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Article
Computer Science and Mathematics
Mathematical and Computational Biology

Laura Jarosz

,

Marcel Ochocki

,

Julia Merta

,

Lajos Pusztai

,

Michal Marczyk

Abstract: Large-scale, multi-center projects have become common in the era of rapid technological development, but protocol standardization remains challenging. In whole-exome sequencing (WES), various exome enrichment kits exhibit variable efficiency across genomic regions, leading to systematic, non-biological batch effects, much stronger than other technical factors. We propose a workflow to minimize the effect of WES capture inconsistencies in single-nucleotide variation (SNV) data. The pipeline consists of quality control, mapping to the genome, variant calling, joint genotyping, and imputing genotypes using reference haplotypes. Variants are then aggregated into gene-level features measuring the burden of deleterious mutations. Finally, a gene-level imputation is performed using a customized algorithm. Namely, if the detection rate of a gene is low in samples enriched with a given capture kit, but high in samples enriched with other kits, missing values in the former group are imputed, as such differences are unlikely to reflect true biology. As a benchmark, we conducted a study on over a thousand breast cancer cases across 11 cohorts, using 8 exome capture kits. We demonstrated that the proposed pipeline leads to a considerable decrease in the batch effect signal, potentially increasing the likelihood of finding true biological signals. The workflow is publicly available here: https://github.com/ZAEDPolSl/WESworkflow.

Article
Computer Science and Mathematics
Mathematical and Computational Biology

Khalid Aldawsari

,

Yahya AlQahtani

,

Fahad Al Basir

Abstract:

This work develops and analyzes a mathematical model of SARS-CoV-2 infection within the human host, incorporating susceptible and infected epithelial cells, viral particles, ACE2 receptors, cytotoxic T lymphocytes (CTLs), and antibodies. The basic reproduction number and equilibrium points are derived, with stability analysis showing that the disease-free equilibrium is maintained when \( \mathcal{R}_0 < 1 \), while an endemic equilibrium arises for \( \mathcal{R}_0 > 1 \). To capture therapeutic intervention, an impulsive control framework based on antibody-mediated drug administration is introduced. Within this framework, the existence and stability of a disease-free periodic orbit are established through the impulsive reproduction number, \( \mathcal{R}_0^{imp} \), with stability ensured when \( \mathcal{R}_0^{imp} < 1 \). Numerical simulations confirm the analytical results, demonstrating the effectiveness of impulsive therapy in achieving viral eradication. Additionally, Hopf bifurcating periodic solutions are observed under elevated viral replication and infection rates. The proposed model provides new insights into the interaction between viral dynamics, immune response, and impulsive therapeutic strategies, offering a rigorous foundation for advancing treatment approaches against SARS-CoV-2.

Article
Computer Science and Mathematics
Mathematical and Computational Biology

Emma Breidenich

,

Joe Cooper

,

Qianzhao Huang - QH

,

Meir Shillor

,

Camille Wagner

Abstract: This work constructs, analyzes and simulates a modified SIR epidemiological model for the spread of a generic long-time disease, in which the coefficients of infectivity and death rate are system variables. Diseases, such as COVID-19, have demonstrated very clearly that infectivity and death rates can change over time, even for the same variant of the virus, due to vaccination, improved treatments, better analysis, better medications, etc. This motivates us to model a generic disease where the infectivity and death rates are state variables as a part of the systems's evolving in time. The model consists of a coupled system of five differential equations. The analysis shows the existence, positivity and boundedness of the solutions. A short discussion of the Endemic (EE) and Disease-Free (DFE) equilibria and their stability is provided. Then, computer simulations depict two typical cases of dynamic behaviors, one when the DFE is stable and attracting, and one in which the EE is stable and attracting. These also show how the system approaches these steady states.

