Computer Science and Mathematics

Abstract: Hepatitis B remains a major public health concern worldwide, particularly in developing nations where poor vaccination coverage, lack of screening, unsafe sexual practices, and delayed treatment fuel its spread. We developed a fractional-order model incorporating vaccination, screening, post-exposure prophylaxis (PEP), acute and chronic infection management, and behavioural measures. Theoretical analysis confirmed the model's existence, uniqueness, positivity, and boundedness. Equilibrium states were identified, and the basic reproduction number (R₀) was derived via the next-generation matrix. The disease-free equilibrium is locally and globally asymptotically stable when R₀< 1, while the endemic equilibrium exists and is globally asymptotically stable when R₀>1. Model fitting and parameter estimation used acute Hepatitis B data from Ireland. Sensitivity analysis identified vaccination, screening, and safe practices as the most influential control factors. Numerical simulations showed that conventional strategies alone are insufficient; higher vaccination coverage, efficient screening, improved safe practices, and effective PEP are essential to reduce transmission. Collectively, these interventions minimize progression to chronic disease, reduce long-term burden, lower complications and mortality, particularly when acute infection management is included.

Abstract: The human microbiome is a complex, dynamic and highly structured ecosystem whose analysis requires computational methods able to capture relationships among microbial taxa, genes, metabolic pathways, host factors, environmental exposures and disease phenotypes. Conventional machine-learning pipelines often represent microbiome samples as independent high-dimensional abundance vectors, thereby neglecting ecological, phylogenetic and functional dependencies among microbial entities. Graph-based learning provides a natural framework for modelling such dependencies, whereas graph contrastive learning (GCL) offers a self- supervised paradigm for learning robust representations from graph-structured data under limited label availability. This survey reviews the emerging intersection between GCL and microbiome data analysis. We first discuss the biological and computational characteristics of microbiome data, including sparsity, zero inflation, compositionality, batch effects, cohort heterogeneity and weak supervision. We then organize microbiome graph representations into taxa–taxa association networks, phylogenetic graphs, sample similarity graphs, microbe– disease association networks, host–microbe graphs, metabolic graphs and heterogeneous multi-omics graphs. Next, we summarize the foundations of GCL, including view generation, positive and negative pair construction, contrastive objectives, negative-free learning and multi-view representation learning.

Abstract: Aqueous humor (AH) is a watery fluid continuously circulating through the posterior and anterior chambers of the human eye and is essential to maintain a healthy intraocular pressure in the eye ball and keep the eye clean from waste products of metabolism and external agents. This paper presents a stationary compartment model of AH dynamics consisting of three integrated modules (M): M1 for AH production, M2 for AH passive flow and M3 for AH drainage. M1 is a zero-dimensional (0D) reduction of the velocity-extended Poisson-Nernst-Planck model and simulates solute transfer and fluid movement across the cellular structure of the ciliary epithelium (CE). M2 is the electric equivalent representation of Poiseuille flow across the series of two linear hydraulic resistors. M3 is a 0D reduction of the Darcy equations for a porous medium and simulates AH flow across the parallel between a nonlinear and a linear resistor. Compared to existing compartment approaches, the present model integrates at the macroscopic scale the multi-physical description of the human eye at the cellular scale. Numerical simulations suggest that (1) sodium channels in the CE are essential for maintaining proper AH dynamics; and (2) increased episcleral vein pressure reduces AH drainage, potentially explaining the development of secondary open-angle glaucoma. These insights advance the understanding of the mechanisms regulating AH dynamics and offer new perspectives for patient-specific therapies.

Abstract: Survival modeling is a crucial area in cancer research and precision oncology, enabling prediction of time-to-event outcomes such as overall, progression-free, and disease-free survival. The Cox proportional hazards model has long been the foundation of prognostic analysis due to its ease of interpretability, but the assumptions of linearity and proportional hazards limit its ability to capture complex, high-dimensional relationships in multi-omics data. Deep learning (DL)–based survival models address these limitations by providing flexible, nonlinear modeling and advanced representation learning. This review provides an overview of advances in survival modeling, tracing the evolution from traditional Cox regression to neural network–based approaches, including feed-forward survival models and modern DL architectures. To predict survival based on molecular and clinical information, two major strategies have emerged: (1) applying neural networks directly to multi-omics and clinical data within a Cox regression framework, (2) using variational autoencoders (VAEs) to learn compact latent representations of multi-omics data that are combined with clinical variables. Here we discuss in detail some recently developed VAE-based methods that improve prognostic performance, focusing on advanced training strategies and architectural designs that integrate unsupervised representation learning with Cox PH or non-linear extension of Cox models. Further, we highlight the opportunities to answer core biological questions and key advances in the DL paradigm such as optimization, regularization, and model interpretability, while noting that challenges remain in reproducibility, benchmarking, and clinical translation. In this review, we underscore the need for robust, interpretable, and standardized approaches to improve risk stratification by uncovering biologically meaningful patterns in multi-omics and clinical data, thereby advancing precision oncology.

