PARAVT: Parallel Voronoi tessellation code
González, R. E.
2016-10-01
In this study, we present a new open source code for massive parallel computation of Voronoi tessellations (VT hereafter) in large data sets. The code is focused for astrophysical purposes where VT densities and neighbors are widely used. There are several serial Voronoi tessellation codes, however no open source and parallel implementations are available to handle the large number of particles/galaxies in current N-body simulations and sky surveys. Parallelization is implemented under MPI and VT using Qhull library. Domain decomposition takes into account consistent boundary computation between tasks, and includes periodic conditions. In addition, the code computes neighbors list, Voronoi density, Voronoi cell volume, density gradient for each particle, and densities on a regular grid. Code implementation and user guide are publicly available at https://github.com/regonzar/paravt.
Symmetry-Break in Voronoi Tessellations
Valerio Lucarini
2009-08-01
Full Text Available We analyse in a common framework the properties of the Voronoi tessellations resulting from regular 2D and 3D crystals and those of tessellations generated by Poisson distributions of points, thus joining on symmetry breaking processes and the approach to uniform random distributions of seeds. We perturb crystalline structures in 2D and 3D with a spatial Gaussian noise whose adimensional strength is α and analyse the statistical properties of the cells of the resulting Voronoi tessellations using an ensemble approach. In 2D we consider triangular, square and hexagonal regular lattices, resulting into hexagonal, square and triangular tessellations, respectively. In 3D we consider the simple cubic (SC, body-centred cubic (BCC, and face-centred cubic (FCC crystals, whose corresponding Voronoi cells are the cube, the truncated octahedron, and the rhombic dodecahedron, respectively. In 2D, for all values α>0, hexagons constitute the most common class of cells. Noise destroys the triangular and square tessellations, which are structurally unstable, as their topological properties are discontinuous in α=0. On the contrary, the honeycomb hexagonal tessellation is topologically stable and, experimentally, all Voronoi cells are hexagonal for small but finite noise with α<0.12. Basically, the same happens in the 3D case, where only the tessellation of the BCC crystal is topologically stable even against noise of small but finite intensity. In both 2D and 3D cases, already for a moderate amount of Gaussian noise (α>0.5, memory of the specific initial unperturbed state is lost, because the statistical properties of the three perturbed regular tessellations are indistinguishable. When α>2, results converge to those of Poisson-Voronoi tessellations. In 2D, while the isoperimetric ratio increases with noise for the perturbed hexagonal tessellation, for the perturbed triangular and square tessellations it is optimised for specific value of noise intensity
Bishop, Joseph E.
2008-09-01
Under extreme loading conditions most often the extent of material and structural fracture is pervasive in the sense that a multitude of cracks are nucleating, propagating in arbitrary directions, coalescing, and branching. Pervasive fracture is a highly nonlinear process involving complex material constitutive behavior, material softening, localization, surface generation, and ubiquitous contact. Two primary applications in which pervasive fracture is encountered are (1) weapons effects on structures and (2) geomechanics of highly jointed and faulted reservoirs. A pure Lagrangian computational method based on randomly close-packed Voronoi tessellations is proposed as a rational approach for simulating the pervasive fracture of materials and structures. Each Voronoi cell is formulated as a finite element using the reproducing kernel method. Fracture surfaces are allowed to nucleate only at the intercell faces. The randomly seeded Voronoi cells provide an unbiased network for representing cracks. In this initial study two approaches for allowing the new surfaces to initiate are studied: (1) dynamic mesh connectivity and the instantaneous insertion of a cohesive traction when localization is detected, and (2) a discontinuous Galerkin approach in which the interelement tractions are an integral part of the variational formulation, but only become active once localization is detected. Pervasive fracture problems are extremely sensitive to initial conditions and system parameters. Dynamic problems exhibit a form of transient chaos. The primary numerical challenge for this class of problems is the demonstration of model objectivity and, in particular, the identification and demonstration of a measure of convergence for engineering quantities of interest.
Identifying Phase Space Boundaries with Voronoi Tessellations
Debnath, Dipsikha; Kilic, Can; Kim, Doojin; Matchev, Konstantin T.; Yang, Yuan-Pao
2016-11-24
Determining the masses of new physics particles appearing in decay chains is an important and longstanding problem in high energy phenomenology. Recently it has been shown that these mass measurements can be improved by utilizing the boundary of the allowed region in the fully differentiable phase space in its full dimensionality. Here we show that the practical challenge of identifying this boundary can be solved using techniques based on the geometric properties of the cells resulting from Voronoi tessellations of the relevant data. The robust detection of such phase space boundaries in the data could also be used to corroborate a new physics discovery based on a cut-and-count analysis.
Identifying Phase Space Boundaries with Voronoi Tessellations
Debnath, Dipsikha; Kilic, Can; Kim, Doojin; Matchev, Konstantin T; Yang, Yuan-Pao
2016-01-01
Determining the masses of new physics particles appearing in decay chains is an important and longstanding problem in high energy phenomenology. Recently it has been shown that these mass measurements can be improved by utilizing the boundary of the allowed region in the fully differentiable phase space in its full dimensionality. Here we show that the practical challenge of identifying this boundary can be solved using techniques based on the geometric properties of the cells resulting from Voronoi tessellations of the relevant data. The robust detection of such phase space boundaries in the data could also be used to corroborate a new physics discovery based on a cut-and-count analysis.
Voronoi Tessellations and Their Application to Climate and Global Modeling
Ju, Lili [University of South Carolina; Ringler, Todd [Los Alamos National Laboratory; Gunzburger, Max [Florida State University
2011-01-01
We review the use of Voronoi tessellations for grid generation, especially on the whole sphere or in regions on the sphere. Voronoi tessellations and the corresponding Delaunay tessellations in regions and surfaces on Euclidean space are defined and properties they possess that make them well-suited for grid generation purposes are discussed, as are algorithms for their construction. This is followed by a more detailed look at one very special type of Voronoi tessellation, the centroidal Voronoi tessellation (CVT). After defining them, discussing some of their properties, and presenting algorithms for their construction, we illustrate the use of CVTs for producing both quasi-uniform and variable resolution meshes in the plane and on the sphere. Finally, we briefly discuss the computational solution of model equations based on CVTs on the sphere.
Spherical Layout Implementation using Centroidal Voronoi Tessellations
Larrea, Martin; Martig, Sergio; Castro, Silvia
2009-01-01
The 3D tree visualization faces multiple challenges: the election of an appropriate layout, the use of the interactions that make the data exploration easier and a metaphor that helps in the process of information understanding. A good combination of these elements will result in a visualization that effectively conveys the key features of a complex structure or system to a wide range of users and permits the analytical reasoning process. In previous works we presented the Spherical Layout, a technique for 3D tree visualization that provides an excellent base to achieve those key features. The layout was implemented using the TriSphere algorithm, a method that discretized the spheres's surfaces with triangles to achieve a uniform distribution of the nodes. The goal of this work was centered in a new algorithm for the implementation of the Spherical layout; we called it the Weighted Spherical Centroidal Voronoi Tessellations (WSCVT). In this paper we present a detailed description of this new implementation an...
Non-obtuse Remeshing with Centroidal Voronoi Tessellation
Yan, Dongming
2015-12-03
We present a novel remeshing algorithm that avoids triangles with small and triangles with large (obtuse) angles. Our solution is based on an extension to Centroidal Voronoi Tesselation (CVT). We augment the original CVT formulation by a penalty term that penalizes short Voronoi edges, while the CVT term helps to avoid small angles. Our results show significant improvements of the remeshing quality over the state of the art.
Doroshkevich, A G; Madsen, S; Doroshkevich, Andrei G.; Gottloeber, Stefan; Madsen, Soeren
1996-01-01
The large-scale matter distribution represents a complex network of structure elements such as voids, clusters, filaments, and sheets. This network is spanned by a point distribution. The global properties of the point process can be measured by different statistical methods, which, however, do not describe directly the structure elements. The morphology of structure elements is an important property of the point distribution. Here we apply the core-sampling method to various Voronoi tessellations. Using the core-sampling method we identify one- and two-dimensional structure elements (filaments and sheets) in these Voronoi tessellations and reconstruct their mean separation along random straight lines. We compare the results of the core-sampling method with the a priori known structure elements of the Voronoi tessellations under consideration and find good agreement between the expected and found structure parameters, even in the presence of substantial noise. We conclude that the core-sampling method is a po...
Probing the sparse tails of redshift distributions with Voronoi tessellations
Granett, B. R.
2017-01-01
We introduce an empirical galaxy photometric redshift algorithm based upon the Voronoi tessellation density estimator in the space of redshift and photometric parameters. Our aim is to use sparse survey datasets to estimate the full shape of the redshift distribution that is defined by the degeneracies in galaxy photometric properties and redshift. We describe the algorithm implementation and provide a proof of concept using the first public data release from the VIMOS Public Extragalactic Redshift Survey (VIPERS PDR-1). We validate the method by comparing against the standard empirical redshift distribution code Trees for Photo-Z (TPZ) on both mock and real data. We find that the Voronoi tessellation algorithm accurately recovers the full shape of the redshift distribution quantified by its second moment and inferred redshift confidence intervals. The analysis allows us to properly account for galaxies in the tails of the distributions that would otherwise be classified as catastrophic outliers. The source code is publicly available at http://bitbucket.org/bengranett/tailz.
Identifying phase-space boundaries with Voronoi tessellations
Debnath, Dipsikha; Matchev, Konstantin T. [University of Florida, Physics Department, Gainesville, FL (United States); Gainer, James S. [University of Hawaii, Department of Physics and Astronomy, Honolulu, HI (United States); Kilic, Can; Yang, Yuan-Pao [The University of Texas at Austin, Theory Group, Department of Physics and Texas Cosmology Center, Austin, TX (United States); Kim, Doojin [University of Florida, Physics Department, Gainesville, FL (United States); CERN, Theory Division, Geneva 23 (Switzerland)
2016-11-15
Determining the masses of new physics particles appearing in decay chains is an important and longstanding problem in high energy phenomenology. Recently it has been shown that these mass measurements can be improved by utilizing the boundary of the allowed region in the fully differentiable phase space in its full dimensionality. Here we show that the practical challenge of identifying this boundary can be solved using techniques based on the geometric properties of the cells resulting from Voronoi tessellations of the relevant data. The robust detection of such phase-space boundaries in the data could also be used to corroborate a new physics discovery based on a cut-and-count analysis. (orig.)
Planar discrete birth-growth Poisson–Voronoi tessellations with the von Neumann neighbourhood
Korobov, A.
2017-02-01
Poisson–Voronoi tessellations are widely used as the generic model for studying various birth-growth processes and resulting morphologies in physics, chemistry, materials science, and related fields. This paper studies planar discrete Poisson–Voronoi tessellations constructed directly by the growth to impingement of random square germs. They materially differ from similar tessellations constructed of the nearest tile loci according to the basic definition. The boundary structure is described in detail. Its peculiarities are used to extend the concept of Gabriel edges to the considered discrete case and also to quantify this concept. The averaged percentage of Gabriel edges appears to be practically independent of the germs density, \\bar{G} = 70%. The studied densities range from 0.01 to 0.000 01. Statistical results are presented for the whole tessellation and also for subsets of random domains with the given number of edges ν. Two sets of results are compared: for edges of each random domain arranged from the longest to the shortest and for edges arranged from the nearest to the most distant. Averaged distances to neighbours in the metric determined by the growth mode of islands are compared with that in the Euclidean metric. Also, the cyclic sequences of edge lengths of random domains are examined. The linearity with respect to ν is revealed for four scaling-related characteristics: the area of random domains, the perimeter length of random domains, the area of complete concentric belts, and the coordinates of maxima of kinetic curves.
The Voronoi Tessellation Cluster Finder in 2 1 Dimensions
Soares-Santos, Marcelle; /Fermilab /Sao Paulo U.; de Carvalho, Reinaldo R.; /Sao Jose, INPE; Annis, James; /Fermilab; Gal, Roy R.; /Hawaii U.; La Barbera, Francesco; /Capodimonte Observ.; Lopes, Paulo A.A.; /Valongo Observ.; Wechsler, Risa H.; Busha, Michael T.; Gerke, Brian F.; /SLAC /KIPAC, Menlo Park
2011-06-23
We present a detailed description of the Voronoi Tessellation (VT) cluster finder algorithm in 2+1 dimensions, which improves on past implementations of this technique. The need for cluster finder algorithms able to produce reliable cluster catalogs up to redshift 1 or beyond and down to 10{sup 13.5} solar masses is paramount especially in light of upcoming surveys aiming at cosmological constraints from galaxy cluster number counts. We build the VT in photometric redshift shells and use the two-point correlation function of the galaxies in the field to both determine the density threshold for detection of cluster candidates and to establish their significance. This allows us to detect clusters in a self-consistent way without any assumptions about their astrophysical properties. We apply the VT to mock catalogs which extend to redshift 1.4 reproducing the ?CDM cosmology and the clustering properties observed in the Sloan Digital Sky Survey data. An objective estimate of the cluster selection function in terms of the completeness and purity as a function of mass and redshift is as important as having a reliable cluster finder. We measure these quantities by matching the VT cluster catalog with the mock truth table. We show that the VT can produce a cluster catalog with completeness and purity >80% for the redshift range up to {approx}1 and mass range down to {approx}10{sup 13.5} solar masses.
The Voronoi Tessellation Cluster Finder in 2 1 Dimensions
Soares-Santos, Marcelle; /Fermilab /Sao Paulo U.; de Carvalho, Reinaldo R.; /Sao Jose, INPE; Annis, James; /Fermilab; Gal, Roy R.; /Hawaii U.; La Barbera, Francesco; /Capodimonte Observ.; Lopes, Paulo A.A.; /Valongo Observ.; Wechsler, Risa H.; Busha, Michael T.; Gerke, Brian F.; /SLAC /KIPAC, Menlo Park
2011-06-23
We present a detailed description of the Voronoi Tessellation (VT) cluster finder algorithm in 2+1 dimensions, which improves on past implementations of this technique. The need for cluster finder algorithms able to produce reliable cluster catalogs up to redshift 1 or beyond and down to 10{sup 13.5} solar masses is paramount especially in light of upcoming surveys aiming at cosmological constraints from galaxy cluster number counts. We build the VT in photometric redshift shells and use the two-point correlation function of the galaxies in the field to both determine the density threshold for detection of cluster candidates and to establish their significance. This allows us to detect clusters in a self-consistent way without any assumptions about their astrophysical properties. We apply the VT to mock catalogs which extend to redshift 1.4 reproducing the ?CDM cosmology and the clustering properties observed in the Sloan Digital Sky Survey data. An objective estimate of the cluster selection function in terms of the completeness and purity as a function of mass and redshift is as important as having a reliable cluster finder. We measure these quantities by matching the VT cluster catalog with the mock truth table. We show that the VT can produce a cluster catalog with completeness and purity >80% for the redshift range up to {approx}1 and mass range down to {approx}10{sup 13.5} solar masses.
Zhao, Q. H.; Li, Y.; Wang, Y.
2016-06-01
This paper presents a novel segmentation method for automatically determining the number of classes in Synthetic Aperture Radar (SAR) images by combining Voronoi tessellation and Reversible Jump Markov Chain Monte Carlo (RJMCMC) strategy. Instead of giving the number of classes a priori, it is considered as a random variable and subject to a Poisson distribution. Based on Voronoi tessellation, the image is divided into homogeneous polygons. By Bayesian paradigm, a posterior distribution which characterizes the segmentation and model parameters conditional on a given SAR image can be obtained up to a normalizing constant; Then, a Revisable Jump Markov Chain Monte Carlo(RJMCMC) algorithm involving six move types is designed to simulate the posterior distribution, the move types including: splitting or merging real classes, updating parameter vector, updating label field, moving positions of generating points, birth or death of generating points and birth or death of an empty class. Experimental results with real and simulated SAR images demonstrate that the proposed method can determine the number of classes automatically and segment homogeneous regions well.
Single- and two-phase flow in microfluidic porous media analogs based on Voronoi tessellation
Wu, Mengjie [Colorado School of Mines, Golden; Xiao, Feng [Colorado School of Mines, Golden; Johnson-Paben, Rebecca [Colorado School of Mines, Golden; Retterer, Scott T [ORNL; Yin, Xiaolong [Colorado School of Mines, Golden; Neeves, Keith B [ORNL
2012-01-01
The objective of this study was to create a microfluidic model of complex porous media for studying single and multiphase flows. Most experimental porous media models consist of periodic geometries that lend themselves to comparison with well-developed theoretical predictions. However, most real porous media such as geological formations and biological tissues contain a degree of randomness and complexity that is not adequately represented in periodic geometries. To design an experimental tool to study these complex geometries, we created microfluidic models of random homogeneous and heterogeneous networks based on Voronoi tessellations. These networks consisted of approximately 600 grains separated by a highly connected network of channels with an overall porosity of 0.11 0.20. We found that introducing heterogeneities in the form of large cavities within the network changed the permeability in a way that cannot be predicted by the classical porosity-permeability relationship known as the Kozeny equation. The values of permeability found in experiments were in excellent agreement with those calculated from three-dimensional lattice Boltzmann simulations. In two-phase flow experiments of oil displacement with water we found that the surface energy of channel walls determined the pattern of water invasion, while the network topology determined the residual oil saturation. These results suggest that complex network topologies lead to fluid flow behavior that is difficult to predict based solely on porosity. The microfluidic models developed in this study using a novel geometry generation algorithm based on Voronoi tessellation are a new experimental tool for studying fluid and solute transport problems within complex porous media.
Zhao, Leyi; Zhao, Xiuyun; Burke, Luke T; Bennett, J Craig; Dunlap, Richard A; Obrovac, Mark N
2017-09-11
A highly crystalline graphite powder was prepared from the low temperature (800-1000 °C) graphitization of renewable hard carbon precursors using a magnesium catalyst. The resulting graphite particles are composed of Voronoi-tessellated regions comprising irregular sheets; each Voronoi-tessellated region having a small "seed" particle located near their centroid on the surface. This suggests nucleated outward growth of graphitic carbon, which has not been previously observed. Each seed particle consists of a spheroidal graphite shell on the inside of which hexagonal graphite platelets are perpendicularly affixed. This results in a unique high surface area graphite with a high degree of graphitization that is made with renewable feedstocks at temperatures far below that conventionally used for artificial graphites. © 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.
High-Performance Computation of Distributed-Memory Parallel 3D Voronoi and Delaunay Tessellation
Peterka, Tom; Morozov, Dmitriy; Phillips, Carolyn
2014-11-14
Computing a Voronoi or Delaunay tessellation from a set of points is a core part of the analysis of many simulated and measured datasets: N-body simulations, molecular dynamics codes, and LIDAR point clouds are just a few examples. Such computational geometry methods are common in data analysis and visualization; but as the scale of simulations and observations surpasses billions of particles, the existing serial and shared-memory algorithms no longer suffice. A distributed-memory scalable parallel algorithm is the only feasible approach. The primary contribution of this paper is a new parallel Delaunay and Voronoi tessellation algorithm that automatically determines which neighbor points need to be exchanged among the subdomains of a spatial decomposition. Other contributions include periodic and wall boundary conditions, comparison of our method using two popular serial libraries, and application to numerous science datasets.
Voro3D: 3D Voronoi tessellations applied to protein structures.
Dupuis, Franck; Sadoc, Jean-François; Jullien, Rémi; Angelov, Borislav; Mornon, Jean-Paul
2005-04-15
Voro3D is an original easy-to-use tool, which provides a brand new point of view on protein structures through the three-dimensional (3D) Voronoi tessellations. To construct the Voronoi cells associated with each amino acid by a number of different tessellation methods, Voro3D uses a protein structure file in the PDB format as an input. After calculation, different structural properties of interest like secondary structures assignment, environment accessibility and exact contact matrices can be derived without any geometrical cut-off. Voro3D provides also a visualization of these tessellations superimposed on the associated protein structure, from which it is possible to model a polygonal protein surface using a model solvent or to quantify, for instance, the contact areas between a protein and a ligand. The software executable file for PC using Windows 98, 2000, NT, XP can be freely downloaded at http://www.lmcp.jussieu.fr/~mornon/voronoi.html franck.dupuis@sanofi-aventis.com; jean-paul-mornon@imcp.jussieu.fr.
2D wireless sensor network deployment based on Centroidal Voronoi Tessellation
Iliodromitis, Athanasios; Pantazis, George; Vescoukis, Vasileios
2017-06-01
In recent years, Wireless Sensor Networks (WSNs) have rapidly evolved and now comprise a powerful tool in monitoring and observation of the natural environment, among other fields. The use of WSNs is critical in early warning systems, which are of high importance today. In fact, WSNs are adopted more and more in various applications, e.g. for fire or deformation detection. The optimum deployment of sensors is a multi-dimensional problem, which has two main components; network and positioning approach. Although lots of work has dealt with the issue, most of it emphasizes on mere network approach (communication, energy consumption) and not on the topography (positioning) of the sensors in achieving ideal geometry. In some cases, it is hard or even impossible to achieve perfect geometry in nodes' deployment. The ideal and desirable scenario of nodes arranged in square or hexagonal grid would raise extremely the cost of the network, especially in unfriendly or hostile environments. In such environments the positions of the sensors have to be chosen among a list of possible points, which in most cases are randomly distributed. This constraint has to be taken under consideration during the WSN planning. Full geographical coverage is in some applications of the same, if not of greater, importance than the network coverage. Cost is a crucial factor at network planning and given that resources are often limited, what matters, is to cover the whole area with the minimum number of sensors. This paper suggests a deployment method for nodes, in large scale and high density WSNs, based on Centroidal Voronoi Tessellation (CVT). It approximates the solution through the geometry of the random points and proposes a deployment plan, for the given characteristics of the study area, in order to achieve a deployment as near as possible to the ideal one.
Stochastic Geometry and Random Tessellations
Møller, Jesper; Stoyan, Dietrich
This paper is to appear in "Tessellations in the Sciences": Virtues, Techniques and Applications of Geometric Tilings", eds. R. van de Weijgaert, G. Vegter, V. Icke and J. Ritzerveld. Springer Verlag....
Initial data for general relativistic SPH with Centroidal Voronoi Tessellations
Pablo, Cruz Pérez Juan
2013-01-01
In this work we present an alternative method to obtain a distribution of particles over an hyper surface, such that they obey a rest-mass density distribution $\\rho(x^i)$. We use density profiles that can be written as $\\rho(x^1,x^2,x^3)=\\rho(x^1) \\rho(x^2) \\rho(x^3)$ in order to be able to use them as a probability density functions. We can find the relation between the chart $x^j$ and a uniform random variable $\\bar{x}^j \\in (0,1)$, say $F(x^j)=\\bar{x}^j$. Using the inverse of this function we relate a set of $N$ arbitrary number of points inside a cube with coordinates $\\{ x^j =F^{-1}(\\bar{x}^j)\\}$ giving the position in order to get the density distribution $\\rho(x^j)$. We get some noise due to the random distribution and we can notice that each time we relax the configuration on the cube we also get a better distribution of the desired physical configuration described with $\\rho(x^j)$. This relaxation of the position of the particles in the cube has been performed a Lloyd's algorithm in 3D and we have u...
Ringler, Todd; Ju, Lili; Gunzburger, Max
2008-11-14
During the next decade and beyond, climate system models will be challenged to resolve scales and processes that are far beyond their current scope. Each climate system component has its prototypical example of an unresolved process that may strongly influence the global climate system, ranging from eddy activity within ocean models, to ice streams within ice sheet models, to surface hydrological processes within land system models, to cloud processes within atmosphere models. These new demands will almost certainly result in the develop of multiresolution schemes that are able, at least regionally, to faithfully simulate these fine-scale processes. Spherical centroidal Voronoi tessellations (SCVTs) offer one potential path toward the development of a robust, multiresolution climate system model components. SCVTs allow for the generation of high quality Voronoi diagrams and Delaunay triangulations through the use of an intuitive, user-defined density function. In each of the examples provided, this method results in high-quality meshes where the quality measures are guaranteed to improve as the number of nodes is increased. Real-world examples are developed for the Greenland ice sheet and the North Atlantic ocean. Idealized examples are developed for ocean–ice shelf interaction and for regional atmospheric modeling. In addition to defining, developing, and exhibiting SCVTs, we pair this mesh generation technique with a previously developed finite-volume method. Our numerical example is based on the nonlinear, shallow water equations spanning the entire surface of the sphere. This example is used to elucidate both the potential benefits of this multiresolution method and the challenges ahead.
Qu, Rui; Liu, Shu-Shen; Zheng, Qiao-Feng; Li, Tong
2017-03-13
Concentration addition (CA) was proposed as a reasonable default approach for the ecological risk assessment of chemical mixtures. However, CA cannot predict the toxicity of mixture at some effect zones if not all components have definite effective concentrations at the given effect, such as some compounds induce hormesis. In this paper, we developed a new method for the toxicity prediction of various types of binary mixtures, an interpolation method based on the Delaunay triangulation (DT) and Voronoi tessellation (VT) as well as the training set of direct equipartition ray design (EquRay) mixtures, simply IDVequ. At first, the EquRay was employed to design the basic concentration compositions of five binary mixture rays. The toxic effects of single components and mixture rays at different times and various concentrations were determined by the time-dependent microplate toxicity analysis. Secondly, the concentration-toxicity data of the pure components and various mixture rays were acted as a training set. The DT triangles and VT polygons were constructed by various vertices of concentrations in the training set. The toxicities of unknown mixtures were predicted by the linear interpolation and natural neighbor interpolation of vertices. The IDVequ successfully predicted the toxicities of various types of binary mixtures.
Spurious dianeutral mixing in a global ocean model using spherical centroidal voronoi tessellations
Zhao, Shimei; Liu, Yudi
2016-12-01
In order to quantitatively evaluate the spurious dianeutral mixing in a global ocean model MPAS-Ocean (Model for Prediction Across Scales) using a spherical centroidal voronoi tessellations developed jointly by the National Center for Atmospheric Research and the Los Alamos National Laboratory in the United States, we choose z* vertical coordinate system in MPAS-Ocean, in which all physical mixing processes, such as convection adjustment and explicit diffusion parameter schemes, are omitted, using a linear equation of state. By calculating the Reference Potential Energy (RPE), front revolution position, time rate of RPE change, probability density function distribution and dimensionless parameter χ, from the perspectives of resolution, viscosity, Horizontal Grid Reynolds Number (HGRN), ReΔ, and momentum transmission scheme, using two ideal cases, overflow and baroclinic eddy channel, we qualitatively analyze the simulation results by comparison with the three non-isopycnal models in Ilicak et al. (2012), i.e., MITGCM, MOM, and ROMS. The results show that the spurious dianeutral mixing in the MPAS-Ocean increases over time. The spurious dianeutral transport is proportional to the HGRN directly and is reduced by increasing the lateral viscosity or using a finer resolution to control HGRN. When the HGRN is less than 10, spurious transport is reduced significantly. When using the proper viscosity closure, MPAS-Ocean performs better than MITGCM and MOM, closely to ROMS, in the 2D case without rotation, and much better than the above-mentioned three ocean models under the condition of 3D space with rotation due to the cell area difference between the hexagon cell and the quadrilateral cell with the same resolution. Both the Zalesak (1979) flux corrected transport scheme and Leith closure in MPAS-Ocean play an excellent role in reducing spurious dianeutral mixing. The performance of Leith scheme is preferable to the condition of three-dimensional baroclinic eddy.
Ward, Logan; Liu, Ruoqian; Krishna, Amar; Hegde, Vinay I.; Agrawal, Ankit; Choudhary, Alok; Wolverton, Chris
2017-07-01
While high-throughput density functional theory (DFT) has become a prevalent tool for materials discovery, it is limited by the relatively large computational cost. In this paper, we explore using DFT data from high-throughput calculations to create faster, surrogate models with machine learning (ML) that can be used to guide new searches. Our method works by using decision tree models to map DFT-calculated formation enthalpies to a set of attributes consisting of two distinct types: (i) composition-dependent attributes of elemental properties (as have been used in previous ML models of DFT formation energies), combined with (ii) attributes derived from the Voronoi tessellation of the compound's crystal structure. The ML models created using this method have half the cross-validation error and similar training and evaluation speeds to models created with the Coulomb matrix and partial radial distribution function methods. For a dataset of 435 000 formation energies taken from the Open Quantum Materials Database (OQMD), our model achieves a mean absolute error of 80 meV/atom in cross validation, which is lower than the approximate error between DFT-computed and experimentally measured formation enthalpies and below 15% of the mean absolute deviation of the training set. We also demonstrate that our method can accurately estimate the formation energy of materials outside of the training set and be used to identify materials with especially large formation enthalpies. We propose that our models can be used to accelerate the discovery of new materials by identifying the most promising materials to study with DFT at little additional computational cost.
Tomellini, Massimo
2017-03-01
On the basis of the Kolmogorov-Johnson-Mehl-Avrami (KJMA) method for space tessellation the kinetics of Voronoi cell filling, by central grain growth, has been studied as a function of the cell size. This is done by solving an integral equation for which a class of solutions is obtained in closed form, where the cell-size probability density is the Gamma distribution function. The computation gives the time evolution of the mean grain size, as a function of cell volume, which is further employed for describing the grain-size probability density function. The present approach is applied to determine, analytically, the exact grain-size distribution function in 1D and the size distributions in 2D and 3D through approximation.
Exact asymptotic statistics of the n-edged face in a 3D Poisson-Voronoi tessellation
Hilhorst, H. J.
2016-05-01
This work considers the 3D Poisson-Voronoi tessellation. It investigates the joint probability distribution {πn}(L) for an arbitrarily selected cell face to be n-edged and for the distance between the seeds of the two adjacent cells to be equal to 2L. For this quantity an exact expression is derived, valid in the limit n\\to ∞ with n 1/6 L fixed. The leading order correction term is determined. Good agreement with earlier Monte Carlo data is obtained. The cell face is shown to be surrounded by a three-dimensional domain that is empty of seeds and is the union of n balls; it is pumpkin-shaped and analogous to the flower of the 2D Voronoi cell. For n\\to ∞ this domain tends towards a torus of equal major and minor radii. The radii scale as n 1/3, in agreement with earlier heuristic work. A detailed understanding is achieved of several other statistical properties of the n-edged cell face.
Many-faced cells and many-edged faces in 3D Poisson-Voronoi tessellations
Hilhorst, H. J.; Lazar, E. A.
2014-10-01
Motivated by recent new Monte Carlo data we investigate a heuristic asymptotic theory that applies to n-faced 3D Poisson-Voronoi cells in the limit of large n. We show how this theory may be extended to n-edged cell faces. It predicts the leading order large-n behavior of the average volume and surface area of the n-faced cell, and of the average area and perimeter of the n-edged face. Such a face is shown to be surrounded by a toroidal region of volume n/λ (with λ the seed density) that is void of seeds. Two neighboring cells sharing an n-edged face are found to have their seeds at a typical distance that scales as n-1/6 and whose probability law we determine. We present a new data set of 4 × 109 Monte Carlo generated 3D Poisson-Voronoi cells, larger than any before. Full compatibility is found between the Monte Carlo data and the theory. Deviations from the asymptotic predictions are explained in terms of subleading corrections whose powers in n we estimate from the data.
Vologzhanina, Anna V; Kats, Svitlana V; Penkova, Larisa V; Pavlenko, Vadim A; Efimov, Nikolay N; Minin, Vadim V; Eremenko, Igor L
2015-10-01
Interaction of 1-(1H-pyrazol-5-yl)ethanone oxime (H2PzOx) with copper(II) chloride in the presence of pyridine afforded a binuclear discrete [Cu2(HPzOx)2Cl2py2] complex, which was characterized by Fourier transform-IR and electron paramagnetic resonance (EPR) spectra, magnetochemistry and high-resolution X-ray diffraction experiments. Multipole refinement of X-ray diffraction data and density-functional theory (DFT) calculations of an isolated molecule allowed charge and spin distributions to be obtained for this compound. Magnetochemistry data, EPR spectra and DFT calculations of an isolated molecule show antiferromagnetic coupling between copper(II) ions. The spin distribution suggests an exchange pathway via the bridging pyrazole ring in the equatorial plane of the CuN4Cl coordination polyhedron, thus providing support for the classical superexchange mechanism; the calculated value of the magnetic coupling constant -2J is equal to 220 cm(-1), which compares well with the experimental value of 203 ± 2 cm(-1). Chemical connectivity was derived by Bader's 'quantum theory of atoms in molecules' and compared with Voronoi tessellation and Hirshfeld surface representations of crystal space. All methodologies gave a similar qualitative and semi-quantitative description of intra- and intermolecular connectivity.
E. Ghazvinian; M.S. Diederichs; R. Quey
2014-01-01
A grain-based distinct element model featuring three-dimensional (3D) Voronoi tessellations (random poly-crystals) is proposed for simulation of crack damage development in brittle rocks. The grain boundaries in poly-crystal structure produced by Voronoi tessellations can represent flaws in intact rock and allow for numerical replication of crack damage progression through initiation and propagation of micro-fractures along grain boundaries. The Voronoi modelling scheme has been used widely in the past for brittle fracture simulation of rock materials. However the difficulty of generating 3D Voronoi models has limited its application to two-dimensional (2D) codes. The proposed approach is implemented in Neper, an open-source engine for generation of 3D Voronoi grains, to generate block geometry files that can be read directly into 3DEC. A series of Unconfined Compressive Strength (UCS) tests are simulated in 3DEC to verify the proposed methodology for 3D simulation of brittle fractures and to investigate the relationship between each micro-parameter and the model’s macro-response. The possibility of nu-merical replication of the classical U-shape strength curve for anisotropic rocks is also investigated in numerical UCS tests by using complex-shaped (elongated) grains that are cemented to one another along their adjoining sides. A micro-parameter calibration procedure is established for 3D Voronoi models for accurate replication of the mechanical behaviour of isotropic and anisotropic (containing a fabric) rocks.
E. Ghazvinian
2014-12-01
Full Text Available A grain-based distinct element model featuring three-dimensional (3D Voronoi tessellations (random poly-crystals is proposed for simulation of crack damage development in brittle rocks. The grain boundaries in poly-crystal structure produced by Voronoi tessellations can represent flaws in intact rock and allow for numerical replication of crack damage progression through initiation and propagation of micro-fractures along grain boundaries. The Voronoi modelling scheme has been used widely in the past for brittle fracture simulation of rock materials. However the difficulty of generating 3D Voronoi models has limited its application to two-dimensional (2D codes. The proposed approach is implemented in Neper, an open-source engine for generation of 3D Voronoi grains, to generate block geometry files that can be read directly into 3DEC. A series of Unconfined Compressive Strength (UCS tests are simulated in 3DEC to verify the proposed methodology for 3D simulation of brittle fractures and to investigate the relationship between each micro-parameter and the model's macro-response. The possibility of numerical replication of the classical U-shape strength curve for anisotropic rocks is also investigated in numerical UCS tests by using complex-shaped (elongated grains that are cemented to one another along their adjoining sides. A micro-parameter calibration procedure is established for 3D Voronoi models for accurate replication of the mechanical behaviour of isotropic and anisotropic (containing a fabric rocks.
Characterization of maximally random jammed sphere packings: Voronoi correlation functions.
Klatt, Michael A; Torquato, Salvatore
2014-11-01
We characterize the structure of maximally random jammed (MRJ) sphere packings by computing the Minkowski functionals (volume, surface area, and integrated mean curvature) of their associated Voronoi cells. The probability distribution functions of these functionals of Voronoi cells in MRJ sphere packings are qualitatively similar to those of an equilibrium hard-sphere liquid and partly even to the uncorrelated Poisson point process, implying that such local statistics are relatively structurally insensitive. This is not surprising because the Minkowski functionals of a single Voronoi cell incorporate only local information and are insensitive to global structural information. To improve upon this, we introduce descriptors that incorporate nonlocal information via the correlation functions of the Minkowski functionals of two cells at a given distance as well as certain cell-cell probability density functions. We evaluate these higher-order functions for our MRJ packings as well as equilibrium hard spheres and the Poisson point process. It is shown that these Minkowski correlation and density functions contain visibly more information than the corresponding standard pair-correlation functions. We find strong anticorrelations in the Voronoi volumes for the hyperuniform MRJ packings, consistent with previous findings for other pair correlations [A. Donev et al., Phys. Rev. Lett. 95, 090604 (2005)PRLTAO0031-900710.1103/PhysRevLett.95.090604], indicating that large-scale volume fluctuations are suppressed by accompanying large Voronoi cells with small cells, and vice versa. In contrast to the aforementioned local Voronoi statistics, the correlation functions of the Voronoi cells qualitatively distinguish the structure of MRJ sphere packings (prototypical glasses) from that of not only the Poisson point process but also the correlated equilibrium hard-sphere liquids. Moreover, while we did not find any perfect icosahedra (the locally densest possible structure in which a
Ramaekers, Pascal; Ries, Mario; Moonen, Chrit T W; de Greef, Martijn
2017-03-01
A major complication for abdominal High Intensity Focused Ultrasound (HIFU) applications is the obstruction of the acoustic beam path by the thoracic cage, which absorbs and reflects the ultrasonic energy leading to undesired overheating of healthy tissues in the pre-focal area. Prior work has investigated the determination of optimized transducer apodization laws, which allow for a reduced rib exposure whilst (partially) restoring focal point intensity through power compensation. Although such methods provide an excellent means of reducing rib exposure, they generally increase the local energy density in the pre-focal area, which similarly can lead to undesired overheating. Therefore, this numerical study aimed at evaluating whether a novel transducer design could provide improvement for intercostal HIFU applications, in particular with respect to the pre-focal area. A combination of acoustic and thermal simulations was used to evaluate 2 mono-element transducers, 2 clinical phased array transducers, and 4 novel transducers based on Fermat's Spiral (FS), two of which were Voronoi-tessellated (VTFS). Binary apodizations were determined for the phased array transducers using a collision detection algorithm. A tissue geometry was modeled to represent an intercostal HIFU sonication in the liver at 30 and 50 mm behind the ribs, including subsequent layers of gel pad, skin, subcutaneous fat, muscle, and liver tissue. Acoustic simulations were then conducted using propagation of the angular spectrum of plane waves (ASPW). The results of these simulations were used to evaluate pre-focal intensity levels. Subsequently, a finite difference scheme based on the Pennes bioheat equation was used for thermal simulations. The results of these simulations were used to calculate both the energy density in the pre-focal skin, fat, and muscle layers, as well as the energy exposure of the ribs. The acoustic simulations showed that for a sonication in a single point without
Koay, Cheng Guan
2012-01-01
Purpose: The purpose of this work is to investigate the hypothesis that uniform sampling measurements that are endowed with antipodal symmetry play an important role when the raw data and image data are related through the Fourier relationship as in q-space diffusion MRI and 3D radial MRI. Currently, it is extremely challenging to generate large uniform antipodally symmetric point sets suitable for 3D radial MRI. A novel approach is proposed to solve this important and long-standing problem. Methods: The proposed method is based upon constrained centroidal Voronoi tessellations of the upper hemisphere with a novel pseudometric. Geometrically intuitive approach to tessellating the upper hemisphere is also proposed. Results: The average time complexity of the proposed centroidal tessellations was shown to be effectively on the order of the product of the number of iterations and the number of generators. For small sample size, the proposed method was comparable to the state-of-the-art iterative method in terms ...
An, Xi-Zhong
2007-08-01
Micro structures of equal sphere packing (ranging from loose to dense packing) generated numerically by discrete element method under different vibration conditions are characterized using Voronoi/Delaunay tessellation, which is applied on a wide range of packing densities. The analysis on micro properties such as the total perimeter, surface area, and the face number distribution of each Voronoi polyhedron, and the pore size distribution in each Voronoi/Delaunay subunit is systematically carried out. The results show that with the increasing density of sphere packing, the Voronoi/Delaunay pore size distribution is narrowed. That indicates large pores to be gradually substituted by small uniformed ones during densification. Meanwhile, the distributions of face number, total perimeter, and surface area of Voronoi polyhedra at high packing densities tend to be narrower and higher, which is in good agreement with those in random loose packing.
AN Xi-Zhong
2007-01-01
@@ Micro structures of equal sphere packing (ranging from loose to dense packing) generated numerically by discrete element method under different vibration conditions are characterized using Voronoi/Delaunay tessellation, which is applied on a wide range of packing densities. The analysis on micro properties such as the total perimeter,surface area, and the face number distribution of each Voronoi polyhedron, and the pore size distribution in each Voronoi/Delaunay subunit is systematically carried out. The results show that with the increasing density of sphere packing, the Voronoi/Delaunay pore size distribution is narrowed. That indicates large pores to be gradually substituted by small uniformed ones during densification. Meanwhile, the distributions of face number,total perimeter, and surface area of Voronoi polyhedra at high packing densities tend to be narrower and higher,which is in good agreement with those in random loose packing.
Nonequilibrium phase transition in directed small-world-Voronoi-Delaunay random lattices
Lima, F. W. S.
2016-01-01
On directed small-world-Voronoi-Delaunay random lattices in two dimensions with quenched connectivity disorder we study the critical properties of the dynamics evolution of public opinion in social influence networks using a simple spin-like model. The system is treated by applying Monte Carlo simulations. We show that directed links on these random lattices may lead to phase diagram with first- and second-order social phase transitions out of equilibrium.
Efficient computation of clipped Voronoi diagram for mesh generation
Yan, Dongming
2013-04-01
The Voronoi diagram is a fundamental geometric structure widely used in various fields, especially in computer graphics and geometry computing. For a set of points in a compact domain (i.e. a bounded and closed 2D region or a 3D volume), some Voronoi cells of their Voronoi diagram are infinite or partially outside of the domain, but in practice only the parts of the cells inside the domain are needed, as when computing the centroidal Voronoi tessellation. Such a Voronoi diagram confined to a compact domain is called a clipped Voronoi diagram. We present an efficient algorithm to compute the clipped Voronoi diagram for a set of sites with respect to a compact 2D region or a 3D volume. We also apply the proposed method to optimal mesh generation based on the centroidal Voronoi tessellation. Crown Copyright © 2011 Published by Elsevier Ltd. All rights reserved.
Velocity field statistics and tessellation techniques : Unbiased estimators of Omega
Van de Weygaert, R; Bernardeau, F; Muller,; Gottlober, S; Mucket, JP; Wambsganss, J
1998-01-01
We describe two new - stochastic-geometrical - methods to obtain reliable velocity field statistics from N-body simulations and from any general density and velocity fluctuation field sampled at a discrete set of locations. These methods, the Voronoi tessellation method and Delaunay tessellation met
Fast topological construction of delaunay triangulations and voronoi diagrams
Tsai, Victor J. D.
1993-11-01
This paper describes a Convex Hull Insertion algorithm for constructing the Delaunay triangulation and the Voronoi diagram of randomly distributed points in the Euclidean plane. The implemented program on IBM-compatible personal computers takes benefits from the partitioning of data points, topological data structures of spatial primitives, and features in C++ programming language such as dynamic memory allocation and class objects. The program can handle arbitrary collections of points, and delivers several output options to link with GIS and CAD systems. Empirical results of various sets of up to 50,000 points show that the proposed algorithm speeds up the construction of both tessellations of irregular points in expected linear time.
Cassidy, Joan
1998-01-01
Describes two sixth-grade lessons on the work of M. C. Escher: (1) the first lesson instructs students on tessellations, or tiles that interlock in a repeated pattern; (2) the second lesson explores Escher's drawings of transitions from two- to three-dimensional space. (DSK)
Particle hydrodynamics with tessellation techniques
Hess, S
2009-01-01
Lagrangian smoothed particle hydrodynamics (SPH) is a well-established approach to model fluids in astrophysical problems, thanks to its geometric flexibility and ability to automatically adjust the spatial resolution to the clumping of matter. However, a number of recent studies have emphasized inaccuracies of SPH in the treatment of fluid instabilities. The origin of these numerical problems can be traced back to spurious surface effects across contact discontinuities, and to SPH's inherent prevention of mixing at the particle level. We here investigate a new fluid particle model where the density estimate is carried out with the help of an auxiliary mesh constructed as the Voronoi tessellation of the simulation particles instead of an adaptive smoothing kernel. This Voronoi-based approach improves the ability of the scheme to represent sharp contact discontinuities. We show that this eliminates spurious surface tension effects present in SPH and that play a role in suppressing certain fluid instabilities. ...
Bayesian analysis of spatial point processes in the neighbourhood of Voronoi networks
Skare, Øivind; Møller, Jesper; Jensen, Eva B. Vedel
2007-01-01
A model for an inhomogeneous Poisson process with high intensity near the edges of a Voronoi tessellation in 2D or 3D is proposed. The model is analysed in a Bayesian setting with priors on nuclei of the Voronoi tessellation and other model parameters. An MCMC algorithm is constructed to sample f...... from biology (animal territories) and material science (alumina grain structure) are presented.......A model for an inhomogeneous Poisson process with high intensity near the edges of a Voronoi tessellation in 2D or 3D is proposed. The model is analysed in a Bayesian setting with priors on nuclei of the Voronoi tessellation and other model parameters. An MCMC algorithm is constructed to sample...
Bayesian analysis of spatial point processes in the neighbourhood of Voronoi networks
Skare, Øivind; Møller, Jesper; Vedel Jensen, Eva B.
A model for an inhomogeneous Poisson process with high intensity near the edges of a Voronoi tessellation in 2D or 3D is proposed. The model is analysed in a Bayesian setting with priors on nuclei of the Voronoi tessellation and other model parameters. An MCMC algorithm is constructed to sample f...... from biology (animal territories) and material science (alumina grain structure) are presented.......A model for an inhomogeneous Poisson process with high intensity near the edges of a Voronoi tessellation in 2D or 3D is proposed. The model is analysed in a Bayesian setting with priors on nuclei of the Voronoi tessellation and other model parameters. An MCMC algorithm is constructed to sample...
Felfer, P; Ceguerra, A V; Ringer, S P; Cairney, J M
2015-03-01
The analysis of the formation of clusters in solid solutions is one of the most common uses of atom probe tomography. Here, we present a method where we use the Voronoi tessellation of the solute atoms and its geometric dual, the Delaunay triangulation to test for spatial/chemical randomness of the solid solution as well as extracting the clusters themselves. We show how the parameters necessary for cluster extraction can be determined automatically, i.e. without user interaction, making it an ideal tool for the screening of datasets and the pre-filtering of structures for other spatial analysis techniques. Since the Voronoi volumes are closely related to atomic concentrations, the parameters resulting from this analysis can also be used for other concentration based methods such as iso-surfaces. Copyright © 2014 Elsevier B.V. All rights reserved.
The Voronoi diagram of circles and its application to the visualization of the growth of particles
Anton, François; Mioc, Darka; Gold, Christopher M.
2009-01-01
Circles are frequently used for modelling the growth of particle aggregates through the Voronoi diagram of circles, that is a special instance of the Johnson-Mehl tessellation. The Voronoi diagram of a set of sites is a decomposition of space into proximal regions. The proximal region of a site...... is the locus of points closer to that site than to any other one. Voronoi diagrams allow one to answer proximity queries after locating a query point in the Voronoi zone it belongs to. The dual graph of the Voronoi diagram is called the Delaunay graph. In this paper, we ﬁrst show a necessary and suﬃcient...
Detecting and extracting clusters in atom probe data: A simple, automated method using Voronoi cells
Felfer, P., E-mail: peter.felfer@sydney.edu.au [Australian Centre for Microscopy and Microanalysis, The University of Sydney, NSW 2006 (Australia); School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, NSW 2006 (Australia); Ceguerra, A.V., E-mail: anna.ceguerra@sydney.edu.au [Australian Centre for Microscopy and Microanalysis, The University of Sydney, NSW 2006 (Australia); School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, NSW 2006 (Australia); Ringer, S.P., E-mail: simon.ringer@sydney.edu.au [Australian Centre for Microscopy and Microanalysis, The University of Sydney, NSW 2006 (Australia); School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, NSW 2006 (Australia); Cairney, J.M., E-mail: julie.cairney@sydney.edu.au [Australian Centre for Microscopy and Microanalysis, The University of Sydney, NSW 2006 (Australia); School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, NSW 2006 (Australia)
2015-03-15
The analysis of the formation of clusters in solid solutions is one of the most common uses of atom probe tomography. Here, we present a method where we use the Voronoi tessellation of the solute atoms and its geometric dual, the Delaunay triangulation to test for spatial/chemical randomness of the solid solution as well as extracting the clusters themselves. We show how the parameters necessary for cluster extraction can be determined automatically, i.e. without user interaction, making it an ideal tool for the screening of datasets and the pre-filtering of structures for other spatial analysis techniques. Since the Voronoi volumes are closely related to atomic concentrations, the parameters resulting from this analysis can also be used for other concentration based methods such as iso-surfaces. - Highlights: • Cluster analysis of atom probe data can be significantly simplified by using the Voronoi cell volumes of the atomic distribution. • Concentration fields are defined on a single atomic basis using Voronoi cells. • All parameters for the analysis are determined by optimizing the separation probability of bulk atoms vs clustered atoms.
Tarnow, Viggo
2002-01-01
harmonic waves at low frequencies, the effective mass density is determined by the friction between air and fibers. The friction is described by the airflow resistivity, which depends on frequency, but for frequencies below 1000 Hz in glass wool with density 15–30 kg/m3, the resistivity to airflow......Sound in glass wool propagates mainly in the air between glass fibers. For sound waves considered here, the distance between fibers is much smaller than the wavelength. Therefore, the sound velocity and attenuation can be computed from an effective mass density and compressibility. For simple...... is constant, and equal to the constant current value. A computation of resistivity from fiber density and diameter will be presented for a model of glass wool that consists of parallel randomly placed fibers with equal diameters. The computation is based on Voronoi polygons, and the results will be compared...
Sequential Voronoi diagram calculations using simple chemical reactions
Costello, Ben de Lacy; Adamatzky, Andy
2012-01-01
In our recent paper [de Lacy Costello et al. 2010] we described the formation of complex tessellations of the plane arising from the various reactions of metal salts with potassium ferricyanide and ferrocyanide loaded gels. In addition to producing colourful tessellations these reactions are naturally computing generalised Voronoi diagrams of the plane. The reactions reported previously were capable of the calculation of three distinct Voronoi diagrams of the plane. As diffusion coupled with a chemical reaction is responsible for the calculation then this is achieved in parallel. Thus an increase in the complexity of the data input does not utilise additional computational resource. Additional benefits of these chemical reactions is that a permanent record of the Voronoi diagram calculation (in the form of precipitate free bisectors) is achieved, so there is no requirement for further processing to extract the calculation results. Previously it was assumed that the permanence of the results was also a potenti...
Limit theory for planar Gilbert tessellations
Schreiber, Tomasz
2010-01-01
A Gilbert tessellation arises by letting linear segments (cracks) in the plane unfold in time with constant speed, starting from a homogeneous Poisson point process of germs in randomly chosen directions. Whenever a growing edge hits an already existing one, it stops growing in this direction. The resulting process tessellates the plane. The purpose of the present paper is to establish law of large numbers, variance asymptotics and a central limit theorem for geometric functionals of such tessellations. The main tool applied is the stabilization theory for geometric functionals.
