Related papers: Initial conditions and evolution of off-diagonal d…
We formalize the intuitive idea of a labelled discrete surface which evolves in time, subject to two natural constraints: the evolution does not propagate information too fast; and it acts everywhere the same.
This paper introduces, up to the author's knowledge, for the first time the generalized initial value problem. In this problem, given an ordinary differential equation defined in some set, the initial conditions are mapped to a subset of…
Evolution by natural selection can be seen an algorithm for generating creative solutions to difficult problems. More precisely, evolution by natural selection is a class of algorithms that share a set of properties. The question we address…
A simple, new method for solving for the $Q^2$ evolution of parton distributions in perturbative QCD using cubic splines is described and applied to the evolution of nonsinglet quark distributions.
In this paper we study the dispersive properties related to a model of peridynamic evolution, governed by a non local initial value problem, in the cases of two and three spatial dimensions. The features of the wave propagation…
In this paper we present a study of the early stages of unstable state evolution of systems with spatial symmetry changes. In contrast to the early time linear theory of unstable evolution described by Cahn, Hilliard, and Cook, we develop a…
We discuss the structure of the ``forward visible'' (FW) parts of double and skewed distributions related to usual distributions through reduction relations. We use factorized models for double distributions (DDs) f(x, alpha) in which one…
The purpose of this paper is to establish first and second order necessary optimality conditions for optimal control problems of stochastic evolution equations with control and state constraints. The control acts both in the drift and…
We discuss a thin film evolution equation for a wetting evaporating liquid on a smooth solid substrate. The model is valid for slowly evaporating small sessile droplets when thermal effects are insignificant, while wettability and…
Diffractive dijet photoproduction is proposed as a probe of the off-diagonal gluon distribution and its evolution. Predictions for the transverse momentum distribution of the jets are given. Differences with DGLAP evolution are highlighted.
Although the theory of density evolution in maps and ordinary differential equations is well developed, the situation is far from satisfactory in continuous time systems with delay. This paper reviews some of the work that has been done…
How do diffusion generative models convert pure noise into meaningful images? In a variety of pretrained diffusion models (including conditional latent space models like Stable Diffusion), we observe that the reverse diffusion process that…
We consider the possibility that the primordial fluctuations (scalar and tensor) might have been standing waves at their moment of creation, whether or not they had a quantum origin. We lay down the general conditions for spatial…
We consider the one-dimensional nonlinear Schr\"odinger equation with a nonlinearity of degree $p>1$. We exhibit measures on the space of initial data for which we describe the non trivial evolution by the linear Schr\"odinger flow and we…
We present a theoretical framework and numerical methods for predicting the large-scale properties of solutions of partial differential equations that are too complex to be properly resolved. We assume that prior statistical information…
We briefly discuss recent research on the spin-averaged parton densities of the proton, focusing on some aspects relevant to hard processes at the LHC. Specifically, after recalling the basic framework and the need for higher-order…
Aspects of the QCD parton densities are briefly reviewed, drawing some parallels to the density matrix formulation of quantum mechanics, exemplified by Wigner functions. We elaborate on the solution of their evolution equations using…
This paper deals with branching processes in varying environment, namely, whose offspring distributions depend on the generations. We provide sufficient conditions for survival or extinction which rely only on the first and second moments…
We present posterior distributions of parameters that characterize the nonperturbative initial input for the Balitsky-Kovchegov evolution equation. The BK equation evolves an initial dipole-target scattering amplitude at moderate…
Using the O(4) linear $\sigma$ model, we address the topic of non-equilibrium relaxation of an inhomogeneous initial configuration due to quantum and thermal fluctuations. The space-time evolution of an inhomogeneous fluctuation of the…