arXiv preprints from January 1, 2026 through September 23, 2026 — 01:09:40 EST
Ion channels and pumps drive ion-selective currents through cell membranes at localized sites, yet a cell's electrical state is routinely summarized by a single transmembrane voltage. Combining theory and numerical simulations, we resolve the spatiotemporal dynamics of charge reorganization driven by a localized current on a spherical...
Pathologic complete response (pCR) is a strong neoadjuvant endpoint, yet 5-15% of complete responders recur and clinical/genomic variables do not reliably identify them. We tested whether pretreatment dynamic contrast-enhanced MRI entropy - intratumoral enhancement heterogeneity - resolves response quality hidden within pCR and...
Reengineered biological systems have the potential to revolutionize chemical and material production, enhance critical mineral recovery, serve as threat sensors and improve human health. Unfortunately, the extreme complexity of organisms has made it difficult to achieve this potential in all but the simplest cases. Recent...
Single-particle cryo-electron microscopy (cryo-EM) pose estimation is traditionally solved anew for each dataset, where iterative refinement is done from scratch while the estimator learns to store the molecule in its weights. In this work, we show that pose inference is a generalizable, specimen-agnostic operation when conditioned...
We study the evolution of cooperation in a finite haploid population whose individuals carry both a strategy and a phenotype on a finite periodic space. Cooperators help with a probability that decays exponentially with phenotypic distance, generating graded phenotype-dependent assortment. Under weak selection and a large-population...
Hippocampal replay is a phenomenon observed in mammals and songbirds where neural activation sequences experienced during wakeful periods are repeated during rest or sleep. This mechanism is believed to play a crucial role in episodic memory consolidation, retrieval, and planning. Interestingly, replay can occur in both forward and...
The 5' untranslated region is a major determinant of translation initiation, and its effect becomes especially important in modified mRNA sequences, where start-codon context, cap-proximal secondary structure, upstream AUGs and upstream open reading frames, and nucleotide chemistry can alter ribosome scanning and initiation...
Network Hamiltonian Models (NHMs) provide an efficient framework for modeling the aggregation of interacting particles (e.g., the condensation of proteins into gel-like, oligomeric, or fibrillar states), representing the system as a network whose edges represent bound interactions. Terms within the network Hamiltonian represent...
Purpose: Nocturnal hypoglycemia (NH) remains a challenge for individuals with type 1 diabetes (T1D), particularly those who are physically active or on multiple daily injections (MDI). We leveraged an explainable evidential neural network model that forecasts minimum overnight glucose to identify NH risk factors and generate...
We establish the existence of a stochastic flow on $L^{\infty} (\mathbb{T})$ for the stochastic Allen-Cahn equation with multiplicative noise \[ (\partial_t - \partial_x^2) u = u - u^3 + σ(u) ξ\quad \text{on} \quad \mathbb{R}_+ \times \mathbb{T}, \] where $ξ$ is space-time white noise and $σ: \mathbb{R} \rightarrow \mathbb{R}$ is...
We prove Dennin's conjecture (Conjecture 8.9 of arXiv:2506.21052) that his variant of dual RSK correspondence is symmetric when restricted to biGrassmannian permutations. For a binary matrix $A$, let $A^\dagger$ denote its transpose-complement, and let $\operatorname{ins}(A)$ and $\operatorname{rec}(A)$ denote its insertion and...
For every integer $d\geq 1$, we construct a countably infinite set $X_d\subset\mathbb{R}^d$ in affine general position, with all pairwise distances rational. When $d$ is odd, $X_d$ may also be chosen so that no $d+2$ points lie on a common sphere. The construction is uniform in $d$: positive Chebyshev square decompositions produce...
We investigate which 3-manifolds bound 4-manifolds that are homeomorphic but not stably diffeomorphic, where stabilising means taking connected sum with copies of $S^2\times S^2$. We show that every closed, orientable 3-manifold admits such fillings, as do certain families of nonorientable 3-manifolds. In contrast we show that for a...
We establish a general structure theorem for local quantum Cuntz--Krieger families associated to finite quantum graphs whose relations are analogous to those of the partial isometries generating an ordinary graph $C^*$-algebra, with the quantum edge correspondence governing composition. We apply this structure theorem to the quantum...
We prove the wall-crossing formula conjectured by Gross--Joyce--Tanaka for equivariant enumerative invariants of CY4 categories equipped with framing functors. We also establish a version for stable pairs with fixed-determinant obstruction theories, as used in earlier applications by the first-named author. The main technical...
The probabilistic formulation of principal component analysis promises statistically grounded solutions to the problem of selecting the number of principal components. However, developing tractable model selection methods is complicated by the fact that the probabilistic principal component analysis (PPCA) model exhibits non-standard...
We establish a Demailly-Kollár type continuity theorem for plurisubharmonic functions with respect to adapted measures on normal complex analytic klt pairs. As applications, we prove the equality of the analytic and divisorial versions of the alpha and delta invariants on compact normal Kähler klt pairs, thereby completing a program...
Let $λ(n)=(-1)^{Ω(n)}$ be the Liouville function. Pilatte proved a fixed power saving for the logarithmically weighted two-point correlation at shift one. More recently, Tao and Teräväinen obtained power-logarithmic two-point estimates uniform over polylogarithmically growing shifts and coefficients outside a common exceptional set of...
An element of a finite group is non-vanishing if no irreducible complex character vanishes on it. We prove that every non-vanishing element of a finite solvable group belongs to the Fitting subgroup. The proof combines the reduction of Isaacs, Navarro, and Wolf with an argument using finite symplectic spaces and Clifford theory.
Pantograph arises in electric trains, material modelling, and the modelling of quantum dot lasers. Pantograph integrodifferential equations are integrodifferential equations involving proportional delays; and they appear in fields such as electrodynamics, epidemiology, control theory, astrophysics, economics, and engineering. This...
The capacity of Low Earth Orbit (LEO) to sustain space operations is under mounting pressure from megaconstellations, legacy fragmentation debris, and new payload classes. Existing assessments of orbital capacity and debris evolution are largely deterministic, tracking mean populations of intact satellites and fragments with ordinary...
We study travelling front solutions of a family of degenerate Fisher-KPP equations $u_t=(u^n u_x)_x+u(1-u^n)$, where $n$ is a positive integer. At the minimal wave speed $c_{\rm min}=\tfrac{1}{\sqrt{1+n}}$, these equations admit sharp front solutions, corresponding to an explicit heteroclinic orbit in the travelling wave phase-space....
For $n$ odd, we enumerate rank $n$ complex topological vector bundles on $\mathbb CP^{n+2}$ with prescribed complex $K$-theory class. The answer exhibits a 24-fold periodicity and is closely related to the enumeration of corank $2$ stably trivial vector bundles.
We prove that the heat semigroup on the circle has optimal complete modified logarithmic Sobolev constant \(1\). The proof is based on a matrix-valued Wirtinger inequality and yields the stronger Bogoliubov--Kubo--Mori Fisher information contraction with rate \(e^{-2t}\). As a consequence, the complete tensorization and transference...
Classical results establish that the Lyapunov exponents of an ergodic measure for linear cocycles over hyperbolic systems can be approximated by the Lyapunov exponents of periodic orbits, provided the cocycle is Hölder continuous. A recent counterexample by Bochi demonstrates that this approximation property fails in general if the...