The Galton--Watson process (GWP) is a discrete-time branching process model that provides a powerful tool for analyzing epidemic data and estimating key epidemiological parameters such as the basic reproduction number. When used with surveillance-based cluster size data, the GWP can also elicit information about the extent of transmission heterogeneity, even when each transmission process is not directly observable. When cluster size distribution data are available, the parameters that govern the transmission can be statistically inferred by using the probability mass function that corresponds to the observed cluster size data. For multi-type GWPs, however, real-world applications remain limited, possibly because of the absence of conceptually and practically straightforward approaches for deriving the closed-form solution of the final size distribution. In the present study, we propose a framework for computing the final size distribution of multi-type GWPs, using a method for the choice of the Cauchy integral contour. We provide examples of how our framework can be applied to both simulated data and real-world data of Middle East respiratory syndrome, and discuss potential pitfalls surrounding the identifiability of parameters for statistical inference when using likelihoods that are not conditioned on extinction.

Human attachment is distinguished by enduring internalized representations that shapes neurodevelopment and social-emotional functioning. However, as unobservable inner processes mixed with social cues and partner-specific factors, the neurocognitive mechanisms of these representations during real-time interaction remain unclear. Using a novel Remote Partner-Belief Manipulation paradigm in 40 child-mother-stranger trios, we experimentally isolated attachment representations in 3-4-year-olds by manipulating children's partner-belief during remote cooperation. The inner processes were captured from synchrony between partners' EEG, showing that children's mother-partner belief, regardless of the actual partner, significantly enhanced interbrain synchrony. This partner-belief modulation concentrated on children's P4 channel (overlaying the attachment-designated right temporoparietal junction), where synchrony strength correlated to attachment security and children's response acceleration due to mother-partner belief. These findings established attachment representations as an independent, endogenous driver of interbrain synchrony, potentially via children's heightened attention towards their attachment figure, implying the role of symbolic attachment activation when separation.

The prefrontal cortex (PFC) maintains goal information for action planning, but how recurrent circuits preserve it in an action-usable form over behavioral timescales remains unclear. Here we ask whether short-term synaptic plasticity (STP) can stabilize goal information as action-usable, goal-conditioned dynamics. We incorporated STP into a PFC-inspired reservoir computing model with basal-ganglia-inspired temporal-difference readout learning, and evaluated paired models with and without STP across 100 independently generated networks in a multistep goal-directed action-selection task with delayed execution. Goal identity was highly decodable during the delay even without STP, so STP was not required to form a linearly readable goal representation. Under state noise, however, success without STP fell from 75.8% to 49.5%, whereas the model with STP remained essentially unchanged (91.8% without noise versus 89.2% under noise; paired Cohen's dz=1.31). Time-resolved decoding, state-space separability, and action-value-difference analyses showed that STP preserved goal information as action-relevant goal-conditioned dynamics available at later action opportunities. Gain-matched and STP-state perturbation controls argued against a simple fixed recurrent-scaling explanation and supported online, history-dependent synaptic modulation. Effective-connectivity analyses showed delay-period goal-specific patterning that increased toward the later part of the trial with STP, where it should be read as goal- and task-state-conditioned patterning; effective connectivity without STP was time-invariant. A grid search identified a facilitation-dominant range of STP time constants associated with high success rates. These results suggest that STP supports robust goal-conditioned dynamics through dynamic modulation of goal-dependent effective recurrent connectivity.