Article
Computer Science and Mathematics
Mathematical and Computational Biology

Danish Sharok Alam Rojas

,

Leonardo Juan Ramirez Lopez

,

Javier Rodriguez Velasquez

Abstract: Long-term Holter analysis requires software tools capable of automating signal preprocessing, temporal segmentation, probabilistic computation, and result visualization in a reproducible and interpretable manner. In this research, a modular software system for automated analysis of cardiac dynamics was developed following a software engineering perspective and an iterative lifecycle based on Scrum, including requirements definition, sprint planning, development, integration, testing, review with a medical specialist, and refinement. The platform was designed to analyze standardized temporal windows of 12, 14, and 18 h extracted from original 24 h Holter-ECG recordings and integrates a frontend, a backend, and a Python® analytical engine within a unified client–server framework. It processes Excel or CSV files containing hourly average heart-rate values, performs structural validation, discretizes the data into 10 beats-per-minute intervals, constructs empirical probability distributions, identifies recurrent dynamic patterns, and generates structured JSON outputs for web-based visualization. A complementary preprocessing module was also implemented for raw PhysioNet ECG signal records, enabling the loading of .hea and .dat files, automated R-peak detection, and extraction of hourly average heart-rate values. The system was evaluated on 113 Holter records from three open-access databases: 85 from SHDB-AF, 19 from the Long-Term ST Database, and 9 from the MIT-BIH Normal Sinus Rhythm Database. Overall structural agreement at the record level was 58.4% (66/113). To conclude, this system provides a reproducible web application pipeline for Holter signal data processing and probabilistic cardiac dynamics analysis, integrating software development, preprocessing, classification, and interpretable visualization within a modular framework.

Article
Computer Science and Mathematics
Mathematical and Computational Biology

Zhaoxu Meng

,

Yong Cui

Abstract: Exploration remains a central challenge in reinforcement learning, especially in sparse-reward settings where extrinsic feedback alone is often insufficient to guide effective behavior. In this work, we develop a curiosity-driven framework that combines a hybrid intrinsic reward with compact predictive representation learning. Specifically, curiosity is quantified by integrating prediction error with the rarity of state-action pairs in a learned latent space. To make novelty estimation more meaningful for high-dimensional observations such as raw pixels, we employ the Information Bottleneck principle to learn low-dimensional representations that suppress irrelevant variability while preserving predictive structure of the environment dynamics. We further investigate two practical ways to optimize predictive information: one based on entropy decomposition and the other based on matrix-based Renyi entropy. Experiments on Acrobot show that the proposed method substantially improves exploration efficiency over ICM, RND, and a $k$-NN novelty baseline. On MountainCar, however, the improvement is less evident, suggesting that the proposed framework is particularly beneficial in environments with high-dimensional observations or more structured dynamics.

Article
Computer Science and Mathematics
Mathematical and Computational Biology

Maxim Polyakov

Abstract: CAR-T cell therapy remains ineffective in most solid tumours because effector cells infiltrate poorly, undergo exhaustion, and face antigen escape within an immunosuppressive microenvironment. To address this, we developed a hybrid framework that combines a mechanistic spatiotemporal model with machine learning for limited patient-specific calibration. At its core, we employed a reaction-diffusion-chemotaxis model describing functional and exhausted CAR-T cells, antigen-positive and antigen-negative tumour subpopulations, a chemoattractant, an immunosuppressive factor, and hypoxia. Gradient boosting combined with nested cross-validation was used as the primary method for parameter inference. Parameters characterising the tumour microenvironment and CAR-T cell exhaustion were recovered most robustly, whereas antigen escape and individualised initial conditions were identified substantially less accurately. As an auxiliary reference point, we also considered a direct empirical baseline for binary clinical outcomes. This baseline indicated that the observed clinical features contained a more stable signal for disease control than for objective response. A favourable response was associated with high CAR-T cell infiltration and cytotoxic potency, whereas resistance was linked to exhaustion, antigen escape, and a suppressive microenvironment. Overall, the proposed approach constitutes an interpretable proof-of-concept platform for limited patient-specific inference of latent parameters and for stratifying the mechanisms underlying response and resistance in CAR-T cell therapy for solid tumours.

