Related papers: An optimization principle for deriving nonequilibr…
We present stochastic homogenization results for viscous Hamilton-Jacobi equations using a new argument which is based only on the subadditive structure of maximal subsolutions (solutions of the "metric problem"). This permits us to give…
We apply a variant of the Nose-Hoover thermostat to derive the Hamiltonian of a nonextensive system that is compatible with the canonical ensemble of the generalized thermostatistics of Tsallis. This microdynamical approach provides a…
Sampling from an unnormalized probability distribution is a fundamental problem in machine learning with applications including Bayesian modeling, latent factor inference, and energy-based model training. After decades of research,…
We consider a kind of stochastic exit time optimal control problems, in which the cost function is defined through a nonlinear backward stochastic differential equation. We study the regularity of the value function for such a control…
We study the problem of optimal portfolio selection under stochastic volatility within a continuous time reinforcement learning framework with portfolio constraints. Exploration is modeled through entropy-regularized relaxed controls, where…
A new method of deriving comparative statics information using generalized compensated derivatives is presented which yields constraint-free semidefiniteness results for any differentiable, constrained optimization problem. More generally,…
We study the optimal control of general stochastic McKean-Vlasov equation. Such problem is motivated originally from the asymptotic formulation of cooperative equilibrium for a large population of particles (players) in mean-field…
We show that classical thermodynamics has a formulation in terms of Hamilton-Jacobi theory, analogous to mechanics. Even though the thermodynamic variables come in conjugate pairs such as pressure/volume or temperature/entropy, the phase…
Physical systems that dissipate, mix and develop turbulence also irreversibly transport statistical density. In statistical physics, laws for these processes have a mathematical form and tractability that depends on whether the description…
The evaluation of the path-integral representation for stochastic processes in the weak-noise limit shows that these systems are governed by a set of equations which are those of a classical dynamics. We show that, even when the noise is…
There has been considerable interest in designing Markov chain Monte Carlo algorithms by exploiting numerical methods for Langevin dynamics, which includes Hamiltonian dynamics as a deterministic case. A prominent approach is Hamiltonian…
In this paper, we present a novel framework for deriving the evolution equation of the level set function in topology optimization, departing from conventional Hamilton-Jacobi based formulations. The key idea is the introduction of an…
Starting at the mesoscopic level with a general formulation of stochastic thermodynamics in terms of Markov jump processes, we identify the scaling conditions that ensure the emergence of a (typically nonlinear) deterministic dynamics and…
We present an exactly-solvable risk-minimizing stochastic differential game for flood management in rivers. The streamflow dynamics follow stochastic differential equations driven by a Levy process. An entropic dynamic risk measure is…
Complex systems are sometimes subject to non Gaussian alpha stable Levy fluctuations. A new method is devised to estimate this uncertain parameter and other system parameters, using observations on either mean exit time or escape…
We introduce and analyze a model for the transport of particles or energy in extended lattice systems. The dynamics of the model acts on a discrete phase space at discrete times but has nonetheless some of the characteristic properties of…
Latent variable models are widely used in social and behavioural sciences, including education, psychology, and political science. With the increasing availability of large and complex datasets, high-dimensional latent variable models have…
We present a Hamiltonian approach for the wellknown Eigen model of the Darwin selection dynamics. Hamiltonization is carried out by means of the embedding of the population variable space, describing behavior of the system, into the space…
In this note, we characterize the solution of a system of elliptic integro-differential equations describing a phe-notypically structured population subject to mutation, selection and migration. Generalizing an approach based on…
A framework for statistical-mechanical analysis of quantum Hamiltonians is introduced. The approach is based upon a gradient flow equation in the space of Hamiltonians such that the eigenvectors of the initial Hamiltonian evolve toward…