Abstract: N-of-1 medicine reasons about one patient at a time using that patient's own molecular data, but lacks standardized evidence architectures. Current strategies depend on fragmented biomarkers, population-level associations, or expert preference, limiting auditability and reproducibility. Here we present SteeraMed Core, a framework that addresses these limitations by representing individual molecular state through PPI-network modules, linking it to candidate interventions via a steerability alignment score, and packaging the result as an auditable evidence chain. Retrospective positive-control evaluation across three disease and one aging methylation cohort supported the PPI-module design. Known drugs were recovered above random chance in rheumatoid arthritis (5.8-fold), breast cancer (5.1-fold), and aging (1.8-fold with literature-convergent candidates niacin and colchicine). In depression, nutraceuticals exceeded baseline recovery particularly in mid-age sub-cohorts (36-55 years, ~2.0-fold enrichment). Patient-level evidence chains, each composed of four layers (perturbed modules, drug-module alignment scores, mechanism annotations, and bootstrap confidence), illustrated how the framework links individual molecular state to ranked candidate interventions, aligning with the FDA Plausible Mechanism Framework's emphasis on traceable mechanistic evidence. These results support PPI modules as effective leverage points that aggregate weak individual signals into coherent functional units. Critically, PPI modules retained above-baseline drug recovery under progressive Gaussian noise, whereas single-gene representations collapsed, confirming greater robustness of module-level alignment. Together, these results establish the core of a Steerable Biomedical World Model that directly addresses the three limitations above: PPI modules replace fragmented biomarkers with coherent functional units; per-patient scoring replaces population-level associations with individual mechanism alignment; and evidence chains from public data replace expert preference with auditable reasoning. This core has been validated through retrospective positive-control recovery, not clinical efficacy. Converting it into a full learning system will require prospective cohorts with paired pre- and post-intervention measurements.

Abstract: Understanding the conditions under which the immune system can suppress or fail to contain a growing tumor remains a central open problem in oncology, with direct implications for the design of immunotherapy protocols. Nutrient availability in the tumor microenvironment is increasingly recognized as a determinant of both tumor aggressiveness and immune cell efficacy, yet the spatial interplay among tumor proliferation, immune infiltration, and nutrient depletion is difficult to disentangle experimentally. This study employs a rigorously analyzed spatiotemporal reaction–diffusion model to identify the parameter regimes — defined by immune cytotoxic strength χ, tumor-driven immune recruitment η, and nutrient consumption rate θ — that determine whether a tumor is controlled, coexists chronically, or escapes immune surveillance entirely. Equilibrium analysis shows that the tumor-free state is unconditionally unstable, while a chronic coexistence state is locally asymptotically stable, establishing a theoretical basis for the observed persistence of tumors under partial immune control. Numerical simulations under two biologically distinct parameter regimes demonstrate spatially resolved outcomes: in the immune-competent regime, cytotoxic infiltration suppresses tumor growth and maintains nutrient availability, whereas in the aggressive regime, rapid nutrient depletion creates a necrotic core in the spatial interior consistent with avascular solid tumor morphology, while the immune response remains spatially peripheral and functionally insufficient. These findings identify critical thresholds in immune killing rate and nutrient supply below which computational models predict inevitable tumor escape, providing quantitative targets for immunotherapy augmentation strategies. High-order implicit time integration (SSHBBDF, order four, A-stable) ensures the biological fidelity of all simulations by resolving the multiscale stiffness inherent in coupled reaction–diffusion cancer models.