Voronoi Based Nanocrystalline Generation Algorithm for Atomistic Simulations
2016-12-22
with implementing ran- domly dispersed Voronoi tessellation algorithms for nanocrystalline construction is 1 Approved for public release; distribution...generate a list of grain centers that are populated with seeds —spherical groups of atoms extracted from a reference file. This method uses a single...the methods and code used to generate a nanocrystalline structure with a single reference file for seed extraction. Some of the code segments detailed
Low-resolution remeshing using the localized restricted voronoi diagram
Yan, Dongming
2014-10-01
A big problem in triangular remeshing is to generate meshes when the triangle size approaches the feature size in the mesh. The main obstacle for Centroidal Voronoi Tessellation (CVT)-based remeshing is to compute a suitable Voronoi diagram. In this paper, we introduce the localized restricted Voronoi diagram (LRVD) on mesh surfaces. The LRVD is an extension of the restricted Voronoi diagram (RVD), but it addresses the problem that the RVD can contain Voronoi regions that consist of multiple disjoint surface patches. Our definition ensures that each Voronoi cell in the LRVD is a single connected region. We show that the LRVD is a useful extension to improve several existing mesh-processing techniques, most importantly surface remeshing with a low number of vertices. While the LRVD and RVD are identical in most simple configurations, the LRVD is essential when sampling a mesh with a small number of points and for sampling surface areas that are in close proximity to other surface areas, e.g., nearby sheets. To compute the LRVD, we combine local discrete clustering with a global exact computation. © 1995-2012 IEEE.
Atomistic simulation of Voronoi-based coated nanoporous metals
Onur Yildiz, Yunus; Kirca, Mesut
2017-02-01
In this study, a new method developed for the generation of periodic atomistic models of coated and uncoated nanoporous metals (NPMs) is presented by examining the thermodynamic stability of coated nanoporous structures. The proposed method is mainly based on the Voronoi tessellation technique, which provides the ability to control cross-sectional dimension and slenderness of ligaments as well as the thickness of coating. By the utilization of the method, molecular dynamic (MD) simulations of randomly structured NPMs with coating can be performed efficiently in order to investigate their physical characteristics. In this context, for the purpose of demonstrating the functionality of the method, sample atomistic models of Au/Pt NPMs are generated and the effects of coating and porosity on the thermodynamic stability are investigated by using MD simulations. In addition to that, uniaxial tensile loading simulations are performed via MD technique to validate the nanoporous models by comparing the effective Young’s modulus values with the results from literature. Based on the results, while it is demonstrated that coating the nanoporous structures slightly decreases the structural stability causing atomistic configurational changes, it is also shown that the stability of the atomistic models is higher at lower porosities. Furthermore, adaptive common neighbour analysis is also performed to identify the stabilized atomistic structure after the coating process, which provides direct foresights for the mechanical behaviour of coated nanoporous structures.
Voronoi diagrams on the sphere
Na, H.-S.; Lee, C.-N.; Cheong, O.
2001-01-01
Given a set of compact sites on a sphere, we show that their spherical Voronoi diagram can be computed by computing two planar Voronoi diagrams of suitably transformed sites in the plane. We also show that a planar furthest-site Voronoi diagram can always be obtained as a portion of a
Voro++: a three-dimensional Voronoi cell library in C++
Rycroft, Chris
2009-01-15
Voro++ is a free software library for the computation of three dimensional Voronoi cells. It is primarily designed for applications in physics and materials science, where the Voronoi tessellation can be a useful tool in the analysis of densely-packed particle systems, such as granular materials or glasses. The software comprises of several C++ classes that can be modified and incorporated into other programs. A command-line utility is also provided that can use most features of the code. Voro++ makes use of a direct cell-by-cell construction, which is particularly suited to handling special boundary conditions and walls. It employs algorithms which are tolerant for numerical precision errors, and it has been successfully employed on very large particle systems.
Wavelets on Planar Tesselations
Bertram, M.; Duchaineau, M.A.; Hamann, B.; Joy, K.I.
2000-02-25
We present a new technique for progressive approximation and compression of polygonal objects in images. Our technique uses local parameterizations defined by meshes of convex polygons in the plane. We generalize a tensor product wavelet transform to polygonal domains to perform multiresolution analysis and compression of image regions. The advantage of our technique over conventional wavelet methods is that the domain is an arbitrary tessellation rather than, for example, a uniform rectilinear grid. We expect that this technique has many applications image compression, progressive transmission, radiosity, virtual reality, and image morphing.
Using 3D Voronoi grids in radiative transfer simulations
Camps, Peter; Saftly, Waad
2013-01-01
Probing the structure of complex astrophysical objects requires effective three-dimensional (3D) numerical simulation of the relevant radiative transfer (RT) processes. As with any numerical simulation code, the choice of an appropriate discretization is crucial. Adaptive grids with cuboidal cells such as octrees have proven very popular, however several recently introduced hydrodynamical and RT codes are based on a Voronoi tessellation of the spatial domain. Such an unstructured grid poses new challenges in laying down the rays (straight paths) needed in RT codes. We show that it is straightforward to implement accurate and efficient RT on 3D Voronoi grids. We present a method for computing straight paths between two arbitrary points through a 3D Voronoi grid in the context of a RT code. We implement such a grid in our RT code SKIRT, using the open source library Voro++ to obtain the relevant properties of the Voronoi grid cells based solely on the generating points. We compare the results obtained through t...
A physics-motivated Centroidal Voronoi Particle domain decomposition method
Fu, Lin; Hu, Xiangyu Y.; Adams, Nikolaus A.
2017-04-01
In this paper, we propose a novel domain decomposition method for large-scale simulations in continuum mechanics by merging the concepts of Centroidal Voronoi Tessellation (CVT) and Voronoi Particle dynamics (VP). The CVT is introduced to achieve a high-level compactness of the partitioning subdomains by the Lloyd algorithm which monotonically decreases the CVT energy. The number of computational elements between neighboring partitioning subdomains, which scales the communication effort for parallel simulations, is optimized implicitly as the generated partitioning subdomains are convex and simply connected with small aspect-ratios. Moreover, Voronoi Particle dynamics employing physical analogy with a tailored equation of state is developed, which relaxes the particle system towards the target partition with good load balance. Since the equilibrium is computed by an iterative approach, the partitioning subdomains exhibit locality and the incremental property. Numerical experiments reveal that the proposed Centroidal Voronoi Particle (CVP) based algorithm produces high-quality partitioning with high efficiency, independently of computational-element types. Thus it can be used for a wide range of applications in computational science and engineering.
Lindenbergh, R.C.
2002-01-01
The classic Voronoi diagram of a configuration of distinct points in the plane associates to each point that part of the plane that is closer to the point than to any other point in the configuration. In this thesis we no longer require all points to be distinct. After the introduction in
Rosanowski, S M; Cogger, N; Rogers, C W; Benschop, J; Stevenson, M A
2012-12-01
We conducted a cross-sectional survey to determine the demographic characteristics of non-commercial horses in New Zealand. A sampling frame of properties with non-commercial horses was derived from the national farms database, AgriBase™. Horse properties were stratified by property size and a generalised random-tessellated stratified (GRTS) sampling strategy was used to select properties (n=2912) to take part in the survey. The GRTS sampling design allowed for the selection of properties that were spatially balanced relative to the distribution of horse properties throughout the country. The registered decision maker of the property, as identified in AgriBase™, was sent a questionnaire asking them to describe the demographic characteristics of horses on the property, including the number and reason for keeping horses, as well as information about other animals kept on the property and the proximity of boundary neighbours with horses. The response rate to the survey was 38% (1044/2912) and the response rate was not associated with property size or region. A total of 5322 horses were kept for recreation, competition, racing, breeding, stock work, or as pets. The reasons for keeping horses and the number and class of horses varied significantly between regions and by property size. Of the properties sampled, less than half kept horses that could have been registered with Equestrian Sports New Zealand or either of the racing codes. Of the respondents that reported knowing whether their neighbours had horses, 58.6% (455/776) of properties had at least one boundary neighbour that kept horses. The results of this study have important implications for New Zealand, which has an equine population that is naïve to many equine diseases considered endemic worldwide. The ability to identify, and apply accurate knowledge of the population at risk to infectious disease control strategies would lead to more effective strategies to control and prevent disease spread during an
3D RECONSTRUCTION OF A MULTISCALE MICROSTRUCTURE BY ANISOTROPIC TESSELLATION MODELS
Hellen Altendorf
2014-05-01
Full Text Available In the area of tessellation models, there is an intense activity to fully understand the classical models of Voronoi, Laguerre and Johnson-Mehl. Still, these models are all simulations of isotropic growth and are therefore limited to very simple and partly convex cell shapes. The here considered microstructure of martensitic steel has a much more complex and highly non convex cell shape, requiring new tessellation models. This paper presents a new approach for anisotropic tessellation models that resolve to the well-studied cases of Laguerre and Johnson-Mehl for spherical germs. Much better reconstructions can be achieved with these models and thus more realistic microstructure simulations can be produced for materials widely used in industry like martensitic and bainitic steels.
Gauge Theories, Tessellations & Riemann Surfaces
He, Yang-Hui
2014-01-01
We study and classify regular and semi-regular tessellations of Riemann surfaces of various genera and investigate their corresponding supersymmetric gauge theories. These tessellations are generalizations of brane tilings, or bipartite graphs on the torus as well as the Platonic and Archimedean solids on the sphere. On higher genus they give rise to intricate patterns. Special attention will be paid to the master space and the moduli space of vacua of the gauge theory and to how their geometry is determined by the tessellations.
Gauge theories, tessellations & Riemann surfaces
He, Yang-Hui [Department of Mathematics, City University,London, EC1V 0HB (United Kingdom); School of Physics, NanKai University,Tianjin, 300071 (China); Merton College, University of Oxford,Oxford, OX1 4JD (United Kingdom); Loon, Mark van [Merton College, University of Oxford,Oxford, OX1 4JD (United Kingdom)
2014-06-10
We study and classify regular and semi-regular tessellations of Riemann surfaces of various genera and investigate their corresponding supersymmetric gauge theories. These tessellations are generalizations of brane tilings, or bipartite graphs on the torus as well as the Platonic and Archimedean solids on the sphere. On higher genus they give rise to intricate patterns. Special attention will be paid to the master space and the moduli space of vacua of the gauge theory and to how their geometry is determined by the tessellations.
Fitting polynomial surfaces to triangular meshes with Voronoi squared distance minimization
Nivoliers, Vincent
2012-11-06
This paper introduces Voronoi squared distance minimization (VSDM), an algorithm that fits a surface to an input mesh. VSDM minimizes an objective function that corresponds to a Voronoi-based approximation of the overall squared distance function between the surface and the input mesh (SDM). This objective function is a generalization of the one minimized by centroidal Voronoi tessellation, and can be minimized by a quasi-Newton solver. VSDM naturally adapts the orientation of the mesh elements to best approximate the input, without estimating any differential quantities. Therefore, it can be applied to triangle soups or surfaces with degenerate triangles, topological noise and sharp features. Applications of fitting quad meshes and polynomial surfaces to input triangular meshes are demonstrated. © 2012 Springer-Verlag London.
Fitting polynomial surfaces to triangular meshes with Voronoi Squared Distance Minimization
Nivoliers, Vincent
2011-12-01
This paper introduces Voronoi Squared Distance Minimization (VSDM), an algorithm that fits a surface to an input mesh. VSDM minimizes an objective function that corresponds to a Voronoi-based approximation of the overall squared distance function between the surface and the input mesh (SDM). This objective function is a generalization of Centroidal Voronoi Tesselation (CVT), and can be minimized by a quasi-Newton solver. VSDM naturally adapts the orientation of the mesh to best approximate the input, without estimating any differential quantities. Therefore it can be applied to triangle soups or surfaces with degenerate triangles, topological noise and sharp features. Applications of fitting quad meshes and polynomial surfaces to input triangular meshes are demonstrated.
Statistical Topology of Three-Dimensional Poisson-Voronoi Cells and Cell Boundary Networks
Lazar, Emanuel A; MacPherson, Robert D; Srolovitz, David J
2014-01-01
Voronoi tessellations of Poisson point processes are widely used for modeling many types of physical and biological systems. In this paper, we analyze simulated Poisson-Voronoi structures containing a total of 250,000,000 cells to provide topological and geometrical statistics of this important class of networks. We also report correlations between some of these topological and geometrical measures. Using these results, we are able to corroborate several conjectures regarding the properties of three-dimensional Poisson-Voronoi networks and refute others. In many cases, we provide accurate fits to these data to aid further analysis. We also demonstrate that topological measures represent powerful tools for describing cellular networks and for distinguishing among different types of networks.
Hydrodynamic simulations on a moving Voronoi mesh
Springel, Volker
2011-01-01
At the heart of any method for computational fluid dynamics lies the question of how the simulated fluid should be discretized. Traditionally, a fixed Eulerian mesh is often employed for this purpose, which in modern schemes may also be adaptively refined during a calculation. Particle-based methods on the other hand discretize the mass instead of the volume, yielding an approximately Lagrangian approach. It is also possible to achieve Lagrangian behavior in mesh-based methods if the mesh is allowed to move with the flow. However, such approaches have often been fraught with substantial problems related to the development of irregularity in the mesh topology. Here we describe a novel scheme that eliminates these weaknesses. It is based on a moving unstructured mesh defined by the Voronoi tessellation of a set of discrete points. The mesh is used to solve the hyperbolic conservation laws of ideal hydrodynamics with a finite volume approach, based on a second-order Godunov scheme with an exact Riemann solver. A...
Rigidly foldable origami gadgets and tessellations.
Evans, Thomas A; Lang, Robert J; Magleby, Spencer P; Howell, Larry L
2015-09-01
Rigidly foldable origami allows for motion where all deflection occurs at the crease lines and facilitates the application of origami in materials other than paper. In this paper, we use a recently discovered method for determining rigid foldability to identify existing flat-foldable rigidly foldable tessellations, which are also categorized. We introduce rigidly foldable origami gadgets which may be used to modify existing tessellations or to create new tessellations. Several modified and new rigidly foldable tessellations are presented.
Rigidly foldable origami gadgets and tessellations
Evans, Thomas A.; Lang, Robert J.; Magleby, Spencer P.; Howell, Larry L.
2015-01-01
Rigidly foldable origami allows for motion where all deflection occurs at the crease lines and facilitates the application of origami in materials other than paper. In this paper, we use a recently discovered method for determining rigid foldability to identify existing flat-foldable rigidly foldable tessellations, which are also categorized. We introduce rigidly foldable origami gadgets which may be used to modify existing tessellations or to create new tessellations. Several modified and new rigidly foldable tessellations are presented. PMID:26473037
A TESSELLATION MODEL FOR CRACK PATTERNS ON SURFACES
Werner Nagel
2011-05-01
Full Text Available This paper presents a model of random tessellations that reflect several features of crack pattern. There are already several theoretical results derivedwhich indicate that thismodel can be an appropriate referencemodel. Some potential applications are presented in a tentative statistical study.
A MICROSTRUCTURAL MODEL BY SPACE TESSELLATION FOR A SINTERED CERAMIC: CERINE
Michel Coster
2011-05-01
Full Text Available This paper deals with the use of probabilistic models such as Voronoi tessellation and the Johnson-Mehl model to simulate microstructures of monophased materials. Sintered cerine was chosen to test the various models. The values of morphological parameters measured, both on such models and real microstructures are in very good agreement. An extension for porous materials is also presented. This work shows that the probabilistic models are very well suited for the simulation and description of ceramic and granular microstructures.
Hexagonal tessellations in image algebra
Eberly, David H.; Wenzel, Dennis J.; Longbotham, Harold G.
1990-11-01
In image algebra '' the concept of a coordinate set X is general in that such a set is simply a subset of ndimensional Euclidean space . The standard applications in 2-dimensional image processing use coordinate sets which are rectangular arrays X 72 x ZZm. However some applications may require other geometries for the coordinate set. We look at three such related applications in the context of image algebra. The first application is the modeling of photoreceptors in primate retinas. These receptors are inhomogeneously distributed on the retina. The largest receptor density occurs in the center of the fovea and decreases radially outwards. One can construct a hexagonal tessellation of the retina such that each hexagon contains approximately the same number of receptors. The resulting tessellation called a sunflower heart2 consists of concentric rings of hexagons whose sizes increase as the radius of the ring increases. The second application is the modeling of the primary visual . The neurons are assumed to be uniformly distributed as a regular hexagonal lattice. Cortical neural image coding is modeled by a recursive convolution of the retinal neural image using a special set of filters. The third application involves analysis of a hexagonally-tessellated image where the pixel resolution is variable .
Voronoi cells, fractal dimensions and fibre composites.
Summerscales, J.; Guild, F. J.; Pearce, N. R. L.; Russell, P. M.
2001-02-01
The use of fibre-reinforced polymer matrix composite materials is growing at a faster rate than the gross domestic product (GDP) in many countries. An improved understanding of their processing and mechanical behaviour would extend the potential applications of these materials. For unidirectional composites, it is predicted that localized absence of fibres is related to longitudinal compression failure. The use of woven reinforcements permits more effective manufacture than for unidirectional fibres. It has been demonstrated experimentally that compression strengths of woven composites are reduced when fibres are clustered. Summerscales predicted that clustering of fibres would increase the permeability of the reinforcement and hence expedite the processing of these materials. Commercial fabrics are available which employ this concept using flow-enhancing bound tows. The net effect of clustering fibres is to enhance processability whilst reducing the mechanical properties. The effects reported above were qualitative correlations. To improve the design tools for reinforcement fabrics we have sought to quantify the changes in the micro/meso-structure of woven reinforcement fabrics. Gross differences in the appearance of laminate sections are apparent for different weave styles. The use of automated image analysis is essential for the quantification of subtle changes in fabric architecture. This paper considers Voronoi tessellation and fractal dimensions for the quantification of the microstructures of woven fibre-reinforced composites. It reviews our studies in the last decade of the process-property-structure relationships for commercial and experimental fabric reinforcements in an attempt to resolve the processing vs. properties dilemma. A new flow-enhancement concept has been developed which has a reduced impact on laminate mechanical properties.
Farthest-Polygon Voronoi Diagrams
Cheong, Otfried; Glisse, Marc; Gudmundsson, Joachim; Hornus, Samuel; Lazard, Sylvain; Lee, Mira; Na, Hyeon-Suk
2010-01-01
Given a family of k disjoint connected polygonal sites in general position and of total complexity n, we consider the farthest-site Voronoi diagram of these sites, where the distance to a site is the distance to a closest point on it. We show that the complexity of this diagram is O(n), and give an O(n log^3 n) time algorithm to compute it. We also prove a number of structural properties of this diagram. In particular, a Voronoi region may consist of k-1 connected components, but if one component is bounded, then it is equal to the entire region.
Anirban Chakraborty
Full Text Available The need for quantification of cell growth patterns in a multilayer, multi-cellular tissue necessitates the development of a 3D reconstruction technique that can estimate 3D shapes and sizes of individual cells from Confocal Microscopy (CLSM image slices. However, the current methods of 3D reconstruction using CLSM imaging require large number of image slices per cell. But, in case of Live Cell Imaging of an actively developing tissue, large depth resolution is not feasible in order to avoid damage to cells from prolonged exposure to laser radiation. In the present work, we have proposed an anisotropic Voronoi tessellation based 3D reconstruction framework for a tightly packed multilayer tissue with extreme z-sparsity (2-4 slices/cell and wide range of cell shapes and sizes. The proposed method, named as the 'Adaptive Quadratic Voronoi Tessellation' (AQVT, is capable of handling both the sparsity problem and the non-uniformity in cell shapes by estimating the tessellation parameters for each cell from the sparse data-points on its boundaries. We have tested the proposed 3D reconstruction method on time-lapse CLSM image stacks of the Arabidopsis Shoot Apical Meristem (SAM and have shown that the AQVT based reconstruction method can correctly estimate the 3D shapes of a large number of SAM cells.
Lattice mechanics of origami tessellations.
Evans, Arthur A; Silverberg, Jesse L; Santangelo, Christian D
2015-07-01
Origami-based design holds promise for developing materials whose mechanical properties are tuned by crease patterns introduced to thin sheets. Although there have been heuristic developments in constructing patterns with desirable qualities, the bridge between origami and physics has yet to be fully developed. To truly consider origami structures as a class of materials, methods akin to solid mechanics need to be developed to understand their long-wavelength behavior. We introduce here a lattice theory for examining the mechanics of origami tessellations in terms of the topology of their crease pattern and the relationship between the folds at each vertex. This formulation provides a general method for associating mechanical properties with periodic folded structures and allows for a concrete connection between more conventional materials and the mechanical metamaterials constructed using origami-based design.
McDonald, Jonathan R
2008-01-01
In 1961 Tullio Regge provided us with a beautiful lattice representation of Einstein's geometric theory of gravity. This Regge Calculus (RC) is strikingly different from the more usual finite difference and finite element discretizations of gravity. In RC the fundamental principles of General Relativity are applied directly to a tessellated spacetime geometry. In this manuscript, and in the spirit of this conference, we reexamine the foundations of RC and emphasize the central role that the Voronoi and Delaunay lattices play in this discrete theory. In particular we describe, for the first time, a geometric construction of the scalar curvature invariant at a vertex. This derivation makes use of a new fundamental lattice cell built from elements inherited from both the simplicial (Delaunay) spacetime and its circumcentric dual (Voronoi) lattice. The orthogonality properties between these two lattices yield an expression for the vertex-based scalar curvature which is strikingly similar to the corresponding and ...
Restructuring surface tessellation with irregular boundary conditions
Tsung-Hsien Wang
2014-12-01
Full Text Available In this paper, the surface tessellation problem is explored, in particular, the task of meshing a surface with the added consideration of incorporating constructible building components. When a surface is tessellated into discrete counterparts, certain unexpected conditions usually occur at the boundary of the surface, in particular, when the surface is being trimmed. For example, irregularly shaped panels form at the trimmed edges. To reduce the number of irregular panels that may form during the tessellation process, this paper presents an algorithmic approach to restructuring the surface tessellation by investigating irregular boundary conditions. The objective of this approach is to provide an alternative way for freeform surface manifestation from a well-structured discrete model of the given surface.
Classification of Noisy Data: An Approach Based on Genetic Algorithms and Voronoi Tessellation
Khan, Abdul Rauf; Schiøler, Henrik; Knudsen, Torben;
2016-01-01
Classification is one of the major constituents of the data-mining toolkit. The well-known methods for classification are built on either the principle of logic or statistical/mathematical reasoning for classification. In this article we propose: (1) a different strategy, which is based......). The results of this study suggest that our proposed methodology is specialized to deal with the classification problem of highly imbalanced classes with significant overlap....... on the portioning of information space; and (2) use of the genetic algorithm to solve combinatorial problems for classification. In particular, we will implement our methodology to solve complex classification problems and compare the performance of our classifier with other well-known methods (SVM, KNN, and ANN...
Classification of Noisy Data: An Approach Based on Genetic Algorithms and Voronoi Tessellation
Khan, Abdul Rauf; Schiøler, Henrik; Knudsen, Torben
2016-01-01
on the portioning of information space; and (2) use of the genetic algorithm to solve combinatorial problems for classification. In particular, we will implement our methodology to solve complex classification problems and compare the performance of our classifier with other well-known methods (SVM, KNN, and ANN...
Classification of Noisy Data: An Approach Based on Genetic Algorithms and Voronoi Tessellation
Khan, Abdul Rauf; Schiøler, Henrik; Knudsen, Torben
on the portioning of information space; and (2) use of the genetic algorithm to solve combinatorial problems for classification. In particular, we will implement our methodology to solve complex classification problems and compare the performance of our classifier with other well-known methods (SVM, KNN, and ANN...
Voronoi Cell Patterns: Application of the size distribution to societal systems
Sathiyanarayanan, Rajesh; González, Diego Luis; Pimpinelli, Alberto; Einstein, T. L.
2012-02-01
In studying the growth of islands on a surface subjected to a particle flux, we found it useful to characterize the distribution of the areas of associated Voronoi (proximity or Wigner-Seitz) cells in terms of the generalized Wigner surmiseootnotetextAP & TLE, PRL 99 (2007) 226102; PRL 104 (2010) 149602 and the gamma distributions. Here we show that the same concepts and distributions are useful in analyzing several problems arising in society.ootnotetextDLG et al., arXiv 1109.3994; RS, Ph.D. dissertation; RS et al., preprint We analyze the 1D problem of the distribution of gaps between parked cars, assuming that successive cars park in the middle of vacant spaces, and compare with published data. We study the formation of second-level administrative divisions, e.g. French arrondissements. We study the actual distribution of arrondissements and the Voronoi tessellation associated with the chief town in each. While generally applicable, there are subtleties in some cases. Lastly, we consider the pattern formed by Paris M'etro stations and show that near the central area, the associated Voronoi construction also has this sort of distribution.
Constructing Two-Dimensional Voronoi Diagrams via Divide-and-Conquer of Envelopes in Space
Setter, Ophir
2009-05-01
We present a general framework for computing two-dimensional Voronoi diagrams of different classes of sites under various distance functions. The framework is sufficiently general to support diagrams embedded on a family of two-dimensional parametric surfaces in $R^3$. The computation of the diagrams is carried out through the construction of envelopes of surfaces in 3-space provided by CGAL (the Computational Geometry Algorithm Library). The construction of the envelopes follows a divide-and-conquer approach. A straightforward application of the divide-and-conquer approach for computing Voronoi diagrams yields algorithms that are inefficient in the worst case. We prove that through randomization the expected running time becomes near-optimal in the worst case. We show how to employ our framework to realize various types of Voronoi diagrams with different properties by providing implementations for a vast collection of commonly used Voronoi diagrams. We also show how to apply the new framework and other exist...
Voronoi analysis of bubbly flows via ultrafast X-ray tomographic imaging
Lau, Yuk Man; Mueller, Karolin; Azizi, Salar; Schubert, Markus [Helmholtz-Zentrum Dresden-Rossendorf e.V., Institute of Fluid Dynamics, Dresden (Germany)
2016-03-15
Although clustering of bubbles plays a significant role in bubble column reactors regarding the heat and mass transfer due to bubble-bubble and flow field interactions, it has yet to be fully understood. Contrary to flows in bubble columns, most literature studies on clustering report numerical and experimental results on dilute or micro-bubbly flows. In this paper, clustering of bubbles in a cylindrical bubble column of 100 mm diameter is experimentally investigated. Ultrafast X-ray tomographic imaging is used to obtain the bubble positions within a hybrid Eulerian framework. By means of Voronoi analysis, the clustering behavior of bubbles is investigated. Experiments are performed with different superficial gas velocities, where Voronoi diagrams are constructed at several column heights. From the PDFs of the Voronoi diagrams, it is shown that the bubble structuring in terms of Voronoi cell volumes develops slower than the bubble size distribution. The latter reaches a steady state earlier with increasing column height. The measured PDFs are compared with the PDF of randomly distributed points, which showed that the amount of bubbles as part of clusters (Voronoi cells < V/ anti V{sub cluster}) as well as bubbles as part of voids (Voronoi cells > V/ anti V{sub void}) increases with the superficial gas velocity. It is found that all experiments have an approximate cluster limit V/ anti V{sub cluster} of 0.63, while the void limit V/ anti V{sub void} varies between 1.5 and 3.0. (orig.)
A tessellated continuum approach to thermal analysis: discontinuity networks
Jiang, C.; Davey, K.; Prosser, R.
2017-01-01
Tessellated continuum mechanics is an approach for the representation of thermo-mechanical behaviour of porous media on tessellated continua. It involves the application of iteration function schemes using affine contraction and expansion maps, respectively, for the creation of porous fractal materials and associated tessellated continua. Highly complex geometries can be produced using a modest number of contraction mappings. The associated tessellations form the mesh in a numerical procedure. This paper tests the hypothesis that thermal analysis of porous structures can be achieved using a discontinuous Galerkin finite element method on a tessellation. Discontinuous behaviour is identified at a discontinuity network in a tessellation; its use is shown to provide a good representation of the physics relating to cellular heat exchanger designs. Results for different cellular designs (with corresponding tessellations) are contrasted against those obtained from direct analysis and very high accuracy is observed.
Multi-Dimensional, Compressible Viscous Flow on a Moving Voronoi Mesh
Muñoz, Diego; Marcus, Robert; Vogelsberger, Mark; Hernquist, Lars
2012-01-01
Numerous formulations of finite volume schemes for the Euler and Navier-Stokes equations exist, but in the majority of cases they have been developed for structured and stationary meshes. In many applications, more flexible mesh geometries that can dynamically adjust to the problem at hand and move with the flow in a (quasi) Lagrangian fashion would, however, be highly desirable, as this can allow a significant reduction of advection errors and an accurate realization of curved and moving boundary conditions. Here we describe a novel formulation of viscous continuum hydrodynamics that solves the equations of motion on a Voronoi mesh created by a set of mesh-generating points. The points can move in an arbitrary manner, but the most natural motion is that given by the fluid velocity itself, such that the mesh dynamically adjusts to the flow. Owing to the mathematical properties of the Voronoi tessellation, pathological mesh-twisting effects are avoided. Our implementation considers the full Navier-Stokes equat...
Naoya Yoshihara
Full Text Available A tessellated fundus is a common characteristic of myopic eyes and is an important clinical marker for the development of retinochoroidal changes. However, the exact cause and significance of tessellated fundi have not been definitively determined. We determined the degree of tessellation in fundi objectively in normal, non-pathological myopic eyes, and correlated the degree of tessellation and the choroidal thickness (CT and axial length (AL. This was a prospective observational cross sectional study. The eyes were classified subjectively into three groups based on the degree of tessellation observed ophthalmoscopically. Digital color fundus photographs were assessed for the degree of tessellation by ImageJ, an image processing program. Three tessellated fundus indices (TFIs were calculated and were compared to the three subjectively-determined groups. The subfoveal and nasal CTs were measured in the optical coherence tomographic images. The correlations between the TFIs and the CT were calculated. Additionally, the correlation between the TFIs and the AL was calculated. One hundred right eyes of 100 healthy volunteers (mean age 25.8±3.9 years were studied. Ophthalmoscopically, 57 eyes were placed in the non-tessellated group, 27 eyes into the weakly tessellated group, and 16 eyes into the strongly tessellated group. There was a significant correlation between the subjective classifications and the TFI values (P<0.05, Kruskal-Wallis test. All of the TFIs were significantly associated with the subfoveal and nasal CT (R = -0.20 to -0.24, P<0.05. The TFIs were not significantly correlated with the ALs. In conclusion, the significant correlation between the subjective and objective classifications of the degree of tessellation indicates that TFIs can be used to classify the degree of tessellation. The results indicate that the differences in the CT account for the degree of tessellation.
Multivariate Voronoi Outlier Detection for Time Series.
Zwilling, Chris E; Wang, Michelle Yongmei
2014-10-01
Outlier detection is a primary step in many data mining and analysis applications, including healthcare and medical research. This paper presents a general method to identify outliers in multivariate time series based on a Voronoi diagram, which we call Multivariate Voronoi Outlier Detection (MVOD). The approach copes with outliers in a multivariate framework, via designing and extracting effective attributes or features from the data that can take parametric or nonparametric forms. Voronoi diagrams allow for automatic configuration of the neighborhood relationship of the data points, which facilitates the differentiation of outliers and non-outliers. Experimental evaluation demonstrates that our MVOD is an accurate, sensitive, and robust method for detecting outliers in multivariate time series data.
Bayesian Image Reconstruction Based on Voronoi Diagrams
Cabrera, G F; Hitschfeld, N
2007-01-01
We present a Bayesian Voronoi image reconstruction technique (VIR) for interferometric data. Bayesian analysis applied to the inverse problem allows us to derive the a-posteriori probability of a novel parameterization of interferometric images. We use a variable Voronoi diagram as our model in place of the usual fixed pixel grid. A quantization of the intensity field allows us to calculate the likelihood function and a-priori probabilities. The Voronoi image is optimized including the number of polygons as free parameters. We apply our algorithm to deconvolve simulated interferometric data. Residuals, restored images and chi^2 values are used to compare our reconstructions with fixed grid models. VIR has the advantage of modeling the image with few parameters, obtaining a better image from a Bayesian point of view.
Kinetic Line Voronoi Operations and Their Reversibility
Mioc, Darka; Anton, François; Gold, Christopher
2010-01-01
In Geographic Information Systems the reversibility of map update operations has not been explored yet. In this paper we are using the Voronoi based Quad-edge data structure to define reversible map update operations. The reversibility of the map operations has been formalised at the lowest level...... explanation using the finite field of residual classes of integers modulo 5: F 5 = ℤ/5ℤ. We show also an isomorphism between the set of complex operations on the kinetic Voronoi diagram of points and open oriented line segments and the set of differences of new and deleted Quad-Edge edges induced...
The Voronoi diagram of circles made easy
Anton, François; Mioc, Darka; Gold, Christopher
2007-01-01
Proximity queries among circles could be effectively answered if the Delaunay graph for sets of circles could be computed in an efficient and exact way. In this paper, we first show a necessary and sufficient condition of connectivity of the Voronoi diagram of circles. Then, we show how the Delau......Proximity queries among circles could be effectively answered if the Delaunay graph for sets of circles could be computed in an efficient and exact way. In this paper, we first show a necessary and sufficient condition of connectivity of the Voronoi diagram of circles. Then, we show how...
Orphan-Free Anisotropic Voronoi Diagrams
Canas, Guillermo D
2011-01-01
We describe conditions under which an appropriately-defined anisotropic Voronoi diagram of a set of sites in Euclidean space is guaranteed to be composed of connected cells in any number of dimensions. These conditions are natural for problems in optimization and approximation, and algorithms already exist to produce sets of sites that satisfy them.
Finding auxetic frameworks in periodic tessellations.
Mitschke, Holger; Schwerdtfeger, Jan; Schury, Fabian; Stingl, Michael; Körner, Carolin; Singer, Robert F; Robins, Vanessa; Mecke, Klaus; Schröder-Turk, Gerd E
2011-06-17
It appears that most models for micro-structured materials with auxetic deformations were found by clever intuition, possibly combined with optimization tools, rather than by systematic searches of existing structure archives. Here we review our recent approach of finding micro-structured materials with auxetic mechanisms within the vast repositories of planar tessellations. This approach has produced two previously unknown auxetic mechanisms, which have Poisson's ratio νss=-1 when realized as a skeletal structure of stiff incompressible struts pivoting freely at common vertices. One of these, baptized Triangle-Square Wheels, has been produced as a linear-elastic cellular structure from Ti-6Al-4V alloy by selective electron beam melting. Its linear-elastic properties were measured by tensile experiments and yield an effective Poisson's ratio νLE≈-0.75, also in agreement with finite element modeling. The similarity between the Poisson's ratios νSS of the skeletal structure and νLE of the linear-elastic cellular structure emphasizes the fundamental role of geometry for deformation behavior, regardless of the mechanical details of the system. The approach of exploiting structure archives as candidate geometries for auxetic materials also applies to spatial networks and tessellations and can aid the quest for inherently three-dimensional auxetic mechanisms.
Hubber, D A; Dale, J
2015-01-01
Ionising feedback from massive stars dramatically affects the interstellar medium local to star forming regions. Numerical simulations are now starting to include enough complexity to produce morphologies and gas properties that are not too dissimilar from observations. The comparison between the density fields produced by hydrodynamical simulations and observations at given wavelengths relies however on photoionisation/chemistry and radiative transfer calculations. We present here an implementation of Monte Carlo radiation transport through a Voronoi tessellation in the photoionisation and dust radiative transfer code MOCASSIN. We show for the first time a synthetic spectrum and synthetic emission line maps of an hydrodynamical simulation of a molecular cloud affected by massive stellar feedback. We show that the approach on which previous work is based, which remapped hydrodynamical density fields onto Cartesian grids before performing radiative transfer/photoionisation calculations, results in significant ...
Voronoi cell patterns: Theoretical model and applications
González, Diego Luis; Einstein, T. L.
2011-11-01
We use a simple fragmentation model to describe the statistical behavior of the Voronoi cell patterns generated by a homogeneous and isotropic set of points in 1D and in 2D. In particular, we are interested in the distribution of sizes of these Voronoi cells. Our model is completely defined by two probability distributions in 1D and again in 2D, the probability to add a new point inside an existing cell and the probability that this new point is at a particular position relative to the preexisting point inside this cell. In 1D the first distribution depends on a single parameter while the second distribution is defined through a fragmentation kernel; in 2D both distributions depend on a single parameter. The fragmentation kernel and the control parameters are closely related to the physical properties of the specific system under study. We use our model to describe the Voronoi cell patterns of several systems. Specifically, we study the island nucleation with irreversible attachment, the 1D car-parking problem, the formation of second-level administrative divisions, and the pattern formed by the Paris Métro stations.
Intrinsic Volumes of the Maximal Facet Process in Higher Dimensional STIT Tessellations
Schreiber, Tomasz
2010-01-01
Stationary and isotropic random tessellations in ${\\Bbb R}^d$ are considered, which are stable under the operation of iteration -- so-called STIT tessellations. These tessellations are constructed by a random process of cell division and we analyze first- and second-order properties of the intrinsic volumes of the collection of all cell-separating facets (so-called maximal or I-facets) at a fixed time $t$ in a convex window $W\\subset{\\Bbb R}^d$. We provide formulas for mean values, exact and asymptotic variances, as well as a characterization of the lower-dimensional face covariance measures. We will focus here on the case $d\\geq 3$, which is more involved than the planar case, treated separately in an earlier paper. Beside the afore mentioned results, we prove central limit theorems for the process of suitably rescaled intrinsic volumes, leading -- in sharp contrast to the situation in the plane -- to non-Gaussian limit distributions.
The art and science of hyperbolic tessellations.
Van Dusen, B; Taylor, R P
2013-04-01
The visual impact of hyperbolic tessellations has captured artists' imaginations ever since M.C. Escher generated his Circle Limit series in the 1950s. The scaling properties generated by hyperbolic geometry are different to the fractal scaling properties found in nature's scenery. Consequently, prevalent interpretations of Escher's art emphasize the lack of connection with nature's patterns. However, a recent collaboration between the two authors proposed that Escher's motivation for using hyperbolic geometry was as a method to deliberately distort nature's rules. Inspired by this hypothesis, this year's cover artist, Ben Van Dusen, embeds natural fractals such as trees, clouds and lightning into a hyperbolic scaling grid. The resulting interplay of visual structure at multiple size scales suggests that hybridizations of fractal and hyperbolic geometries provide a rich compositional tool for artists.
RICH: Open-source Hydrodynamic Simulation on a Moving Voronoi Mesh
Yalinewich, Almog; Steinberg, Elad; Sari, Re'em
2015-02-01
We present here RICH, a state-of-the-art two-dimensional hydrodynamic code based on Godunov’s method, on an unstructured moving mesh (the acronym stands for Racah Institute Computational Hydrodynamics). This code is largely based on the code AREPO. It differs from AREPO in the interpolation and time-advancement schemeS as well as a novel parallelization scheme based on Voronoi tessellation. Using our code, we study the pros and cons of a moving mesh (in comparison to a static mesh). We also compare its accuracy to other codes. Specifically, we show that our implementation of external sources and time-advancement scheme is more accurate and robust than is AREPO when the mesh is allowed to move. We performed a parameter study of the cell rounding mechanism (Lloyd iterations) and its effects. We find that in most cases a moving mesh gives better results than a static mesh, but it is not universally true. In the case where matter moves in one way and a sound wave is traveling in the other way (such that relative to the grid the wave is not moving) a static mesh gives better results than a moving mesh. We perform an analytic analysis for finite difference schemes that reveals that a Lagrangian simulation is better than a Eulerian simulation in the case of a highly supersonic flow. Moreover, we show that Voronoi-based moving mesh schemes suffer from an error, which is resolution independent, due to inconsistencies between the flux calculation and the change in the area of a cell. Our code is publicly available as open source and designed in an object-oriented, user-friendly way that facilitates incorporation of new algorithms and physical processes.
Moment analysis of the Delaunay tessellation field estimator
Lieshout, M.N.M. van
2009-01-01
The Campbell-Mecke theorem is used to derive explicit expressions for the mean and variance of Schaap and Van de Weygaert's Delaunay tessellation field estimator. Special attention is paid to Poisson processes.
A tesselated probabilistic representation for spatial robot perception and navigation
Elfes, Alberto
1989-01-01
The ability to recover robust spatial descriptions from sensory information and to efficiently utilize these descriptions in appropriate planning and problem-solving activities are crucial requirements for the development of more powerful robotic systems. Traditional approaches to sensor interpretation, with their emphasis on geometric models, are of limited use for autonomous mobile robots operating in and exploring unknown and unstructured environments. Here, researchers present a new approach to robot perception that addresses such scenarios using a probabilistic tesselated representation of spatial information called the Occupancy Grid. The Occupancy Grid is a multi-dimensional random field that maintains stochastic estimates of the occupancy state of each cell in the grid. The cell estimates are obtained by interpreting incoming range readings using probabilistic models that capture the uncertainty in the spatial information provided by the sensor. A Bayesian estimation procedure allows the incremental updating of the map using readings taken from several sensors over multiple points of view. An overview of the Occupancy Grid framework is given, and its application to a number of problems in mobile robot mapping and navigation are illustrated. It is argued that a number of robotic problem-solving activities can be performed directly on the Occupancy Grid representation. Some parallels are drawn between operations on Occupancy Grids and related image processing operations.
Adaptive membership functions for handwritten character recognition by Voronoi-based image zoning.
Pirlo, Giuseppe; Impedovo, Donato
2012-09-01
In the field of handwritten character recognition, image zoning is a widespread technique for feature extraction since it is rightly considered to be able to cope with handwritten pattern variability. As a matter of fact, the problem of zoning design has attracted many researchers who have proposed several image-zoning topologies, according to static and dynamic strategies. Unfortunately, little attention has been paid so far to the role of feature-zone membership functions that define the way in which a feature influences different zones of the zoning method. The result is that the membership functions defined to date follow nonadaptive, global approaches that are unable to model local information on feature distributions. In this paper, a new class of zone-based membership functions with adaptive capabilities is introduced and its effectiveness is shown. The basic idea is to select, for each zone of the zoning method, the membership function best suited to exploit the characteristics of the feature distribution of that zone. In addition, a genetic algorithm is proposed to determine-in a unique process-the most favorable membership functions along with the optimal zoning topology, described by Voronoi tessellation. The experimental tests show the superiority of the new technique with respect to traditional zoning methods.
Fernandez-Fuentes Narcis
2011-08-01
Full Text Available Abstract Background Protein binding site prediction by computational means can yield valuable information that complements and guides experimental approaches to determine the structure of protein complexes. Predictions become even more relevant and timely given the current resolution of protein interaction maps, where there is a very large and still expanding gap between the available information on: (i which proteins interact and (ii how proteins interact. Proteins interact through exposed residues that present differential physicochemical properties, and these can be exploited to identify protein interfaces. Results Here we present VORFFIP, a novel method for protein binding site prediction. The method makes use of broad set of heterogeneous data and defined of residue environment, by means of Voronoi Diagrams that are integrated by a two-steps Random Forest ensemble classifier. Four sets of residue features (structural, energy terms, sequence conservation, and crystallographic B-factors used in different combinations together with three definitions of residue environment (Voronoi Diagrams, sequence sliding window, and Euclidian distance have been analyzed in order to maximize the performance of the method. Conclusions The integration of different forms information such as structural features, energy term, evolutionary conservation and crystallographic B-factors, improves the performance of binding site prediction. Including the information of neighbouring residues also improves the prediction of protein interfaces. Among the different approaches that can be used to define the environment of exposed residues, Voronoi Diagrams provide the most accurate description. Finally, VORFFIP compares favourably to other methods reported in the recent literature.
A Fractal Comparison of Escher and Koch Tesselations
Van Dusen, Ben; Taylor, Richard
2012-01-01
M.C. Eschers tessellations have captured the imaginations of both artists and mathematicians. Circle Limit III is the most intricate of his tessellations, featuring patterns that repeat at increasingly fine scales. Although his patterns follow a scaling law determined by hyperbolic geometry, his work is often mistakenly described as following fractal geometry. Here, we perform a 'box counting' scaling analysis on Circle Limit III and an equivalent monofractal pattern based on a Koch Snowflake. Whereas our analysis highlights the expected visual differences between Eschers hyperbolic patterns and the simple monofractal, the analysis also identifies unexpected similarities between Eschers work and the bifractal poured paintings of Jackson Pollock.
Potts model on directed small-world Voronoi-Delaunay lattices
Marques, R. M.; Lima, F. W. S.; Costa Filho, Raimundo N.
2016-06-01
The critical properties of the Potts model with q = 3 and 4 states in two-dimensions on directed small-world Voronoi-Delaunay random lattices with quenched connectivity disorder are investigated. This disordered system is simulated by applying the Monte Carlo update heat bath algorithm. The Potts model on these directed small-world random lattices presents in fact a second-order phase transition with new critical exponents for q = 3 and value of the rewiring probability p = 0.01, but for q = 4 the system exhibits only a first-order phase transition independent of p (0 < p < 1).
Duals of Orphan-Free Anisotropic Voronoi Diagrams are Triangulations
Canas, Guillermo D
2011-01-01
We show that, under mild conditions on the underlying metric, duals of appropriately defined anisotropic Voronoi diagrams are embedded triangulations. Furthermore, they always triangulate the convex hull of the vertices, and have other properties that parallel those of ordinary Delaunay triangulations. These results apply to the duals of anisotropic Voronoi diagrams of any set of vertices, so long as the diagram is orphan-free.
Pereira, Sebastián; Campusano, Luis E.; Hitschfeld-Kahler, Nancy; Pizarro, Daniel; Haines, Christopher P.; Clowes, Roger G.; Marinello, Gabriel; Söchting, Ilona K.
2017-04-01
This paper is the first in a series, presenting a new galaxy cluster finder based on a three-dimensional Voronoi Tesselation plus a maximum likelihood estimator, followed by gapping-filtering in radial velocity(VoML+G). The scientific aim of the series is a reassessment of the diversity of optical clusters in the local universe. A mock galaxy database mimicking the southern strip of the magnitude(blue)-limited 2dF Galaxy Redshift Survey (2dFGRS), for the redshift range 0.009 N g ≥ 5, and 14% with N g mean rates of ˜75% and ˜90%, respectively. The VoML+G cluster velocity dispersions are found to be compatible with those corresponding to “Millennium clusters” over the 300-1000 km s-1 interval, i.e., for cluster halo masses in excess of ˜3.0 × 1013 M ⊙ h -1.
Cloning Voronoi Diagrams via Retroactive Data Structures
Dickerson, Matthew T; Goodrich, Michael T
2010-01-01
We address the problem of replicating a Voronoi diagram $V(S)$ of a planar point set $S$ by making proximity queries, which are of three possible (in decreasing order of information content): 1. the exact location of the nearest site(s) in $S$; 2. the distance to and label(s) of the nearest site(s) in $S$; 3. a unique label for every nearest site in $S$. We provide algorithms showing how queries of Type 1 and Type 2 allow an exact cloning of $V(S)$ with $O(n)$ queries and $O(n \\log^2 n)$ processing time. We also prove that queries of Type 3 can never exactly clone $V(S)$, but we show that with $O(n \\log\\frac{1}{\\epsilon})$ queries we can construct an $\\epsilon$-approximate cloning of $V(S)$. In addition to showing the limits of nearest-neighbor database security, our methods also provide one of the first natural algorithmic applications of retroactive data structures.
Voronoi, Genetic Algorithms and Their Tandem Application in Wireless Sensor Network Deployment
V. Violet Juli
2014-12-01
Full Text Available Wireless Sensor Network (WSN had become almost an indispensible especially the demand for data acquisition from national security to disaster mitigation management, weather data to environmental changes and from many more agencies. The effectiveness and efficacy of WSN dependent on the strength and weakness of the deployment of the sensor nodes which collect and transmit the data. The success of data acquisition in any network depended upon the adequacy of coverage by the sensor nodes; which in turn depended on the method of deployment and redeployment. Since deterministic deployment of nodes could not always be done, random deployment was adopted as a compulsion rather than an option. The random deployment of sensors by nature provided poor network coverage and leading to unsatisfactory data acquisition. Therefore, a better method was sought-after to redeploy the sensors that were deployed earlier at random. Hence, the compelling need had resulted in the development of numerous algorithms for suitably moving the sensors for maximum coverage. Such algorithms were of standalone ones or hybrid/combination in nature. One such combination algorithm termed as Voronoi-Genetic Algorithm (V-GA a combination/tandom application of Voronoi Vertex Averaging Algorithm (VVAA and Genetic Algorithm (GA was analyzed in this study. The displacement and coverage performance were studied, analyzed and compared with that of random deployment and redeployment by the earlier proposed algorithms namely VVAA and GA by the same researcher.
Efficient Delaunay Tessellation through K-D Tree Decomposition
Morozov, Dmitriy; Peterka, Tom
2017-08-21
Delaunay tessellations are fundamental data structures in computational geometry. They are important in data analysis, where they can represent the geometry of a point set or approximate its density. The algorithms for computing these tessellations at scale perform poorly when the input data is unbalanced. We investigate the use of k-d trees to evenly distribute points among processes and compare two strategies for picking split points between domain regions. Because resulting point distributions no longer satisfy the assumptions of existing parallel Delaunay algorithms, we develop a new parallel algorithm that adapts to its input and prove its correctness. We evaluate the new algorithm using two late-stage cosmology datasets. The new running times are up to 50 times faster using k-d tree compared with regular grid decomposition. Moreover, in the unbalanced data sets, decomposing the domain into a k-d tree is up to five times faster than decomposing it into a regular grid.
Voronoi-based localisation algorithm for mobile sensor networks
Guan, Zixiao; Zhang, Yongtao; Zhang, Baihai; Dong, Lijing
2016-11-01
Localisation is an essential and important part in wireless sensor networks (WSNs). Many applications require location information. So far, there are less researchers studying on mobile sensor networks (MSNs) than static sensor networks (SSNs). However, MSNs are required in more and more areas such that the number of anchor nodes can be reduced and the location accuracy can be improved. In this paper, we firstly propose a range-free Voronoi-based Monte Carlo localisation algorithm (VMCL) for MSNs. We improve the localisation accuracy by making better use of the information that a sensor node gathers. Then, we propose an optimal region selection strategy of Voronoi diagram based on VMCL, called ORSS-VMCL, to increase the efficiency and accuracy for VMCL by adapting the size of Voronoi area during the filtering process. Simulation results show that the accuracy of these two algorithms, especially ORSS-VMCL, outperforms traditional MCL.
TOOL PATH PLANNING USING VORONOI DIAGRAM AND THREE STACKS
无
2001-01-01
Based on the object-oriented data structure of Vor onoi diagram, the algorithm of the trimmed offset generating and the optimal too l path planning of the pocket machining for multiply connected polygonal domains are studied. The intersection state transition rule is improved in this algorit hm. The intersection is between the trimmed offsets and Voronoi polygon. On this basis, the trimmed offset generating and the optimal tool path planning are mad e with three stacks(I-stack, C-stack and P-stack)in different monotonous pouc hes of Voronoi diagram. At the same time, a merging method of Voronoi diagram an d offsets generating for multiply connected polygonal domains is also presented. The above algorithms have been implemented in NC machining successfully, and th e efficiency is fully verified.
Geometric and spectral consequences of curvature bounds on tessellations
Keller, Matthias
2016-01-01
This is a chapter of a forthcoming Lecture Notes in Mathematics "Modern Approaches to Discrete Curvature" edited by L. Najman and P. Romon. It provides a survey on geometric and spectral consequences of curvature bounds. The geometric setting are tessellations of surfaces with finite and vanishing genus. We consider a curvature arising as an angular defect. Several of the results presented here have analogues in Riemannian geometry. In some cases one can go even beyond the Riemannian results ...
