Related papers: Properties of linear integral equations related to…

It was recently shown by Jimbo, Miwa and Smirnov that the correlation functions of a generalized XXZ chain associated with an inhomogeneous six-vertex model with disorder parameter $\alpha$ and with arbitrary inhomogeneities on the…

We study certain functions arising in the context of the calculation of correlation functions of the XXZ spin chain and of integrable field theories related with various scaling limits of the underlying six-vertex model. We show that…

We derive an analog of the master equation obtained recently for correlation functions of the XXZ chain for a wide class of quantum integrable systems described by the R-matrix of the six-vertex model, including in particular continuum…

Investigation of the generalized trigonometric and hyperbolic functions containing two parameters has been a very active research area over the last decade. We believe, however, that their monotonicity and convexity properties with respect…

We examine the majorization properties of general thermal-like mixed states depending on a set of parameters. Sufficient conditions which ensure the increase in mixedness, and hence of any associated entropic form, when these parameters are…

Sparse models for high-dimensional linear regression and machine learning have received substantial attention over the past two decades. Model selection, or determining which features or covariates are the best explanatory variables, is…

The entanglement theory in quantum systems with internal symmetries is rich due to the spontaneous creation of entangled pairs of charge/anti-charge particles at the entangling surface. We call these pair creation operators the bi-local…

We study generalised linear regression and classification for a synthetically generated dataset encompassing different problems of interest, such as learning with random features, neural networks in the lazy training regime, and the hidden…

The proper generalized decomposition is applied to a static electrothermal model subject to uncertainties. A reduced model that circumvents the curse of dimensionality is obtained. The quadratic electrothermal coupling term is non-standard…

One of the major open problems in machine learning is to characterize generalization in the overparameterized regime, where most traditional generalization bounds become inconsistent even for overparameterized linear regression. In many…

At the heart of machine learning lies the question of generalizability of learned rules over previously unseen data. While over-parameterized models based on neural networks are now ubiquitous in machine learning applications, our…

We establish several properties of the solutions to the linear integral equations describing the infinite volume properties of the XXZ spin-1/2 chain in the disordered regime. In particular, we obtain lower and upper bounds for the dressed…

We derive finite temperature versions of integral formulae for the two-point correlation functions in the antiferromagnetic XXZ chain. The derivation is based on the summation of density matrix elements characterizing a finite chain segment…

We introduce a log-gas model that is a generalization of a random matrix ensemble with an additional interaction, whose strength depends on a parameter $\gamma$. The equilibrium density is computed by numerically solving the Riemann-Hilbert…

We investigate a general framework of multiplicative multitask feature learning which decomposes each task's model parameters into a multiplication of two components. One of the components is used across all tasks and the other component is…

While bare diagrammatic series are merely Taylor expansions in powers of interaction strength, dressed diagrammatic series, built on fully or partially dressed lines and vertices, are usually constructed by reordering the bare diagrams,…

I present here a simple proof that, under general regularity conditions, the standard parametrization of generalized linear mixed model is identifiable. The proof is based on the assumptions of generalized linear mixed models on the first…

We propose a generalized functional linear regression model for a regression situation where the response variable is a scalar and the predictor is a random function. A linear predictor is obtained by forming the scalar product of the…

We present a conjecture for the density matrix of a finite segment of the XXZ chain coupled to a heat bath and to a constant longitudinal magnetic field. It states that the inhomogeneous density matrix, conceived as a map which associates…

We generalize a recently investigated lattice model of semiflexible polymers formed under equilibrium polymerization in a solution and conduct a comprehensive investigation of its melting properties. The model is characterized by six…