Abstract: Nonlinear dynamical systems often exhibit complex collective behavior arising from the interaction of multiple elementary modes. In this work we investigate the aggregation of a countable family of dynamical modes generated by Lotka-Volterra systems and study the resulting structure in a Hilbert space of observables. The classical Lotka-Volterra equations form a fundamental class of nonlinear models describing interacting populations through coupled differential equations, while Koopman operator theory provides a framework in which nonlinear dynamics can be represented as a linear evolution acting on observable functions.We show that a countable aggregation of such dynamical modes admits a well-defined limit in a Hilbert space when the coefficients belong to l2. The resulting aggregated observable evolves according to the associated Koopman semigroup, yielding a linear representation of the underlying nonlinear dynamics in the observable space. We further prove that the geometry induced by this aggregated dynamics admits a canonical class of equivalent metrics generated by coercive operators, ensuring that the stability topology of the system is independent of the particular metric chosen within this class.Finally, we illustrate the theoretical framework by introducing a social risk functional defined as a quadratic observable associated with the induced metric. This example demonstrates how application-specific quantities can naturally arise from the geometric structure generated by aggregated nonlinear dynamics.

Abstract: Hantaviruses are emerging zoonotic pathogens responsible for two severe clinical syndromes: (i) haemorrhagic fever with renal syndrome (HFRS) and (ii) hantavirus cardiopulmonary syndrome (HCPS), collectively causing more than 200,000 human cases annually worldwide. Despite their public-health importance, the molecular mechanisms governing the host response and the population-level dynamics of rodent- to-human spillover remain incompletely characterised. The timeliness of this frame- work is underscored by the April–May 2026 outbreak of Andes orthohantavirus aboard 9 the MV Hondius cruise ship – the first such cluster in a maritime setting, with three deaths reported across multiple countries (WHO Disease Outbreak News: https://www.who.int/emergencies/disease-outbreak-news/item/2026-DON599). This event revealed critical gaps in existing models that treat humans solely as dead-end spillover hosts. Here, we present an integrated computational study that combines three complementary analyses. Preliminarly, we performed the first phylogenetic analysis of such virus, idenifying as Orthoantavirus andensense the responsible for the vessel outbreak. Second, we performed a downstream transcriptomic analysis of Hantaan virus (HTNV)-infected human umbilical vein endothelial cells (HUVECs) using publicly available RNA-seq data (GEO accession GSE133751, n = 3 per group), identifying 184 upregulated and 19 downregulated evidencing the role of dominated by interferon-stimulated genes (ISGs), including CXCL10, CXCL11, MX2, DDX58, IRF7, STAT1, OASL, and CMPK2. We constructed a protein–protein interaction (PPI) network from STRING (176 nodes, 3,210 edges) and applied a composite network centrality score to rank regulatory hubs, identifying ISG15, IRF1, CXCL10, STAT1, and DDX58 as the most central nodes. Pathway enrichment analysis con- firms strong activation of interferon signalling (Reactome, p = 1.3×10⁻⁶³), antiviral defence (Gene Ontology, p = 3.8 × 10⁻⁵⁸), and NF-κB pathways, with concurrent suppression of ribosomal translation. We finally developed a coupled SEIRD epi-demiological model that explicitly represents rodent-to-rodent and rodent-to-human transmission with logistic rodent population growth. Preliminary simulation analysis demonstrates that reducing human exposure to rodent excreta is substantially more effective than rodent population control alone for reducing human disease burden, and that rodent control in isolation can paradoxically increase human cases through a dilution-like effect. The integrated framework provides molecular and epidemiological insights relevant to hantavirus surveillance, therapeutic target identification, and 35 public-health intervention design.

Abstract: Amid COVID-19-related in-person school closures in 2021, an agent-based simulation grounded in social impact theory was implemented and documented to investigate the effects of in-person school closure on nonmedical prescription opioid use among adolescents in Ontario, Canada. The results of model simulations forecasted an alarming rebound effect in the opioid use prevalence after the lifting of in-person school closures and identified secure medication storage in households as an effective strategy for mitigating associated risks. This study evaluates this result by comparing the baseline projection from the previously published study with newly released 2023 data from the Ontario Student Drug Use and Health Survey. Furthermore, it employs the developed agent-based model to simulate the projection through 2030 and assesses the efficacy of secure medication storage in households for the coming years. The study confirms that the previously published simulation projection for 2023 closely aligns with observed data, showing nonmedical prescription opioid use prevalence among Ontario adolescents nearly doubling from 2021 to 2023. Additionally, the results show that nonmedical prescription opioid use prevalence among youth is projected to remain at these elevated levels. Critically, the findings suggest that the temporal window for effective secure medication storage interventions has elapsed, and these interventions are now expected to have minimal impact on reducing this increase, even when applied extensively. The agreement between reported predictions and observed data demonstrates that a simulation model with relevant conceptual foundation can accurately predict future trends and provide sufficient lead time for policymakers to implement interventions within critical time-sensitive windows to alter undesirable trajectories before public health crises escalate.