Article
Computer Science and Mathematics
Mathematical and Computational Biology

Yazeed Mohammed Al-Olofi

Abstract: We present a unified hierarchical theory of brain dynamics derived entirely from first principles. The foundation is a geometric principle: any self‑similar hierarchical system seeking maximal harmony must satisfy Euclid's equation, whose unique solution is the golden ratio Φ ≈ 1.618. This geometric principle is embodied biologically in an efficiency functional balancing information transfer, spectral interference, and dynamical stability, which also yields Φ as the optimal frequency spacing between adjacent bands. From this single seed we sequentially derive eleven theorems that together form a complete mathematical pyramid. Theorem 0 establishes the Euclidean geometric principle. Theorem 1 proves the optimality of Φ in the biological context. Theorem 2 determines the number of frequency bands N = 7 from the biological range (0.5–200 Hz) and stability analysis. Theorem 3 introduces the control parameter β ∈ [0,1] regulating information flow direction, with critical values Φ⁻¹ ≈ 0.618 and Φ⁻² ≈ 0.382 from bifurcation analysis. Theorem 4 derives the optimal coupling coefficients κ₀ = ½Φ⁻¹ ≈ 0.309 from an information‑energy trade‑off. Theorem 5 gives the optimal phase shifts φ↑ = π/4, φ↓ = –π/4 from time‑reversal symmetry and interference minimization. Theorem 6 reveals 28 attractors (4 per band) with elementary geometric forms (cube, hexagon, pentagon, square, triangle, spiral, point) via group‑theoretic analysis. Theorem 7 provides analytical phase‑amplitude coupling (PAC) values as simple functions of Φ. Theorem 8 establishes the linear correlation between mean PAC and Φ‑coherence. Theorem 9 derives the temporal decrease of PA‑FCI before acute events from critical transition theory. Theorem 10 yields the universal warning threshold PA‑FCI_th = 0.55 from critical slowing‑down analysis. Theorem 11 gives the linear PA‑FCI formula with theoretically derived weights. Numerical simulations of the full nonlinear system confirm all derivations with deviations below 0.3%. This work constitutes the complete mathematical foundation of the A7-HBM-ΩΦ framework, complementing the computational simulations presented in [1], the sleep microstate analysis in [2], and the preliminary theoretical formulation in [3]. The theoretical derivations presented here have been experimentally validated using simultaneous EEG‑ECG recordings from healthy, epileptic, and cardiac patients [4], confirming the predictive power of the eleven theorems. In this updated and expanded version, we further integrate a unified causal framework that links multiscale self‑similarity [5,6], self‑organized criticality [7,8], hierarchical oscillations [10,11,15], and optimization constraints to the emergence of Φ as the optimal solution, and we present the full experimental validation across seven independent datasets. The model unifies geometry, physics, and biology, demonstrating that the brain's hierarchical organization follows from geometric principle.

Article
Computer Science and Mathematics
Mathematical and Computational Biology

Bowen Lou

,

Shuxin Mo

Abstract: Personalized treatment for early-stage non-small cell lung cancer (NSCLC), particularly in choosing between SBRT and surgery, is challenging due to complex, heterogeneous patient data. We introduce MM-Care, a novel deep learning framework for objective, interpretable, and personalized treatment decision support. MM-Care integrates patient-specific CT imaging, clinical indicators, and genomic data through a sophisticated multi-branch neural network. Its core innovations include multi-modal feature extraction, an adaptive Transformer-based fusion network for deep inter-modal interaction, and a dual-task prediction head for overall survival and local control across both interventions. An explainable decision report module, utilizing feature importance methods, enhances clinical trust. Evaluated on public and proprietary cohorts comprising thousands of patients, MM-Care consistently outperforms traditional models and deep learning baselines. Our experiments demonstrate superior prognostic performance for survival and local control. Ablation studies validate critical architectural contributions. Human evaluation with oncologists confirms high trust, utility, and interpretability, showing significant time savings and strong agreement with expert consensus. MM-Care also achieves high accuracy in aligning with retrospectively identified optimal treatment choices. These results highlight MM-Care's robust capability to provide precise, patient-specific prognostic predictions and optimal treatment recommendations, poised to significantly enhance personalized medicine in early-stage NSCLC.

