scenario in the biological domain.

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Selection 4

**A**: Peptides have aroused great interest due to their potential as therapeutic agents (Wang et al., 2022)**B**: Here, we focus on peptide generation by diffusion models.**C**: Currently, there are several reviews (Wan et al., 2022; Ge et al., 2022; Goles et al., 2024) that summarize the application of generative models to peptides

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**A**: Activation of GABAB receptors initiates a signaling cascade that can lead to the opening of potassium channels and inhibition of adenylate cyclase activity. This results in the slow and prolonged inhibitory effects of GABA, contributing to the overall inhibitory tone in the nervous system.**B**: GABAA receptors are ionotropic receptors that function as ligand-gated chloride channels. When GABA binds to these receptors, the channel opens, allowing chloride ions to enter the neuron**C**: This influx of chloride ions causes hyperpolarization of the neuronal membrane, making it less likely for the neuron to fire an action potential. GABAA receptors act quickly and are primarily responsible for the rapid inhibitory effects of GABA. In contrast, GABAB receptors are metabotropic receptors that are coupled to G-proteins

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**A**: We compared our model to an end-to-end baseline derived from Shen et al. (2019) [11], aligned with our goals of spatially accurate reconstructions. **B**: While recent image reconstruction models, such as diffusion models, produce high-resolution outputs, our study prioritizes spatial accuracy and interpretability in an end-to-end framework**C**: Diffusion models, though effective in generating detailed images, have objectives distinct from ours, given their reliance on separate generative processes rather than latent representation learning

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**A**: **B**: Noticed that all those are encoded in Branish and none of them has been assigned weight yet**C**: This function G takes the state as input, based on its knowledgement of the world, it will output a matrix of gist, which might be possible actions in IG and thoughts, answers, and questions in TG

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**A**: By exploring its applications across multiple disciplines, we aimed to inspire further exploration and application of the FHN model in diverse scientific domains. **B**: In conclusion, we hope our review will serve as a guide for understanding and using the diverse dynamical behaviors offered by the FHN model**C**: Throughout our analysis, stability analyses and bifurcation studies provided insights into the observed dynamics

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**A**: On the other hand, phase shifts smaller than π𝜋\piitalic_π lead to connections with the preceding excited region, resulting in connective pulses that propagate in the same direction as the driving wave (Supp. Fig. S5B).**B**: Specifically, phase shifts greater than π𝜋\piitalic_π prompt the system to connect with the forthcoming excited region, producing connective pulses that travel opposite to the driving wave (Fig. 9)**C**: In another instance, narrowing the driving pulse strengthens the phase shifts. With optimal diffusion levels, the system can link with the nearest excited region, generating connective pulses

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**A**: MPNN operates on a graph consisting of a set of vertices and edges**B**: We follow Dauparas et al**C**: (2022); Ganea et al. (2022) and set as initial node features a positional encoding that reflects the residue’s ordering within the sequence, while for the edge features, we use a concatenation of pairwise distance features, relative orientation features and relative positional embeddings.

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**A**: A future research direction is deriving the brain’s slow dynamics and learning mechanisms**B**: Promising results have emerged in simplified neuron models [12]. Transferring the approach to realistic neuron models creates a data-driven possibility to recover biological slow dynamics.**C**: Training many parameters over extended periods allows black-box models, such as neural networks representing protein networks, to act as homeostatic-control agents within cells

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**A**: In extreme cases this mismatch in individual fitness and population viability can lead to evolutionary suicide, where viable populations adapt in a way that they can no longer persist (Parvinen, 2005; Ferriere and Legendre, 2013). Conversely, because of the interplay between evolutionary and ecological processes (such as fluctuation in host densities), parasites should evolve toward decreased virulence (Lenski and May, 1994). Moreover, co-infection of hosts (singly infected cells remain susceptible and can be infected again) (Alizon, 2013) can result in feedback loops between the rate at which susceptible individuals acquire a disease (the force of infection) and virulence: when double infections are common increased virulence is favored; however, increased pathogen virulence decreases the force of infection, favoring decreased virulence once more (van Baalen and Sabelis, 1995). **B**: Still, since selection acts first and foremost on the level of individuals, traits which produce more offspring should generally increase in frequency. This suggests tensions between selective pressures on individual phages and the viability of the phage population overall**C**: A natural expectation is that larger burst sizes would benefit the phage population. However, our analysis suggests that thereby phages also deplete their resources for further replication

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**A**: An advantage, in contrast, is that DNA-based approaches are well suited for parallelization. These (dis)advantages are familiar from DNA computing in general.**B**: This can certainly not be said about DNA computers. Their computational speed depends on how fast the chemical reactions take place, which can be of the order of many minutes**C**: A further aspect to note here are the time scales involved here. Photonic neural networks (see the chapters by Kathy Lüdge/Lina Jaurigue and by Lennart Meyer/Rongyang Xu/Wolfram Pernice) have the attractive feature that they operate with the speed of light, i.e., they are extremely fast

