arXiv preprints from January 1, 2026 through July 21, 2026 — 15:56:44 EST
In this paper, we introduce Mackey functors for a t.d.l.c. group and define the cohomological dimension of this group over the Mackey category. We then compare this dimension to the rational discrete cohomological dimension defined by Castellano and Weigel, as well as to the Bredon cohomological dimension of that t.d.l.c. group with...
We develop a data-driven algorithm for automatically selecting the regularisation parameter in Bayesian inversion under random tree Besov priors. One of the key challenges in Bayesian inversion is the construction of priors that are both expressive and computationally feasible. Random tree Besov priors, introduced in Kekkonen et al....
A preordered topological space is a topological space with a preordering. We exhibit a Stone-like duality for preordered topological spaces, Inspired by a similar duality for bitopological spaces, due to Jung-Moshier and Jakl, and by a duality for preordered sets due to Bonsangue, Jacobs and Kok.
Conditions are established for rank three partial isometries to have circular components contained in their Kippenhahn curves. In particular, such matrices with circular numerical ranges are described. It is also established that the Gau-Wang-Wu conjecture holds for matrices under consideration.
The \emph{Monge-Ampère} torsion deficit of an open, bounded convex set $Ω\subset\R^n$ of class $C^2$ is the normalized gap between the value of the torsion functional evaluated on $Ω$ and its value on the ball with the same $(n-1)$-quermassintegral as $Ω$. Using the technique of the \emph{shape derivative}, we prove that the ratio...
Polychromatic electromagnetic fields are typically expanded as integrals over monochromatic fields, such as plane waves, multipolar fields, or Bessel beams. However, monochromatic fields do not belong to the Hilbert space of free Maxwell fields, since their norms diverge. Moreover, the continuous frequency integrals involved in such...
In this note, we consider the so-called field-road diffusion model in a bounded domain, consisting of two parabolic PDEs posed on sets of different dimensions and coupled through (symmetric) nonlinear exchange terms. We propose a new and rather direct functional inequalities approach to prove the exponential decay of a relative...
We study the Brownian loop measure on hyperbolic surfaces for Brownian motion with a constant killing rate. We compute the mass of Brownian loops with killing in a free homotopy class and then relate the total mass of loops in all essential homotopy classes to the Selberg zeta function when the surface is geometrically finite. As an...
Two digraphs of order $n$ are said to pack if they can be found as edge-disjoint subgraphs of the complete digraph of order $n$. It is well established that if the sum of the sizes of the two digraphs is at most $2n-2$, then they pack, with this bound being sharp. However, it is sufficient for the size of the smaller digraph to be...
In this paper, we investigate the geodesic structure and the associated Kantorovich-type duality for a Benamou-Brenier-type transportation metric defined on the space of nonnegative measures over a finite reversible Markov chain. The metric is introduced through a dynamic formulation that combines transport and source costs along...
In this paper, we investigate the geometric properties associated with the $\mathfrak{g}$-stability of surfaces with boundary whose null expansion satisfies $Θ^{+} = h \geq 0$. First, we show that a $\mathfrak{g}$-stable hypersurface with free boundary admits a metric of positive scalar curvature with minimal boundary under suitable...
We investigate a Benamou--Brenier type transportation metric for nonnegative measures on a finite reversible Markov chain, which endows the space of measures with a Riemannian structure. Using this geometric framework, we identify a generalized heat equation with source as the gradient flow of the discrete entropy. Moreover, by means...
We show that given an $n$-vertex graph $G$ of diameter 3 we can decide if $G$ is $3$-colourable in time $2^{O(n^{2/3-\varepsilon})}$ for any $\varepsilon < 1/33$. This improves on the previous best algorithm of $2^{O((n\log n)^{2/3})}$ from Dębski, Piecyk and Rzążewski [Faster 3-coloring of small-diameter graphs, ESA 2021].
In this paper, we establish the non-abelian Hodge correspondence over compact Kähler spaces with Kawamata log terminal (klt) singularities as well as over their regular loci, thereby extending the result of Greb-Kebekus-Peternell-Taji for projective klt varieties to the context of compact Kähler klt spaces. The proof relies on two key...
In this paper, we introduce a generalization of Reproducing Kernel Banach Spaces (RKBS), which we term \emph{Generalized Reproducing Kernel Banach Spaces} (GRKBS). The motivation stems from recent results showing that classical fully connected neural networks can be understood as finite-dimensional subspaces of RKBS. Our...
We study period growth in co-context-free groups, giving general results and looking at specific examples such as Thompson groups $T$ and $V$ and the Houghton groups $H_m$. Along the way, we give a refined upper bound on the word metric in Thompson $V$, as well as efficient algorithms to determine if elements of $V$ are torsion, and...
In this study, we investigate the incompressible generalised Navier-Stokes-Voigt equations within a bounded domain $Ω\subset \mathbb{R}^d$, where $d \geq 2$. The governing momentum equation is expressed as: $$ \partial_t(\boldsymbol{v}- κΔ\boldsymbol{v}) + \nabla \cdot (\boldsymbol{v} \otimes \boldsymbol{v}) + \nabla π- ν\nabla...
The restless multi-armed bandit problem is a paradigmatic modeling framework for optimal dynamic priority allocation in stochastic models of wide-ranging applications that has been widely investigated and applied since its inception in a seminal paper by Whittle in the late 1980s. The problem has generated a vast and fast-growing...
In this work, we study projection-based model order reduction (MOR) for switched linear systems (SLS) in control form, where the projection matrices are obtained from the solutions of generalized Lyapunov equations (GLEs). We investigate how numerical inaccuracies in solving the GLEs propagate through the MOR process and impact the...
We provide a complete classification of quaternionic skew-Hermitian symmetric spaces, namely symmetric spaces that admit a torsion-free ${\rm SO}^{*}(2n){\rm Sp}(1)$-structure for arbitrary $n>1$. Moreover, we prove that any homogeneous quaternionic skew-Hermitian manifold is necessarily a symmetric space.
Several complexity measures such as degree, sparsity and multiplicative index for cryptographic functions including the Diffie-Hellman mapping and the discrete logarithm in a finite field have been studied in the literature. In 2022, Reis and Wang introduced another complexity measure, the additive index, of a self-mapping of a finite...
We show that a non-universal Polish group can induce a complete orbit equivalence relation, which answers a question of Sabok from \cite{OPENPROBLEMS}.
We propose analogs of the generalized MICZ-Kepler system on the three-dimensional sphere and the two-sheet hyperboloid. We construct their energy spectra and normalized wave functions and find that they depend on two quantum numbers, which suggests that the systems are minimally superintegrable.
The first-order optimality conditions of sparse bilinear least squares problems are studied. The so-called T-type and N-type stationary points for this problem are characterized in terms of tangent cone and normal cone in Bouligand and Clarke senses, and another stationarity concept called the coordinate-wise minima is introduced and...
This paper considers what we propose to call multi-gear bandits, which are Markov decision processes modeling a generic dynamic and stochastic project fueled by a single resource and which admit multiple actions representing gears of operation naturally ordered by their increasing resource consumption. The optimal operation of a...