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We introduce new zeta functions related to an endomorphism $\phi$ of a discrete group $\Gamma$. They are of two types: counting numbers of fixed ($\rho\sim \rho\circ\phi^n$) irreducible representations for iterations of $\phi$ from an…
Submodular function maximization has found a wealth of new applications in machine learning models during the past years. The related supermodular maximization models (submodular minimization) also offer an abundance of applications, but…
In this article, we consider the family of functions $f$ analytic in the unit disk $|z|<1$ with the normalization $f(0)=0=f'(0)-1$ and satisfying the condition $\big |\big (z/f(z)\big )^{2}f'(z)-1\big |<\lambda $ for some $0<\lambda \leq…
We introduce the Deletable Bloom filter (DlBF) as a new spin on the popular data structure based on compactly encoding the information of where collisions happen when inserting elements. The DlBF design enables false-negative-free deletions…
We introduce a new family of Schur functions $s_{\lambda/\mu;a,b}(x/y)$ that depend on two sets of variables and two sequences of parameters. These free fermionic Schur functions have a hidden symmetry between the two sets of parameters…
We introduce new families of cylindric symmetric functions as subcoalgebras in the ring of symmetric functions $\Lambda$ (viewed as a Hopf algebra) which have non-negative structure constants. Combinatorially these cylindric symmetric…
This paper presents the generalized formulations of fundamental schemes for efficient unconditionally stable implicit finite-difference time-domain (FDTD) methods. The fundamental schemes constitute a family of implicit schemes that feature…
The complete knowledge of a theory is encoded in its correlation functions. Thus non-perturbative effects, like confinement in QCD, is necessarily contained in these correlation functions. As a consequence, a number of confinement scenarios…
This paper proposes a new second-order symmetric algorithm for solving decoupled forward-backward stochastic differential equations. Inspired by the alternating direction implicit splitting method for partial differential equations, we…
Many examples of zeta functions in number theory and combinatorics are special cases of a construction in homotopy theory known as a decomposition space. This article aims to introduce number theorists to the relevant concepts in homotopy…
Zero-shot Learning (ZSL) aims to enable classifiers to identify unseen classes. This is typically achieved by generating visual features for unseen classes based on learned visual-semantic correlations from seen classes. However, most…
Planar functions are functions over a finite field that have optimal combinatorial properties and they have applications in several branches of mathematics, including algebra, projective geometry and cryptography. There are two relevant…
Derivative-free optimization (DFO) is the mathematical study of the optimization algorithms that do not use derivatives. One branch of DFO focuses on model-based DFO methods, where an approximation of the objective function is used to guide…
This paper presents a novel approach for synthesizing control barrier functions (CBFs) from high relative degree safety constraints: Rectified CBFs (ReCBFs). We begin by discussing the limitations of existing High-Order CBF approaches and…
Superintegrable systems of 2nd order in 3 dimensions with exactly 3-parameter potentials are intriguing objects. Next to the nondegenerate 4-parameter potential systems they admit the maximum number of symmetry operators but their symmetry…
This work presents mixed variational flows (MixFlows), a new variational family that consists of a mixture of repeated applications of a map to an initial reference distribution. First, we provide efficient algorithms for i.i.d. sampling,…
Zeroing neural networks (ZNNs) have demonstrated outstanding performance on time-varying optimization and control problems. Nonetheless, few studies are committed to illustrating the relationship among different ZNNs and the derivation of…
Most computational studies in chemistry and materials science are based on the use of density functional theory. Although the exact density functional is unknown, several density functional approximations (DFAs) offer a good balance of…
A new family of Gaussian-type SIGMA basis sets, termed reduced SIGMA basis sets, is introduced and preliminarily tested. Sharing the same composition as Dunning basis sets, they enhance performance by reducing linear dependencies in large…
Attempts to separate the power of classical and quantum models of computation have a long history. The ultimate goal is to find exponential separations for computational problems. However, such separations do not come a dime a dozen: while…