Recently, the mapping of the replicator equation onto Bayes' theorem has been recognised, leading to an analogy between evolutionary dynamics and Bayesian learning. However, this analogy holds only for pure selection in infinite populations and breaks down when mutations -- a central mechanism of evolution -- are introduced. Here I propose that evolution by natural selection, at least for populations of haploid replicators in static environments, is best understood not as a learning process but as a process of causal inference. Each mutation event constitutes a natural experiment in which the parent serves as the control and the mutant offspring as the treated unit. Natural selection screens the causal effect of the mutation on fitness, retaining mutations with non-negative effects. I formalise this view within the Neyman-Rubin potential-outcomes framework. I first develop the general theory using a generic fitness outcome and show how the core identification assumptions in causal inference (Stable Unit Treatment Value Assumption, Consistency, Unconfoundedness, Positivity) map onto evolutionary biology. Using the unnormalised quasispecies equation, I prove that the intergenerational change in mean fitness decomposes exactly into a selection term -- recovering Fisher's Fundamental Theorem -- plus a mutation term that corresponds to a fitness-weighted average of the cumulated effect of all mutations over all parental genotypes. I show that this decomposition extends, under suitable assumptions, to the generalised replicator-mutator equation and that the frequencies of populations of matched parents-offspring update in proportion to the average causal effect of mutations on fitness.

We consider continuous Prisoner's Dilemma played in spatial setting by group-structured populations. The population dynamics consists of individual-level birth and death and group-level fission and extinction events. Each individual plays games with all other individuals within their group, while groups play games against their nearest neighbours. Payoffs from individual-level games affect birth rates of individuals, and payoffs from group-level games affect group extinction and fission probabilities. We show that a certain level of cooperation is maintained due to specific between-group dynamics even though the within-group evolution by itself always results in a complete loss of cooperation. The spatial nature of games and resulting fissioning and extinction events is essential for the evolution of cooperation: without it cooperation is never maintained. Analyzing various scenarios of between-group fission and extinction events, we find that higher levels of cooperation evolve when the selection affecting fission and extinction events is local rather than global.

Multi-view video recordings are increasingly used to capture the 3D movements of animals in experimental settings, yet extracting rich 3D representations from these recordings remains challenging. Supervised pose estimation requires extensive manual annotation, while general-purpose 3D reconstruction models trained on generic scene datasets fail on the specialized imagery and sparse-view setting of laboratory experiments. We address these limitations with BEAST3D, a self-supervised pretraining framework that learns 3D visual representations from unlabeled, calibrated multi-view video. BEAST3D uses a vision transformer to predict 3D Gaussian splats that reconstruct held-out views through differentiable rendering, while simultaneously segmenting the animal from the background. BEAST3D reconstructs 3D structure with as few as four views by conditioning directly on known camera parameters--unlike general-purpose models, which must estimate camera geometry from dense overlapping viewpoints that are seldom available in lab settings. Through comprehensive evaluation across four species, we demonstrate that BEAST3D produces rich, viewpoint-invariant features that transfer effectively to three downstream tasks: novel view synthesis, which validates the quality of the learned 3D representations; multi-view pose estimation, which provides the sparse keypoint trajectories widely used in behavioral analysis; and neural encoding, which relates 3D behavioral features to simultaneously recorded neural activity. BEAST3D thus establishes a versatile framework for behavioral analysis that leverages 3D structure in modern multi-view laboratory recordings.

Communication is typically understood as indication: signals that transfer information from sender to receiver. We present a minimal predator avoidance task in which pairs of evolved CTRNN agents use communication for robust survival, and in which agents hear their own vocalizations, as in natural systems. Across 112 perfect-fitness agents from over 2,000 evolutionary runs, three dominant strategies emerge (accounting for 81% of agents): safety calling (39%), where agents signal from safe cover; alarm indication (22%), where agents vocalize when a threat is present without relying on self-hearing; and self-regulatory calling (20%), where agents depend on hearing their own call to sustain escape behavior. Self-hearing dependency is common among agents that call during an active threat (47%), but rare among agents that call only after reaching safe cover (10%; p < 10^-4). This pattern is consistent with a difference in causal order: safety callers act then communicate, while self-regulatory callers communicate in order to act. Removing self-hearing selectively impairs self-regulatory callers (fitness 0.40) while safety callers remain functional (0.90; p < 10^-9). These results show that communication can evolve to serve the caller's own behavioral regulation, not just information transfer to others.

