相关论文: Probabilistic potential theory and induction of dy…
We develop a new framework of uncertainty variables to model uncertainty. An uncertainty variable is characterized by an uncertainty set, in which its realization is bound to lie, while the conditional uncertainty is characterized by a set…
Using a new Bayesian method for solving inverse quantum problems, potentials of quantum systems are reconstructed from coordinate measurements in non-stationary states. The approach is based on two basic inputs: 1. a likelihood model,…
We show that the quantum-mechanical probability distribution involving complex probability amplitudes can be derived from three natural conditions imposed on a relativistically invariant probability function describing the motion of a…
This paper is concerned with the study of the consistency of a variational method for probability measure quantization, deterministically realized by means of a minimizing principle, balancing power repulsion and attraction potentials. The…
We propose a generalization of the Poincar\'e-Birkhoff Theorem on area-preserving twist maps to area-preserving twist maps that are random with respect to an ergodic probability measure. The classical theory is a particular instance of the…
A variational Perturbation theory based on the functional integral approach is formulated for many-particle systems. Using the variational action obtained through Jensen-Peierls' inequality, a perturbative expansion scheme for the…
Probabilistic regression techniques in control and robotics applications have to fulfill different criteria of data-driven adaptability, computational efficiency, scalability to high dimensions, and the capacity to deal with different…
Using connection with quantum field theory, the infinitesimal covariant abelian gauge transformation laws of relativistic two-particle constraint theory wave functions and potentials are established and weak invariance of the corresponding…
A program invariant is a property that holds for every execution of the program. Recent work suggest to infer likely-only invariants, via dynamic analysis. A likely invariant is a property that holds for some executions but is not…
We seek to establish qualitative convergence results to a general class of evolution PDEs described by gradient flows in optimal transportation distances. These qualitative convergence results come from dynamical systems under the general…
The concept of gauge invariance can be considered one of the most subtle and useful concept in theoretical physics since it can permit the comprehension of difficult systems in physics with an arbitrary choice of a reference frame at every…
We present a first-principles implementation of spatial scale invariance as a local gauge symmetry in geometry dynamics using the method of best matching . In addition to the 3-metric, the proposed scale invariant theory also contains a…
It is often claimed that Bayesian methods, in particular Bayes factor methods for hypothesis testing, can deal with optional stopping. We first give an overview, using elementary probability theory, of three different mathematical meanings…
We propose a path integral formulation for scale invariant quantum field theories. We do it by modifying the functional integration measure in such a way that the partition function is always exactly scale invariant, at the cost of having…
The dynamical properties of the gauge theory of Born-Infeld type action, which is expected as the high-energy effective theory, are investigated by adding a complex scalar field to this gauge system. Especially the Coleman-Weinberg…
The aim of this note is to introduce a notion of dynamical entropy, which we call infinite-product entropy, for probability measures on (countable) infinite cartesian product of any measurable space with itself. The idea behind the…
In this paper a new framework has been applied to the design of controllers which encompasses nonlinearity, hysteresis and arbitrary density functions of forward models and inverse controllers. Using mixture density networks, the…
One of the main concepts in quantum physics is a density matrix, which is a symmetric positive definite matrix of trace one. Finite probability distributions can be seen as a special case when the density matrix is restricted to be…
We propose that a quantum particle in a potential in one space dimension can be described by a probabilistic cellular automaton. While the simple updating rule of the automaton is deterministic, the probabilistic description is introduced…
New integral formulas involving the Meijer $G$-function are derived using recent results concerning distributional characterisations and distributional transformations in probability theory.