Related papers: Studies on the Lorenz model
Latent factor models are increasingly popular for modeling multi-relational knowledge graphs. By their vectorial nature, it is not only hard to interpret why this class of models works so well, but also to understand where they fail and how…
In this paper we provide a conceptual overview of latent variable models within a probabilistic modeling framework, an overview that emphasizes the compositional nature and the interconnectedness of the seemingly disparate models commonly…
We carry a systematic study of possible models based on the local gauge group SU(3)_c X SU(3)_L X U(1)_X. Old and new models emerge from the analysis.
We investigate the presence of localized solutions in models described by a single real scalar field with generalized dynamics. The study offers a method to solve very intricate nonlinear ordinary differential equations, and we illustrate…
In this work we further develop a nonlocal calculus theory (initially introduced in [5]) associated with singular fractional-type operators which exhibit kernels with finite support of interactions. The applicability of the framework to…
A monograph on the mathematical aspects of Special Relativity, focusing on the Lorentz group and the properties of relativistic transformations in mechanics and electrodynamics. Manuscript of published book, with added appendices.
A method of representation of a solution as segments of the series in powers of the step of the independent variable is expanded for solving complex systems of ordinary differential equations (ODE): the Lorenz system and other systems. A…
The purpose of this paper is to explain clearly why nonlocality must be an essential part of the theory of relativity. In the standard local version of this theory, Lorentz invariance is extended to accelerated observers by assuming that…
We study the interplay between different models of the same irreducible representation of the $F$-points of a reductive group over a local field.
The notion of analyticity is studied in the context of hypercomplex numbers. A critical review of the problems arising from the conventional approach is given. We describe a local analyticity condition which yields the desired type of…
We study the linear elasticity system subject to singular forces. We show existence and uniqueness of solutions in two frameworks: weighted Sobolev spaces, where the weight belongs to the Muckenhoupt class $A_2$; and standard Sobolev spaces…
In the special theory of relativity, Lorentz invariance is extended in Minkowski spacetime from ideal inertial observers to actual observers by means of the hypothesis of locality, which postulates that accelerated observers are always…
This article studies the problem of reconstructing the topology of a network of interacting agents via observations of the state-evolution of the agents. We focus on the large-scale network setting with the additional constraint of…
Localization of a set of nodes is an important and a thoroughly researched problem in robotics and sensor networks. This paper is concerned with the theory of localization from inner-angle measurements. We focus on the challenging case…
We give a systematic treatment to the concept of hypoellipticity, putting it into an abstract form which allows us to deal with several different notions within the same framework. We then investigate when a notion of hypoellipticity…
We review recent progress on Horn's problem, which asks for a description of the possible eigenspectra of the sum of two matrices with known eigenvalues. After revisiting the classical case, we consider several generalizations in which the…
We propose a method to investigate modular structure in networks based on fitted probabilistic model, where the connection probability between nodes is related to a set of introduced local attributes. The attributes, as parameters of the…
For a given singularity of a plane curve we consider the locus of nodal deformations of the singularity with the given number of nodes and describe possible components of the locus. As applications, we solve the local symplectic isotopy for…
Classical light bending is investigated for weak gravitational fields in the presence of hypothetical local Lorentz violation. Using an effective field theory framework that describes general deviations from local Lorentz invariance, we…
In this article, we study local models associated to certain Shimura varieties. In particular, we present a resoultion of their singularities. As a consequence, we are able to determine the alternating semisimple trace of the geometric…