In this study, five distinct COVID-19 models developed in different countries, each designed to reflect the prevailing epidemiological condition at the time of formulation, are examined. The models are reformulated while still maintaining their original structure, using their common transmissions from one compartment to the other. Modified Patankar-Runge-Kutta (MPRK) methods are then applied to approximate the solutions of the resulting system of nonlinear ordinary differential equations (ODEs) representing each model to produce unconditionally positive approximations and to preserve the conservative part of the ODEs. In particular, we incorporate the numerical solution into a cost function to improve the estimates for the non-autonomous model hyperparameters. In a first step we obtain piecewise constant parameters that fit real data. Later we perform a WENO reconstruction in a post-process to approximate the true time-dependent coefficients inside the ODEs. As a proof-of-concept, we apply our approach to improve the parameters of a paper concerned with modeling COVID-19 in Ghana, where we can make 5-day predictions within a 10% error range.

Protein-protein interactions (PPIs) are essential for many biological processes. However, existing PPI prediction approaches suffer from two major limitations: they overlook the hierarchical organization of proteins, particularly meso-scale motifs that critically regulate PPIs, and fail to effectively integrate sequence, structure, and function modalities. To address these limitations, we propose MMM-PPI, a Hierarchical Motif-based Multi-Modal protein Encoder for PPI Prediction that constructs PPI embeddings in a bottom-up multi-modal manner across three scales. At the micro-scale, we encode three modal residue features; at the meso-scale, a novel multimodal motif encoder aggregates residues into spatially-informed motif embeddings; at the macro-scale, a multimodal protein encoder integrates motifs into protein embeddings by jointly modeling motif importance and inter-modal correlations. The pre-trained encoder can be used off-the-shelf for large-scale PPI prediction. Extensive experiments on multiple PPI datasets show that MMM-PPI outperforms state-of-the-art multi-label PPI prediction models, particularly under challenging data partitions and limited data scenarios. Codes are in https://github.com/yzf-code/MMM-PPI.

Purpose: To compare dual-energy X-ray absorptiometry (DXA)-derived hip skeletal phenotypes in relation to hip fracture risk using prespecified confounder adjustment and to assess whether phenotypes ranked by their backdoor-adjusted average treatment effects (ATEs) improve risk stratification. Methods: We analyzed 21,098 UK Biobank participants with linked health records, hip DXA-derived skeletal measures, and prespecified covariates. Sixteen phenotypes spanning bone mineral content (BMC), bone mineral density (BMD), and T-score across hip-related regions were evaluated. Confounder selection was guided by a prespecified directed acyclic graph (DAG). Backdoor-adjusted ATEs were estimated on the absolute risk-difference scale per standard deviation (SD) increase. Effect heterogeneity was evaluated for total femur BMD, and downstream prediction was assessed using clinical variables combined with phenotypes ranked by ATE magnitude. Results: Among 21,098 participants, 115 had hip fractures. All 16 phenotypes showed negative backdoor-adjusted ATEs per SD increase. The largest ATEs were observed for total femur BMC and total femur BMD, each with a risk difference of -0.0047, corresponding to approximately 4.7 fewer hip fractures per 1,000 participants per SD higher phenotype value. Conditional effects of total femur BMD were stronger among older participants and those with lower BMI. In prediction, clinical variables plus the top 11 ATE-ranked phenotypes achieved higher AUC than FRAX with femoral neck BMD (0.842 vs. 0.709), with higher sensitivity (0.748 vs. 0.443) and similar specificity (0.793 vs. 0.777). Conclusion: DXA-derived hip skeletal phenotypes differed in their backdoor-adjusted ATEs. Phenotype-level causal evaluation may help identify informative DXA measures for risk stratification.

