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In this paper, we develop a multiscale hierarchy framework for objective molecular dynamics (OMD), a reduced order molecular dynamics with a certain symmetry, that connects it to the statistical kinetic equation, and the macroscopic…
Neukirch developed an axiomatic and explicit approach to class field theory. This was applied to local fields and number fields but was never done for global function fields since he believed that geometric approach is more suitable.…
A form of stochastic perturbation theory is described, where the representative stochastic fields are generated instantaneously rather than through a Markov process. The correctness of the procedure is established to all orders of the…
We introduce a method to obtain one-dimensional collective variables for studying rarely occurring transitions between two metastable states separated by a high free energy barrier. No previous information, not even approximated, on the…
I present an unbiased method of mapping particles to distribution functions and vice versa. This method alone defines the canonical formulation of statistical mechanics, since it can be used to derive the principle of maximum entropy in…
Atmospheric trace-gas inversion refers to any technique used to predict spatial and temporal fluxes using mole-fraction measurements and atmospheric simulations obtained from computer models. Studies to date are most often of a…
We show how kinetic theory, the statistics of classical particles obeying Newtonian dynamics, can be formulated as a field theory. The field theory can be organized to produce a self-consistent perturbation theory expansion in an effective…
We propose a reformulation of quantum field theory (QFT) as a relativistic statistical field theory. This rewriting embeds a collapse model within an interacting QFT and thus provides a possible solution to the measurement problem.…
An algebraic formalism for the study of a system of charged particles interacting with an external quantum field is developed. The notion of monoidal categories with duality is used for the description of composite systems and corresponding…
A novel framework for the analysis of observation statistics on time discrete linear evolutions in Banach space is presented. The model differs from traditional models for stochastic processes and, in particular, clearly distinguishes…
Large scale structure surveys will likely become the next leading cosmological probe. In our universe, matter perturbations are large on short distances and small at long scales, i.e. strongly coupled in the UV and weakly coupled in the IR.…
This paper deals with the kinetic theory modeling of crowd dynamics with the aim of showing how the dynamics at the micro-scale is transferred to the dynamics of collective behaviors. The derivation of a new model is followed by a…
This paper aims to systematically solve stochastic team optimization of large-scale system, in a rather general framework. Concretely, the underlying large-scale system involves considerable weakly-coupled cooperative agents for which the…
In astronomical and cosmological studies one often wishes to infer some properties of an infinite-dimensional field indexed within a finite-dimensional metric space given only a finite collection of noisy observational data. Bayesian…
We propose a large-scale scaling viewpoint for deriving mesoscopic dynamics from interacting particle systems and apply it to the Cucker--Smale flocking model. In contrast with the classical mean-field regime leading to the Vlasov-type…
We develop methodology for the estimation of the functional mean and the functional principal components when the functions form a spatial process. The data consist of curves $X(\mathbf{s}_k;t),t\in[0,T],$ observed at spatial locations…
We study the emergent dynamics of an anisotropic universe in the context of Group Field Theory condensate cosmology, with a scalar field playing the role of a relational clock. According to different definitions of ``isotropy'', two…
The purpose of this paper is presenting a theoretical basis for the study of $\omega$-Hamiltonian vector fields in a more general approach than the classical one. We introduce the concepts of $\omega$-symplectic group and…
We review recent progress in Bipartite Field Theories. We cover topics such as their gauge dynamics, emergence of toric Calabi-Yau manifolds as master and moduli spaces, string theory embedding, relationships to on-shell diagrams,…
The field equations of modified gravity theories, when considering a homogeneous and isotropic cosmological model, always become autonomous differential equations. This relies on the fact that in such models all variables only depend on…