Related papers: A diffusion generated method for computing Dirichl…
Symbolic regression refers to the task of finding a closed-form mathematical expression to fit a set of data points. Genetic programming based techniques are the most common algorithms used to tackle this problem, but recently,…
We present a thorough tight-binding analysis of the band structure of a wide variety of lattices belonging to the class of honeycomb and Kagome systems including several mixed forms combining both lattices. The band structure of these…
We introduce diffusions on a space of interval partitions of the unit interval that are stationary with the Poisson-Dirichlet laws with parameters $(\alpha,0)$ and $(\alpha,\alpha)$. The construction has two steps. The first is a general…
We study "distance spheres": the set of points lying at constant distance from a fixed arbitrary subset $K$ of $[0,1]^d$. We show that, away from the regions where $K$ is "too dense" and a set of small volume, we can decompose $[0,1]^d$…
We point out that a proper use of the Hoeffding--ANOVA decomposition for symmetric statistics of finite urn sequences, previously introduced by the author, yields a decomposition of the space of square-integrable functionals of a…
This work is concerned with the Dirac points for the honeycomb lattice with impenetrable obstacles arranged periodically in a homogeneous medium. We consider both the Dirichlet and Neumann eigenvalue problems and prove the existence of…
We study Hilbert schemes of points on a smooth projective Calabi-Yau 4-fold $X$. We define $\mathrm{DT}_4$ invariants by integrating the Euler class of a tautological vector bundle $L^{[n]}$ against the virtual class. We conjecture a…
We construct a recurrent diffusion process with values in the space of probability measures over an arbitrary closed Riemannian manifold of dimension $d\ge 2$. The process is associated with the Dirichlet form defined by integration of the…
We consider a multivariate version of the so-called Lancaster problem of characterizing canonical correlation coefficients of symmetric bivariate distributions with identical marginals and orthogonal polynomial expansions. The marginal…
In the d dimensional Euclidean space, any set of n+1 independent random points, uniformly distributed in the interior of a unit ball of center O, determines almost surely a circumsphere of center C and of radius R, with n positive and less…
A k-dissimilarity map on a finite set X is a function D : X \choose k \rightarrow R assigning a real value to each subset of X with cardinality k, k \geq 2. Such functions, also sometimes known as k-way dissimilarities, k-way distances, or…
We propose a diffusion-based algorithm for separating the inter and outer layer surfaces from double-layered point clouds, particularly those exhibiting the "double surface artifact" caused by truncation in Truncated Signed Distance…
In this paper, we derive explicit sharp two-sided estimates of the Dirichlet heat kernels for a class of symmetric subordinate diffusion processes with diffusive components in $C^{1, \alpha}(\alpha\in (0, 1])$ open sets in $\mathbb R^d$…
We introduce topological prismatoids, a combinatorial abstraction of the (geometric) prismatoids recently introduced by the second author to construct counter-examples to the Hirsch conjecture. We show that the `strong $d$-step Theorem'…
Given a maximal geodesic lamination $\lambda$ on a closed oriented surface $S$ of genus $g$, the space of $d$-pleated surfaces with pleating locus $\lambda$ is an open subset of $\mathrm{Hom}(\pi_1(S),\mathsf{PGL}_d(\mathbb{C}))$ obtained…
We construct symmetric self-similar diffusions with sub-Gaussian heat kernel estimates on two types of polygon carpets, which are natural generalizations of planner Sierpinski carpets (SC). The first ones are called perfect polygon carpets…
This paper proposes a new Helmholtz decomposition based windowed Green function (HD-WGF) method for solving the time-harmonic elastic scattering problems on a half-space with Dirichlet boundary conditions in both 2D and 3D. The Helmholtz…
In this work we determine the wavefront set of certain eigendistributions of the Laplace-Beltrami operator on the de Sitter space. Let G = SO_{1,n}(R)_e be the connected component of identity of Lorentz group and let H = SO_{1,n-1}(R)_e, a…
Given five points in a three-dimensional euclidean space, one can consider five tetrahedra, using those points as vertices. We present a pentagon-like formula containing the product of three volumes of those tetrahedra in its l.h.s. and the…
Equilateral triangle-shaped graphene nanoislands with a lateral dimension of $n$ benzene rings are known as $[n]$triangulenes. Individual $[n]$triangulenes are open-shell molecules, with single-particle electronic spectra that host $n-1$…