AI for scientific discovery is entering an agentic era, where protein-engineering systems are expected to prioritize future wet-lab experiments rather than merely fit static measurements. We introduce TadA-Bench, a million-variant wet-lab replay benchmark from 31 TadA directed-evolution rounds for future-round discovery toward agentic protein engineering. TadA-Bench preserves the campaign chronology and defines a fixed-data replay task: given earlier experimental rounds, models rank variants that appear only in later rounds. It provides aligned DNA, RNA, and protein views, and uses Seq2Graph, a graph-based label-unification pipeline, to reconcile noisy enrichment measurements into consistent cross-round activity labels. Random-split controls show strong interpolation, but future-round ranking and finite-budget candidate selection are much weaker. Controlled analyses suggest that evolutionary coverage is more informative than local data density, positioning TadA-Bench as a reproducible wet-lab replay substrate for future-round discovery toward agentic protein engineering; the data and code are released on Hugging Face and GitHub.

Traits that are exaggerated in one sex relative to the other sex might be more vulnerable to stressor exposure because the development and expression of these traits are costly. Sex differences in such traits should therefore be smaller in populations with high stressor exposure. We tested this prediction in humans by examining the magnitude of men's advantage in spatial cognition and women's advantage in emotion recognition across nations that varied in their level of development. As predicted, men's advantage in spatial cognition was larger in nations relatively buffered from stressors. However, in contrast to our prediction, women's advantage in emotion recognition was constant across nations, suggesting aspects of men's cognition might be particularly vulnerable to early or current conditions. The samples were biased toward higher income and healthier individuals for nations in which men's spatial cognition was compromised; thus, we are likely underestimating the effects of living conditions on men's spatial cognition. The results further our understanding of how social and environmental conditions can have sex-specific effects on human cognition.

Representations of the world, arguably, contain information about features (e.g. something is blue, something is a circle) but also information about which features are part of the same object (e.g. the circle is blue), which we call binding information. Any system with the ability to understand scenes with multiple objects must be able to solve the binding problem: it needs to know which features belong together. However, despite work showing that Vision Transformers (ViTs) know which patches belong together, it is not known whether current deep learning models learn to exhibit binding information, i.e., for features. We may believe that there is not much binding information, after all misattributing features to wrong objects is a common failure of ViT-based architectures, especially in scenes with objects sharing features. Here we formalize the binding problem with an information-theoretic approach, and introduce a probing method to measure binding information in model representations. We perform experiments on ViTs, measuring binding from different components of the architecture, such as the image summary token [CLS] or the spatial tokens. We use datasets with different binding challenges, such as feature sharing, occlusion, and natural features, while comparing the performance of several pre-trained ViTs. Overall, our research demonstrates binding as a key ingredient to strong visual recognition and reasoning.

This paper proposes, for the first time, a rigorous formal definition of the concept of Machine Theory of Mind, based on principles supported by evidence from cognitive psychology, neuroscience and artificial intelligence, and uses the above as a lens to examine state-of-the-art and current efforts in the field, driving a potential agenda for further research there able to "crack" the problem. It also advances a general holistic meta-model for Machine Theory of Mind, and examines the state of the art when it comes to empirically benchmarking such models.

Objective: Diseases such as age-related macular degeneration and retinitis pigmentosa cause the degradation of the photoreceptor layer. One approach to restore vision is to electrically stimulate the surviving retinal ganglion cells with a microelectrode array such as epiretinal implants. Epiretinal implants are known to generate visible anisotropic shapes elongated along the axon fascicles of neighboring retinal ganglion cells. Recent work has demonstrated that to obtain isotropic pixel-like shapes, it is possible to map axon fascicles and avoid stimulating them by inactivating electrodes or lowering stimulation current levels. Avoiding axon fascicle stimulation aims to remove brushstroke-like shapes in favor of a more reduced set of pixel-like shapes. Approach: In this study, we propose the use of isotropic and anisotropic shapes to render intelligible images on the retina of a virtual patient in a reinforcement learning environment named rlretina. The environment formalizes the task as using brushstrokes in a stroke-based rendering task. Main Results: We train a deep reinforcement learning agent that learns to assemble isotropic and anisotropic shapes to form an image. We investigate which error-based or perception-based metrics is adequate to reward the agent. The agent is trained in a model-based data generation fashion using the psychophysically validated axon map model to render images as perceived by different virtual patients. We show that the agent can generate more intelligible images compared to the naive method in different virtual patients. Significance: This work shares a new way to address epiretinal stimulation that constitutes a first step towards improving visual acuity in artificially-restored vision using anisotropic phosphenes.