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**A**: (2023) developed a model using Bidirectional Encoder Representations from Transformers (BERT) contextual embeddings (Devlin et al., 2018) to predict MEG signals. In terms of decoding, one paper (Défossez et al., 2023) successfully reconstructed audio from MEG signals through contrastive learning which was based on aligning signals with the latent space generated by the wav2vec2 library (Baevski et al., 2020). These efforts demonstrate the potential of using MEG data to reconstruct the stimulus that has generated it.**B**: So far, research in brain encoding for speech and language processing has primarily used functional Magnetic Resonance Imaging (fMRI) (Huth et al., 2012; Antonello et al., 2023; Caucheteux et al., 2023). These studies have contributed to the development of both linear and nonlinear models that map stimuli to brain activity from fMRI signals. Previous work focused on e.g**C**: enhancements in network scaling and uncovering associations between brain activity and specific auditory and semantic processing tasks (Caucheteux and King, 2022). However, limitations in the temporal resolution of fMRI, which are particularly relevant in speech decoding due to the high-frequency content of the stimuli, have led researchers to explore MEG data collected during exposure to auditory stimuli. On the encoding side, Oota et al

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Selection 2

**A**: In a homogeneous attractant environment, after a large number of runs and tumbles the net displacement of the cell is zero. But in presence of an attractant concentration gradient, runs in the favorable direction are extended and those in the opposite direction are shortened, giving rise to a chemotactic drift [27, 28, 29, 30, 31].**B**: In this work, we use reinforcement learning to study a model that has been motivated by the phenomenon of bacterial chemotaxis [15, 16, 17]. Certain bacteria like E.coli, S.typhimurium, B.subtilis are known to show chemotaxis where they can move along a chemical gradient in their environment [18, 19, 20]**C**: When these microorganisms experience concentration gradient of an attractant chemical in their surroundings, they show a tendency to migrate towards regions of higher attractant concentration [21, 22, 23, 24]. This migration happens via run-and-tumble motion, which is characterized by persistent movement along a particular direction (run), punctuated by abrupt change of direction (tumble) [25, 26]

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**A**: Neural encoding models, particularly those designed to predict neural activity from naturalistic images, significantly enhance our understanding of how visual stimuli are processed and represented in the brain**B**: Such models are crucial for developing advanced visual neuroprosthetics aimed at simulating neural activity to possibly restore vision. Nevertheless, the application of these models must be undertaken with prudence, given the intricate nature of brain functionality and its interaction with the environment. **C**: These models, incorporating aspects of retinotopy, are pivotal in elucidating the complex relationship between external visual environments and their corresponding neural responses

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**A**: Future research should be focused on further investigation and characterization of the differences in the results produced by traditional DGE and XAI techniques and their biological relevance, being the XAI techniques not limited to SHAP. Other interesting directions would include, introducing more data modalities, adding more features into the training data like RNA velocity and use of more sophisticated NN models.**B**: A subset of genes and altered pathways are only detected using the proposed XAI approach and are missed by a traditional differential expression method, which underestimates their potential contribution to the disease**C**: The use of NN models with XAI techniques offers a more detailed analysis of gene expression at single-cell resolution when compared with traditional techniques

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**A**: Existing software tools that implement these corrections are PoPoolation (3, 4), poolfstat (5, 6), and npstat (2). These tools however lack usability, do not scale to contemporary large datasets, and do not support haplotype-corrected frequencies in low-coverage E&R experiments such as those from HAF-pipe or other HARP-based pipelines (7, 8). **B**: Typical population genetic statistics, such as measures of diversity (θ𝜃\thetaitalic_θ, Tajima’s D) and differentiation (FST), hence need to be adapted to correct for the induced biases**C**: The pooling of a finite number of individuals from the population, as well as the finite number of reads being sequenced from each individual, introduce two levels of sampling noise in allele counts (2)

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**A**: Additionally, techniques employing recurrent neural architectures have been employed for the sequential modeling of amino acids [35]. [36] introduced a novel approach that utilizes neural networks to emulate an energy landscape, facilitating the inference of protein folds**B**: The groundbreaking AlphaFold algorithm [21, 37] has significantly raised the bar in terms of accuracy for protein structure prediction. It is important to highlight, however, that proteins are structurally simple, primarily linear molecules, which is in contrast to the complex and branched configurations often found in general molecules, including various ring structures. This structural disparity makes the direct application of protein-folding methodologies less suitable for the intricate task of predicting the conformation of general molecular structures. Hence, there is a compelling need for distinct modeling techniques that are tailored to address the unique challenges posed by non-protein molecular structures.**C**: The field of protein topology prediction has experienced rapid expansion, with a multitude of innovative methodologies emerging. These innovations encompass a range of approaches, including the use of flow-based models [34, 26], which effectively map the conformations of protein main chains

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Selection 4

**A**: Thus we were able to obtain the exact solutions of the KPP equation which to the best of our knowledge were not known before. Additionally we obtain the exact analytical traveling wave solutions of the generalized Burgers–Huxley equation.**B**: (6)**C**: In this paper we will use the method of exclusion of the independent variable benguria ; rosu ; kogan3 ; kogan4 ; kogan5 , which allows to reduce the problem of integration of the second order ODE to the problem of integration of the first order ODE, to obtain the exact solutions of Eq

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Selection 2

**A**: Stochasticity in ecological systems is typically categorized into two main types: demographic stochasticity and environmental stochasticity Lande et al. (2003)**B**: Demographic stochasticity arises from random variation in the reproductive success of individuals. For instance, each individual might have an equal probability of producing either zero or two offspring**C**: In contrast, environmental stochasticity affects entire populations in a correlated manner. For example, during favorable years, each individual may, on average, produces two offspring, whereas in unfavorable years, this average might drop to just one-half.

