相关论文: Viruses and Fullerenes - Symmetry as a Common Thre…

We study what happens when coherence fails. Categories with a tensor product and a natural associativity isomorphism that does not necessarily satisfy the pentagon coherence requirements (called associative categories) are considered.…

Several well known polytopal constuctions are examined from the functorial point of view. A naive analogy between the Billera-Sturmfels fiber polytope and the abelian kernel is disproved by an infinite explicit series of polytopes. A…

The packaging of genetic material within a protein shell, called the capsid, marks a pivotal step in the life cycle of numerous single-stranded RNA viruses. Understanding how hundreds, or even thousands, of proteins assemble around the…

Let $(\mathcal C,\otimes,1)$ be an abelian symmetric monoidal category satisfying certain conditions and let $X$ be a scheme over $(\mathcal C,\otimes,1)$ in the sense of To\"en and Vaqui\'{e}. In this paper we show that when $X$ is…

We work out the notion of mirror symmetry for abelian varieties and study its properties. Our construction are based on the correspondence between two $Q$--algebraic groups. One is the Hodge (or special Mumford--Tate) group. The second…

We present an atomic cluster expansion (ACE) for carbon that improves over available classical and machine learning potentials. The ACE is parameterized from an exhaustive set of important carbon structures at extended volume and energy…

The Buckminsterfullerene is an inorganic molecule consisting of 60 carbon atoms in the shape of a soccer ball. It was used in [Juhas et al., Nature 2006] to showcase algorithms that find the correct shape of a protein from limited data…

We obtain analogues of classical results on automorphism groups of holomorphic fiber bundles, in the setting of group schemes. Also, we establish a lifting property of the connected automorphism group, for torsors under abelian varieties.…

In our [Higher-order preconnections in synthetic differential geometry of jet bundles, Beitr\"{a}ge zur Algebra und Geometrie, 45 (2004), 677-696] we have established the affine bundle theorem in the synthetic approach to jet bundles in…

A general algebraic approach, incorporating both invariance groups and dynamic symmetry algebras, is developed to reveal hidden coherent structures (closed complexes and configurations) in quantum many-body physics models due to symmetries…

We introduce new objects, called $(G,c)$-bands, associated with a simple simply-connected algebraic group $G$, and a Coxeter element $c$ in its Weyl group. We show that bands of a given type are the $K$-points of an infinite dimensional…

We give a construction and algorithmic description of the fusion ring of permutation extensions of an arbitrary modular tensor category using a combinatorial approach inspired by the physics of anyons and symmetry defects in bosonic…

The orientational correlation scheme introduced earlier for tetrahedral molecules is extended for being able to classify orientational correlations between pairs of high symmetry molecules. While in the original algorithm a given…

Symmetry detection can improve various machine learning tasks. In the context of continuous symmetry detection, current state of the art experiments are limited to detecting affine transformations. Under the manifold assumption, we outline…

A series of simulations aimed at elucidating the self-assembly dynamics of spherical virus capsids is described. This little-understood phenomenon is a fascinating example of the complex processes that occur in the simplest of organisms.…

Until recently, a careful derivation of the fusion structure of anyons from some underlying physical principles has been lacking. In [Shi et al., Ann. Phys., 418 (2020)], the authors achieved this goal by starting from a conjectured form of…

We show that the fermionic exclusion principle in scattering problems manifests itself through constraints implied by unitarity and the optical theorem. Configurations that formally allow identical fermions to appear in the same quantum…

An orbit polytope is the convex hull of an orbit under a finite group $G \leq \operatorname{GL}(d,\mathbb{R})$. We develop a general theory of possible affine symmetry groups of orbit polytopes. For every group, we define an open and dense…

Quasiperiodic patterns described by polyhedral "atomic surfaces" and admitting matching rules are considered. It is shown that the cohomology ring of the continuous hull of such patterns is isomorphic to that of the complement of a torus…

Associated to any affine space A endowed with a metric structure of arbitrary signature we consider the space of affine functionals operating on the space of quadratic functions of A. On this functional space we characterize a symmetric…