arXiv preprints from January 1, 2026 through September 12, 2026 — 01:02:47 EST
This study applied a mathematical tool from Topological Data Analysis (TDA), called the Mapper algorithm, to gene expression data from more than 1,000 TCGA-BRCA patients to identify hidden molecular patterns associated with survival. Patients located near high-risk regions of the network showed significantly poorer survival, and...
Multimodal Contrastive Learning (CL) has shown significant performance in aligning representations across various data modalities and improving downstream tasks, especially in healthcare. It works by minimizing the distance between matched (positive) data modalities, while maximizing the distance between mismatched (negative) samples....
Deterministic evolutionary game theory makes no distinction between a monomorphic population of individuals all of whom share a mixed evolutionarily stable strategy and a polymorphic population of players of pure strategies present in a ratio that reproduces the mixed strategy on average. The so-called trembling hand hypothesis posits...
Resource scarcity can fundamentally encourage antisocial behaviour, whereas resource abundance can promote fair behaviour. Experimental evidence indeed suggests that scarcity induces spiteful behaviour, while repeated interactions enhance fairness. However, existing studies of game--environment feedback systems are largely confined to...
Meditative expertise involves sustained attention, rapid recovery from distraction, and coordinated dynamics of large-scale brain networks. We present a computational phenomenology of focused-attention meditation traversing four attractor states: breath focus, mind-wandering, meta-awareness, and redirect attention. Within a...
Processes such as incomplete lineage sorting (ILS) and reticulate evolution (arising, for example, from hybridization and lateral gene transfer (LGT)) are known to cause discordance between gene trees and species trees, complicating phylogenetic inference. While the multispecies coalescent model has led to a rich theoretical...
A six-degree-of-freedom (6-DOF) nonlinear lumped-parameter biodynamic model of the seated human upper body is formulated to predict human response under different unknown loading conditions. The model consists of six anatomically partitioned cascade body segments: pelvis, lower torso, central torso, upper torso, neck, and head. The...
Biomolecular condensates are continually remodeled by biochemical reactions that can exhibit non-Markovian, history-dependent dynamics. We develop a theory of active phase separation with non-Markovian reactions and show that delayed reaction feedback destabilizes stationary droplets: when the memory time becomes comparable to the...
Spatially resolved omics studies increasingly combine transcriptomic and epigenomic assays, yet downstream analysis is often still performed using single-modality pipelines. We present LATTICE (Latent Alignment of Tissue-level and Transcriptomic Information for Cross-modal Embedding), a graph-based self-supervised framework that...
Gene expression is a stochastic process that allows for fluctuations in protein levels that can give rise to phenotypic heterogeneity within a population of genetically identical cells. Thus, there is great interest in quantifying how natural variation (noise) in gene expression is impacted by cellular control mechanisms, such as the...
Food webs have been extensively studied from both ecological and mathematical aspects. However, most of the models studied in this area do not capture the effects of infectious diseases simultaneously. Recently, the idea of including an infectious disease in a food web model has been investigated. We study and simulate a small food...
Robust and accurate neural decoders are integral to neurotechnologies such as brain-computer interfaces and closed-loop experiments. Recent work has shown that tokenizing neural data at the spike level facilitates multi-session pretraining and delivers state-of-the-art decoding performance. However, current spike-based models are...
Human-centered adaptive systems require behavioral models that are both psychologically interpretable and mathematically analyzable. Many existing predictors either operate as black-box input-output mappings or provide limited access to latent internal dynamics. This paper addresses this gap by modeling behavior as a...
Genomic foundation models such as Evo 2 learn rich sequence representations, but their value for biosecurity screening is largely unexplored. We ask how much biosecurity-relevant signal is linearly accessible in these representations by training minimal linear and attention probes on frozen Evo 2 layer-26 activations, without...
Hamilton-Jacobi Reachability (HJR) is a central framework in safe control theory. While HJR has traditionally focused on a few fundamental tasks, there is increasing interest in scaling to more complex objectives. Recent works have studied the exact decomposition of the value functions for two fundamental dual-objective tasks in the...
Transient synaptic memory has emerged as a potential mechanism for maintaining short-term information even in the absence of persistent neuronal activity. However, it remains unclear whether the hidden synaptic state alone contains sufficient information to predict the future evolution of neuronal networks after activity has ceased....
We propose a definition of the reduction type of a curve over a discretely valued field in terms of the special fibre of an arbitrary regular model. We show that under this definition, the reduction type in terms of the minimal regular model determines and reduction type in terms of the minimal regular normal crossings model and vice...
Computation of zigzag persistence has progressed in recent years, with results showing that complexities of many problems closely align with those in the non-zigzag setting. The major efficiency gap now lies in the updating of zigzag representatives. In this paper, we propose efficient algorithms for updating zigzag representatives...
This paper establishes a new characterization of simple closed curves on a closed orientable surface. Let $Γ$ be the fundamental group of a closed orientable surface. We prove that if an element $g\inΓ$ has the same possible images as a given simple closed curve $γ\in Γ$ under epimorphisms from $Γ$ to every finite group, then $g$...
A random sequence sampled from a known continuous distribution is observed with the objective to choose an item with the overall rank one. A rejected item cannot be recalled and is immediately erased from the memory. Under this memory constraint, the choice problem is not amenable to recursive methods of optimal stopping and becomes a...
We construct stationary solutions of the three-dimensional incompressible Euler equations with helical symmetry and support in a neighborhood of a helix. The solutions are piecewise smooth and arise from a nonlinear overdetermined elliptic boundary value problem associated with a stream-function formulation. A distinguishing feature...
We study randomly advected incompressible Navier-Stokes equations, where the advecting field is a mean-zero, divergence-free, space-time stationary velocity field with smooth order-one correlations. We introduce a two-parameter family of models in which the advection is accelerated on a fast temporal scale $\varepsilon^2$ and has...
We show that the Erdős-Rogers function $f_{s,s+1}(n)$ satisfies $$f_{s,s+1}(n) = Θ( \sqrt{n \log n} )$$ for every $s \ge 2$. More precisely, we construct a $K_{s+1}$-free graph on $n$ vertices in which every set of at least $C(s)\sqrt{n \log n}$ vertices contains a copy of $K_s$ for some constant $C(s)$, which implies the upper bound....
While quantum computers promise to solve classically intractable problems, identifying the point at which fault-tolerant quantum computation outperforms the best classical algorithms for practical applications remains an outstanding challenge. Here we establish a concrete quantum-classical crossover for quantum many-body dynamics...
It is well-known that combinatorial circuits are modeled mathematically by string diagrams in monoidal categories. Given a gate set $Σ$, the circuits over $Σ$ can be thought of as string diagrams in the free monoidal category generated by $Σ$. In this model, circuit semantics are then given by monoidal functors out of this free...