Related papers: Boundary complexity and surface entropy of 2-multi…
The Random Permutation Set (RPS) is a new type of set proposed recently, which can be regarded as the generalization of evidence theory. To measure the uncertainty of RPS, the entropy of RPS and its corresponding maximum entropy have been…
We present a spectrally-accurate scheme to turn a boundary integral formulation for an elliptic PDE on a single unit cell geometry into one for the fully periodic problem. Applications include computing the effective permeability of…
Asymptotically tight lower bounds are derived for the Input/Output (I/O) complexity of a class of dynamic programming algorithms including matrix chain multiplication, optimal polygon triangulation, and the construction of optimal binary…
The Shifted Boundary Method (SBM) trades some part of the burden of body-fitted meshing for increased algebraic complexity. While the resulting linear systems retain the standard $\mathcal{O}(h^{-2})$ conditioning of second-order operators,…
We show that the values of entropies of multidimensional shifts of finite type (SFTs) are characterized by a certain computation-theoretic property: a real number $h\geq 0$ is the entropy of such an SFT if and only if it is right…
Boundary integral equations are an efficient and accurate tool for the numerical solution of elliptic boundary value problems. The solution is expressed as a layer potential; however, the error in its evaluation grows large near the…
Error bounds have been studied for more than seventy years, beginning with the seminal result of Hoffman (1952) [{\it J. Res. Natl. Bur. Standards}, 49 (1952), 263--265], which establishes an upper bound for the distance from an arbitrary…
Interfacial Stokes flow can be efficiently computed using the Boundary Integral Equation method. In 3D, the fluid velocity at a target point is given by a 2D surface integral over all interfaces, thus reducing the dimension of the problem.…
Characterization of entropy functions is of fundamental importance in information theory. By imposing constraints on their Shannon outer bound, i.e., the polymatroidal region, one obtains the faces of the region and entropy functions on…
Performing highly accurate simulations of droplet systems is a challenging problem. This is primarily due to the interface dynamics which is complicated further by the addition of surfactants. This paper presents a boundary integral method…
Threshold automata are a formalism for modeling and analyzing fault-tolerant distributed algorithms, recently introduced by Konnov, Veith, and Widder, describing protocols executed by a fixed but arbitrary number of processes. We conduct…
In this paper, we consider a compact Riemannian manifold with boundary, endowed with a magnetic potential $\alpha$ and a potential $U$. For brevity, this type of systems are called $\MP$-systems. On simple $\MP$-systems, we consider both…
Let $N$ be a compact, connected, nonorientable surface of genus $g$ with $n$ boundary components with $g \geq 5$, $n \geq 0$. Let $\mathcal{T}(N)$ be the two-sided curve complex of $N$. If $\lambda :\mathcal{T}(N) \rightarrow…
We show that the complexity of the Markov bases of multidimensional tables stabilizes eventually if a single table dimension is allowed to vary. In particular, if this table dimension is beyond a computable bound, the Markov bases consist…
The System of Linear Equations Problem (SLEP) is specified by a complex invertible matrix $A$, the condition number $\kappa$ of $A$, a vector $b$, a Hermitian matrix $M$ and an accuracy $\epsilon$, and the task is to estimate $x^\dagger…
In the noisy query model, the (binary) return value of every query (possibly repeated) is independently flipped with some fixed probability $p \in (0, 1/2)$. In this paper, we obtain tight bounds on the noisy query complexity of several…
Genome rearrangements are events in which large blocks of DNA exchange pieces during evolution. The analysis of such events is a tool for understanding evolutionary genomics, based on finding the minimum number of rearrangements to…
The immersed boundary (IB) method has been used as a means to simulate fluid-membrane interactions in a wide variety of biological and engineering applications. Although the numerical convergence of the method has been empirically verified,…
We consider fundamental algorithmic number theoretic problems and their relation to a class of block structured Integer Linear Programs (ILPs) called $2$-stage stochastic. A $2$-stage stochastic ILP is an integer program of the form $\min…
A numerical algorithm to compute the topological entropy of multimodal maps is proposed. This algorithm results from a closed formula containing the so-called min-max symbols, which are closely related to the kneading symbols. Furthermore,…