Responsive envelope tessellation and stochastic rotation of 4-fold penttiles
2014-01-01
This paper reports on the design and control of a responsive envelope based on the rotation of tessellated components. The study investigates responsive and dynamic approaches for building facades and envelopes to regulate solar shading, light control, views and thermal gain within the building. It is well known that near real-time visual output from computational simulation can significantly impact the prediction of dynamic building-environment interactions and lead to the development of sma...
Responsive envelope tessellation and stochastic rotation of 4-fold penttiles
Sambit Datta
2014-06-01
Full Text Available This paper reports on the design and control of a responsive envelope based on the rotation of tessellated components. The study investigates responsive and dynamic approaches for building facades and envelopes to regulate solar shading, light control, views and thermal gain within the building. It is well known that near real-time visual output from computational simulation can significantly impact the prediction of dynamic building-environment interactions and lead to the development of smart, adaptable, net zero energy buildings. To address these motivations, this paper reports the development of an experimental simulation of a responsive envelope based on using a 4-fold penttile scheme. The simulation is developed using a novel pentagonal approach involving component (tile design, tessellation and control methods. The paper further elaborates on the geometry and control aspects of the facade subdivision and presents the results of applying this tessellation geometry to a building envelope shading study based on facade components with rotation. Finally, it tests the “responsiveness” to multiple performance metrics by applying a non-deterministic exploration method for the stochastic rotation of individual panels. The sophisticated evaluation of alternative envelope configurations for a set of performance criteria require a tighter computational coupling between modelling and control of dynamic geometry.
Path planning of the robot assembly based on Voronoi diagram
FU Zhuang; ZHAO Yan-zheng
2008-01-01
Based on the concepts of Voronoi diagram that describes geometry information of the robot assembly in C space, the position vector path parameter equation of the assembly movement between the step shaft and two-sided beating bracket was given. And the path planning strategy of the component initiative assembly was put forward as well. Theoretical analysis proves that using the Voronoi diagram to do the geometry reasoning on the assembly space can evaluate the feasibility of the component assembly, and can present the reference posi-tion vector path of the component movement from the initial configuration to the objective configuration, there-fore improves the flexibility of the robot initiative assembly.
GPU Based Detection of Topological Changes in Voronoi Diagrams
Bernaschi, Massimo; Sbragaglia, Mauro
2016-01-01
The Voronoi diagrams are an important tool having theoretical and practical applications in a large number of fields. We present a new procedure, implemented as a set of CUDA kernels, which detects, in a general and efficient way, topological changes in case of dynamic Voronoi diagrams whose generating points move in time. The solution that we provide has been originally developed to identify plastic events during simulations of soft-glassy materials based on a Lattice Boltzmann model with frustrated-short range attractive and mid/long-range repulsive-interactions. Along with the description of our approach, we present also some preliminary physics results.
GPU based detection of topological changes in Voronoi diagrams
Bernaschi, M.; Lulli, M.; Sbragaglia, M.
2017-04-01
The Voronoi diagrams are an important tool having theoretical and practical applications in a large number of fields. We present a new procedure, implemented as a set of CUDA kernels, which detects, in a general and efficient way, topological changes in case of dynamic Voronoi diagrams whose generating points move in time. The solution that we provide has been originally developed to identify plastic events during simulations of soft-glassy materials based on a lattice Boltzmann model with frustrated-short range attractive and mid/long-range repulsive-interactions. Along with the description of our approach, we present also some preliminary physics results.
A Voronoi Interface approach to cell aggregate electropermeabilization
Guittet, Arthur; Poignard, Clair; Gibou, Frederic
2017-03-01
We present a Voronoi Interface approach to the study of cell electropermeabilization. We consider the nonlinear electropermeabilization model of Poignard et al. [20], which takes into account the jump in the voltage potential across cells' membrane. The jump condition is imposed in a sharp manner, using the Voronoi Interface Method of Guittet et al. [14], while adaptive Quad/Oc-tree grids are employed to automatically refine near the cells boundary for increased accuracy. Numerical results are provided to illustrate the accuracy of the methods. We also carry out simulations in three spatial dimensions to investigate the influence of shadowing and of the cells shape on the degree of permeabilization.
MeshVoro: A Three-Dimensional Voronoi Mesh Building Tool for the TOUGH Family of Codes
Freeman, C. M.; Boyle, K. L.; Reagan, M.; Johnson, J.; Rycroft, C.; Moridis, G. J.
2013-09-30
Few tools exist for creating and visualizing complex three-dimensional simulation meshes, and these have limitations that restrict their application to particular geometries and circumstances. Mesh generation needs to trend toward ever more general applications. To that end, we have developed MeshVoro, a tool that is based on the Voro (Rycroft 2009) library and is capable of generating complex threedimensional Voronoi tessellation-based (unstructured) meshes for the solution of problems of flow and transport in subsurface geologic media that are addressed by the TOUGH (Pruess et al. 1999) family of codes. MeshVoro, which includes built-in data visualization routines, is a particularly useful tool because it extends the applicability of the TOUGH family of codes by enabling the scientifically robust and relatively easy discretization of systems with challenging 3D geometries. We describe several applications of MeshVoro. We illustrate the ability of the tool to straightforwardly transform a complex geological grid into a simulation mesh that conforms to the specifications of the TOUGH family of codes. We demonstrate how MeshVoro can describe complex system geometries with a relatively small number of grid blocks, and we construct meshes for geometries that would have been practically intractable with a standard Cartesian grid approach. We also discuss the limitations and appropriate applications of this new technology.
Effective conductivity of the rectangular and hexagonal tessellations in the plane
Barash, L. Yu., E-mail: barash@itp.ac.ru; Khalatnikov, I. M. [Landau Institute for Theoretical Physics (Russian Federation)
2015-08-15
The effective conductivity of the two-dimensional periodic polygonal tessellations in the plane is determined using the perturbation theory and numerically. A diagram technique in perturbation theory for the effective conductivity of the tesselations in the plane is established using oblique coordinates. Calculations for the three color hexagonal tesselation have been carried out. A numerical method is developed for obtaining effective conductivity with high accuracy both when the perturbation theory is applicable and when the conductivities of the tessellation components are substantially different. For small differences between the conductivities of the components, the approach of the perturbation theory agrees with the numerical results.
Voss, Florian; Schmidt, Volker
2009-01-01
We consider spatial stochastic models, which can be applied e.g. to telecommunication networks with two hierarchy levels. In particular, we consider two Cox processes concentrated on the edge set of a random tessellation, where the points can describe the locations of low-level and high-level network components, respectively, and the edge set the underlying infrastructure of the network, like road systems, railways, etc. Furthermore, each low-level component is marked with the shortest path along the edge set to the nearest high-level component. We investigate the typical shortest path length of the resulting marked point process, which is an important characteristic e.g. in performance analysis and planning of telecommunication networks. In particular, we show that its distribution converges to simple parametric limit distributions if a certain scaling factor converges to zero and infinity, respectively. This can be used to approximate the density of the typical shortest path length by analytical formulae.
Map updates in a dynamic Voronoi data structure
Mioc, Darka; Antón Castro, Francesc/François; Gold, C. M.;
2006-01-01
the complex operations. This resulted in a new formal model for map updates, similar to "cellular encoding", where each update is uniquely characterized by the numbers of newly created and inactivated Voronoi regions. This research shows that the result of the formalization of the operations on the dynamic...
On kinetic line Voronoi operations and finite fields
Mioc, Darka; Anton, François; Gold, Christopher
2009-01-01
of integers modulo 5: F5 = Z/5Z. We show also an isomorphism between the set of complex operations on the kinetic Voronoi diagram of points and open oriented line segments and the set of differences of new and deleted quad-edge edges induced by these operations, and its explanation using the finite field F15...
Voronoi Cell Patterns: theoretical model and application to submonolayer growth
González, Diego Luis; Einstein, T. L.
2012-02-01
We use a simple fragmentation model to describe the statistical behavior of the Voronoi cell patterns generated by a homogeneous and isotropic set of points in 1D and in 2D. In particular, we are interested in the distribution of sizes of these Voronoi cells. Our model is completely defined by two probability distributions in 1D and again in 2D, the probability to add a new point inside an existing cell and the probability that this new point is at a particular position relative to the preexisting point inside this cell. In 1D the first distribution depends on a single parameter while the second distribution is defined through a fragmentation kernel; in 2D both distributions depend on a single parameter. The fragmentation kernel and the control parameters are closely related to the physical properties of the specific system under study. We apply our model to describe the Voronoi cell patterns of island nucleation for critical island sizes i=0,1,2,3. Experimental results for the Voronoi cells of InAs/GaAs quantum dots are also described by our model.
Level Sets and Voronoi based Feature Extraction from any Imagery
Sharma, O.; Anton, François; Mioc, Darka
2012-01-01
Polygon features are of interest in many GEOProcessing applications like shoreline mapping, boundary delineation, change detection, etc. This paper presents a unique new GPU-based methodology to automate feature extraction combining level sets, or mean shift based segmentation together with Voronoi...
A general Voronoi summation formula for GL(n,Z)
Miller, Stephen D
2009-01-01
In an earlier paper we derived an analogue of the classical Voronoi summation formula for automorphic forms on GL(3), by using the theory of automorphic distributions. The purpose of the present paper is to apply this theory to derive the analogous formulas for GL(n).
A.A. Burbelko
2013-01-01
Full Text Available The study presents a mathematical model of the crystallisation of nodular graphite cast iron. The proposed model is based on micro- andmacromodels, in which heat flow is analysed at the macro level, while micro level is used for modelling of the diffusion of elements. The use of elementary diffusion field in the shape of an averaged Voronoi polyhedron [AVP] was proposed. To determine the geometry of the averaged Voronoi polyhedron, Kolmogorov statistical theory of crystallisation was applied. The principles of a differential mathematical formulation of this problem were discussed. Application of AVP geometry allows taking into account the reduced volume fraction of the peripheral areas of equiaxial grains by random contacts between adjacent grains.As a result of the simulation, the cooling curves were plotted, and the movement of "graphite-austenite" and "austenite-liquid” phaseboundaries was examined. Data on the microsegregation of carbon in the cross-section of an austenite layer in eutectic grains wereobtained. Calculations were performed for different particle densities and different wall thicknesses. The calculation results were compared with experimental data.
EVALUATING THE EULER-POINCARÉ CHARACTERISTIC OF A SET USING A SPATIAL TESSELLATION
Jean-Paul Jernot
2011-05-01
Full Text Available A new formula is established to evaluate the Euler-Poincaré characteristic of a polyconvex subset X in Rd starting only from measurements of X in the cells of a tessellation. Simplifications occur when X is a union of cells of the tessellation, leading to another formula that unifies and extends several classical digitization results.
Ringler, Todd D [Los Alamos National Laboratory; Gunzburger, Max [FLORIDA STATE UNIV; Ju, Lili [UNIV OF SOUTH CAROLINA
2008-01-01
During the next decade and beyond, climate system models will be challenged to resolve scales and processes that are far beyond their current scope. Each climate system component has its prototypical example of an unresolved process that may strongly influence the global climate system, ranging from eddy activity within ocean models, to ice streams within ice sheet models, to surface hydrological processes within land system models, to cloud processes within atmosphere models. These new demands will almost certainly result in the develop of multi-resolution schemes that are able, at least regional to faithfully simulate these fine-scale processes. Spherical Centroidal Voronoi Tessellations (SCVTs) offer one potential path toward the development of robust, multi-resolution climate system component models, SCVTs allow for the generation of high quality Voronoi diagrams and Delaunay triangulations through the use of an intuitive, user-defined density function, each of the examples provided, this method results in high-quality meshes where the quality measures are guaranteed to improve as the number of nodes is increased. Real-world examples are developed for the Greenland ice sheet and the North Atlantic ocean. Idealized examples are developed for ocean-ice shelf interaction and for regional atmospheric modeling. In addition to defining, developing and exhibiting SCVTs, we pair this mesh generation technique with a previously developed finite-volume method. Our numerical example is based on the nonlinear shallow-water equations spanning the entire surface of the sphere. This example is used to elucidate both the potential benefits of this multi-resolution method and the challenges ahead.
Canaliculi in the tessellated skeleton of cartilaginous fishes
Dean, M.N.; Socha, J.J.; Hall, B.K.; Summers, A.P. (UCI); (Dalhousie U.); (VPI-SU)
2010-08-04
The endoskeletal elements of sharks and rays are comprised of an uncalcified, hyaline cartilage-like core overlain by a thin fibro-ceramic layer of mineralized hexagonal tiles (tesserae) adjoined by intertesseral fibers. The basic spatial relationships of the constituent tissues (unmineralized cartilage, mineralized cartilage, fibrous tissue) are well-known - endoskeletal tessellation is a long-recognized synapomorphy of elasmobranch fishes - but a high-resolution and three-dimensional (3D) understanding of their interactions has been hampered by difficulties in sample preparation and lack of technologies adequate for visualizing microstructure and microassociations. We used cryo-electron microscopy and synchrotron radiation tomography to investigate tessellated skeleton ultrastructure but without damage to the delicate relationships between constituent tissues or to the tesserae themselves. The combination of these techniques allowed visualization of never before appreciated internal structures, namely passages connecting the lacunar spaces within tesserae. These intratesseral 'canaliculi' link consecutive lacunar spaces into long lacunar strings, radiating outward from the center of tesserae. The continuity of extracellular matrix throughout the canalicular network may explain how chondrocytes in tesserae remain vital despite encasement in mineral. Extracellular fluid exchange may also permit transmission of nutrients, and mechanical and mineralization signals among chondrocytes, in a manner similar to the canalicular network in bone. These co-adapted mechanisms for the facilitated exchange of extracellular material suggest a level of parallelism in early chondrocyte and osteocyte evolution.
A LAGUERRE VORONOI BASED SCHEME FOR MESHING PARTICLE SYSTEMS.
Bajaj, Chandrajit
2005-06-01
We present Laguerre Voronoi based subdivision algorithms for the quadrilateral and hexahedral meshing of particle systems within a bounded region in two and three dimensions, respectively. Particles are smooth functions over circular or spherical domains. The algorithm first breaks the bounded region containing the particles into Voronoi cells that are then subsequently decomposed into an initial quadrilateral or an initial hexahedral scaffold conforming to individual particles. The scaffolds are subsequently refined via applications of recursive subdivision (splitting and averaging rules). Our choice of averaging rules yield a particle conforming quadrilateral/hexahedral mesh, of good quality, along with being smooth and differentiable in the limit. Extensions of the basic scheme to dynamic re-meshing in the case of addition, deletion, and moving particles are also discussed. Motivating applications of the use of these static and dynamic meshes for particle systems include the mechanics of epoxy/glass composite materials, bio-molecular force field calculations, and gas hydrodynamics simulations in cosmology.
Voronoi Diagram Based Optimization of Dynamic Reactive Power Sources
Huang, Weihong [University of Tennessee (UT); Sun, Kai [University of Tennessee (UT); Qi, Junjian [University of Tennessee (UT); Xu, Yan [ORNL
2015-01-01
Dynamic var sources can effectively mitigate fault-induced delayed voltage recovery (FIDVR) issues or even voltage collapse. This paper proposes a new approach to optimization of the sizes of dynamic var sources at candidate locations by a Voronoi diagram based algorithm. It first disperses sample points of potential solutions in a searching space, evaluates a cost function at each point by barycentric interpolation for the subspaces around the point, and then constructs a Voronoi diagram about cost function values over the entire space. Accordingly, the final optimal solution can be obtained. Case studies on the WSCC 9-bus system and NPCC 140-bus system have validated that the new approach can quickly identify the boundary of feasible solutions in searching space and converge to the global optimal solution.
Voronoi poles-based saliency feature detection from point clouds
Xu, Tingting; Wei, Ning; Dong, Fangmin; Yang, Yuanqin
2016-12-01
In this paper, we represent a novel algorithm for point cloud feature detection. Firstly, the algorithm estimates the local feature for each sample point by computing the ratio of the distance from the inner voronoi pole and the outer voronoi pole to the surface. Then the surface global saliency feature is detected by adding the results of the difference of Gaussian for local feature under different scales. Compared with the state of the art methods, our algorithm has higher computing efficiency and more accurate feature detection for sharp edge. The detected saliency features are applied as the weights for surface mesh simplification. The numerical results for mesh simplification show that our method keeps the more details of key features than the traditional methods.
A Hierarchical Sensor Network Based on Voronoi Diagram
SHANG Rui-qiang; ZHAO Jian-li; SUN Qiu-xia; WANG Guang-xing
2006-01-01
A hierarchical sensor network is proposed which places the sensing and routing capacity at different layer nodes.It thus simplifies the hardware design and reduces cost. Adopting Voronoi diagram in the partition of backbone network,a mathematical model of data aggregation based on hierarchical architecture is given. Simulation shows that the number of transmission data packages is sharply cut down in the network, thus reducing the needs in the bandwidth and energy resources and is thus well adapted to sensor networks.
Heterogeneous locational optimisation using a generalised Voronoi partition
Guruprasad, K. R.; Ghose, Debasish
2013-06-01
In this paper a generalisation of the Voronoi partition is used for locational optimisation of facilities having different service capabilities and limited range or reach. The facilities can be stationary, such as base stations in a cellular network, hospitals, schools, etc., or mobile units, such as multiple unmanned aerial vehicles, automated guided vehicles, etc., carrying sensors, or mobile units carrying relief personnel and materials. An objective function for optimal deployment of the facilities is formulated, and its critical points are determined. The locally optimal deployment is shown to be a generalised centroidal Voronoi configuration in which the facilities are located at the centroids of the corresponding generalised Voronoi cells. The problem is formulated for more general mobile facilities, and formal results on the stability, convergence and spatial distribution of the proposed control laws responsible for the motion of the agents carrying facilities, under some constraints on the agents' speed and limit on the sensor range, are provided. The theoretical results are supported with illustrative simulation results.
Tessellating cushions: four-point functions in N=4 SYM
Eden, Burkhard
2016-01-01
We consider a class of planar tree-level four-point functions in N=4 SYM in a special kinematic regime: one BMN operator with two scalar excitations and three half-BPS operators are put onto a line in configuration space; additionally, for the half-BPS operators a co-moving frame is chosen in flavour space. In configuration space, the four-punctured sphere is naturally triangulated by tree-level planar diagrams. We demonstrate on a number of examples that each tile can be associated with a modified hexagon form-factor in such a way as to efficiently reproduce the tree-level four-point function. Our tessellation is not of the OPE type, fostering the hope of finding an independent, integrability-based approach to the computation of planar four-point functions.
Noneuclidean Tessellations and their relation to Reggie Trajectories
Lavenda, B H
2013-01-01
The coefficients in the confluent hypergeometric equation specify the Regge trajectories and the degeneracy of the angular momentum states. Bound states are associated with real angular momenta while resonances are characterized by complex angular momenta. With a centrifugal potential, the half-plane is tessellated by crescents. The addition of an electrostatic potential converts it into a hydrogen atom, and the crescents into triangles which may have complex conjugate angles; the angle through which a rotation takes place is accompanied by a stretching. Rather than studying the properties of the wave functions themselves, we study their symmetry groups. A complex angle indicates that the group contains loxodromic elements. Since the domain of such groups is not the disc, hyperbolic plane geometry cannot be used. Rather, the theory of the isometric circle is adapted since it treats all groups symmetrically. The pairing of circles and their inverses is likened to pairing particles with their antiparticles whic...
Overview of the Research Progress in the Earth Tessellation Grid
ZHAO Xuesheng
2016-12-01
Full Text Available By analyzing the related literatures on the earth tessellation grid (ETG in recent 10 years, the research achievements in this field are systematic reviewed in four aspects, i.e. the earth subdivision modeling (include quadrangle subdivision, equal-area subdivision and 3D subdivision, encoding computation (include hierarchical encoding computation, filling curve encoding computation and integer coordinate encoding computation, grid quality assessment (include evaluation criteria, evaluation factors, and propagation trend in diffferent levels and typical applications (include government agency applications,business software applications and industry applications. The structural characteristics, applicable models and their shortcomings in the different grid models are given in details. Finally, some advanced academic problems in the ETG are given based on the completeness of basic theory, the efficiency of grid computing, and the reliability of grid quality.
Anton, François
2008-01-01
This is an American Mathematical Society (AMS) MathSciNet Review of the paper by Lucarini, Valerio (I-BOLO-P)......This is an American Mathematical Society (AMS) MathSciNet Review of the paper by Lucarini, Valerio (I-BOLO-P)...
Anton, François
2008-01-01
This is an American Mathematical Society (AMS) MathSciNet Review of the paper by Lucarini, Valerio (I-BOLO-P)......This is an American Mathematical Society (AMS) MathSciNet Review of the paper by Lucarini, Valerio (I-BOLO-P)...
Voronoi Structural Evolution of Bulk Silicon upon Melting
ZHANG Shi-Liang; ZHANG Xin-Yu; WANG Lin-Min; QI Li; ZHANG Su-Hong; ZHU Yan; LIU Ri-Ping
2011-01-01
@@ The Voronoi structural evolution of silicon upon melting is investigated using a molecular dynamics simulation.At temperatures below the melting point, the solid state system is identified to have a four-fold coordination structure .As the temperature increases, the five-fold coordination and six-fold coordination structures and are observed.This is explained in terms of increasing atomic displacement due to thermal motion and the trapping of the moving atoms by others.At temperatures above the melting point, nearly ali of the four-fold coordination structures grows into multiple-fold coordination ones.%The Voronoi structural evolution of silicon upon melting is investigated using a molecular dynamics simulation. At temperatures below the melting point, the solid state system is identified to have a four-told coordination structure (4,0,0,0). As the temperature increases, the five-fold coordination (2,3,0,0) and six-fold coordination structures (2,2,2,0) and (0,6,0,0) are observed. This is explained in terms of increasing atomic displacement due to thermal motion and the trapping of the moving atoms by others. At temperatures above the melting point, nearly all of the four-fold coordination structures grows into multiple-fold coordination ones.
Voronoi-Based Curvature and Feature Estimation from Point Clouds.
Mérigot, Quentin; Ovsjanikov, Maks; Guibas, Leonidas
2011-06-01
We present an efficient and robust method for extracting curvature information, sharp features, and normal directions of a piecewise smooth surface from its point cloud sampling in a unified framework. Our method is integral in nature and uses convolved covariance matrices of Voronoi cells of the point cloud which makes it provably robust in the presence of noise. We show that these matrices contain information related to curvature in the smooth parts of the surface, and information about the directions and angles of sharp edges around the features of a piecewise-smooth surface. Our method is applicable in both two and three dimensions, and can be easily parallelized, making it possible to process arbitrarily large point clouds, which was a challenge for Voronoi-based methods. In addition, we describe a Monte-Carlo version of our method, which is applicable in any dimension. We illustrate the correctness of both principal curvature information and feature extraction in the presence of varying levels of noise and sampling density on a variety of models. As a sample application, we use our feature detection method to segment point cloud samplings of piecewise-smooth surfaces.
Peptide tessellation yields micrometre-scale collagen triple helices
Tanrikulu, I. Caglar; Forticaux, Audrey; Jin, Song; Raines, Ronald T.
2016-11-01
Sticky-ended DNA duplexes can associate spontaneously into long double helices; however, such self-assembly is much less developed with proteins. Collagen is the most prevalent component of the extracellular matrix and a common clinical biomaterial. As for natural DNA, the ~103-residue triple helices (~300 nm) of natural collagen are recalcitrant to chemical synthesis. Here we show how the self-assembly of short collagen-mimetic peptides (CMPs) can enable the fabrication of synthetic collagen triple helices that are nearly a micrometre in length. Inspired by the mathematics of tessellations, we derive rules for the design of single CMPs that self-assemble into long triple helices with perfect symmetry. Sticky ends thus created are uniform across the assembly and drive its growth. Enacting this design yields individual triple helices that, in length, match or exceed those in natural collagen and are remarkably thermostable, despite the absence of higher-order association. The symmetric assembly of CMPs provides an enabling platform for the development of advanced materials for medicine and nanotechnology.
Tessellated structure from motion for midrange perception and tactical planning
Shim, Minbo; Yilma, Samson
2009-05-01
A typical structure from motion (SFM) technique is to construct 3-D structures from the observation of the motions of salient features tracked over time. Although the sparse feature-based SFM provides additional solutions to robotic platforms as a tool to augment navigation performance, the technique often fails to produce dense 3-D structures due to the sparseness that is introduced during the feature selection and matching processes. For midrange sensing and tactical planning, it is important to have a dense map that is able to provide not only 3-D coordinates of features, but also clustered terrain information around the features for better thematic representation of the scene. In order to overcome the shortfalls embedded in the sparse feature-based SFM, we propose an approach that uses Voronoi decomposition with an equidistance-based triangulation that is applied to each of segmented and classified regions. The set of the circumcenters of the circum-hyperspheres used in the triangulation is formed with the feature points extracted from the SFM processing. We also apply flat surface detection to find traversable surface for a robotic vehicle to be able to maneuver safely on.
The DOE Knowledge Base Mthodology for the Creation of an Optimal Spatial Tessellation
Hipp, J.R.; Moore, S.G.; Shepherd, E.; Young, C.J
1998-10-20
The DOE Knowledge Base is a library of detailed information whose purpose is to improve the capability of the United States National Data Center (USNDC) to monitor compliance with the Comprehensive Test Ban Treaty (CTBT). Much of the data contained by the Knowledge Base is spatial in nature, and some of it is used to improve the accuracy with which seismic locations are determined while maintaining or improving current calculational perfor- mance. In this presentation, we define and describe the methodology used to create spatial tessellations of seismic data which are utilized with a gradient-modified natural-neighbor interpolation method to evaluate travel-time corrections. The goal is to interpolate a specified correction surface, or a group of them, with prescribed accuracy and surface smoothness requirements, while minimizing the number of data points necessary to represent the surface. Maintain- ing accuracy is crucial toward improving the precision of seismic origin location. Minimizing the number of nodes in the tessellation improves calculational and data access efficiency and performance. The process requires two initialization steps and an iterated 7 step algorithm for inserting new tessellation nodes. First, M residual data from ground truth events are included in the tessellation. These data remain fixed throughout the creation of the triangular tessellation. Next, a coarse grid of nodes is laid over the region to be tessellated. The coarse grid is necessary to define the boundary of the region to be tessellated. Next the 7 step iterated algorithm is performed to add new nodes to the tessellation to ensure that accuracy and smoothness requirements are met. These steps include 1) all data points in the tessellation are linked together to form a triangular tessellation using p standard Delaunay tessellation technique; 2) all of the data points, excluding the original data and boundruy nodes, are smoothed using a length-weighted Laplacian smoother to
Neyrinck, Mark C
2012-01-01
Tessellations are valuable both conceptually and for analysis in the study of the large-scale structure of the universe. They provide a conceptual model for the 'cosmic web,' and are of great use to analyze cosmological data. Here we describe tessellations in another set of coordinates, of the initially flat sheet of dark matter that gravity folds up in rough analogy to origami. The folds that develop are called caustics, and they tessellate space into stream regions. Tessellations of the dark-matter sheet are also useful in simulation analysis, for instance for density measurement, and to identify structures where streams overlap.
Practical Conditions for Well-behaved-ness of Anisotropic Voronoi Diagrams
Canas, Guillermo D
2012-01-01
Recently, simple conditions for well-behaved-ness of anisotropic Voronoi diagrams have been proposed. While these conditions ensure well-behaved-ness of two types of practical anisotropic Voronoi diagrams, as well as the geodesic-distance one, in any dimension, they are both prohibitively expensive to evaluate, and not well-suited for typical problems in approximation or optimization. We propose simple conditions that can be efficiently evaluated, and are better suited to practical problems of approximation and optimization. The practical utility of this analysis is enhanced by the fact that orphan-free anisotropic Voronoi diagrams have embedded triangulations as duals.
Approximating the Generalized Voronoi Diagram of Closely Spaced Objects
Edwards, John; Daniel, Eric; Pascucci, Valerio; Bajaj, Chandrajit
2016-01-01
We present an algorithm to compute an approximation of the generalized Voronoi diagram (GVD) on arbitrary collections of 2D or 3D geometric objects. In particular, we focus on datasets with closely spaced objects; GVD approximation is expensive and sometimes intractable on these datasets using previous algorithms. With our approach, the GVD can be computed using commodity hardware even on datasets with many, extremely tightly packed objects. Our approach is to subdivide the space with an octree that is represented with an adjacency structure. We then use a novel adaptive distance transform to compute the distance function on octree vertices. The computed distance field is sampled more densely in areas of close object spacing, enabling robust and parallelizable GVD surface generation. We demonstrate our method on a variety of data and show example applications of the GVD in 2D and 3D. PMID:27540272
A Voronoi-based spatial algebra for spatial relations
无
2002-01-01
Spatial relation between spatial objects is a very important topic for spatial reasoning, query and analysis in geographical information systems (GIS). The most popular models in current use have fundamental deficiencies in theory. In this paper, a generic algebra for spatial relations is presented, in which (i) appropriate operators from set operators (i.e. union, intersection, difference, difference by, symmetric difference, etc.) are utilized to distinguish the spatial relations between neighboring spatial objects; (ii) three types of values are used for the computational results of set operations-content, dimension and number of connected components; and (iii) a spatial object is treated as a whole but the Voronoi region of an object is employed to enhance its interaction with its neighbours. This algebra overcomes the shortcomings of the existing models and it can effectively describe the relations of spatial objects.
Dynamic load balancing algorithm for molecular dynamics based on Voronoi cells domain decompositions
Fattebert, J.-L. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Richards, D.F. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Glosli, J.N. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2012-12-01
We present a new algorithm for automatic parallel load balancing in classical molecular dynamics. It assumes a spatial domain decomposition of particles into Voronoi cells. It is a gradient method which attempts to minimize a cost function by displacing Voronoi sites associated with each processor/sub-domain along steepest descent directions. Excellent load balance has been obtained for quasi-2D and 3D practical applications, with up to 440·10^{6} particles on 65,536 MPI tasks.
A. A. Burbelko; J. Początek; M. Królikowski
2013-01-01
The study presents a mathematical model of the crystallisation of nodular graphite cast iron. The proposed model is based on micro- andmacromodels, in which heat flow is analysed at the macro level, while micro level is used for modelling of the diffusion of elements. The use of elementary diffusion field in the shape of an averaged Voronoi polyhedron [AVP] was proposed. To determine the geometry of the averaged Voronoi polyhedron, Kolmogorov statistical theory of crystallisation was applied....
MOMENTS OF THE LENGTH OF LINE SEGMENTS IN HOMOGENEOUS PLANAR STIT TESSELLATIONS
Christoph Thäle
2011-05-01
Full Text Available Homogeneous planar tessellations stable under iteration (STIT tessellations are considered. Using recent results about the joint distribution of direction and length of the typical I-, K- and J-segment we prove closed formulas for the first, second and higher moments of the length of these segments given their direction. This especially leads to themean values and variances of these quantities andmean value relations as well as general moment relationships. Moreover, the relation between these mean values and certain conditional mean values (and also higher moments is discussed. The results are also illustrated for several examples.
Seamless Heterogeneous 3D Tessellation via DWT Domain Smoothing and Mosaicking
Puech William
2010-01-01
Full Text Available With todays geobrowsers, the tessellations are far from being smooth due to a variety of reasons: the principal being the light difference and resolution heterogeneity. Whilst the former has been extensively dealt with in the literature through classic mosaicking techniques, the latter has got little attention. We focus on this latter aspect and present two DWT domain methods to seamlessly stitch tiles of heterogeneous resolutions. The first method is local in that each of the tiles that constitute the view, is subjected to one of the three context-based smoothing functions proposed for horizontal, vertical, and radial smoothing, depending on its localization in the tessellation. These functions are applied at the DWT subband level and followed by an inverse DWT to give a smoothened tile. In the second method, though we assume the same tessellation scenario, the view field is thought to be of a sliding window which may contain parts of the tiles from the heterogeneous tessellation. The window is refined in the DWT domain through mosaicking and smoothing followed by a global inverse DWT. Rather than the traditional sense, the mosaicking employed over here targets the heterogeneous resolution. Perceptually, this second method has shown better results than the first one. The methods have been successfully applied to practical examples of both the texture and its corresponding DEM for seamless 3D terrain visualization.
On the Use of Laguerre Tessellations for Representations of 3D Grain Structures
Lyckegaard, Allan; Lauridsen, Erik Mejdal; Ludwig, Wolfgang
2011-01-01
Accurate descriptions of 3D grain structures in polycrystalline materials are of key interest as the grain structure is closely correlated to the macroscopic properties of the material. In the present study, we investigate the accuracy of using Laguerre tessellations to represent 3D grain structu...
Incremental Construction of Generalized Voronoi Diagrams on Pointerless Quadtrees
Quanjun Yin
2014-01-01
Full Text Available In robotics, Generalized Voronoi Diagrams (GVDs are widely used by mobile robots to represent the spatial topologies of their surrounding area. In this paper we consider the problem of constructing GVDs on discrete environments. Several algorithms that solve this problem exist in the literature, notably the Brushfire algorithm and its improved versions which possess local repair mechanism. However, when the area to be processed is very large or is of high resolution, the size of the metric matrices used by these algorithms to compute GVDs can be prohibitive. To address this issue, we propose an improvement on the current algorithms, using pointerless quadtrees in place of metric matrices to compute and maintain GVDs. Beyond the construction and reconstruction of a GVD, our algorithm further provides a method to approximate roadmaps in multiple granularities from the quadtree based GVD. Simulation tests in representative scenarios demonstrate that, compared with the current algorithms, our algorithm generally makes an order of magnitude improvement regarding memory cost when the area is larger than 210×210. We also demonstrate the usefulness of the approximated roadmaps for coarse-to-fine pathfinding tasks.
Positioning localities from spatial assertions based on Voronoi neighboring
无
2010-01-01
With the rapid development of Internet,much spatial information contained in non-structured or semi-structured documents is available on the World Wide Web.In such documents,localities are always textually described using spatial relationships and named places,instead of numerical coordinates.Hence,extracting positional information from locality descriptions is an important task.In this paper,we bridge two aspects of locality descriptions,namely generating locality descriptions and positioning localities,and provide a method to compute probability density according to the selection probability of a reference object to describe the position of the target object.Refinement operation on uncertainty field is used to deal with locality description involving multiple reference objects.Three metrics are introduced to measure the results of positioning localities.We choose the mixed selection probability function based on Euclidean distance and Voronoi stolen-area to compute probability density function.Finally,we use three cases to demonstrate the proposed methods.
Voronoi network modelling of multicrystalline silicon solar cells
Donolato, C.
2000-01-01
A model of a multicrystalline silicon solar cell with columnar grains having different carrier recombination properties is constructed from a two-dimensional Voronoi network. The prismatic grains are approximated by cylinders embedded in an effective medium with diffusion length Le , and the charge collection probability icons/Journals/Common/varphi" ALT="varphi" ALIGN="TOP"/> (r ) within each grain is calculated by solving a three-dimensional diffusion equation. The value of Le is calculated self-consistently through the integral of icons/Journals/Common/varphi" ALT="varphi" ALIGN="TOP"/> over the cell volume. The function icons/Journals/Common/varphi" ALT="varphi" ALIGN="TOP"/> also allows the calculation of the contribution of the base to the reverse saturation current of the cell. Numerical examples illustrate the influence of areal inhomogeneities and grain boundary recombination on the value of Le , dark current and open-circuit voltage. It is found that small-area grains with low lifetime mainly reduce the open-circuit voltage without significantly lowering Le and the photocurrent. Histograms obtained for multicrystalline cells by the light beam induced current technique are simulated and compared with experiment.
Reaction Diffusion Voronoi Diagrams: From Sensors Data to Computing
Alejandro Vázquez-Otero
2015-05-01
Full Text Available In this paper, a new method to solve computational problems using reaction diffusion (RD systems is presented. The novelty relies on the use of a model configuration that tailors its spatiotemporal dynamics to develop Voronoi diagrams (VD as a part of the system’s natural evolution. The proposed framework is deployed in a solution of related robotic problems, where the generalized VD are used to identify topological places in a grid map of the environment that is created from sensor measurements. The ability of the RD-based computation to integrate external information, like a grid map representing the environment in the model computational grid, permits a direct integration of sensor data into the model dynamics. The experimental results indicate that this method exhibits significantly less sensitivity to noisy data than the standard algorithms for determining VD in a grid. In addition, previous drawbacks of the computational algorithms based on RD models, like the generation of volatile solutions by means of excitable waves, are now overcome by final stable states.
Gold, Christopher M.; Mioc, Darka; Anton, François
2008-01-01
This chapter presents a methodology for automated cartographic data in- put, drawing and editing. This methodology is based on kinematic algorithms for point and line Delaunay triangulation and the Voronoi diagram. It allows one to automate some parts of the manual digitization process and the to......This chapter presents a methodology for automated cartographic data in- put, drawing and editing. This methodology is based on kinematic algorithms for point and line Delaunay triangulation and the Voronoi diagram. It allows one to automate some parts of the manual digitization process...... as part of the research has been presented. We also describe two reversible line-drawing methods for cartographic applications based on the kinetic (moving-point) Voronoi diagram. Our ob jectives were to optimize the user’s ability to draw and edit the map, rather than to produce the most eﬃcient batch...
Gold, Christopher M.; Mioc, Darka; Anton, François
2008-01-01
This chapter presents a methodology for automated cartographic data in- put, drawing and editing. This methodology is based on kinematic algorithms for point and line Delaunay triangulation and the Voronoi diagram. It allows one to automate some parts of the manual digitization process...... as part of the research has been presented. We also describe two reversible line-drawing methods for cartographic applications based on the kinetic (moving-point) Voronoi diagram. Our ob jectives were to optimize the user’s ability to draw and edit the map, rather than to produce the most eﬃcient batch...... and the topological editing of maps that preserve map updates. The manual digitization process is replaced by computer assisted skeletonization using scanned paper maps. We are using the Delaunay triangulation and the Voronoi diagram in order to extract the skeletons that are guaranteed to be topologically correct...
Spatio-temporal map generalizations with the hierarchical Voronoi data structure
Mioc, Darka; Anton, François; Gold, Christopher M.
of map objects, together with their temporal and spatial adjacency relationships. In this paper, we present new solutions to the problems of spatio-temporal generalizations using the hierarchical Voronoi spatio-temporal data structure. The application of the hierarchical Voronoi data structure presented...... in this research is in spatio-temporal map generalization, which is needed for reasoning about dynamic aspects of the world, primarily about actions, events and processes. This provides an advance in the domain of map generalization as we are able to deal not only with the cartographic objects, but also...... implemented in commercial GIS systems. In this research, we used the Voronoi spatial data model for map generalizations. We were able to demonstrate that the map generalization does not affect only spatial objects (points, lines or polygons), but also the events corresponding to the creation and modification...
On the Large-Scale Structure of the Universe as given by the Voronoi Diagrams
L.Zaninetti
2006-01-01
The size distributions of 2D and 3D Voronoi cells and of cells of Vp(2,3),-2D cut of 3D Voronoi diagram-are explored, with the single-parameter (re-scaled) gamma distribution playing a central role in the analytical fitting. Observational evidence for a cellular universe is briefly reviewed. A simulated Vp(2,3) map with galaxies lying on the cell boundaries is constructed to compare, as regards general appearance, with the observed CfA map of galaxies and voids, the parameters of the simulation being so chosen as to reproduce the largest observed void size.
Wang, Y.; Li, Y.; Zhao, Q. H.
2016-06-01
This paper presents a Synthetic Aperture Radar (SAR) image segmentation approach with unknown number of classes, which is based on regular tessellation and Reversible Jump Markov Chain Monte Carlo (RJMCMC') algorithm. First of all, an image domain is portioned into a set of blocks by regular tessellation. The image is modeled on the assumption that intensities of its pixels in each homogeneous region satisfy an identical and independent Gamma distribution. By Bayesian paradigm, the posterior distribution is obtained to build the region-based image segmentation model. Then, a RJMCMC algorithm is designed to simulate from the segmentation model to determine the number of homogeneous regions and segment the image. In order to further improve the segmentation accuracy, a refined operation is performed. To illustrate the feasibility and effectiveness of the proposed approach, two real SAR image is tested.
Radical tessellation of the packing of spheres with a log-normal size distribution
Yi, L. Y.; Dong, K. J.; Zou, R. P.; Yu, A. B.
2015-09-01
The packing of particles with a log-normal size distribution is studied by means of the discrete element method. The packing structures are analyzed in terms of the topological properties such as the number of faces per radical polyhedron and the number of edges per face, and the metric properties such as the perimeter and area per face and the perimeter, area, and volume per radical polyhedron, obtained from the radical tessellation. The effect of the geometric standard deviation in the log-normal distribution on these properties is quantified. It is shown that when the size distribution gets wider, the packing becomes denser; thus the radical tessellation of a particle has decreased topological and metric properties. The quantitative relationships obtained should be useful in the modeling and analysis of structural properties such as effective thermal conductivity and permeability.
ColDICE: A parallel Vlasov-Poisson solver using moving adaptive simplicial tessellation
Sousbie, Thierry; Colombi, Stéphane
2016-09-01
Resolving numerically Vlasov-Poisson equations for initially cold systems can be reduced to following the evolution of a three-dimensional sheet evolving in six-dimensional phase-space. We describe a public parallel numerical algorithm consisting in representing the phase-space sheet with a conforming, self-adaptive simplicial tessellation of which the vertices follow the Lagrangian equations of motion. The algorithm is implemented both in six- and four-dimensional phase-space. Refinement of the tessellation mesh is performed using the bisection method and a local representation of the phase-space sheet at second order relying on additional tracers created when needed at runtime. In order to preserve in the best way the Hamiltonian nature of the system, refinement is anisotropic and constrained by measurements of local Poincaré invariants. Resolution of Poisson equation is performed using the fast Fourier method on a regular rectangular grid, similarly to particle in cells codes. To compute the density projected onto this grid, the intersection of the tessellation and the grid is calculated using the method of Franklin and Kankanhalli [65-67] generalised to linear order. As preliminary tests of the code, we study in four dimensional phase-space the evolution of an initially small patch in a chaotic potential and the cosmological collapse of a fluctuation composed of two sinusoidal waves. We also perform a "warm" dark matter simulation in six-dimensional phase-space that we use to check the parallel scaling of the code.
Zou, Chengzhe; Harne, Ryan L.
2017-05-01
Methods of guiding acoustic energy arbitrarily through space have long relied on digital controls to meet performance needs. Yet, more recent attention to adaptive structures with unique spatial configurations has motivated mechanical signal processing (MSP) concepts that may not be subjected to the same functional and performance limitations as digital acoustic beamforming counterparts. The periodicity of repeatable structural reconfiguration enabled by origami-inspired tessellated architectures turns attention to foldable platforms as frameworks for MSP development. This research harnesses principles of MSP to study a tessellated, star-shaped acoustic transducer constituent that provides on-demand control of acoustic energy guiding via folding-induced shape reconfiguration. An analytical framework is established to probe the roles of mechanical and acoustic geometry on the far field directivity and near field focusing of sound energy. Following validation by experiments and verification by simulations, parametric studies are undertaken to uncover relations between constituent topology and acoustic energy delivery to arbitrary points in the free field. The adaptations enabled by folding of the star-shaped transducer reveal capability for restricting sound energy to angular regions in the far field while also introducing means to modulate sound energy by three orders-of-magnitude to locations near to the transducer surface. In addition, the modeling philosophy devised here provides a valuable approach to solve general sound radiation problems for foldable, tessellated acoustic transducer constituents of arbitrary geometry.
Nassar, H.; Lebée, A.; Monasse, L.
2017-01-01
Origami tessellations are particular textured morphing shell structures. Their unique folding and unfolding mechanisms on a local scale aggregate and bring on large changes in shape, curvature and elongation on a global scale. The existence of these global deformation modes allows for origami tessellations to fit non-trivial surfaces thus inspiring applications across a wide range of domains including structural engineering, architectural design and aerospace engineering. The present paper suggests a homogenization-type two-scale asymptotic method which, combined with standard tools from differential geometry of surfaces, yields a macroscopic continuous characterization of the global deformation modes of origami tessellations and other similar periodic pin-jointed trusses. The outcome of the method is a set of nonlinear differential equations governing the parametrization, metric and curvature of surfaces that the initially discrete structure can fit. The theory is presented through a case study of a fairly generic example: the eggbox pattern. The proposed continuous model predicts correctly the existence of various fittings that are subsequently constructed and illustrated.
Ontogeny, morphology and mechanics of the tessellated skeleton of cartilaginous fishes
Dean, Mason N.
2009-12-01
The members of the successful and diverse lineage of elasmobranch fishes (sharks, rays and relatives) possess endoskeletons fashioned entirely of cartilage. This is counterintuitive because cartilage, unlike bone, lacks a major blood supply and has limited capacity for repair; yet these fishes exhibit particularly dynamic lifestyles and high levels of performance. The functionality of this skeletal tissue is likely due to its mineralization: in most skeletal elements, the soft cartilage core is tiled (tessellated) with an outer rind of abutting hydroxyapatite blocks called tesserae, joined together by intertesseral fibers and overlain by the fibrous perichondrium. This basic composite arrangement of tissues has been appreciated for over a century, but available techniques have limited the ability to examine elasmobranch cartilage adequately---without artifacts, in 3-dimensions and at high resolution---so that its development, mechanics and phylogeny might be contextualized among vertebrate skeletal tissues. I summarize the history, nomenclature and challenges relating to study of tessellated cartilage (Chapter 1) and present a low temperature microscopy technique to facilitate visualization of all tissue components in situ (Chapter 2). I use that technique in tandem with synchrotron microtomography to examine the ultrastructure of tesserae (Chapter 3) and the development of tessellated cartilage across ontogeny (Chapter 4). Finally, I examine the ways in which selection acts on skeletal morphology by examining cranial anatomy across 40 species of batoid fishes (rays and relatives) in the contexts of ecology and phylogeny (Chapter 5). There are some similarities between mineralizing bone and elasmobranch cartilage (e.g. the flattening of peripheral cells in the unmineralized phase, decreases in cellular density with mineralization, the presence of canaliculi connecting entombed cells). However, the ability for tessellated cartilage to grow (through enlargement of
Reversibility of the Quad-Edge operations in the Voronoi data structure
Mioc, Darka; Anton, François; Gold, Christopher
2007-01-01
In Geographic Information Systems the reversibility of map update operations have not been explored yet. In this paper we are using the Voronoi based Quad-edge data structure to define reversible map update operations. The reversibility of the map operations have been formalised at the lowest level...
Point Cluster Analysis Using a 3D Voronoi Diagram with Applications in Point Cloud Segmentation
Shen Ying
2015-08-01
Full Text Available Three-dimensional (3D point analysis and visualization is one of the most effective methods of point cluster detection and segmentation in geospatial datasets. However, serious scattering and clotting characteristics interfere with the visual detection of 3D point clusters. To overcome this problem, this study proposes the use of 3D Voronoi diagrams to analyze and visualize 3D points instead of the original data item. The proposed algorithm computes the cluster of 3D points by applying a set of 3D Voronoi cells to describe and quantify 3D points. The decompositions of point cloud of 3D models are guided by the 3D Voronoi cell parameters. The parameter values are mapped from the Voronoi cells to 3D points to show the spatial pattern and relationships; thus, a 3D point cluster pattern can be highlighted and easily recognized. To capture different cluster patterns, continuous progressive clusters and segmentations are tested. The 3D spatial relationship is shown to facilitate cluster detection. Furthermore, the generated segmentations of real 3D data cases are exploited to demonstrate the feasibility of our approach in detecting different spatial clusters for continuous point cloud segmentation.
基于Voronoi图的定性路径%Qualitative path based on Voronoi diagram
王晓东; 廖士中
2009-01-01
Qualitative path is a basic concept in qualitative spatial reasoning.A qualitative path representation and reasoning method based on Voronoi diagram is presented.The method uses the adjacent relationship to represent qualitative position and qualitative path.Specifically,the qualitative position is represented by the neighbors of the Voronoi diagram region the moving point lies in,and the qualitative path is represented by a series of qualitative positions the moving point passes through.Further-more,a qualitative path reasoning algorithm is designed and implemented.With the initial Voronoi diagram and the number of edges of all Voronoi regions at different moments,the algorithm can update the dynamic Voronoi diagram,find the qualitative path,and identify the moving point.Experiment results illuminate that the method is promising.%定性路径是定性空间推理的一个基本概念.给出了一个基于Voronoi图的定性路径表示与推理方法.该方法应用Voronoi图的邻近关系来表示定性位置和定性路径,即用运动点所在Voronoi区域的邻域来表示定性位置,用运动点所经过的定性位置序列来表示定性路径.设计并实现了一个定性路径推理算法,基于初始Voronoi图及不同时刻所有Voronoi区域的边数来动态更新Voronoi图邻近关系,可识别出运动点并找出定性路径.实验结果表明.该方法是可行的.
Gao, Wei; Feng, Shi-Dong; Zhang, Shi-Liang; Qi, Li; Liu, Ri-Ping
2015-12-01
Molecular dynamics simulation is used to investigate the relationship between Voronoi entropy and viscosity for rapid solidification processing of Zr36Cu64 binary alloy melt. The simulation results at different temperatures, cooling rates, and pressures, show that Voronoi entropy is able to accurately describe the relationship of the transition between the cluster structure and the viscosity of Zr36Cu64 binary alloy melt through Voronoi polyhedron analysis. That is, the higher the degree of order of the microstructure, the lower the Voronoi entropy is and the higher the viscosity is. The simulation provides an important reference for studying metallic glass with high glass-forming ability. Project supported by the National Basic Research Program of China (Grant No. 2013CB733000) and the National Natural Science Foundation of China (Grant Nos. 51271161 and 51271162).
Exact computation of the Voronoi Diagram of spheres in 3D, its topology and its geometric invariants
Anton, François; Mioc, Darka; Santos, Marcelo
2011-01-01
In this paper, we are addressing the exact computation of the Delaunay graph (or quasi-triangulation) and the Voronoi diagram of spheres using Wu’s algorithm. Our main contribution is first a methodology for automated derivation of invariants of the Delaunay empty circumcircle predicate for spheres...... and the Voronoi vertex of four spheres, then the application of this methodology to get all geometrical invariants that intervene in this problem and the exact computation of the Delaunay graph and the Voronoi diagram of spheres. To the best of our knowledge, there does not exist a comprehensive treatment...... of the exact computation with geometrical invariants of the Delaunay graph and the Voronoi diagram of spheres. Starting from the system of equations defining the zero-dimensional algebraic set of the problem, we are following Wu’s algorithm to transform the initial system into an equivalent Wu characteristic...
