Related papers: Complexity of Path-Following Methods for the Eigen…
We consider the problem of finding a Hamiltonian path with precedence constraints in the form of a partial order on the vertex set. This problem is known as Partially Ordered Hamiltonian Path Problem (POHPP). Here, we study the complexity…
Large-scale eigenvalue problems arise in various fields of science and engineering and demand computationally efficient solutions. In this study, we investigate the subspace approximation for parametric linear eigenvalue problems, aiming to…
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…
Maximum a posteriori (MAP) estimation, like all Bayesian methods, depends on prior assumptions. These assumptions are often chosen to promote specific features in the recovered estimate. The form of the chosen prior determines the shape of…
We propose an approach to compute inner and outer-approximations of the sets of values satisfying constraints expressed as arbitrarily quantified formulas. Such formulas arise for instance when specifying important problems in control such…
This paper explores topological complexity in the finite equivariant setting. We first define and study an equivariant version of Tanaka's combinatorial complexity for finite topological spaces. We explore the relationships between this…
Path analysis is a model class of structural equation modeling (SEM), which it describes causal relations among measured variables in the form of a multiple linear regression. This paper presents two estimation formulations, one each for…
We show how polynomial path orders can be employed efficiently in conjunction with weak innermost dependency pairs to automatically certify polynomial runtime complexity of term rewrite systems and the polytime computability of the…
We investigate the use of piecewise linear systems, whose coefficient matrix is a piecewise constant function of the solution itself. Such systems arise, for example, from the numerical solution of linear complementarity problems and in the…
We extend path analysis by giving sufficient conditions for computing the partial covariance of two random variables from their covariance. This is specifically done by correcting the covariance with the product of some partial variance…
Given two real symmetric matrices, their eigenvalue configuration is the relative arrangement of their eigenvalues on the real line. In this paper, we consider the following problem: given two parametric real symmetric matrices and an…
A new path integral approach of quantum gravity based on relational variables and quantum test objects is presented. We take as a basic variables the squared invariant distance. This invariant quantity is technically simpler to work with…
Localization is a characteristic phenomenon of space-inhomogeneous quantum walks in one dimension, where particles remain localized around their initial position. The existence of eigenvalues of time evolution operators is a necessary and…
We study the classical problem of computing geometric thickness, i.e., finding a straight-line drawing of an input graph and a partition of its edges into as few parts as possible so that each part is crossing-free. Since the problem is…
Given a satisfiable instance of 1-in-3 SAT, it is NP-hard to find a satisfying assignment for it, but it may be possible to efficiently find a solution subject to a weaker (not necessarily Boolean) predicate than `1-in-3'. There is a…
This paper investigates a path-following method inspired by the semismooth$^*$ approach for solving algebraic inclusions, with a primary emphasis on the role of uniform subregularity. Uniform subregularity is crucial for ensuring the…
The fractional Sturm-Liouville eigenvalue problem appears in many situations, e.g., while solving anomalous diffusion equations coming from physical and engineering applications. Therefore to obtain solutions or approximation of solutions…
We present a method to approximate pairwise distance on a graph, having an amortized sub-linear complexity in its size. The proposed method follows the so called heat method due to Crane et al. The only additional input are the values of…
The method of characteristics is a key tool for studying consistency of equations of motion; it allows issues such as predictability, maximal propagation speed, superluminality, unitarity and acausality to be addressed without requiring…
We analyze the behavior of a quantum system described by a one-dimensional asymmetric potential consisting of a step plus a harmonic barrier. We solve the eigenvalue equation by the integral representation method, which allows us to…