Related papers: The Boolean SATisfiability Problem and the orthogo…

We consider the group isomorphism problem: given two finite groups G and H specified by their multiplication tables, decide if G and H are isomorphic. The n^(log n) barrier for group isomorphism has withstood all attacks --- even for the…

We discuss some geometrical properties of the underlying N=2 geometry which encompasses some low--energy aspects of N=1 orientifolds as well as four dimensional N=2 Lagrangians including bulk and open string moduli.In the former case we…

In this paper we introduce a new approach to variational problems on the space Riem(M^n) of Riemannian structures (i.e. isometry classes of Riemannan metrics) on any fixed compact manifold M^n of dimension n >= 5. This approach often…

This paper consists of two related parts. In the first part we give a self-contained proof of homological stability for the spaces C_n(M;X) of configurations of n unordered points in a connected open manifold M with labels in a…

We discuss the wellposedness of the Neumann problem on a half-space for the Kohn-Laplacian in the Heisenberg group. We then construct the Neumann function and explicitly represent the solution of the associated inhomogeneous problem.

In 1999 Chas and Sullivan showed that the homology of the free loop space of an oriented manifold admits the structure of a Batalin-Vilkovisky algebra. In this paper we give a direct description of this Batalin-Vilkovisky algebra in the…

We define and study the complexity of robust polynomials for Boolean functions and the related fault-tolerant quantum decision trees, where input bits are perturbed by noise. We compare several different possible definitions. Our main…

We give a unified treatment to optimization problems that can be expressed in the form of nonnegative-real-weighted Boolean constraint satisfaction problems. Creignou, Khanna, Sudan, Trevisan, and Williamson studied the complexity of…

We construct new families of two-ended $O(m)\times O(n)$-invariant solutions to the Allen- Cahn equation \Delta u+u-u3=0 in $\mathbb{R}^{N+1}$, with $N\ge 7$, whose zero level sets diverge logarithmically from the Lawson cone at infinity.…

Let $G$ be a finite group. The aim of this paper is to study the number of solutions $S\subseteq G$ of the equation $\mho^{\{n\}}(S)=L$, where $L$ is a non-empty subset of $G$, $n$ is a positive integer and $\mho^{\{n\}}(S)=\{ s^n \ | \…

We consider a class of homogeneous manifolds over a simple Lie group which appears in the problem of classification of homogeneous manifolds with reductive subgroups of maximal rank as stabilizer of a point. We prove that any manifold of…

We consider the algebra of invariants of $d$-tuples of $n\times n$ matrices under the action of the orthogonal group by simultaneous conjugation over an infinite field of characteristic $p$ different from two. It is well-known that this…

We show that in a relativistically covariant formulation of the two-body bound state problem, the bound state spectrum is in agreement, up to relativistic corrections, with the non-relativistic bound state spectrum. The solution is achieved…

An intriguing open problem in general relativity is whether a stationary equilibrium configuration of multiple, physically relevant black holes can exist. In such a hypothetical setup, the gravitational attraction would need to be balanced…

A solution manifold is the collection of points in a $d$-dimensional space satisfying a system of $s$ equations with $s<d$. Solution manifolds occur in several statistical problems including hypothesis testing, curved-exponential families,…

We determine the spaces of states of the two-dimensional $O(n)$ and $Q$-state Potts models with generic parameters $n,Q\in \mathbb{C}$ as representations of their known symmetry algebras. While the relevant representations of the conformal…

Let $(M,g)$ be a closed Riemannian manifold of dimension $n$, and $k\geq 1$ an integer such that $n>2k$. We show that there exists $B_0>0$ such that for all $u \in H^{k}(M)$, \[\|u\|_{L^{2^\sharp}(M)}^2 \leq K_0^2 \int_M |\Delta_g^{k/2}…

Constraint satisfaction problem (CSP) is a well-studied combinatorial search problem, in which we are asked to find an assignment of values to given variables so as to satisfy all of given constraints. We study a reconfiguration variant of…

The 1-in-3 and Not-All-Equal satisfiability problems for Boolean CNF formulas are two well-known NP-hard problems. In contrast, the promise 1-in-3 vs. Not-All-Equal problem can be solved in polynomial time. In the present work, we…

In this work we are concerned with the multiplicity of the eigenvalues of the Neumann Laplacian in regions of Rn which are invariant under the natural action of a compact subgroup G of O(n). We give a partial positive answer (in the Neumann…