ColDICE: A parallel Vlasov–Poisson solver using moving adaptive simplicial tessellation
Sousbie, Thierry, E-mail: tsousbie@gmail.com [Institut d' Astrophysique de Paris, CNRS UMR 7095 and UPMC, 98bis, bd Arago, F-75014 Paris (France); Department of Physics, The University of Tokyo, Tokyo 113-0033 (Japan); Research Center for the Early Universe, School of Science, The University of Tokyo, Tokyo 113-0033 (Japan); Colombi, Stéphane, E-mail: colombi@iap.fr [Institut d' Astrophysique de Paris, CNRS UMR 7095 and UPMC, 98bis, bd Arago, F-75014 Paris (France); Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502 (Japan)
2016-09-15
Resolving numerically Vlasov–Poisson equations for initially cold systems can be reduced to following the evolution of a three-dimensional sheet evolving in six-dimensional phase-space. We describe a public parallel numerical algorithm consisting in representing the phase-space sheet with a conforming, self-adaptive simplicial tessellation of which the vertices follow the Lagrangian equations of motion. The algorithm is implemented both in six- and four-dimensional phase-space. Refinement of the tessellation mesh is performed using the bisection method and a local representation of the phase-space sheet at second order relying on additional tracers created when needed at runtime. In order to preserve in the best way the Hamiltonian nature of the system, refinement is anisotropic and constrained by measurements of local Poincaré invariants. Resolution of Poisson equation is performed using the fast Fourier method on a regular rectangular grid, similarly to particle in cells codes. To compute the density projected onto this grid, the intersection of the tessellation and the grid is calculated using the method of Franklin and Kankanhalli [65–67] generalised to linear order. As preliminary tests of the code, we study in four dimensional phase-space the evolution of an initially small patch in a chaotic potential and the cosmological collapse of a fluctuation composed of two sinusoidal waves. We also perform a “warm” dark matter simulation in six-dimensional phase-space that we use to check the parallel scaling of the code.
Magnetic flux pinning in superconductors with hyperbolic-tessellation arrays of pinning sites
Misko, V. R.; Nori, Franco
2012-05-01
We study magnetic flux interacting with arrays of pinning sites (APSs) placed on vertices of hyperbolic tessellations (HTs). We show that, due to the gradient in the density of pinning sites, HT APSs are capable of trapping vortices for a broad range of applied magnetic fluxes. Thus, the penetration of magnetic field in HT APSs is essentially different from the usual scenario predicted by the Bean model. We demonstrate that, due to the enhanced asymmetry of the surface barrier for vortex entry and exit, this HT APS could be used as a “capacitor” to store magnetic flux.
Random spatial processes and geostatistical models for soil variables
Lark, R. M.
2009-04-01
Geostatistical models of soil variation have been used to considerable effect to facilitate efficient and powerful prediction of soil properties at unsampled sites or over partially sampled regions. Geostatistical models can also be used to investigate the scaling behaviour of soil process models, to design sampling strategies and to account for spatial dependence in the random effects of linear mixed models for spatial variables. However, most geostatistical models (variograms) are selected for reasons of mathematical convenience (in particular, to ensure positive definiteness of the corresponding variables). They assume some underlying spatial mathematical operator which may give a good description of observed variation of the soil, but which may not relate in any clear way to the processes that we know give rise to that observed variation in the real world. In this paper I shall argue that soil scientists should pay closer attention to the underlying operators in geostatistical models, with a view to identifying, where ever possible, operators that reflect our knowledge of processes in the soil. I shall illustrate how this can be done in the case of two problems. The first exemplar problem is the definition of operators to represent statistically processes in which the soil landscape is divided into discrete domains. This may occur at disparate scales from the landscape (outcrops, catchments, fields with different landuse) to the soil core (aggregates, rhizospheres). The operators that underly standard geostatistical models of soil variation typically describe continuous variation, and so do not offer any way to incorporate information on processes which occur in discrete domains. I shall present the Poisson Voronoi Tessellation as an alternative spatial operator, examine its corresponding variogram, and apply these to some real data. The second exemplar problem arises from different operators that are equifinal with respect to the variograms of the
Analyzing the reflections from single ommatidia in the butterfly compound eye with Voronoi diagrams.
Vanhoutte, Kurt J A; Michielsen, Kristel F L; Stavenga, Doekele G
2003-12-30
This paper presents a robust method for the automated segmentation and quantitative measurement of reflections from single ommatidia in the butterfly compound eye. Digital pictures of the butterfly eye shine recorded with a digital camera are processed to yield binary images from which single facet centers can be extracted using a morphological image analysis procedure. The location of the facet centers is corrected by fitting in-line facet centers to a second-order polynomial. Based on the new centers a Voronoi diagram is constructed. In the case of the eye shine images, the Voronoi diagram defines a hexagonal lattice that overlaps with the original facet borders, allowing instantaneous quantification of the reflections from single ommatidia. We provide two typical examples to demonstrate that the developed technique may be a powerful tool to characterize in vivo the heterogeneity of butterfly eyes and to study the dynamic control of the light flux by the pupil mechanism.
ZHANG Hong-wu; WANG Hui
2006-01-01
The Voronoi cell finite element method (VCFEM) is adopted to overcome the limitations of the classic displacement based finite element method in the numerical simulation of heterogeneous materials. The parametric variational principle and quadratic programming method are developed for elastic-plastic Voronoi finite element analysis of two-dimensional problems. Finite element formulations are derived and a standard quadratic programming model is deduced from the elastic-plastic equations. Influence of microscopic heterogeneities on the overall mechanical response of heterogeneous materials is studied in detail. The overall properties of heterogeneous materials depend mostly on the size, shape and distribution of the material phases of the microstructure. Numerical examples are presented to demonstrate the validity and effectiveness of the method developed.
Connolly Surface on an Atomic Structure via Voronoi Diagram of Atoms
Joonghyun Ryu; Rhohun Park; Deok-Soo Kim
2006-01-01
One of the most important geometric structures of a protein is the Connolly surface of protein since a Connolly surface plays an important role in protein folding, docking, interactions between proteins, amongst other things. This paper presents an algorithm for precisely and efficiently computing the Connolly surface of a protein using a proposed geometric construct called β-shape based on the Voronoi diagram of atoms in the protein. Given the Voronoi diagram of atoms based on the Euclidean distance from the atom surfaces, the proposed algorithm first computes a β-shape with an appropriate probe. Then, the Connolly surface is computed by employing the blending operation on the atomic complex of the protein by the given probe.
APPLICATION OF VORONOI DIAGRAM TO MASK-BASED INTERCEPTING PHASE-SPACE MEASUREMENTS
Halavanau, A. [Fermilab; Ha, G. [POSTECH
2017-05-19
Intercepting multi-aperture masks (e.g. pepper pot or multislit mask) combined with a downstream transversedensity diagnostics (e.g. based on optical transition radiation or employing scintillating media) are commonly used for characterizing the phase space of charged particle beams and the associated emittances. The required data analysis relies on precise calculation of the RMS sizes and positions of the beamlets originated from the mask which drifted up to the analyzing diagnostics. Voronoi diagram is an efficient method for splitting a plane into subsets according to the distances between given vortices. The application of the method to analyze data from pepper pot and multislit mask based measurement is validated via numerical simulation and applied to experimental data acquired at the Argonne Wakefield Accelerator (AWA) facility. We also discuss the application of the Voronoi diagrams to quantify transverselymodulated beams distortion.
A Study on Selecting the Shortest Routes by Voronoi Diagram in Route Networks of GIS
无
2000-01-01
The problems of fast determining shortest paths through a polygonal subdivisionplanar with n vertices are considered in GIS. Distances are measured according to an Euclideanmetric. A geographical information system (GIS)has a collection of nearest neighborhoodoperations and this collection serves as a useful toolbox for spatial analysis. These operationsare undertaken through the Voronoi diagrams. This paper presents a novel algorithm thatconstructs a “shortest route set” with respect to a given source point and a target point byVoronoi diagrams. It will help to improve the efficiency of traditional algorithms, e. g. , Djkstraalgorithm, on selecting the shortest routes. Moreover, the novel algorithm can check theconnectivity in a complex network between the source point and target one.
Measuring the Scalar Curvature with Clocks and Photons: Voronoi-Delaunay Lattices in Regge Calculus
McDonald, Jonathan R
2008-01-01
The Riemann scalar curvature plays a central role in Einstein's geometric theory of gravity. We describe a new geometric construction of this scalar curvature invariant at an event (vertex) in a discrete spacetime geometry. This allows one to constructively measure the scalar curvature using only clocks and photons. Given recent interest in discrete pre-geometric models of quantum gravity, we believe is it ever so important to reconstruct the curvature scalar with respect to a finite number of communicating observers. This derivation makes use of a new fundamental lattice cell built from elements inherited from both the original simplicial (Delaunay) spacetime and its circumcentric dual (Voronoi) lattice. The orthogonality properties between these two lattices yield an expression for the vertex-based scalar curvature which is strikingly similar to the corresponding hinge-based expression in Regge calculus (deficit angle per unit Voronoi dual area). In particular, we show that the scalar curvature is simply a ...
The Voronoi Diagram for the Euclidean Traveling Salesman Problem Is Piecemeal Quartic and Hyperbolic
1990-06-01
ceiling function is of cubic order as predicted by the analysis. Acknowledgments The research has greatly benefited from discussions with Gerald ...The Science of Computing. Exploring tole Nature and Power of Algorithms. Addison-Wesley. Reading MA. � 1989 [H21 Held, M . and R M Karp , "The...34Traveling salesman cycles are not always subgrapris of Voronoi duals", Information Processing .etters 16(l):11-12. January 1983. (K21 Karp , R.M
Voronoi analysis of the short-range atomic structure in iron and iron-carbon melts
Sobolev, Andrey; Mirzoev, Alexander
2015-08-01
In this work, we simulated the atomic structure of liquid iron and iron-carbon alloys by means of ab initio molecular dynamics. Voronoi analysis was used to highlight changes in the close environments of Fe atoms as carbon concentration in the melt increases. We have found, that even high concentrations of carbon do not affect short-range atomic order of iron atoms — it remains effectively the same as in pure iron melts.
ColDICE: a parallel Vlasov-Poisson solver using moving adaptive simplicial tessellation
Sousbie, Thierry
2015-01-01
Resolving numerically Vlasov-Poisson equations for initially cold systems can be reduced to following the evolution of a three-dimensional sheet evolving in six-dimensional phase-space. We describe a public parallel numerical algorithm consisting in representing the phase-space sheet with a conforming, self-adaptive simplicial tessellation of which the vertices follow the Lagrangian equations of motion. The algorithm is implemented both in six- and four-dimensional phase-space. Refinement of the tessellation mesh is performed using the bisection method and a local representation of the phase-space sheet at second order relying on additional tracers created when needed at runtime. In order to preserve in the best way the Hamiltonian nature of the system, refinement is anisotropic and constrained by measurements of local Poincar\\'e invariants. Resolution of Poisson equation is performed using the fast Fourier method on a regular rectangular grid, similarly to particle in cells codes. To compute the density proj...
A Hybrid Vector Quantization Combining a Tree Structure and a Voronoi Diagram
Yeou-Jiunn Chen
2014-01-01
Full Text Available Multimedia data is a popular communication medium, but requires substantial storage space and network bandwidth. Vector quantization (VQ is suitable for multimedia data applications because of its simple architecture, fast decoding ability, and high compression rate. Full-search VQ can typically be used to determine optimal codewords, but requires considerable computational time and resources. In this study, a hybrid VQ combining a tree structure and a Voronoi diagram is proposed to improve VQ efficiency. To efficiently reduce the search space, a tree structure integrated with principal component analysis is proposed, to rapidly determine an initial codeword in low-dimensional space. To increase accuracy, a Voronoi diagram is applied to precisely enlarge the search space by modeling relations between each codeword. This enables an optimal codeword to be efficiently identified by rippling an optimal neighbor from parts of neighboring Voronoi regions. The experimental results demonstrated that the proposed approach improved VQ performance, outperforming other approaches. The proposed approach also satisfies the requirements of handheld device application, namely, the use of limited memory and network bandwidth, when a suitable number of dimensions in principal component analysis is selected.
Voronoi diagram-based spheroid model for microwave scattering of complex snow aggregates
Honeyager, Ryan; Liu, Guosheng; Nowell, Holly
2016-02-01
Methods to model snow aggregate scattering properties at microwave frequencies can be divided into structurally explicit and implicit techniques. Explicit techniques, such as the discrete dipole approximation (DDA), determine scattering and backscatter cross-sections assuming full knowledge of a given snow particle's structure. Such calculations are computationally expensive. Implicit techniques, such as using the T-matrix method (TMM) with optically soft spheroids, model equivalent particles with variable mass, bulk density and aspect ratio according to an effective-medium approximation. It is highly desirable that there should be a good agreement between modeled aggregate cross-sections using both methods. A Voronoi bounding-neighbor algorithm is presented in this study to determine the bulk equivalent density of complex three-dimensional snow aggregates. While mass and aspect ratio are easily parameterized quantities, attempts to parameterize the bulk density of snowflakes have usually relied on a bounding ellipsoid, which can be determined from a flake's radius of gyration, root mean square mean or simply from its maximum diameter. We compared the Voronoi algorithm against existing bounding spheroid approaches and mass-effective density relations at ten frequencies from 10.65 to 183.31 GHz, using a set of 1005 aggregates with maximum dimensions from a few hundred microns to several centimeters. When using the Voronoi-determined effective density, the asymmetry parameter, scattering, and backscatter cross-sections determined using the TMM reasonably match those for DDA-computed snow aggregates. From Ku to W-band, soft spheroids can reproduce cross-sections for aggregates up to 9 mm in maximum dimension. Volume-integrated cross-sections always agree to within 25% of DDA. As the DDA is computationally expensive, this offers a fast alternative that efficiently evaluates scattering properties at microwave frequencies.
Morphological algorithms based on Voronoi and Delaunay graphs: microscopic and medical applications
Bertin, Etienne; Marcelpoil, Raphael; Chassery, Jean-Marc
1992-06-01
We illustrate a cooperation between Voronoi diagram and Mathematical Morphology in 2-D and 3-D. Domains of application are multiple: 2-D image segmentation, and 3-D image representation, cellular sociology in 2-D and 3-D. The principal tool that we use is the algorithm of research of connected components in a graph abiding by constraints. The originality takes place in the choice of the constraint parameters. Other tools are used: binary dilation, labeling, and influence zone on graphs. The graph support of our work is the Voronoi diagram, well known for its power of modelling for natural reality. The dual graph of this space partition is the Delaunay graph containing all the neighboring information. The first developed application concerns a method for 2-D and 3-D images segmentation. We have elaborated tools to measure intra-graph structures distance, search of connected component under constraints to extract a 3-d object included in a volume data. The second application we developed concerns the theory of cellular sociology where the set of points identified the location of cells. Our method makes it possible to determine for a given set of cells, a model including its nearest homogeneous set, and the intrinsic disorder to which it refers. In this paper, our methods will be discussed and illustrated in the biological domain.
Comparison of selected approaches for urban roughness determination based on voronoi cells
Ketterer, Christine; Gangwisch, Marcel; Fröhlich, Dominik; Matzarakis, Andreas
2017-01-01
Wind speed is reduced above urban areas due to their high aerodynamic roughness. This not only holds for above the urban canopy. The local vertical wind profile is modified. Aerodynamic roughness (both roughness length and displacement height) therefore is relevant for many fields within human biometeorology, e.g. for the identification of ventilation paths, the concentration and dispersion of air pollutants at street level or to simulate wind speed and direction in urban environments and everything depending on them. Roughness, thus, also shows strong influence on human thermal comfort. Currently, roughness parameters are mostly estimated using classifications. However, such classifications only provide limited assessment of roughness in urban areas. In order to calculate spatially resolved roughness on the micro-scale, three different approaches were implemented in the SkyHelios model. For all of them, the urban area is divided into reference areas for each of the obstacles using a voronoi diagram. The three approaches are based on building and [+one of them also on] vegetation (trees and forests) data. They were compared for the city of Stuttgart, Germany. Results show that the approach after Bottema and Mestayer (J Wind Eng Ind Aerodyn 74-76:163-173 1998) on the spatial basis of a voronoi diagram provides the most plausible results.
IMPROVING 9-INTERSECTION MODEL BY REPLACING THE COMPLEMENT WITH VORONOI REGION
无
2000-01-01
9-intersection model is the most popular framework used for formalizing the spatial relations between two spatial objects A and B. It transforms the topological relation ships between two simple spatial objects A and B into point-set topology problem in terms of the intersections of A's boundary ( A), interior (A0) and exterior (A - ) with B's bound ary ( B),interior (B0) and exterior (B-). It is shown in this paper that there exist some limitations of the original 9-intersection model due to its definition of an object's exterior as its complement,and it is difficult to distinguish different disjoint relations and relations be tween complex objects with holes, difficult or even impossible to compute the intersections with the two object' s complements ( A ∩ B -, A0 ∩ B -, A - ∩ B, A- ∩ B0 and A - ∩ B - )since the complements are infinitive. The authors suggest to re-define the exterior of spa tial object by replacing the complement with its Voronoi region. A new Voronoi-based 9-in- tersection (VNI) is proposed and used for formalizing topological relations between spatial objects. By improving the 9-interscetion model, it is now possible to distinguish disjoint rela tions and to deal with objects with boles. Also it is possible to compute the exterior-based in tersections and manipulate spatial relations with the VNI.
Cooperation among cancer cells as public goods games on Voronoi networks.
Archetti, Marco
2016-05-07
Cancer cells produce growth factors that diffuse and sustain tumour proliferation, a form of cooperation that can be studied using mathematical models of public goods in the framework of evolutionary game theory. Cell populations, however, form heterogeneous networks that cannot be described by regular lattices or scale-free networks, the types of graphs generally used in the study of cooperation. To describe the dynamics of growth factor production in populations of cancer cells, I study public goods games on Voronoi networks, using a range of non-linear benefits that account for the known properties of growth factors, and different types of diffusion gradients. The results are surprisingly similar to those obtained on regular graphs and different from results on scale-free networks, revealing that network heterogeneity per se does not promote cooperation when public goods diffuse beyond one-step neighbours. The exact shape of the diffusion gradient is not crucial, however, whereas the type of non-linear benefit is an essential determinant of the dynamics. Public goods games on Voronoi networks can shed light on intra-tumour heterogeneity, the evolution of resistance to therapies that target growth factors, and new types of cell therapy.
Measuring the Scalar Curvature with Clocks and Photons: Voronoi-Delaunay Lattices in Regge Calculus
Miller, Warner; McDonald, Jonathan
2008-04-01
The Riemann scalar curvature plays a central role in Einstein's geometric theory of gravity. We describe a new geometric construction of this scalar curvature invariant at an event (vertex) in a discrete spacetime geometry. This allows one to constructively measure the scalar curvature using only clocks and photons. Given recent interest in discrete pre-geometric models of quantum gravity, we believe it is ever so important to reconstruct the curvature scalar with respect to a finite number of communicating observers. This derivation makes use of a fundamental lattice cell built from elements inherited from both the original simplicial (Delaunay) spacetime and its circumcentric dual (Voronoi) lattice. The orthogonality properties between these two lattices yield an expression for the vertex-based scalar curvature which is strikingly similar to the corresponding hinge-based expression in Regge Calculus (deficit angle per unit Voronoi dual area). In particular, we show that the scalar curvature is simply a vertex-based weighted average of deficits per weighted average of dual areas.
Transformation and Self-Similarity Properties of Gamma and Weibull Fragment Size Distributions
2015-12-01
Monte Carlo Estimates of the Distributions of the Random Polygons of the Voronoi Tessellation with Respect to a Poisson Process, Journal of...BELVOIR, VA 22060-6201 ATTN: DTIC/ OCA DEPARTMENT OF DEFENSE CONTRACTORS QUANTERION SOLUTIONS, INC. 1680 TEXAS STREET, SE KIRTLAND AFB, NM 87117-5669 ATTN: DTRIAC
Jae-Kwan Kim
2014-04-01
Full Text Available Voronoi diagrams are powerful for solving spatial problems among particles and have been used in many disciplines of science and engineering. In particular, the Voronoi diagram of three-dimensional spheres, also called the additively-weighted Voronoi diagram, has proven its powerful capabilities for solving the spatial reasoning problems for the arrangement of atoms in both molecular biology and material sciences. In order to solve application problems, the dual structure, called the quasi-triangulation, and its derivative structure, called the beta-complex, are frequently used with the Voronoi diagram itself. However, the Voronoi diagram, the quasi-triangulation, and the beta-complexes are sometimes regarded as somewhat difficult for ordinary users to understand. This paper presents the twodimensional counterparts of their definitions and introduce the BetaConcept program which implements the theory so that users can easily learn the powerful concept and capabilities of these constructs in a plane. The BetaConcept program was implemented in the standard C++ language with MFC and OpenGL and freely available at Voronoi Diagram Research Center (http://voronoi.hanyang.ac.kr.
Variability of Fiber Elastic Moduli in Composite Random Fiber Networks Makes the Network Softer
Ban, Ehsan; Picu, Catalin
2015-03-01
Athermal fiber networks are assemblies of beams or trusses. They have been used to model mechanics of fibrous materials such as biopolymer gels and synthetic nonwovens. Elasticity of these networks has been studied in terms of various microstructural parameters such as the stiffness of their constituent fibers. In this work we investigate the elasticity of composite fiber networks made from fibers with moduli sampled from a distribution function. We use finite elements simulations to study networks made by 3D Voronoi and Delaunay tessellations. The resulting data collapse to power laws showing that variability in fiber stiffness makes fiber networks softer. We also support the findings by analytical arguments. Finally, we apply these results to a network with curved fibers to explain the dependence of the network's modulus on the variation of its structural parameters.
Percolation line, response functions, and Voronoi polyhedra analysis in supercritical water
J. Škvor
2012-06-01
Full Text Available The problem of a physical relevance (meaning of percolation in supercritical fluids is addressed considering a primitive model of water. Two different criteria, physical and configurational, are used for the cluster definition in Monte Carlo simulations over a range of pressures to determine the percolation line and skewness, and a theoretical analytic equation of state is used to evaluate response functions. It is found that both criteria yield practically the same percolation line. However, unlike the findings for simple fluids, the loci of the response function extrema exhibit density/pressure dependence quite different from that of the percolation line. The only potential coincidence between the loci of the extrema of a thermodynamic property and a detectable structural change is found for the coefficient of isothermal compressibility and Voronoi neighbors distribution skewness maximum.
Generalized Voronoi Partition Based Multi-Agent Search using Heterogeneous Sensors
Guruprasad, K R
2009-01-01
In this paper we propose search strategies for heterogeneous multi-agent systems. Multiple agents, equipped with communication gadget, computational capability, and sensors having heterogeneous capabilities, are deployed in the search space to gather information such as presence of targets. Lack of information about the search space is modeled as an uncertainty density distribution. The uncertainty is reduced on collection of information by the search agents. We propose a generalization of Voronoi partition incorporating the heterogeneity in sensor capabilities, and design optimal deployment strategies for multiple agents, maximizing a single step search effectiveness. The optimal deployment forms the basis for two search strategies, namely, {\\em heterogeneous sequential deploy and search} and {\\em heterogeneous combined deploy and search}. We prove that the proposed strategies can reduce the uncertainty density to arbitrarily low level under ideal conditions. We provide a few formal analysis results related ...
Brownian Dynamics of a Suspension of Particles with Constrained Voronoi Cell Volumes
Singh, John P.
2015-06-23
© 2015 American Chemical Society. Solvent-free polymer-grafted nanoparticle fluids consist of inorganic core particles fluidized by polymers tethered to their surfaces. The attachment of the suspending fluid to the particle surface creates a strong penalty for local variations in the fluid volume surrounding the particles. As a model of such a suspension we perform Brownian dynamics of an equilibrium system consisting of hard spheres which experience a many-particle potential proportional to the variance of the Voronoi volumes surrounding each particle (E = α(V
Clifford Algebra-Based Voronoi Algorithm%Voronoi生成的Clifford代数实现方法
易琳; 袁林旺; 俞肇元; 罗文; 闾国年
2011-01-01
引入具有维度融合、坐标无关等特性的Clifford几何代数,构建不同维度统一Voronoi生成框架及算法流程.定义了可支撑不同维度、不同对象间距离、相交及对偶关系的几何、拓扑运算,基于多重向量设计了可支撑不同维度地理对象的统一存储结构及关系表达机制,实现了基于Clifford代数的多维统一Voronoi生成算法.以中国城市气象数据为例进行了算法验证,并分析了算法复杂度.结果表明,该算法可根据输入数据维度自适应地实现相应维度的Voronoi分析,可为以维度统一为特征的GIS分析算法实现提供借鉴.%Based on the superiority of Clifford algebra in multi-dimensional diffusion and coordinate freeing, the unified multi-dimensional generation framework and the algorithm flow of Voronoi have been constructed. Geometric operations and topological operations are defined, which can calculate the distance, intersection and dual among different dimensions and different types of geometric objects. And the unified storage structure and expression mechanism for different dimensional objects are designed with multivector. Finally,2D & 3D experiments and comparison analysis of complexity and accuracy are given to validate the algorithm. The work proves that the designed algorithm is effective and feasible to multi-dimensional Voronoi analysis,and geometric algebra provides a new math tool to establish multi-dimensional unified spatial analysis algorithms.
Brownian Dynamics of a Suspension of Particles with Constrained Voronoi Cell Volumes.
Singh, John P; Walsh, Stuart D C; Koch, Donald L
2015-06-23
Solvent-free polymer-grafted nanoparticle fluids consist of inorganic core particles fluidized by polymers tethered to their surfaces. The attachment of the suspending fluid to the particle surface creates a strong penalty for local variations in the fluid volume surrounding the particles. As a model of such a suspension we perform Brownian dynamics of an equilibrium system consisting of hard spheres which experience a many-particle potential proportional to the variance of the Voronoi volumes surrounding each particle (E = α(Vi-V0)(2)). The coefficient of proportionality α can be varied such that pure hard sphere dynamics is recovered as α → 0, while an incompressible array of hairy particles is obtained as α → ∞. As α is increased the distribution of Voronoi volumes becomes narrower, the mean coordination number of the particle increases and the variance in the number of nearest neighbors decreases. The nearest neighbor peaks in the pair distribution function are suppressed and shifted to larger radial separations as the constraint acts to maintain relatively uniform interstitial regions. The structure factor of the model suspension satisfies S(k=0) → 0 as α → ∞ in accordance with expectation for a single component (particle plus tethered fluid) incompressible system. The tracer diffusivity of the particles is reduced by the volume constraint and goes to zero at ϕ ∼ 0.52, indicating an earlier glass transition than has been observed in hard sphere suspensions. The total pressure of the suspension grows in proportion to (αkBT)(1/2) as the strength of the volume-constraint potential grows. This stress arises primarily from the interparticle potential forces, while the hard-sphere collisional contribution to the stress is suppressed by the volume constraint.
ERA-Interim forced H-TESSEL and WRF schemes for modeling ground
Rocha, M. J.; Dutra, E.; Vieira, G.; Miranda, P.; Fragoso, M.; Ramos, M.
2009-04-01
Permafrost is central to the carbon cycle and to the climate system and is recognized by the WCRP/WMO as a key element of the Earth System in which research efforts should focus. Compared with the Arctic, very little is known about the distribution, thickness, and properties of permafrost in the Antarctic. The main reason for this is the scarce network of permafrost temperature monitoring boreholes, as well as the short number of active layer monitoring sites. According to the IPCC in the last decades regions underlain by permafrost have been reduced in extent, and a warming of the ground has been observed in many areas. This study focus on Livingston and Deception Islands (South Shetlands), located in the Antarctic Peninsula region, one of the Earth's regions where warming has been more significant in the last 50 years. Our work is integrated in a project focusing on studying the influence of climate change on permafrost temperatures, which includes systematic and long-term terrain monitoring and also modeling using mesoscale meteorological models. A significant contribution will be the evaluation of the possibilities for using the mesoscale modeling approaches to other areas of the Antarctic Peninsula where no data exist on permafrost temperatures. Climate variability of the Antarctic Peninsula region was studied using the new reanalysis product from ECMWF Era-Interim and observational data from meteorological monitoring sites and boreholes run by our group. Monthly and annual cycles of near surface climate variables are compared. The modeling approach includes the H-TESSEL (Hydrology Tiled ECMWF Scheme for Surface Exchanges over Land) and the WRF (Weather Research and Forecasting), both forced with ERA-Interim for modeling ground temperatures in the study region. Simulations of both land surface and mesoscale models are compared with the observational data of soil temperatures. Preliminary results are presented and show that our approach can provide a good tool
HybVOR: A Voronoi-Based 3D GIS Approach for Camera Surveillance Network Placement
Reda Yaagoubi; Mabrouk El Yarmani; Abdullah Kamel; Walid Khemiri
2015-01-01
As a consequence of increasing safety concerns, camera surveillance has been widely adopted as a way to monitor public spaces. One of the major challenges of camera surveillance is to design an optimal method for camera network placement in order to ensure the greater possible coverage. In addition, this method must consider the landscape of the monitored environment to take into account the existing objects that may influence the deployment of such a network. In this paper, a new Voronoi-bas...
HybVOR: A Voronoi-Based 3D GIS Approach for Camera Surveillance Network Placement
Reda Yaagoubi
2015-05-01
Full Text Available As a consequence of increasing safety concerns, camera surveillance has been widely adopted as a way to monitor public spaces. One of the major challenges of camera surveillance is to design an optimal method for camera network placement in order to ensure the greater possible coverage. In addition, this method must consider the landscape of the monitored environment to take into account the existing objects that may influence the deployment of such a network. In this paper, a new Voronoi-based 3D GIS oriented approach named “HybVOR” is proposed for surveillance camera network placement. The “HybVOR” approach aims to achieve a coverage near 100% through three main phases. First, a Voronoi Diagram from buildings’ footprints is generated and cameras are placed on the Voronoi Edges. Second, the level of coverage is assessed by calculating a viewshed based on a raster Digital Surface Model of the region of interest. Finally, the visibility of the main buildings’ entrances is evaluated based on a 3D vector model that contains these features. The effectiveness of the “HybVOR” approach is demonstrated through a case study that corresponds to an area of interest in Jeddah Seaport in the Kingdom of Saudi Arabia.
MESHLESS METHOD FOR 2D MIXED-MODE CRACK PROPAGATION BASED ON VORONOI CELL
LouLullang; ZengPan
2003-01-01
A meshless method integrated with linear elastic fracture mechanics (LEFM) is presented for 2D mixed-mode crack propagation analysis. The domain is divided automatically into sub-domains based on Voronoi cells, which are used for quadrature for the potential energy. The continuous crack propagation is simulated with an incremental crack-extension method which assumes a piecewise linear discretization of the unknown crack path. For each increment of the crack extension, the meshless method is applied to carry out a stress analysis of the cracked structure. The J-integral, which can be decomposed into mode I and mode II for mixed-mode crack, is used for the evaluation of the stress intensity factors (SIFs). The crack-propagation direction, predicted on an incremental basis, is computed by a criterion defined in terms of the SIFs. The flowchart of the proposed procedure is presented and two numerical problems are analyzed with this method. The meshless results agree well with the experimental ones, which validates the accuracy and efficiency of the method.
李谦; 徐永安; 马骁; 缪静姣
2014-01-01
以微分几何曲率计算公式为理论基础，对常用的Mark Meyer离散点云曲率估算方法进行改进，提出基于Voronoi区域面积的改进Mark Meyer算法。针对Mark Meyer算法中Voronoi区域面积的计算进行改进，对于Voronoi区域中存在钝角的情形进行详细论述并且改进钝角三角形的计算公式，同时给出更为准确的面积计算方法。将该算法应用于球面、柱面、抛物面、马鞍面，计算结果表明该算法提高了离散点云曲率估算的精度和稳定性。%Taking on the calculation formula of differential geometric curvature as theoretical foundation , Mark Meyer ’ s estima-tion methods of discrete point cloud curvature are improved , the thesis puts forward an improved Mark Meyer algorithm on the ba-sis of Voronoi area .The calculation of Mark Meyer algorithm on the basis of Voronoi area is improved , the existence of an obtuse angle in Voronoi area situation is discussed in detail and the formula of the obtuse triangle is improved , at the same time , it gives a more accurate method of calculating the area .The algorithm is applied in spherical , cylindrical, parabolic, saddle surface.The calculation results show that this algorithm enhances the estimation accuracy and stability of discrete point cloud curvature .
The DEEP2 Galaxy Redshift Survey: The Voronoi-Delaunay Method Catalog of Galaxy Groups
Gerke, Brian F.; /UC, Berkeley; Newman, Jeffrey A.; /LBNL, NSD; Davis, Marc; /UC, Berkeley /UC, Berkeley, Astron.Dept.; Marinoni, Christian; /Brera Observ.; Yan, Renbin; Coil, Alison L.; Conroy, Charlie; Cooper, Michael C.; /UC, Berkeley, Astron.Dept.; Faber, S.M.; /Lick Observ.; Finkbeiner, Douglas P.; /Princeton U. Observ.; Guhathakurta, Puragra; /Lick Observ.; Kaiser, Nick; /Hawaii U.; Koo, David C.; Phillips, Andrew C.; /Lick Observ.; Weiner, Benjamin J.; /Maryland U.
2012-02-14
We use the first 25% of the DEEP2 Galaxy Redshift Survey spectroscopic data to identify groups and clusters of galaxies in redshift space. The data set contains 8370 galaxies with confirmed redshifts in the range 0.7 {<=} z {<=} 1.4, over one square degree on the sky. Groups are identified using an algorithm (the Voronoi-Delaunay Method) that has been shown to accurately reproduce the statistics of groups in simulated DEEP2-like samples. We optimize this algorithm for the DEEP2 survey by applying it to realistic mock galaxy catalogs and assessing the results using a stringent set of criteria for measuring group-finding success, which we develop and describe in detail here. We find in particular that the group-finder can successfully identify {approx}78% of real groups and that {approx}79% of the galaxies that are true members of groups can be identified as such. Conversely, we estimate that {approx}55% of the groups we find can be definitively identified with real groups and that {approx}46% of the galaxies we place into groups are interloper field galaxies. Most importantly, we find that it is possible to measure the distribution of groups in redshift and velocity dispersion, n({sigma}, z), to an accuracy limited by cosmic variance, for dispersions greater than 350 km s{sup -1}. We anticipate that such measurements will allow strong constraints to be placed on the equation of state of the dark energy in the future. Finally, we present the first DEEP2 group catalog, which assigns 32% of the galaxies to 899 distinct groups with two or more members, 153 of which have velocity dispersions above 350 km s{sup -1}. We provide locations, redshifts and properties for this high-dispersion subsample. This catalog represents the largest sample to date of spectroscopically detected groups at z {approx} 1.
The DEEP2 Galaxy Redshift Survey: The Voronoi-Delaunay Method Catalog of Galaxy Groups
Gerke, Brian F.; /UC, Berkeley; Newman, Jeffrey A.; /LBNL, NSD; Davis, Marc; /UC, Berkeley /UC, Berkeley, Astron.Dept.; Marinoni, Christian; /Brera Observ.; Yan, Renbin; Coil, Alison L.; Conroy, Charlie; Cooper, Michael C.; /UC, Berkeley, Astron.Dept.; Faber, S.M.; /Lick Observ.; Finkbeiner, Douglas P.; /Princeton U. Observ.; Guhathakurta, Puragra; /Lick Observ.; Kaiser, Nick; /Hawaii U.; Koo, David C.; Phillips, Andrew C.; /Lick Observ.; Weiner, Benjamin J.; /Maryland U.
2012-02-14
We use the first 25% of the DEEP2 Galaxy Redshift Survey spectroscopic data to identify groups and clusters of galaxies in redshift space. The data set contains 8370 galaxies with confirmed redshifts in the range 0.7 {<=} z {<=} 1.4, over one square degree on the sky. Groups are identified using an algorithm (the Voronoi-Delaunay Method) that has been shown to accurately reproduce the statistics of groups in simulated DEEP2-like samples. We optimize this algorithm for the DEEP2 survey by applying it to realistic mock galaxy catalogs and assessing the results using a stringent set of criteria for measuring group-finding success, which we develop and describe in detail here. We find in particular that the group-finder can successfully identify {approx}78% of real groups and that {approx}79% of the galaxies that are true members of groups can be identified as such. Conversely, we estimate that {approx}55% of the groups we find can be definitively identified with real groups and that {approx}46% of the galaxies we place into groups are interloper field galaxies. Most importantly, we find that it is possible to measure the distribution of groups in redshift and velocity dispersion, n({sigma}, z), to an accuracy limited by cosmic variance, for dispersions greater than 350 km s{sup -1}. We anticipate that such measurements will allow strong constraints to be placed on the equation of state of the dark energy in the future. Finally, we present the first DEEP2 group catalog, which assigns 32% of the galaxies to 899 distinct groups with two or more members, 153 of which have velocity dispersions above 350 km s{sup -1}. We provide locations, redshifts and properties for this high-dispersion subsample. This catalog represents the largest sample to date of spectroscopically detected groups at z {approx} 1.
Adamou, Ibrahim
2013-01-01
RESUMEN: Este trabajo consta de tres partes principales : el calculo de las bisectrices de dos curvas o de un punto y una curva en el plano, de la superficie bisectriz de dos superficies en R3, y del diagrama de Voronoi de una familia finita de semirrectas paralelas y con la misma orientación en R3. Estos temas están estrechamente relacionados y tienen aplicaciones en CAD/CAGD y en Geometría Computacional. Se presenta un nuevo método para determinar, utilizando la regla de Cramer generalizada...
Augenbaum, J. M.
1985-01-01
A Lagrangian scheme using the Voronoi mesh is applied to study shallow water flow on a sphere. Discrete approximations to the shallow water equations are obtained for the surfaces of a nonrotating and a rotating sphere, and discrete differential operators are defined for the gradient and the divergence on the sphere. Dissipation is put into the model, when needed, by merging fluid points when they get too close to each other. The full numerical scheme is described and results of numerical computations on various test cases are given, including zonal flow and the Riemann problem.
THE DEEP2 GALAXY REDSHIFT SURVEY: THE VORONOI-DELAUNAY METHOD CATALOG OF GALAXY GROUPS
Gerke, Brian F. [KIPAC, SLAC National Accelerator Laboratory, 2575 Sand Hill Road, MS 29, Menlo Park, CA 94725 (United States); Newman, Jeffrey A. [Department of Physics and Astronomy, 3941 O' Hara Street, Pittsburgh, PA 15260 (United States); Davis, Marc [Department of Physics and Department of Astronomy, Campbell Hall, University of California-Berkeley, Berkeley, CA 94720 (United States); Coil, Alison L. [Center for Astrophysics and Space Sciences, University of California, San Diego, 9500 Gilman Drive, MC 0424, La Jolla, CA 92093 (United States); Cooper, Michael C. [Center for Galaxy Evolution, Department of Physics and Astronomy, University of California-Irvine, Irvine, CA 92697 (United States); Dutton, Aaron A. [Department of Physics and Astronomy, University of Victoria, Victoria, BC V8P 5C2 (Canada); Faber, S. M.; Guhathakurta, Puragra; Koo, David C.; Phillips, Andrew C. [UCO/Lick Observatory, University of California-Santa Cruz, Santa Cruz, CA 95064 (United States); Konidaris, Nicholas; Lin, Lihwai [Astronomy Department, Caltech 249-17, Pasadena, CA 91125 (United States); Noeske, Kai [Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218 (United States); Rosario, David J. [Max Planck Institute for Extraterrestrial Physics, Giessenbachstr. 1, 85748 Garching bei Muenchen (Germany); Weiner, Benjamin J.; Willmer, Christopher N. A. [Steward Observatory, University of Arizona, 933 North Cherry Avenue, Tucson, AZ 85721 (United States); Yan, Renbin [Department of Astronomy and Astrophysics, University of Toronto, 50 St. George Street, Toronto, ON M5S 3H4 (Canada)
2012-05-20
We present a public catalog of galaxy groups constructed from the spectroscopic sample of galaxies in the fourth data release from the Deep Extragalactic Evolutionary Probe 2 (DEEP2) Galaxy Redshift Survey, including the Extended Groth Strip (EGS). The catalog contains 1165 groups with two or more members in the EGS over the redshift range 0 < z < 1.5 and 1295 groups at z > 0.6 in the rest of DEEP2. Twenty-five percent of EGS galaxies and fourteen percent of high-z DEEP2 galaxies are assigned to galaxy groups. The groups were detected using the Voronoi-Delaunay method (VDM) after it has been optimized on mock DEEP2 catalogs following similar methods to those employed in Gerke et al. In the optimization effort, we have taken particular care to ensure that the mock catalogs resemble the data as closely as possible, and we have fine-tuned our methods separately on mocks constructed for the EGS and the rest of DEEP2. We have also probed the effect of the assumed cosmology on our inferred group-finding efficiency by performing our optimization on three different mock catalogs with different background cosmologies, finding large differences in the group-finding success we can achieve for these different mocks. Using the mock catalog whose background cosmology is most consistent with current data, we estimate that the DEEP2 group catalog is 72% complete and 61% pure (74% and 67% for the EGS) and that the group finder correctly classifies 70% of galaxies that truly belong to groups, with an additional 46% of interloper galaxies contaminating the catalog (66% and 43% for the EGS). We also confirm that the VDM catalog reconstructs the abundance of galaxy groups with velocity dispersions above {approx}300 km s{sup -1} to an accuracy better than the sample variance, and this successful reconstruction is not strongly dependent on cosmology. This makes the DEEP2 group catalog a promising probe of the growth of cosmic structure that can potentially be used for cosmological tests.
Wei Tu
2015-10-01
Full Text Available Vehicle routing optimization (VRO designs the best routes to reduce travel cost, energy consumption, and carbon emission. Due to non-deterministic polynomial-time hard (NP-hard complexity, many VROs involved in real-world applications require too much computing effort. Shortening computing time for VRO is a great challenge for state-of-the-art spatial optimization algorithms. From a spatial-temporal perspective, this paper presents a spatial-temporal Voronoi diagram-based heuristic approach for large-scale vehicle routing problems with time windows (VRPTW. Considering time constraints, a spatial-temporal Voronoi distance is derived from the spatial-temporal Voronoi diagram to find near neighbors in the space-time searching context. A Voronoi distance decay strategy that integrates a time warp operation is proposed to accelerate local search procedures. A spatial-temporal feature-guided search is developed to improve unpromising micro route structures. Experiments on VRPTW benchmarks and real-world instances are conducted to verify performance. The results demonstrate that the proposed approach is competitive with state-of-the-art heuristics and achieves high-quality solutions for large-scale instances of VRPTWs in a short time. This novel approach will contribute to spatial decision support community by developing an effective vehicle routing optimization method for large transportation applications in both public and private sectors.
田猛; 亢新刚; 李杨; 孔雷; 徐光; 杨英军
2015-01-01
In the natural uneven-aged mixed forest of Changbai Mountains , with four fixed standard ground of 2 hm2 and the con-tinuous data of 30 years, we used the Voronoi polygons to divide the space , and then discussed the relation between the size class and the volume growth in the unit area to determine the area potentially available of each species .The relation-ship between the different tree diameters class and the growth per unit area in different tree species was a unimodal curve , and the unimodal curve of the highest point on each were not identical .In the Changbai Mountains , when selective cutting operations in the natural uneven-aged mixed forest with different age , the largest diameter class was 46, 44, 40, 36 and 28 cm for spruce, fir, Korean pine, basswood, maple and birch, respectively.%以长白山林区天然异龄混交林为研究对象，基于4块固定标准地（总面积2hm 2）30多年的定株观测数据，采用Voronoi 图空间分割方法，对各树种潜在生长空间的确定，得到了各树种单位面积平均蓄积生长量。结果表明：各树种单位面积平均蓄积生长量出现最大值的径级各不相同；在长白山林区，对天然异龄混交林进行径级择伐作业时，云杉、冷杉、红松、椴树、枫桦允许保留的最大径级分别为46、44、40、36、28 cm。
Barella-Ortiz, Anaïs; Polcher, Jan; de Rosnay, Patricia; Piles, Maria; Gelati, Emiliano
2017-01-01
L-band radiometry is considered to be one of the most suitable techniques to estimate surface soil moisture (SSM) by means of remote sensing. Brightness temperatures are key in this process, as they are the main input in the retrieval algorithm which yields SSM estimates. The work exposed compares brightness temperatures measured by the SMOS mission to two different sets of modelled ones, over the Iberian Peninsula from 2010 to 2012. The two modelled sets were estimated using a radiative transfer model and state variables from two land-surface models: (i) ORCHIDEE and (ii) H-TESSEL. The radiative transfer model used is the CMEM. Measured and modelled brightness temperatures show a good agreement in their temporal evolution, but their spatial structures are not consistent. An empirical orthogonal function analysis of the brightness temperature's error identifies a dominant structure over the south-west of the Iberian Peninsula which evolves during the year and is maximum in autumn and winter. Hypotheses concerning forcing-induced biases and assumptions made in the radiative transfer model are analysed to explain this inconsistency, but no candidate is found to be responsible for the weak spatial correlations at the moment. Further hypotheses are proposed and will be explored in a forthcoming paper. The analysis of spatial inconsistencies between modelled and measured TBs is important, as these can affect the estimation of geophysical variables and TB assimilation in operational models, as well as result in misleading validation studies.
Chi-Chang Chen
2015-01-01
Full Text Available The relay node placement problem in wireless sensor network (WSN aims at deploying the minimum number of relay nodes over the network so that each sensor can communicate with at least one relay node. When the deployed relay nodes are homogeneous and their communication ranges are circular, one way to solve the WSN relay node placement problem is to solve the minimum geometric disk cover (MGDC problem first and place the relay nodes at the centers of the covering disks and then, if necessary, deploy additional relay nodes to meet the connection requirement of relay nodes. It is known that the MGDC problem is NP-complete. A novel linear time approximation algorithm for the MGDC problem is proposed, which identifies covering disks using the regular hexagon tessellation of the plane with bounded area. The approximation ratio of the proposed algorithm is (5+ϵ, where 0<ϵ≤15. Experimental results show that the worst case is rare, and on average the proposed algorithm uses less than 1.7 times the optimal disks of the MGDC problem. In cases where quick deployment is necessary, this study provides a fast 7-approximation algorithm which uses on average less than twice the optimal number of relay nodes in the simulation.
Mohammad Reza Yossefi
2014-02-01
Full Text Available Objective: To determine the helminth parasites of Natrix natrix Linnaeus, 1758 (N. natrix and Natrix tessellata Laurenti, 1768 (N. tessellate in north of Iran. Methods: Eighteen snakes including nine N. natrix and nine N. tessellata from Mazandaran Province, north of Iran were collected and examined during March 2011 to October 2011 for helminth parasites. The collected specimens were fixed and preserved in 70% ethanol. Results: All of the examined snakes (100% were infected with parasitic helminth. The list of extracted helminths both in N. natrix and N. tessellata includes one Nematode: Rhabdias fuscovenosa (larva, one Digenea: Telorchis assula and one Cestoda: Ophiotaenia europaea. The infection rate of Ophiotaenia europaea, Telorchis assula and Rhabdias fuscovenosa (larva from collected snakes were 100%, 83.3% and 61.1%, respectively. Moreover, in the current investigation the morphological characteristics of the collected helminths were described elaborately. Conclusions: This is the first survey on helminth parasites from N. tessellata in Iran and the helminthes are reported for the first time from this host in Iran.
A method of polycrystal finite element modeling based on Voronoi diagram%一种基于Voronoi图的多晶体有限元建模方法
郑战光; 汪兆亮; 冯强; 袁帅; 王佳祥
2016-01-01
建立多晶体的细观有限元模型是研究多晶体材料局部塑性变形不均匀性的前提与基础,为了灵活地构建高可靠度的材料微结构模型,在前人研究成果的基础上提出一种基于Voronoi图并结合单元编号区域排布特点,能直接根据模型中得到的单元编号顺序依次求取单元形心坐标的构图方法就显得极为关键。该方法首先是生成特定平面或空间域里的随机点与Voronoi图基本信息,再结合单元编号区域排布特点依次直接求取中心点坐标,接着判断单元归属于距离最近的晶核所在的晶粒内,并将所得晶粒编号及单元编号以set集合形式添加到INP文件的Part部分,进而得到Voronoi多晶体有限元模型,最后以构建含10个晶粒的二维和三维多晶体模型为例和文献对比分析来进行实现与验证。结果显示：该方法可以依据单元编号区域排布特点直接得到单元编号且更加容易实现依次求取单元形心坐标,并在一定程度上降低了单元形心坐标处理的数据量和单元归属判断的难度,通过对比分析该方法建立的模型精度更接近于文献中的精确模型,它们之间的最大偏差仅为25.47 MPa,较对比文献的简化模型最小偏差还要低0.07 MPa。表明该方法可为研究人员快速构建多晶材料的Voronoi细观有限元模型提供一定的技术参考。%The mesoscopic polycrystal finite element ( PFE) model is the premise and foundation to study the local plastic deformation of polycrystalline materials. In order to construct a reliable micro-structure model of materials flexibly, a modeling method had been proposed on the basis of Voronoi diagram and regional distribution charact-eristics of units. The areal coordinates of the units could be calculated in sequence directly through the units’ num-bers by the method. Firstly, the random points and the Voronoi information in a specific plane or domain were generated. Then
Kurata, Akira; Kono, Atsushi; Coenen, Adriaan; Saru-Chelu, Raluca G.; Krestin, Gabriel P. [Erasmus University Medical Center, Department of Radiology, Rotterdam (Netherlands); Sakamoto, Tsuyoshi [AZE inc, Development Division, Chiyoda, Tokyo (Japan); Kido, Teruhito; Mochizuki, Teruhito [Ehime University Graduate School of Medicine, Department of Radiology, Toon, Ehime (Japan); Higashino, Hiroshi [Yotsuba Circulation Clinic, Department of Radiology, Matsuyama, Ehime (Japan); Abe, Mitsunori [Yotsuba Circulation Clinic, Department of Cardiology, Matsuyama, Ehime (Japan); Feyter, Pim J. de; Nieman, Koen [Erasmus University Medical Center, Department of Radiology, Rotterdam (Netherlands); Erasmus University Medical Center, Department of Cardiology, Rotterdam (Netherlands)
2015-01-15
The purpose of this study was to estimate the myocardial area at risk (MAAR) using coronary computed tomography angiography (CTA) and Voronoi algorithm-based myocardial segmentation in comparison with single-photon emission computed tomography (SPECT). Thirty-four patients with coronary artery disease underwent 128-slice coronary CTA, stress/rest thallium-201 SPECT, and coronary angiography (CAG). CTA-based MAAR was defined as the sum of all CAG stenosis (>50 %) related territories (the ratio of the left ventricular volume). Using automated quantification software (17-segment model, 5-point scale), SPECT-based MAAR was defined as the number of segments with a score above zero as compared to the total 17 segments by summed stress score (SSS), difference (SDS) score map, and comprehensive SPECT interpretation with either SSS or SDS best correlating CAG findings (SSS/SDS). Results were compared using Pearson's correlation coefficient. Forty-nine stenoses were observed in 102 major coronary territories. Mean value of CTA-based MAAR was 28.3 ± 14.0 %. SSS-based, SDS-based, and SSS/SDS-based MAAR was 30.1 ± 6.1 %, 20.1 ± 15.8 %, and 26.8 ± 15.7 %, respectively. CTA-based MAAR was significantly related to SPECT-based MAAR (r = 0.531 for SSS; r = 0.494 for SDS; r = 0.814 for SSS/SDS; P < 0.05 in each). CTA-based Voronoi algorithm myocardial segmentation reliably quantifies SPECT-based MAAR. (orig.)