Article
Computer Science and Mathematics
Mathematical and Computational Biology

Yujie You

,

Yuzhu Ji

,

Feixiang Zhao

,

Ming Xiao

,

Le Zhang

Abstract: Biological time series data characterizes the dynamic evolution of biological systems and plays a crucial role in genetic inheritance, disease diagnosis, and biological microenvironment. However, accurate prediction for biological time-series data remains challenging due to their pronounced time-varying, non-stationary, and noisy characteristics. Existing approaches often fail to capture latent distribution shifts and the coupled evolution of global and local patterns, limiting both predictive performance and interpretability. Thus, this study firstly proposes a time-varying neural network (TVNN) model that combine frequency-domain information with Koopman embedding theory. TVNN model Koopman transition matrices are used to model global dynamics and local time-varying behaviors for pattern extraction. Secondly, a time-varying pattern recognition large language model (TVPRLLM) is introduced to recognize and interpret the extracted time-varying patterns, enabling the discovery of their potential biological significance. Thirdly, we have developed such a biological time series predictive platform that can offer visualization, data analysis, and predictive services. Experimental results demonstrate that TVNN model outperforms existing mainstream methods in predicting on biological time-varying time series.

Article
Computer Science and Mathematics
Mathematical and Computational Biology

Michael Timothy Bennett

Abstract: Functional information measures how rare functional configurations are. Wong and colleagues argue that selection should drive a law of increasing functional information. This is often read as a claim that complexity must increase. Here I give a different interpretation, which is that survivors tend to be the systems that did not overcommit. I model a system as a policy π, meaning a bundle of commitments expressed in a finite embodied vocabulary. New selection pressures arrive as a set of future requirements drawn from the unobserved outcome set U. A currently viable policy leaves an unobserved buffer Bπ ⊆ U of outcomes it still permits. Under a maximally ignorant novelty model, the survival probability of π is exactly 2|Bπ| − |U|. Under any exchangeable novelty prior, survival remains monotone in Bπ. So persistence under novelty favours weak policies, where weakness counts the compatible completions left open. I define degree of future function as survival probability and functional information as Hazen and Szostak rarity within the currently viable set. Conditioning on persistence reweights the viable set toward larger buffers and therefore toward higher functional information. This yields a mathematical analogue of the proposed law under explicit assumptions. Supplementary analysis quantifies how much structured novelty is needed before that buffer size ordering can reverse. In fully enumerated toy worlds, weakness maximisation improves mean log survival probability relative to random choice. Weakness and simplicity are not the same thing. Weakness helps a system persist under novelty, because it keeps more futures compatible. Simplicity helps a system persist because there is less to break, which obviates the need for repair. Complexity requires self-repair to persist, increasing weakness. Life is persistent complexity. In between complex life and simple nonlife is the void of the unviable: complexity which is not alive.

