arXiv preprints from January 1, 2026 through September 5, 2026 — 10:13:45 EST
Recent advances in audio-language modeling have been driven by large-scale audio captioning datasets. However, existing datasets remain limited by low semantic diversity, generic descriptions lacking acoustic details, and one-to-one audio-caption mappings that poorly reflect the inherent ambiguity of auditory perception. We introduce...
In this lecture note, we present a concise and self-contained derivation of the discrete-time Kalman filter equations that requires only a basic understanding of least squares estimation. The treatment is designed to minimize mathematical overhead while preserving both rigor and generality.
The increasing density of connected vehicles can place substantial pressure on fixed roadside infrastructure, particularly when the available communication resources become insufficient to accommodate temporary traffic surges. This paper investigates auxiliary unmanned aerial vehicle (UAV) assistance as a flexible mechanism for...
Learning graph structures from data is a fundamental problem that spans a wide range of signal processing and machine learning tasks. While significant effort has been made to tackle the problem, existing research has largely evolved along two parallel directions. The first seeks to infer the topology of an individual graph from...
Recent advances in equation discovery methods such as SINDy have highlighted the growing interest in identifying governing parameters and models directly from data. In this work, we take a complementary approach grounded in analysis and numerical PDE methods: we recover an unknown viscosity in steady Navier-Stokes equations (NSE) from...
We develop a localized persistent theory of commutative algebra for Stanley-Reisner rings, based on local cohomology supported at a coordinate prime rather than at the maximal ideal. The construction is modeled on the persistent Stanley-Reisner theory of Suwayyid and Wei (arXiv:2503.23482) and its functorial development for graphs and...
We study how far gradient descent (GD) can be accelerated by predetermined stepsizes in smooth convex optimization. Going beyond the classical $Ω(n^{-2})$ first-order oracle lower bound of Nemirovsky and Yudin, we prove an $Ω(n^{-1.6342})$ non-anytime lower bound and an $Ω(n^{-1.2408})$ anytime lower bound. These improve the recent...
Temporal graphs model dynamic networks by assigning positive integer time labels to the edges, while information propagates along temporal paths, whose edge labels are traversed in nondecreasing order. A temporal $α$-spanner of a temporal graph with $n$ vertices is a temporal subgraph that approximates the minimum-hop temporal...
We construct realizable-volume models over any field for the factorially normalized homogeneous Lascoux, Lascoux-atom, and positive Grothendieck packets. Their volume minors include normalized key polynomials, Demazure atoms, Schubert polynomials, and all sign-corrected homogeneous Grothendieck components. Over $\mathbb C$, these...
This article equips the universal moduli spaces of non-degenerate $\mathbb{Z}/2\mathbb{Z}$ harmonic spinors with the structure of a tame Fréchet manifold and proves that the projection map to the parameter space is uniformly Fredholm. This recovers earlier work of Donaldson, Parker, and Takahashi in a unified framework.
A $B$-coloring of a graph is a proper edge-coloring in which every $4$-cycle is rainbow, and $q_B(G)$ denotes the minimum number of colors in such a coloring. Let $Δ_2(G)$ denote the maximum number of common neighbors of two distinct vertices of $G$. We prove that, for integers $1\le d\leΔ$, every finite simple $d$-degenerate graph...
The exact N-soliton solutions are derived for the coupled negative first order Klein-Gordon (CNKG) equation subject to vanishing boundary conditions by using the inverse scattering method via Gelfand-Levitan-Marchenko equation. Based on the zero-curvature representation, the conservation laws, integrals of motion, and Hamiltonian...
The first paper worked out one family of four lattices in full -- $|\det| = 12, 24, 36$ and $72$. This paper generalizes it. We enumerate the 44 symmetrizable rank-three hyperbolic Cartan matrices and their 56 depth-one edits, 100 root bases in all, and compute the obstruction space $S_{5/2}(ρ_L)$ of the 98 within our weight-$5/2$...
We prove the global existence and uniqueness of strong solutions to a constrained version of the damped nonlinear wave equation $$ \vartheta_{tt}+γ\vartheta_t-Δ\vartheta+|\vartheta|^{p-2}\vartheta=0 $$ on a smooth bounded domain $\varOmega\subset\mathbb{R}^d$, where the evolution is projected onto the tangent space of the Hilbert...
This survey paper provides a comprehensive study of unitarily invariant norms on the algebra of $n \times n$ matrices. This investigation leads naturally to the theory of symmetric gauge functions, a class of norms on $\mathbb{R}^n$ characterized by invariance and monotonicity properties. We develop the necessary framework by...
We give an example showing that the dual of an algebraic matroid need not be algebraic. Our example is a matroid of rank 6 on 10 elements which is algebraic in characteristic 2. It is obtained by gluing an algebraic realization of the non-Fano matroid to a realization of the Fano matroid. Its dual is shown not to be algebraic using...
Data-consistent inversion (DCI) constructs probability measures whose push-forward distributions agree with observed data, while iterative data-consistent inversion (iDCI) extends this framework to generalized stochastic inverse problems by enforcing multiple push-forward constraints sequentially. Although iDCI avoids the direct...
The divisible sandpile on $\mathbb{Z}^d$ starts from i.i.d. masses at each site, and, in each discrete time step, a site with mass above one keeps one unit and sends the excess equally to its neighbors. Levine, Murugan, Peres and Ugurcan (2016) showed that at mean one this process explodes, with every site emitting infinite mass. We...
Let $R$ be a discrete valuation ring. We prove that every proper flat finitely presented commutative $R$-group scheme $P$ fits into an exact sequence \[ 0\longrightarrow E\longrightarrow P\longrightarrow B\longrightarrow0, \] where $E$ is finite flat and $B$ is an abelian scheme. For a quasiabelian model---that is, a proper flat...
We study the category of dual operator spaces equipped with an action of a locally compact quantum group $\mathbb{G}$. The Fubini crossed product functor $-\rtimes^\mathcal{F} \mathbb{G}$ and the weak$^*$-crossed product functor $-\bar{\rtimes}\mathbb{G}$ are shown to be equal if and only if $\mathbb{G}$ has the approximation property...
In the parking model, each site of the $d$-dimensional lattice independently starts with one car with probability $p$ or one parking spot with probability $1-p$. Cars move according to independent discrete-time simple random walks and park at the first spot they find free. We prove that in the critical regime $p=1/2$, the expected...
Modern portfolio management increasingly demands a balance between traditional risk-adjusted returns and strict Environmental, Social, and Governance (ESG) mandates. Current Reinforcement Learning (RL) approaches typically optimize for a single ESG provider, neglecting the significant divergence in rating methodologies across the...
Trade durations in high-frequency foreign exchange data exhibit increased occurrence near integer values. To address this empirical phenomenon, we propose the granularity-adjusted autoregressive conditional duration (GA-ACD) model. It is based on a novel two-component mixture distribution consisting of a standard generalized gamma...
This paper develops uniform inference and certified capacity decisions for an estimated financial stability boundary. Conditional risk, temporary cross-impact, and effective risk-bearing capacity are jointly estimated from dependent observations. Conventional pointwise inference is reliable at a separated simple spectral root but can...
This paper develops a mechanism through which costly changes in the representations used for portfolio choice can contribute to persistent signed order flow. Heterogeneous switching thresholds and opportunity volatility generate heterogeneous residence times, and renewal aggregation maps their execution-weighted tail into the decay of...