2011-01-01
Background The Prospective Space-Time scan statistic (PST) is widely used for the evaluation of space-time clusters of point event data. Usually a window of cylindrical shape is employed, with a circular or elliptical base in the space domain. Recently, the concept of Minimum Spanning Tree (MST) was applied to specify the set of potential clusters, through the Density-Equalizing Euclidean MST (DEEMST) method, for the detection of arbitrarily shaped clusters. The original map is cartogram transformed, such that the control points are spread uniformly. That method is quite effective, but the cartogram construction is computationally expensive and complicated. Results A fast method for the detection and inference of point data set space-time disease clusters is presented, the Voronoi Based Scan (VBScan). A Voronoi diagram is built for points representing population individuals (cases and controls). The number of Voronoi cells boundaries intercepted by the line segment joining two cases points defines the Voronoi distance between those points. That distance is used to approximate the density of the heterogeneous population and build the Voronoi distance MST linking the cases. The successive removal of edges from the Voronoi distance MST generates sub-trees which are the potential space-time clusters. Finally, those clusters are evaluated through the scan statistic. Monte Carlo replications of the original data are used to evaluate the significance of the clusters. An application for dengue fever in a small Brazilian city is presented. Conclusions The ability to promptly detect space-time clusters of disease outbreaks, when the number of individuals is large, was shown to be feasible, due to the reduced computational load of VBScan. Instead of changing the map, VBScan modifies the metric used to define the distance between cases, without requiring the cartogram construction. Numerical simulations showed that VBScan has higher power of detection, sensitivity and positive
Takahashi Ricardo HC
2011-04-01
Full Text Available Abstract Background The Prospective Space-Time scan statistic (PST is widely used for the evaluation of space-time clusters of point event data. Usually a window of cylindrical shape is employed, with a circular or elliptical base in the space domain. Recently, the concept of Minimum Spanning Tree (MST was applied to specify the set of potential clusters, through the Density-Equalizing Euclidean MST (DEEMST method, for the detection of arbitrarily shaped clusters. The original map is cartogram transformed, such that the control points are spread uniformly. That method is quite effective, but the cartogram construction is computationally expensive and complicated. Results A fast method for the detection and inference of point data set space-time disease clusters is presented, the Voronoi Based Scan (VBScan. A Voronoi diagram is built for points representing population individuals (cases and controls. The number of Voronoi cells boundaries intercepted by the line segment joining two cases points defines the Voronoi distance between those points. That distance is used to approximate the density of the heterogeneous population and build the Voronoi distance MST linking the cases. The successive removal of edges from the Voronoi distance MST generates sub-trees which are the potential space-time clusters. Finally, those clusters are evaluated through the scan statistic. Monte Carlo replications of the original data are used to evaluate the significance of the clusters. An application for dengue fever in a small Brazilian city is presented. Conclusions The ability to promptly detect space-time clusters of disease outbreaks, when the number of individuals is large, was shown to be feasible, due to the reduced computational load of VBScan. Instead of changing the map, VBScan modifies the metric used to define the distance between cases, without requiring the cartogram construction. Numerical simulations showed that VBScan has higher power of detection
War Material Storage Area Division Based on Voronoi Diagram%基于Voronoi图的战备物资储备区域划分
姚学宾; 王丰
2014-01-01
Considering the characteristics and war material reserves Voronoi diagram features on war mate-rial reserve zoning and classification principles of the influencing factors analysis based on the proposed im-plementation based on Voronoi diagram zoning war material reserves geometric method.We superimposed and adjusted the seven military naming Voronoi diagram,taking fully into account their economic and geo-graphical space 33 capital cities and municipalities which have different Voronoi diagram and undertake strategic combat missions in different cities,to obtain 7 +1 regional reserve mode.It provides a new re-search ideas for the layout of war material storage area and lays a solid foundation.%综合考虑战备物资储备的特点和Voronoi图的特性，在对战备物资储备区域划分的影响因素和划分原则分析的基础上提出了基于Voronoi图实现的战备物资储备区域划分的几何方法；并充分考虑其经济性和地理空间的33个省会城市和直辖市的Voronoi图和具有不同战略意义担负不同作战任务的七大军区命名城市Voronoi图进行叠加和调整，构建了7＋1的区域储备模式；为战备物资储备区域划分提供了一种新的研究思路，为战备物资储备布局研究打下了结实的基础。
赵艳丽; 赵小虎; 刘康明
2013-01-01
Path routing for Unmanned Combat Aerial Vehicle (UCAV) can be defined as the task of Unmanned Combat Aerial Vehicle automatically executing,which is a complex optimization problem.It is very hard to get the optimal solution in polynomial time.Therefore,in this paper a path planning method was proposed based on Voronoi diagram and Quantum-behaved Particle Swarm Optimization (QPSO) algorism.Firstly,the cost model for path planning of UCAV was defined by totally consideration for the radar threat and fuel consumption,and the Voronoi diagram was generated according to the given threat source.And then the initial path planning set was constructed by initial sites,the vertex of Voronoi diagram and the final sites.Finally,in order to conquer the problem of PSO algorism that has the defects of falling to optimal location,the Cauchy mutation random number was introduced to improve the global search ability of QPSO algorism,and using the improved QPSO algorism to plan path the specific algorism was defined.The result of simulation experiment shows the method proposed in this paper can obtain the optimal solution for UCAV,and it has the optimal cost 280in comparison with PSO 600 and QPSO 350,respectively.Meanwhile,at the mean time,when the iteration time is 250,the improved QPSO in our paper is in convergence,so it can provide not only the optimal solution but also the rapid convergence speed.Thus it has big superiority over the other methods.%无人机(UCAV)是自主控制执行任务的无人驾驶飞机,其航路规划是一类复杂优化问题,因此难以在多项式时间内获取精确解,为此提出了一种基于Voronoi图和量子粒子群(QPSO)算法的UCAV航路规划方法.首先,在综合考虑航路的雷达威胁和燃油耗费的基础上定义了航路规划的代价模型；然后,根据已知的威胁源生成Voronoi图,通过连接起点、Voronoi图中顶点以及终点获得初始规划解集；最后,通过引入柯西变异随机数和扰动对QPSO
Zuohua Miao
2016-07-01
Full Text Available Rapid urbanization has caused numerous problems, and the urban spatial structure has been a hot topic in sustainable development management. Urban spatial structure is affected by a series of factors. Thus, the research model should synthetically consider the spatial and non-spatial relationship of every element. Here, we propose an extended Voronoi diagram for exploring the urban land spatial pattern. In essence, we first used a principal component analysis method to construct attribute evaluation indicators and obtained the attribute distance for each indicator. Second, we integrated spatial and attribute distances to extend the comparison distance for Voronoi diagrams, and then, we constructed the Voronoi aggregative homogeneous map of the study area. Finally, we make a spatial autocorrelation analysis by using GeoDA and SPSS software. Results show that: (1 the residential land cover aggregation is not significant, but spatial diffusion is obvious; (2 the commercial land cover aggregation is considerable; and (3 the spatial agglomeration degree of the industrial land cover is increased and mainly located in urban fringes. According to the neo-Marxist theory, we briefly analyzed the driving forces for shaping the urban spatial structure. To summarize, our approach yields important insights into the urban spatial structure characterized by attribute similarity with geospatial proximity, which contributes to a better understanding of the urban growth mechanism. In addition, it explicitly identifies ongoing urban transformations, potentially supporting the planning for sustainable urban land use and protection.
Schröder, C; Neumayr, G; Steinhauser, O
2009-05-21
Three different mixtures of 1-butyl-3-methyl-imidazolium tetrafluoroborate with water have been studied by means of molecular dynamics simulations. Based on the classical Lopes-Padua force field trajectories of approximately 60 ns were computed. This is the third part of a series concerning the collective network of 1-butyl-3-methyl-imidazolium tetrafluoroborate/water mixtures. The first part [C. Schröder et al., J. Chem. Phys. 127, 234503 (2007)] dealt with the orientational structure and static dielectric constants. The second part [C. Schröder et al., J. Chem. Phys. 129, 184501 (2008)] was focused on the decomposition of the dielectric spectrum of these mixtures. In this work the focus lies on the characterization of the neighborhood of ionic liquids by means of the Voronoi decomposition. The Voronoi algorithm is a rational tool to uniquely decompose the space around a reference molecule without using any empirical parameters. Thus, neighborhood relations, direct and indirect ones, can be extracted and were used in combination with g-coefficients. These coefficients represent the generalization of the traditional radial distribution function in order to include the mutual positioning and orientation of anisotropic molecules. Furthermore, the Voronoi method provides, as a by-product, the mutual coordination numbers of molecular species.
Complete topology of cells, grains, and bubbles in three-dimensional microstructures.
Lazar, Emanuel A; Mason, Jeremy K; MacPherson, Robert D; Srolovitz, David J
2012-08-31
We introduce a general, efficient method to completely describe the topology of individual grains, bubbles, and cells in three-dimensional polycrystals, foams, and other multicellular microstructures. This approach is applied to a pair of three-dimensional microstructures that are often regarded as close analogues in the literature: one resulting from normal grain growth (mean curvature flow) and another resulting from a random Poisson-Voronoi tessellation of space. Grain growth strongly favors particular grain topologies, compared with the Poisson-Voronoi model. Moreover, the frequencies of highly symmetric grains are orders of magnitude higher in the grain growth microstructure than they are in the Poisson-Voronoi one. Grain topology statistics provide a strong, robust differentiator of different cellular microstructures and provide hints to the processes that drive different classes of microstructure evolution.
Abellanas, B.; Abellanas, M.; Pommerening, A.; Lodares, D.; Cuadros, S.
2016-07-01
Aim of the study. a) To present a new version of the forest simulator Vorest, an individual-based spatially explicit model that uses weighted Voronoi diagrams to simulate the natural dynamics of forest stands with closed canopies. b) To apply the model to the current dynamics of a Grazalema pinsapo stand to identify the nature of its competition regime and the stagnation risks it is currently facing. Area of study: Sierra del Pinar de Grazalema (S Spain) Material and methods: Two large plots representative of Grazalema pinsapo stands were used to fit and validate the model (plus 6 accesory plots to increase the availability of mortality data). Two inventories were carried out in 1998 and 2007 producing tree size and location data. We developed a forest simulator based on three submodels: growth, competition and mortality. The model was fitted, evaluated and validated for Grazalema plots. The simulation outputs were used to infer the expected evolution of structural diversity of forest stands. Main results: Vorest has proved to be a good tool for simulating dynamics of natural closed stands. The application to Grazalema pinsapo stands has allowed assessing the nature of the main processes that are driving its development pathway. We have found that the prevailing size-asymmetric competition dominates the self-thinning process in small-sized trees. At the same time, there is an active tree-size differentiation process. Research highlights: Vorest has proved to be a good tool for simulating natural stands with closed canopies. The Grazalema pinsapo stand under consideration is currently undergoing a natural process of differentiation, avoiding long-term stagnation. (Author)
基于局部聚类的网络Voronoi图生成方法研究%A Method for Integrating Network Voronoi and Spatial Clustering
佘冰; 叶信岳; 房会会; 吴玲; 朱欣焰; 程叶青
2015-01-01
The planar space assumption of spatial cluster detection is invalid in the real world. The network space has opened a new gate to finer-scale spatial analysis, and provides a perspective for human dynamics. The urban street network is shaped by social and economic forces over time and also reflects the influences of governmental policies and cultural values. In the real world, any phenomenon whose location is represented through a street address system is inherently constrained by the street network. Hence, both events and their movements are constrained by the street network in the urban area. For example, the street-side business will cause more traffic, which lead to both management and commuting costs. Since the spatial point process is in-herently probabilistic, it’s hard to set a fixed set of criteria, which would otherwise be dealt with as a spatial optimization problem. The weight of a given street segment will vary across space and over time when the ac-tivities of street-side business on this focal segment and nearby ones are considered. It is crucial to incorporate this information into urban management and urban studies, because equally-weighted street segments do not exist in the real world. The extension of Voronoi diagrams to the network space provides a useful tool in esti-mating service area in cities. Weighted Voronoi diagrams have been widely adopted to describe the capacity constraints. This proposed method develops a network Voronoi diagram with weighted links based on spatial cluster analysis. It borrows the strength from two large and growing literatures:Voronoi diagram and spatial cluster analysis. The weight is a central component in the construction of weighted Voronoi in urban street net-work. The weights are generated using local Moran’s I statistic. The weights, either additive or multiplicative, are normalized and transformed into the link length for constructing network Voronoi diagrams. The Monte Carlo simulation process is
Ruiz, Osvaldo; Schouwenaars, Rafael; Ramírez, Edgar I.; Jacobo, Víctor H.; Ortiz, Armando
2011-10-01
Trabecular bone, rather than being considered as a homogeneous material, must be analysed as a structure of interconnected beam and plate-like elements. The arrangement and morphology of these elements depend on the specific tissue studied as well as on the physiology of the individual. It is therefore impossible to define the mechanical properties trabecular bone in general. To estimate the properties of an individual structure, flexible numerical models must be developed, which allow the calculation of elastic constants and resistance of tissue previously characterised by non-destructive observation. Voxel-based modelling of structures observed by X-ray microtomography is computation intensive. Here, synthetic 2D-microstructures are analysed, constructed as a collection of Voronoi-cells obtained from the observation of plane sections of cancellous bone. The effect of architecture (vertebra and femur), bone density and loss of trabecular connectivity was researched. The study confirms findings of earlier experimental and numerical studies relating to the effect of these parameters; the technique is efficient in terms of experimental effort and numerical analysis. Consequently, the use of synthetic microstructures based on a Voronoi-cell approximation of the real bone architecture may be a promising approach for the prediction of the mechanical properties of trabecular bone.
Ruvalcaba S, J.L.; Bucio, L. [IFUNAM, A.P. 20-364, 01000 Mexico D.F. (Mexico); Marin, M.E.; Velasquez, A. [Museo del Templo Mayor-INAH, Seminario No. 8, Col. Centro 06060 Mexico D.F. (Mexico)
2005-07-01
For the study of minerals and semiprecious stones, such as turquoise, it is necessary to use a combined analysis in order to determine crystalline minerals phases and elemental com- position. In this way, it is possible to identify mineralogical substitutions in the crystals and to perform sourcing by trace elemental analysis. In this work, the analysis focused on the study of surface alterations of tessels from a disc found in the 99 offering from Templo Mayor of Tenochtitlan. Rutherford Backscattering Spectrometry and Particle Induced X-ray Emission (PIXE) Spectrometries using protons and alpha particles were applied to determine surface elemental analysis of tessels of different colours (blue, green, white). For mineralogical identification, standard X-ray Diffraction was used. (Author)
Muhammad Usman Sheikh
2013-10-01
Full Text Available Mobile operators commonly use macro cells with traditional wide beam antennas for wider coverage in thecell, but future capacity demands cannot be achieved by using them only. It is required to achieve maximumpractical capacity from macro cells by employing higher order sectorization and by utilizing all possibleantenna solutions including smart antennas. This paper presents enhanced tessellation for 6-sector sitesand proposes novel layout for 12-sector sites. The main target of this paper is to compare the performanceof conventional wide beam antenna, switched beam smart antenna, adaptive beam antenna and differentnetwork layouts in terms of offering better received signal quality and user throughput. Splitting macro cellinto smaller micro or pico cells can improve the capacity of network, but this paper highlights theimportance of higher order sectorization and advance antenna techniques to attain high Signal toInterference plus Noise Ratio (SINR, along with improved network capacity. Monte Carlo simulations atsystem level were done for Dual Cell High Speed Downlink Packet Access (DC-HSDPA technology withmultiple (five users per Transmission Time Interval (TTI at different Intersite Distance (ISD. Theobtained results validate and estimate the gain of using smart antennas and higher order sectorization withproposed network layout.
一种平面点集Voronoi图的细分算法%A Subdivision Algorithm for Voronoi Diagram of Planar Point Set
寿华好; 袁子薇; 缪永伟; 王丽萍
2013-01-01
Voronoi diagram is one of the most important concepts in computational geometry, It is applied widely in computer graphics, computational geometry, computer aided geometric design, finite element grid partition, robot trajectory control, pattern recognition, meteorology and geology. Based on quadtree data structure and interval arithmetic technique, a new subdivision algorithm for Voronoi diagram of a planar point set is proposed. A comparison of this subdivision algorithm with the well known incremental algorithm and grid expansion method is conducted. Test results show that the subdivision algorithm is more efficient. The most important is that the idea of subdivision algorithm is very simple and therefore it is easy to implement.%Voronoi图是计算几何中的重要概念之一,在计算机图形学、计算几何、计算机辅助几何设计、有限元网格划分、机器人轨迹控制、模式识别、气象学和地质学研究中得到广泛应用.借助于四又树和区间算术,提出了一种新的构造平面点集Voronoi图的细分算法,并且和经典的增量算法、栅格扩张法进行了比较,结果显示新细分算法更为有效.最重要的是细分算法原理简单,很容易编程实现.
Random lattice structures. Modelling, manufacture and FEA of their mechanical response
Malians, G.; Sarafis, I. T.; Lazaridis, T.; Varoutoglou, A.; Tsakataras, G.
2016-11-01
The implementation of lightweight structures in various applications, especially in Aerospace/ Automotive industries and Orthopaedics, has become a necessity due to their exceptional mechanical properties with respect to reduced weight. In this work we present a Voronoi tessellation based algorithm, which has been developed for modelling stochastic lattice structures. With the proposed algorithm, is possible to generate CAD geometry with controllable structural parameters, such as porosity, cell number and strut thickness. The digital structures were transformed into physical objects through the combination of 3D printing technics and investment casting. This process was applied to check the mechanical behaviour of generated digital models. Until now, the only way to materialize such structures into physical objects, was feasible through 3D printing methods such as Selective Laser Sintering/ Melting (SLS/ SLM). Investment casting possesses numerous advantages against SLS or SLA, with the major one being the material variety. On the other hand, several trials are required in order to calibrate the process parameters to have successful castings, which is the major drawback of investment casting. The manufactured specimens were subjected to compression tests, where their mechanical response was registered in the form of compressive load - displacement curves. Also, a finite element model was developed, using the specimens’ CAD data and compression test parameters. The FE assisted calculation of specimen plastic deformation is identical with the one of the physical object, which validates the conclusions drawn from the simulation results. As it was observed, strut contact is initiated when specimen deformation is approximately 5mm. Although FE calculated compressive force follows the same trend for the first 3mm of compression, then diverges because of the elasto-plastic FE model type definition and the occurred remeshing steps.
John A Long
, interpreted as a transitional step toward the tessellated prismatic calcified cartilage that is recognized as the main diagnostic character of the chondrichthyans.
S. Sarkar; S.H.L Kriebitzsch; M.A. van der Hoef; J.A.M. Kuipers
2009-01-01
nding the large particles becomes less in case ofa bidisperse mixture, as compared to a monodisperse system with the same volume fraction. We further investigated this discrepancy by calculating the volume per particle by means of Voronoi tessellation.
Najmeh Neysani Samany
2013-01-01
Full Text Available Space and time are two dominant factors in context-aware pervasive systems which determine whether an entity is related to the moving user or not. This paper specifically addresses the use of spatio-temporal relations for detecting spatio-temporally relevant contexts to the user. The main contribution of this work is that the proposed model is sensitive to the velocity and direction of the user and applies customized Multi Interval Algebra (MIA with Voronoi Continuous Range Query (VCRQ to introduce spatio-temporally relevant contexts according to their arrangement in space. In this implementation the Spatio-Temporal Relevancy Model for Context-Aware Systems (STRMCAS helps the tourist to find his/her preferred areas that are spatio-temporally relevant. The experimental results in a scenario of tourist navigation are evaluated with respect to the accuracy of the model, performance time and satisfaction of users in 30 iterations of the algorithm. The evaluation process demonstrated the efficiency of the model in real-world applications.
Meutzner, Falk; Münchgesang, Wolfram; Kabanova, Natalya A; Zschornak, Matthias; Leisegang, Tilmann; Blatov, Vladislav A; Meyer, Dirk C
2015-11-09
With the constant growth of the lithium battery market and the introduction of electric vehicles and stationary energy storage solutions, the low abundance and high price of lithium will greatly impact its availability in the future. Thus, a diversification of electrochemical energy storage technologies based on other source materials is of great relevance. Sodium is energetically similar to lithium but cheaper and more abundant, which results in some already established stationary concepts, such as Na-S and ZEBRA cells. The most significant bottleneck for these technologies is to find effective solid ionic conductors. Thus, the goal of this work is to identify new ionic conductors for Na ions in ternary Na oxides. For this purpose, the Voronoi-Dirichlet approach has been applied to the Inorganic Crystal Structure Database and some new procedures are introduced to the algorithm implemented in the programme package ToposPro. The main new features are the use of data mined values, which are then used for the evaluation of void spaces, and a new method of channel size calculation. 52 compounds have been identified to be high-potential candidates for solid ionic conductors. The results were analysed from a crystallographic point of view in combination with phenomenological requirements for ionic conductors and intercalation hosts. Of the most promising candidates, previously reported compounds have also been successfully identified by using the employed algorithm, which shows the reliability of the method.
Programming curvature using origami tessellations
Dudte, Levi H.; Vouga, Etienne; Tachi, Tomohiro; Mahadevan, L.
2016-05-01
Origami describes rules for creating folded structures from patterns on a flat sheet, but does not prescribe how patterns can be designed to fit target shapes. Here, starting from the simplest periodic origami pattern that yields one-degree-of-freedom collapsible structures--we show that scale-independent elementary geometric constructions and constrained optimization algorithms can be used to determine spatially modulated patterns that yield approximations to given surfaces of constant or varying curvature. Paper models confirm the feasibility of our calculations. We also assess the difficulty of realizing these geometric structures by quantifying the energetic barrier that separates the metastable flat and folded states. Moreover, we characterize the trade-off between the accuracy to which the pattern conforms to the target surface, and the effort associated with creating finer folds. Our approach enables the tailoring of origami patterns to drape complex surfaces independent of absolute scale, as well as the quantification of the energetic and material cost of doing so.
Gulliver, Eric A.
The objective of this thesis to identify and develop techniques providing direct comparison between simulated and real packed particle mixture microstructures containing submicron-sized particles. This entailed devising techniques for simulating powder mixtures, producing real mixtures with known powder characteristics, sectioning real mixtures, interrogating mixture cross-sections, evaluating and quantifying the mixture interrogation process and for comparing interrogation results between mixtures. A drop and roll-type particle-packing model was used to generate simulations of random mixtures. The simulated mixtures were then evaluated to establish that they were not segregated and free from gross defects. A powder processing protocol was established to provide real mixtures for direct comparison and for use in evaluating the simulation. The powder processing protocol was designed to minimize differences between measured particle size distributions and the particle size distributions in the mixture. A sectioning technique was developed that was capable of producing distortion free cross-sections of fine scale particulate mixtures. Tessellation analysis was used to interrogate mixture cross sections and statistical quality control charts were used to evaluate different types of tessellation analysis and to establish the importance of differences between simulated and real mixtures. The particle-packing program generated crescent shaped pores below large particles but realistic looking mixture microstructures otherwise. Focused ion beam milling was the only technique capable of sectioning particle compacts in a manner suitable for stereological analysis. Johnson-Mehl and Voronoi tessellation of the same cross-sections produced tessellation tiles with different the-area populations. Control charts analysis showed Johnson-Mehl tessellation measurements are superior to Voronoi tessellation measurements for detecting variations in mixture microstructure, such as altered
Flavio Astolpho Vieira Souto Rezende
2000-06-01
Full Text Available No planejamento de recursos em saúde é importante o conhecimento da área de abrangência de uma unidade. Os Diagramas de Voronoi constituem uma técnica para tal; são polígonos construídos de tal forma que as bordas de polígonos adjacentes encontram-se eqüidistantes de seus respectivos pontos geradores. Uma modificação nas áreas de abrangência assim definidas é sua ponderação (Diagramas de Voronoi ponderados, representando a capacidade da unidade de forma mais real. No presente trabalho foram utilizados, como pontos geradores, 21 hospitais gerais públicos no Rio de Janeiro, RJ. Inicialmente foram criados os Diagramas de Voronoi sem ponderação, e, a partir destes, os diagramas ponderados, empregando-se como variável de ponderação as estimativas de internação anual para cada unidade. Na divisão clássica, áreas de abrangência similares foram atribuídas a hospitais com características diferenciadas, problema esse contornado no método ponderado. O método é de simples implementação e visualização, utiliza dados de fácil acesso e independe de parâmetros arbitrários ou geopolíticos. Portanto, esses diagramas podem fornecer, a gerentes de saúde, uma visão mais realista para o planejamento da demanda de suas unidades.
Levices, Quentin
2016-01-01
Las espumas metálicas son materiales complejos que existen desde hace varias décadas. Son utilizadas en un amplio rango de aplicaciones incluida la disipación de calor de dispositivos electrónicos. Este proyecto trata del estudio computacional de tres tipos de estructura de espumas metálicas de células abiertas diseñadas por el método de Voronoi como disipadores de calor. Este modelo es muy utilizado para modelizar espumas metálicas, permite obtener estructuras porosas con poro...
Edgington, Eugene
2007-01-01
Statistical Tests That Do Not Require Random Sampling Randomization Tests Numerical Examples Randomization Tests and Nonrandom Samples The Prevalence of Nonrandom Samples in Experiments The Irrelevance of Random Samples for the Typical Experiment Generalizing from Nonrandom Samples Intelligibility Respect for the Validity of Randomization Tests Versatility Practicality Precursors of Randomization Tests Other Applications of Permutation Tests Questions and Exercises Notes References Randomized Experiments Unique Benefits of Experiments Experimentation without Mani
王俊; 周树道; 罗炜; 金永奇
2012-01-01
A technology based on ant colony optimization and Voronoi diagram was used to achieve the intelligent route planning for unmanned aircraft. The Voronoi weighted direction diagram was created by the threat sources dis- tribution and the threat costs. Then the ant colony optimization was used to find out the best route from all the pos- sible routes. Simulation was carried out to find the best route by the Matlab software in the end, the results showed the method is effective.%提出了基于蚁群优化算法与Voronoi图的无人飞行器智能航迹规划技术。根据威胁源分布以及威胁代价函数构建出加权有向Voronoi图，利用蚁群优化算法在可行路径集合中寻找最优航迹，通过Matlab软件仿真验证了该方法的可行性。
何兵; 刘刚; 闫建峥; 黄宁
2013-01-01
A new route planning method is proposed, which adopts the quantum genetic algorithm based on the Voronoi Diagram (VD). Firstly, the Voronoi diagram space of the aircraft was established by building up the Voronoi diagrams of start point, target point and threats. Secondly, some improvements was made to the traditional quantum genetic algorithm, such as introducing dynamic changing mechanism of quantum gate rotating, adding quantum crossover operation and quantum mutation operation, to make it had better searching efficiency. Simulation was made and the results of route planning using the Improved Quantum Genetic Algorithm (IQGA) were given. The simulation results show that the IQGA-VD has better convergence speed and searching efficiency than the GA-VD algorithm.%以飞行器航迹规划为应用背景,提出一种基于Voronoi图和量子遗传算法的飞行器航迹规划方法.首先,建立威胁源的V图,并构建发射点、目标点与威胁源的V图赋权有向图,从而建立飞行器航迹规划V图空间；然后,对传统量子遗传算法进行改进,引入了量子门旋转角步长动态调整机制；并增加了量子交叉操作和量子变异操作,使得改进后的量子遗传算法具有更高的搜索效率,采用改进后的量子遗传算法求解V图空间中的最优航迹；最后,进行了仿真实验.仿真结果表明,基于V图和量子遗传算法的航路规划方法是可行和有效的.
简献忠; 曹树建; 郭强
2015-01-01
字符分割是验证码字符识别的关键。为了解决粘连字符构成的验证码分割成功率低的问题，提出了一种基于SOM（self-organizing maps）神经网络聚类与维诺图（Voronoi）骨架形态分析相结合的粘连字符分割算法。该算法通过连通分量区分粘连字符，然后利用Voronoi 图获得粘连字符的骨架形态，提取粘连字符的骨架特征点；根据SOM聚类后的拓扑神经元分布确定分割点，完成粘连字符骨架的分割与复原。用网络验证码图片集进行了测试，实验效果与滴水法和连通分量提取法对比显示了该分割算法的优越性。该算法对各种字符粘连类型及字体倾斜扭曲的验证码均能准确分割，为粘连字符分割提供了一种新的方法。%Character segmentation is the point in CAPTCHA recognition.As the connected characters in CAPTCHA would be segmented with a low success rate,this paper proposed a character segmentation algorithm based on the clustering of the tou-ching region via self-organizing maps and skeletonization via Voronoi.Firstly,it used connected-component-based method to confirm connected character pairs,and selected feature points through a skeletonization process by Voronoi.Then determined the segmentation points by the neurons of SOM,leading to the final segmentation and character restoration.The results from the tests on the online CAPTCHA collections show that this algorithm achieves a better performance than the drop-fall and the con-nected-component-based algorithms.It can segment varieties of connected and distorted CAPTCHA,providing a new method for the segmentation of connected characters.
Modeling for Ultrasonic Health Monitoring of Foams with Embedded Sensors
Wang, L.; Rokhlin, S. I.; Rokhlin, Stanislav, I.
2005-01-01
In this report analytical and numerical methods are proposed to estimate the effective elastic properties of regular and random open-cell foams. The methods are based on the principle of minimum energy and on structural beam models. The analytical solutions are obtained using symbolic processing software. The microstructure of the random foam is simulated using Voronoi tessellation together with a rate-dependent random close-packing algorithm. The statistics of the geometrical properties of random foams corresponding to different packing fractions have been studied. The effects of the packing fraction on elastic properties of the foams have been investigated by decomposing the compliance into bending and axial compliance components. It is shown that the bending compliance increases and the axial compliance decreases when the packing fraction increases. Keywords: Foam; Elastic properties; Finite element; Randomness
GUO TieXin; CHEN XinXiang
2009-01-01
The purpose of this paper is to provide a random duality theory for the further development of the theory of random conjugate spaces for random normed modules.First,the complicated stratification structure of a module over the algebra L(μ,K) frequently makes our investigations into random duality theory considerably different from the corresponding ones into classical duality theory,thus in this paper we have to first begin in overcoming several substantial obstacles to the study of stratification structure on random locally convex modules.Then,we give the representation theorem of weakly continuous canonical module homomorphisms,the theorem of existence of random Mackey structure,and the random bipolar theorem with respect to a regular random duality pair together with some important random compatible invariants.
无
2009-01-01
The purpose of this paper is to provide a random duality theory for the further development of the theory of random conjugate spaces for random normed modules. First, the complicated stratification structure of a module over the algebra L(μ, K) frequently makes our investigations into random duality theory considerably difierent from the corresponding ones into classical duality theory, thus in this paper we have to first begin in overcoming several substantial obstacles to the study of stratification structure on random locally convex modules. Then, we give the representation theorem of weakly continuous canonical module homomorphisms, the theorem of existence of random Mackey structure, and the random bipolar theorem with respect to a regular random duality pair together with some important random compatible invariants.
Protecting Location Privacy with Voronoi Diagram over Road Networks%路网环境下基于Voronoi图的位置隐私保护方法
赵平; 马春光; 高训兵; 朱蔚
2013-01-01
位置隐私泄露已经成为限制LBS应用普及的主要因素,而现有的位置隐私保护方法大都没有考虑移动用户所处的环境背景——道路网络.针对此问题,提出了一种基于路网环境的位置隐私保护方法,该方法主要包含3个部分:(1)利用Voronoi图原理构造路网V图,以满足用户路段多样性要求；(2)提出一种新的隐私模型——Vk-隐私模型,其兼顾匿名集内所有用户的隐私需求,并有效保证服务质量；(3)基于Vk-隐私模型提出一种新的位置匿名算法,它对同一V区内的多个用户进行共同匿名处理,以提高匿名效率和安全性.方法充分考虑了道路网络的结构特点,兼顾了用户的隐私需求与服务质量.通过理论分析论证了方法的抗推断攻击特性,并通过实验验证了方法的可行性.%Location privacy disclosure has become main constraint of LBS applications,while most existing location privacyprotection methods do not consider the background of mobile users--the road network.A location privacy protection method over road networks was presented.This method consists of three phases.First,in order to meet the requirement of segmentl-diversity,the road-network Voronoi diagram is constructed based on the structure of the road network.Second,VK-privacy model is put forward.It satisfies all the users' privacy requirement in the cloaking set and effectively insures the QoS of LBS.Finally,a clocking algorithm based on VK-privacy model is presented,which improves processing efficiency and safety by cloaking multiple users in the same V-region together.The method takes full account of the structure characteristics of road networks and leverages users' privacy requirement and QoS of LBS.The robustness against inference attacksof the method was proved through theoretical analysis,and the feasibility of the method was proved by the experimental data.
涂伟; 李清泉; 方志祥
2014-01-01
Due to multiGconstraints and multiGobjectives,the optimization for large scale multiGdepot logistics routing problem is very difficult.A spatial heuristics algorithm is proposed based on the network Voronoi diagram.From the spatial perspective,two involved spatial issues in the multiGdepot logistics routing problem are service area partition and routing optimization.By using of depots’network Voronoi diagram,service area is coarsely partitioned and refined according to the goods storage in each depot.For the routing optimization,the local search space is limited within the spatial neighbors of customers.The proposed heuristics minimizes the used vehicles number and the total routes length.An experiment on several large scale logistics distribution instances in Shenzhen,China was implemented to validate the performance of the proposed heuristics algorithm.Results indicated that it provided high quality solution for large scale instances with 6400 customers in no more than 15 minutes.The proposed heuristics algorithm could be widely used in eGcommerce,express delivery,public utility in city to promote logistics efficiency.%由于存在多约束和多个优化目标，物流配送决策非常困难.本文针对城市多仓库物流配送问题，提出基于网络Voronoi 图的空间启发式优化方法.从空间角度将多仓库物流配送优化分解为区域分割和路径优化两个空间子问题.基于网络Voronoi 覆盖进行服务区域初始划分，顾及仓库容量差异，进行区域边界修正，并创建初始解.路径优化将局部搜索范围限定在网络 K近邻内，只搜索最有可能的空间邻域，迭代改进解的质量.该算法最小化路径数量和路径长度.利用深圳市的大规模多仓库物流配送问题测试算法性能.试验结果表明：本文方法能够在15 min 内求解6400个客户点的大规模物流配送问题，解的质量优于ArcGIS<10．8％，计算时间约为其21．2％.
Stephanov, M A; Wettig, T
2005-01-01
We review elementary properties of random matrices and discuss widely used mathematical methods for both hermitian and nonhermitian random matrix ensembles. Applications to a wide range of physics problems are summarized. This paper originally appeared as an article in the Wiley Encyclopedia of Electrical and Electronics Engineering.
郭帅; 马书根; 李斌; 王明辉; 王越超
2011-01-01
针对基于混合米制地图机器人同步定位与地图创建(Simultaneous localization and mapping,SLAM)中地图划分方法不完善的问题,提出了基于Voronoi地图表示方法的同步定位与地图创建算法VorSLAM.该算法在全局坐标系下创建特征地图,并根据此特征地图使用Voronoi图唯一地划分地图空间,在每一个划分内部创建一个相对于特征的局部稠密地图.特征地图与各个局部地图最终一起连续稠密地描述了环境.Voronoi地图表示方法解决了地图划分的唯一性问题,理论证明局部地图可以完整描述该划分所对应的环境轮廓.该地图表示方法一个基本特点是特征与局部地图一一对应,每个特征都关联一个定义在该特征上的局部地图.基于该特点,提出了一个基于形状匹配的数据关联算法,用以解决传统数据关联算法出现的多重关联问题.一个公寓弧形走廊的实验验证了VorSLAM算法和基于形状匹配的数据关联方法的有效性.%To solve the problem that the current map division methods in the hybrid metric map based simultaneous localization and mapping (SLAM) are not complete, this paper proposes an algorithm "VorSLAM", which uses a new map representation based on Voronoi diagram. The VorSLAM builds a feature based map in the global reference frame firstly. By operating Voronoi diagram on the feature map, it then divides the whole environment space uniquely into a series of local regions, in which dense local maps are built. The feature map together with the local maps gives the environment a continuous and dense description. The map representation based on Voronoi diagram ensures that the map division is unique. In each region, the local environment coutour is proven to be described completely by the corresponding local map. A basic character of the proposed map representation is that each global feature associates with a local dense map, which is defined relative to this feature
胡平; 唐斌; 褚永彬; 黄圣波
2015-01-01
城市作为一个社会、经济和物质实体，对周围区域有着吸引和辐射影响，城市空间影响范围反映了一个城市的综合实力，是城市综合实力在地理空间上的体现。对城市空间影响范围的分析与划分，有利于明确城市间空间相互作用的状况，对研究城市的合理布局，促进区域社会主义市场经济的发展有重要的意义。通过选取反映城市综合实力的13项指标，经主成分分析后得到四川省21个城市的综合实力得分值作为权重，采用加权Voronoi图划分得到四川省主要城市的空间影响范围图。研究结果表明，利用加权Voronoi图能够较为真实地反映出四川省主要城市的空间影响范围，为城市规划和区域经济发展提供引导与决策服务。%As a social, economic and material entities, city has attractive and radiant influence on the surrounding area. The city’s affected coverage which reflects the comprehensive strength of a city is the embodiment of city’s comprehensive strength on the geographic space. It is not only advantageous to make clear spatial interaction situation among cities, also has important significance to the study on reasonable layout of city and promoting development of regional socialist market economic by analysing and dividing city’s affected coverage. Thirteen indicators which reflect the comprehensive strength of city are selected to calculate overall strength scores of the 21 cities in Sichuan Province by conducting principal component analysis. Using the obtained city overall strength scores as weights, major city’s affected coverage in Sichuan Province is divided by applying weighted Voronoi diagram. The result shows that using weighted Voronoi diagram can reflect relatively real city’s affected coverage in Sichuan Province. Moreover, the city’s affected coverage could provide guidance and decision-making service for urban planning and regional economic
ajansen; kwhitefoot; panteltje1; edprochak; sudhakar, the
2014-07-01
In reply to the physicsworld.com news story “How to make a quantum random-number generator from a mobile phone” (16 May, http://ow.ly/xFiYc, see also p5), which describes a way of delivering random numbers by counting the number of photons that impinge on each of the individual pixels in the camera of a Nokia N9 smartphone.
Practical Statistics for the Voids Between Galaxies
Zaninetti, L.
2010-12-01
Full Text Available The voids between galaxies are identified withthe volumes of the Poisson Voronoi tessellation.Two new survival functions for the apparent radii of voids are derived. The sectional normalized area ofthe Poisson Voronoi tessellation is modelledby the Kiang function and by the exponential function. Two new survival functions with equivalent sectional radius are therefore derived; they represent an alternative to the survival function of voids between galaxies as given by the self-similar distribution. The spatial appearance of slices of the 2dF Galaxy Redshift Survey is simulated.
Mehta, Madan Lal
1990-01-01
Since the publication of Random Matrices (Academic Press, 1967) so many new results have emerged both in theory and in applications, that this edition is almost completely revised to reflect the developments. For example, the theory of matrices with quaternion elements was developed to compute certain multiple integrals, and the inverse scattering theory was used to derive asymptotic results. The discovery of Selberg's 1944 paper on a multiple integral also gave rise to hundreds of recent publications. This book presents a coherent and detailed analytical treatment of random matrices, leading
CARR,ROBERT D.; VEMPALA,SANTOSH
2000-01-25
The authors present a new technique for the design of approximation algorithms that can be viewed as a generalization of randomized rounding. They derive new or improved approximation guarantees for a class of generalized congestion problems such as multicast congestion, multiple TSP etc. Their main mathematical tool is a structural decomposition theorem related to the integrality gap of a relaxation.
Tapiero, Charles S.; Vallois, Pierre
2016-11-01
The premise of this paper is that a fractional probability distribution is based on fractional operators and the fractional (Hurst) index used that alters the classical setting of random variables. For example, a random variable defined by its density function might not have a fractional density function defined in its conventional sense. Practically, it implies that a distribution's granularity defined by a fractional kernel may have properties that differ due to the fractional index used and the fractional calculus applied to define it. The purpose of this paper is to consider an application of fractional calculus to define the fractional density function of a random variable. In addition, we provide and prove a number of results, defining the functional forms of these distributions as well as their existence. In particular, we define fractional probability distributions for increasing and decreasing functions that are right continuous. Examples are used to motivate the usefulness of a statistical approach to fractional calculus and its application to economic and financial problems. In conclusion, this paper is a preliminary attempt to construct statistical fractional models. Due to the breadth and the extent of such problems, this paper may be considered as an initial attempt to do so.
Tessellating with Logo: Effects on Visual Literacy.
Knupfer, Nancy Nelson; Clark, Barbara I.
This investigation of the potential of a Logo environment to develop visual literacy skills in elementary school students focused on the recognition of Escher-type geometric constructions by second and sixth grade students. Four research questions were addressed: (1) whether students can use higher-order and creative thinking skills in using…
Tessellating with Logo: Effects on Visual Literacy.
Knupfer, Nancy Nelson; Clark, Barbara I.
This investigation of the potential of a Logo environment to develop visual literacy skills in elementary school students focused on the recognition of Escher-type geometric constructions by second and sixth grade students. Four research questions were addressed: (1) whether students can use higher-order and creative thinking skills in using…
Programming curvature using origami tessellations.
Dudte, Levi H; Vouga, Etienne; Tachi, Tomohiro; Mahadevan, L
2016-05-01
Origami describes rules for creating folded structures from patterns on a flat sheet, but does not prescribe how patterns can be designed to fit target shapes. Here, starting from the simplest periodic origami pattern that yields one-degree-of-freedom collapsible structures-we show that scale-independent elementary geometric constructions and constrained optimization algorithms can be used to determine spatially modulated patterns that yield approximations to given surfaces of constant or varying curvature. Paper models confirm the feasibility of our calculations. We also assess the difficulty of realizing these geometric structures by quantifying the energetic barrier that separates the metastable flat and folded states. Moreover, we characterize the trade-off between the accuracy to which the pattern conforms to the target surface, and the effort associated with creating finer folds. Our approach enables the tailoring of origami patterns to drape complex surfaces independent of absolute scale, as well as the quantification of the energetic and material cost of doing so.
Tessellation of SoHO Magnetograms
R. Srikant; Jagdev Singh
2000-09-01
A gradient based algorithm which divides arbitrary images into non-overlapping surface filling tiles of opposite polarity is used to study the flux and size distributions of large scale magnetic flux concentrations in solar and heliospheric observatory (SoHO) magnetograms. The mean absolute flux and size of the concentrations at the considered scale is found to be about 1.7 × 1018Mx and 5.2Mm for both polarities. The form of the flux distribution is characterized by a skewness of 3 = 4.9 and a kurtosis of 4, = 42.8. The fall in the distribution in the range 6.5 × 1017Mx to 5 × 1018Mx is described by an exponential fit, in agreement with a model for the sustenance of quiet region flux.
VIDE: The Void IDentification and Examination toolkit
Sutter, P M; Hamaus, Nico; Pisani, Alice; Wandelt, Benjamin D; Warren, Michael S; Villaescusa-Navarro, Francisco; Zivick, Paul; Mao, Qingqing; Thompson, Benjamin B
2014-01-01
We present VIDE, the Void IDentification and Examination toolkit, an open-source Python/C++ code for finding cosmic voids in galaxy redshift surveys and N-body simulations, characterizing their properties, and providing a platform for more detailed analysis. At its core, VIDE uses a greatly enhanced version of ZOBOV (Neyinck 2008) to calculate a Voronoi tessellation for estimating the density field and a watershed transform to construct voids. The watershed levels are used to place voids in a hierarchical tree. VIDE provides significant additional functionality for both pre- and post-processing: for example, VIDE can work with volume- or magnitude-limited galaxy samples with arbitrary survey geometries, or dark matter particles or halo catalogs in a variety of common formats. It can also randomly subsample inputs and includes a Halo Occupation Distribution model for constructing mock galaxy populations. VIDE outputs a summary of void properties in plain ASCII, and provides a Python API to perform many analysi...
Transdimensional imaging of random velocity inhomogeneities in Nankai subduction zone
Takahashi, T.; Obana, K.; Yamamoto, Y.; Kaiho, Y.; Nakanishi, A.; Kodaira, S.; Kaneda, Y.
2014-12-01
The Nankai trough in southwestern Japan is a convergent margin where the Philippine Sea plate is subducting beneath the Eurasian plate. We have conducted five seismic observations with ocean bottom seismograms (OBSs) from 2008 to 2012 to elucidate detailed seismic structures and its relations with fault segments of large earthquakes. These observations covered the entire area of the Nankai trough, but quantity and quality of data are not spatially uniform because of different observing lengths and various noises. Waveform data of OBSs suggests variously-sized anomalies of random velocity inhomogeneity (i.e., scattering strength) in this subduction zone. To clarify details of random inhomogeneity structures, we conducted a transdimensional imaging of random inhomogeneities by means of the reversible jump Markov Chain Monte Carlo (rjMCMC) without assuming smooth spatial distributions of unknown parameters. We applied the rjMCMC for the inversion of peak delay times of S-wave envelopes at 4-8, 8-16, and 16-32 Hz, where the peak delay time is defined as the time lag from the S-wave onset to its maximal amplitude arrival. This delay time mainly reflects the accumulated multiple forward scattering effect due to random inhomogeneities. We assumed the von Karman type power spectral density function (PSDF) for random velocity fluctuation, and estimated two parameters related with the PSDF at large wavenumber. Study area is partitioned by discrete Voronoi cells of which number and spatial sizes are variable. Estimated random inhomogeneities show clear lateral variations along the Nankai trough. The strongest inhomogeneity on the Nankai trough was found near the subducted Kyushu-Palau ridge that is located at the western margin of the fault segments. We also find a horizontal variation of inhomogeneity along the non-volcanic tremor zone. Relatively strong inhomogeneities in this tremor zone were imaged beneath west Shikoku and Kii-Peninsula. These anomalies were not clearly
Simulation technique for hard-disk models in two dimensions
Fraser, Diane P.; Zuckermann, Martin J.; Mouritsen, Ole G.
1990-01-01
A method is presented for studying hard-disk systems by Monte Carlo computer-simulation techniques within the NpT ensemble. The method is based on the Voronoi tesselation, which is dynamically maintained during the simulation. By an analysis of the Voronoi statistics, a quantity is identified...... that is extremely sensitive to structural changes in the system. This quantity, which is derived from the edge-length distribution function of the Voronoi polygons, displays a dramatic change at the solid-liquid transition. This is found to be more useful for locating the transition than either the defect density...
Gurau, Razvan
2017-01-01
Written by the creator of the modern theory of random tensors, this book is the first self-contained introductory text to this rapidly developing theory. Starting from notions familiar to the average researcher or PhD student in mathematical or theoretical physics, the book presents in detail the theory and its applications to physics. The recent detections of the Higgs boson at the LHC and gravitational waves at LIGO mark new milestones in Physics confirming long standing predictions of Quantum Field Theory and General Relativity. These two experimental results only reinforce today the need to find an underlying common framework of the two: the elusive theory of Quantum Gravity. Over the past thirty years, several alternatives have been proposed as theories of Quantum Gravity, chief among them String Theory. While these theories are yet to be tested experimentally, key lessons have already been learned. Whatever the theory of Quantum Gravity may be, it must incorporate random geometry in one form or another....
Random functions and turbulence
Panchev, S
1971-01-01
International Series of Monographs in Natural Philosophy, Volume 32: Random Functions and Turbulence focuses on the use of random functions as mathematical methods. The manuscript first offers information on the elements of the theory of random functions. Topics include determination of statistical moments by characteristic functions; functional transformations of random variables; multidimensional random variables with spherical symmetry; and random variables and distribution functions. The book then discusses random processes and random fields, including stationarity and ergodicity of random
Existence of isostatic, maximally random jammed monodisperse hard-disk packings.
Atkinson, Steven; Stillinger, Frank H; Torquato, Salvatore
2014-12-30
We generate jammed packings of monodisperse circular hard-disks in two dimensions using the Torquato-Jiao sequential linear programming algorithm. The packings display a wide diversity of packing fractions, average coordination numbers, and order as measured by standard scalar order metrics. This geometric-structure approach enables us to show the existence of relatively large maximally random jammed (MRJ) packings with exactly isostatic jammed backbones and a packing fraction (including rattlers) of [Formula: see text]. By contrast, the concept of random close packing (RCP) that identifies the most probable packings as the most disordered misleadingly identifies highly ordered disk packings as RCP in 2D. Fundamental structural descriptors such as the pair correlation function, structure factor, and Voronoi statistics show a strong contrast between the MRJ state and the typical hyperstatic, polycrystalline packings with [Formula: see text] that are more commonly obtained using standard packing protocols. Establishing that the MRJ state for monodisperse hard disks is isostatic and qualitatively distinct from commonly observed polycrystalline packings contradicts conventional wisdom that such a disordered, isostatic packing does not exist due to a lack of geometrical frustration and sheds light on the nature of disorder. This prompts the question of whether an algorithm may be designed that is strongly biased toward generating the monodisperse disk MRJ state.
Bishop, Joseph E.; Emery, John M.; Battaile, Corbett C.; Littlewood, David J.; Baines, Andrew J.
2016-05-01
Two fundamental approximations in macroscale solid-mechanics modeling are (1) the assumption of scale separation in homogenization theory and (2) the use of a macroscopic plasticity material model that represents, in a mean sense, the multitude of inelastic processes occurring at the microscale. With the goal of quantifying the errors induced by these approximations on engineering quantities of interest, we perform a set of direct numerical simulations (DNS) in which polycrystalline microstructures are embedded throughout a macroscale structure. The largest simulations model over 50,000 grains. The microstructure is idealized using a randomly close-packed Voronoi tessellation in which each polyhedral Voronoi cell represents a grain. An face centered cubic crystal-plasticity model is used to model the mechanical response of each grain. The overall grain structure is equiaxed, and each grain is randomly oriented with no overall texture. The detailed results from the DNS simulations are compared to results obtained from conventional macroscale simulations that use homogeneous isotropic plasticity models. The macroscale plasticity models are calibrated using a representative volume element of the idealized microstructure. Ultimately, we envision that DNS modeling will be used to gain new insights into the mechanics of material deformation and failure.
Regional SAR Image Segmentation Based on Fuzzy Clustering with Gamma Mixture Model
Li, X. L.; Zhao, Q. H.; Li, Y.
2017-09-01
Most of stochastic based fuzzy clustering algorithms are pixel-based, which can not effectively overcome the inherent speckle noise in SAR images. In order to deal with the problem, a regional SAR image segmentation algorithm based on fuzzy clustering with Gamma mixture model is proposed in this paper. First, initialize some generating points randomly on the image, the image domain is divided into many sub-regions using Voronoi tessellation technique. Each sub-region is regarded as a homogeneous area in which the pixels share the same cluster label. Then, assume the probability of the pixel to be a Gamma mixture model with the parameters respecting to the cluster which the pixel belongs to. The negative logarithm of the probability represents the dissimilarity measure between the pixel and the cluster. The regional dissimilarity measure of one sub-region is defined as the sum of the measures of pixels in the region. Furthermore, the Markov Random Field (MRF) model is extended from pixels level to Voronoi sub-regions, and then the regional objective function is established under the framework of fuzzy clustering. The optimal segmentation results can be obtained by the solution of model parameters and generating points. Finally, the effectiveness of the proposed algorithm can be proved by the qualitative and quantitative analysis from the segmentation results of the simulated and real SAR images.