Article
Computer Science and Mathematics
Mathematical and Computational Biology

Maxim Polyakov

Abstract: Although chimeric antigen receptor T-cell therapy (CAR-T) has shown substantial efficacy in haematological malignancies, its application to solid tumours remains limited by antigenic heterogeneity, poor effector-cell infiltration, and an immunosuppressive tumour microenvironment. This study aimed to develop a mathematical model of the spatiotemporal dynamics of a solid tumour under CAR-T cell therapy, incorporating the main determinants of therapeutic resistance. We propose a reaction–diffusion model formulated as a system of partial differential equations describing functional and exhausted CAR-T cells, antigen-positive and antigen-negative tumour subpopulations, and chemokine, immunosuppressive, and hypoxic fields. The model was analysed using steady-state analysis and numerical simulations based on a finite-difference scheme. The simulations showed that therapeutic outcome is governed by the combined effects of CAR-T cell infiltration, functional exhaustion, and tumour antigen escape. The model reproduced partial tumour regression followed by persistence of a residual tumour population, the emergence of an antigen-negative component under therapeutic pressure, and reduced treatment efficacy under more strongly immunosuppressive and hypoxic microenvironmental conditions. Repeated simulated CAR-T-cell administration improved tumour control, albeit with diminishing returns. Overall, the proposed model provides a useful framework for analysing resistance mechanisms and optimising CAR-T cell therapy protocols for solid tumours.

Article
Computer Science and Mathematics
Mathematical and Computational Biology

Najme Soleimani

,

Maria Misiura

,

Ali Maan

,

Sir-Lord Wiafe

,

Jennalyn Burnette

,

Asia Hemphill

,

Vonetta Dotson

,

Rebecca Ellis

,

Tricia King

,

Erin Tone

+1 authors

Abstract: Understanding how lifestyle factors influence the dynamic organization of intrinsic brain networks in young adulthood is critical for identifying mechanisms that support cognitive health during a formative developmental period. In this study, we examined whether an 8-week physical activity and cognitive training intervention altered dynamic functional network connectivity (dFNC) patterns in undergraduate students and how these neural dynamics related to physical activity levels, sedentary behavior, and cognitive performance. Resting-state fMRI data were decomposed using a constrained ICA framework to extract 53 intrinsic connectivity networks, from which 10 dynamic connectivity states were identified and individualized via constrained dynamic double functional independent primitives (c-ddFIPs). We quantified state occupancy, convergence, and divergence to characterize network flexibility. Occupancy analyses showed modest but consistent associations linking greater physical activity with increased time in integrative, higher-order states (especially states 6 and 7) and reduced time in segregated or sensory-weighted states. Convergence and divergence analyses further revealed that physically active individuals demonstrated stronger differentiation between integrative and low-engagement states, whereas sedentary behavior corresponded to greater similarity among segregated configurations. Cognitive measures—particularly working memory—showed parallel relationships, aligning improved performance with more flexible and well-differentiated dynamic patterns. Together, these findings suggest that physical activity in young adults is associated with enhanced neural flexibility, characterized by greater engagement and differentiation of integrative connectivity states that support executive and other cognitive functions.

Article
Computer Science and Mathematics
Mathematical and Computational Biology

Guillermo Vázquez

,

Alberto Martín-Pérez

,

Angel Perez-Nuñez

,

Alfonso Lagares

,

Eduardo Juarez

,

Cesar Sanz

Abstract: Accurate in-vivo brain tumor detection using hyperspectral imaging (HSI), a non-invasive technique that captures spectral information beyond the visible range, is challenging due to the complexity of biological tissues and the difficulty in distinguishing malignant from healthy areas. Conventional neural network-based methods often misclassify tumor tissue as blood vessels, largely due to high vascularization and the scarcity of annotated data. To address this issue, this work proposes an underexplored approach that decomposes the problem into two tasks: (1) segmentation of the brain cortical surface and its blood vessels, and (2) segmentation of biological tissues within the segmented craniotomy site. The cortical segmentation task is addressed independently of the segmentation model used in the second stage. To achieve this, a set of pseudo-labels is generated from RGB and HSI captures acquired during in-vivo brain surgeries. These pseudo-labels support a multimodal training strategy that leverages both imaging domains, yielding a model capable of segmenting the craniotomy site and the blood vessels contained in it. The model is further refined on HSI using weakly supervised fine-tuning with sparse ground truth annotations. The final segmentation map combines cortical and tissue segmentation outputs, considering only cortex pixels not overlapped by vessels as potential tumor regions. This simplifies the HSI tissue segmentation task, reframing it as a binary segmentation of healthy vs. other tissues, while still enabling a comprehensive multiclass output. The proposed method achieves up to a 15.48\% increase in F1 score for the tumor class, while segmenting the brain cortex with a mean Dice Similarity Coefficient (DSC) of 92.08\% and accurately detecting 95.42\% of labeled blood vessel samples in the HSI dataset.

