Related papers: Derivative formula for capacities
Anytime approximation algorithms that compute the probabilities of queries over probabilistic databases can be of great use to statistical learning tasks. Those approaches have been based so far on either (i) sampling or (ii)…
We consider diffusion type equations with a distributed order derivative in the time variable. This derivative is defined as the integral in $\alpha$ of the Caputo-Dzhrbashian fractional derivative of order $\alpha \in (0,1)$ with a certain…
The aim of this tutorial survey is to revisit the basic theory of relaxation processes governed by linear differential equations of fractional order. The fractional derivatives are intended both in the Rieamann-Liouville sense and in the…
The direct application of the definition of sorting in lattices is impractical because it leads to an algorithm with exponential complexity. In this paper we present for distributive lattices a recursive formulation to compute the sort of a…
Recent literature in the last Maximum Entropy workshop introduced an analogy between cumulative probability distributions and normalized utility functions. Based on this analogy, a utility density function can de defined as the derivative…
In this paper we create a model of particle motion on a three-dimensional lattice using discrete random walk with small steps. We rigorously construct a probability space of the particle trajectories. Unlike deterministic approach in…
We investigate active lattice walks: biased continuous time random walks which perform orientational diffusion between lattice directions in one and two spatial dimensions. We study the occupation probability of an arbitrary site on the…
From physical perspective, derivatives can be viewed as mathematical idealizations of the linear growth. The linear growth condition has special properties, which make it preferred. The manuscript investigates the general properties of the…
We recalculate the beta functions of higher derivative gravity in four dimensions using the one--loop approximation to an Exact Renormalization Group Equation. We reproduce the beta functions of the dimensionless couplings that were known…
When proving theorems from large sets of logical assertions, it can be helpful to restrict the search for a proof to those assertions that are relevant, that is, closely related to the theorem in some sense. For example, in the Watson…
The phenomenological textbook equations for the charge and heat transport are extensively used in a number of fields ranging from semiconductor devices to thermoelectricity. We provide a rigorous derivation of transport equations by solving…
An irreducible canonical approach to second-class constraints reducible of an arbitrary order is given. This method generalizes our previous results from [Europhys. Lett. 50 (2000) 169, J. Phys. A: Math. Theor. 40 (2007) 14537] for first-…
We present a method to compute high-order derivatives of the total energy which can be used in the framework of density functional theory. We provide a proof of the $2n+1$ theorem for a general class of energy functionals in which the…
Techniques of `dynamic renormalization', developed earlier for undirected percolation and the contact model, are adapted to the setting of directed percolation, thereby obtaining solutions of several problems for directed percolation on…
We consider the Cauchy problem in the Euclidean space for a doubly degenerate parabolic equation with a space-dependent exponential weight, roughly speaking of the type of the exponential of a power of the distance from the origin. We…
The recent quantum information boom has effected a resurgence of interest in unitary coupled cluster (UCC) theory. Our group's interest in local energy landscapes of unitary ans\"atze prompted us to investigate the classical approach of…
The E=mc^2 relationship is not unique to special relativity. Einstein published one exact derivation from special relativity and two approximate derivations that used general extensions to Newtonian mechanics, and an exact derivation is…
In two previous papers the author introduced a multiplication of distributions in one dimension and he proved that two one-dimensional Dirac delta functions and their derivatives can be multiplied, at least under certain conditions. Here,…
The unique third-order invariant variational equation in three-dimensional (pseudo)Euclidean space is derived.
Network calculus is an elegant theory which uses envelopes to determine the worst-case performance bounds in a network. Statistical network calculus is the probabilistic version of network calculus, which strives to retain the simplicity of…