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**A**: The curve catches also the rise in cases that began in mid-October.**B**: Since the gap between the curve and the data is smaller from July, we can deduce that a better monitoring policy is induced by the introduction of Green Pass obligation (notice that the Green Pass can also be granted if swabs are negative)**C**: In Figure 22 we show the trend of positive individuals in the GP case, and observe that it matches available data

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Selection 3

**A**: There are three key steps in Dual-RAG-IF: 1) Mutation region identification: Mutation regions can be determined either manually or automatically. For manual design, the input must include a target 2D structure in dot-bracket notation defining with the target dual graph, along with a sequence that marks mutation regions by representing residues as ’N’**B**: Each candidate is evaluated by applying two 2D folding programs (such as NUPACK[24], IPknot[25], and PKNOTS[26]) capable of handling pseudoknots to verify the resulting fold, and a sequence is considered successful when both programs agree on the target fold. In our application, we use the NUPACK and IPknot packages. 3) Sequence optimization: The candidate sequences are ordered by minimal mutations, ensuring an optimal final design.**C**: For automatic design, we only need the target dual graph information, and the entire sequence is taken as the mutation region. 2) Candidate sequence generation: Candidate sequences with mutations are generated using a genetic algorithm

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**A**: Fig. 3(a) shows the evolution of ΦΦ\Phiroman_Φ for (i) an initially uniform distribution for F𝐹Fitalic_F, and (ii) a distribution F𝐹Fitalic_F consisting of randomly placed Gaussian spherical clusters of equal standard deviation. The long–time states of ΦΦ\Phiroman_Φ for both (i) and (ii) show an significant increase over the static uniform RanGEF case, as previously computed in Fig. 2(d)**B**: To compare the cases (i) and (ii), we compute the angular average of RanGEF,**C**: Moreover, the long–time concentration profile of chromatin-bound RanGEF shows a sharply varying spatial profile within the nucleus, with a significant accumulation at the NE

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**A**: Allosteric regulation is one of the most relevant transduction mechanisms at the molecular level [11, 35, 36]**B**: Ion binding in metal sensor proteins is a brilliant example of the exploitation of this multi-scale strategy, in which the affinity of the molecule to the DNA substrate is modulated through the control of the distal ion coordination site [2, 3].**C**: The system-wide modifications that one or few atoms, interacting in very local regions, induce on the whole protein make allostery an exquisitely multi-scale process, whose versatility and consequent ubiquity are paired by the complexity of its investigation

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**A**: We let the drug effectiveness γ𝛾\gammaitalic_γ to be a free parameter instead of fixing it**B**: This allows for variability in how different patients respond to the drug, and provides a more accurate assessment of how close the initial total cancer cell population is to the carrying capacity, i.e**C**: how close x⁢(0)𝑥0x(0)italic_x ( 0 ) is to 1111.

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**A**: In Fig. 4 and in Figs. S3-7 of the supplementary material calibration curves for all uncertainty measures across all molecules are shown for GPR with Coulomb as well as GPR with SOAP. In nearly all cases, the GPR standard deviation demonstrates much better global calibration, with notably lower miscalibration areas compared to the other two uncertainty measures. The only exception is GPR with Coulomb for benzene. Here, the calibration curve for the GPR standard deviation shows a relatively high miscalibration area, which exceeds that of the two sets uncertainty measure. **B**: In Fig. 3, calibration curves for all three uncertainty measures are shown. We exemplary show calibration curves of GPR with SOAP for rMD17 benzene and WS22 SMA**C**: The calibration curve for the GPR standard deviation is nearly diagonal and has a low miscalibration area, indicating relatively good calibration across the dataset. In contrast, the two sets and bootstrap uncertainty measures show much poorer calibration, with significantly higher miscalibration areas

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**A**: Notably, XATGRN’s robust performance highlights its ability to handle the skewed degree challenge more effectively compared to DeepFGRN and DGCGRN. However, it is worth noting that in certain cases, such as the human COVID-19, breast cancer, and lung cancer datasets, the recall of XATGRN is slightly lower than that of DeepFGRN.**B**: These results demonstrate that XATGRN effectively captures the complex regulatory interactions within gene networks and accurately predicts both the presence and types of regulatory relationships**C**: Our XATGRN achieves the highest AUC, recall, F1-score, and precision across the DREAM5 network1 and all four E.coli datasets

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Selection 4

**A**: The human induced pluripotent stem cell (hiPSC) line BIHi250-A (https://hpscreg.eu/cell-line/BIHi250-A) was cultivated in Essential 8 medium prepared according to the original recipe [60] and grown on Geltrex (Thermo, A1413302) coated tissue culture plates**B**: Media change was performed daily for six days with one double-feed on day 7**C**: Cells were passaged when confluency reached approximately 80%. Mouse embryonic fibroblasts (MEFs) immortalized by limited dilution were grown in tissue culture flasks and cultivated in DMEM/F-12 (Thermo, 11320033) supplemented with 5% FBS (PAN Biotech, P30-3030M) and passaged when a confluency of approximately 80% was reached. All cell cultures were kept at 37°C and 5% CO2.

