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Stresses and Liftings of Cell-Complexes
  • K. Rybnikov
  • Mathematics, Computer Science
  • Discret. Comput. Geom.
  • 1 June 1999
TLDR
This paper introduces a general notion of stress on cell-complexes and reports on connections between stresses and liftings (generalization of C10 -splines) of d -dimensional cell- complexes in Rd . Expand
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Efficient pseudo-random number generators for biomolecular simulations on graphics processors
Langevin Dynamics, Monte Carlo, and all-atom Molecular Dynamics simulations in implicit solvent, widely used to access the microscopic transitions in biomolecules, require a reliable source of randomExpand
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The Theory of Quality Translations with Applications to Tilings
TLDR
In this paper, we consider a broad class of simply connected complexes that includes, for example, the face-to-face tilings ofEnandSn. We obtain some theorems on colouring the cells of a complex, and we generalize the main part of Voronoi?s famous theorem on primitive parallelohedra 16. Expand
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Estimation of Euler Characteristic from Point Data
Determination of the geometry and topology of a 3-dimensional body is an important problem appearing in Computer Aided Design, medical tomography, crystallography, molecular biology, etc. The methodsExpand
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An Infinite Series of Perfect Quadratic Forms and Big Delaunay Simplexes in Z^n
George Voronoi (1908-09) introduced two important reduction methods for positive quadratic forms: the reduction with perfect forms, and the reduction with L-type domains. A form is perfect if can beExpand
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Voronoi-Dickson Hypothesis on Perfect Forms and L-types
George Voronoi (1908, 1909) introduced two important reduction methods for positive quadratic forms: the reduction with perfect forms, and the reduction withLtype domains, often called domains ofExpand
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On Voronoi ’ s two tilings of the cone of metrical forms
In his last two papers Georges Voronoi introduced two tilings for the cone of metrical forms for lattices, the tiling by perfect domains and the tiling by lattice type domains. Both areExpand
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Generation of random numbers on graphics processors: forced indentation in silico of the bacteriophage HK97.
The use of graphics processing units (GPUs) in simulation applications offers a significant speed gain as compared to computations on central processing units (CPUs). Many simulation methods requireExpand
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Confident Predictability: Identifying reliable gene expression patterns for individualized tumor classification using a local minimax kernel algorithm
TLDR
We devise a local minimax kernel learning algorithm that is capable of making individualized prediction in several microarray cancer gene expression data sets and achieve significantly lower error rate for a substantial identifiable subset of patients. Expand
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Criteria for Balance in Abelian Gain Graphs, with Applications to Piecewise-Linear Geometry
TLDR
We propose a criterion for balance in abelian gain graphs that is broader than previous ones, but which has the drawback that it is not valid for all groups. Expand
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