Related papers: A Matrix Model with BMS$_3$ Constraints
We introduce a problem class we call Polynomial Constraint Satisfaction Problems, or PCSP. Where the usual CSPs from computer science and optimization have real-valued score functions, and partition functions from physics have monomials,…
In this paper, we introduce the Maximum Matrix Contraction problem, where we aim to contract as much as possible a binary matrix in order to maximize its density. We study the complexity and the polynomial approximability of the problem.…
Partition functions of certain classes of "spin glass" models in statistical physics show strong connections to combinatorial graph invariants. Also known as homomorphism functions they allow for the representation of many such invariants,…
We reconstruct a matrix product state (MPS) in reduced spaces using density matrix. This scheme applies to a MPS built on a blocked quantum lattice. Each block contains $N$ physical sites that have a local space of rank $R$. The simulation…
Spectral decomposition of matrices is a recurring and important task in applied mathematics, physics and engineering. Many application problems require the consideration of matrices of size three with spectral decomposition over the real…
We adapt the VMR (valleys-to-mountains reflections) algorithm, originally devised by us for simulations of SOS models, to the BCSOS model. It is the first time that a cluster algorithm is used for a model with constraints. The performance…
Matrix partition problems generalize a number of natural graph partition problems, and have been studied for several standard graph classes. We prove that each matrix partition problem has only finitely many minimal obstructions for split…
Block tridiagonal matrices arise in applied mathematics, physics, and signal processing. Many applications require knowledge of eigenvalues and eigenvectors of block tridiagonal matrices, which can be prohibitively expensive for large…
A Maple implementation of partitioned matrices is described. A recursive block data structure is used, with all operations preserving the block abstraction. These include constructor functions, ring operations such as addition and product,…
We show that partition functions of various matrix models can be obtained by acting on elementary functions with exponents of W-operators. A number of illustrations is given, including the Gaussian Hermitian matrix model, Hermitian model in…
In this paper, we consider the problem of approximating a given matrix with a matrix whose eigenvalues lie in some specific region \Omega, within the complex plane. More precisely, we consider three types of regions and their intersections:…
Boolean matrix factorization (BMF) has many applications in data mining, bioinformatics, and network analysis. The goal of BMF is to decompose a given binary matrix as the Boolean product of two smaller binary matrices, revealing underlying…
We use the implicitization procedure to generate polynomial equality constraints on the set of distributions induced by local interventions on variables governed by a causal Bayesian network with hidden variables. We show how we may reduce…
We construct the characters for the highest weight representations of the 3d Bondi-Metzner-Sachs (BMS$_3$) algebra. We then use these to construct the partition function and show how to use BMS modular transformations to obtain a density of…
A matrix-compression algorithm is derived from a novel isogenic block decomposition for square matrices. The resulting compression and inflation operations possess strong functorial and spectral-permanence properties. The basic observation…
We investigate finite-dimensional constrained structured optimization problems, featuring composite objective functions and set-membership constraints. Offering an expressive yet simple language, this problem class provides a modeling…
When mass-deformed ABJM theory is considered on S(3), the partition function of the theory localises and is given by a matrix model. We solve this model at large-N in the decompactification limit, where the radius of the three-sphere is…
We consider the problem of learning a low-rank matrix, constrained to lie in a linear subspace, and introduce a novel factorization for modeling such matrices. A salient feature of the proposed factorization scheme is it decouples the…
We introduce a general framework of matrix-form combinatorial Riemann boundary value problem (cRBVP) to characterize the integrability of functional equations arising in lattice walk enumerations. A matrix cRBVP is defined as integrable if…
We propose a major revision of the format XCSP 2.1, called XCSP3, to build integrated representations of combinatorial constrained problems. This new format is able to deal with mono/multi optimization, many types of variables, cost…