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**A**: MyESL took 5.255.255.255.25 minutes to read and pre-process input datasets and less than 1111 minute to build the ESL model and process result files. The peak memory usage for this analysis was 1.31.31.31.3 GB.**B**: We analyzed a fungus dataset containing amino acid sequence alignments of 1,23312331,2331 , 233 genes from 86868686 yeast species (Shen et al., 2016, 2017). We built an ESL model for a clade (44444444 species), where all species received a +11+1+ 1 label, while the remaining 42424242 species were assigned −11-1- 1**C**: The combined sequence alignments from all genes contained 609,013609013609,013609 , 013 sites, and the total number of bit columns was 4,105,44441054444,105,4444 , 105 , 444, distributed among 1,23312331,2331 , 233 groups. We used weighted class balance and set the position and group sparsity parameter values at 0.10.10.10.1 and 0.20.20.20.2, respectively

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Selection 4

**A**: An estimated probability is counted as correct if it falls on the right side of 0.5. If we chose a single peer’s probability rating at random, the accuracy of our collective inferences about the claims would match the average accuracy of the peers: about 62% for the set of 1,200 general-knowledge claims in our online experiment (Fig**B**: We first consider the accuracy achieved by simple methods for aggregating the judgments. The accuracy of an individual person or collective inference algorithm is defined as the rate of correct answers**C**: 2). Trusting a random peer does not benefit from the wisdom of the crowd.

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Selection 1

**A**: While diffusion models have shown promising performance, they are not without limitations. Due to their iterative nature, requiring thousands of steps to generate outputs, diffusion models often suffer from inefficiencies in sampling. In the context of molecular conformation generation, some diffusion model variants have reduced the number of sampling steps from thousands to tens or even a single step, but this often comes at the expense of accuracy, leading to suboptimal results \parencitejing2022torsional, fan2023ec.**B**: Deep learning methods, on the other hand, enable atom-level research, eliminating the dependence on fixed templates**C**: With the advancement and success of diffusion models in image generation \parenciterombach2022high, ramesh2022hierarchical, these approaches have also been adopted in chemistry \parencitehoogeboom2022equivariant, abramson2024accurate, song2024equivariant, including molecular conformation generation

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Selection 2

**A**: This study begins with an introduction in Section I, followed by a review of related works in Section II**B**: The background study is detailed in Section III, methodology is detailed in Section IV, results are analyzed in Section V, and limitations with future work are discussed in Section VI**C**: Finally, Section VII summarizes the study.

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Selection 3

**A**: Additionally, learning discrete states independently becomes prohibitively costly when estimating dynamics for a population that contains multiple independent subgroups. In this scenario, SLDS learns distinct systems for each potential combination of dynamics**B**: For example, switched systems often learn approximate dynamics which have discontinuities along the boundaries of the switches. This can be well suited to capturing sudden changes in dynamics, but may not accurately represent smooth transitions between dynamical modes. Approximating smooth transitions requires increasing the number of linear states available to capture intermediate stages**C**: However, the number of possibilities grows exponentially as the number of subgroups and dynamical modes increases, rendering it combinatorially impractical. Moreover, this challenge is compounded during inference where the learned systems are rigid and cannot adapt to capture similar dynamics. Instead, SLDS must learn new distinct states to accurately represent subtle variations of similar dynamics. For a fixed number of parameters, dLDS improves the expressivity of the switching linear approach by offering a controlled way to flexibly modify and reuse learned linear regimes.

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**A**: The family subsets have varying sizes in terms of interactions ( from 19K to 220K), number of proteins ( from 100 to 1K), and number of compounds (from 10K to 120K). **B**: These datasets include interactions belonging to different protein superfamilies, including membrane receptors, ion channels, transporters, transcription factors, epigenetic regulators, and enzymes with five subgroups (i.e., transferases, proteases, hydrolases, oxidoreductases, and other enzymes)**C**: ProtBENCH [37] contains protein family-specific bioactivity datasets

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**A**: To overcome this limitation, we have introduced virtual adversarial training as a means to improve the model generalizability (see Method 4.6)**B**: Given the vast diversity of HLA and TCR repertoires, the experimentally validated bindings currently available are limited and even biased, posing a tough challenge of overfitting in the development of prediction model**C**: Specifically, we apply adversarial perturbations to the sequence embeddings to generate virtual adversaries that aim to maximize the loss function. The adversarial training makes our model less sensitive to slight changes in input sequences, thereby significantly improves the performance (see Method 4.8).

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**A**: By providing a simultaneous handle on the multiple timescales that govern behavior such as cruising and wandering, differential modulation of speed and egocentric direction preference, our approach sets the stage for dissecting the underlying brain circuits for navigation in a transparent vertebrate brain. Along with the serotoninergic modulation of motor activity mentioned previously, we can dissect how multiple brain regions function together to give rise to this hierarchy of timescales in behavior**B**: The hindbrain oscillator, also called anterior rhombencephalic turning region has been identified as one brain region that confers a persistence of the left/right steering in the larval zebrafish (dunn2016brain, wolf2017sensorimotor). We hypothesize that the interplay of this region with the mesencephalic locomotor region (MLR, carbo2023mesencephalic), the nucleus of the medial longitudinal fasciculus (wang2014selective, berg2023brainstem), projecting onto the reticular formation (orger2008control, carbo2023mesencephalic) could explain the dynamics we uncover**C**: In particular, the modulation of the MLR by dopamine released from posterior tuberculum (carbo2023mesencephalic) could explain the long-lived persistence of cruising behaviors. There is already some evidence for this in mice, where dopamine release has been associated with long time scale (seconds to minutes) persistence of motor sequences (markowitz2023spontaneous).

