Related papers: One-Way Functions and Polynomial Time Dimension
Distribution of loops in a one-dimensional random walk (RW), or, equivalently, neutral segments in a sequence of positive and negative charges is important for understanding the low energy states of randomly charged polymers. We investigate…
We study a numerical method to compute probability density functions of solutions of stochastic differential equations. The method is sometimes called the numerical path integration method and has been shown to be fast and accurate in…
This paper presents the novel `uniqueness tree' algorithm, as one possible method for determining whether two finite, undirected graphs are isomorphic. We prove that the algorithm has polynomial time complexity in the worst case, and that…
In this work, we continue the line of research on the complexity of distributions (Viola, Journal of Computing 2012), and study samplers defined by low degree polynomials. An $n$-tuple $P = (P_1,\dots, P_n)$ of functions $P_i \colon…
We establish a connection between continuous-variable quantum computing and high-dimensional integration by showing that the outcome probabilities of continuous-variable instantaneous quantum polynomial (CV-IQP) circuits are given by…
We develop a formal framework for the behavioral comparison of linear systems across different time domains. We accomplish this by introducing the notion of system interpolation, which determines whether the input-state trajectories of a…
A continuous selection of polynomial functions is a continuous function whose domain can be partitioned into finitely many pieces on which the function coincides with a polynomial. Given a set of finitely many polynomials, we show that…
Consider an $s$-dimensional function being evaluated at $n$ points of a low discrepancy sequence (LDS), where the objective is to approximate the one-dimensional functions that result from integrating out $(s-1)$ variables. Here, the…
We study approximations of the partition function of dense graphical models. Partition functions of graphical models play a fundamental role is statistical physics, in statistics and in machine learning. Two of the main methods for…
We consider various notions of holomorphic extendability of complex valued functions defined on subsets of $\mathbf C^n$, including one-sided extendability. We show that in the relevant function spaces, these phenomena of holomorphic…
We consider the statistical properties of the gravitational field F in an infinite one-dimensional homogeneous Poisson distribution of particles, using an exponential cut-off of the pair interaction to control and study the divergences…
Recently, Stull [18], [17] resolved a long-standing open problem posed by Lutz, on whether the set of effective Hausdorff dimensions of points on a straight line in $\mathbb{R}^2$ -- the effective dimension spectrum of the line -- contains…
In this article, we close a gap in the literature by proving existence of invariant measures for reflected SPDEs with only one reflecting barrier. This is done by arguing that the sequence (u(t, .)) is tight in the space of probability…
We consider the distribution of free path lengths, or the distance between consecutive bounces of random particles, in an n-dimensional rectangular box. If each particle travels a distance R, then, as R tends to infinity the free path…
Special bases of orthogonal polynomials are defined, that are suited to expansions of density and potential perturbations under strict particle number conservation. Particle-hole expansions of the density response to an arbitrary…
In this paper, we first consider the graph of $(F_1,F_{2},\cdots,F_{n})$ on $\overline{\mathbb{D}}^{n},$ where $F_{j}(z)=\bar{z}^{m_{j}}_{j}+R_{j}(z),j=1,2,\cdots,n,$ which has non-isolated CR-singularities if $m_{j}>1$ for some…
A famous result due to Ko and Friedman (1982) asserts that the problems of integration and maximisation of a univariate real function are computationally hard in a well-defined sense. Yet, both functionals are routinely computed at great…
A constructive version of Hausdorff dimension is developed using constructive supergales, which are betting strategies that generalize the constructive supermartingales used in the theory of individual random sequences. This constructive…
Polynomial approximations to boolean functions have led to many positive results in computer science. In particular, polynomial approximations to the sign function underly algorithms for agnostically learning halfspaces, as well as…
We investigate $(2+1)$-dimensional discretized directed polymers in Gaussian random media. By numerically calculating the probability distribution function of overlap between two independent and identical systems on a common random…