There are several ways for constructing (bigger) networks from smaller networks. We consider here the cartesian and the Kronecker (tensor) product networks. Our main aim is to determine a relation between the lattices of synchrony subspaces for a product network and the component networks of the product. In this sense, we show how to obtain the lattice of regular synchrony subspaces for a produ...

An irregular lattice model is proposed for simulating quasistatic fracture in softening materials. Lattice elements are defined on the edges of a Delaunay tessellation of the medium. The dual sVoronoid tessellation is used to scale the elemental stiffness terms in a manner that renders the lattice elastically homogeneous. This property enables the accurate modeling of heterogeneity, as demonstr...

Solitons are localized nonlinear waves and occur in many branches of physics. Their properties have provided a deep and fundamental understanding of complex nonlinear systems. In recent years, there has been considerable interest in studying solitons in systems with periodic potentials or lattices, in particular, those that can be generated in nonlinear optical materials [1]–[5]. In periodic la...

In many fields observations are performed irregularly along time, due to either measurement limitations or lack of a constant immanent rate. While discrete-time Markov models (as Dynamic Bayesian Networks) introduce either inefficient computation or an information loss to reasoning about such processes, continuous-time Markov models assume either a discrete state space (as Continuous-Time Bayes...

GIS applications have recently begun to emerge on the Internet. The management of three-dimensional geographic datasets in this distributed environment poses a particularly challenging problem, which highlights the need for a good data representation. This paper presents a new multiresolution data representation: the Wavelet Triangulated Irregular Network (WTIN). Compared to the traditional cel...

Convolutional kernels are basic and vital components of deep Convolutional Neural Networks (CNN). In this paper, we equip convolutional kernels with shape attributes to generate the deep Irregular Convolutional Neural Networks (ICNN). Compared to traditional CNN applying regular convolutional kernels like 3× 3, our approach trains irregular kernel shapes to better fit the geometric variations o...

We describe a hierarchical data structure for representing a digital terrain (height eld) which contains approximations of the terrain at diierent levels of detail. The approximations are based on triangulations of the underlying two-dimensional space using right-angled triangles. The methods we discuss allow the approximation to precisely represent the surface in certain areas while coarsely a...

We address the problem of designing compact data structures for encoding a Triangulated Irregular Network (TIN). In particular, we study the problem of compressing connectivity, i.e., the information describing the topological structure of the TIN, and we propose two new compression methods which have diierent purposes. The goal of the rst method is to minimize the number of bits needed to enco...

Resonances in an electric circuit occur when capacitive and inductive components are present together. Such resonances appear admittance measurements depending on the circuit's parameters driving AC frequency. In this study, we analyze impedance characteristics of nontrivial topolectrical circuits such as one- two-dimensional Su-Schrieffer-Heeger reveal that size-dependent anomalous inevitably ...

We propose that Kreimer’s method of Feynman diagram renormalization via a Hopf algebra of rooted trees can be fruitfully employed in the analysis of block spin renormalization or coarse graining of inhomogeneous statistical systems. Examples of such systems include spin foam formulations of non-perturbative quantum gravity as well as lattice gauge and spin systems on irregular lattices and/or w...