Adhesion and the Geometry of the Cosmic Web
Hidding, Johan; Vegter, Gert; Jones, Bernard J T
2012-01-01
We present a new way to formulate the geometry of the Cosmic Web in terms of Lagrangian space. The Adhesion model has an ingenious geometric interpretation out of which the spine of the Cosmic Web emerges naturally. Within this context we demonstrate a deep connection of the relation between Eulerian and Lagrangian space with that between Voronoi and Delaunay tessellations.
Geometry and Morphology of the Cosmic Web : Analyzing Spatial Patterns in the Universe
van de Weygaert, Rien; Jones, Bernard J. T.; Platen, Erwin; Aragon-Calvo, Miguel A.; Anton, F
2009-01-01
We review the analysis of the Cosmic Web by means of an extensive toolset based on the use of Delaunay and Voronoi tessellations. The Cosmic Web is the salient and pervasive foamlike pattern in which matter has organized itself on scales of a few up to more than a hundred Megaparsec. The weblike spa
Simulating the influence of crop spatial patterns on canola yield
Griepentrog, H.W.; Nielsen, J.; Olsen, Jannie Maj
2011-01-01
plant uniformity on the yield of oil seed rape. Voronoi polygons (tessellations) which define the area closer to an individual than to any other individual were used as a measure of the area available to each plant, and corrections were included for extreme polygon shape and eccentricity of the plant...
Dapkūnas, Justas; Timinskas, Albertas; Olechnovič, Kliment; Margelevičius, Mindaugas; Dičiūnas, Rytis; Venclovas, Česlovas
2016-12-22
The PPI3D web server is focused on searching and analyzing the structural data on protein-protein interactions. Reducing the data redundancy by clustering and analyzing the properties of interaction interfaces using Voronoi tessellation makes this software a highly effective tool for addressing different questions related to protein interactions.
Results in Computational Geometry: Geometric Embeddings and Query- Retrieval Problems
1990-11-01
D. Bolker. Generalized dirichlet tesselations. Geometriae Dedicata, 20:209-243, 1986. [5] F. Aurenhammer. Power diagrams: properties, algorithms, and...voronoi diagrams. Geometriae Dedicata, 27:65-75, 1988. [9] V. E. Benes. Optimal rearrangeable multistage connecting networks. Bell System Technical
Random fixed points and random differential inclusions
Nikolaos S. Papageorgiou
1988-01-01
Full Text Available In this paper, first, we study random best approximations to random sets, using fixed point techniques, obtaining this way stochastic analogues of earlier deterministic results by Browder-Petryshyn, KyFan and Reich. Then we prove two fixed point theorems for random multifunctions with stochastic domain that satisfy certain tangential conditions. Finally we consider a random differential inclusion with upper semicontinuous orientor field and establish the existence of random solutions.
Khirevich, Siarhei; Höltzel, Alexandra; Daneyko, Anton; Seidel-Morgenstern, Andreas; Tallarek, Ulrich
2011-09-16
The mass transport properties of bulk random sphere packings depend primarily on the bed (external) porosity ε, but also on the packing microstructure. We investigate the influence of the packing microstructure on the diffusive tortuosity τ=D(m)/D(eff), which relates the bulk diffusion coefficient (D(m)) to the effective (asymptotic) diffusion coefficient in a porous medium (D(eff)), by numerical simulations of diffusion in a set of computer-generated, monodisperse, hard-sphere packings. Variation of packing generation algorithm and protocol yielded four Jodrey-Tory and two Monte Carlo packing types with systematically varied degrees of microstructural heterogeneity in the range between the random-close and the random-loose packing limit (ε=0.366-0.46). The distinctive tortuosity-porosity scaling of the packing types is influenced by the extent to which the structural environment of individual pores varies in a packing, and to quantify this influence we propose a measure based on Delaunay tessellation. We demonstrate that the ratio of the minimum to the maximum void face area of a Delaunay tetrahedron around a pore between four adjacent spheres, (A(min)/A(max))(D), is a measure for the structural heterogeneity in the direct environment of this pore, and that the standard deviation σ of the (A(min)/A(max))(D)-distribution considering all pores in a packing mimics the tortuosity-porosity scaling of the generated packing types. Thus, σ(A(min)/A(max))(D) provides a structure-transport correlation for diffusion in bulk, monodisperse, random sphere packings. Copyright © 2011 Elsevier B.V. All rights reserved.
Further Developments in Characterizing Capture Zone Distributions (CZD) in Island Growth
Einstein, T. L.; Pimpinelli, Alberto; González, Diego Luis
2014-03-01
As argued previously, analysis of the distribution of the areas of capture zones (i.e. proximity polygons [or Voronoi tesselations] with respect to island centers) is often the best way to extract the critical nucleus size in studies of epitaxial growth. For non-Poisson deposition (i.e. when island nucleation is not fully random) the areas of these Voronoi cells can be well described by the generalized Wigner distribution (GWD), particularly in the central region around the mean area where the distribution is largest. We discuss several recent applications to experimental systems, catelogued in a recent minireview,[2] showing how this perspective leads to insights about the critical nucleus size. In contrast, several (but not all) studies have shown that the GWD may not describe the numerical data from painstaking simulations in both tails.2 We discuss some refinements that have been proposed, as well as scaling forms. Finally, we comment on applications to social phenomena. Emphasis is on very recent developments. Work at UMD supported by NSF CHE 13-05892 & NSF MRSEC DMR 05-20471.
Einstein, Theodore L.; Pimpinelli, Alberto; González, Diego Luis; Morales-Cifuentes, Josue R.
2015-09-01
In studies of epitaxial growth, analysis of the distribution of the areas of capture zones (i.e. proximity polygons or Voronoi tessellations with respect to island centers) is often the best way to extract the critical nucleus size i. For non-random nucleation the normalized areas s of these Voronoi cells are well described by the generalized Wigner distribution (GWD) Pβ(s) = asβ exp(-bs2), particularly in the central region 0.5 < s < 2 where data are least noisy. Extensive Monte Carlo simulations reveal inadequacies of our earlier mean field analysis, suggesting β = i + 2 for diffusion-limited aggregation (DLA). Since simulations generate orders of magnitude more data than experiments, they permit close examination of the tails of the distribution, which differ from the simple GWD form. One refinement is based on a fragmentation model. We also compare island-size distributions. We compare analysis by island-size distribution and by scaling of island density with flux. Modifications appear for attach-limited aggregation (ALA). We focus on the experimental system para-hexaphenyl on amorphous mica, comparing the results of the three analysis techniques and reconciling their results via a novel model of hot precursors based on rate equations, pointing out the existence of intermediate scaling regimes between DLA and ALA.
Morphology and linear-elastic moduli of random network solids.
Nachtrab, Susan; Kapfer, Sebastian C; Arns, Christoph H; Madadi, Mahyar; Mecke, Klaus; Schröder-Turk, Gerd E
2011-06-17
The effective linear-elastic moduli of disordered network solids are analyzed by voxel-based finite element calculations. We analyze network solids given by Poisson-Voronoi processes and by the structure of collagen fiber networks imaged by confocal microscopy. The solid volume fraction ϕ is varied by adjusting the fiber radius, while keeping the structural mesh or pore size of the underlying network fixed. For intermediate ϕ, the bulk and shear modulus are approximated by empirical power-laws K(phi)proptophin and G(phi)proptophim with n≈1.4 and m≈1.7. The exponents for the collagen and the Poisson-Voronoi network solids are similar, and are close to the values n=1.22 and m=2.11 found in a previous voxel-based finite element study of Poisson-Voronoi systems with different boundary conditions. However, the exponents of these empirical power-laws are at odds with the analytic values of n=1 and m=2, valid for low-density cellular structures in the limit of thin beams. We propose a functional form for K(ϕ) that models the cross-over from a power-law at low densities to a porous solid at high densities; a fit of the data to this functional form yields the asymptotic exponent n≈1.00, as expected. Further, both the intensity of the Poisson-Voronoi process and the collagen concentration in the samples, both of which alter the typical pore or mesh size, affect the effective moduli only by the resulting change of the solid volume fraction. These findings suggest that a network solid with the structure of the collagen networks can be modeled in quantitative agreement by a Poisson-Voronoi process.
Random broadcast on random geometric graphs
Bradonjic, Milan [Los Alamos National Laboratory; Elsasser, Robert [UNIV OF PADERBORN; Friedrich, Tobias [ICSI/BERKELEY; Sauerwald, Tomas [ICSI/BERKELEY
2009-01-01
In this work, we consider the random broadcast time on random geometric graphs (RGGs). The classic random broadcast model, also known as push algorithm, is defined as: starting with one informed node, in each succeeding round every informed node chooses one of its neighbors uniformly at random and informs it. We consider the random broadcast time on RGGs, when with high probability: (i) RGG is connected, (ii) when there exists the giant component in RGG. We show that the random broadcast time is bounded by {Omicron}({radical} n + diam(component)), where diam(component) is a diameter of the entire graph, or the giant component, for the regimes (i), or (ii), respectively. In other words, for both regimes, we derive the broadcast time to be {Theta}(diam(G)), which is asymptotically optimal.
Completely random signed measures
Hellmund, Gunnar
Completely random signed measures are defined, characterized and related to Lévy random measures and Lévy bases.......Completely random signed measures are defined, characterized and related to Lévy random measures and Lévy bases....
Matricially free random variables
Lenczewski, Romuald
2008-01-01
We show that the operatorial framework developed by Voiculescu for free random variables can be extended to arrays of random variables whose multiplication imitates matricial multiplication. The associated notion of independence, called matricial freeness, can be viewed as a generalization of both freeness and monotone independence. At the same time, the sums of matricially free random variables, called random pseudomatrices, are closely related to Gaussian random matrices. The main results presented in this paper concern the standard and tracial central limit theorems for random pseudomatrices and the corresponding limit distributions which can be viewed as matricial generalizations of semicirle laws.
Precise algorithm to generate random sequential addition of hard hyperspheres at saturation.
Zhang, G; Torquato, S
2013-11-01
The study of the packing of hard hyperspheres in d-dimensional Euclidean space R^{d} has been a topic of great interest in statistical mechanics and condensed matter theory. While the densest known packings are ordered in sufficiently low dimensions, it has been suggested that in sufficiently large dimensions, the densest packings might be disordered. The random sequential addition (RSA) time-dependent packing process, in which congruent hard hyperspheres are randomly and sequentially placed into a system without interparticle overlap, is a useful packing model to study disorder in high dimensions. Of particular interest is the infinite-time saturation limit in which the available space for another sphere tends to zero. However, the associated saturation density has been determined in all previous investigations by extrapolating the density results for nearly saturated configurations to the saturation limit, which necessarily introduces numerical uncertainties. We have refined an algorithm devised by us [S. Torquato, O. U. Uche, and F. H. Stillinger, Phys. Rev. E 74, 061308 (2006)] to generate RSA packings of identical hyperspheres. The improved algorithm produce such packings that are guaranteed to contain no available space in a large simulation box using finite computational time with heretofore unattained precision and across the widest range of dimensions (2≤d≤8). We have also calculated the packing and covering densities, pair correlation function g(2)(r), and structure factor S(k) of the saturated RSA configurations. As the space dimension increases, we find that pair correlations markedly diminish, consistent with a recently proposed "decorrelation" principle, and the degree of "hyperuniformity" (suppression of infinite-wavelength density fluctuations) increases. We have also calculated the void exclusion probability in order to compute the so-called quantizer error of the RSA packings, which is related to the second moment of inertia of the average
On Gaussian random supergravity
Bachlechner, Thomas C. [Department of Physics, Cornell University,Physical Sciences Building 428, Ithaca, NY 14853 (United States)
2014-04-08
We study the distribution of metastable vacua and the likelihood of slow roll inflation in high dimensional random landscapes. We consider two examples of landscapes: a Gaussian random potential and an effective supergravity potential defined via a Gaussian random superpotential and a trivial Kähler potential. To examine these landscapes we introduce a random matrix model that describes the correlations between various derivatives and we propose an efficient algorithm that allows for a numerical study of high dimensional random fields. Using these novel tools, we find that the vast majority of metastable critical points in N dimensional random supergravities are either approximately supersymmetric with |F|≪M{sub susy} or supersymmetric. Such approximately supersymmetric points are dynamical attractors in the landscape and the probability that a randomly chosen critical point is metastable scales as log (P)∝−N. We argue that random supergravities lead to potentially interesting inflationary dynamics.
On Gaussian random supergravity
Bachlechner, Thomas C.
2014-04-01
We study the distribution of metastable vacua and the likelihood of slow roll inflation in high dimensional random landscapes. We consider two examples of landscapes: a Gaussian random potential and an effective supergravity potential defined via a Gaussian random superpotential and a trivial Kähler potential. To examine these landscapes we introduce a random matrix model that describes the correlations between various derivatives and we propose an efficient algorithm that allows for a numerical study of high dimensional random fields. Using these novel tools, we find that the vast majority of metastable critical points in N dimensional random supergravities are either approximately supersymmetric with | F| ≪ M susy or supersymmetric. Such approximately supersymmetric points are dynamical attractors in the landscape and the probability that a randomly chosen critical point is metastable scales as log( P ) ∝ - N. We argue that random supergravities lead to potentially interesting inflationary dynamics.
On Gaussian Random Supergravity
Bachlechner, Thomas C
2014-01-01
We study the distribution of metastable vacua and the likelihood of slow roll inflation in high dimensional random landscapes. We consider two examples of landscapes: a Gaussian random potential and an effective supergravity potential defined via a Gaussian random superpotential and a trivial Kahler potential. To examine these landscapes we introduce a random matrix model that describes the correlations between various derivatives and we propose an efficient algorithm that allows for a numerical study of high dimensional random fields. Using these novel tools, we find that the vast majority of metastable critical points in N dimensional random supergravities are either approximately supersymmetric with |F|<< M_{susy} or supersymmetric. Such approximately supersymmetric points are dynamical attractors in the landscape and the probability that a randomly chosen critical point is metastable scales as log(P)\\propto -N. We argue that random supergravities lead to potentially interesting inflationary dynamics...
On Gaussian random supergravity
Bachlechner, Thomas C.
2014-01-01
We study the distribution of metastable vacua and the likelihood of slow roll inflation in high dimensional random landscapes. We consider two examples of landscapes: a Gaussian random potential and an effective supergravity potential defined via a Gaussian random superpotential and a trivial K\\"ahler potential. To examine these landscapes we introduce a random matrix model that describes the correlations between various derivatives and we propose an efficient algorithm that allows for a nume...
Quantum Random Number Generators
Herrero-Collantes, Miguel; Garcia-Escartin, Juan Carlos
2016-01-01
Random numbers are a fundamental resource in science and engineering with important applications in simulation and cryptography. The inherent randomness at the core of quantum mechanics makes quantum systems a perfect source of entropy. Quantum random number generation is one of the most mature quantum technologies with many alternative generation methods. We discuss the different technologies in quantum random number generation from the early devices based on radioactive decay to the multipl...
Quantum random number generator
Stipcevic, M
2006-01-01
We report upon a novel principle for realization of a fast nondeterministic random number generator whose randomness relies on intrinsic randomness of the quantum physical processes of photonic emission in semiconductors and subsequent detection by the photoelectric effect. Timing information of detected photons is used to generate binary random digits-bits. The bit extraction method based on restartable clock theoretically eliminates both bias and autocorrelation while reaching efficiency of almost 0.5 bits per random event. A prototype has been built and statistically tested.
Liu, Jianping; Kjaergard, Lise Lotte; Gluud, Christian
2002-01-01
The quality of randomization of Chinese randomized trials on herbal medicines for hepatitis B was assessed. Search strategy and inclusion criteria were based on the published protocol. One hundred and seventy-six randomized clinical trials (RCTs) involving 20,452 patients with chronic hepatitis B....../150) of the studies were imbalanced at the 0.05 level of probability for the two treatments and 13.3% (20/150) imbalanced at the 0.01 level in the randomization. It is suggested that there may exist misunderstanding of the concept and the misuse of randomization based on the review....
Quantum random number generation
Ma, Xiongfeng; Yuan, Xiao; Cao, Zhu; Qi, Bing; Zhang, Zhen
2016-06-01
Quantum physics can be exploited to generate true random numbers, which have important roles in many applications, especially in cryptography. Genuine randomness from the measurement of a quantum system reveals the inherent nature of quantumness—coherence, an important feature that differentiates quantum mechanics from classical physics. The generation of genuine randomness is generally considered impossible with only classical means. On the basis of the degree of trustworthiness on devices, quantum random number generators (QRNGs) can be grouped into three categories. The first category, practical QRNG, is built on fully trusted and calibrated devices and typically can generate randomness at a high speed by properly modelling the devices. The second category is self-testing QRNG, in which verifiable randomness can be generated without trusting the actual implementation. The third category, semi-self-testing QRNG, is an intermediate category that provides a tradeoff between the trustworthiness on the device and the random number generation speed.
Random walks, random fields, and disordered systems
Černý, Jiří; Kotecký, Roman
2015-01-01
Focusing on the mathematics that lies at the intersection of probability theory, statistical physics, combinatorics and computer science, this volume collects together lecture notes on recent developments in the area. The common ground of these subjects is perhaps best described by the three terms in the title: Random Walks, Random Fields and Disordered Systems. The specific topics covered include a study of Branching Brownian Motion from the perspective of disordered (spin-glass) systems, a detailed analysis of weakly self-avoiding random walks in four spatial dimensions via methods of field theory and the renormalization group, a study of phase transitions in disordered discrete structures using a rigorous version of the cavity method, a survey of recent work on interacting polymers in the ballisticity regime and, finally, a treatise on two-dimensional loop-soup models and their connection to conformally invariant systems and the Gaussian Free Field. The notes are aimed at early graduate students with a mod...
Quantum random number generators
Herrero-Collantes, Miguel; Garcia-Escartin, Juan Carlos
2017-01-01
Random numbers are a fundamental resource in science and engineering with important applications in simulation and cryptography. The inherent randomness at the core of quantum mechanics makes quantum systems a perfect source of entropy. Quantum random number generation is one of the most mature quantum technologies with many alternative generation methods. This review discusses the different technologies in quantum random number generation from the early devices based on radioactive decay to the multiple ways to use the quantum states of light to gather entropy from a quantum origin. Randomness extraction and amplification and the notable possibility of generating trusted random numbers even with untrusted hardware using device-independent generation protocols are also discussed.
Randomness and Differentiability
Brattka, Vasco; Nies, André
2011-01-01
We characterize some major algorithmic randomness notions via differentiability of effective functions. (1) We show that a real number z in [0,1] is computably random if and only if every nondecreasing computable function [0,1]->R is differentiable at z. (2) A real number z in [0,1] is weakly 2-random if and only if every almost everywhere differentiable computable function [0,1]->R is differentiable at z. (3) Recasting results of the constructivist Demuth (1975) in classical language, we show that a real z is ML random if and only if every computable function of bounded variation is differentiable at z, and similarly for absolutely continuous functions. We also use the analytic methods to show that computable randomness of a real is base invariant, and to derive preservation results for randomness notions.
Gurau, Razvan
2016-09-01
This article is preface to the SIGMA special issue ''Tensor Models, Formalism and Applications'', http://www.emis.de/journals/SIGMA/Tensor_Models.html. The issue is a collection of eight excellent, up to date reviews on random tensor models. The reviews combine pedagogical introductions meant for a general audience with presentations of the most recent developments in the field. This preface aims to give a condensed panoramic overview of random tensors as the natural generalization of random matrices to higher dimensions.
Weizhi Wu
2006-01-01
In this paper,the concept of a random rough set which includes the mechanisms of numeric and non-numeric aspects of uncertain knowledge is introduced. It is proved that for any belief structure and its inducing belief and plausibility measures there exists a random approximation space such that the associated lower and upper probabilities are respectively the given belief and plausibility measures, and vice versa. And for a random approximation space generated from a totally random set, its inducing lower and upper probabilities are respectively a pair of necessity and possibility measures.
Hidden symmetries in jammed systems
Morse, Peter K.; Corwin, Eric I.
2016-07-01
There are deep, but hidden, geometric structures within jammed systems, associated with hidden symmetries. These can be revealed by repeated transformations under which these structures lead to fixed points. These geometric structures can be found in the Voronoi tesselation of space defined by the packing. In this paper we examine two iterative processes: maximum inscribed sphere (MIS) inversion and a real-space coarsening scheme. Under repeated iterations of the MIS inversion process we find invariant systems in which every particle is equal to the maximum inscribed sphere within its Voronoi cell. Using a real-space coarsening scheme we reveal behavior in geometric order parameters which is length-scale invariant.
李鑫; 戎蒙恬; 刘涛; 周亮
2013-01-01
The lower accuracy of hot spot temperature estimation on microprocessors can lead to a higher probability of false alarms and unnecessary responses,which results in a reduction of the reliability of computer systems.In this paper,an improved thermal reconstruction method based on dynamic Voronoi diagram with non-uniform sampling on multicore processors has been proposed.Experimental results indicate that the proposed method significantly outperforms spectral analysis techniques in both thermal reconstruction error and hot spot temperature error.It can he better applied in dynamic thermal management techniques to achieve global and local thermal monitoring.%微处理器热监控中不精确的热点温度估计会导致错误的预警和不必要的响应.为了更好的监控微处理器的运行温度,提出了一种基于动态Voronoi图的多核处理器非均匀采样热重构改进方法.实验结果表明:该方法比现有的频谱技术在热重构平均温度误差和热点温度误差精度方面有了一定提高,能够有效运用在动态热管理技术中实现精确的全局和局部温度监控.
Klatt, Michael A.; Torquato, Salvatore
2016-08-01
In the first paper of this series, we introduced Voronoi correlation functions to characterize the structure of maximally random jammed (MRJ) sphere packings across length scales. In the present paper, we determine a variety of different correlation functions that arise in rigorous expressions for the effective physical properties of MRJ sphere packings and compare them to the corresponding statistical descriptors for overlapping spheres and equilibrium hard-sphere systems. Such structural descriptors arise in rigorous bounds and formulas for effective transport properties, diffusion and reactions constants, elastic moduli, and electromagnetic characteristics. First, we calculate the two-point, surface-void, and surface-surface correlation functions, for which we derive explicit analytical formulas for finite hard-sphere packings. We show analytically how the contact Dirac delta function contribution to the pair correlation function g2(r ) for MRJ packings translates into distinct functional behaviors of these two-point correlation functions that do not arise in the other two models examined here. Then we show how the spectral density distinguishes the MRJ packings from the other disordered systems in that the spectral density vanishes in the limit of infinite wavelengths; i.e., these packings are hyperuniform, which means that density fluctuations on large length scales are anomalously suppressed. Moreover, for all model systems, we study and compute exclusion probabilities and pore size distributions, as well as local density fluctuations. We conjecture that for general disordered hard-sphere packings, a central limit theorem holds for the number of points within an spherical observation window. Our analysis links problems of interest in material science, chemistry, physics, and mathematics. In the third paper of this series, we will evaluate bounds and estimates of a host of different physical properties of the MRJ sphere packings that are based on the
Anisotropy of the monomer random walk in a polymer melt: local-order and connectivity effects
Bernini, S.; Leporini, D.
2016-05-01
The random walk of a bonded monomer in a polymer melt is anisotropic due to local order and bond connectivity. We investigate both effects by molecular-dynamics simulations on melts of fully-flexible linear chains ranging from dimers (M = 2) up to entangled polymers (M = 200). The corresponding atomic liquid is also considered a reference system. To disentangle the influence of the local geometry and the bond arrangements, and to reveal their interplay, we define suitable measures of the anisotropy emphasising either the former or the latter aspect. Connectivity anisotropy, as measured by the correlation between the initial bond orientation and the direction of the subsequent monomer displacement, shows a slight enhancement due to the local order at times shorter than the structural relaxation time. At intermediate times—when the monomer displacement is comparable to the bond length—a pronounced peak and then decays slowly as t -1/2, becoming negligible when the displacement is as large as about five bond lengths, i.e. about four monomer diameters or three Kuhn lengths. Local-geometry anisotropy, as measured by the correlation between the initial orientation of a characteristic axis of the Voronoi cell and the subsequent monomer dynamics, is affected at shorter times than the structural relaxation time by the cage shape with antagonistic disturbance by the connectivity. Differently, at longer times, the connectivity favours the persistence of the local-geometry anisotropy, which vanishes when the monomer displacement exceeds the bond length. Our results strongly suggest that the sole consideration of the local order is not enough to understand the microscopic origin of the rattling amplitude of the trapped monomer in the cage of the neighbours.
Asymptotics of Random Contractions
Hashorva, Enkelejd; Tang, Qihe
2010-01-01
In this paper we discuss the asymptotic behaviour of random contractions $X=RS$, where $R$, with distribution function $F$, is a positive random variable independent of $S\\in (0,1)$. Random contractions appear naturally in insurance and finance. Our principal contribution is the derivation of the tail asymptotics of $X$ assuming that $F$ is in the max-domain of attraction of an extreme value distribution and the distribution function of $S$ satisfies a regular variation property. We apply our result to derive the asymptotics of the probability of ruin for a particular discrete-time risk model. Further we quantify in our asymptotic setting the effect of the random scaling on the Conditional Tail Expectations, risk aggregation, and derive the joint asymptotic distribution of linear combinations of random contractions.
Shiffman, Bernard
2010-01-01
We introduce several notions of `random fewnomials', i.e. random polynomials with a fixed number f of monomials of degree N. The f exponents are chosen at random and then the coefficients are chosen to be Gaussian random, mainly from the SU(m + 1) ensemble. The results give limiting formulas as N goes to infinity for the expected distribution of complex zeros of a system of k random fewnomials in m variables. When k = m, for SU(m + 1) polynomials, the limit is the Monge-Ampere measure of a toric Kaehler potential on CP^m obtained by averaging a `discrete Legendre transform' of the Fubini-Study symplectic potential at f points of the unit simplex in R^m.
Cappellini, Valerio [' Mark Kac' Complex Systems Research Centre, Uniwersytet Jagiellonski, ul. Reymonta 4, 30-059 Krakow (Poland); Sommers, Hans-Juergen [Fachbereich Physik, Universitaet Duisburg-Essen, Campus Duisburg, 47048 Duisburg (Germany); Bruzda, Wojciech; Zyczkowski, Karol [Instytut Fizyki im. Smoluchowskiego, Uniwersytet Jagiellonski, ul. Reymonta 4, 30-059 Krakow (Poland)], E-mail: valerio@ictp.it, E-mail: h.j.sommers@uni-due.de, E-mail: w.bruzda@uj.edu.pl, E-mail: karol@cft.edu.pl
2009-09-11
Ensembles of random stochastic and bistochastic matrices are investigated. While all columns of a random stochastic matrix can be chosen independently, the rows and columns of a bistochastic matrix have to be correlated. We evaluate the probability measure induced into the Birkhoff polytope of bistochastic matrices by applying the Sinkhorn algorithm to a given ensemble of random stochastic matrices. For matrices of order N = 2 we derive explicit formulae for the probability distributions induced by random stochastic matrices with columns distributed according to the Dirichlet distribution. For arbitrary N we construct an initial ensemble of stochastic matrices which allows one to generate random bistochastic matrices according to a distribution locally flat at the center of the Birkhoff polytope. The value of the probability density at this point enables us to obtain an estimation of the volume of the Birkhoff polytope, consistent with recent asymptotic results.
Cappellini, V; Bruzda, W; Zyczkowski, K
2009-01-01
Ensembles of random stochastic and bistochastic matrices are investigated. While all columns of a random stochastic matrix can be chosen independently, the rows and columns of a bistochastic matrix have to be correlated. We evaluate the probability measure induced into the Birkhoff polytope of bistochastic matrices by applying the Sinkhorn algorithm to a given ensemble of random stochastic matrices. For matrices of order N=2 we derive explicit formulae for the probability distributions induced by random stochastic matrices with columns distributed according to the Dirichlet distribution. For arbitrary $N$ we construct an initial ensemble of stochastic matrices which allows one to generate random bistochastic matrices according to a distribution locally flat at the center of the Birkhoff polytope. The value of the probability density at this point enables us to obtain an estimation of the volume of the Birkhoff polytope, consistent with recent asymptotic results.
Quantum random number generator
Pooser, Raphael C.
2016-05-10
A quantum random number generator (QRNG) and a photon generator for a QRNG are provided. The photon generator may be operated in a spontaneous mode below a lasing threshold to emit photons. Photons emitted from the photon generator may have at least one random characteristic, which may be monitored by the QRNG to generate a random number. In one embodiment, the photon generator may include a photon emitter and an amplifier coupled to the photon emitter. The amplifier may enable the photon generator to be used in the QRNG without introducing significant bias in the random number and may enable multiplexing of multiple random numbers. The amplifier may also desensitize the photon generator to fluctuations in power supplied thereto while operating in the spontaneous mode. In one embodiment, the photon emitter and amplifier may be a tapered diode amplifier.
Randomness: quantum versus classical
Khrennikov, Andrei
2015-01-01
Recent tremendous development of quantum information theory led to a number of quantum technological projects, e.g., quantum random generators. This development stimulates a new wave of interest in quantum foundations. One of the most intriguing problems of quantum foundations is elaboration of a consistent and commonly accepted interpretation of quantum state. Closely related problem is clarification of the notion of quantum randomness and its interrelation with classical randomness. In this short review we shall discuss basics of classical theory of randomness (which by itself is very complex and characterized by diversity of approaches) and compare it with irreducible quantum randomness. The second part of this review is devoted to the information interpretation of quantum mechanics (QM) in the spirit of Zeilinger and Brukner (and QBism of Fuchs et al.) and physics in general (e.g., Wheeler's "it from bit") as well as digital philosophy of Chaitin (with historical coupling to ideas of Leibnitz). Finally, w...
Randomness: Quantum versus classical
Khrennikov, Andrei
2016-05-01
Recent tremendous development of quantum information theory has led to a number of quantum technological projects, e.g. quantum random generators. This development had stimulated a new wave of interest in quantum foundations. One of the most intriguing problems of quantum foundations is the elaboration of a consistent and commonly accepted interpretation of a quantum state. Closely related problem is the clarification of the notion of quantum randomness and its interrelation with classical randomness. In this short review, we shall discuss basics of classical theory of randomness (which by itself is very complex and characterized by diversity of approaches) and compare it with irreducible quantum randomness. We also discuss briefly “digital philosophy”, its role in physics (classical and quantum) and its coupling to the information interpretation of quantum mechanics (QM).
Random attractors for asymptotically upper semicompact multivalue random semiflows
无
2007-01-01
The present paper studied the dynamics of some multivalued random semiflow. The corresponding concept of random attractor for this case was introduced to study asymptotic behavior. The existence of random attractor of multivalued random semiflow was proved under the assumption of pullback asymptotically upper semicompact, and this random attractor is random compact and invariant. Furthermore, if the system has ergodicity, then this random attractor is the limit set of a deterministic bounded set.
A random walk with a branching system in random environments
Ying-qiu LI; Xu LI; Quan-sheng LIU
2007-01-01
We consider a branching random walk in random environments, where the particles are reproduced as a branching process with a random environment (in time), and move independently as a random walk on Z with a random environment (in locations). We obtain the asymptotic properties on the position of the rightmost particle at time n, revealing a phase transition phenomenon of the system.
Gurau, Razvan
2016-01-01
Preface to the SIGMA special issue "Tensor Models, Formalism and Applications." The SIGMA special issue "Tensor Models, Formalism and Applications" is a collection of eight excellent, up to date reviews \\cite{Ryan:2016sundry,Bonzom:2016dwy,Rivasseau:2016zco,Carrozza:2016vsq,Krajewski:2016svb,Rivasseau:2016rgt,Tanasa:2015uhr,Gielen:2016dss} on random tensor models. The reviews combine pedagogical introductions meant for a general audience with presentations of the most recent developments in the field. This preface aims to give a condensed panoramic overview of random tensors as the natural generalization of random matrices to higher dimensions.
Aperiodic Quantum Random Walks
Ribeiro, P; Mosseri, R; Ribeiro, Pedro; Milman, Perola; Mosseri, Remy
2004-01-01
We generalize the quantum random walk protocol for a particle in a one-dimensional chain, by using several types of biased quantum coins, arranged in aperiodic sequences, in a manner that leads to a rich variety of possible wave function evolutions. Quasiperiodic sequences, following the Fibonacci prescription, are of particular interest, leading to a sub-ballistic wavefunction spreading. In contrast, random sequences leads to diffusive spreading, similar to the classical random walk behaviour. We also describe how to experimentally implement these aperiodic sequences.
de Matos, Christiano J S; Brito-Silva, Antônio M; Gámez, M A Martinez; Gomes, Anderson S L; de Araújo, Cid B
2007-01-01
We investigate the effects of two dimensional confinement on the lasing properties of a classical random laser system operating in the incoherent feedback (diffusive) regime. A suspension of 250nm rutile (TiO2) particles in a Rhodamine 6G solution was inserted into the hollow core of a photonic crystal fiber (PCF) generating the first random fiber laser and a novel quasi-one-dimensional RL geometry. Comparison with similar systems in bulk format shows that the random fiber laser presents an efficiency that is at least two orders of magnitude higher.
Nakagawa, Toshio
2014-01-01
Exploring random maintenance models, this book provides an introduction to the implementation of random maintenance, and it is one of the first books to be written on this subject. It aims to help readers learn new techniques for applying random policies to actual reliability models, and it provides new theoretical analyses of various models including classical replacement, preventive maintenance and inspection policies. These policies are applied to scheduling problems, backup policies of database systems, maintenance policies of cumulative damage models, and reliability of random redundant systems. Reliability theory is a major concern for engineers and managers, and in light of Japan’s recent earthquake, the reliability of large-scale systems has increased in importance. This also highlights the need for a new notion of maintenance and reliability theory, and how this can practically be applied to systems. Providing an essential guide for engineers and managers specializing in reliability maintenance a...
Wanscher, Jørgen Bundgaard; Sørensen, Majken Vildrik
2006-01-01
highly uniform multidimensional draws, which are highly relevant for todays traffic models. This paper shows among others combined shuffling and scrambling seems needless, that scrambling gives the lowest correlation and that there are detectable differences between random numbers, dependent...
Gallesco, Christophe; Popov, Serguei; Vachkovskaia, Marina
2010-01-01
A spider consists of several, say $N$, particles. Particles can jump independently according to a random walk if the movement does not violate some given restriction rules. If the movement violates a rule it is not carried out. We consider random walk in random environment (RWRE) on $\\Z$ as underlying random walk. We suppose the environment $\\omega=(\\omega_x)_{x \\in \\Z}$ to be elliptic, with positive drift and nestling, so that there exists a unique positive constant $\\kappa$ such that $\\E[((1-\\omega_0)/\\omega_0)^{\\kappa}]=1$. The restriction rules are kept very general; we only assume transitivity and irreducibility of the spider. The main result is that the speed of a spider is positive if $\\kappa/N>1$ and null if $\\kappa/N<1$. In particular, if $\\kappa/N <1$ a spider has null speed but the speed of a (single) RWRE is positive.
MISHINA, Yohei; MURATA, Ryuei; YAMAUCHI, Yuji; YAMASHITA, Takayoshi; FUJIYOSHI, Hironobu
2015-01-01
.... Within machine learning, a Random Forest is a multi-class classifier with high-performance classification, achieved using bagging and feature selection, and is capable of high-speed training and classification...
2010-01-01
We consider the problem of reinforcement learning in high-dimensional spaces when the number of features is bigger than the number of samples. In particular, we study the least-squares temporal difference (LSTD) learning algorithm when a space of low dimension is generated with a random projection from a high-dimensional space. We provide a thorough theoretical analysis of the LSTD with random projections and derive performance bounds for the resulting algorithm. We also show how the error of...
Zyczkowski, K.; Slomczynski, W.; Kus, M.; Sommers, H. -J.
2001-01-01
An ensemble of random unistochastic (orthostochastic) matrices is defined by taking squared moduli of elements of random unitary (orthogonal) matrices distributed according to the Haar measure on U(N) (or O(N), respectively). An ensemble of symmetric unistochastic matrices is obtained with use of unitary symmetric matrices pertaining to the circular orthogonal ensemble. We study the distribution of complex eigenvalues of bistochastic, unistochastic and ortostochastic matrices in the complex p...
Quantum randomness and unpredictability
Jaeger, Gregg [Quantum Communication and Measurement Laboratory, Department of Electrical and Computer Engineering and Division of Natural Science and Mathematics, Boston University, Boston, MA (United States)
2017-06-15
Quantum mechanics is a physical theory supplying probabilities corresponding to expectation values for measurement outcomes. Indeed, its formalism can be constructed with measurement as a fundamental process, as was done by Schwinger, provided that individual measurements outcomes occur in a random way. The randomness appearing in quantum mechanics, as with other forms of randomness, has often been considered equivalent to a form of indeterminism. Here, it is argued that quantum randomness should instead be understood as a form of unpredictability because, amongst other things, indeterminism is not a necessary condition for randomness. For concreteness, an explication of the randomness of quantum mechanics as the unpredictability of quantum measurement outcomes is provided. Finally, it is shown how this view can be combined with the recently introduced view that the very appearance of individual quantum measurement outcomes can be grounded in the Plenitude principle of Leibniz, a principle variants of which have been utilized in physics by Dirac and Gell-Mann in relation to the fundamental processes. This move provides further support to Schwinger's ''symbolic'' derivation of quantum mechanics from measurement. (copyright 2016 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Modelling the dynamics of stem cells in colonic crypts
Sirio, Orozco-Fuentes; Barrio, Rafael A.
2017-02-01
We present a theoretical and computational framework to model the colonic crypt organisation in the human intestine. We construct a theoretical and computational framework to model the colonic crypt behaviour, using a Voronoi tessellation to represent each cell and elastic forces between them we addressed how their dynamical disfunction can lead to tumour masses and cancer. Our results indicate that for certain parameters the crypt is in a homeostatic state, but slight changes on their values can disrupt this behaviour.
Sunflower Array Antenna with Adjustable Density Taper
Maria Carolina Viganó; Giovanni Toso; Gerard Caille; Cyril Mangenot; Lager, Ioan E.
2009-01-01
A deterministic procedure to design a nonperiodic planar array radiating a rotationally symmetric pencil beam pattern with an adjustable sidelobe level is proposed. The elements positions are derived by modifying the peculiar locations of the sunflower seeds in such a way that the corresponding spatial density fits a Taylor amplitude tapering law which guarantees the pattern requirements in terms of beamwidth and sidelobe level. Different configurations, based on a Voronoi cell spatial tessel...
Thermodynamically consistent mesoscopic fluid particle models for a van der Waals fluid
Serrano, Mar; Español, Pep
2000-01-01
The GENERIC structure allows for a unified treatment of different discrete models of hydrodynamics. We first propose a finite volume Lagrangian discretization of the continuum equations of hydrodynamics through the Voronoi tessellation. We then show that a slight modification of these discrete equations has the GENERIC structure. The GENERIC structure ensures thermodynamic consistency and allows for the introduction of correct thermal noise. In this way, we obtain a consistent discrete model ...
Pycobra: A Python Toolbox for Ensemble Learning and Visualisation
Guedj, Benjamin; Srinivasa Desikan, Bhargav
2017-01-01
We introduce \\texttt{pycobra}, a Python library devoted to ensemble learning (regression and classification) and visualisation. Its main assets are the implementation of several ensemble learning algorithms, a flexible and generic interface to compare and blend any existing machine learning algorithm available in Python libraries (as long as a \\texttt{predict} method is given), and visualisation tools such as Voronoi tessellations. \\texttt{pycobra} is fully \\texttt{scikit-learn} compatible an...
Fatigue-crack-initiation numerical modelling of a Ni-base powder metallurgy alloy
2012-01-01
A simplified three-dimensional numerical model was presented to simulate the micro-crack nucleation and growth to some predefined dimension(approximately 0.38 mm) on the throat surface of a Ni-base powder metallurgy(PM) specimen.The numerical simulation of micro-crack initiation was based on the Tanaka-Mura micro-crack initiation models,where individual grains of the mesoscopic model were simulated using the Voronoi tessellation.Four improvements were made in the model.(1) Considering crack initiation along with 12 principal slip systems on octahedral slip planes of face centered cubic(FCC) crystal in three-dimensional(3-D) models.(2) Considering the effect of secondary phase precipitate due to impinging slip and dislocation pileup.(3) The Tanaka-Mura theory of fatigue-crack-initiation from notches was applied to simulate the crack initiation from another crack tip.(4) The coalescence of random initiated micro-cracks was simulated once they intersected with each other and a macro-crack was finally formed.The calculated results were in good agreement with the experimental data which verified the rationality of the simulation model.The applicability of the proposed model for treating fatigue-crack-initiation life in engineering structures was preliminarily achieved.%A simplified three-dimensional numerical model was presented to simulate the micro-crack nucleation and growth to some predefined dimension（approximately 0.38 mm） on the throat surface of a Ni-base powder metallurgy（PM） specimen.The numerical simulation of micro-crack initiation was based on the Tanaka-Mura micro-crack initiation models,where individual grains of the mesoscopic model were simulated using the Voronoi tessellation.Four improvements were made in the model.（1） Considering crack initiation along with 12 principal slip systems on octahedral slip planes of face centered cubic（FCC） crystal in three-dimensional（3-D） models.（2） Considering the effect of secondary phase
Generating random density matrices
Zyczkowski, Karol; Nechita, Ion; Collins, Benoit
2010-01-01
We study various methods to generate ensembles of quantum density matrices of a fixed size N and analyze the corresponding probability distributions P(x), where x denotes the rescaled eigenvalue, x=N\\lambda. Taking a random pure state of a two-partite system and performing the partial trace over one subsystem one obtains a mixed state represented by a Wishart--like matrix W=GG^{\\dagger}, distributed according to the induced measure and characterized asymptotically, as N -> \\infty, by the Marchenko-Pastur distribution. Superposition of k random maximally entangled states leads to another family of explicitly derived distributions, describing singular values of the sum of k independent random unitaries. Taking a larger system composed of 2s particles, constructing $s$ random bi-partite states, performing the measurement into a product of s-1 maximally entangled states and performing the partial trace over the remaining subsystem we arrive at a random state characterized by the Fuss-Catalan distribution of order...
Random hypergraphs and algorithmics
Andriamampianina, Tsiriniaina
2008-01-01
Hypergraphs are structures that can be decomposed or described; in other words they are recursively countable. Here, we get exact and asymptotic enumeration results on hypergraphs by mean of exponential generating functions. The number of hypergraph component is bounded, as a generalisation of Wright inequalities for graphs: the proof is a combinatorial understanding of the structure by inclusion exclusion. Asymptotic results are obtained, thanks to generating functions proofs are at the end very easy to read, through complex analysis by saddle point method. By this way, we characterized: - the components with a given number of vertices and of hyperedges by the expected size of a random hypermatching in these structures. - the random hypergraphs (evolving hyperedge by hyperedge) according to the expected number of hyperedges when the first cycle appears in the evolving structure. This work is an open road to further works on random hypergraphs such as threshold phenomenon, tools used here seem to be sufficien...
Marini, Andrea
2015-01-01
Manipulating and controlling the optical energy flow inside random media is a research frontier of photonics and the basis of novel laser designs. In particular, light amplification in randomly dispersed active inclusions under external pumping has been extensively investigated, although it still lacks external tunability, reproducibility, and control over the beam spatial pattern, thus hindering its application in practical devices. Here we show that a graphene random metamaterial provides the means to overcome these limitations through its extraordinarily-low threshold for saturable absorption. The nonlinear properties of nano-graphene combined with an optically pumped gain medium allow us to controllably tune the system from chaotic to stable single-mode lasing. Our results hold great potential for the development of single-mode cavity-free lasers with engineered beam patterns in disordered media.
Yoneyama, Kazuki; Miyagawa, Satoshi; Ohta, Kazuo
This work focuses on a vulnerability of hash functions due to sloppy usages or implementations in the real world. If our cryptographic research community succeeded in the development of a perfectly secure random function as the random oracle, it might be broken in some sense by invalid uses. In this paper, we propose a new variant of the random oracle model in order to analyze the security of cryptographic protocols under the situation of an invalid use of hash functions. Our model allows adversaries to obtain contents of the hash list of input and output pairs arbitrarily. Also, we analyze the security of several prevailing protocols (FDH, OAEP, Cramer-Shoup cryptosystem, Kurosawa-Desmedt cryptosystem, NAXOS) in our model. As the result of analyses, we clarify that FDH and Cramer-Shoup cryptosystem are still secure but others are insecure in our model. This result shows the separation between our model and the standard model.
Paolini, Enrico; Stefanovic, Cedomir; Liva, Gianluigi
2015-01-01
, in which the structure of the access protocol can be mapped to a structure of an erasure-correcting code defined on graph. This opens the possibility to use coding theory and tools for designing efficient random access protocols, offering markedly better performance than ALOHA. Several instances of coded......The rise of machine-to-machine communications has rekindled the interest in random access protocols as a support for a massive number of uncoordinatedly transmitting devices. The legacy ALOHA approach is developed under a collision model, where slots containing collided packets are considered...... as waste. However, if the common receiver (e.g., base station) is capable to store the collision slots and use them in a transmission recovery process based on successive interference cancellation, the design space for access protocols is radically expanded. We present the paradigm of coded random access...
Some case studies of random walks in dynamic random environments
Soares dos Santos, Renato
2012-01-01
This thesis is dedicated to the study of random walks in dynamic random environments. These are models for the motion of a tracer particle in a disordered medium, which is called a static random environment if it stays constant in time, or dynamic otherwise. The evolution of the random walk is defi
RANDOM SINGULAR INTEGRAL OF RANDOM PROCESS WITH SECOND ORDER MOMENT
Wang Chuanrong
2005-01-01
This paper discussses the random singular integral of random process with second order moment, establishes the concepts of the random singular integral and proves that it's a linear bounded operator of space Hα(L)(m, s). Then Plemelj formula and some other properties for random singular integral are proved.
Ohira, Toru
2016-01-01
We present here a system with collection of random walks relaying a signal in one dimension with a presence of a delay. We are interested in the time for a signal to travel from one end (start) to the other end (finish) of the lined group of random walkers. It is found that there is an optimal number of walkers for the signal to travel fastest if the delay is present. We discuss implications of this model and associated behaviors to physical and biological systems.
Freno, Antonino
2011-01-01
This book presents an exciting new synthesis of directed and undirected, discrete and continuous graphical models. Combining elements of Bayesian networks and Markov random fields, the newly introduced hybrid random fields are an interesting approach to get the best of both these worlds, with an added promise of modularity and scalability. The authors have written an enjoyable book---rigorous in the treatment of the mathematical background, but also enlivened by interesting and original historical and philosophical perspectives. -- Manfred Jaeger, Aalborg Universitet The book not only marks an
Bruzda, Wojciech [Mark Kac Complex Systems Research Centre, Institute of Physics, Jagiellonian University, ul. Reymonta 4, 30-059 Krakow (Poland)], E-mail: wojtek@gorce.if.uj.edu.pl; Cappellini, Valerio [Mark Kac Complex Systems Research Centre, Institute of Physics, Jagiellonian University, ul. Reymonta 4, 30-059 Krakow (Poland); Sommers, Hans-Juergen [Fachbereich Physik, Universitaet Duisburg-Essen, Campus Duisburg, 47048 Duisburg (Germany); Zyczkowski, Karol [Mark Kac Complex Systems Research Centre, Institute of Physics, Jagiellonian University, ul. Reymonta 4, 30-059 Krakow (Poland); Centrum Fizyki Teoretycznej, Polska Akademia Nauk, Al. Lotnikow 32/44, 02-668 Warszawa (Poland)
2009-01-12
We define a natural ensemble of trace preserving, completely positive quantum maps and present algorithms to generate them at random. Spectral properties of the superoperator {phi} associated with a given quantum map are investigated and a quantum analogue of the Frobenius-Perron theorem is proved. We derive a general formula for the density of eigenvalues of {phi} and show the connection with the Ginibre ensemble of real non-symmetric random matrices. Numerical investigations of the spectral gap imply that a generic state of the system iterated several times by a fixed generic map converges exponentially to an invariant state.
Zyczkowski, Karol [Centrum Fizyki Teoretycznej, Polska Akademia Nauk, Al. Lotnikow 32/44, 02-668 Warsaw (Poland); Kus, Marek [Centrum Fizyki Teoretycznej, Polska Akademia Nauk, Al. Lotnikow 32/44, 02-668 Warsaw (Poland); Slomczynski, Wojciech [Instytut Matematyki, Uniwersytet Jagiellonski, ul. Reymonta 4, 30-059 Cracow (Poland); Sommers, Hans-Juergen [Fachbereich 7 Physik, Universitaet Essen, 45117 Essen (Germany)
2003-03-28
An ensemble of random unistochastic (orthostochastic) matrices is defined by taking squared moduli of elements of random unitary (orthogonal) matrices distributed according to the Haar measure on U(N) (or O(N)). An ensemble of symmetric unistochastic matrices is obtained with use of unitary symmetric matrices pertaining to the circular orthogonal ensemble. We study the distribution of complex eigenvalues of bistochastic, unistochastic and orthostochastic matrices in the complex plane. We compute averages (entropy, traces) over the ensembles of unistochastic matrices and present inequalities concerning the entropies of products of bistochastic matrices.
Competition on the rocks: community growth and tessellation.
Espen Jettestuen
Full Text Available Crustose lichen communities on rocks exhibit fascinating spatial mosaics resembling political maps of nations or municipalities. Although the establishment and development of biological populations are important themes in ecology, our understanding of the formation of such patterns on the rocks is still in its infancy. Here, we present a novel model of the concurrent growth, establishment and interaction of lichens. We introduce an inverse technique based on Monte Carlo simulations to test our model on field samples of lichen communities. We derive an expression for the time needed for a community to cover a surface and predict the historical spatial dynamics of field samples. Lichens are frequently used for dating the time of exposure of rocks in glacial deposits, lake retreats or rock falls. We suggest our method as a way to improve the dating.
View-Dependent Tessellation and Simulation of Ocean Surfaces
Anna Puig-Centelles
2014-01-01
Full Text Available Modeling and rendering realistic ocean scenes have been thoroughly investigated for many years. Its appearance has been studied and it is possible to find very detailed simulations where a high degree of realism is achieved. Nevertheless, among the solutions to ocean rendering, real-time management of the huge heightmaps that are necessary for rendering an ocean scene is still not solved. We propose a new technique for simulating the ocean surface on GPU. This technique is capable of offering view-dependent approximations of the mesh while maintaining coherence among the extracted approximations. This feature is very important as most solutions previously presented must retessellate from the initial mesh. Our solution is able to use the latest extracted approximation when refining or coarsening the mesh.
The DTFE public software: The Delaunay Tessellation Field Estimator code
Cautun, Marius C.; van de Weygaert, Rien
2011-01-01
We present the DTFE public software, a code for reconstructing fields from a discrete set of samples/measurements using the maximum of information contained in the point distribution. The code is written in C++ using the CGAL library and is parallelized using OpenMP. The software was designed for th
The DTFE public software : The Delaunay Tessellation Field Estimator code
Cautun, Marius C.; van de Weygaert, Rien
2011-01-01
We present the DTFE public software, a code for reconstructing fields from a discrete set of samples/measurements using the maximum of information contained in the point distribution. The code is written in C++ using the CGAL library and is parallelized using OpenMP. The software was designed for th
Adaptive Geometry Shader Tessellation for Massive Geometry Display
2015-03-01
but concurrent experiments with another approach using Intel’s Embree raytracing engine indicate raytracing requires approximately 30 s of... raytracing . An additional problem arose when performance testing indicated that a significant portion of the bottleneck in OSG’s rasterization-based...satisfying 30 frames/s. This strongly suggests that a hybrid raytracing /rasterization rendering system would be ideal for SLAD applications. Both NVIDIA and
[Intel random number generator-based true random number generator].