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**A**: In the presence of the error signal, SGD in a single neuron model leads to a local plasticity rule, that could be plausibly implemented in a biological neuron, unlike in multi-layer networks (see Appendix C). Finally, it will be interesting to investigate the computational abilities of a neuron with non-linear dendrites in a purely unsupervised learning setting. **B**: In cerebellar Purkinje cells, this teaching signal could be implemented by the climbing fiber input, which has been shown to correlate with error in motor tasks. In cortical pyramidal cells, the presence of error signals is more speculative**C**: Another important future direction concerns synaptic plasticity algorithms. Here, we have investigated a simple plasticity algorithm (SGD) in a standard supervised learning scenario, in which a teaching signal is available to the neuron

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Selection 3

**A**: (c,d) Performance of neural network architectures across datasets. Bar plots indicate the mean test set performance (with error bars denoting the standard deviation), in comparison with the XGBoost baseline (dashed line: average performance, shaded area: standard deviation). Performance was quantified as balanced accuracy in classification (c), and as concordance index in regression (d).**B**: The similarity was quantified as the Tanimoto coefficient on extended connectivity fingerprints39, and the maximum similarity was reported. Different distributions can be observed in the classification (a) and regression (b) datasets, with the former containing more dissimilar molecules on average**C**: Figure 2: Overview of dataset similarity and of model performance. (a,b) Distribution of test set similarities in comparison with training set molecules

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**A**: Moreover,**B**: While this is obvious for directed networks and level-1 semi-directed networks, for higher-level semi-directed networks it takes some care to prove that the intuitive definition works**C**: Reflecting the relative complexity of restricting a semi-directed network to a subset of its taxa, we show that this process is well-defined (see Section 4)

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**A**: Notably, we observed that smaller initial gains can paradoxically hinder learning. This result is explained by our analysis of the Lyapunov exponent, which is crucial for the stability and information propagation within the network. We found that smaller initial gains resulted in larger deviations of the Lyapunov exponent from zero before training, indicating a greater challenge in achieving the balanced dynamical properties necessary for effective learning**B**: To address this challenge, we brought the gradient flossing method into the biologically plausible learning framework, leading to performance improvement for suboptimal initial weight magnitudes. Overall, these findings provide insights into how variations in initial connectivity may influence learning in neural circuits, offering predictions that can guide future experimental work. Additionally, these findings have practical implications for the design of neuromorphic chips, where optimizing initial weight configurations could enhance the efficiency and effectiveness of energy-efficient biologically plausible learning algorithms. **C**: This study highlights the role of initial weight magnitude in shaping the learning dynamics of biologically plausible rules, predicting its importance in neural circuit learning. While the influence of initial connectivity on learning has been extensively explored in the realm of backpropagation-based learning, our work is novel because it extends this inquiry to biologically plausible settings. Our findings demonstrate that, similar to backpropagation through time (BPTT), the choice of initial weight magnitude in e-prop — a biologically plausible learning rule — has a profound impact on learning performance

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**A**: Pre-training set. 2,372,675 SMILES strings were obtained from ChEMBL v33 44**B**: SMILES strings longer than 80 tokens were dropped. The final set consisting of 1,584,858 molecules was randomly divided into training (n𝑛nitalic_n = 1,500,000), validation (n𝑛nitalic_n= 40,000), and test splits (n𝑛nitalic_n = 44,858).**C**: Salts were removed and molecules composed only of C, H, O, N, S, P, F, Cl, Br, I atoms were retained. The SMILES strings of the remaining compounds were sanitized, canonicalized, and the charge and sterochemistry annotations were removed

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Selection 3

**A**: The primary limitation for both the semi- and fully-automated segmentation tracking methods is the accuracy of the segmentations, which can have downstream effects on length and width predictions for animals**B**: In turbid water, the pectoral and caudal fins are occasionally left out of the segmentation, or the caudal lobe will be segmented separately from the rest of the body. In addition, obtaining precise biometrics from segmentation masks may be challenging in aerial videos where drone metadata isn’t available. Ultimately, the quality of the drone aerial imagery has a significant effect on the accuracy of detection and segmentation for any marine and terrestrial species (Ramos et al., 2022).**C**: When the shark is swimming near the seafloor in very shallow water, SAM 2 will occasionally segment the shadow of the shark along with the shark itself

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**A**: To start using the SpinPath JavaScript tool, the user first selects a WSI and uploads it to the program. The OpenSeadragon.js package is then used to display the image in a viewer, allowing the user to move and zoom into the image as needed**B**: Using the GeoTiff.js and Transformers.js libraries to access the WSI data and implement the user’s selected model and feature extractor in JavaScript, respectively, The program then automatically handles patching, patch embedding, and aggregating results. The results and logits are then displayed to the user, and the user is given the option to download the patch coordinates and attention scores in the form of GeoJSON data.**C**: Once loaded, the user can then select regions for analysis using the Annotorious package. The user can then click the “Run Model Analysis” button to run their selected model on the annotated regions

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**A**: However, in finite systems the absorbing configuration can always be achieved, even in the supercritical phase. To avoid this issue, we apply a quasi-stationary method to characterize the dynamics of the model. Specifically, we apply a reactivation method [28, 29] in which we perform a reinfection of one individual (randomly chosen) every time the dynamics reaches the absorbing configuration.**B**: In epidemic models, the absorbing state refers to the configuration without infected individuals**C**: If this state is reached, the dynamics stops

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**A**: Since the cluster mass is the only parameter in our modeling, the spectrum of masses for the catalytic reactants should be sparse, so that catalysts are rare**B**: In many catalytic reactions, only a small subset of the reactants are catalytic**C**: Here we treat an extreme model where only monomers are catalytic. In Appendix A we briefly consider the model where clusters with ‘magic’ masses 2nsuperscript2𝑛2^{n}2 start_POSTSUPERSCRIPT italic_n end_POSTSUPERSCRIPT are catalytic.

