Related papers: Orthogonal and Symplectic Black Box Groups, Revisi…
We compute the Chow-Witt rings of the classifying spaces for the symplectic and special linear groups. In the structural description we give, contributions from real and complex realization are clearly visible. In particular, the…
We describe a novel switching algorithm based on a ``reverse'' Monte Carlo method, in which the potential is stochastically modified before the system configuration is moved. This new algorithm facilitates a generalized formulation of…
Morphisms to finite semigroups can be used for recognizing omega-regular languages. The so-called strongly recognizing morphisms can be seen as a deterministic computation model which provides minimal objects (known as the syntactic…
Black-box optimization, a rapidly growing field, faces challenges due to limited knowledge of the objective function's internal mechanisms. One promising approach to address this is the Stochastic Order Oracle Concept. This concept, similar…
Multiple orthogonal polynomials are traditionally studied because of their connections to number theory and approximation theory. In recent years they were found to be connected to certain models in random matrix theory. In this paper we…
It is conjectured that the symplectic structure of space-time is superior to the metric one. Instead of the commonly adopted pseudo-orthogonal groups SO(1,d-1), d\ge4, the complex symplectic ones Sp(2l,C), l\ge1 are proposed as the local…
We develop a novel procedure for estimating the optimizer of general convex stochastic optimization problems of the form $\min_{x\in\mathcal{X}} \mathbb{E}[F(x,\xi)]$, when the given data is a finite independent sample selected according to…
We propose a Monte Carlo algorithm designed to simulate quantum as well as classical systems at equilibrium, bridging the algorithmic gap between quantum and classical thermal simulation algorithms. The method is based on a novel…
In an earlier book of Arthur, the endoscopic classification of representations of quasi-split orthogonal and symplectic groups was established. Later Mok gave that of quasi-split unitary groups. After that, Kaletha, Minguez, Shin, and White…
The circular orthogonal and circular symplectic ensembles are mapped onto free, non-hermitian fermion systems. As an illustration, the two-level form factors are calculated.
Any search or sampling algorithm for solution of inverse problems needs guidance to be efficient. Many algorithms collect and apply information about the problem on the fly, and much improvement has been made in this way. However, as a…
An improved algorithm is proposed for Monte Carlo methods to study fermion systems interacting with adiabatical fields. To obtain a weight for each Monte Carlo sample with a fixed configuration of adiabatical fields, a series expansion…
We show that certain orderable groups admit no isolated left orders. The groups we consider are cyclic amalgamations of a free group with a general orderable group, the HNN extensions of free groups over cyclic subgroups, and a particular…
Generalized rules for building and flipping clusters in the quantum Monte Carlo loop algorithm are presented for the XXZ-model in a uniform magnetic field along the Z-axis. As is demonstrated for the Heisenberg antiferromagnet it is…
In this paper, we consider the problem of deciding the existence of real solutions to a system of polynomial equations having real coefficients, and which are invariant under the action of the symmetric group. We construct and analyze a…
Constrained second-order convex optimization algorithms are the method of choice when a high accuracy solution to a problem is needed, due to their local quadratic convergence. These algorithms require the solution of a constrained…
We design new deterministic and randomized algorithms for computational problems in free solvable groups. In particular, we prove that the word problem and the power problem can be solved in quasi-linear time and the conjugacy problem can…
An algorithm for irreducible decomposition of representations of finite groups over fields of characteristic zero is described. The algorithm uses the fact that the decomposition induces a partition of the invariant inner product into a…
Statistical depth functions provide center-outward orderings in spaces of dimension larger than one, where a natural ordering does not exist. The numerical evaluation of such depth functions can be computationally prohibitive, even for…
A method based on multicanonical Monte Carlo is applied to the calculation of large deviations in the largest eigenvalue of random matrices. The method is successfully tested with the Gaussian orthogonal ensemble (GOE), sparse random…