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Arbitrary harmonic functions as Bose--Einstein condensates

arXiv:2601.22883v1 Announce Type: new Abstract: We show that a suitable choice of boundary conditions for the Laplacian allows for the appearance of an an arbitrary...

Uncoupled Dirac-Yang-Mills Pairs on Closed Riemannian Spin Manifolds

arXiv:2601.22886v1 Announce Type: new Abstract: We study the Dirac-Yang-Mills equations on closed spin manifolds with a focus on uncoupled solutions, i.e. solutions for which the...

Grassmannian Geometry and Global Convergence of Variable Projection for Neural Networks

arXiv:2601.22897v1 Announce Type: new Abstract: Training deep neural networks and Physics-Informed Neural Networks (PINNs) often leads to ill-conditioned and stiff optimization problems. A key structural...

Neuroscience Engineering

Status Updating via Integrated Sensing and Communication: Freshness Optimisation

arXiv:2601.22901v1 Announce Type: new Abstract: This paper studies strategic design in an integrated sensing and communication (ISAC) architecture for status updating of remotely navigating agents....

Policy Space & Astronomy

Rigidity of circle polyhedra and hyperideal polyhedra: the tangency case

arXiv:2601.22903v1 Announce Type: new Abstract: We prove the global rigidity of proper triangulated convex hyperbolic circle polyhedra on the sphere $\mathbb{S}^2$. These circle polyhedra correspond...

Mathematics World News

Examples of finitely presented groups with strong fixed point properties and property (T)

arXiv:2601.22907v1 Announce Type: new Abstract: We construct a finitely presented group with property (T) which can not act on on reasonable spaces. Such group is...

Reducibility of self-maps in monoid and its related invariants

arXiv:2601.22908v1 Announce Type: new Abstract: Given a positive integer $k$, we investigate the $k$-redcibility of self-maps in the monoid $\AA^k(X\vee Y)$, consisting of self-maps that...

Psychology Policy

Feedback Control via Integrated Sensing and Communication: Uncertainty Optimisation

arXiv:2601.22912v1 Announce Type: new Abstract: This paper studies strategic design in an integrated sensing and communication (ISAC) architecture for feedback control of cyber-physical systems. We...

Policy Chemistry

Left Ehresmann monoids with a proper basis

arXiv:2601.22923v1 Announce Type: new Abstract: This article gives an abstract characterisation of a class of left Ehresmann monoids possessing certain universal properties. It is known...

Policy

Poset modules of the $0$-Hecke algebras of type $B$

arXiv:2601.22926v1 Announce Type: new Abstract: In 2001, Chow developed the theory of the $B_n$ posets $P$ and the type $B$ $P$-partition enumerators $K^B_P$. To provide...

Prescribed $T$-curvature flow on the four-dimensional unit ball

arXiv:2601.22934v1 Announce Type: new Abstract: In this paper, we study the prescribed $T$-curvature problem on the unit ball $\mathbb{B}^4$ of $\mathbb{R} ^4$ via the $T$-curvature...

Local Well-posedness and Blow-up for the Restricted Fourth-Order Prandtl Equation

arXiv:2601.22940v1 Announce Type: new Abstract: We prove local well-posedness and finite-time blow-up for a restricted fourth-order Prandtl equation posed on the half-line with clamped boundary...

Software Mathematics

Compact group Rohlin actions and $G$-kernels on von Neumann algebras

arXiv:2601.22941v1 Announce Type: new Abstract: We provide a new construction of a topological group model for the string group of a compact, simple, and simply-connected...

FNWoS: Fractional Neural Walk-on-Spheres Methods for High-Dimensional PDEs Driven by $\alpha$-stable L\'{e}vy Process on Irregular Domains

arXiv:2601.22942v1 Announce Type: new Abstract: In this paper, we develop a highly parallel and derivative-free fractional neural walk-on-spheres method (FNWoS) for solving high-dimensional fractional Poisson...

Neuroscience Mathematics

Persuasive Privacy

arXiv:2601.22945v1 Announce Type: new Abstract: We propose a novel framework for measuring privacy from a Bayesian game-theoretic perspective. This framework enables the creation of new,...

Cybersecurity Policy

On polynomial functors and polynomial comonads over infinity groupoids

arXiv:2601.22968v1 Announce Type: new Abstract: We show that single-variable polynomial functors over the category $\mathcal{S}$ of infinity groupoids, as defined by Gepner-Haugseng-Kock, are exactly colimits...

Periods of Ehrhart coefficients of rational polytopes

arXiv:2601.22992v1 Announce Type: new Abstract: Let $\mathcal{P} \subseteq \mathbb{R}^{n}$ be a polytope whose vertices have rational coordinates. By a seminal result of E. Ehrhart, the...

Policy

A Remark on Stability Conditions on Smooth Projective Varieties

arXiv:2601.22994v1 Announce Type: new Abstract: Let $X$ be a smooth projective variety over $\mathbb C$. In this paper, we prove that $\mathrm{D}^b(X)$, the bounded derived...

Policy

Baire-type properties of topological vector spaces

arXiv:2601.23008v1 Announce Type: new Abstract: Burzyk, Kli\'{s} and Lipecki proved that every topological vector space (tvs) $E$ with the property $(K)$ is a Baire space....

On the finiteness of prime trees and their relation to modular forms

arXiv:2601.23016v1 Announce Type: new Abstract: In this paper, we introduce the prime trees associated with a finite subset $P$ of the set of all prime...

The uniqueness theorem for Kasparov theory

arXiv:2601.23029v1 Announce Type: new Abstract: Answering a question of Carri\'on et al in their recent landmark paper on C*-algebra classification, we prove a general uniqueness...

Mathematics Energy

Breaking the Stochasticity Barrier: An Adaptive Variance-Reduced Method for Variational Inequalities

arXiv:2601.23034v1 Announce Type: new Abstract: Stochastic non-convex non-concave optimization, formally characterized as Stochastic Variational Inequalities (SVIs), presents unique challenges due to rotational dynamics and the...

Software Biology

Accelerated Inertial Gradient Algorithms with Vanishing Tikhonov Regularization

arXiv:2601.23035v1 Announce Type: new Abstract: In this paper, we study an explicit Tikhonov-regularized inertial gradient algorithm for smooth convex minimization with Lipschitz continuous gradient. The...