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**A**: By optimising over these convex sets with a given set of rate parameters, one can obtain upper and lower bounds on the moments. These bounds provide error guarantees for predicting moments, unlike approximation methods based on system size expansion or moment closure. Whether similar approaches could be utilised to provide error bounds for parameter inference has remained unexplored heretofore. **B**: In recent years, a few authors have obtained theoretically guaranteed bounds on the stationary moments (Kuntz et al., 2016; Sakurai and Hori, 2017; Ghusinga et al., 2017; Dowdy and Barton, 2018a, b; Sakurai and Hori, 2018a; Kuntz et al., 2019; Hori, 2020; Sakurai and Hori, 2022) and the transient moments (Dowdy and Barton, 2018b; Sakurai and Hori, 2018b; Holtorf and Barton, 2023) of stochastic reaction networks**C**: These approaches rely on convex optimisation of sets constrained by moment equations, a set of equations involving the moments and the reaction rate parameters, and positive semidefinite constraints on the moments

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**A**: We emphasise that we have assumed that the probability of selecting a link connecting nodes in opposite states, σ𝜎\sigmaitalic_σ, is independent of the degree of the nodes which it connects. This is a shortcoming of the homogeneous pair approximation**B**: Extensions have been proposed, such as the heterogeneous pair approximation [34], which allows σ𝜎\sigmaitalic_σ to depend on degree. Similarly, we assume an infinite graph**C**: The stochastic pair approximation [45] accounts for finite-size corrections. However, here, we do not consider these extensions.

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**A**: We achieve this balance by designing a novel GP kernel function that defines a smooth, locally linear prior on dynamics. While our main focus is on providing an alternative to the rSLDS, the gpSLDS also contributes a new prior which allows for more interpretable learning of dynamics and fixed points than standard priors in the GP-SDE framework (e.g., the RBF kernel). Our implementation of the gpSLDS is available at: https://github.com/lindermanlab/gpslds.**B**: The gpSLDS combines the modeling advantages of the GP-SDE with the structured flexbility of the rSLDS**C**: To address these limitations of the rSLDS, we propose a new class of models called the Gaussian Process Switching Linear Dynamical System (gpSLDS)

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**A**: Participants diagnosed with NDs were categorized into aforementioned groups based on disease specific clinical diagnostic criteria diagnosis: **B**: These participants were either categorized as healthy (CTL) or diagnosed and treated for a ND by a subspecialist neurologist or geriatric psychiatrist from Johns Hopkins Hospital**C**: The authors of this study collected a dataset from 113 participants from a larger digital biomarker cohort, NeuroLogical Signals, which our group has previously reported [18, 19, 20, 21, 22, 23]

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**A**: To the best of our knowledge, this is with the very recent exception of [4] the only known example of an explicit primal-dual algorithm in phylogenetics**B**: [13]). We suspect that unpacking many of these integer linear programming formulations to study properties of the linear programming relaxations could be a very fruitful line of research. The recent duality-based 2-approximation algorithm for agreement forests [12] is a good example of this potential. **C**: This is interesting, since the polyhedral angle on phylogenetics problems dates back to at least 1992 [5] and integer linear programming has been used quite frequently in the field (see e.g

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**A**: It is also assumed**B**: The infected cells produce new viruses at the rate m⁢dI𝑚subscript𝑑𝐼md_{I}italic_m italic_d start_POSTSUBSCRIPT italic_I end_POSTSUBSCRIPT during their life; and dVsubscript𝑑𝑉d_{V}italic_d start_POSTSUBSCRIPT italic_V end_POSTSUBSCRIPT is the death rate of new virions, where m𝑚mitalic_m is any positive integer**C**: of lytic effect

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**A**: In Fig.3 an input at location 13 generates a set of values across a range of nearby nodes**B**: In Fig 3a, the recursion creates a symmetrical gradient. In Fig 3b, a reward node is connected to node 16, In Fig 3c, the de-inforcement function is activated, providing the impetus for the agent to choose the highest visible value (node 14). Note that node values are normalized so max = 1.**C**: Figure 3: Node values exhibit a gradient across a simple graph

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**A**: This artificial category acts as a segmentation tool within the vast, undetermined space of potential arguments and predicates [52]. These arguments and predicates may align with existing human-like categories or form entirely novel “alien-like” categories that could represent statistical constructs [11] or “polysemic concepts” [14, 53] not directly relatable to human cognitive categories. **B**: Each synthetic category is created during the training phase by the neural network itself**C**: In our epistemological framework, synthetic categories, much like human categories [74], are immanent cognitive constructs

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**A**: Seasonal antigenic prediction, particularly for influenza A H3N2, has benefited from machine learning approaches that help forecast viral evolution, supporting timely vaccine updates [304]. Finally, phylogenetic analyses have identified optimal influenza virus candidates for seasonal vaccines, underscoring the significance of LLMs in guiding vaccine development against anticipated strains [316]. **B**: Additionally, antigenic prediction plays a crucial role in designing effective influenza vaccines, especially for rapidly evolving strains. Statistical analyses of antigenic similarity, such as those conducted for influenza A (H3N2), highlight the potential of machine learning models in mapping antigenic drift and optimizing strain selection for seasonal vaccines [313]**C**: Moreover, cellular correlates of protection identified through human influenza virus challenges have advanced our understanding of immune responses to oral vaccines, demonstrating the applicability of machine learning models in immune signature identification [314]. Blood inflammatory biomarkers have also been analyzed to differentiate COVID-19 from influenza cases, showcasing the predictive power of LLMs in clinical biomarker differentiation [315]

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Selection 2

**A**: Due to its ubiquitous applications, collagen needs to be thermally stable**B**: Collagen is one of the most abundant proteins in animals and has numerous applications in the field of medicine 90**C**: Yu et al.51 have experimentally gathered the melting temperature of 633 different primary sequences of collagen to investigate their thermal stability. The higher the melting temperature, the greater the stability of collagen.

