Research
Research
Research
Research
8,773+ open-access research outputs.
In 1967 Hajnal and Juh{\'a}sz showed that the cardinality of a first-countable Hausdorff space with the countable chain condition has cardinality at most $\mathfrak{c}$, the cardinality of the real li…
Hill functions, dominant in gene regulatory network modeling, carry fundamental limitations: at non-integer cooperativity exponents, routine when fitting dose-response data, derivatives diverge at the…
In this paper we propose a finite-dimensional and deterministic approach to the study of invariant sets of certain nonautonomous differential inclusions naturally arising in the context of random and …
Core-nilpotent endomorphisms over an arbitrary vector space form the largest subset of the ring of endomorphisms over that arbitrary vector space which admit a decomposition as sum of two endomorphism…
Behling, Bello-Cruz, Lara-Urdaneta, Oviedo, and Santos showed that the circumcentric direction $d$ of a finitely generated polyhedral cone $\KK\subset\RR^n$ admits an inscribed Euclidean ball of radiu…
In this note we give generalizations and prove 'minimalistic' refinements of the t-birational Section Conjecture (t-BSC), cf. [Be], by doing both: First, by extending the class of base fields over whi…
Optimization modeling underpins real-world decision-making in logistics, manufacturing, energy, and public services, but reliably solving such problems from natural-language requirements remains chall…
Let $K$ be an algebraically closed and complete non-archimedean and non-trivially valued field, and let $G$ be a reductive group scheme acting on a flat projective scheme $X$ defined over the base rin…
We establish a necessary condition for pseudoprimality and a sufficient condition for primality of Fermat numbers, based on a congruence involving the exponent $(F_n-1)/4$. Moreover, in connection wit…
This paper presents the mechatronic design, dynamic modeling, and experimental validation of a three-degree-of-freedom (3-DOF) micro parallel robot featuring a prismatic-spherical (3PS) topology actua…
We prove that the (suitably rescaled) moments of certain discrete measures on the unit interval, which are related to the numerical evaluation of zeta series with missing digits in radix $b$, are asym…
In Part I, we proved that a rational model for the fiberwise THH transfer of a map $f$ of fibrations over a base space is given by the Hochschild homology transfer of a cdga model of $f$. In this pape…
We introduce dilogarithm identities through a beta integral-based technique that we apply to construct new 3 and 6-term functional identities of the type $\sum r^{-1}_i L(X_i) \in \pi^2 \mathbf{Q}$. W…
The additive structure of $\mathbb{F}_1$-modules (in the sense of Segal's $\Gamma$-sets) differs fundamentally from that of abelian groups: addition is encoded through a family of $n$-ary hyper-operat…
In this paper, we study the moduli space of Higgs pairs, which can be considered as a generalization of holomorphic pairs. Higgs pairs are an example of quiver bundles. We introduce the notion of $\ta…
We show that for quasi-compact smooth rigid analytic spaces, the extension functor sends holonomic D-modules to coadmissible D-cap-modules which are of finite length as weakly holonomic D-cap-modules.…
We study a fixed-core absorption problem for regular induced subgraphs. A set is q-modular if all induced degrees are congruent modulo q. Given a q-modular witness A and a retained core U subset A, we…
Let $N$ be a finite set of cardinality $n$, and $a\in N$. A submodular function $f$ on $N$ with $f(a)=1$ is defined to be $a$-reduced if, for any decomposition $f=g+h$ into submodular functions where …
We prove lower bounds on learning the M\"obius or Liouville function with a variety of standard learning techniques, including kernel methods, noisy gradient methods, and correlational statistical que…
We study control systems on the tangent bundle of a smooth manifold induced by vertical lifts of vector fields. The Vertical dynamics acts exclusively along the fibers, leaving the base point unchange…
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