Abstract: We show that a single Hodgkin–Huxley (HH) neuron with Pyragas-type delayed feedback control (DFC) can store multiple symbols as stable periodic orbits, where the specific orbit is selected by tuning the DFC gain K and time delay τ. Sweeping the (K,τ) parameter plane at fixed bias current Ibias=10.0μA/cm2 reveals 207 orbit types across 12 topological categories, with inter-spike interval (ISI) means from 5.9 to 56.9 ms. We establish: (i) a write protocol that reliably locks orbits with 13.9 ms median settling time; (ii) a novel Pattern-Oriented Limit-cycle Decoder (POLD) that reads orbits at 100% accuracy from only 5 observed ISIs; (iii) a full write–read–erase (W–R–E) cycle with 100% read accuracy, 92% erase verification, and no decay over hold durations up to 50 s; and (iv) a fully validated 12-symbol memory capacity, with a read-discriminable upper bound of 67 symbols (11.2× over rate coding) pending write-viability confirmation for the extended set. Reliable orbit addressing needs delay precision of ±2%, which constitutes a write-precision specification and not a fundamental capacity limit. These findings show that parametric delayed feedback is a viable mechanism for limit-cycle-based information storage in conductance-based spiking neurons. The biological interpretation is analogical, not direct: the ±2% delay-precision requirement exceeds what has been demonstrated for biological autaptic variability, and the orbit-coded memory framing is best understood as a computational proof-of-principle aimed at neuromorphic engineering, not as a claim about biological working memory.

Abstract: Recent medical world-model rubrics have mainly described a linear progression from representation and forecasting to action-conditioned simulation, counterfactual evaluation, and planning/control. This Perspective starts from a different goal: biomedical world models should not merely predict likely trajectories, but help make biological trajectories steerable. Steerability requires five linked functions: defining state, measuring state, specifying intervention-induced state movement, simulating alternative transitions, and inspecting deviations. We therefore propose the Deductively Constrained Capomics World Model, a closed-loop architecture organized around five corresponding constraint checkpoints: CP1 state representation, CP2 intrinsic-capability quantification, CP3 intervention-response semantics, CP4 counterfactual transition, and CP5 quality-control feedback. The framework shifts biomedical world modeling from a “what-if” simulator toward a quality-controlled “why-not” steering system, in which failed or unexpected transitions can be traced to state measurement, intervention specification, module response, state transition, or downstream phenotypic propagation. Within this architecture, module-level intrinsic capability (mIC) provides the proposed state variable, and Capomics provides its measurement framework. In the current prototype, DNA methylation is used to estimate module-level mIC values and assemble them into an mIC vector, while other omics and physiological readouts may be incorporated in future implementations. The accompanying depression case study illustrates how the cycle can be instantiated as a thought experiment for state-matched intervention reasoning and deviation inspection. The framework does not claim validated treatment planning or guaranteed efficacy; it is intended as a hypothesis-generating scaffold for biomedical world models, longitudinal intervention studies, and future biomedical applications.

Abstract: Proviral integration — the molecular event that converts HIV infection from reversible to permanent— defines a finite window during which post-exposure prophylaxis (PEP) can succeed. Using a three-state absorbing Markov model parameterized on established HIV-1 kinetic constants, we prove that PEP efficacy decays monotonically to zero and derive the critical prevention window as a function of integrationkinetics rather than drug potency. This window is approximately three-fold shorter for parenteral (injection) than mucosal (sexual) exposure, yielding a parenteral tcrit of 16–28 hours versus 68–76 hours mucosally. For people who inject drugs, empirically documented structural access delays place fewer than 5% of exposures within the parenteral window, bounding expected population-level PEP efficacy below 10%—a failure determined by integration timing, not pharmacology.

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.

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.

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.

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.

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.

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.

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.

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.