CAB

BAC

BCA

CAB

Selection 2

**A**: We are interested in what would happen if grazers and browsers are added into a purely competitive environment among plants and whether trees, grass, grazers, and browsers can coexist. Therefore, we focus on the co-existence steady state of four species (which is unique) in the proposed savanna system (1.1) and study related traveling wave solutions, which may provide important information about the transition dynamics between the co-existence state and other steady states**B**: To obtain our results, we employ the upper-lower solution method widely used in related studies. However, due to the absence of linear reaction terms in our herbivore equations for G𝐺Gitalic_G and B𝐵Bitalic_B, the usual form of exponential functions for the lower solutions does not work in our case. To overcome this difficulty, we introduce Gaussian-like functions at one end of the real line domain and successfully find suitable lower solutions for our problem.**C**: We demonstrate the existence of two types of traveling waves, the waves transitioning from the extinction state to the co-existence state and the waves from a grass-vegetation state (where only grass and grazers exist) to the co-existence state. Our results indicate that under suitable conditions, the co-existence state of four species may be dominant or more stable compared to other steady states in the sense of wave dynamics

ABC

BCA

BAC

ACB

Selection 4

**A**: Transformer architectures excel at capturing global features from textual data**B**: The Transformer encoder comprises two sub-layers: a multi-head attention layer and a fully-connected feed-forward layer. Each sub-layer is followed by a residual connection and layer normalization to normalize input values for all neurons in the same layer [27], as illustrated in Fig 1. **C**: Building on this capability, we leverage the attention mechanism of the Transformer to model global relationships within molecular structures

CAB

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ACB

Selection 4

**A**: In this package, we integrate tools for protein structure downloading and processing, interface-fitted tetrahedral mesh generation, parameter assignment, and the output of mesh data files, electrostatic potential functions, and ionic concentration functions in formats compatible with visualization tools such as ParaView**B**: To enable broad applications, we have implemented the NSMPB finite element iterative solver in Python and Fortran as a software package**C**: The NSMPB package also seamlessly integrates the Fortran subroutines that we wrote to handle computationally intensive tasks. With these efforts, we have not only simplified the usage of the NSMPB package but also improved the performance of our NSMPB package.

ACB

BCA

BAC

CAB

Selection 3

**A**: These evaluation metrics are defined below in terms of true positive (TP), true negative (TN), false positive (FP), and false negative (FN) cases. **B**: We investigated a number of performance metrics to evaluate and compare our proposed method to existing ones**C**: These metrics are namely accuracy, precision, recall, f1-score [66], kappa score[67] , and AUC value in ROC analysis

ACB

CAB

BAC

ACB

Selection 2

**A**: Clinical Trial Matching**B**: Many studies have focused on learning patient retrieval and enrollment information for predicting individual patient outcomes within clinical trials, rather than making overall predictions about trial success. Doctor2Vec [1] learns representations for medical providers from EHR data, and for trials from their descriptions and categorical information, in order to address data insufficiency issues such as trial recruitment in less populated countries**C**: DeepEnroll [28] encodes enrollment criteria and patient records into a shared latent space for matching inference. COMPOSE [7] encodes structured patient records into multiple levels based on medical ontology and used the eligibility criteria embedding as queries to enable dynamic patient-trial matching. In contrast, our work focuses on predicting the clinical trial outcome directly based on drug molecules, target diseases, and eligibility criteria.

ABC

BAC

CBA

Selection 1

**A**: In particular, the notations in [64] will be used. It is convenient to recall the following definitions (from [64]), **B**: Owing to the large size of the 2-group behavior model (making the computation of the eigenvalues of its Jacobian evaluated at the respective DFE less tractable mathematically), the linearization approach will be combined with some results related to the properties of Metzler matrices [62, 63]**C**: The stability of the three non-trivial DFE of the 2-group behavior model (G1DFE, G2DFE, and G3DFE) will be analyzed using standard linearization

CAB

CBA

ACB

CAB

Selection 2

**A**: The methods of both Zou and Zhang, (2015) and Castoe et al., (2009) require that the foreground lineages share the same amino acid. However, there are cases where replicated changes in protein function arise from different amino acids at the same site (Zhen et al., , 2012; Mohammadi et al., , 2022). One approach to address this is to relax the requirement for each foreground lineage to have evolved the same amino acid. For example, this can be achieved running the above two methods multiple times for different subsets of the foreground lineages**B**: However this approach is computationally intensive for studies with a large number of foreground lineages (Fukushima and Pollock, , 2023). Chabrol et al., (2018) developed a model that inherently accommodates situations where some foreground species have different amino acids. Their approach steps away from explicit ancestral sequence reconstruction and instead uses a Continuous Time Markov Model of sequence evolution to determine the likelihood of replicated amino acid transitions occurring in the phylogeny branches leading to the foreground lineages. The ConDor workflow (Morel et al., (2024), available as a web-based tool) can also facilitate some foreground lineages not sharing a particular amino acid by allowing the user to specify a minimum number of lineages required to share the same amino acid substitution**C**: Their approach was designed to account for potential uncertainty in phenotypic classification, which can be common in viral studies. The Profile Change with One Change (PCOC) method (Rey et al., , 2018) takes a different approach to modeling variation in the amino acids of the foreground lineages by identifying sites where the foreground lineages have a different amino acid preference (e.g. a preference for a hydrophobic versus hydrophilic amino-acid) compared to the background lineages. While the other approaches focus solely on the most common amino acid in the foreground lineages, PCOC uses all the amino acids in the foreground lineage to determine changes in amino acid profile. Additionally, both the “PC” and “OC” components of the model can be used independently, allowing for analysis of a range of amino acid replication scenarios.

