Related papers: A central partition of molecular conformational sp…
In a previous paper we introduced examples of Hamiltonian mappings with phase space structures resembling circle packings. We now concentrate on one particular mapping and present numerical evidence which supports the conjecture that the…
This paper defines the basis of a new hierarchical framework for segmentation algorithms based on energy minimization schemes. This new framework is based on two formal tools. First, a combinatorial pyramid encode efficiently a hierarchy of…
Hollow-section columns are one of the mechanically superior structures with high buckling resistance and high bending stiffness. The mechanical properties of the column are strongly influenced by the cross-sectional shape. Therefore, when…
Spatial organization of proteins in cells is important for many biological functions. In general, the nonlinear, spatially coupled models for protein-pattern formation are only accessible to numerical simulations, which has limited insight…
We investigate the geometrical structure of multipartite states based on the construction of toric varieties. We show that the toric variety represents the space of general pure states and projective toric variety defines the space of…
Many machine learning algorithms represent input data with vector embeddings or discrete codes. When inputs exhibit compositional structure (e.g. objects built from parts or procedures from subroutines), it is natural to ask whether this…
The notion of a coherent space is a nonlinear version of the notion of a complex Euclidean space: The vector space axioms are dropped while the notion of inner product is kept. Coherent spaces provide a setting for the study of geometry in…
We study various properties of the vibrational normal modes for Coulomb-interacting particles in two-dimensional irregular confinement using numerical simulations. By analyzing the participation ratio and spectral statistics, we…
In this work, we study the long time asymptotics of a coagulation model which describes the evolution of a system of particles characterized by their volume and surface area. The aggregation mechanism takes place in two stages: collision…
Recently several authors studied the segregation of particles for a system composed of mono-dispersed inelastic spheres contained in a box divided by a wall in the middle. The system exhibited a symmetry breaking leading to an…
This work deals with the topological classification of germs of singular foliations on $(\mathbb C^{2},0)$. Working in a suitable class of foliations we fix the topological invariants given by the separatrix set, the Camacho-Sad indices and…
A theoretical study of the structure formation observed very recently [Phys. Rev. Lett. 90, 128303 (2003)] in binary colloids is presented. In our model solely the dipole-dipole interaction of the particles is considered,…
Characterizing structural and dynamic properties of proteins and large macromolecular assemblies is crucial to understand the molecular mechanisms underlying biological functions. In the field of Structural Biology, no single method…
Recently the phase space structures governing reaction dynamics in Hamiltonian systems have been identified and algorithms for their explicit construction have been developed. These phase space structures are induced by saddle type…
We expose (without proofs) a unified computational approach to integrable structures (including recursion, Hamiltonian, and symplectic operators) based on geometrical theory of partial differential equations. We adopt a coordinate based…
This thesis is basically devoted to matroids -- fundamental structure of combinatorial optimization -- though some of our results concern simplicial complexes, or Euclidean spaces. We study old and new problems for these structures, with…
When spatial constraint for the constituents (e.g., atom or particle) of system is once given, disordered structure for non-interacting system in equilibrium states is symmetric with respect to equiatomic composition. Meanwhile, when the…
This is a survey of the theory of complex projective (CP^1) structures on compact surfaces. After some preliminary discussion and definitions, we concentrate on three main topics: (1) Using the Schwarzian derivative to parameterize the…
This paper solves the problem of computing conformal structures of general 2-manifolds represented as triangle meshes. We compute conformal structures in the following way: first compute homology bases from simplicial complex structures,…
Two-dimensional colloidal suspensions exposed to periodic external fields exhibit a variety of molecular crystalline phases. There two or more colloids assemble at lattice sites of potential minima to build new structural entities, referred…