Related papers: Computing symmetries and recursion operators of ev…
In this paper, we consider a new nonlocal approximation to the linear Stokes system with periodic boundary conditions in two and three dimensional spaces . A relaxation term is added to the equation of nonlocal divergence free equation,…
We extend the symbolic representation to the ring of N=1 supersymmetric differential polynomials, and demonstrate that operations on the ring, such as the super derivative, Frechet derivative and super commutator, can be carried out in the…
We present a comprehensive analysis of an algorithm for evaluating high-dimensional polynomials that are invariant under permutations and rotations. The key bottleneck is the contraction of a high-dimensional symmetric and sparse tensor…
In this short paper, we characterize symmetric locality. In designing algorithms, compilers, and systems, data movement is a common bottleneck in high-performance computation, in which we improve cache and memory performance. We study a…
We study the numerical simulation of supersymmetric models having a local Nicolai map. The mapping can be regarded as a stochastic equation and its numerical integration provides an algorithm for the simulation of the original model. In…
We discuss a microscopic framework for phenomenological boson-fermion models of nuclear structure based on the U($n/m$) type of superalgebras. The generalized Dyson mapping of fermion collective superalgebras provides a basis to do so and…
We pursue the study of one-dimensional symmetry of solutions to nonlinear equations involving nonlocal operators. We consider a vast class of nonlinear operators and in a particular case it covers the fractional $p-$Laplacian operator. Just…
Symmetries in mixed-integer (nonlinear) programs (MINLP), if not handled appropriately, are known to negatively impact the performance of (spatial) branch-and-bound algorithms. Usually one thus tries to remove symmetries from the problem…
Let $\mathbf{B}$ be a basis for an $r$-dimensional algebra $A$ over a field or commutative ring with unity. The semifusions of $\mathbf{B}$ are the partitions of $\mathbf{B}$ whose characteristic functions form the basis of a subalgebra of…
In this paper we develop proximal methods for statistical learning. Proximal point algorithms are useful in statistics and machine learning for obtaining optimization solutions for composite functions. Our approach exploits closed-form…
We introduce polynomial couplings, a generalization of probabilistic couplings, to develop an algorithm for the computation of equivalence relations which can be interpreted as a lifting of probabilistic bisimulation to polynomial…
Application of nonparametric and semiparametric regression techniques to high-dimensional time series data has been hampered due to the lack of effective tools to address the ``curse of dimensionality.'' Under rather weak conditions, we…
In this paper, we present a cluster algorithm for the numerical simulations of non-additive hard-core mixtures. This algorithm allows one to simulate and equilibrate systems with a number of particles two orders of magnitude larger than…
An algorithm is presented for the computation of the topology of a non-reduced space curve defined as the intersection of two implicit algebraic surfaces. It computes a Piecewise Linear Structure (PLS) isotopic to the original space curve.…
A computationally efficient method to solve non-convex programming problems with linear equality constraints is presented. The proposed method is based on a recursively feasible and descending sequential convex programming procedure proven…
We consider a framework for the construction of iterative schemes for operator equations that combine low-rank approximation in tensor formats and adaptive approximation in a basis. Under fairly general assumptions, we obtain a rigorous…
In this paper, we study a new model of nonlocal geometric equations which appears in tomographic reconstruction when using the level-set method. We treat two additional difficulties which make the work original. On one hand, the level lines…
Model reduction of large nonlinear systems often involves the projection of the governing equations onto linear subspaces spanned by carefully-selected modes. The criteria to select the modes relevant for reduction are usually…
We develop new adaptive algorithms for temporal integration of nonlinear evolution equations on tensor manifolds. These algorithms, which we call step-truncation methods, are based on performing one time step with a conventional…
In geometry of nonlinear partial differential equations, recursion operators that act on symmetries of an equation $\mathcal{E}$ are understood as B\"{a}cklund auto-transformations of the equation $\mathcal{TE}$ tangent to $\mathcal{E}$. We…