BAC

ABC

CAB

Selection 2

**A**: While it is true that between minutes 5 and 6 more than one ant reaches the barrier, the process would then be mediated by multiple ants seeking information, retaining it, and triggering a cascade**B**: From the moment this effective ant reaches the barrier, it remains activated and triggers a panic avalanche among its nestmates. **C**: This, along with the finite nature of information retention, leads us to conclude that a more simplified mechanism explaining the shift in the CM can be understood as a single “effective ant” representing several informed ants

ACB

CBA

CAB

CBA

Selection 1

**A**: To this end, we recruited three raters to annotate Chapter 9 of Harry Potter across the two domains**B**: Furthermore, we examined whether domain-specific fine-tuning would specifically bolster the model’s capability in predicting MEG responses associated with words from that domain, as compared to words outside that domain**C**: We release these annotations as a resource for the dataset to facilitate further analysis. Details on the annotation process can be found in Appendix H. Examples of each phenomenon within the Harry Potter text can be found in Appendix I.

BAC

ABC

ACB

BCA

Selection 1

**A**: This NEM method to study games in the thermodynamic limit, is applicable to any two-player two-strategy game, both cooperative like Public Goods game or non-cooperative like Hawk-Dove game or Prisoner’s dilemma game, since we are making an exact mapping to the spin-1/2 Ising model via Nash equilibrium**B**: In fact in a recent work, our group has worked on the Nash equilibrium mapping in the context of the vaccination game, in the thermodynamic limit, see Ref. [19]. **C**: Thus be it the battle of sexes(BoS) or, game of chicken or, Volunteer’s dilemma, or the vaccination game, all these games can be understood in the thermodynamic limit via the Nash equilibrium mapping

CBA

ABC

BCA

ACB

Selection 4

**A**: (2022; 2024), the authors proposed models to identify time delays between cross-regional brain interactions, overcoming the challenge of distinguishing indirect, concurrent, and bi-directional interactions in two or more populations**B**: However, their model focuses on analyzing sessions individually and is not intended to uncover the full underlying set of transition matrices, but rather to recognize meaningful time delays that can imply interactions. Other models addressed multi-regional interactions through a communication subspace Semedo et al. (2019) using dimensionality reduction, or by Generalized Linear Models (GLMs), with either Poisson (Yates et al., 2017) or Gaussian (Yates et al., 2017) statistics**C**: In Gokcen et al

ACB

BAC

BCA

Selection 4

**A**: Hence, the population is considered to be composed of cell sub-populations in two different states: up-regulated and down-regulated bacteria, namely motile m𝑚mitalic_m and static s𝑠sitalic_s, respectively, and the concentration of autoinducers is given by q𝑞qitalic_q. As autoinducers are produced by both sub-populations at a rate r𝑟ritalic_r (see [38]), and the bacteria can either switch or remain in their category, we assume that: **B**: When a bacterium responds to an external stimulus by increasing the amount of a cellular component, the process is up-regulated, and it is down-regulated otherwise. To put it another way, the dynamics of the bacteria are regulated by both, autoinducers as well as growth of the bacteria population itself**C**: In order to capture the key qualitative ingredients of QS mechanisms in bacteria, we follow a simplified approach. In so doing, we assume that the autoinducers bind to receptors that enhance the expression of a particular gene, and its production also directly depends on the bacteria population (e. g. [25])

CBA

BCA

BAC

BCA

Selection 1

**A**: However, a regime configuration based on a more natural classification of traits, i.e., shape of the antlers, results in an MGPM that is more plausible in explaining the process that generated observed data.**B**: We showed how an MGPM with multiple regimes does not necessarily result in a better fit to the observed data than using a single process on the whole tree**C**: We illustrate how our method can be used to test several evolutionary hypotheses in a real world setting

ABC

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BCA

CBA

Selection 4

**A**: Regarding PI feature, SHTE has a higher mean pitch interval (2.512.512.512.51) with more variability (STD 1.011.011.011.01), indicating a wider range of interval sizes**B**: The generated data has a mean interval of 2.332.332.332.33 with a smaller standard deviation (0.320.320.320.32), indicating it varies less than SHTE but more than Bach. The KLD values for PI are 0.110.110.110.11 (SHTE) and 0.040.040.040.04 (Bach), showing that the generated data’s pitch interval distribution aligns better with Bach. The overlap areas are 0.550.550.550.55 with SHTE and 0.710.710.710.71 with Bach, again indicating that the generated data’s intervals are closer to those in Bach. **C**: Bach has a lower mean interval (1.921.921.921.92) and less variation, suggesting smoother transitions between notes

CAB

ACB

CAB

ABC

Selection 2