Related papers: Constructive Matrix Theory for Higher Order Intera…

We show how to represent a class of expressions involving discrete sums over partitions as matrix models. We apply this technique to the partition functions of 2* theories, i.e. Seiberg-Witten theories with the massive hypermultiplet in the…

We have substantially extended the high-temperature and low-magnetic-field (and the related low-temperature and high-magnetic-field) bivariate expansions of the free energy for the conventional three-dimensional Ising model and for a…

We extend the twin-space formulation of the hierarchical equations of motion approach in combination with the matrix product state representation (introduced in J. Chem. Phys. 150, 234102, [2019]) to nonequilibrium scenarios where the open…

We present a novel robust framework for systematically constructing $D$-dimensional four-point higher-derivative contact amplitudes. Our modular block ("LEGO"-like) approach builds amplitudes directly from manifestly gauge-invariant…

The matrices and their sub-blocks are introduced into the study of determining various extensions in the sense of Dung's theory of argumentation frameworks. It is showed that each argumentation framework has its matrix representations, and…

Complex networks have become the main paradigm for modelling the dynamics of interacting systems. However, networks are intrinsically limited to describing pairwise interactions, whereas real-world systems are often characterized by…

We introduce a flexible framework for high-dimensional matrix estimation to incorporate side information for both rows and columns. Existing approaches, such as inductive matrix completion, often impose restrictive structure-for example, an…

This talk reports on various aspects of the divergence of perturbative expansions in the context of matching QCD onto heavy quark effective theory. Implications for exclusive and inclusive decays of heavy mesons are discussed.

This paper revisits building machine learning algorithms that involve interactions between entities, such as those between financial assets in an actively managed portfolio, or interactions between users in a social network. Our goal is to…

In this work I apply a recently proposed improvement procedure, originally conceived to reduce finite lattice spacing effects in transfer matrices for dilute Fermi systems, to tuning operators for the calculation of observables. I…

It is shown that a very simple multiplicative random complex matrix model generalizes the large-N phase structure found in the unitary case: A perturbative regime is joined to a non-perturbative regime at a point where the smoothness of…

Tree-structured neural network architectures for sentence encoding draw inspiration from the approach to semantic composition generally seen in formal linguistics, and have shown empirical improvements over comparable sequence models by…

We study adaptive network models in which coupling weights evolve on a fast time scale relative to the phase dynamics of the nodes. Using Geometric Singular Perturbation Theory (GSPT), we prove that, although the microscopic system is…

We present a procedure in which known solutions to reflection equations for interaction-round-a-face lattice models are used to construct new solutions. The procedure is particularly well-suited to models which have a known fusion hierarchy…

The structure of large-scale social networks has predominantly been articulated using generative models, a form of average-case analysis. This chapter surveys recent proposals of more robust models of such networks. These models posit…

The low energy structure of a theory containing light and heavy particle species which are separated by a mass gap can adequately be described by an effective theory which contains only the light particles. In this work we present a…

We study "on-shell constructibility" of tree amplitudes from recursion relations in general 4-dimensional local field theories with any type of particles, both massless and massive. Our analysis applies to renormalizable as well as…

We propose a method for obtaining parsimonious decompositions of networks into higher order interactions which can take the form of arbitrary motifs.The method is based on a class of analytically solvable generative models, where vertices…

This work addresses nonperturbative effects in both matrix models and topological strings, and their relation with the large-order behavior of the 1/N expansion. We study instanton configurations in generic one-cut matrix models, obtaining…

When predictive models are used to support complex and important decisions, the ability to explain a model's reasoning can increase trust, expose hidden biases, and reduce vulnerability to adversarial attacks. However, attempts at…