Human behaviour during epidemics affects infectious disease dynamics, but quantifying this remains deeply challenging. Here we introduce the Epi-LLM framework: a novel integration of agent-based modelling, real-life epigames, and large language models (LLMs) in which a synthetic society of agents reasons and adapts dynamically over an outbreak contact network. Comparing synthetic agent behaviour against a no-intervention SEIR baseline and human participant data from the AUIB epigame study, we find that LLM agents across four different architectures reduced peak active infections, with quarantine compliance peaking at 58-65% on day six of the 15-day simulation. A binomial generalised linear model showed that perceived health severity was the strongest predictor of quarantine behaviour ($β= 0.33, p = 0.002$), yielding a pseudo-$R^2$ of 0.055, comparable to the 0.072 observed in the human trial. LLM architecture is a key determinant of epidemic dynamics: low-variance architectures offer greater internal validity for testing behavioural rules, while high-variance models may better represent real-world decision-making. Geographic labels alone do not induce culturally differentiated behaviour; explicit attitudinal parameterisation is required. This proof-of-principle work lays the groundwork for deploying the Epi-LLM framework as a scalable, risk-free simulation environment for pandemic preparedness research.

To migrate, cells exert traction forces on the extracellular matrix (ECM) -- a biopolymer network that often exhibits nonlinear strain-stiffening elasticity. Cellular tractions can therefore stiffen the ECM. At the same time, cells exert stronger tractions on stiffer ECM. Here, we show theoretically that this traction-stiffness feedback can produce traction bistability and hysteresis. As a result, increasing either the ECM's nonlinear elasticity or cellular contractility leads to a discontinuous transition from low to high tractions. This traction jump might trigger collective cell migration as the ECM stiffens, for example during development and tumor progression. Moreover, the bistable behavior might provide robustness to cellular traction forces when cells migrate through mechanically heterogeneous environments.

Structure-based drug design increasingly employs LLM agents to iteratively refine ligands against a target pocket, yet a viable ligand must satisfy two often-conflicting objectives -- binding affinity and druggability -- which single optimization steps rarely improve together. To quantify this difficulty, we introduce two diagnostic metrics: the first measures how often a single edit improves both objectives, and the second measures how often a gain on one objective comes with a loss on the other. Applying these diagnostics to current LLM-agent pipelines exposes a consistent failure mode: the agent performs molecular editing without knowing how the pocket-ligand complex responds to local modifications, thus rarely achieving joint improvement. Inspired by medicinal chemists, who probe the pocket-ligand complex with controlled analog edits before choosing an optimization direction, we propose \textbf{PROBE}, an optimization framework built around edit-response probing. PROBE first decomposes the ligand into editable sites and builds a pocket-specific \textbf{site map} that flags where joint gains are plausible, where the two objectives are likely in tension, and where liability substructures should be changed; it then performs controlled probe edits whose responses are distilled into an \textbf{EditManual}. Guided by the site map and EditManual, PROBE runs an iterative multi-agent loop in which an affinity agent, a druggability agent, and a co-optimization agent jointly produce edits. On the CrossDocked2020 benchmark, PROBE achieves state-of-the-art performance and substantially mitigates the failure modes exposed by our diagnostics metrics.

