Related papers: Extended Configurational Polyhedra Based on Graph …
We introduce the concept of geometric extremal graphical models, which are defined through the gauge function of the limit set obtained from suitably scaled random vectors in light-tailed margins. For block graphs, we prove results relating…
In \cite{Sz13-1} we defined and described the {\it regular infinite or bounded} $p$-gonal prism tilings in $\SLR$ space. We proved that there exist infinitely many regular infinite $p$-gonal face-to-face prism tilings $\cT^i_p(q)$ and…
In this thesis, we construct and classify planar noncommutative phase spaces by the coadjoint orbit method on the anisotropic and absolute time kinematical groups. We show that noncommutative symplectic structures can be generated in the…
A deterministic method for synthesizing the interconnect topologies optimized for the required properties is proposed. The method is based on the original description of graphs by projections, on establishing the bijective correspondence of…
We study the analytic and topological invariants associated with complex normal surface singularities. Our goal is to provide topological formulae for several discrete analytic invariants whenever the analytic structure is generic (with…
We use the structure theory of minimal dynamical systems to show that, for a general group $\Gamma$, a tame, metric, minimal dynamical system $(X, \Gamma)$ has the following structure: \begin{equation*} \xymatrix {& \tilde{X} \ar[dd]_\pi…
Detection of crystal structures from particle positions of crystalline assemblies formed in computer simulations is an unsolved problem. The standard protocol, formulated in the reciprocal space, for structure determination from…
For any finite set $\A$ of $n$ points in $\R^2$, we define a $(3n-3)$-dimensional simple polyhedron whose face poset is isomorphic to the poset of ``non-crossing marked graphs'' with vertex set $\A$, where a marked graph is defined as a…
Symmetry groups allow to transform solutions of differential equations continuously into other solutions. This property can be used for the observability analysis of infinite-dimensional systems with input and output. In this contribution,…
Crystallographic defects play a key role in determining the properties of crystalline materials. The new class of two-dimensional materials, foremost graphene, have enabled atomically resolved studies of defects, such as vacancies, grain…
Associated with a symmetric Clifford system $\{P_0, P_1,\cdots, P_{m}\}$ on $\mathbb{R}^{2l}$, there is a canonical vector bundle $\eta$ over $S^{l-1}$. For $m=4$ and $8$, we construct explicitly its characteristic map, and determine…
In this paper we study the homology and cohomology of confguration spaces of two distinct particles on a graph. Our main tool is intersection theory for cycles in graphs. We obtain an explicit description of the cohomology algebra of the…
We propose a method for inferring the conditional indepen- dence graph (CIG) of a high-dimensional discrete-time Gaus- sian vector random process from finite-length observations. Our approach does not rely on a parametric model (such as,…
The rapid progress in precisely designing the surface decoration of patchy colloidal particles offers a new, yet unexperienced freedom to create building entities for larger, more complex structures in soft matter systems. However, it is…
The efforts associated with parametrization of continuum-based models for crystal plasticity are a significant obstacle for the routine use of these models in materials science and engineering. While phenomenological constitutive…
We introduce a variational method for the approximation of ground states of strongly interacting spin systems in arbitrary geometries and spatial dimensions. The approach is based on weighted graph states and superpositions thereof. These…
We discuss Cauchy type decompositions of crystal graphs for general linear Lie superalgebras. More precisely, we consider bicrystal graph structures on various sets of matrices of non-negative integers, and obtain their decompositions with…
We discuss existing and new computational analysis techniques to classify local atomic arrangements in large-scale atomistic computer simulations of crystalline solids. This article includes a performance comparison of typical analysis…
The vertices of a finite state system are usually a subset of the natural numbers. Most algorithms relative to these systems only use this fact to select vertices. For infinite state systems, however, the situation is different: in…
Crystalline structure prediction is an essential prerequisite for designing materials with targeted properties. Yet, it is still an open challenge in materials design and drug discovery. Despite recent advances in computational materials…