Brief Report
Computer Science and Mathematics
Mathematical and Computational Biology

Pietro Hiram Guzzi

,

Annamaria Defilippo

,

Ugo Lomoio

,

Fabiola Boccuto

,

Patrizia Vizza

,

Alessandro Gallo

,

Antonio Pullano

,

Filomena Talarico

,

Salvatore Fregola

,

Pierangelo Veltri

Abstract: The rugged morphology and dispersed settlements of the Calabrian region pose long-standing barriers to timely and equitable access to healthcare, particularly for elderly and fragile populations living in mountainous areas. In this paper, we present a telemedicine ecosystem specifically designed for Calabria that integrates certified wearable wristbands, secure communication infrastructure, and intelligent back-end services to enable continuous home monitoring and rapid clinical intervention. Building on the SidlyCare platform, the system acquires real-time physiological signals (heart rate and oxygen saturation), streams them to a central server through encrypted channels, and applies machine learning and deep learning-based anomaly detection models to identify both acute and insidious deteriorations in patient status. Alerts are propagated via a multi-stakeholder workflow involving patients, family caregivers, general practitioners, non-profit organizations, and local health authorities, who interact with the platform through role-specific dashboards that support longitudinal visualization, risk stratification, and integration with existing electronic health record infrastructures. A pilot case study in a tele-home care programme for elderly patients in Calabria demonstrates the feasibility and potential of this architecture to improve safety, foster patient engagement, and strengthen continuity of care in geographically isolated communities, offering a scalable blueprint for territorial telemedicine in similar rural and mountainous contexts.

Review
Computer Science and Mathematics
Mathematical and Computational Biology

Cromwel Tepap Zemnou

,

Gabriel Tchuente Kamsu

,

Ramelle Ngakam

,

Etienne Junior Tcheumeni

Abstract: The pharmaceutical industry is undergoing a transformative revolution driven by artificial intelligence, fundamentally reshaping drug discovery and early development processes. This comprehensive review examines how AI technologies from machine learning to deep neural networks are enhancing predictive accuracy and operational efficiency across the entire development pipeline. By analyzing complex biological data, these computational approaches enable unprecedented precision in target identification, lead optimization, and preclinical assessment, significantly accelerating therapeutic development. However, substantial challenges persist in implementation, including data harmonization issues, model interpretability constraints, and integration barriers within existing regulatory frameworks. This analysis critically evaluates both the transformative potential and practical limitations of AI applications, highlighting their capacity to not only streamline development pipelines but also pioneer innovative approaches in personalized medicine and novel therapeutic solutions for complex diseases, while addressing the critical hurdles that must be overcome for successful integration into pharmaceutical research and development.

