Related papers: A Dynamic Programming Approach to the Parisi Funct…

Building on the discussion in PRA 93, 042510 (2016), we present a systematic derivation of gradient corrections to the kinetic-energy functional and the one-particle density, in particular for two-dimensional systems. We derive the leading…

In this paper, we develop approximate dynamic programming methods for stochastic systems modeled as Markov Decision Processes, given both soft performance criteria and hard constraints in a class of probabilistic temporal logic called…

We have studied the Parisi overlap distribution for the three dimensional Ising spin glass in the Migdal-Kadanoff approximation. For temperatures T around 0.7Tc and system sizes upto L=32, we found a P(q) as expected for the full Parisi…

The aim of this paper is to study the asymptotic properties of a class of kernel conditional mode estimates whenever functional stationary ergodic data are considered. To be more precise on the matter, in the ergodic data setting, we…

We present a substantial extension of our constraint-based approach for development of orbital-free (OF) kinetic-energy (KE) density functionals intended for the calculation of quantum-mechanical forces in multi-scale molecular dynamics…

This paper presents an efficient approach to image segmentation that approximates the piecewise-smooth (PS) functional in [12] with explicit solutions. By rendering some rational constraints on the initial conditions and the final solutions…

We study theoretically and numerically a family of multi-point dynamic susceptibilities that quantify the strength and characteristic lengthscales of dynamic heterogeneities in glass-forming materials. We use general theoretical arguments…

Standard sparse pseudo-input approximations to the Gaussian process (GP) cannot handle complex functions well. Sparse spectrum alternatives attempt to answer this but are known to over-fit. We suggest the use of variational inference for…

We describe the large deviations above its typical value of the maximal energy of a spin glass with +/-1 spins. Thanks to the relatively explicit description of the rate function we identify, we then show that the latter is asymptotically…

We consider approximate dynamic programming for the infinite-horizon stationary $\gamma$-discounted optimal control problem formalized by Markov Decision Processes. While in the exact case it is known that there always exists an optimal…

We provide a representation formula for viscosity solutions to an elliptic Dirichlet problem involving Pucci's extremal operators. This is done through a dynamic programming principle derived from Denis, Hu and Peng (2010). The formula can…

Sparsity-promoting terms are incorporated into the objective functions of optimal control problems in order to ensure that optimal controls vanish on large parts of the underlying domain. Typical candidates for those terms are integral…

The study of spin-glass dynamics, long considered the paradigmatic complex system, has reached important milestones. The availability of single crystals has allowed the experimental measurement of spin-glass coherence lengths of almost…

A stochastic minimization method for a real-space wavefunction, $\Psi({\bf r}_{1},{\bf r}_{2}\ldots{\bf r}_{n})$, constrained to a chosen density, $\rho({\bf r})$, is developed. It enables the explicit calculation of the Levy constrained…

The efficient representation of random fields on geometrically complex domains is crucial for Bayesian modelling in engineering and machine learning. Today's prevalent random field representations are either intended for unbounded domains…

The analytical solution to the out-of-equilibrium dynamics of mean-field spin glasses has profoundly shaped our understanding of glassy dynamics, which take place in many diverse physical systems. In particular, the idea that during the…

The richness of the mean-field solution of simple glasses leaves many of its features challenging to interpret. A minimal model that illuminates glass physics the same way the random energy model clarifies spin glass behavior would…

A novel mathematical treatment is proposed for computing the time evolution of dynamic nuclear polarization processes in the low temperature thermal mixing regime. Without assuming any a priori analytical form for the electron polarization,…

We study the free energy of mixed $p$-spin spin glass models enriched with an additional magnetic field given by the canonical Gaussian field associated with a Ruelle probability cascade. We prove that this free energy converges to the…

Ramsey spectroscopy has become a powerful technique for probing non-equilibrium dynamics of internal (pseudospin) degrees of freedom of interacting systems. In many theoretical treatments, the key to understanding the dynamics has been to…