Plasticity is a fundamental property of complex systems, such as the brain or an organism. Yet it typically remains a descriptive concept inferred retrospectively from observed outcomes, such as modifications in activity or morphology. Here, the network-based operationalization of plasticity is further formalized as the ratio between system size and connectivity strength among system elements. Within this framework, system size determines the dimensionality of the accessible state space, while connectivity strength tunes the system's regime. An optimal range of plasticity -- balancing capacity for change and capacity to maintain coherence -- emerges at intermediate connectivity strength. Notably, this balance coincides with the critical regime, which provides a theoretically motivated benchmark that enables a normalized unit of measure, termed effective plasticity, and comparisons of adaptive efficacy across diverse systems. Plasticity is thus transformed into a predictive tool that quantifies a system's capacity for change before it occurs. Its validity is supported across disciplines and, in particular, by evidence from psychopathology where it anticipates transitions between mental states. At a mechanistic level, plasticity acts as a structural tuning parameter for criticality, reframing their relationship as causal, with plasticity driving criticality rather than merely accompanying it. Furthermore, this network-based operationalization explains how larger systems can more robustly maintain critical dynamics. Crucially, the proposed perspective distinguishes functional regime shifts from thermodynamic phase changes, identifying plasticity as the system-level regulator that shapes and constrains the dynamic repertoire. This framework is applicable across domains, including ecology, economics, and social systems, and may foster cross-disciplinary integration within complexity science.

Ecologists have long debated whether biological communities are fundamentally continuous or composed of discrete units. Continuum views emphasize smooth compositional change and ambiguous boundaries, whereas classification-based approaches rely on discrete community types for analysis and management. We show how biological grouping, particularly species formation, can emerge from interactions among populations governed by number-theoretic structure. In our framework, a species is identified with a $p$-Sylow subgroup of a community occupying a single niche; this identification is suported by a topological analysis. We call the resulting framework the patch with zeta dominance (PzDom) model. We then examine the system's topological properties in detail and demonstrate that both hierarchical organization and temporal ordering are induced by a one-dimensional probability space endowed with an appropriate topology. To clarify the appearance of induced fractal structure and its relation to renormalization, we develop a theoretical account based on a new observation: the scaling parameters that play the role of magnetization analogs coincide exactly with the imaginary parts of the nontrivial zeros of the Riemann zeta function. In the PzDom model, all required computations reduce to the time-dependent density of individuals. The PzDom framework reconciles these perspectives by showing that continuous community variation, represented by small $s$, can give rise to discrete species-level structure when number-theoretic constraints stabilize specific configurations. Thus, continuity and discreteness emerge as different dynamical phases of the same system, offering a unified explanation for long-standing debates in community ecology and the **species problem**.

Humans rehearse possible futures offline, as in mental practice and perhaps dreaming, suggesting that world models may support task learning away from the environment. Standard machine learning world models compress visual input into latent vectors, discarding the spatial structure that characterizes sensory cortex. We propose isomorphic world models: architectures that preserve sensory topology, so physics prediction becomes geometric propagation rather than abstract state transition. We implement this idea with motor-gated neural fields, where activity evolves through local lateral connectivity and motor commands multiplicatively modulate specific channels. Across three experiments, the same architecture learns ballistic prediction without ``teleporting,'' improves a catching policy offline by propagating task error through a frozen learned world model, and develops body-selective motor channels without body labels. These results provide preliminary evidence that physical prediction, offline task learning, and body-linked representation share a common computational substrate: action-conditional prediction within a spatial map.

High-dimensional chaotic dynamics can emerge in a large random recurrent neural network when the synaptic gain crosses a threshold. Recent works showed that the kinetic energy of neural activity links the chaotic dynamics and the supporting unstable fixed points (equilibria) in the phase space. Here, we investigate the kinetic-energy-centric properties of random recurrent neural networks by combining dynamical mean-field theory with extensive numerical simulations. We find that the average kinetic energy shifts continuously from zero to a positive value at the known critical value of coupling variance (synaptic gain) and exhibits a cubic scaling behavior near the critical point from above. This scaling behavior is supported by numerical simulations and provides a quantitative characterization of how fast the dynamics change during the onset of chaos as well as how far the chaotic dynamics are away from the unstable fixed points. The steady-state activity distribution is further calculated by the theory and compared with simulations on finite-size systems from the kinetic-energy optimization perspective as well. The activity distribution is also analyzed in a geometric angle, revealing that although the original chaotic dynamics and the gradient dynamics of the kinetic energy are arranged in a shell-like structure, they are well separated in the polar direction. The trajectory length on the chaotic manifold can be derived from the stationary kinetic energy, and the associated stationary behavior is analyzed as well.

