Related papers: Parquet Approximation for Large N Matrix Higgs Mod…
We give a simple proof of why there is a Matrix theory approximation for a membrane shaped like an arbitrary Riemann surface. As corollaries, we show that noncompact membranes cannot be approximated by matrices and that the Poisson algebra…
Effective Lagrangians are a useful tool for a data-driven approach to physics beyond the Standard Model at the LHC. However, for the new physics scales accessible at the LHC, the effective operator expansion is only relatively slowly…
We are concerned with an approximation problem for a symmetric positive semidefinite matrix due to motivation from a class of nonlinear machine learning methods. We discuss an approximation approach that we call {matrix ridge…
The inverse of a large matrix can often be accurately approximated by a polynomial of degree significantly lower than the order of the matrix. The iteration polynomial generated by a run of the GMRES algorithm is a good candidate, and its…
The static vortex solution in Abelian Higgs model with small ratio of vector and Higgs particle masses is considered. Several formulae approximating this solution are discussed. The accuracy of these approximations is tested by numerical…
Large graphs are present in a variety of domains, including social networks, civil infrastructure, and the physical sciences to name a few. Graph generation is similarly widespread, with applications in drug discovery, network analysis and…
We study the problem of approximating the Ising model partition function with complex parameters on bounded degree graphs. We establish a deterministic polynomial-time approximation scheme for the partition function when the interactions…
A brief review of the role of the Higgs mechanism and the ensuing Higgs particle in the Minimal Standard Model is given. Then the property of triviality of the scalar sector in the Minimal Standard Model and the upper bound on the Higgs…
In transferring some results from universal Taylor series to the case of Pad\'e approximants we obtain stronger results, such as, universal approximation on compact sets of arbitrary connectivity and generic results on planar domains of any…
We consider the approximate computation of spectral projectors for symmetric banded matrices. While this problem has received considerable attention, especially in the context of linear scaling electronic structure methods, the presence of…
We consider quantum spin systems defined on finite sets $V$ equipped with a metric. In typical examples, $V$ is a large, but finite subset of Z^d. For finite range Hamiltonians with uniformly bounded interaction terms and a unique, gapped…
We study the problem of approximating orthogonal matrices so that their application is numerically fast and yet accurate. We find an approximation by solving an optimization problem over a set of structured matrices, that we call extended…
The girth of a matrix is the least number of linearly dependent columns, in contrast to the rank which is the largest number of linearly independent columns. This paper considers the construction of {\it high-girth} matrices, whose…
Computation of the trace of a matrix function plays an important role in many scientific computing applications, including applications in machine learning, computational physics (e.g., lattice quantum chromodynamics), network analysis and…
With the assumption of classical scale invariance at the Planck scale, the DFSZ axion model can generate the Higgs mass terms of the appropriate size through technically natural parameters and may be valid up to the Planck scale. We discuss…
This paper describes a suite of algorithms for constructing low-rank approximations of an input matrix from a random linear image of the matrix, called a sketch. These methods can preserve structural properties of the input matrix, such as…
multiplication operator on a Hilbert space may be approximated with finite sections by choosing an orthonormal basis of the Hilbert space. Nonzero multiplication operators on $L^2$ spaces of functions are never compact and then such…
We characterize the realizability of a quotient of matroids, over an infinite field $K$, in terms of the realizability over $K$ of a single matroid associated to it, called the Higgs major. This result extends to realizability of flag…
A fast method of an arbitrary high order for approximating volume potentials is proposed, which is effective also in high dimensional cases. Basis functions introduced in the theory of approximate approximations are used. Results of…
We summarize some aspects of matrix models from the approaches directly based on their properties at finite N.