Related papers: Extended Configurational Polyhedra Based on Graph …
Multi-component aggregates are being intensively researched in various fields because of their highly tunable properties and wide applications. Due to the complex configurational space of these systems, research would greatly benefit from a…
Scheme-theoretic methods are used to classify ternary quadratic forms with values in line bundles over arbitrary schemes and to canonically determine the isomorphisms between them. The association of a quadratic bundle to its even Clifford…
We want to introduce a construction of spherical designs from finite graphs with the theory of crystal lattice. We start from a finite graph, and we consider standard realization of the crystal lattices as the maximal Abelian covering of…
Atomic-level modeling performed at large scales enables the investigation of mesoscale materials properties with atom-by-atom resolution. The spatial complexity of such cross-scale simulations renders them unsuitable for simple human visual…
We propose a highly coarse-grained simulation model for crystalline polymer solids with crystalline lamellar structures. The mechanical properties of a crystalline polymer solid are mainly determined by the crystalline lamellar structures.…
Reliable and robust methods of predicting the crystal structure of a compound, based only on its chemical composition, is crucial to the study of materials and their applications. Despite considerable ongoing research efforts, crystal…
When flat or on a firm mechanical substrate, the atomic composition and atomistic structure of two-dimensional crystals dictate their chemical, electronic, optical, and mechanical properties. These properties change when the two-dimensional…
It is well known that not every combinatorial configuration admits a geometric realization with points and lines. Moreover, some of them do not even admit realizations with pseudoline arrangements, i.e., they are not topological. In this…
Determining the atomic-level structure of crystalline solids is critically important across a wide array of scientific disciplines. The challenges associated with obtaining samples suitable for single-crystal diffraction, coupled with the…
The evolution of the atomic structures of the combinatorial library of Sm-substituted thin film BiFeO3 along the phase transition boundary from the ferroelectric rhombohedral phase to the non-ferroelectric orthorhombic phase is explored…
The graph isomorphism (GI) problem, which asks whether two graphs are structurally identical, occupies a unique position in computational complexity -- it is neither known to be solvable in polynomial time, nor proven to be NP-complete. We…
We introduce a new combinatorial abstraction for the graphs of polyhedra. The new abstraction is a flexible framework defined by combinatorial properties, with each collection of properties taken providing a variant for studying the…
We characterise rigid graphs for cylindrical normed spaces $Z=X\oplus_\infty \mathbb{R}$ where $X$ is a finite dimensional real normed linear space and $Z$ is endowed with the product norm. In particular, we obtain purely combinatorial…
The graphical structure of Probabilistic Graphical Models (PGMs) represents the conditional independence (CI) relations that hold in the modeled distribution. Every separator in the graph represents a conditional independence relation in…
Crystal Structure Prediction (CSP) is crucial in various scientific disciplines. While CSP can be addressed by employing currently-prevailing generative models (e.g. diffusion models), this task encounters unique challenges owing to the…
We investigate the structure of conformally rigid graphs. Graphs are conformally rigid if introducing edge weights cannot increase (decrease) the second (last) eigenvalue of the Graph Laplacian. Edge-transitive graphs and distance-regular…
Many interesting geometric structures can be described as regular infinitesimal flag structures, which occur as the underlying structures of parabolic geometries. Among these structures we have for instance conformal structures, contact…
Let $M$ be a subset of vector space or projective space. The authors define the \emph{generalized configuration space} of $M$ which is formed by $n$-tuples of elements of $M$ where any $k$ elements of each $n$-tuple are linearly…
We study the use of polyhedral discretizations for the solution of heat diffusion and elastodynamic problems in computer graphics. Polyhedral meshes are more natural for certain applications than pure triangular or quadrilateral meshes,…
Symmetric edge polytopes are a recent and well-studied family of centrally symmetric polytopes arising from graphs. In this paper, we introduce a generalization of this family to arbitrary simplicial complexes. We show how topological…