Low-rank recurrent neural networks (lrRNNs) are a class of models that uncover low-dimensional latent dynamics underlying neural population activity. Although their functional connectivity is low-rank, it lacks independence interpretations, making it difficult to assign distinct computational roles to different latent dimensions. To address this, we propose the Factored Recurrent Neural Network (FacRNN), a generative lrRNN framework that assumes group-wise independence among latent dynamics while allowing flexible within-group entanglement. These independent latent groups allow latent dynamics to evolve separately, but are internally rich for complex computation. We reformulate the lrRNN under a variational autoencoder (VAE) framework, enabling us to introduce a partial correlation penalty that encourages independence between groups of latent dimensions. Experiments on synthetic, monkey M1, and mouse voltage imaging data show that FacRNN consistently improves the disentanglement and interpretability of learned neural latent trajectories in low-dimensional space and low-rank connectivity over baseline lrRNNs that do not encourage group-wise independence.

Computational modeling of single-cell gene expression is crucial for understanding cellular processes, but generating realistic expression profiles remains a major challenge. This difficulty arises from the count nature of gene expression data and complex latent dependencies among genes. Existing generative models often impose artificial gene orderings or rely on shallow neural network architectures. We introduce a scalable latent diffusion model for single-cell gene expression data, which we refer to as scLDM, that respects the fundamental exchangeability property of the data. Our VAE uses fixed-size latent variables leveraging a unified Multi-head Cross-Attention Block (MCAB) architecture, which serves dual roles: permutation-invariant pooling in the encoder and permutation-equivariant unpooling in the decoder. We enhance this framework by replacing the Gaussian prior with a latent diffusion model using Diffusion Transformers and linear interpolants, enabling high-quality generation with multi-conditional classifier-free guidance. We show its superior performance in a variety of experiments for both observational and perturbational single-cell data, as well as downstream tasks like cell-level classification.

The complementarity-determining regions of antibodies are loop structures that are key to their interactions with antigens, and of high importance to the design of novel biologics. Since the 1980s, categorizing the diversity of CDR structures into canonical clusters has enabled the identification of key structural motifs of antibodies. However, existing approaches have limited coverage and cannot be readily incorporated into protein foundation models. Here we introduce ImmunoGlobulin LOOp Tokenizer, Igloo, a multimodal antibody loop tokenizer that encodes backbone dihedral angles and sequence. Igloo is trained using a contrastive learning objective to map loops with similar backbone dihedral angles closer together in latent space. Igloo can efficiently retrieve the closest matching loop structures from a structural antibody database, outperforming existing methods on identifying similar H3 loops by 5.9\%. Igloo assigns tokens to all loops, addressing the limited coverage issue of canonical clusters, while retaining the ability to recover canonical loop conformations. To demonstrate the versatility of Igloo tokens, we show that they can be incorporated into protein language models with IglooLM and IglooALM. On predicting binding affinity of heavy chain variants, IglooLM outperforms the base protein language model on 8 out of 10 antibody-antigen targets. Additionally, it is on par with existing state-of-the-art sequence-based and multimodal protein language models, performing comparably to models with $7\times$ more parameters. IglooALM samples antibody loops which are diverse in sequence and more consistent in structure than state-of-the-art antibody inverse folding models. Igloo demonstrates the benefit of introducing multimodal tokens for antibody loops for encoding the diverse landscape of antibody loops, improving protein foundation models, and for antibody CDR design.