Huang, Feng; Shen, Hong
2004-09-01
To establish a true random number generator on the basis of certain Intel chips. The random numbers were acquired by programming using Microsoft Visual C++ 6.0 via register reading from the random number generator (RNG) unit of an Intel 815 chipset-based computer with Intel Security Driver (ISD). We tested the generator with 500 random numbers in NIST FIPS 140-1 and X(2) R-Squared test, and the result showed that the random number it generated satisfied the demand of independence and uniform distribution. We also compared the random numbers generated by Intel RNG-based true random number generator and those from the random number table statistically, by using the same amount of 7500 random numbers in the same value domain, which showed that the SD, SE and CV of Intel RNG-based random number generator were less than those of the random number table. The result of u test of two CVs revealed no significant difference between the two methods. Intel RNG-based random number generator can produce high-quality random numbers with good independence and uniform distribution, and solves some problems with random number table in acquisition of the random numbers.
Ben-Ari, Morechai
2004-01-01
The term "random" is frequently used in discussion of the theory of evolution, even though the mathematical concept of randomness is problematic and of little relevance in the theory. Therefore, since the core concept of the theory of evolution is the non-random process of natural selection, the term random should not be used in teaching the…
Testing for Subcellular Randomness
Okunoye, Babatunde O
2008-01-01
Statistical tests were conducted on 1,000 numbers generated from the genome of Bacteriophage T4, obtained from GenBank with accession number AF158101.The numbers passed the non-parametric, distribution-free tests.Deoxyribonucleic acid was discovered to be a random number generator, existent in nature.
Randomness Of Amoeba Movements
Hashiguchi, S.; Khadijah, Siti; Kuwajima, T.; Ohki, M.; Tacano, M.; Sikula, J.
2005-11-01
Movements of amoebas were automatically traced using the difference between two successive frames of the microscopic movie. It was observed that the movements were almost random in that the directions and the magnitudes of the successive two steps are not correlated, and that the distance from the origin was proportional to the square root of the step number.
Jorge Berger
2004-03-01
Full Text Available I review some selected situations in which order builds up from randomness, or a losing trend turns into winning. Except for Section 4 (which is mine, all cases are well documented and the price paid to achieve order is apparent.
Uniform random number generators
Farr, W. R.
1971-01-01
Methods are presented for the generation of random numbers with uniform and normal distributions. Subprogram listings of Fortran generators for the Univac 1108, SDS 930, and CDC 3200 digital computers are also included. The generators are of the mixed multiplicative type, and the mathematical method employed is that of Marsaglia and Bray.
Poisson Random Variate Generation.
1981-12-01
Poisson have been proposed. Atkinson [5] includes the approach developed in Marsaglia £15) and Norman and Cannon £16) which is based on composition...34, Naval Research Logistics Quarterly, 26, 3, 403-413. 15. Marsaglia , G. (1963). "Generating Discrete Random Variables in a Computer", Communications
Photographic dataset: random peppercorns
Helenius, Teemu
2016-01-01
This is a photographic dataset collected for testing image processing algorithms. The idea is to have sets of different but statistically similar images. In this work the images show randomly distributed peppercorns. The dataset is made available at www.fips.fi/photographic_dataset.php .
Capacity constrained blue-noise sampling on surfaces
Zhang, Sen
2015-11-27
We present a novel method for high-quality blue-noise sampling on mesh surfaces with prescribed cell-sizes for the underlying tessellation (capacity constraint). Unlike the previous surface sampling approach that only uses capacity constraints as a regularizer of the Centroidal Voronoi Tessellation (CVT) energy, our approach enforces an exact capacity constraint using the restricted power tessellation on surfaces. Our approach is a generalization of the previous 2D blue noise sampling technique using an interleaving optimization framework. We further extend this framework to handle multi-capacity constraints. We compare our approach with several state-of-the-art methods and demonstrate that our results are superior to previous work in terms of preserving the capacity constraints.
Nandan, Shyam; Ouillon, Guy; Sornette, Didier; Wiemer, Stefan
2016-04-01
The ETAS model is widely employed to model the spatio-temporal distribution of earthquakes, generally using spatially invariant parameters, which is most likely a gross simplification considering the extremely heterogeneous structure of the Earth's crust. We propose an efficient method for the estimation of spatially varying parameters, using an expectation maximization (EM) algorithm and spatial Voronoi tessellations. We assume that each Voronoi cell is characterized by a set of eight constant ETAS parameters. For a given number of randomly distributed cells, Vi=1 to N, we jointly invert the ETAS parameters within each cell using an EM algorithm. This process is progressively repeated several times for a given N (which controls the complexity), which is itself increased incrementally. We use the Bayesian Information Criterion (BIC) to rank all the inverted models given their likelihood and complexity and select the top 1% models to compute the average model at any location. Using a synthetic catalog, we also check that the proposed method correctly inverts the known parameters. We apply the proposed method to earthquakes (M>=3) included in the ANSS catalog that occurred within the time period 1981-2016 in the spatial polygon defined by RELM/CSEP around California. The results indicate significant spatial variation of the ETAS parameters. Using these spatially variable estimates of ETAS parameters, we are better equipped to answer some important questions: (1) What is the seismic hazard (both long- and short-term) in a given region? (2) What kind of earthquakes dominate triggering? (3) are there regions where earthquakes are most likely preceded by foreshocks? Last but not the least, a possible correlation of the spatially varying ETAS parameters with spatially variable geophysical properties can lead to an improved understanding of the physics of earthquake triggering beside providing physical meaning to the parameters of the purely statistical ETAS model.
Locally-orthogonal, unstructured grid-generation for general circulation modelling on the sphere
Engwirda, Darren
2016-01-01
An algorithm for the generation of non-uniform, locally-orthogonal staggered unstructured grids on spheroidal geometries is described. This technique is designed to generate high-quality staggered Voronoi/Delaunay dual meshes appropriate for general circulation modelling on the sphere, including applications to atmospheric simulation, ocean-modelling and numerical weather predication. Using a recently developed Frontal-Delaunay refinement technique, a method for the construction of guaranteed-quality, unstructured spheroidal Delaunay triangulations is introduced. A locally-orthogonal polygonal grid, derived from the associated Voronoi diagram, is computed as the staggered dual. The initial staggered Voronoi/Delaunay tessellation is iteratively improved through hill-climbing optimisation techniques. It is shown that this approach typically produces grids with very high element quality and smooth grading characteristics, while imposing relatively low computational expense. Initial results are presented for a se...
Voiculescu, Dan; Nica, Alexandru
1992-01-01
This book presents the first comprehensive introduction to free probability theory, a highly noncommutative probability theory with independence based on free products instead of tensor products. Basic examples of this kind of theory are provided by convolution operators on free groups and by the asymptotic behavior of large Gaussian random matrices. The probabilistic approach to free products has led to a recent surge of new results on the von Neumann algebras of free groups. The book is ideally suited as a textbook for an advanced graduate course and could also provide material for a seminar. In addition to researchers and graduate students in mathematics, this book will be of interest to physicists and others who use random matrices.
Hashing, Randomness and Dictionaries
Pagh, Rasmus
time and memory space. To some extent we also consider lower bounds, i.e., we attempt to show limitations on how efficient algorithms are possible. A central theme in the thesis is randomness. Randomized algorithms play an important role, in particular through the key technique of hashing. Additionally...... algorithms community. We work (almost) exclusively with a model, a mathematical object that is meant to capture essential aspects of a real computer. The main model considered here (and in most of the literature on dictionaries) is a unit cost RAM with a word size that allows a set element to be stored...... in one word. We consider several variants of the dictionary problem, as well as some related problems. The problems are studied mainly from an upper bound perspective, i.e., we try to come up with algorithms that are as efficient as possible with respect to various computing resources, mainly computation...
Jaeger, Manfred
2009-01-01
We investigate the relation between the behavior of non-deterministic systems under fairness constraints, and the behavior of probabilistic systems. To this end, first a framework based on computable stopping strategies is developed that provides a common foundation for describing both fair...... and probabilistic behavior. On the basis of stopping strategies it is then shown that fair behavior corresponds in a precise sense to random behavior in the sense of Martin-Löf's definition of randomness. We view probabilistic systems as concrete implementations of more abstract non-deterministic systems. Under...... this perspective the question is investigated what probabilistic properties are needed in such an implementation to guarantee (with probability one) certain required fairness properties in the behavior of the probabilistic system. Generalizing earlier concepts of ε -bounded transition probabilities, we introduce...
Anwer Khurshid
2012-07-01
Full Text Available Normal 0 false false false EN-US X-NONE X-NONE In this paper, it is shown that a complex multivariate random variable is a complex multivariate normal random variable of dimensionality if and only if all nondegenerate complex linear combinations of have a complex univariate normal distribution. The characteristic function of has been derived, and simpler forms of some theorems have been given using this characterization theorem without assuming that the variance-covariance matrix of the vector is Hermitian positive definite. Marginal distributions of have been given. In addition, a complex multivariate t-distribution has been defined and the density derived. A characterization of the complex multivariate t-distribution is given. A few possible uses of this distribution have been suggested.
Kahle, Matthew
2009-01-01
We study the expected topological properties of Cech and Vietoris-Rips complexes built on randomly sampled points in R^d. These are, in some cases, analogues of known results for connectivity and component counts for random geometric graphs. However, an important difference in this setting is that homology is not monotone in the underlying parameter. In the sparse range, we compute the expectation and variance of the Betti numbers, and establish Central Limit Theorems and concentration of measure. In the dense range, we introduce Morse theoretic arguments to bound the expectation of the Betti numbers, which is the main technical contribution of this article. These results provide a detailed probabilistic picture to compare with the topological statistics of point cloud data.
Hokr, Brett H; Mason, John D; Beier, Hope T; Rockwll, Benjamin A; Thomas, Robert J; Noojin, Gary D; Petrov, Georgi I; Golovan, Leonid A; Yakovlev, Vladislav V
2013-01-01
Propagation of light in a highly scattering medium is among the most fascinating optical effect that everyone experiences on an everyday basis and possesses a number of fundamental problems which have yet to be solved. Conventional wisdom suggests that non-linear effects do not play a significant role because the diffusive nature of scattering acts to spread the intensity, dramatically weakening these effects. We demonstrate the first experimental evidence of lasing on a Raman transition in a bulk three-dimensional random media. From a practical standpoint, Raman transitions allow for spectroscopic analysis of the chemical makeup of the sample. A random Raman laser could serve as a bright Raman source allowing for remote, chemically specific, identification of powders and aerosols. Fundamentally, the first demonstration of this new light source opens up an entire new field of study into non-linear light propagation in turbid media, with the most notable application related to non-invasive biomedical imaging.
Exponential random graph models
Fronczak, Agata
2012-01-01
Nowadays, exponential random graphs (ERGs) are among the most widely-studied network models. Different analytical and numerical techniques for ERG have been developed that resulted in the well-established theory with true predictive power. An excellent basic discussion of exponential random graphs addressed to social science students and researchers is given in [Anderson et al., 1999][Robins et al., 2007]. This essay is intentionally designed to be more theoretical in comparison with the well-known primers just mentioned. Given the interdisciplinary character of the new emerging science of complex networks, the essay aims to give a contribution upon which network scientists and practitioners, who represent different research areas, could build a common area of understanding.
Random vibrations theory and practice
Wirsching, Paul H; Ortiz, Keith
1995-01-01
Random Vibrations: Theory and Practice covers the theory and analysis of mechanical and structural systems undergoing random oscillations due to any number of phenomena— from engine noise, turbulent flow, and acoustic noise to wind, ocean waves, earthquakes, and rough pavement. For systems operating in such environments, a random vibration analysis is essential to the safety and reliability of the system. By far the most comprehensive text available on random vibrations, Random Vibrations: Theory and Practice is designed for readers who are new to the subject as well as those who are familiar with the fundamentals and wish to study a particular topic or use the text as an authoritative reference. It is divided into three major sections: fundamental background, random vibration development and applications to design, and random signal analysis. Introductory chapters cover topics in probability, statistics, and random processes that prepare the reader for the development of the theory of random vibrations a...
Palindromic random trigonometric polynomials
Conrey, J. Brian; Farmer, David W.; Imamoglu, Özlem
2008-01-01
We show that if a real trigonometric polynomial has few real roots, then the trigonometric polynomial obtained by writing the coefficients in reverse order must have many real roots. This is used to show that a class of random trigonometric polynomials has, on average, many real roots. In the case that the coefficients of a real trigonometric polynomial are independently and identically distributed, but with no other assumptions on the distribution, the expected fraction of real zeros is at l...
Quenched moderate deviations principle for random walk in random environment
无
2010-01-01
We derive a quenched moderate deviations principle for the one-dimensional nearest random walk in random environment,where the environment is assumed to be stationary and ergodic.The approach is based on hitting time decomposition.
Certified randomness in quantum physics.
Acín, Antonio; Masanes, Lluis
2016-12-07
The concept of randomness plays an important part in many disciplines. On the one hand, the question of whether random processes exist is fundamental for our understanding of nature. On the other, randomness is a resource for cryptography, algorithms and simulations. Standard methods for generating randomness rely on assumptions about the devices that are often not valid in practice. However, quantum technologies enable new methods for generating certified randomness, based on the violation of Bell inequalities. These methods are referred to as device-independent because they do not rely on any modelling of the devices. Here we review efforts to design device-independent randomness generators and the associated challenges.
Certified randomness in quantum physics
Acín, Antonio; Masanes, Lluis
2016-12-01
The concept of randomness plays an important part in many disciplines. On the one hand, the question of whether random processes exist is fundamental for our understanding of nature. On the other, randomness is a resource for cryptography, algorithms and simulations. Standard methods for generating randomness rely on assumptions about the devices that are often not valid in practice. However, quantum technologies enable new methods for generating certified randomness, based on the violation of Bell inequalities. These methods are referred to as device-independent because they do not rely on any modelling of the devices. Here we review efforts to design device-independent randomness generators and the associated challenges.
Random Response of Linear Viscoelastic Systems under Random Excitation
张天舒; 方同
2001-01-01
A method of analyzing random response of linear viscoelastic systems under random excitation has been presented. The covariance matrices of random responses of a single-degree-freedom linear viscoelastic system subjected to stationary white noise and filtered white noise excitations have been obtained in closed form. For illustration, a numerical example has been included. It is observed that viscoelasticity has damping effect on the mean square random responses of the system, the higher is viscoelastic behavior, the higher the damping effect.
ON THE RANGE OF RANDOM WALKS IN RANDOM ENVIRONMENT
ZHOUXIANYIN
1995-01-01
The range of roaldom walk on Zd in symmetric random environment is investigated. As results, it is proved that the strong law of large numbers for the range of random walk oil Zd in some random environments holds if d > 3, and a weak law of large numbers holds for d = 1.
Randomizing Roaches: Exploring the "Bugs" of Randomization in Experimental Design
Wagler, Amy; Wagler, Ron
2014-01-01
Understanding the roles of random selection and random assignment in experimental design is a central learning objective in most introductory statistics courses. This article describes an activity, appropriate for a high school or introductory statistics course, designed to teach the concepts, values and pitfalls of random selection and assignment…
李文; 张博
2012-01-01
Distance decay and Voronoi graph were applied to assess population size, area and number of people per unit area that green space serves in Harbin based on CIS map and field research. And the distribution of public parks in Harbin was evaluated. Result shows that the Wetland Park, lilac Park, Sports Park serve less than 300 people per hectare, and they develop well. Landscape Square, Lesong Square, Cnangqing Park, Jianguo Park, Qingbin Park, Taiping Park, and Shangzhi Park serve more than 40 000 people per hectare. Those parks cannot meet the needs of inhabitants. Three recommendations are put forward: to establish new public parks in some places in Harbin, increase investment in construction and maintenance of infrastructure in public parks, and to establish new public parks in the suburbs.%将哈尔滨市2009年GIS图和实地调研相结合,运用距离衰减和Voronoi图分析方法估计了哈尔滨城市公园绿地的服务总人数、面积及单位面积服务的人数,并对哈尔滨城市公园绿地布局进行了分析评价.结果表明:湿地公园、丁香公园、体育公园每公顷服务人数均小于300人,公园绿地发展良好；开发区景观广场、乐松广场、长青公园、建国公园、清滨公园、太平公园,尚志公园每公顷面积服务人数均已超过40 000人,无法满足周围游人的需要.根据研究结果提出了3点建议:局部地段建立新的公园绿地；加强对公园基础服务设施的建设和养护资金的投入；在郊区建立新的公园.
Recurrence for random dynamical systems
Marie, Philippe
2009-01-01
This paper is a first step in the study of the recurrence behavior in random dynamical systems and randomly perturbed dynamical systems. In particular we define a concept of quenched and annealed return times for systems generated by the composition of random maps. We moreover prove that for super-polynomially mixing systems, the random recurrence rate is equal to the local dimension of the stationary measure.
Random numbers from vacuum fluctuations
Shi, Yicheng; Chng, Brenda; Kurtsiefer, Christian
2016-07-01
We implement a quantum random number generator based on a balanced homodyne measurement of vacuum fluctuations of the electromagnetic field. The digitized signal is directly processed with a fast randomness extraction scheme based on a linear feedback shift register. The random bit stream is continuously read in a computer at a rate of about 480 Mbit/s and passes an extended test suite for random numbers.
Random recursive trees and the elephant random walk
Kürsten, Rüdiger
2016-03-01
One class of random walks with infinite memory, so-called elephant random walks, are simple models describing anomalous diffusion. We present a surprising connection between these models and bond percolation on random recursive trees. We use a coupling between the two models to translate results from elephant random walks to the percolation process. We calculate, besides other quantities, exact expressions for the first and the second moment of the root cluster size and of the number of nodes in child clusters of the first generation. We further introduce another model, the skew elephant random walk, and calculate the first and second moment of this process.
Precise Asymptotics for Random Matrices and Random Growth Models
Zhong Gen SU
2008-01-01
The author considers the largest eigenvalues of random matrices from Gaussian unitary ensemble and Laguerre unitary ensemble, and the rightmost charge in certain random growth models.We obtain some precise asymptotics results, which are in a sense similar to the precise asymptotics for sums of independent random variables in the context of the law of large numbers and complete convergence. Our proofs depend heavily upon the upper and lower tail estimates for random matrices and random growth models. The Tracy-Widom distribution plays a central role as well.
Bartsch, Christian; Kochler, Thomas; Müller, Sebastian; Popov, Serguei
2011-01-01
We consider a branching random walk on $\\Z$, where the particles behave differently in visited and unvisited sites. Informally, each site on the positive half-line contains initially a cookie. On the first visit of a site its cookie is removed and particles at positions with a cookie reproduce and move differently from particles on sites without cookies. Therefore, the movement and the reproduction of the particles depend on the previous behaviour of the population of particles. We study the question if the process is recurrent or transient, i.e., whether infinitely many particles visit the origin or not.
Barlow, Martin T; Sousi, Perla
2010-01-01
A recurrent graph $G$ has the infinite collision property if two independent random walks on $G$, started at the same point, collide infinitely often a.s. We give a simple criterion in terms of Green functions for a graph to have this property, and use it to prove that a critical Galton-Watson tree with finite variance conditioned to survive, the incipient infinite cluster in $\\Z^d$ with $d \\ge 19$ and the uniform spanning tree in $\\Z^2$ all have the infinite collision property. For power-law combs and spherically symmetric trees, we determine precisely the phase boundary for the infinite collision property.
Random Cell Identifiers Assignment
Robert Bestak
2012-01-01
Full Text Available Despite integration of advanced functions that enable Femto Access Points (FAPs to be deployed in a plug-and-play manner, the femtocell concept still cause several opened issues to be resolved. One of them represents an assignment of Physical Cell Identifiers (PCIs to FAPs. This paper analyses a random based assignment algorithm in LTE systems operating in diverse femtocell scenarios. The performance of the algorithm is evaluated by comparing the number of confusions for various femtocell densities, PCI ranges and knowledge of vicinity. Simulation results show that better knowledge of vicinity can significantly reduce the number of confusions events.
Deift, Percy
2009-01-01
This book features a unified derivation of the mathematical theory of the three classical types of invariant random matrix ensembles-orthogonal, unitary, and symplectic. The authors follow the approach of Tracy and Widom, but the exposition here contains a substantial amount of additional material, in particular, facts from functional analysis and the theory of Pfaffians. The main result in the book is a proof of universality for orthogonal and symplectic ensembles corresponding to generalized Gaussian type weights following the authors' prior work. New, quantitative error estimates are derive
Mathe, Laszlo; Lungeanu, Florin; Rasmussen, Peter Omand;
2010-01-01
This paper presents a new fixed carrier frequency random PWM method, where a new type of carrier wave is proposed for modulation. Based on the measurements, it is shown that the spread effect of the discrete components from the motor current spectra is very effective independent of the modulation...... index. The flat motor current spectrum generates an acoustical noise close to the white noise, which may improve the acoustical performance of the drive. The new carrier wave is easy to implement digitally, without employing any external circuits. The modulation method can be used in open, as well...
Senno, Gabriel; Bendersky, Ariel; Figueira, Santiago
2016-07-01
The concepts of randomness and non-locality are intimately intertwined outcomes of randomly chosen measurements over entangled systems exhibiting non-local correlations are, if we preclude instantaneous influence between distant measurement choices and outcomes, random. In this paper, we survey some recent advances in the knowledge of the interplay between these two important notions from a quantum information science perspective.
Investigating the Randomness of Numbers
Pendleton, Kenn L.
2009-01-01
The use of random numbers is pervasive in today's world. Random numbers have practical applications in such far-flung arenas as computer simulations, cryptography, gambling, the legal system, statistical sampling, and even the war on terrorism. Evaluating the randomness of extremely large samples is a complex, intricate process. However, the…
Random Selection for Drug Screening
Center for Human Reliability Studies
2007-05-01
Simple random sampling is generally the starting point for a random sampling process. This sampling technique ensures that each individual within a group (population) has an equal chance of being selected. There are a variety of ways to implement random sampling in a practical situation.
Strong Decomposition of Random Variables
Hoffmann-Jørgensen, Jørgen; Kagan, Abram M.; Pitt, Loren D.;
2007-01-01
A random variable X is stongly decomposable if X=Y+Z where Y=Φ(X) and Z=X-Φ(X) are independent non-degenerated random variables (called the components). It is shown that at least one of the components is singular, and we derive a necessary and sufficient condition for strong decomposability...... of a discrete random variable....
Random Numbers and Quantum Computers
McCartney, Mark; Glass, David
2002-01-01
The topic of random numbers is investigated in such a way as to illustrate links between mathematics, physics and computer science. First, the generation of random numbers by a classical computer using the linear congruential generator and logistic map is considered. It is noted that these procedures yield only pseudo-random numbers since…
Investigating the Randomness of Numbers
Pendleton, Kenn L.
2009-01-01
The use of random numbers is pervasive in today's world. Random numbers have practical applications in such far-flung arenas as computer simulations, cryptography, gambling, the legal system, statistical sampling, and even the war on terrorism. Evaluating the randomness of extremely large samples is a complex, intricate process. However, the…
How Random Is Quantum Randomness? An Experimental Approach
Calude, Cristian S; Dumitrescu, Monica; Svozil, Karl
2009-01-01
Our aim is to experimentally study the possibility of distinguishing between quantum sources of randomness--recently proved to be theoretically incomputable--and some well-known computable sources of pseudo-randomness. Incomputability is a necessary, but not sufficient "symptom" of "true randomness". We base our experimental approach on algorithmic information theory which provides characterizations of algorithmic random sequences in terms of the degrees of incompressibility of their finite prefixes. Algorithmic random sequences are incomputable, but the converse implication is false. We have performed tests of randomness on pseudo-random strings (finite sequences) of length $2^{32}$ generated with software (Mathematica, Maple), which are cyclic (so, strongly computable), the bits of $\\pi$, which is computable, but not cyclic, and strings produced by quantum measurements (with the commercial device Quantis and by the Vienna IQOQI group). Our empirical tests indicate quantitative differences, some statisticall...
Mak, Chi H; Pham, Phuong; Afif, Samir A; Goodman, Myron F
2015-09-01
Enzymes that rely on random walk to search for substrate targets in a heterogeneously dispersed medium can leave behind complex spatial profiles of their catalyzed conversions. The catalytic signatures of these random-walk enzymes are the result of two coupled stochastic processes: scanning and catalysis. Here we develop analytical models to understand the conversion profiles produced by these enzymes, comparing an intrusive model, in which scanning and catalysis are tightly coupled, against a loosely coupled passive model. Diagrammatic theory and path-integral solutions of these models revealed clearly distinct predictions. Comparison to experimental data from catalyzed deaminations deposited on single-stranded DNA by the enzyme activation-induced deoxycytidine deaminase (AID) demonstrates that catalysis and diffusion are strongly intertwined, where the chemical conversions give rise to new stochastic trajectories that were absent if the substrate DNA was homogeneous. The C→U deamination profiles in both analytical predictions and experiments exhibit a strong contextual dependence, where the conversion rate of each target site is strongly contingent on the identities of other surrounding targets, with the intrusive model showing an excellent fit to the data. These methods can be applied to deduce sequence-dependent catalytic signatures of other DNA modification enzymes, with potential applications to cancer, gene regulation, and epigenetics.
Mak, Chi H.; Pham, Phuong; Afif, Samir A.; Goodman, Myron F.
2015-09-01
Enzymes that rely on random walk to search for substrate targets in a heterogeneously dispersed medium can leave behind complex spatial profiles of their catalyzed conversions. The catalytic signatures of these random-walk enzymes are the result of two coupled stochastic processes: scanning and catalysis. Here we develop analytical models to understand the conversion profiles produced by these enzymes, comparing an intrusive model, in which scanning and catalysis are tightly coupled, against a loosely coupled passive model. Diagrammatic theory and path-integral solutions of these models revealed clearly distinct predictions. Comparison to experimental data from catalyzed deaminations deposited on single-stranded DNA by the enzyme activation-induced deoxycytidine deaminase (AID) demonstrates that catalysis and diffusion are strongly intertwined, where the chemical conversions give rise to new stochastic trajectories that were absent if the substrate DNA was homogeneous. The C →U deamination profiles in both analytical predictions and experiments exhibit a strong contextual dependence, where the conversion rate of each target site is strongly contingent on the identities of other surrounding targets, with the intrusive model showing an excellent fit to the data. These methods can be applied to deduce sequence-dependent catalytic signatures of other DNA modification enzymes, with potential applications to cancer, gene regulation, and epigenetics.
Mak, Chi H.; Pham, Phuong; Afif, Samir A.; Goodman, Myron F.
2015-01-01
Enzymes that rely on random walk to search for substrate targets in a heterogeneously dispersed medium can leave behind complex spatial profiles of their catalyzed conversions. The catalytic signatures of these random-walk enzymes are the result of two coupled stochastic processes: scanning and catalysis. Here we develop analytical models to understand the conversion profiles produced by these enzymes, comparing an intrusive model, in which scanning and catalysis are tightly coupled, against a loosely coupled passive model. Diagrammatic theory and path-integral solutions of these models revealed clearly distinct predictions. Comparison to experimental data from catalyzed deaminations deposited on single-stranded DNA by the enzyme activation-induced deoxycytidine deaminase (AID) demonstrates that catalysis and diffusion are strongly intertwined, where the chemical conversions give rise to new stochastic trajectories that were absent if the substrate DNA was homogeneous. The C → U deamination profiles in both analytical predictions and experiments exhibit a strong contextual dependence, where the conversion rate of each target site is strongly contingent on the identities of other surrounding targets, with the intrusive model showing an excellent fit to the data. These methods can be applied to deduce sequence-dependent catalytic signatures of other DNA modification enzymes, with potential applications to cancer, gene regulation, and epigenetics. PMID:26465508
Estrada, Ernesto
2015-01-01
A generalization of the random geometric graph (RGG) model is proposed by considering a set of points uniformly and independently distributed on a rectangle of unit area instead of on a unit square \\left[0,1\\right]^{2}. The topological properties, such as connectivity, average degree, average path length and clustering, of the random rectangular graphs (RRGs) generated by this model are then studied as a function of the rectangle sides lengths a and b=1/a, and the radius r used to connect the nodes. When a=1 we recover the RGG, and when a\\rightarrow\\infty the very elongated rectangle generated resembles a one-dimensional RGG. We provided computational and analytical evidence that the topological properties of the RRG differ significantly from those of the RGG. The connectivity of the RRG depends not only on the number of nodes as in the case of the RGG, but also on the side length of the rectangle. As the rectangle is more elongated the critical radius for connectivity increases following first a power-law an...
Funaki, Tadahisa
2016-01-01
Interfaces are created to separate two distinct phases in a situation in which phase coexistence occurs. This book discusses randomly fluctuating interfaces in several different settings and from several points of view: discrete/continuum, microscopic/macroscopic, and static/dynamic theories. The following four topics in particular are dealt with in the book. Assuming that the interface is represented as a height function measured from a fixed-reference discretized hyperplane, the system is governed by the Hamiltonian of gradient of the height functions. This is a kind of effective interface model called ∇φ-interface model. The scaling limits are studied for Gaussian (or non-Gaussian) random fields with a pinning effect under a situation in which the rate functional of the corresponding large deviation principle has non-unique minimizers. Young diagrams determine decreasing interfaces, and their dynamics are introduced. The large-scale behavior of such dynamics is studied from the points of view of the hyd...
Noginov, Mikhail A
2005-01-01
Random lasers are the simplest sources of stimulated emission without cavity, with the feedback provided by scattering in a gain medium. First proposed in the late 60’s, random lasers have grown to a large research field. This book reviews the history and the state of the art of random lasers, provides an outline of the basic models describing their behavior, and describes the recent advances in the field. The major focus of the book is on solid-state random lasers. However, it also briefly describes random lasers based on liquid dyes with scatterers. The chapters of the book are almost independent of each other. So, the scientists or engineers interested in any particular aspect of random lasers can read directly the relevant section. Researchers entering the field of random lasers will find in the book an overview of the field of study. Scientists working in the field can use the book as a reference source.
Randomness Testing of Compressed Data
Chang, Weiling; Yun, Xiaochun; Wang, Shupeng; Yu, Xiangzhan
2010-01-01
Random Number Generators play a critical role in a number of important applications. In practice, statistical testing is employed to gather evidence that a generator indeed produces numbers that appear to be random. In this paper, we reports on the studies that were conducted on the compressed data using 8 compression algorithms or compressors. The test results suggest that the output of compression algorithms or compressors has bad randomness, the compression algorithms or compressors are not suitable as random number generator. We also found that, for the same compression algorithm, there exists positive correlation relationship between compression ratio and randomness, increasing the compression ratio increases randomness of compressed data. As time permits, additional randomness testing efforts will be conducted.
Stabilizing Randomly Switched Systems
Chatterjee, Debasish
2008-01-01
This article is concerned with stability analysis and stabilization of randomly switched systems under a class of switching signals. The switching signal is modeled as a jump stochastic (not necessarily Markovian) process independent of the system state; it selects, at each instant of time, the active subsystem from a family of systems. Sufficient conditions for stochastic stability (almost sure, in the mean, and in probability) of the switched system are established when the subsystems do not possess control inputs, and not every subsystem is required to be stable. These conditions are employed to design stabilizing feedback controllers when the subsystems are affine in control. The analysis is carried out with the aid of multiple Lyapunov-like functions, and the analysis results together with universal formulae for feedback stabilization of nonlinear systems constitute our primary tools for control design
Randomized robot navigation algorithms
Berman, P. [Penn State Univ., University Park, PA (United States); Blum, A. [Carnegie Mellon Univ., Pittsburgh, PA (United States); Fiat, A. [Tel-Aviv Univ. (Israel)] [and others
1996-12-31
We consider the problem faced by a mobile robot that has to reach a given target by traveling through an unmapped region in the plane containing oriented rectangular obstacles. We assume the robot has no prior knowledge about the positions or sizes of the obstacles, and acquires such knowledge only when obstacles are encountered. Our goal is to minimize the distance the robot must travel, using the competitive ratio as our measure. We give a new randomized algorithm for this problem whose competitive ratio is O(n4/9 log n), beating the deterministic {Omega}({radical}n) lower bound of [PY], and answering in the affirmative an open question of [BRS] (which presented an optimal deterministic algorithm). We believe the techniques introduced here may prove useful in other on-line situations in which information gathering is part of the on-line process.
Finite Random Domino Automaton
Bialecki, Mariusz
2012-01-01
Finite version of Random Domino Automaton (FRDA) - recently proposed a toy model of earthquakes - is investigated. Respective set of equations describing stationary state of the FRDA is derived and compared with infinite case. It is shown that for the system of big size, these equations are coincident with RDA equations. We demonstrate a non-existence of exact equations for size N bigger then 4 and propose appropriate approximations, the quality of which is studied in examples obtained within Markov chains framework. We derive several exact formulas describing properties of the automaton, including time aspects. In particular, a way to achieve a quasi-periodic like behaviour of RDA is presented. Thus, based on the same microscopic rule - which produces exponential and inverse-power like distributions - we extend applicability of the model to quasi-periodic phenomena.
Random Access Transport Capacity
Andrews, Jeffrey G; Kountouris, Marios; Haenggi, Martin
2009-01-01
We develop a new metric for quantifying end-to-end throughput in multihop wireless networks, which we term random access transport capacity, since the interference model presumes uncoordinated transmissions. The metric quantifies the average maximum rate of successful end-to-end transmissions, multiplied by the communication distance, and normalized by the network area. We show that a simple upper bound on this quantity is computable in closed-form in terms of key network parameters when the number of retransmissions is not restricted and the hops are assumed to be equally spaced on a line between the source and destination. We also derive the optimum number of hops and optimal per hop success probability and show that our result follows the well-known square root scaling law while providing exact expressions for the preconstants as well. Numerical results demonstrate that the upper bound is accurate for the purpose of determining the optimal hop count and success (or outage) probability.
Random Projection Trees Revisited
Dhesi, Aman
2010-01-01
The Random Projection Tree structures proposed in [Freund-Dasgupta STOC08] are space partitioning data structures that automatically adapt to various notions of intrinsic dimensionality of data. We prove new results for both the RPTreeMax and the RPTreeMean data structures. Our result for RPTreeMax gives a near-optimal bound on the number of levels required by this data structure to reduce the size of its cells by a factor $s \\geq 2$. We also prove a packing lemma for this data structure. Our final result shows that low-dimensional manifolds have bounded Local Covariance Dimension. As a consequence we show that RPTreeMean adapts to manifold dimension as well.
Malarz, K; Szekfu, B; Kulakowski, K
2006-01-01
We consider the average probability X of being informed on a gossip in a given social network. The network is modeled within the random graph theory of Erdos and Renyi. In this theory, a network is characterized by two parameters: the size N and the link probability p. Our experimental data suggest three levels of social inclusion of friendship. The critical value p_c, for which half of agents are informed, scales with the system size as N^{-\\gamma} with \\gamma\\approx 0.68. Computer simulations show that the probability X varies with p as a sigmoidal curve. Influence of the correlations between neighbors is also evaluated: with increasing clustering coefficient C, X decreases.
Vempala, Santosh S
2005-01-01
Random projection is a simple geometric technique for reducing the dimensionality of a set of points in Euclidean space while preserving pairwise distances approximately. The technique plays a key role in several breakthrough developments in the field of algorithms. In other cases, it provides elegant alternative proofs. The book begins with an elementary description of the technique and its basic properties. Then it develops the method in the context of applications, which are divided into three groups. The first group consists of combinatorial optimization problems such as maxcut, graph coloring, minimum multicut, graph bandwidth and VLSI layout. Presented in this context is the theory of Euclidean embeddings of graphs. The next group is machine learning problems, specifically, learning intersections of halfspaces and learning large margin hypotheses. The projection method is further refined for the latter application. The last set consists of problems inspired by information retrieval, namely, nearest neig...
Associative Hierarchical Random Fields.
Ladický, L'ubor; Russell, Chris; Kohli, Pushmeet; Torr, Philip H S
2014-06-01
This paper makes two contributions: the first is the proposal of a new model-The associative hierarchical random field (AHRF), and a novel algorithm for its optimization; the second is the application of this model to the problem of semantic segmentation. Most methods for semantic segmentation are formulated as a labeling problem for variables that might correspond to either pixels or segments such as super-pixels. It is well known that the generation of super pixel segmentations is not unique. This has motivated many researchers to use multiple super pixel segmentations for problems such as semantic segmentation or single view reconstruction. These super-pixels have not yet been combined in a principled manner, this is a difficult problem, as they may overlap, or be nested in such a way that the segmentations form a segmentation tree. Our new hierarchical random field model allows information from all of the multiple segmentations to contribute to a global energy. MAP inference in this model can be performed efficiently using powerful graph cut based move making algorithms. Our framework generalizes much of the previous work based on pixels or segments, and the resulting labelings can be viewed both as a detailed segmentation at the pixel level, or at the other extreme, as a segment selector that pieces together a solution like a jigsaw, selecting the best segments from different segmentations as pieces. We evaluate its performance on some of the most challenging data sets for object class segmentation, and show that this ability to perform inference using multiple overlapping segmentations leads to state-of-the-art results.
Saksala, Timo
2016-10-01
This paper deals with numerical modelling of rock fracture under dynamic loading. For this end, a combined continuum damage-embedded discontinuity model is applied in finite element modelling of crack propagation in rock. In this model, the strong loading rate sensitivity of rock is captured by the rate-dependent continuum scalar damage model that controls the pre-peak nonlinear hardening part of rock behaviour. The post-peak exponential softening part of the rock behaviour is governed by the embedded displacement discontinuity model describing the mode I, mode II and mixed mode fracture of rock. Rock heterogeneity is incorporated in the present approach by random description of the rock mineral texture based on the Voronoi tessellation. The model performance is demonstrated in numerical examples where the uniaxial tension and compression tests on rock are simulated. Finally, the dynamic three-point bending test of a semicircular disc is simulated in order to show that the model correctly predicts the strain rate-dependent tensile strengths as well as the failure modes of rock in this test. Special emphasis is laid on modelling the loading rate sensitivity of tensile strength of Laurentian granite.
Shu, Ting; Zhang, Bob; Yan Tang, Yuan
2017-04-01
Researchers have recently discovered that Diabetes Mellitus can be detected through non-invasive computerized method. However, the focus has been on facial block color features. In this paper, we extensively study the effects of texture features extracted from facial specific regions at detecting Diabetes Mellitus using eight texture extractors. The eight methods are from four texture feature families: (1) statistical texture feature family: Image Gray-scale Histogram, Gray-level Co-occurance Matrix, and Local Binary Pattern, (2) structural texture feature family: Voronoi Tessellation, (3) signal processing based texture feature family: Gaussian, Steerable, and Gabor filters, and (4) model based texture feature family: Markov Random Field. In order to determine the most appropriate extractor with optimal parameter(s), various parameter(s) of each extractor are experimented. For each extractor, the same dataset (284 Diabetes Mellitus and 231 Healthy samples), classifiers (k-Nearest Neighbors and Support Vector Machines), and validation method (10-fold cross validation) are used. According to the experiments, the first and third families achieved a better outcome at detecting Diabetes Mellitus than the other two. The best texture feature extractor for Diabetes Mellitus detection is the Image Gray-scale Histogram with bin number=256, obtaining an accuracy of 99.02%, a sensitivity of 99.64%, and a specificity of 98.26% by using SVM. Copyright © 2017 Elsevier Ltd. All rights reserved.
Importance of randomness in biological networks: A random matrix analysis
Sarika Jalan
2015-02-01
Random matrix theory, initially proposed to understand the complex interactions in nuclear spectra, has demonstrated its success in diverse domains of science ranging from quantum chaos to galaxies. We demonstrate the applicability of random matrix theory for networks by providing a new dimension to complex systems research. We show that in spite of huge differences these interaction networks, representing real-world systems, posses from random matrix models, the spectral properties of the underlying matrices of these networks follow random matrix theory bringing them into the same universality class. We further demonstrate the importance of randomness in interactions for deducing crucial properties of the underlying system. This paper provides an overview of the importance of random matrix framework in complex systems research with biological systems as examples.
Random Intercept and Random Slope 2-Level Multilevel Models
Rehan Ahmad Khan
2012-11-01
Full Text Available Random intercept model and random intercept & random slope model carrying two-levels of hierarchy in the population are presented and compared with the traditional regression approach. The impact of students’ satisfaction on their grade point average (GPA was explored with and without controlling teachers influence. The variation at level-1 can be controlled by introducing the higher levels of hierarchy in the model. The fanny movement of the fitted lines proves variation of student grades around teachers.
Random discrete Schroedinger operators from random matrix theory
Breuer, Jonathan [Institute of Mathematics, Hebrew University of Jerusalem, Jerusalem 91904 (Israel); Forrester, Peter J [Department of Mathematics and Statistics, University of Melbourne, Parkville, Vic 3010 (Australia); Smilansky, Uzy [Department of Physics of Complex Systems, Weizmann Institute, Rehovot 76100 (Israel)
2007-02-02
We investigate random, discrete Schroedinger operators which arise naturally in the theory of random matrices, and depend parametrically on Dyson's Coulomb gas inverse temperature {beta}. They are similar to the class of 'critical' random Schroedinger operators with random potentials which diminish as vertical bar x vertical bar{sup -1/2}. We show that as a function of {beta} they undergo a transition from a regime of (power-law) localized eigenstates with a pure point spectrum for {beta} < 2 to a regime of extended states with a singular continuous spectrum for {beta} {>=} 2. (fast track communication)
RENEWAL THEOREM FOR (L, 1)-RANDOM WALK IN RANDOM ENVIRONMENT
洪文明; 孙鸿雁
2013-01-01
We consider a random walk on Z in random environment with possible jumps{-L, · · · ,-1, 1}, in the case that the environment{ωi: i∈Z}are i.i.d.. We establish the renewal theorem for the Markov chain of “the environment viewed from the particle” in both annealed probability and quenched probability, which generalize partially the results of Kesten (1977) and Lalley (1986) for the nearest random walk in random environment on Z, respectively. Our method is based on the intrinsic branching structure within the (L, 1)-RWRE formulated in Hong and Wang (2013).
Evaluation of a novel therapeutic focused ultrasound transducer based on Fermat’s spiral
Ramaekers, P.; de Greef, M.; Berriet, R.; Moonen, C. T. W.; Ries, M.
2017-06-01
The purpose of this study was to evaluate a novel phased array transducer design rule for therapeutic focused ultrasound applications. This design rule uses the discretized Fermat’s spiral to determine the positioning of the transducer elements for a given number of elements and f-number. Using this principle, three variations of Fermat’s spiral were generated, aimed at (1) grating lobe minimization, (2) side lobe minimization, and (3) an optimized element packing efficiency. For each spiral, sparse layouts using identical circular elements and fully populated layouts based on additional Voronoi tessellation were evaluated numerically. Evaluation criteria included the element size distribution, beam steering capabilities, focal plane pressure distribution, prefocal pressure distribution, and practical considerations. Finally, one Voronoi-tessellated design with a focal length and aperture diameter of 16 cm and a natural frequency of 1.3 MHz was evaluated experimentally through hydrophone measurements. The numerical evaluation showed that while sparse arrays possess superior beam steering capabilities for a given number of elements, the focal point quality and prefocal pressure distribution is substantially more favorable when using the Voronoi-tessellated designs. Beam steering was shown to be feasible with the tessellated designs for lateral deflections up to 10 mm and axial deflections up to 20 mm. The experimental evaluation showed that such a transducer is capable of inducing 40.00 MPa rarefactional and 237.50 MPa compressional peak pressure levels at 800 W instantaneous acoustic output power under free-field conditions, making the system potentially relevant for thermal ablation therapy, histotripsy applications, and shockwave-enhanced heating.
Some general random Taylor series
孙道椿; 余家荣
1996-01-01
Kahane has studied the value distribution of Gauss-Taylor series where is a complex Gauss sequence and The value distribution of more general random Taylor series is considered, where {Xn} is a sequence of real or complex random variables of independent, symmetric and equally distributed with finite non-zero fourth moment (the classical Gauss, Steinhaus and Rademacher random variables are special cases of such variables). First a theorem on the growth of characteristic functions is proved by a method which is completely different from Kahane’s. Then it is applied to proving that the range of general random Taylor series is almost surely dense everywhere in the complex plane and that if the random variable is bounded and continuous, the random series surely has no finite Nevanlinna deficient value.
Fractional random walk lattice dynamics
Michelitsch, Thomas; Riascos, Alejandro Perez; Nowakowski, Andrzeij; Nicolleau, Franck
2016-01-01
We analyze time-discrete and continuous `fractional' random walks on undirected regular networks with special focus on cubic periodic lattices in $n=1,2,3,..$ dimensions.The fractional random walk dynamics is governed by a master equation involving {\\it fractional powers of Laplacian matrices $L^{\\frac{\\alpha}{2}}$}where $\\alpha=2$ recovers the normal walk.First we demonstrate thatthe interval $0\\textless{}\\alpha\\leq 2$ is admissible for the fractional random walk. We derive analytical expressions for fractional transition matrix and closely related the average return probabilities. We further obtain thefundamental matrix $Z^{(\\alpha)}$, and the mean relaxation time (Kemeny constant) for the fractional random walk.The representation for the fundamental matrix $Z^{(\\alpha)}$ relates fractional random walks with normal random walks.We show that the fractional transition matrix elements exihibit for large cubic $n$-dimensional lattices a power law decay of an $n$-dimensional infinite spaceRiesz fractional deriva...
Conditional acceptability of random variables
Tasos C Christofides
2016-06-01
Full Text Available Abstract Acceptable random variables introduced by Giuliano Antonini et al. (J. Math. Anal. Appl. 338:1188-1203, 2008 form a class of dependent random variables that contains negatively dependent random variables as a particular case. The concept of acceptability has been studied by authors under various versions of the definition, such as extended acceptability or wide acceptability. In this paper, we combine the concept of acceptability with the concept of conditioning, which has been the subject of current research activity. For conditionally acceptable random variables, we provide a number of probability inequalities that can be used to obtain asymptotic results.
Randomness-optimal Steganography
Kiayias, Aggelos; Shashidhar, Narasimha
2009-01-01
Steganographic protocols enables one to "embed" covert messages into inconspicous data over a public communication channel in such a way that no one, aside from the sender and the intended receiver can even detect the presence of the secret message. In this paper, we provide a new provably-secure, private-key steganographic encryption protocol. We prove the security of our protocol in the complexity-theoretic framework where security is quantified as the advantage (compared to a random guess) that the adversary has in distinguishing between innocent covertext and stegotext that embeds a message of his choice. The fundamental building block of our steganographic encryption protocol is a "one-time stegosystem" that allows two parties to transmit messages of length at most that of the shared key with information-theoretic security guarantees. The employment of a pseudorandom generator (PRG) permits secure transmission of longer messages in the same way that such a generator allows the use of one-time pad encrypt...
Random eigenvalue problems revisited
S Adhikari
2006-08-01
The description of real-life engineering structural systems is associated with some amount of uncertainty in specifying material properties, geometric parameters, boundary conditions and applied loads. In the context of structural dynamics it is necessary to consider random eigenvalue problems in order to account for these uncertainties. Within the engineering literature, current methods to deal with such problems are dominated by approximate perturbation methods. Some exact methods to obtain joint distribution of the natural frequencies are reviewed and their applicability in the context of real-life engineering problems is discussed. A new approach based on an asymptotic approximation of multi-dimensional integrals is proposed. A closed-form expression for general order joint moments of arbitrary numbers of natural frequencies of linear stochastic systems is derived. The proposed method does not employ the ‘small randomness’ assumption usually used in perturbation based methods. Joint distributions of the natural frequencies are investigated using numerical examples and the results are compared with Monte Carlo simulation.
Allometric Exponent and Randomness
Yi, Su Do; Minnhagen, Petter; 10.1088/1367-2630/15/4/043001
2013-01-01
An allometric height-mass exponent $\\gamma$ gives an approximative power-law relation $ \\propto H^\\gamma$ between the average mass $$ and the height $H$, for a sample of individuals. The individuals in the present study are humans but could be any biological organism. The sampling can be for a specific age of the individuals or for an age-interval. The body-mass index (BMI) is often used for practical purposes when characterizing humans and it is based on the allometric exponent $\\gamma=2$. It is here shown that the actual value of $\\gamma$ is to large extent determined by the degree of correlation between mass and height within the sample studied: no correlation between mass and height means $\\gamma=0$, whereas if there was a precise relation between mass and height such that all individuals had the same shape and density then $\\gamma=3$. The connection is demonstrated by showing that the value of $\\gamma$ can be obtained directly from three numbers characterizing the spreads of the relevant random Gaussian ...
Random allocation software for parallel group randomized trials
Saghaei Mahmood
2004-11-01
Full Text Available Abstract Background Typically, randomization software should allow users to exert control over the different aspects of randomization including block design, provision of unique identifiers and control over the format and type of program output. While some of these characteristics have been addressed by available software, none of them have all of these capabilities integrated into one package. The main objective of the Random Allocation Software project was to enhance the user's control over different aspects of randomization in parallel group trials, including output type and format, structure and ordering of generated unique identifiers and enabling users to specify group names for more than two groups. Results The program has different settings for: simple and blocked randomizations; length, format and ordering of generated unique identifiers; type and format of program output; and saving sessions for future use. A formatted random list generated by this program can be used directly (without further formatting by the coordinator of the research team to prepare and encode different drugs or instruments necessary for the parallel group trial. Conclusions Random Allocation Software enables users to control different attributes of the random allocation sequence and produce qualified lists for parallel group trials.
Random distributed feedback fibre lasers
Turitsyn, Sergei K.; Babin, Sergey A.; Churkin, Dmitry V.; Vatnik, Ilya D.; Nikulin, Maxim; Podivilov, Evgenii V.
