arXiv preprints from January 1, 2026 through September 22, 2026 — 04:22:22 EST
NuRadioMC is a framework for the simulation of ultra-high-energy neutrino detectors that measure the radio signal emitted in neutrino-induced particle cascades used in different radio neutrino experiments. We present an extension to the analytic raytracing method for multilayered exponential refractive index models, where the full...
Protein-protein interaction (PPI) network alignment combines topological and sequence information to identify conserved modules across species, but global alignment remains challenging: heuristics sacrifice optimality, while exact methods lack scalability. We model the alignment as a weighted maximum common induced subgraph problem...
Let $(R,\mathfrak m)$ be a Noetherian local ring and $J$ be an arbitrary ideal of $R$. Suppose that $f_1,\ldots,f_r$ is a $J$-filter regular sequence in $R$ and $I=(f_1,\ldots,f_r)$. In this paper, we establish an improved upper bound for the perturbation index of the associated graded ring $\mathrm{gr}_J(R/I)$, refining the bound...
We consider the adjacency matrix of a random directed $d$-regular graph on $N$ vertices. For fixed $d\geq 2$, we prove that the empirical eigenvalue density converges in probability to the oriented Kesten--McKay law as $N\to \infty$. The key technical input is the small-ball probability estimate for the smallest singular value. The...
We apply the variational method of Weighted Energy Dissipation (WED) to obtain a global-in-time approximation of solutions to fourth order degenerate parabolic equations of Cahn-Hilliard type. Differently from the standard approach to the existence theory, WED induces an elliptic regularization in time, not in space. The confinement...
Let an infinite sequence of independent and identically distributed random variables over a countable alphabet generate a graph by joining consecutive symbols and suppressing repeated edges. We determine the exact tail and local asymptotics of the limiting degree distributions of this range-renewal graph. If the ordered sampling...
Suppose that the eventual use of data is not known when the data are reduced or collected. This note considers two simple boundary cases. In a finite statistical experiment, a statistic preserves the Bayes risk for every finite later decision problem if and only if it is sufficient. Hence, when the minimal sufficient statistic is...
Inspired by questions related to inverse problems and shape optimization, we derive an asymptotic expansion of the voltage potential, solution to a model elliptic second-order partial differential equation, under small perturbations of its boundary conditions. More precisely, the homogeneous Dirichlet or homogeneous Neumann boundary...
We complete the local classification, up to isometry, of $2$-dimensional pseudo-Riemannian metrics (i.e. both Riemannian and Lorentzian), admitting a projective symmetry algebra of dimension at least two. The new contribution is the treatment of the non-regular case: we obtain a complete list of mutually non-isometric normal forms in...
We compute the limit of the eigenvalue of the $k$-Hessian operator on the unit ball in $\mathbb{R}^n$ when $k\rightarrow \infty$, assuming that the ratio $\frac{n}{k}$ remains fixed. When $n< 2ke$, we moreover identify the limit of the corresponding eigenfunctions. We also derive monotonicity results and consider when the ratio varies in $n$.
Relative ($τ$) is equivalent to a statement that the sequence of Cayley graphs associated to group quotients $Γ_q=Γ/N_q$, $q\in\mathbb{N}$, form an expander family. There is a philosophy that expander graphs give rise to good mixing; for instance, one has exponential mixing for the geodesic flow uniformly the along a family of...
We study a natural extension of Ramsey theory relative to the classes of maximally planar and maximally outerplanar graphs. This can be seen as a continuation of the study of `Planar Ramsey theory', introduced by Axenovich et al. The question we ask is the following: For a fixed family $\mathcal{K}$ of graphs and a pair of graphs...
We investigate the best $L_2$ approximation of mixed Sobolev spaces by shallow neural networks with $n$ neurons and general activation functions. We first establish an activation-independent Fourier-block principle: if an activation has univariate approximation order $ρ$ in the sense of the Fourier-block property, then the global...
A total coloring of a graph is an assignment of colors to its vertices and edges so that adjacent or incident elements receive distinct colors, and it is equitable when the cardinalities of any two color classes differ by at most one. Stemock conjectured that every $4$-total coloring of a cubic graph of order less than $20$ is...
Large language models (LLMs) are increasingly used to formulate optimization models from natural-language problem descriptions, yet realistic operations research (OR) requests are often incomplete: missing objectives, constraints, or business rules can change the resulting mathematical program. Existing evaluations largely assume a...
This paper proves a generalisation of Coleman's isomorphism (between norm compatible cyclotomic units and a group of invertible power series) to various cohomology theories evaluated on proper regular $p$-adic formal schemes, for future applications to Iwasawa theory. This generalisation is an immediate consequence of a description,...
We investigate reflected diffusion in a bounded domain subject to two independent, competing stopping mechanisms: an exponentially distributed bulk lifetime of rate $p$ and a surface reaction triggered when the boundary local time exceeds an independent exponential threshold of rate $q$. Denoting by $T$ the stopping time and by $L$...
We develop an energy-optimal generalized scalar auxiliary variable (EOP-GSAV) framework for nonlinear index-one port-Hamiltonian differential-algebraic equations (pH-DAEs). Exploiting the port-Hamiltonian structure, we separate the nonlinear effort, interconnection, and dissipation terms from a constant implicit core. The resulting...
We consider a rectangular random matrix formed by adding a rank-one term to a matrix with independent entries. The direction on the left side of that term is estimated by the leading left singular vector, and the error is multiplied by the square of the size of the added term. For entries with mean zero and variance one, we identify...
We investigate the Weyl representation of the canonical commutation relations for a model describing a quantized massive scalar field under the influence of an external potential. The main problem is to determine whether the Weyl representation remains equivalent to or becomes inequivalent to the original one when the mass and/or...
Creativity researchers often distinguish between two stages of the creative process: generation versus selection. While much is known about the psychology of idea generation (e.g., the factors that lead to a greater number of novel and useful ideas), less is understood about the nature of selection, or how generation and selection...
Measuring the intergenerational transmission of lifetime economic status is complicated by researchers often only observing snapshots of income at specific ages. Consequently, standard practice estimates intergenerational mobility using income averages, introducing life-cycle bias that compromises reliability and comparability across...
We represent a non-Bayesian agent as one who does not completely trust the information they receive. The behavioral expression of complete trust lies in a homogeneity property of Bayesian updating: posterior beliefs do not change if a signal is made arbitrarily rare by scaling down its likelihood vector. We show that simply dropping...
This paper analyzes the implementation of blockchain-based integrity mechanisms in Greek Fiscal Electronic Mechanisms (FEMs) and the central tax information system eSEND. The study examines the cryptographic architecture of fiscal devices, including Electronic Cash Registers, Fiscal Printers, Fiscal Signing Machines, and FEMAS...
Long COVID is a condition usually defined by persisting symptoms following infection by the SARS-CoV-2 virus beyond the acute phase of infection. The condition has a significant impact on healthcare systems, the economy, and the individuals living with it. Due to the diverse and extensive symptomatology of long COVID, symptom...