Related papers: Lattice Structures for Attractors III
A method by Peres is used to draw spectra of the interacting boson model as lattices in the plane of energy versus an arbitrary observable average (or variance). Ordered (disordered) lattices are signatures of regularity (chaos) in both…
When continuous fields are expanded in a wavelet basis, a D-dimensional continuum action becomes a (D+1)-dimensional lattice action on the naively discretized Poincare-patch coordinates of an Euclidean AdS(D+1). New possible criteria for…
We investigate the properties of PT-symmetric tight-binding models by considering both bounded and unbounded models. For the bounded case, we obtain closed form expressions for the corresponding energy spectra and we analyze the structure…
A new concept called biased derivative is proposed. It has a potential to better understand and model some aspects of dynamical systems associated with creating bubbles.
We introduce the concept of basis for a lattice. This basis plays a vital role to determine the completeness and consistency of the lattice. Weighted lattices are introduced and its complexity is formulated. Some axiomatic systems,…
A formalism is derived to analyze the scattering of a conducting structure based on the characteristic modes of another structure whose surface is a superset of the first structure. This enables the analysis and comparison of different…
The paper introduces and studies differentially positive systems, that is, systems whose linearization along an arbitrary trajectory is positive. A generalization of Perron Frobenius theory is developed in this differential framework to…
We study the transport and localization properties of scalar vibrations on a lattice with random bond strength by means of the transfer matrix method. This model has been recently suggested as a means to investigate the vibrations and heat…
The notion of multidimensional quadrilateral lattice is introduced. It is shown that such a lattice is characterized by a system of integrable discrete nonlinear equations. Different useful formulations of the system are given. The…
In this paper, we define a property, trimness, for lattices. Trimness is a not-necessarily-graded generalization of distributivity; in particular, if a lattice is trim and graded, it is distributive. Trimness is preserved under taking…
The analysis of global dynamics, particularly the identification and characterization of attractors and their regions of attraction, is essential for complex nonlinear and hybrid systems. Combinatorial methods based on Conley's index theory…
We describe a procedure to introduce general dependence structures on a set of Dirichlet processes. Dependence can be in one direction to define a time series or in two directions to define spatial dependencies. More directions can also be…
Over the last few years lattice techniques have been used to investigate candidate theories of new physics beyond the Standard Model. This review gives a survey of results from these studies. Most of these investigations have been of…
We introduce a representation learning framework for spatial trajectories. We represent partial observations of trajectories as probability distributions in a learned latent space, which characterize the uncertainty about unobserved parts…
Discrete partially ordered sets can be turned into distance spaces in several ways. The distance functions may or may not satisfy the triangle inequality, and restriction of the distance to finite chains may or may not coincide with the…
We analyse various structural and order-theoretical aspects of abstract separation systems and partial lattices, as well as the relationship between the different submodularity conditions one can impose on them.
We present a progress overview focused on the recent theoretical and experimental advances in the area of soliton manipulation in optical lattices. Optical lattices offer the possibility to engineer and to control the diffraction of light…
Symmetries are known to dictate important physical properties and can be used as a design principle in particular in wave physics, including wave structures and the resulting propagation dynamics. Local symmetries, in the sense of a…
Every lattice is isomorphic to a lattice whose elements are sets of sets, and whose operations are intersection and an operation extending the union of two sets of sets A and B by the set of all sets in which the intersection of an element…
In this paper, we consider the direct and inverse problems of the description of lattice positive random fields by various systems of finite-dimensional (as well as one-point) probability distributions parameterized by boundary conditions.…