A cholera transmission model is formulated that incorporates water-borne and horizontal transmissions as well as infectivity of deceased individuals. The model includes an Allee effect for the bacteria in the environment and imperfect and waning vaccination. Mathematical properties of the model are investigated, with an environmental bistability shown to combine with a vaccine-driven one, although a computational search for the latter fails to detect its presence in realistic parameter ranges. The computational analysis also considers the interplay between vaccination strategy, vaccine efficacy and waning, as well as the effect of transmission of the disease during funeral rites. The effect of control scenarios such as WASH or Safe and dignified burials are assessed.

The classical and extended deficiency one theorems by Feinberg apply to reaction networks with mass-action kinetics that have independent linkage classes or subnetworks, each with a deficiency of at most one and exactly one absorbing strong component. The theorems assume the existence of a positive equilibrium and guarantee the existence of a unique positive equilibrium in every stoichiometric compatibility class. In our work, we use the $\textit{monomial dependency}$ which extends the concept of deficiency. First, we provide a dependency one theorem for parametrized systems of polynomial equations that are essentially univariate and decomposable. As our main result, we present a corresponding theorem for mass-action systems, which permits subnetworks with arbitrary deficiency and arbitrary number of absorbing strong components. Finally, to complete the picture, we derive the extended deficiency one theorem as a special case of our more general dependency one theorem.

Removing noise from piecewise constant (PWC) signals, is a challenging signal processing problem arising in many practical contexts. For example, in exploration geosciences, noisy drill hole records need separating into stratigraphic zones, and in biophysics, jumps between molecular dwell states need extracting from noisy fluorescence microscopy signals. Many PWC denoising methods exist, including total variation regularization, mean shift clustering, stepwise jump placement, running medians, convex clustering shrinkage and bilateral filtering; conventional linear signal processing methods are fundamentally unsuited however. This paper shows that most of these methods are associated with a special case of a generalized functional, minimized to achieve PWC denoising. The minimizer can be obtained by diverse solver algorithms, including stepwise jump placement, convex programming, finite differences, iterated running medians, least angle regression, regularization path following, and coordinate descent. We introduce novel PWC denoising methods, which, for example, combine global mean shift clustering with local total variation smoothing. Head-to-head comparisons between these methods are performed on synthetic data, revealing that our new methods have a useful role to play. Finally, overlaps between the methods of this paper and others such as wavelet shrinkage, hidden Markov models, and piecewise smooth filtering are touched on.

In this paper we propose a modified cross correlation method to align images from the same class in single-particle electron microscopy of highly non-spherical structures. In this new method, First we coarsely align projection images, and then re-align the resulting images using the cross correlation (CC) method. The coarse alignment is obtained by matching the centers of mass and the principal axes of the images. The distribution of misalignment in this coarse alignment can be quantified based on the statistical properties of the additive background noise. As a consequence, the search space for re-alignment in the cross correlation method can be reduced to achieve better alignment. In order to overcome problems associated with false peaks in the cross correlations function, we use artificially blurred images for the early stage of the iterative cross correlation method and segment the intermediate class average from every iteration step. These two additional manipulations combined with the reduced search space size in the cross correlation method yield better alignments for low signal-to-noise ratio images than both classical cross correlation and maximum likelihood(ML) methods.

This paper examines the objective of optimally harvesting a single species in a stochastic environment. This problem has previously been analyzed in Alvarez (2000) using dynamic programming techniques and, due to the natural payoff structure of the price rate function (the price decreases as the population increases), no optimal harvesting policy exists. This paper establishes a relaxed formulation of the harvesting model in such a manner that existence of an optimal relaxed harvesting policy can not only be proven but also identified. The analysis embeds the harvesting problem in an infinite-dimensional linear program over a space of occupation measures in which the initial position enters as a parameter and then analyzes an auxiliary problem having fewer constraints. In this manner upper bounds are determined for the optimal value (with the given initial position); these bounds depend on the relation of the initial population size to a specific target size. The more interesting case occurs when the initial population exceeds this target size; a new argument is required to obtain a sharp upper bound. Though the initial population size only enters as a parameter, the value is determined in a closed-form functional expression of this parameter.