Article
Computer Science and Mathematics
Mathematical and Computational Biology

Javier Burgos-Salcedo

Abstract: The origin of life's rapid emergence (~10⁹ years) and universal biochemical features (homochirality, conserved metabolic pathways) present a fundamental puzzle: random chemical search in configuration space predicts timescales exceeding 10¹²³ years, rendering biogenesis essentially impossible within cosmic history. We present a comprehensive theoretical framework unifying Penrose's Conformal Cyclic Cosmology (CCC) with sheaf-theoretic descriptions of prebiotic chemical organization. We suggest that biological information from extinct systems in the previous cosmic Aeon (Aeonn) can survive the conformal boundary transition (ℐ⁺n → ℐ⁻(n+1)) through squeezed quantum states with squeezing parameter r ~ 10⁸⁶, which suppress decoherence over timescales approaching 10⁹⁷ years. This information, encoded in photonic field correlations, establishes topological attractors in the chemical configuration space of the subsequent Aeon (Aeon(n+1)) via modified Casimir forces. Using formal concept analysis and sheaf theory, we show that microenvironmental integration satisfying locality and gluing conditions enables coherent assembly of inherited structural motifs, reducing effective search space by ~10⁶⁴ orders of magnitude. The framework makes seven falsifiable predictions including universal homochirality (enantiomeric excess ~0.2% from photonic bias amplified by autocatalysis), convergent metabolic network topology across independent biogenesis events, and specific cosmic microwave background non-Gaussian signatures at ℓ ~ 1000-3000. Numerical simulations of molecular dynamics in squeezed electromagnetic vacua demonstrate biogenesis timescales of τbio ~ 10⁹ years, consistent with terrestrial observations. This work provides the first physically viable mechanism for trans-Aeon biological information transfer, resolving the combinatorial impossibility problem and suggesting life is an iteratively optimized feature of cosmic evolution rather than a contingent chemical accident.

Article
Computer Science and Mathematics
Mathematical and Computational Biology

José A. Rodrigues

Abstract: Cancer represents a dynamic and evolving ecosystem driven by complex interactions among genetically and phenotypically diverse cell populations. Within the tumor microenvironment, cells engage in both competitive and cooperative behaviors that determine their collective evolutionary fate. To capture these dynamics, we employ evolutionary game theory to investigate the coexistence and adaptation of four representative tumor phenotypes: proliferative (P), invasive (I), resistant (R), and cooperative (C). Using a four-strategy evolutionary game-theoretic framework, we show that explicitly including a cooperative phenotype qualitatively expands the range of polymorphic and noise-sustained coexistence regimes observed in the model, enabling coexistence regimes that cannot arise in reduced three-strategy models. Numerical simulations reveal that frequency-dependent selection promotes stable polymorphisms or oscillatory coexistence among phenotypes, explaining persistent intratumoral heterogeneity. Incorporating stochastic replicator equations further demonstrates that random fluctuations can sustain rare phenotypes, induce transient dominance shifts, and generate noise-driven evolutionary transitions. To explore environmental modulation, we extend the model to analyze tumor evolution under acidic microenvironmental conditions and under pH-buffered therapeutic interventions. Acidity enhances the fitness of invasive and resistant cells, driving the system toward aggressive, therapy-tolerant equilibria. In contrast, buffering restores cooperative and proliferative dominance, illustrating that ecological control of the tumor microenvironment can redirect evolutionary trajectories. Collectively, this work unifies deterministic and stochastic evolutionary game theory approaches to show how tumor heterogeneity arises from eco-evolutionary feedbacks, stochastic fluctuations, and environmental pressures. The results suggest that evolution-informed, microenvironment-modulating interventions may influence selective pressures in ways that favor less aggressive evolutionary outcomes, providing a conceptual basis for adaptive therapeutic strategies.

Review
Computer Science and Mathematics
Mathematical and Computational Biology

Shriya Bhat

,

Rishab Jain

,

Wesley Greenblatt

Abstract: The antibiotic pipeline has stalled: most recent approvals reflect incremental modifications of existing scaffolds, while antimicrobial resistance continues to outpace discovery. Antimicrobial peptides (AMPs) offer a compelling alternative because of rapid, multi-modal activity, but clinical translation has been limited by toxicity, serum instability, and the prohibitive cost of synthesizing and testing large libraries. Recent progress in protein language models (pLMs) changes the computational landscape by providing embeddings that capture sequence context and biophysical regularities from massive unlabeled datasets. However, pLMs alone are not a design solution. We propose a technique coupling pLM-derived representations to diffusion or discrete flow-based generative models that can explore non-homologous regions of peptide space while being steered by multi-objective guidance. This framework supports direct optimization for potency, selectivity, and developability during generation, compressing hit discovery and early optimization into a single in silico loop. Conditioning generation on target and safety predictors could shift AMPs from membrane-lytic ‘blunt instruments’ toward more selective, target-aware therapeutics.

