Related papers: Approximate conservation laws in perturbed integra…
In this paper, a general framework for the analysis of a connection between the training of artificial neural networks via the dynamics of Markov chains and the approximation of conservation law equations is proposed. This framework allows…
Integrable systems offer rare examples of solvable many-body problems in the quantum world. Due to the fine-tuned structure, their realization in nature and experiment is never completely accurate, therefore effects of integrability are…
Motivated by the desire to numerically calculate rigorous upper and lower bounds on deviation probabilities over large classes of probability distributions, we present an adaptive algorithm for the reconstruction of increasing real-valued…
A new approach to maximum likelihood learning of discrete graphical models and RBM in particular is introduced. Our method, Perturb and Descend (PD) is inspired by two ideas (I) perturb and MAP method for sampling (II) learning by…
Approximations of functions with finite data often do not respect certain "structural" properties of the functions. For example, if a given function is non-negative, a polynomial approximation of the function is not necessarily also…
Interatomic potentials are essential to go beyond ab initio size limitations, but simulation results depend sensitively on potential parameters. Forward propagation of parameter variation is key for uncertainty quantification, whilst…
Conservation laws are key theoretical and practical tools for understanding, characterizing, and modeling nonlinear dynamical systems. However, for many complex systems, the corresponding conserved quantities are difficult to identify,…
We develop a technique to construct analytical solutions of the linear perturbations of inflation with a nonlinear dispersion relation, due to quantum effects of the early universe. Error bounds are given and studied in detail. The…
Conserved quantities increasingly underpin the inference of physical models. Recently new conserved quantities have been found in this context, that currently lack an interpretation. Here, we show that irreversible reactions in CRNs and…
We propose a new method for discretizing the time variable in integrable lattice systems while maintaining the locality of the equations of motion. The method is based on the zero-curvature (Lax pair) representation and the lowest-order…
Probabilistic models help us encode latent structures that both model the data and are ideally also useful for specific downstream tasks. Among these, mixture models and their time-series counterparts, hidden Markov models, identify…
We show that the so-called hidden potential symmetries considered in a recent paper [Gandarias M., Physica A, 2008, V.387, 2234-2242] are ordinary potential symmetries that can be obtained using the method introduced by Bluman and…
The long-term dynamics of many dynamical systems evolve on an attracting, invariant "slow manifold" that can be parameterized by a few observable variables. Yet a simulation using the full model of the problem requires initial values for…
A simple method is proposed to estimate the instantaneous correlations between state variables in a hybrid system from the empirical correlations between observable market quantities such as spot rate, stock price and implied volatility.…
We calculate perturbative Wilson loops of various sizes up to loop order $n=20$ at different lattice sizes for pure plaquette and tree-level improved Symanzik gauge theories using the technique of Numerical Stochastic Perturbation Theory.…
Optimization problems with an auxiliary latent variable structure in addition to the main model parameters occur frequently in computer vision and machine learning. The additional latent variables make the underlying optimization task…
We propose the use of controlled perturbations to address the challenging question of optimal active-set prediction for interior point methods. Namely, in the context of linear programming, we consider perturbing the inequality…
We study in general algebras Gratzer's notion of congruence preserving function, characterizing functions in terms of stability under inverse image of particular Boolean algebras of subsets generated from any subset of the algebra.…
In this work we present a rather general approach to approximate the solutions of nonlocal conservation laws. In a first step, we approximate the nonlocal term with an appropriate quadrature rule applied to the spatial discretization. Then,…
We present a detailed analysis of the structure of the conservation laws in quantum integrable chains of the XYZ-type and in the Hubbard model. With the use of the boost operator, we establish the general form of the XYZ conserved charges…