Related papers: Generalized multicritical one-matrix models
We propose a method for characterizing large complex networks by introducing a new matrix structure, unique for a given network, which encodes structural information; provides useful visualization, even for very large networks; and allows…
We study an operation in matroid theory that allows one to transition a given matroid into another with more bases via relaxing a \emph{stressed subset}. This framework provides a new combinatorial characterization of the class of split…
The existence of an interpolating master action does not guarantee the same spectrum for the interpolated dual theories. In the specific case of a generalized self-dual (GSD) model defined as the addition of the Maxwell term to the…
In statistical physics, the multivariate hard-core model describes a system of particles, each of which receives its own fugacity. In graph-theoretic language, the partition function of the model translates to the multivariate independence…
We solve a supersymmetric matrix model with a general potential. While matrix models usually describe surfaces, supersymmetry enforces a cancellation of bosonic and fermionic loops and only diagrams corresponding to so-called branched…
We develop a theory of average sizes of kernels of generic matrices with support constraints defined in terms of graphs and hypergraphs. We apply this theory to study unipotent groups associated with graphs. In particular, we establish…
We consider a teacher-student model of supervised learning with a fully-trained two-layer neural network whose width $k$ and input dimension $d$ are large and proportional. We provide an effective theory for approximating the Bayes-optimal…
We show that the CJT thermodynamic potential of dynamical quark models with a quark propagator represented by complex conjugate mass poles inevitably exhibits thermodynamic instabilities. We find that the minimal coupling of the quark…
We present a very simple yet powerful generalization of a previously described model and algorithm for estimation of multiple dipoles from magneto/electro-encephalographic data. Specifically, the generalization consists in the introduction…
Mueller polarimetry involves a variety of instruments and technologies whose importance and scope of applications are rapidly increasing. The exploitation of these powerful resources depends strongly on the mathematical models that underlie…
We define the interpolated polynomial multiple zeta values as a generalization of all of multiple zeta values, multiple zeta-star values, interpolated multiple zeta values, symmetric multiple zeta values, and polynomial multiple zeta…
This is a book on higher-categorical diagrams, including pasting diagrams. It aims to provide a thorough and modern reference on the subject, collecting, revisiting and expanding results scattered across the literature, informed by recent…
We prove that the inclusion from oriented graph complex into graph complex with at least one source is a quasi-isomorphism, showing that homology of the "sourced" graph complex is also equal to the homology of standard Kontsevich's graph…
We study the generalization of shifted Jack polynomials to arbitrary multiplicity free spaces. In a previous paper (math.RT/0006004) we showed that these polynomials are eigenfunctions for commuting difference operators. Our central result…
We show how polynomial mappings of degree k from a union of disjoint intervals onto [-1,1] generate a countable number of special cases of a certain generalization of the Chebyshev Polynomials. We also derive a new expression for these…
Matroid is a generalization of many fundamental objects in combinatorial mathematics , and matroid intersection problem is a classical subject in combinatorial optimization . However , only the intersection of two matroids are well…
We propose a novel theoretical framework for barycentric interpolation, using concepts recently developed in mathematical physics. Generalized barycentric coordinates are defined similarly to Shepard's method, using positive geometries -…
We define a convex-polynomial to be one that is a convex combination of the monomials $\{1, z, z^2, \ldots\}$. This paper explores the intimate connection between peaking convex-polynomials, interpolating convex-polynomials, invariant…
This paper solves the combinatorics relating the intersection theory of $\psi$-classes of Hassett spaces to that of $\overline{\mathcal{M}}_{g,n}$. A generating function for intersection numbers of $\psi$ classes on all Hassett spaces is…
We introduce a notion of duality (due to Brylawski) that generalizes matroid duality to arbitrary rank functions. This generalized duality allows for generalized operations (deletion and contraction) and a generalized polynomial based on…