相关论文: Fingerprints, lemniscates and quadratic differenti…

Two-dimensional almost-Riemannian structures are generalized Riemannian structures on surfaces for which a local orthonormal frame is given by a Lie bracket generating pair of vector fields that can become collinear. Generically, there are…

We show that the results we had obtained on diagonals of nine and ten parameters families of rational functions using creative telescoping, yielding modular forms expressed as pullbacked $ _2F_1$ hypergeometric functions, can be obtained,…

We extend the classical Bernstein technique to the setting of integro-differential operators. As a consequence, we provide first and one-sided second derivative estimates for solutions to fractional equations, including some convex fully…

We investigate the problem of numerical differentiation of bivariate functions from weighted Wiener classes using Chebyshev polynomial expansions. We develop and analyze a new version of the truncation method based on Chebyshev polynomials…

Neuroscientific studies of drawing-like movements usually analyze neural representation of either geometric (eg. direction, shape) or temporal (eg. speed) features of trajectories rather than trajectory's representation as a whole. This…

One of the main purposes of this article is to give functional equations and differential equations between Bernstein basis functions and generating functions of B-spline curves. Using these equations, very useful formulas containing the…

Mumford showed that Schottky subgroups of $PGL(2,K)$ give rise to certain curves, now called Mumford curves, over a non-Archimedean field K. Such curves are foundational to subjects dealing with non-Archimedean varieties, including…

Given a smooth cubic hypersurface $X$ over a finite field of characteristic greater than 3 and two generic points on $X$, we use a function field analogue of the Hardy-Littlewood circle method to obtain an asymptotic formula for the number…

Recent works have shown that generative models leave traces of their underlying generative process on the generated samples, broadly referred to as fingerprints of a generative model, and have studied their utility in detecting synthetic…

We propose a machine learning pipeline for forensic shoeprint pattern matching that improves on the accuracy and generalisability of existing methods. We extract 2D coordinates from shoeprint scans using edge detection and align the two…

Motivated by Lazer-Leach type results, we study the existence of periodic solutions for systems of functional-differential equations at resonance with an arbitrary even-dimensional kernel and linear deviating terms involving a general delay…

We prove the existence of classical solutions to the Dirichlet problem for a class of fully nonlinear elliptic equations of curvature type on Riemannian manifolds. We also derive new second derivative boundary estimates which allows us to…

We consider a plane polynomial vector field $P(x,y)dx+Q(x,y)dy$ of degree $m>1$. To each algebraic invariant curve of such a field we associate a compact Riemann surface with the meromorphic differential $\omega=dx/P=dy/Q$. The asymptotic…

We develop a set of techniques that enable us to effectively recover Besov rough analysis from p-variation rough analysis. Central to our approach are new metric groups, in which some objects in rough path theory that have been previously…

We study the Schlesinger system of partial differential equations in the case when the unknown matrices of arbitrary size $(p\times p)$ are triangular and the eigenvalues of each matrix form an arithmetic progression with a rational…

Authentication of individuals via palmprint based biometric system is becoming very popular due to its reliability as it contains unique and stable features. In this paper, we present a novel approach for palmprint recognition and its…

We start discussing basic properties of Lie groupoids and Lie pseudo-groups in view of applying these techniques to the analysis of Jordan-H\"older resolutions and the subsequent integration of partial differential equations which is the…

The $\varepsilon$-form of a system of differential equations for Feynman integrals has led to tremendeous progress in our abilities to compute Feynman integrals, as long as they fall into the class of multiple polylogarithms. It is…

In this work, we present a method to generate a configurational level fingerprint for polymers using the Bead-Spring-Model. Unlike some of the previous fingerprinting approaches that employ monomer-level information where atomistic…

We survey solvability of equations in wreath products of groups, and prove that the quadratic diophantine problem is solvable in wreath products of Abelian groups. We consider the related question of determining commutator width, and prove…