Related papers: Artin approximation compatible with a change of va…
Several construction methods for rational approximations to functions of one real variable are described in the present paper; the computational results that characterize the comparative accuracy of these methods are presented; an effect of…
Ordinary Differential Equations are generally too complex to be solved analytically. Approximations thereof can be obtained by general purpose numerical methods. However, even though accurate schemes have been developed, they remain…
A large body of work has demonstrated that parameterized artificial neural networks (ANNs) can efficiently describe ground states of numerous interesting quantum many-body Hamiltonians. However, the standard variational algorithms used to…
This paper is concerned with complexity theoretic aspects of a general formulation of quantum game theory that models strategic interactions among rational agents that process and exchange quantum information. In particular, we prove that…
In this technical note, we introduce and analyze AWNN: an adaptively weighted nearest neighbor method for performing matrix completion. Nearest neighbor (NN) methods are widely used in missing data problems across multiple disciplines such…
Nash equilibrium is one of the most influential solution concepts in game theory. With the development of computer science and artificial intelligence, there is an increasing demand on Nash equilibrium computation, especially for Internet…
We introduce and study on examples a notion of the Artin shape for a motive related to a projective homogenous variety. We apply it to the problem of finding the complete motivic decomposition of the variety. Our examples cover unitary…
The preferences of players in non-cooperative games represent their choice in the set of available options, which meet the completeness property if players are able to compare any pair of available options. In the existing literature, the…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
A method is suggested for treating those complicated physical problems for which exact solutions are not known but a few approximation terms of a calculational algorithm can be derived. The method permits one to answer the following rather…
Solutions of an optimization problem are sensitive to changes caused by approximations or parametric perturbations, especially in the nonconvex setting. This paper shows that solutions of substitute problems, constructed from Rockafellian…
We consider approximation problems for a special space of d variate functions. We show that the problems have small number of active variables, as it has been postulated in the past using concentration of measure arguments. We also show…
A new method to represent and approximate rotation matrices is introduced. The method represents approximations of a rotation matrix $Q$ with linearithmic complexity, i.e. with $\frac{1}{2}n\lg(n)$ rotations over pairs of coordinates,…
In this paper, we investigate the convergence of solutions of a stochastic representation of the three-dimensional Navier-Stokes equations to those of their primitive equations counterpart. Our analysis covers both weak and strong…
Finite differences have been widely used in mathematical theory as well as in scientific and engineering computations. These concepts are constantly mentioned in calculus. Most frequently-used difference formulas provide excellent…
Approximation algorithms for classical constraint satisfaction problems are one of the main research areas in theoretical computer science. Here we define a natural approximation version of the QMA-complete local Hamiltonian problem and…
This paper provides a numerical approach for solving the linear stochastic Volterra integral equation using Walsh function approximation and the corresponding operational matrix of integration. A convergence analysis and error analysis of…
In this paper, we first describe a matricial Newton-type algorithm designed to solve the multivariable spectrum approximation problem. We then prove its global convergence. Finally, we apply this approximation procedure to multivariate…
Let $\mathcal{X} \to Y$ be a birational map from a smooth Artin stack to a (possibly singular) variety. We prove a change of variables formula that relates motivic integrals over arcs of $Y$ to motivic integrals over arcs of $\mathcal{X}$.…
We study Nash implementation by stochastic mechanisms, and provide a surprisingly simple full characterization, which is in sharp contrast to the classical, albeit complicated, full characterization in Moore and Repullo (1990).