Article
Computer Science and Mathematics
Mathematical and Computational Biology

A.C. Demidont

Abstract: Antiretroviral agents for HIV prevention are typically evaluated in terms of trial efficacyand programmatic coverage, but rarely in terms of whether they admit a true mathematicalsolution to prevention. Here we introduce the Prevention Theorem, which formalizesprevention for a given exposure e as the condition R0(e) = 0, meaning that the probability of establishing a productive, transmissible infection is exactly zero. Within this framework,post-exposure prophylaxis (PEP) is not delayed treatment but a time-dependent operatoracting on within-host infection establishment dynamics. Using a mechanistic model of reservoirseeding and proviral integration, we derive the PEP Window Corollary: PEP can enforce R0(e) = 0 only when initiated within a finite biological window prior to irreversible integrationand initial reservoir establishment. Beyond this window, all reachable system statessatisfy R0(e) > 0 and are irreducible by post-exposure intervention. Parameterization usingvirological data indicates that this window extends to approximately 72 hours for mucosalexposures but is compressed to roughly 12–24 hours for parenteral exposures due to bypass ofearly immune bottlenecks. As an applied example, we show that structural access delays inhigh-risk populations—such as people who inject drugs—frequently exceed this compressedparenteral window. Consequently, for such exposures the condition R0(e) = 0 is mathematicallyand biologically unreachable before access is even attempted, rendering the failure ofpost-exposure prevention a consequence of violated biological boundary conditions ratherthan pharmacological efficacy.

Article
Computer Science and Mathematics
Mathematical and Computational Biology

Ngo Cheung

Abstract: Background: Major depressive disorder (MDD) is increasingly viewed through a neuroplasticity lens, with developmental synaptic pruning emerging as a potential core liability. Genetic evidence implicates pruning pathways, while rapid-acting antidepressants like ketamine promote synaptogenesis, suggesting that excessive early elimination leaves circuits vulnerable to later stress. Few computational models, however, capture the specific MDD pattern of latent fragility collapsing under perturbation, followed by recovery via limited plasticity enhancement.Methods: An overparameterized feed-forward neural network (∼396,000 parameters) was trained on a noisy four-class Gaussian cluster task to represent dense early connectivity. Excessive pruning (95% magnitude-based weight removal, per-layer) simulated adolescent over-elimination. Fragility was assessed under input perturbations and internal neural noise (post-activation Gaussian injections at varying intensities) modeling neuromodulatory disruption. Recovery involved gradient-guided regrowth (50% of pruned connections, prioritized by loss-reduction potential) followed by fine-tuning. Comparisons included random regrowth and a sparsity sweep to identify thresholds.Results: The intact network showed robust performance across conditions. Pruning induced sharp collapse (clean accuracy ∼51%, standard noisy ∼43%), with pronounced sensitivity to internal noise (moderate stress accuracy ∼31%) exceeding input noise effects. Gradient-guided regrowth plus fine-tuning restored near-baseline accuracy (clean/standard ∼100%) and robustness (combined stress ∼97%) despite ∼47% persistent sparsity. Targeted regrowth slightly outperformed random under high stress. A critical threshold emerged around 93% sparsity, beyond which combined-stress performance dropped abruptly (>44 percentage points).Conclusions: Excessive pruning generates threshold-like intrinsic fragility consistent with stress-triggered MDD relapse, while targeted, limited synaptogenesis efficiently compensates without full density restoration. These findings support a pruning-mediated plasticity deficit as a mechanistic framework for MDD vulnerability and highlight the therapeutic potential of activity-dependent plasticity enhancement. The model provides a testable scaffold for linking polygenic pruning risk to circuit-level decompensation and rapid treatment response.

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