Related papers: Polynomial algorithm for exact calculation of part…

The monomer-dimer model is fundamental in statistical mechanics. However, it is $#P$-complete in computation, even for two dimensional problems. A formulation in matrix permanent for the partition function of the monomer-dimer model is…

We study the zeros in the complex plane of the partition function for the Ising model coupled to $2d$ quantum gravity for complex magnetic field and for complex temperature. We compute the zeros by using the exact solution coming from a two…

We compute the nonlinearity of Boolean functions with Groebner basis techniques, providing two algorithms: one over the binary field and the other over the rationals. We also estimate their complexity. Then we show how to improve our…

In this paper, we give a polynomial-time algorithm for deciding whether an input bipartite graph admits a 2-layer fan-planar drawing, resolving an open problem posed in several papers since 2015.

We present a linear time algorithm for computing a cycle separator in a planar graph that is (arguably) simpler than previously known algorithms. Our algorithm builds on, and is somewhat similar to, previous algorithms for computing…

We demonstrate a fast spin-s spherical harmonic transform algorithm, which is flexible and exact for band-limited functions. In contrast to previous work, where spin transforms are computed independently, our algorithm permits the…

The most efficient way to calculate strong bisimilarity is by calculation the relational coarsest partition on a transition system. We provide the first linear time algorithm to calculate strong bisimulation using parallel random access…

Analyzing large graph data is an essential part of many modern applications, such as social networks. Due to its large computational complexity, distributed processing is frequently employed. This requires graph data to be divided across…

Lars Onsager and Bruria Kaufman calculated the partition function of the Ising model exactly in 1944 and 1949. Since then there have been many developments in the exact solution of similar, but usually more complicated, models. Here I shall…

One fruitful formulation of Deep Networks (DNs) enabling their theoretical study and providing practical guidelines to practitioners relies on Piecewise Affine Splines. In that realm, a DN's input-mapping is expressed as per-region affine…

We give explicit formulas to compute most of the decomposition numbers of reductions modulo 2 of irreducible spin representations of symmetric groups indexed by partitions with at most 2 parts. In many of the still open cases small upper…

We compute the contour integral for the partition function of an $\mathcal{N}=2$ $SU(2)$ topologically twisted theory on $\mathbb{CP}^2$, dimensionally reducing from an $\mathcal{N}=1$ theory on $S^5$. Earlier works presented the partition…

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 give an FPTAS for approximating the partition function of the hard-core model for bipartite graphs when there is sufficient imbalance in the degrees or fugacities between the sides $(L,R)$ of the bipartition. This includes, among others,…

A graph has a perfect partition if all its perfect matchings can be partitioned so that each part is a 1-factorization of the graph. Let $L_{rm, r}=K_{rm,rm}-mK_{r,r}$. We first give a formula to count the number of perfect matchings of…

We study the problem of approximating the partition function of the ferromagnetic Ising model in graphs and hypergraphs. Our first result is a deterministic approximation scheme (an FPTAS) for the partition function in bounded degree graphs…

We describe an algorithm for splitting permutation representations of finite group over fields of characteristic zero into irreducible components. The algorithm is based on the fact that the components of the invariant inner product in…

This paper presents some algorithms in linear algebraic groups. These algorithms solve the word problem and compute the spinor norm for orthogonal groups. This gives us an algorithmic definition of the spinor norm. We compute the double…

Motivated by performance optimization of large-scale graph processing systems that distribute the graph across multiple machines, we consider the balanced graph partitioning problem. Compared to the previous work, we study the…

We are interested in the fast computation of the exact value of integrals of polynomial functions over convex polyhedra. We present speed ups and extensions of the algorithms presented in previous work. We present the new software…