Related papers: A diffusion generated method for computing Dirichl…
The geometrical diffraction theory, in the sense of Keller,is here reconsidered as an obstacle problem in the Riemannian geometry. The first result is the proof of the existence and the analysis of the main properties of the diffracted…
It is well known that algebro-geometric solutions of the KdV hierarchy are constructed from the Riemann theta functions associated with hyperelliptic curves, and that soliton solutions can be obtained by rational (singular) limits of the…
Subgraph matching is a core task in graph analytics, widely used in domains such as biology, finance, and social networks. Existing top-k diversified methods typically focus on maximizing vertex coverage, but often return results in the…
In this paper, we discuss the 2D convection-diffusion-reaction equation with variable smooth coefficients and the Dirichlet boundary condition on a complicated, thin, and curved domain. We propose the fourth-order compact FDM at every grid…
For $d\ge 1$, we construct a compact subset $K\subseteq \mathbb {R}^{d+1}$ containing a $d$-sphere of every radius between $1$ and $2$, such that for every $\delta\in (0,1)$, the $\delta$-neighbourhood of $K$ has Lebesgue measure $\lesssim…
While the mathematical foundations of score-based generative models are increasingly well understood for unconstrained Euclidean spaces, many practical applications involve data restricted to bounded domains. This paper provides a…
From a scalar field defined at the corner of a cube, an isosurface can be extracted using the Marching Cube algorithm. The isosurface separates the cell into two or more partial cells. A similar situation arises when an material interface…
Roughly speaking, the regular subspace of a Dirichlet form is also a regular Dirichlet form on the same state space. It inherits the same form of original Dirichlet form but possesses a smaller domain. What we are concerned in this paper…
A convenient technique for calculating completed topological tensor products of functional Frechet or DF spaces is developed. The general construction is applied to proving kernel theorems for a wide class of spaces of smooth and entire…
Starting with a transient irreducible diffusion process $X^0$ on a locally compact separable metric space $(D, d)$, one can construct a canonical symmetric reflected diffusion process $\bar X$ on a completion $D^*$ of $(D, d)$ through the…
We introduce the {\it diffusion $K$-means} clustering method on Riemannian submanifolds, which maximizes the within-cluster connectedness based on the diffusion distance. The diffusion $K$-means constructs a random walk on the similarity…
We consider the optimization problem of maximizing the $k$-th Laplacian eigenvalue, $\lambda_{k}$, over flat $d$-dimensional tori of fixed volume. For $k=1$, this problem is equivalent to the densest lattice sphere packing problem. For…
In this article, discrete variants of several results from vector calculus are studied for classical finite difference summation by parts operators in two and three space dimensions. It is shown that existence theorems for scalar/vector…
We use a dictionary between lattice point counting inside dilated d-dimensional ellipsoids (Euclidean counting) and counting of lifts of a closed horosphere that intersect a ball of increasing radius, to obtain two types of results.…
This work discusses the application of an affine reconstructed nodal DG method for unstructured grids of triangles. Solving the diffusion terms in the DG method is non-trivial due to the solution representations being piecewise continuous.…
This paper proposes a new method which builds a simplex based approximation of a $d-1$-dimensional manifold $M$ separating a $d$-dimensional compact set into two parts, and an efficient algorithm classifying points according to this…
Let $F\in \mathbb{K}[X, Y ]$ be a polynomial of total degree $D$ defined over a perfect field $\mathbb{K}$ of characteristic zero or greater than $D$. Assuming $F$ separable with respect to $Y$ , we provide an algorithm that computes the…
Cohesive subgraph mining in bipartite graphs becomes a popular research topic recently. An important structure k-bitruss is the maximal cohesive subgraph where each edge is contained in at least k butterflies (i.e., (2, 2)-bicliques). In…
In this paper we give explicit closed forms for the semi-reproducing kernels associated with thinplate spline interpolation on the sphere. Polyharmonic or thinplate splines for ${\mathbb R}^d$ were introduced by Duchon and have become a…
This paper introduces an efficient algorithm for persistence diagram computation, given an input piecewise linear scalar field $f$ defined on a $d$-dimensional simplicial complex $K$, with $d \leq 3$. Our work revisits the seminal algorithm…