Related papers: Space-Time Models based on Random Fields with Loca…
We study long time behavior of some nonlinear discrete velocity kinetic equations in the one and three dimensions with periodic boundary conditions. We prove the exponential time decay of solutions towards the global equilibrium in the…
Space-time covariance modeling under the Lagrangian framework has been especially popular to study atmospheric phenomena in the presence of transport effects, such as prevailing winds or ocean currents, which are incompatible with the…
We discuss the time evolution of the wave function which is solution of a stochastic Schroedinger equation describing the dynamics of a free quantum particle subject to spontaneous localizations in space. We prove global existence and…
Concise, accurate descriptions of physical systems through their conserved quantities abound in the natural sciences. In data science, however, current research often focuses on regression problems, without routinely incorporating…
The nature of cosmic time is illuminated using Hamilton-Jacobi theory for general relativity. For problems of interest to cosmology, one may solve for the phase of the wavefunctional by using a line integral in superspace. Each contour of…
Quantum dynamical time-evolution of bosonic fields is shown to be equivalent to a stochastic trajectory in space-time, corresponding to samples of a statistical mechanical steady-state in a higher dimensional quasi-time. This is proved…
We study the effective dynamics of an open scalar field interacting with a strongly-coupled two-dimensional rotating CFT plasma. The effective theory is determined by the real-time correlation functions of the thermal plasma. We employ…
The construction of physical models with local time-reparametrization invariance is reviewed. Negative-energy contributions to the hamiltonian are shown to be crucial for the realization of this reparametrization symmetry. The covariant…
We study the qualitative homogenization of second order viscous Hamilton-Jacobi equations in space-time stationary ergodic random environments. Assuming that the Hamiltonian is convex and superquadratic in the momentum variable (gradient)…
The Boltzmann distribution of an ideal gas is determined by the Hamiltonian function generating single particle dynamics. Systems with higher complexity often exhibit topological constraints, which are independent of the Hamiltonian and may…
We consider a stationary spatio-temporal random process and assume that we have a sample. By defining a sequence of discrete Fourier transforms at canonical frequencies at each location, and using these complex valued random varables as…
Space-time non-commutative theories are non-local in time. We develop the Hamiltonian formalism for non-local field theories in d space-time dimensions by considering auxiliary d+1 dimensional field theories which are local with respect to…
Effective field theory provides a perturbative framework to study the evolution of cosmological large-scale structure. We investigate the underpinnings of this approach, and suggest new ways to compute correlation functions of cosmological…
We develop a novel framework for describing quantum fluctuations in field theory, with a focus on cosmological applications. Our method uniquely circumvents the use of operator/Hilbert-space formalism, instead relying on a systematic…
Quantum computers can be used to simulate nonlinear non-Hamiltonian classical dynamics on phase space by using the generalized Koopman-von Neumann formulation of classical mechanics. The Koopman-von Neumann formulation implies that the…
In this paper, we propose a Bayesian matrix-variate spatiotemporal modeling framework for jointly analyzing multiple response variables observed at spatial locations over time. The approach relaxes the standard assumption of spatial…
Data assimilation in models representing spatio-temporal phenomena poses a challenge, particularly if the spatial histogram of the variable appears with multiple modes. The traditional Kalman model is based on a Gaussian initial…
We show the skills of a data-driven low-dimensional linear model in predicting the spatio-temporal evolution of turbulent Rayleigh-B\'enard convection. The model is based on dynamic mode decomposition with delay-embedding, which provides a…
The covariant Dirac equation in Robertson-Walker space-time is studied under the comoving coordinates. The exact forms of the spatial factor of wave function are respectively acquired in closed, spatially flat, and open universes.
We introduce a Bayesian approach for multivariate spatio-temporal prediction for high-dimensional count-valued data. Our primary interest is when there are possibly millions of data points referenced over different variables, geographic…