Institute of Mathematical Sciences

Curly Kakeya: The Hausdorff dimension of sets containing circles or line segments in many directions

In this paper, we establish a lower bound for the Hausdorff dimension of a set 𝐾 ⊂ ℝ 𝑛 that contains a dilated and translated copy of every meridian, that is, of every ( 𝑑 − 2 ) -dimensional sphere passing through the poles of 𝑆 𝑑 − 1 , a ( 𝑑 − 1 ) -dimensional sphere, with 3 ≤ 𝑑...

Kernel $$K$$-Means Clustering of Distributional Data

Abstract We consider the problem of clustering a sample of probability distributions from a random distribution on $$\mathbb R^d$$ R d . Our proposed partitioning method makes use of a symmetric, positive-definite kernel $$k$$ k and its associated reproducing kernel Hilbert space...

The Weak Banach–Saks Property for Hölder Spaces

ABSTRACT We investigate the weak Banach–Saks property in the setting of Hölder spaces over metric spaces. We show that, for every infinite metric space and every , the Hölder space fails to have the weak Banach–Saks property.

Spectrum of p‐adic linear differential equations II: Variation of the spectrum

Abstract This paper explores the spectrum of ‐adic linear differential equations, extending previous findings to quasi‐smooth Berkovich curves. It focuses on the relationship between the spectrum and the radii of convergence by investigating the continuity and variation of the sp...

Regularization of singular time-dependent Lagrangian systems

Abstract One approach to studying the dynamics of a singular Lagrangian system is to attempt to regularize it, that is, to find an equivalent and regular system. In the case of time-independent singular Lagrangians, an approach due to A. Ibort and J. Marín-Solano is to use the co...

Evolutionary Weighted Hodge Laplacian Descriptors for rs-fMRI Brain Networks

Abstract Complex biological networks often exhibit multiscale organization that is not fully characterized by pairwise edge weights or fixed graph summaries, motivating compact descriptors that retain both topological and spectral information. Here, we present an evolutionary wei...

Rainbow Directed Cycles of Order 4 in the Complete Biorientation of $$K_n$$

Let $$\overleftrightarrow {K_n}$$ be the complete biorientation of $$K_n$$ . Given a coloring of the arcs of $$\overleftrightarrow {K_n}$$ , a subdigraph D of $$\overleftrightarrow {K_n}$$ will be called rainbow if no two arcs of D receive the same color. For an integer n, let $$...

A new receptivity mechanism for the second-mode instability in hypersonic boundary layers

Direct numerical simulations of the flow over a compound delta-wing model reveal a novel receptivity mechanism for the second-mode instability in hypersonic boundary layers. This mechanism involves disturbances that propagate obliquely upward from the wall, interact with the shoc...

Learning in Lost-Sales Inventory Systems with Stochastic Lead Times and Random Supplies

Supply uncertainty, characterized by stochastic lead times and random supply quantities, has attracted increasing attention from academia, industries, and governments, particularly in the aftermath of the COVID-19 pandemic. In this paper, we consider the problem of managing lost-...

Cauchy identities for staircase matrices

Abstract The well‐known Cauchy identity expresses the product of terms for indexing entries of a rectangular ‐matrix as a sum over partitions of products of Schur polynomials: . Algebraically, this identity comes from the decomposition of the symmetric algebra of the space of rec...

Holographic is Hamiltonian, relatively

Abstract We show that a relative holographic energy coincides with the relative Hamiltonian energy.

Generative geospatial modelling with geometric algebra

Abstract The integration of data-driven and knowledge-driven approaches in generative geospatial modelling (GGM) is often hindered by their mathematical incompatibilities. Here, we propose a geometric algebra (GA)-based framework that employs a unified multi-vector representation...