arXiv preprints from January 1, 2026 through September 9, 2026 — 02:30:30 EST
We express a family of basic cellular integrals over moduli spaces of curves explicitly in terms of multiple zeta values, answering a question of Brown. Moreover, we study a priori the weights appearing in these integrals and find a relation that expresses the odd-dimensional integrals in terms of the even-dimensional ones. We also...
Let $S_k$ be a sequence of compact hyperbolic surfaces of increasing volume which locally converges to a random rooted surface. We show that if the normalized sum of the reciprocal lengths of very short simple closed geodesics converges to 0, then the normalized logarithm of the determinant of the Laplacian of $S_k$ converges to a...
We mathematically axiomatise the stochastics of counterfactuals, by introducing two related frameworks, called counterfactual probability spaces and counterfactual causal spaces, which we collectively term counterfactual spaces. They are, respectively, probability and causal spaces whose underlying measurable spaces are products of...
This paper presents a safe feedback control framework for nonlinear control-affine systems with parametric uncertainty by leveraging adaptive dynamic programming (ADP) with barrier-state augmentation. The developed ADP-based controller enforces control invariance by optimizing a value function that explicitly penalizes the barrier...
We use contemporary mathematical notation to describe the method for determining the age of the ecclesiastical moon as mandated by pope Gregory XIII and elaborated in the book of Christopher Clavius \emph{Romani calendarii explicatio}. The algorithm is first introduced by using the tabular method employed by liturgical books such as...
Multiple polylogarithms are periods of variations of mixed Tate motives. Conjecturally, they deliver all such periods. We introduce deformations of multiple polylogarithms depending on a complex parameter h. We call them quantum polylogarithms. Their asymptotic expansion as h goes to 0 recovers multiple polylogarithms. The quantum...
In this short note we prove ``effective" geometric ergodicity (i.e a Perron-Frobenius theorem) for Markov chains in random mixing dynamical environment satisfying a random non-uniform version of the Doeblin condition. Effectivity here means that all the random variables involved in the random exponential rates are integrable with...
We present an approach to detecting Zariski pairs in conic line arrangements. Our method introduces a combinatorial condition that reformulates the tubular neighborhood homeomorphism criterion arising in the definition of Zariski pairs. This allows for a classification of arrangements into combinatorial equivalence classes, which we...
Advances in artificial intelligence (AI) and deep learning have raised concerns about its increasing energy consumption, while demand for deploying AI in mobile devices and machines at the edge is growing. Binary neural networks (BNNs) have recently gained attention as energy and memory efficient models suitable for resource...
We study Prym varieties of ramified (at precisely two points) double covers of smooth irreducible complex projectives curves that admit an automorphism of prime order $p>2$. Using Galois theory, we give an explicit constructions of Prym varieties that are not isomorphic to jacobians (even if one ignores the polarizations).
The method of imsets, introduced by Studený, provides a geometric and combinatorial description of conditional independence statements. Elementary conditional independence statements over a finite set of discrete random variables correspond to column vectors of a matrix generating a polyhedral cone, and the associated toric ideals...
This paper introduces a hybrid computational framework for the multi-frequency inverse source problem governed by the Helmholtz equation. By integrating a classical Fourier method with a deep convolutional neural network, we address the challenges inherent in sparse and noisy far-field data. The Fourier method provides a...
In a closed fibered hyperbolic 3-manifold M ,the inclusion of a fiber S, with S and M lifted to the universal covers, gives an exponentially distorted embedding of the hyperbolic plane into hyperbolic 3-space. Nevertheless, Cannon and Thurston showed that there is a map from the circle at infinity of the hyperbolic plane to the...
We study cocentral split abelian Hopf algebra extensions over an algebraically closed field of characteristic zero. The kernel is $k^V$ and the quotient is $kΓ$, where $V$ is finite abelian and $Γ$ acts on $V$. For a fixed action, we describe these extensions by crossed families of normalized group 2-cocycles on $V$, modulo changes of...
We propose a Jacobi-like relative value iteration (RVI) algorithm and a Gauss-Seidel-like implementation for the ergodic risk-sensitive control (ERSC) problem of a controlled discrete time Markov chain (DTMC) on a finite state space. Under the assumption that the DTMC is irreducible and recurrent under every stationary Markov policy,...
Let $k$ be a field, and let $X$ be a smooth projective surface over $k$. Fix a Lefschetz pencil on $X$, and let $C$ be its fibre at the generic point of $\mathbb P^1$. The closed immersion of $C$ in to $X_{k(t)}$ induces the Gysin homomorphism from the Jacobian $A$ of the curve $C$ to the Chow group $A_0(X_{k(t)})$ of $0$-cycles of...