Related papers: Time Ordering, Energy Ordering, and Factorization
We discuss representing and reasoning with knowledge about the time-dependent utility of an agent's actions. Time-dependent utility plays a crucial role in the interaction between computation and action under bounded resources. We present a…
We propose a new approach to temporal inference, inspired by the Pearlian causal inference paradigm - though quite different from Pearl's approach formally. Rather than using directed acyclic graphs, we make use of factored sets, which are…
The combined increase of energy demand and environmental pollution at a global scale is entailing a rethinking of the production models in sustainable terms. As a consequence, energy suppliers are starting to adopt strategies that flatten…
Results of research of possibility of transformation of a difference equation into a system of the first-order difference equation are presented. In contrast to the method used previously, an unknown grid function is split into two new…
Process mining starts from event data. The ordering of events is vital for the discovery of process models. However, the timestamps of events may be unreliable or imprecise. To further complicate matters, also causally unrelated events may…
In the present paper a new concept of representability is introduced, which can be applied to not total and also to intransitive relations (semiorders in particular). This idea tries to represent the orderings in the simplest manner,…
Some results are reviewed and developments are presented on the study of Time in quantum mechanics as an observable, canonically conjugate to energy. Operators for the observable Time are investigated in particle and photon quantum theory.…
A clear explanation is given on how the causal, psychological, and electrodynamic time arrows emerge from the thermodynamic time arrow.
In this survey paper we consider some applications of the Wright function with special emphasis of its key role in the partial differential equations of fractional order. It was found that the Green function of the time-fractional…
Conservation laws are discussed in conjunction with quantum-mechanical indeterminacies of the corresponding observables. The considered examples show that the connections between energy and its indeterminacy may be quite intricate. The…
Matrix factorization is a powerful data analysis tool. It has been used in multivariate time series analysis, leading to the decomposition of the series in a small set of latent factors. However, little is known on the statistical…
In this paper, we numerically address the inverse problem of identifying a time-dependent coefficient in the time-fractional diffusion equation. An a priori estimate is established to ensure uniqueness and stability of the solution. A fully…
Recently, a factorization theorem was proposed for partonic flavor evolution as defined by the net flavor of the Winner-Take-All axis of a jet. We validate the factorization theorem through explicit calculation at two-loop order, and in the…
In quantum mechanics the kinetic energy term for a single particle is usually written in the form of the Laplace-Beltrami operator. This operator is a factor ordering of the classical kinetic energy. We investigate other relatively simple…
The scalar difference equation $x_{n+1}=f_{n}(x_{n},x_{n-1},...,x_{n-k})$ may exhibit symmetries in its form that allow for reduction of order through substitution or a change of variables. Such form symmetries can be defined generally…
A new concept of internal time (viewed as a scalar temporal field) is introduced which allows one to solve the energy problem in General Relativity. The law of energy conservation means that the total energy density of the full system of…
In thermodynamics, quantum coherences - superpositions between energy eigenstates - behave in distinctly nonclassical ways. Recently mathematical frameworks have emerged to account for these features and have provided a range of novel…
There has been considerable recent study in "sub-diffusion" models that replace the standard parabolic equation model by a one with a fractional derivative in the time variable. There are many ways to look at this newer approach and one…
We show that the correct way to extract parton distribution functions from the reduced Ioffe-time distribution (RITD), a ratio of the Ioffe-time distribution for a moving hadron and a hadron at rest, is through a factorization formula. This…
Ordered logics and type systems have been used in a variety of applications including computational linguistics, memory allocation, stream processing, logical frameworks, parametricity, and enforcing security protocols. In most…