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In this article we prove lower and upper bounds for class numbers of algebraic curves defined over finite fields. These bounds turn out to be better than most of the previously known bounds obtained using combinatorics. The methods used in…
A numerical scheme for computing arc-length parametrized curves of low bending energy that are confined to convex domains is devised. The convergence of the discrete formulations to a continuous model and the unconditional stability of an…
At finite N the number of restricted Schur polynomials is greater than or equal to the number of generalized restricted Schur polynomials. In this note we study this discrepancy and explain its origin. We conclude that, for quiver gauge…
We establish a sharp adjoint Fourier restriction inequality for the end-point Tomas-Stein restriction theorem on the circle under a certain arithmetic constraint on the support set of the Fourier coefficients of the given function. Such…
Given n general points p_1, p_2,..., p_n \in P^r, it is natural to ask whether there is a curve of given degree d and genus g passing through them; by counting dimensions a natural conjecture is that such a curve exists if and only if \[n…
In this work we deal with the problem of support estimation under shape restrictions. The shape restriction we deal with is an extension of the notion of convexity named alpha-convexity. Instead of assuming, as in the convex case, the…
The writhe of a space curve fragment is considered for various boundary conditions. An expression for the writhe as a function of arclength for an arbitrary space curve is obtained. The formula is built on the base of closing the tangent…
The work of this paper is devoted to obtaining strong laws for intermediately trimmed sums of random variables with infinite means. Particularly, we provide conditions under which the intermediately trimmed sums of independent but not…
The van der Geer-van der Vlugt curves are Artin-Schreier coverings of the affine line defined by linearized polynomials over finite fields. We give several criteria for them to be maximal or minimal, i.e. attaining the upper or lower bound…
Shape constraints in nonparametric regression provide a powerful framework for estimating regression functions under realistic assumptions without tuning parameters. However, most existing methods$\unicode{x2013}$except additive…
The goal of the paper is to study the angle between two curves in the framework of metric (and metric measure) spaces. More precisely, we give a new notion of angle between two curves in a metric space. Such a notion has a natural interplay…
A principal curve serves as a powerful tool for uncovering underlying structures of data through 1-dimensional smooth and continuous representations. On the basis of optimal transport theories, this paper introduces a novel principal curve…
We establish Gaussian limits for general measures induced by binomial and Poisson point processes in d-dimensional space. The limiting Gaussian field has a covariance functional which depends on the density of the point process. The general…
We propose a general method for optimization with semi-infinite constraints that involve a linear combination of functions, focusing on the case of the exponential function. Each function is lower and upper bounded on sub-intervals by…
We explain how the maximum energy of the Quantum MaxCut, XY, and EPR Hamiltonians on a graph $G$ are related to the spectral radii of the token graphs of $G$. From numerical study, we conjecture new bounds for these spectral radii based on…
This paper is devoted to the theoretical and numerical investigation of an augmented Lagrangian method for the solution of optimization problems with geometric constraints. Specifically, we study situations where parts of the constraints…
We use techniques from algebraic and extremal combinatorics to derive upper bounds on the number of independent sets in several (hyper)graphs arising from finite geometry. In this way, we obtain asymptotically sharp upper bounds for partial…
We give a combinatorial description of closed curves on oriented surfaces in terms of certain permutations, called charts. We describe automorphisms of curves in terms of charts and compute the total number of curves counted with…
We investigate the properties of a fairly large class of boundary conditions for the linearised Einstein equations in the Riemannian setting, ones which generalise the linearised counterpart of boundary conditions proposed by Anderson.…
The approximation of probability measures on compact metric spaces and in particular on Riemannian manifoldsby atomic or empirical ones is a classical task in approximation and complexity theory with a wide range of applications. Instead of…