Related papers: Loop expansion around the Bethe-Peierls approximat…
In this work, we extend and apply effective field theory techniques to systematically understand a subset of lattice artifacts which pollute the lattice correlation functions for a few processes of physical interest. Where possible, we…
For the kinetic energy of 1d model finite systems the leading corrections to local approximations as a functional of the potential are derived using semiclassical methods. The corrections are simple, non-local functionals of the potential.…
It is known that certain theories with extended supersymmetry can be discretized in such a way as to preserve an exact fermionic symmetry. In the simplest model of this kind, we show that this residual supersymmetric invariance is actually…
Given two bounded convex sets $X\subseteq\RR^m$ and $Y\subseteq\RR^n,$ specified by membership oracles, and a continuous convex-concave function $F:X\times Y\to\RR$, we consider the problem of computing an $\eps$-approximate saddle point,…
Computing the theta series of an arbitrary lattice, and more specifically a related quantity known as the flatness factor, has been recently shown to be important for lattice code design in various wireless communication setups. However,…
Many machine learning tasks can be formulated in terms of predicting structured outputs. In frameworks such as the structured support vector machine (SVM-Struct) and the structured perceptron, discriminative functions are learned by…
A general approach for the description of spin systems on hierarchial lattices with coordination number $q$ as a dynamical variable is proposed. The ferromagnetic Ising model on the Bethe lattice was studied as a simple example…
We consider the problem of model reduction of parametrized PDEs where the goal is to approximate any function belonging to the set of solutions at a reduced computational cost. For this, the bottom line of most strategies has so far been…
We consider adaptive approximations of the parameter-to-solution map for elliptic operator equations depending on a large or infinite number of parameters, comparing approximation strategies of different degrees of nonlinearity: sparse…
The past few years have witnessed the development of a comprehensive theory to describe integrable systems out of equilibrium, in which the Bethe ansatz formalism has been tailored to address specific problems arising in this context. While…
Various studies have already considered radiative corrections in Lorentz-violating models unveiling many instances where a minimal or nonminimal operator generates, via loop corrections, a contribution to the photon sector of the…
One of the very few mathematically rigorous nonlinear model reduction methods is the restriction of a dynamical system to a low-dimensional, sufficiently smooth, attracting invariant manifold. Such manifolds are usually found using local…
The matrix completion problem consists of finding or approximating a low-rank matrix based on a few samples of this matrix. We propose a new algorithm for matrix completion that minimizes the least-square distance on the sampling set over…
Algorithms for computing local minima of smooth objective functions enjoy a mature theory as well as robust and efficient implementations. By comparison, the theory and practice of saddle search is destitute. In this paper we present…
We propose an efficient strategy to infer sparse Hopfield network based on magnetizations and pairwise correlations measured through Glauber samplings. This strategy incorporates the $\ell_{1}$ regularization into the Bethe approximation by…
Belief propagation (BP) can be a useful tool to approximately contract a tensor network, provided that the contributions from any closed loops in the network are sufficiently weak. In this manuscript we describe how a loop series expansion…
It is shown in the framework of the N-component scalar model that the saddle point structure may generate non-trivial renormalization group flow. The spinodal phase separation can be described in this manner and a flat action is found as an…
We present a framework for approximating the metric TSP based on a novel use of matchings. Traditionally, matchings have been used to add edges in order to make a given graph Eulerian, whereas our approach also allows for the removal of…
In this note we analyze the use of Pad\'e approximants for downward continuation beyond the radius of convergence of spherical harmonic expansions (SHEs), and for identifying the complex singularities of the gravitational potential. SHEs…
For the exploration of the phase diagram of QCD, effective Polyakov loop theories derived from lattice QCD provide a valuable tool in the heavy quark mass regime. In practice, the evaluation of these theories is complicated by the…