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This paper concerns the parameter estimation problem for the quadratic potential energy in interacting particle systems from continuous-time and single-trajectory data. Even though such dynamical systems are high-dimensional, we show that…
A simplified climate model based on maximum entropy production, described by a variational principle, is revisited and an analytical solution to its Euler-Lagrange equation is found. Mindful of controversy about maximum or minimum entropy…
Quantum states of a two-component Fermi trapped gas are described by introducing an effective trap frequency, determined via variational techniques. Closed expressions for the contribution of a contact interaction potential to the total…
For the exactly solved reduced BCS model an electrostatic analogy exists; in particular it served to obtain the exact thermodynamic limit of the model from the Richardson Bethe ansatz equations. We present an electrostatic analogy for a…
We find the free-energy in the thermodynamic limit of a one dimensional XY model associated to a system of N qubits. The coupling among the sigma_i^z is a long range two bodies random interaction. The randomness in the couplings is the…
Problems of probabilistic inference and decision making under uncertainty commonly involve continuous random variables. Often these are discretized to a few points, to simplify assessments and computations. An alternative approximation is…
We introduce an adaptive superconvergent finite element method for a class of mixed formulations to solve partial differential equations involving a diffusion term. It combines a superconvergent postprocessing technique for the primal…
We study the parameter estimation problem in mixture models with observational nonidentifiability: the full model (also containing hidden variables) is identifiable, but the marginal (observed) model is not. Hence global maxima of the…
We introduce a unified statistical framework for quantifying system-environment coupling by treating the interaction energy $V_\mathcal{SE}$ as a stochastic variable. Using a reference-particle decomposition, we derive exact, closed-form…
In this study, we extend the lower bound on the average of the local energy of the Ising model with quenched randomness [J. Phys. Soc. Jpn. 76, 074711 (2007)] obtained for a symmetric distribution to an asymmetric one. Compared with the…
One of the assumptions leading to the Gross-Pitaevskii Equation (GPE) is that the interaction between atom pairs can be written effectively as a \delta -function so that the interaction range of the particles is assumed to vanish. A simple…
This paper delves into a nonparametric estimation approach for the interaction function within diffusion-type particle system models. We introduce two estimation methods based upon an empirical risk minimization. Our study encompasses an…
We present an algorithm based on maximum likelihood for the estimation and renormalization (marginalization) of exponential densities. The moment-matching problem resulting from the maximization of the likelihood is solved as an…
We consider a mixed finite element method for a biharmonic equation with clamped boundary conditions based on biorthogonal systems with weakly imposed Dirichlet boundary condition. We show that the weak imposition of the boundary condition…
In this paper, we present an energy method for the system of Boltzmann equations in the multicomponent mixture case, based on a micro-macro decomposition. More precisely, the perturbation of a solution to the Boltzmann equation around a…
We describe a simple method to compute the Cramer-Rao limit of a high energy experiment, i.e., the smallest error with which a parameter can in principle be determined in a reaction. This precision remains a theoretical paradigm since it…
In this paper, we prove that the standard adaptive finite element method with a (modified) `maximum marking strategy' is `instance optimal' for the `total error', being the sum of the energy error and the oscillation. This result will be…
We study the approximability of instances of the minimum entropy set cover problem, parameterized by the average frequency of a random element in the covering sets. We analyze an algorithm combining a greedy approach with another one biased…
Different rate theories yielded similar forms of rates constants consistent with the phenomenological Arrhenius law, although they were derived from various branches of physics including classical thermodynamics, statistical and quantum…
We present an exact electrovacuum solution of Einstein-Maxwell equations with infinite sets of multipole moments which can be used to describe the exterior gravitational field of a rotating charged mass distribution. We show that in the…