2014-09-01
The concept of random lasers exploiting multiple scattering of photons in an amplifying disordered medium in order to generate coherent light without a traditional laser resonator has attracted a great deal of attention in recent years. This research area lies at the interface of the fundamental theory of disordered systems and laser science. The idea was originally proposed in the context of astrophysics in the 1960s by V.S. Letokhov, who studied scattering with “negative absorption” of the interstellar molecular clouds. Research on random lasers has since developed into a mature experimental and theoretical field. A simple design of such lasers would be promising for potential applications. However, in traditional random lasers the properties of the output radiation are typically characterized by complex features in the spatial, spectral and time domains, making them less attractive than standard laser systems in terms of practical applications. Recently, an interesting and novel type of one-dimensional random laser that operates in a conventional telecommunication fibre without any pre-designed resonator mirrors-random distributed feedback fibre laser-was demonstrated. The positive feedback required for laser generation in random fibre lasers is provided by the Rayleigh scattering from the inhomogeneities of the refractive index that are naturally present in silica glass. In the proposed laser concept, the randomly backscattered light is amplified through the Raman effect, providing distributed gain over distances up to 100 km. Although an effective reflection due to the Rayleigh scattering is extremely small (˜0.1%), the lasing threshold may be exceeded when a sufficiently large distributed Raman gain is provided. Such a random distributed feedback fibre laser has a number of interesting and attractive features. The fibre waveguide geometry provides transverse confinement, and effectively one-dimensional random distributed feedback leads to the generation
Random distributed feedback fibre lasers
Turitsyn, Sergei K., E-mail: s.k.turitsyn@aston.ac.uk [Aston Institute of Photonic Technologies, Aston University, Birmingham B4 7ET (United Kingdom); Novosibirsk State University, 2 Pirogova str., 630090, Novosibirsk (Russian Federation); Babin, Sergey A. [Novosibirsk State University, 2 Pirogova str., 630090, Novosibirsk (Russian Federation); Institute of Automation and Electrometry SB RAS, 1 Ac. Koptug. ave., 630090, Novosibirsk (Russian Federation); Churkin, Dmitry V. [Aston Institute of Photonic Technologies, Aston University, Birmingham B4 7ET (United Kingdom); Novosibirsk State University, 2 Pirogova str., 630090, Novosibirsk (Russian Federation); Institute of Automation and Electrometry SB RAS, 1 Ac. Koptug. ave., 630090, Novosibirsk (Russian Federation); Vatnik, Ilya D.; Nikulin, Maxim [Institute of Automation and Electrometry SB RAS, 1 Ac. Koptug. ave., 630090, Novosibirsk (Russian Federation); Podivilov, Evgenii V. [Novosibirsk State University, 2 Pirogova str., 630090, Novosibirsk (Russian Federation); Institute of Automation and Electrometry SB RAS, 1 Ac. Koptug. ave., 630090, Novosibirsk (Russian Federation)
2014-09-10
The concept of random lasers exploiting multiple scattering of photons in an amplifying disordered medium in order to generate coherent light without a traditional laser resonator has attracted a great deal of attention in recent years. This research area lies at the interface of the fundamental theory of disordered systems and laser science. The idea was originally proposed in the context of astrophysics in the 1960s by V.S. Letokhov, who studied scattering with “negative absorption” of the interstellar molecular clouds. Research on random lasers has since developed into a mature experimental and theoretical field. A simple design of such lasers would be promising for potential applications. However, in traditional random lasers the properties of the output radiation are typically characterized by complex features in the spatial, spectral and time domains, making them less attractive than standard laser systems in terms of practical applications. Recently, an interesting and novel type of one-dimensional random laser that operates in a conventional telecommunication fibre without any pre-designed resonator mirrors–random distributed feedback fibre laser–was demonstrated. The positive feedback required for laser generation in random fibre lasers is provided by the Rayleigh scattering from the inhomogeneities of the refractive index that are naturally present in silica glass. In the proposed laser concept, the randomly backscattered light is amplified through the Raman effect, providing distributed gain over distances up to 100 km. Although an effective reflection due to the Rayleigh scattering is extremely small (∼0.1%), the lasing threshold may be exceeded when a sufficiently large distributed Raman gain is provided. Such a random distributed feedback fibre laser has a number of interesting and attractive features. The fibre waveguide geometry provides transverse confinement, and effectively one-dimensional random distributed feedback leads to the
Fractal Structure of Random Matrices
Hussein, M S
2000-01-01
A multifractal analysis is performed on the universality classes of random matrices and the transition ones.Our results indicate that the eigenvector probability distribution is a linear sum of two chi-squared distribution throughout the transition between the universality ensembles of random matrix theory and Poisson .
WEAK UNCORRELATEDNESS OF RANDOM VARIABLES
Sofiya Ostrovska
2006-01-01
New measures of independence for n random variables, based on their moments, are studied. A scale of degrees of independence for random variables which starts with uncorrelatedness (for n = 2) and finishes at independence is constructed. The scale provides a countable linearly ordered set of measures of independence.
A Borderline Random Fourier Series
Talagrand, Michel
1995-01-01
Consider a mean zero random variable $X$, and an independent sequence $(X_n)$ distributed like $X$. We show that the random Fourier series $\\sum_{n\\geq 1} n^{-1} X_n \\exp(2i\\pi nt)$ converges uniformly almost surely if and only if $E(|X|\\log\\log(\\max(e^e, |X|))) < \\infty$.
Local Interaction on Random Graphs
Hans Haller
2010-08-01
Full Text Available We analyze dynamic local interaction in population games where the local interaction structure (modeled as a graph can change over time: A stochastic process generates a random sequence of graphs. This contrasts with models where the initial interaction structure (represented by a deterministic graph or the realization of a random graph cannot change over time.
Forecasting Using Random Subspace Methods
T. Boot (Tom); D. Nibbering (Didier)
2016-01-01
textabstractRandom subspace methods are a novel approach to obtain accurate forecasts in high-dimensional regression settings. We provide a theoretical justification of the use of random subspace methods and show their usefulness when forecasting monthly macroeconomic variables. We focus on two appr
A brief note regarding randomization.
Senn, Stephen
2013-01-01
This note argues, contrary to claims in this journal, that the possible existence of indefinitely many causal factors does not invalidate randomization. The effect of such factors has to be bounded by outcome, and since inference is based on a ratio of between-treatment-group to within-treatment-group variation, randomization remains valid.
Jung, P.; Talkner, P.
2010-09-01
A simple way to convert a purely random sequence of events into a signal with a strong periodic component is proposed. The signal consists of those instants of time at which the length of the random sequence exceeds an integer multiple of a given number. The larger this number the more pronounced the periodic behavior becomes.
Better Randomness with Single Photons
Oberreiter, Lukas
2014-01-01
Randomness is one of the most important resources in modern information science, since encryption founds upon the trust in random numbers. Since it is impossible to prove if an existing random bit string is truly random, it is relevant that they be generated in a trust worthy process. This requires specialized hardware for random numbers, for example a die or a tossed coin. But when all input parameters are known, their outcome might still be predicted. A quantum mechanical superposition allows for provably true random bit generation. In the past decade many quantum random number generators (QRNGs) were realized. A photonic implementation is described as a photon which impinges on a beam splitter, but such a protocol is rarely realized with non-classical light or anti-bunched single photons. Instead, laser sources or light emitting diodes are used. Here we analyze the difference in generating a true random bit string with a laser and with anti-bunched light. We show that a single photon source provides more r...
Aging transition by random errors
Sun, Zhongkui; Ma, Ning; Xu, Wei
2017-02-01
In this paper, the effects of random errors on the oscillating behaviors have been studied theoretically and numerically in a prototypical coupled nonlinear oscillator. Two kinds of noises have been employed respectively to represent the measurement errors accompanied with the parameter specifying the distance from a Hopf bifurcation in the Stuart-Landau model. It has been demonstrated that when the random errors are uniform random noise, the change of the noise intensity can effectively increase the robustness of the system. While the random errors are normal random noise, the increasing of variance can also enhance the robustness of the system under certain conditions that the probability of aging transition occurs reaches a certain threshold. The opposite conclusion is obtained when the probability is less than the threshold. These findings provide an alternative candidate to control the critical value of aging transition in coupled oscillator system, which is composed of the active oscillators and inactive oscillators in practice.
Aging transition by random errors
Sun, Zhongkui; Ma, Ning; Xu, Wei
2017-01-01
In this paper, the effects of random errors on the oscillating behaviors have been studied theoretically and numerically in a prototypical coupled nonlinear oscillator. Two kinds of noises have been employed respectively to represent the measurement errors accompanied with the parameter specifying the distance from a Hopf bifurcation in the Stuart-Landau model. It has been demonstrated that when the random errors are uniform random noise, the change of the noise intensity can effectively increase the robustness of the system. While the random errors are normal random noise, the increasing of variance can also enhance the robustness of the system under certain conditions that the probability of aging transition occurs reaches a certain threshold. The opposite conclusion is obtained when the probability is less than the threshold. These findings provide an alternative candidate to control the critical value of aging transition in coupled oscillator system, which is composed of the active oscillators and inactive oscillators in practice. PMID:28198430
An introduction to random sets
Nguyen, Hung T
2006-01-01
The study of random sets is a large and rapidly growing area with connections to many areas of mathematics and applications in widely varying disciplines, from economics and decision theory to biostatistics and image analysis. The drawback to such diversity is that the research reports are scattered throughout the literature, with the result that in science and engineering, and even in the statistics community, the topic is not well known and much of the enormous potential of random sets remains untapped.An Introduction to Random Sets provides a friendly but solid initiation into the theory of random sets. It builds the foundation for studying random set data, which, viewed as imprecise or incomplete observations, are ubiquitous in today''s technological society. The author, widely known for his best-selling A First Course in Fuzzy Logic text as well as his pioneering work in random sets, explores motivations, such as coarse data analysis and uncertainty analysis in intelligent systems, for studying random s...
Papakonstantinou, Periklis A.; Woodruff, David P.; Yang, Guang
2016-09-01
Generating random bits is a difficult task, which is important for physical systems simulation, cryptography, and many applications that rely on high-quality random bits. Our contribution is to show how to generate provably random bits from uncertain events whose outcomes are routinely recorded in the form of massive data sets. These include scientific data sets, such as in astronomics, genomics, as well as data produced by individuals, such as internet search logs, sensor networks, and social network feeds. We view the generation of such data as the sampling process from a big source, which is a random variable of size at least a few gigabytes. Our view initiates the study of big sources in the randomness extraction literature. Previous approaches for big sources rely on statistical assumptions about the samples. We introduce a general method that provably extracts almost-uniform random bits from big sources and extensively validate it empirically on real data sets. The experimental findings indicate that our method is efficient enough to handle large enough sources, while previous extractor constructions are not efficient enough to be practical. Quality-wise, our method at least matches quantum randomness expanders and classical world empirical extractors as measured by standardized tests.
Papakonstantinou, Periklis A.; Woodruff, David P.; Yang, Guang
2016-01-01
Generating random bits is a difficult task, which is important for physical systems simulation, cryptography, and many applications that rely on high-quality random bits. Our contribution is to show how to generate provably random bits from uncertain events whose outcomes are routinely recorded in the form of massive data sets. These include scientific data sets, such as in astronomics, genomics, as well as data produced by individuals, such as internet search logs, sensor networks, and social network feeds. We view the generation of such data as the sampling process from a big source, which is a random variable of size at least a few gigabytes. Our view initiates the study of big sources in the randomness extraction literature. Previous approaches for big sources rely on statistical assumptions about the samples. We introduce a general method that provably extracts almost-uniform random bits from big sources and extensively validate it empirically on real data sets. The experimental findings indicate that our method is efficient enough to handle large enough sources, while previous extractor constructions are not efficient enough to be practical. Quality-wise, our method at least matches quantum randomness expanders and classical world empirical extractors as measured by standardized tests. PMID:27666514
Randomized Consensus Processing over Random Graphs: Independence and Convergence
Shi, Guodong
2011-01-01
Various consensus algorithms over random networks have been investigated in the literature. In this paper, we focus on the role that randomized individual decision-making plays to consensus seeking under stochastic communications. At each time step, each node will independently choose to follow the consensus algorithm, or to stick to current state by a simple Bernoulli trial with time-dependent success probabilities. This node decision strategy characterizes the random node-failures on a communication networks, or a biased opinion selection in the belief evolution over social networks. Connectivity-independent and arc-independent graphs are defined, respectively, to capture the fundamental nature of random network processes with regard to the convergence of the consensus algorithms. A series of sufficient and/or necessary conditions are given on the success probability sequence for the network to reach a global consensus with probability one under different stochastic connectivity assumptions, by which a comp...
CONCEPTUAL ANALYSIS AND RANDOM ATTRACTOR FOR DISSIPATIVE RANDOM DYNAMICAL SYSTEMS
Li Yuhong; Zdzistaw Brze(z)niak; Zhou Jianzhong
2008-01-01
The aim of this work is to understand better the long time behaviour of asymptotically compact random dynamical systems (RDS), which can be generated by solutions of some stochastic partial differential equations on unbounded domains. The conceptual analysis for the long time behavior of RDS will be done through some examples. An application of those analysis will be demonstrated through the proof of the existence of random attractors for asymptotically compact dissipative RDS.
Random linear codes in steganography
Kamil Kaczyński
2016-12-01
Full Text Available Syndrome coding using linear codes is a technique that allows improvement in the steganographic algorithms parameters. The use of random linear codes gives a great flexibility in choosing the parameters of the linear code. In parallel, it offers easy generation of parity check matrix. In this paper, the modification of LSB algorithm is presented. A random linear code [8, 2] was used as a base for algorithm modification. The implementation of the proposed algorithm, along with practical evaluation of algorithms’ parameters based on the test images was made.[b]Keywords:[/b] steganography, random linear codes, RLC, LSB
Reactive particles in random flows.
Károlyi, György; Tél, Tamás; de Moura, Alessandro P S; Grebogi, Celso
2004-04-30
We study the dynamics of chemically or biologically active particles advected by open flows of chaotic time dependence, which can be modeled by a random time dependence of the parameters on a stroboscopic map. We develop a general theory for reactions in such random flows, and derive the reaction equation for this case. We show that there is a singular enhancement of the reaction in random flows, and this enhancement is increased as compared to the nonrandom case. We verify our theory in a model flow generated by four point vortices moving chaotically.
Random processes in nuclear reactors
Williams, M M R
1974-01-01
Random Processes in Nuclear Reactors describes the problems that a nuclear engineer may meet which involve random fluctuations and sets out in detail how they may be interpreted in terms of various models of the reactor system. Chapters set out to discuss topics on the origins of random processes and sources; the general technique to zero-power problems and bring out the basic effect of fission, and fluctuations in the lifetime of neutrons, on the measured response; the interpretation of power reactor noise; and associated problems connected with mechanical, hydraulic and thermal noise sources
Orthogonal polynomials and random matrices
Deift, Percy
2000-01-01
This volume expands on a set of lectures held at the Courant Institute on Riemann-Hilbert problems, orthogonal polynomials, and random matrix theory. The goal of the course was to prove universality for a variety of statistical quantities arising in the theory of random matrix models. The central question was the following: Why do very general ensembles of random n {\\times} n matrices exhibit universal behavior as n {\\rightarrow} {\\infty}? The main ingredient in the proof is the steepest descent method for oscillatory Riemann-Hilbert problems.
Quantum entanglement from random measurements
Tran, Minh Cong; Dakić, Borivoje; Arnault, François; Laskowski, Wiesław; Paterek, Tomasz
2015-11-01
We show that the expectation value of squared correlations measured along random local directions is an identifier of quantum entanglement in pure states, which can be directly experimentally assessed if two copies of the state are available. Entanglement can therefore be detected by parties who do not share a common reference frame and whose local reference frames, such as polarizers or Stern-Gerlach magnets, remain unknown. Furthermore, we also show that in every experimental run, access to only one qubit from the macroscopic reference is sufficient to identify entanglement, violate a Bell inequality, and, in fact, observe all phenomena observable with macroscopic references. Finally, we provide a state-independent entanglement witness solely in terms of random correlations and emphasize how data gathered for a single random measurement setting per party reliably detects entanglement. This is only possible due to utilized randomness and should find practical applications in experimental confirmation of multiphoton entanglement or space experiments.
Lowest Eigenvalues of Random Hamiltonians
Shen, J J; Arima, A; Yoshinaga, N
2008-01-01
In this paper we present results of the lowest eigenvalues of random Hamiltonians for both fermion and boson systems. We show that an empirical formula of evaluating the lowest eigenvalues of random Hamiltonians in terms of energy centroids and widths of eigenvalues are applicable to many different systems (except for $d$ boson systems). We improve the accuracy of the formula by adding moments higher than two. We suggest another new formula to evaluate the lowest eigenvalues for random matrices with large dimensions (20-5000). These empirical formulas are shown to be applicable not only to the evaluation of the lowest energy but also to the evaluation of excited energies of systems under random two-body interactions.
Random Matrices, Boundaries and Branes
Niedner, Benjamin
2016-01-01
This thesis is devoted to the application of random matrix theory to the study of random surfaces, both discrete and continuous; special emphasis is placed on surface boundaries and the associated boundary conditions in this formalism. In particular, using a multi-matrix integral with permutation symmetry, we are able to calculate the partition function of the Potts model on a random planar lattice with various boundary conditions imposed. We proceed to investigate the correspondence between the critical points in the phase diagram of this model and two-dimensional Liouville theory coupled to conformal field theories with global $\\mathcal{W}$-symmetry. In this context, each boundary condition can be interpreted as the description of a brane in a family of bosonic string backgrounds. This investigation suggests that a spectrum of initially distinct boundary conditions of a given system may become degenerate when the latter is placed on a random surface of bounded genus, effectively leaving a smaller set of ind...
Random Selection for Drug Screening
Center for Human Reliability Studies
2007-05-01
Sampling is the process of choosing some members out of a group or population. Probablity sampling, or random sampling, is the process of selecting members by chance with a known probability of each individual being chosen.
Random walks on reductive groups
Benoist, Yves
2016-01-01
The classical theory of Random Walks describes the asymptotic behavior of sums of independent identically distributed random real variables. This book explains the generalization of this theory to products of independent identically distributed random matrices with real coefficients. Under the assumption that the action of the matrices is semisimple – or, equivalently, that the Zariski closure of the group generated by these matrices is reductive - and under suitable moment assumptions, it is shown that the norm of the products of such random matrices satisfies a number of classical probabilistic laws. This book includes necessary background on the theory of reductive algebraic groups, probability theory and operator theory, thereby providing a modern introduction to the topic.
Solid-Phase Random Glycosylation
Agoston, K.; Kröger, Lars; Dekany, Gyula
2009-01-01
Two different approaches were employed to study solid phase random glycosylations to obtain oligosaccharide libraries. In approach I, Wang resin esters were attached to the acceptors structures. Following their glycosylation and resin cleavage, the peracetylated components of the oligosaccharide ...
Cluster randomization and political philosophy.
Chwang, Eric
2012-11-01
In this paper, I will argue that, while the ethical issues raised by cluster randomization can be challenging, they are not new. My thesis divides neatly into two parts. In the first, easier part I argue that many of the ethical challenges posed by cluster randomized human subjects research are clearly present in other types of human subjects research, and so are not novel. In the second, more difficult part I discuss the thorniest ethical challenge for cluster randomized research--cases where consent is genuinely impractical to obtain. I argue that once again these cases require no new analytic insight; instead, we should look to political philosophy for guidance. In other words, the most serious ethical problem that arises in cluster randomized research also arises in political philosophy.
Quantifying randomness in real networks.
Orsini, Chiara; Dankulov, Marija M; Colomer-de-Simón, Pol; Jamakovic, Almerima; Mahadevan, Priya; Vahdat, Amin; Bassler, Kevin E; Toroczkai, Zoltán; Boguñá, Marián; Caldarelli, Guido; Fortunato, Santo; Krioukov, Dmitri
2015-10-20
Represented as graphs, real networks are intricate combinations of order and disorder. Fixing some of the structural properties of network models to their values observed in real networks, many other properties appear as statistical consequences of these fixed observables, plus randomness in other respects. Here we employ the dk-series, a complete set of basic characteristics of the network structure, to study the statistical dependencies between different network properties. We consider six real networks--the Internet, US airport network, human protein interactions, technosocial web of trust, English word network, and an fMRI map of the human brain--and find that many important local and global structural properties of these networks are closely reproduced by dk-random graphs whose degree distributions, degree correlations and clustering are as in the corresponding real network. We discuss important conceptual, methodological, and practical implications of this evaluation of network randomness, and release software to generate dk-random graphs.
Snakes and perturbed random walks
Basak, Gopal
2011-01-01
In this paper we study some properties of random walks perturbed at extrema, which are generalizations of the walks considered e.g., in Davis (1999). This process can also be viewed as a version of {\\em excited random walk}, studied recently by many authors. We obtain a few properties related to the range of the process with infinite memory. We also prove the Strong law, Central Limit Theorem, and the criterion for the recurrence of the perturbed walk with finite memory.
A local limit theorem for random walks in random scenery and on randomly oriented lattices
Castell, Fabienne; Pène, Françoise; Schapira, Bruno
2010-01-01
Random walks in random scenery are processes defined by $Z_n:=\\sum_{k=1}^n\\xi_{X_1+...+X_k}$, where $(X_k,k\\ge 1)$ and $(\\xi_y,y\\in\\mathbb Z)$ are two independent sequences of i.i.d. random variables. We assume here that their distributions belong to the normal domain of attraction of stable laws with index $\\alpha\\in (0,2]$ and $\\beta\\in (0,2]$ respectively. These processes were first studied by H. Kesten and F. Spitzer, who proved the convergence in distribution when $\\alpha\
The MIXMAX random number generator
Savvidy, Konstantin G.
2015-11-01
In this paper, we study the randomness properties of unimodular matrix random number generators. Under well-known conditions, these discrete-time dynamical systems have the highly desirable K-mixing properties which guarantee high quality random numbers. It is found that some widely used random number generators have poor Kolmogorov entropy and consequently fail in empirical tests of randomness. These tests show that the lowest acceptable value of the Kolmogorov entropy is around 50. Next, we provide a solution to the problem of determining the maximal period of unimodular matrix generators of pseudo-random numbers. We formulate the necessary and sufficient condition to attain the maximum period and present a family of specific generators in the MIXMAX family with superior performance and excellent statistical properties. Finally, we construct three efficient algorithms for operations with the MIXMAX matrix which is a multi-dimensional generalization of the famous cat-map. First, allowing to compute the multiplication by the MIXMAX matrix with O(N) operations. Second, to recursively compute its characteristic polynomial with O(N2) operations, and third, to apply skips of large number of steps S to the sequence in O(N2 log(S)) operations.
An introduction to random interlacements
Drewitz, Alexander; Sapozhnikov, Artëm
2014-01-01
This book gives a self-contained introduction to the theory of random interlacements. The intended reader of the book is a graduate student with a background in probability theory who wants to learn about the fundamental results and methods of this rapidly emerging field of research. The model was introduced by Sznitman in 2007 in order to describe the local picture left by the trace of a random walk on a large discrete torus when it runs up to times proportional to the volume of the torus. Random interlacements is a new percolation model on the d-dimensional lattice. The main results covered by the book include the full proof of the local convergence of random walk trace on the torus to random interlacements and the full proof of the percolation phase transition of the vacant set of random interlacements in all dimensions. The reader will become familiar with the techniques relevant to working with the underlying Poisson Process and the method of multi-scale renormalization, which helps in overcoming the ch...
Random walk of passive tracers among randomly moving obstacles
Gori, Matteo; Floriani, Elena; Nardecchia, Ilaria; Pettini, Marco
2016-01-01
Background: This study is mainly motivated by the need of understanding how the diffusion behaviour of a biomolecule (or even of a larger object) is affected by other moving macromolecules, organelles, and so on, inside a living cell, whence the possibility of understanding whether or not a randomly walking biomolecule is also subject to a long-range force field driving it to its target. Method: By means of the Continuous Time Random Walk (CTRW) technique the topic of random walk in random environment is here considered in the case of a passively diffusing particle in a crowded environment made of randomly moving and interacting obstacles. Results: The relevant physical quantity which is worked out is the diffusion cofficient of the passive tracer which is computed as a function of the average inter-obstacles distance. Coclusions: The results reported here suggest that if a biomolecule, let us call it a test molecule, moves towards its target in the presence of other independently interacting molecules, its m...
The parabolic Anderson model random walk in random potential
König, Wolfgang
2016-01-01
This is a comprehensive survey on the research on the parabolic Anderson model – the heat equation with random potential or the random walk in random potential – of the years 1990 – 2015. The investigation of this model requires a combination of tools from probability (large deviations, extreme-value theory, e.g.) and analysis (spectral theory for the Laplace operator with potential, variational analysis, e.g.). We explain the background, the applications, the questions and the connections with other models and formulate the most relevant results on the long-time behavior of the solution, like quenched and annealed asymptotics for the total mass, intermittency, confinement and concentration properties and mass flow. Furthermore, we explain the most successful proof methods and give a list of open research problems. Proofs are not detailed, but concisely outlined and commented; the formulations of some theorems are slightly simplified for better comprehension.
Postprocessing for quantum random number generators: entropy evaluation and randomness extraction
Ma, Xiongfeng; Xu, Feihu; Xu, He; Tan, Xiaoqing; Qi, Bing; Lo, Hoi-Kwong
2012-01-01
Quantum random-number generators (QRNGs) can offer a means to generate information-theoretically provable random numbers, in principle. In practice, unfortunately, the quantum randomness is inevitably mixed with classical randomness due to classical noises. To distill this quantum randomness, one needs to quantify the randomness of the source and apply a randomness extractor. Here, we propose a generic framework for evaluating quantum randomness of real-life QRNGs by min-entropy, and apply it...
贺贤华; 杨昕; 毛熙彦; 贺灿飞
2016-01-01
influencing area of each pole using the method of Weighted Voronoi diagram. This dia-gram suggested the direction for rural settlement was to relocate and develop. The two example towns in this study had different characteristics. The land was generally flatter, but the level of water and public facility was still low in Chongkan, while the distribution of rural residential land was scattered, but the infrastructure level was high in Shi-long. After the optimization of the layout, Chongkan had 222 developing settlements with 0. 813 km2 rural residen-tial land;Shilong had 416 developing settlements with 0. 301 km2 rural residential land. This research could con-tribute to the technical basis for town planning as well as New-style urbanization plan, and provide an approach to adjust the rural residential land in Southwest China under the circumstance of reducing rural population.%中国的城市化进程伴随着农村人口向城市大量转移,使得乡村普遍面临人口流失、 耕地撂荒及居民点闲置等问题,严重限制农村地区的经济发展,影响基础设施与公共服务设施的配置效率.优化农村居民点布局,实现资源的集约节约利用是国家新型城镇化规划的重要内容.文章以重庆市潼南县崇龛镇与巴南区石龙镇为例,探讨西南地区农村居民点空间布局优化的科学方法.首先,结合西南地区特有的自然人文条件,运用GIS空间分析技术与景观格局指数分析居民点分布特征;然后,构建包括限制性评价与适宜性评价两个阶段的西南地区居民点综合评价体系;基于对未来乡村发展趋势的判断,依据公平与效率原则,将现有居民点划分为发展型、 保留型及迁并型等3类;在此基础上,运用加权Voronoi图确定重点发展型居民点的增长极引力范围,明确迁并型居民点与保留型居民点的发展方向,最终确定农村居民点布局的优化方案.经过优化,崇龛镇基于效率原则确定出222个重
Wave propagation and scattering in random media
Ishimaru, Akira
1978-01-01
Wave Propagation and Scattering in Random Media, Volume 2, presents the fundamental formulations of wave propagation and scattering in random media in a unified and systematic manner. The topics covered in this book may be grouped into three categories: waves in random scatterers, waves in random continua, and rough surface scattering. Random scatterers are random distributions of many particles. Examples are rain, fog, smog, hail, ocean particles, red blood cells, polymers, and other particles in a state of Brownian motion. Random continua are the media whose characteristics vary randomly an
The XXZ Heisenberg model on random surfaces
Ambjørn, J., E-mail: ambjorn@nbi.dk [The Niels Bohr Institute, Copenhagen University, Blegdamsvej 17, DK-2100 Copenhagen (Denmark); Institute for Mathematics, Astrophysics and Particle Physics (IMAPP), Radbaud University Nijmegen, Heyendaalseweg 135, 6525 AJ, Nijmegen (Netherlands); Sedrakyan, A., E-mail: sedrak@nbi.dk [The Niels Bohr Institute, Copenhagen University, Blegdamsvej 17, DK-2100 Copenhagen (Denmark); Yerevan Physics Institute, Br. Alikhanyan str. 2, Yerevan-36 (Armenia)
2013-09-21
We consider integrable models, or in general any model defined by an R-matrix, on random surfaces, which are discretized using random Manhattan lattices. The set of random Manhattan lattices is defined as the set dual to the lattice random surfaces embedded on a regular d-dimensional lattice. They can also be associated with the random graphs of multiparticle scattering nodes. As an example we formulate a random matrix model where the partition function reproduces the annealed average of the XXZ Heisenberg model over all random Manhattan lattices. A technique is presented which reduces the random matrix integration in partition function to an integration over their eigenvalues.
The XXZ Heisenberg model on random surfaces
Ambjorn, J
2013-01-01
We consider integrable models, or in general any model defined by an $R$-matrix, on random surfaces, which are discretized using random Manhattan lattices. The set of random Manhattan lattices is defined as the set dual to the lattice random surfaces embedded on a regular d-dimensional lattice. They can also be associated with the random graphs of multiparticle scattering nodes. As an example we formulate a random matrix model where the partition function reproduces the annealed average of the XXZ Heisenberg model over all random Manhattan lattices. A technique is presented which reduces the random matrix integration in partition function to an integration over their eigenvalues.
Advances in randomized parallel computing
Rajasekaran, Sanguthevar
1999-01-01
The technique of randomization has been employed to solve numerous prob lems of computing both sequentially and in parallel. Examples of randomized algorithms that are asymptotically better than their deterministic counterparts in solving various fundamental problems abound. Randomized algorithms have the advantages of simplicity and better performance both in theory and often in practice. This book is a collection of articles written by renowned experts in the area of randomized parallel computing. A brief introduction to randomized algorithms In the aflalysis of algorithms, at least three different measures of performance can be used: the best case, the worst case, and the average case. Often, the average case run time of an algorithm is much smaller than the worst case. 2 For instance, the worst case run time of Hoare's quicksort is O(n ), whereas its average case run time is only O( n log n). The average case analysis is conducted with an assumption on the input space. The assumption made to arrive at t...
How random are complex networks
Orsini, Chiara; Jamakovic, Almerima; Mahadevan, Priya; Colomer-de-Simón, Pol; Vahdat, Amin; Bassler, Kevin E; Toroczkai, Zoltán; Boguñá, Marián; Caldarelli, Guido; Fortunato, Santo; Krioukov, Dmitri
2015-01-01
Represented as graphs, real networks are intricate combinations of order and disorder. Fixing some of the structural properties of network models to their values observed in real networks, many other properties appear as statistical consequences of these fixed observables, plus randomness in other respects. Here we employ the $dk$-series, a complete set of basic characteristics of the network structure, to study the statistical dependencies between different network properties. We consider six real networks---the Internet, US airport network, human protein interactions, technosocial web of trust, English word network, and an fMRI map of the human brain---and find that many important local and global structural properties of these networks are closely reproduced by $dk$-random graphs whose degree distributions, degree correlations, and clustering are as in the corresponding real network. We discuss important conceptual, methodological, and practical implications of this evaluation of network randomness.
Generating random networks and graphs
Coolen, Ton; Roberts, Ekaterina
2017-01-01
This book supports researchers who need to generate random networks, or who are interested in the theoretical study of random graphs. The coverage includes exponential random graphs (where the targeted probability of each network appearing in the ensemble is specified), growth algorithms (i.e. preferential attachment and the stub-joining configuration model), special constructions (e.g. geometric graphs and Watts Strogatz models) and graphs on structured spaces (e.g. multiplex networks). The presentation aims to be a complete starting point, including details of both theory and implementation, as well as discussions of the main strengths and weaknesses of each approach. It includes extensive references for readers wishing to go further. The material is carefully structured to be accessible to researchers from all disciplines while also containing rigorous mathematical analysis (largely based on the techniques of statistical mechanics) to support those wishing to further develop or implement the theory of rand...
Free probability and random matrices
Mingo, James A
2017-01-01
This volume opens the world of free probability to a wide variety of readers. From its roots in the theory of operator algebras, free probability has intertwined with non-crossing partitions, random matrices, applications in wireless communications, representation theory of large groups, quantum groups, the invariant subspace problem, large deviations, subfactors, and beyond. This book puts a special emphasis on the relation of free probability to random matrices, but also touches upon the operator algebraic, combinatorial, and analytic aspects of the theory. The book serves as a combination textbook/research monograph, with self-contained chapters, exercises scattered throughout the text, and coverage of important ongoing progress of the theory. It will appeal to graduate students and all mathematicians interested in random matrices and free probability from the point of view of operator algebras, combinatorics, analytic functions, or applications in engineering and statistical physics.
RANDOM VARIABLE WITH FUZZY PROBABILITY
吕恩琳; 钟佑明
2003-01-01
Mathematic description about the second kind fuzzy random variable namely the random variable with crisp event-fuzzy probability was studied. Based on the interval probability and using the fuzzy resolution theorem, the feasible condition about a probability fuzzy number set was given, go a step further the definition arid characters of random variable with fuzzy probability ( RVFP ) and the fuzzy distribution function and fuzzy probability distribution sequence of the RVFP were put forward. The fuzzy probability resolution theorem with the closing operation of fuzzy probability was given and proved. The definition and characters of mathematical expectation and variance of the RVFP were studied also. All mathematic description about the RVFP has the closing operation for fuzzy probability, as a result, the foundation of perfecting fuzzy probability operation method is laid.
Triangulation in Random Refractive Distortions.
Alterman, Marina; Schechner, Yoav Y; Swirski, Yohay
2017-03-01
Random refraction occurs in turbulence and through a wavy water-air interface. It creates distortion that changes in space, time and with viewpoint. Localizing objects in three dimensions (3D) despite this random distortion is important to some predators and also to submariners avoiding the salient use of periscopes. We take a multiview approach to this task. Refracted distortion statistics induce a probabilistic relation between any pixel location and a line of sight in space. Measurements of an object's random projection from multiple views and times lead to a likelihood function of the object's 3D location. The likelihood leads to estimates of the 3D location and its uncertainty. Furthermore, multiview images acquired simultaneously in a wide stereo baseline have uncorrelated distortions. This helps reduce the acquisition time needed for localization. The method is demonstrated in stereoscopic video sequences, both in a lab and a swimming pool.
A Randomized Experiment Comparing Random and Cutoff-Based Assignment
Shadish, William R.; Galindo, Rodolfo; Wong, Vivian C.; Steiner, Peter M.; Cook, Thomas D.
2011-01-01
In this article, we review past studies comparing randomized experiments to regression discontinuity designs, mostly finding similar results, but with significant exceptions. The latter might be due to potential confounds of study characteristics with assignment method or with failure to estimate the same parameter over methods. In this study, we…
On the local time of random processes in random scenery
Castell, Fabienne; Pène, Françoise; Schapira, Bruno
2012-01-01
Random walks in random scenery are processes defined by $Z_n:=\\sum_{k=1}^n\\xi_{X_1+...+X_k}$, where basically $(X_k,k\\ge 1)$ and $(\\xi_y,y\\in\\mathbb Z)$ are two independent sequences of i.i.d. random variables. We assume here that $X_1$ is $\\ZZ$-valued, centered and with finite moments of all orders. We also assume that $\\xi_0$ is $\\ZZ$-valued, centered and square integrable. In this case H. Kesten and F. Spitzer proved that $(n^{-3/4}Z_{[nt]},t\\ge 0)$ converges in distribution as $n\\to \\infty$ toward some self-similar process $(\\Delta_t,t\\ge 0)$ called Brownian motion in random scenery. In a previous paper, we established that ${\\mathbb P}(Z_n=0)$ behaves asymptotically like a constant times $n^{-3/4}$, as $n\\to \\infty$. We extend here this local limit theorem: we give a precise asymptotic result for the probability for $Z$ to return to zero simultaneously at several times. As a byproduct of our computations, we show that $\\Delta$ admits a bi-continuous version of its local time process which is locally H\\"o...
Markov Random Field Surface Reconstruction
Paulsen, Rasmus Reinhold; Bærentzen, Jakob Andreas; Larsen, Rasmus
2010-01-01
) and knowledge about data (the observation model) in an orthogonal fashion. Local models that account for both scene-specific knowledge and physical properties of the scanning device are described. Furthermore, how the optimal distance field can be computed is demonstrated using conjugate gradients, sparse......A method for implicit surface reconstruction is proposed. The novelty in this paper is the adaption of Markov Random Field regularization of a distance field. The Markov Random Field formulation allows us to integrate both knowledge about the type of surface we wish to reconstruct (the prior...
Bose condensation in (random traps
V.A. Zagrebnov
2009-01-01
Full Text Available We study a non-interacting (perfect Bose-gas in random external potentials (traps. It is shown that a generalized Bose-Einstein condensation in the random eigenstates manifests if and only if the same occurs in the one-particle kinetic-energy eigenstates, which corresponds to the generalized condensation of the free Bose-gas. Moreover, we prove that the amounts of both condensate densities are equal. This statement is relevant for justification of the Bogoliubov approximation} in the theory of disordered boson systems.
Random Walks Estimate Land Value
Blanchard, Ph
2010-01-01
Expected urban population doubling calls for a compelling theory of the city. Random walks and diffusions defined on spatial city graphs spot hidden areas of geographical isolation in the urban landscape going downhill. First--passage time to a place correlates with assessed value of land in that. The method accounting the average number of random turns at junctions on the way to reach any particular place in the city from various starting points could be used to identify isolated neighborhoods in big cities with a complex web of roads, walkways and public transport systems.
Random matrix theory within superstatistics.
Abul-Magd, A Y
2005-12-01
We propose a generalization of the random matrix theory following the basic prescription of the recently suggested concept of superstatistics. Spectral characteristics of systems with mixed regular-chaotic dynamics are expressed as weighted averages of the corresponding quantities in the standard theory assuming that the mean level spacing itself is a stochastic variable. We illustrate the method by calculating the level density, the nearest-neighbor-spacing distributions, and the two-level correlation functions for systems in transition from order to chaos. The calculated spacing distribution fits the resonance statistics of random binary networks obtained in a recent numerical experiment.
Truncations of random unitary matrices
Zyczkowski, K; Zyczkowski, Karol; Sommers, Hans-Juergen
1999-01-01
We analyze properties of non-hermitian matrices of size M constructed as square submatrices of unitary (orthogonal) random matrices of size N>M, distributed according to the Haar measure. In this way we define ensembles of random matrices and study the statistical properties of the spectrum located inside the unit circle. In the limit of large matrices, this ensemble is characterized by the ratio M/N. For the truncated CUE we derive analytically the joint density of eigenvalues from which easily all correlation functions are obtained. For N-M fixed and N--> infinity the universal resonance-width distribution with N-M open channels is recovered.
Neutron transport in random media
Makai, M. [KFKI Atomic Energy Research Institute, Budapest (Hungary)
1996-08-01
The survey reviews the methods available in the literature which allow a discussion of corium recriticality after a severe accident and a characterization of the corium. It appears that to date no one has considered the eigenvalue problem, though for the source problem several approaches have been proposed. The mathematical formulation of a random medium may be approached in different ways. Based on the review of the literature, we can draw three basic conclusions. The problem of static, random perturbations has been solved. The static case is tractable by the Monte Carlo method. There is a specific time dependent case for which the average flux is given as a series expansion.
a randomized controlled clinical trial
2013-01-01
In this study we aimed to evaluate the effectiveness of Iyengar yoga in chronic neck pain by means of a randomized clinical trial. 77 with chronic neck pain who scored > 40 mm on a 100-mm visual analog scale (VAS) were randomized to a nine week Iyengar yoga program with weekly 90-minute classes or to a self-care/exercise program. The primary outcome measure was change of mean pain at rest (VAS) from baseline to week ten. Secondary outcomes included pain at motion, functional disabilit...
Random number generators and causality
Larrondo, H.A. [Facultad de Ingenieria, Universidad Nacional de Mar del Plata, Juan B. Justo 4302, 7600 Mar del Plata (Argentina)]. E-mail: larrondo@fi.mdp.edu.ar; Martin, M.T. [Instituto de Fisica (IFLP), Facultad de Ciencias Exactas, Universidad Nacional de La Plata and Argentina' s National Council (CONICET), C.C. 727, 1900 La Plata (Argentina)]. E-mail: mtmartin@venus.unlp.edu.ar; Gonzalez, C.M. [Facultad de Ingenieria, Universidad Nacional de Mar del Plata, Juan B. Justo 4302, 7600 Mar del Plata (Argentina)]. E-mail: cmgonzal@fi.mdp.edu.ar; Plastino, A. [Instituto de Fisica (IFLP), Facultad de Ciencias Exactas, Universidad Nacional de La Plata and Argentina' s National Council (CONICET), C.C. 727, 1900 La Plata (Argentina)]. E-mail: plastino@venus.unlp.edu.ar; Rosso, O.A. [Chaos and Biology Group, Instituto de Calculo, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Pabellon II, Ciudad Universitaria, 1428 Ciudad de Buenos Aires (Argentina)]. E-mail: oarosso@fibertel.com.ar
2006-04-03
We advance a prescription to randomize physical or algorithmic Random Number Generators (RNG's) that do not pass Marsaglia's DIEHARD test suite and discuss a special physical quantifier, based on an intensive statistical complexity measure, that is able to adequately assess the improvements produced thereby. Eight RNG's are evaluated and the associated results are compared to those obtained by recourse to Marsaglia's DIEHARD test suite. Our quantifier, which is evaluated using causality arguments, can forecast whether a given RNG will pass the above mentioned test.
Random number generators and causality
Larrondo, H. A.; Martín, M. T.; González, C. M.; Plastino, A.; Rosso, O. A.
2006-04-01
We advance a prescription to randomize physical or algorithmic Random Number Generators (RNG's) that do not pass Marsaglia's DIEHARD test suite and discuss a special physical quantifier, based on an intensive statistical complexity measure, that is able to adequately assess the improvements produced thereby. Eight RNG's are evaluated and the associated results are compared to those obtained by recourse to Marsaglia's DIEHARD test suite. Our quantifier, which is evaluated using causality arguments, can forecast whether a given RNG will pass the above mentioned test.
Consistency of Random Survival Forests.
Ishwaran, Hemant; Kogalur, Udaya B
2010-07-01
We prove uniform consistency of Random Survival Forests (RSF), a newly introduced forest ensemble learner for analysis of right-censored survival data. Consistency is proven under general splitting rules, bootstrapping, and random selection of variables-that is, under true implementation of the methodology. Under this setting we show that the forest ensemble survival function converges uniformly to the true population survival function. To prove this result we make one key assumption regarding the feature space: we assume that all variables are factors. Doing so ensures that the feature space has finite cardinality and enables us to exploit counting process theory and the uniform consistency of the Kaplan-Meier survival function.
A Mixed Effects Randomized Item Response Model
Fox, J.-P.; Wyrick, Cheryl
2008-01-01
The randomized response technique ensures that individual item responses, denoted as true item responses, are randomized before observing them and so-called randomized item responses are observed. A relationship is specified between randomized item response data and true item response data. True item response data are modeled with a (non)linear…
Randomness as a resource for design
Leong, T.; Vetere, F.; Howard, Steve
2006-01-01
Randomness is being harnessed in the design of some interactive systems. This is observed in random blogs, random web searching, and in particular Apple's iPod Shuffle. Yet the role of randomness in design of interactive systems in not well understood. This paper reports on an empirical study exa...
Ultra-fast Quantum Random Number Generator
Yicheng, Shi
We describe a series of Randomness Extractors for removing bias and residual correlations in random numbers generated from measurements on noisy physical systems. The structures of the randomness extractors are based on Linear Feedback Shift Registers (LFSR). This leads to a significant simplification in the implementation of randomness extractors.
Random Fill Cache Architecture (Preprint)
2014-10-01
RR2 adder -a = 11111100 2n-1=000001118 8 RNG 8 R=10010011 R’=00000011 adder i 8 26 Sign extension R’ – a = 11111111 Demand miss line address 26 8 i-1...critical path only consists of one adder that adds the demand miss line address i and the bounded random number (as shown by the dotted arrow). V
Fatigue Reliability under Random Loads
Talreja, R.
1979-01-01
, with the application of random loads, the initial homogeneous distribution of strength changes to a two-component distribution, reflecting the two-stage fatigue damage. In the crack initiation stage, the strength increases initially and then decreases, while an abrupt decrease of strength is seen in the crack...... propagation stage. The consequences of this behaviour on the fatigue reliability are discussed....
Gambling strategies for random sequences
George Davie
2010-01-01
There is a general consensus that it is not possible to gamble successfully against a random se-quence. This consensus is based on results from probability theory that all gambling systems arein some sense futile and the idea that at any stage of the sequence, the next outcome is entirelyunpredictable.
Stalled ERP at Random Textiles
Brumberg, Robert; Kops, Eric; Little, Elizabeth; Gamble, George; Underbakke, Jesse; Havelka, Douglas
2016-01-01
Andre Raymond, Executive Vice President of Sales and Marketing for Random Textiles Co. Inc. (RTC), stood in front of the podium to address his team of 70 sales consultants in Las Vegas, NV. The organization had increased market share and achieved record sales over the past three years; however, in the shadow of this success lurked an obstacle that…
Beyond the random phase approximation
Olsen, Thomas; Thygesen, Kristian S.
2013-01-01
We assess the performance of a recently proposed renormalized adiabatic local density approximation (rALDA) for ab initio calculations of electronic correlation energies in solids and molecules. The method is an extension of the random phase approximation (RPA) derived from time-dependent density...
Universality in random quantum networks
Novotný, Jaroslav; Alber, Gernot; Jex, Igor
2015-12-01
Networks constitute efficient tools for assessing universal features of complex systems. In physical contexts, classical as well as quantum networks are used to describe a wide range of phenomena, such as phase transitions, intricate aspects of many-body quantum systems, or even characteristic features of a future quantum internet. Random quantum networks and their associated directed graphs are employed for capturing statistically dominant features of complex quantum systems. Here, we develop an efficient iterative method capable of evaluating the probability of a graph being strongly connected. It is proven that random directed graphs with constant edge-establishing probability are typically strongly connected, i.e., any ordered pair of vertices is connected by a directed path. This typical topological property of directed random graphs is exploited to demonstrate universal features of the asymptotic evolution of large random qubit networks. These results are independent of our knowledge of the details of the network topology. These findings suggest that other highly complex networks, such as a future quantum internet, may also exhibit similar universal properties.
Random scalar fields and hyperuniformity
Ma, Zheng; Torquato, Salvatore
2017-06-01
Disordered many-particle hyperuniform systems are exotic amorphous states of matter that lie between crystals and liquids. Hyperuniform systems have attracted recent attention because they are endowed with novel transport and optical properties. Recently, the hyperuniformity concept has been generalized to characterize two-phase media, scalar fields, and random vector fields. In this paper, we devise methods to explicitly construct hyperuniform scalar fields. Specifically, we analyze spatial patterns generated from Gaussian random fields, which have been used to model the microwave background radiation and heterogeneous materials, the Cahn-Hilliard equation for spinodal decomposition, and Swift-Hohenberg equations that have been used to model emergent pattern formation, including Rayleigh-Bénard convection. We show that the Gaussian random scalar fields can be constructed to be hyperuniform. We also numerically study the time evolution of spinodal decomposition patterns and demonstrate that they are hyperuniform in the scaling regime. Moreover, we find that labyrinth-like patterns generated by the Swift-Hohenberg equation are effectively hyperuniform. We show that thresholding (level-cutting) a hyperuniform Gaussian random field to produce a two-phase random medium tends to destroy the hyperuniformity of the progenitor scalar field. We then propose guidelines to achieve effectively hyperuniform two-phase media derived from thresholded non-Gaussian fields. Our investigation paves the way for new research directions to characterize the large-structure spatial patterns that arise in physics, chemistry, biology, and ecology. Moreover, our theoretical results are expected to guide experimentalists to synthesize new classes of hyperuniform materials with novel physical properties via coarsening processes and using state-of-the-art techniques, such as stereolithography and 3D printing.
Random matrix theory and multivariate statistics
Diaz-Garcia, Jose A.; Jáimez, Ramon Gutiérrez
2009-01-01
Some tools and ideas are interchanged between random matrix theory and multivariate statistics. In the context of the random matrix theory, classes of spherical and generalised Wishart random matrix ensemble, containing as particular cases the classical random matrix ensembles, are proposed. Some properties of these classes of ensemble are analysed. In addition, the random matrix ensemble approach is extended and a unified theory proposed for the study of distributions for real normed divisio...
Random density matrices versus random evolution of open system
Pineda, Carlos; Seligman, Thomas H.
2015-10-01
We present and compare two families of ensembles of random density matrices. The first, static ensemble, is obtained foliating an unbiased ensemble of density matrices. As criterion we use fixed purity as the simplest example of a useful convex function. The second, dynamic ensemble, is inspired in random matrix models for decoherence where one evolves a separable pure state with a random Hamiltonian until a given value of purity in the central system is achieved. Several families of Hamiltonians, adequate for different physical situations, are studied. We focus on a two qubit central system, and obtain exact expressions for the static case. The ensemble displays a peak around Werner-like states, modulated by nodes on the degeneracies of the density matrices. For moderate and strong interactions good agreement between the static and the dynamic ensembles is found. Even in a model where one qubit does not interact with the environment excellent agreement is found, but only if there is maximal entanglement with the interacting one. The discussion is started recalling similar considerations for scattering theory. At the end, we comment on the reach of the results for other convex functions of the density matrix, and exemplify the situation with the von Neumann entropy.
Random tensor theory: extending random matrix theory to random product states
Ambainis, Andris; Hastings, Matthew B
2009-01-01
We consider a problem in random matrix theory that is inspired by quantum information theory: determining the largest eigenvalue of a sum of p random product states in (C^d)^{otimes k}, where k and p/d^k are fixed while d grows. When k=1, the Marcenko-Pastur law determines (up to small corrections) not only the largest eigenvalue ((1+sqrt{p/d^k})^2) but the smallest eigenvalue (min(0,1-sqrt{p/d^k})^2) and the spectral density in between. We use the method of moments to show that for k>1 the largest eigenvalue is still approximately (1+sqrt{p/d^k})^2 and the spectral density approaches that of the Marcenko-Pastur law, generalizing the random matrix theory result to the random tensor case. Our bound on the largest eigenvalue has implications for a recently proposed quantum data hiding scheme due to Leung and Winter. Since the matrices we consider have neither independent entries nor unitary invariance, we need to develop new techniques for their analysis. The main contribution of this paper is to give three dif...
The Sticky Geometry of the Cosmic Web
Hidding, Johan; Vegter, Gert; Jones, Bernard J T; Teillaud, Monique
2012-01-01
In this video we highlight the application of Computational Geometry to our understanding of the formation and dynamics of the Cosmic Web. The emergence of this intricate and pervasive weblike structure of the Universe on Megaparsec scales can be approximated by a well-known equation from fluid mechanics, the Burgers' equation. The solution to this equation can be obtained from a geometrical formalism. We have extended and improved this method by invoking weighted Delaunay and Voronoi tessellations. The duality between these tessellations finds a remarkable and profound reflection in the description of physical systems in Eulerian and Lagrangian terms. The resulting Adhesion formalism provides deep insight into the dynamics and topology of the Cosmic Web. It uncovers a direct connection between the conditions in the very early Universe and the complex spatial patterns that emerged out of these under the influence of gravity.
Structural Analysis of the SDSS Cosmic Web I.Nonlinear Density Field Reconstructions
Platen, Erwin; Jones, Bernard J T; Vegter, Gert; Aragon-Calvo, Miguel A
2011-01-01
We investigate the ability of three reconstruction techniques to analyze and investigate weblike features and geometries in a discrete distribution of objects. The three methods are the linear Delaunay Tessellation Field Estimator (DTFE), its higher order equivalent Natural Neighbour Field Estimator (NNFE) and a version of Kriging interpolation adapted to the specific circumstances encountered in galaxy redshift surveys, the Natural Lognormal Kriging technique. DTFE and NNFE are based on the local geometry defined by the Voronoi and Delaunay tessellations of the galaxy distribution. The three reconstruction methods are analysed and compared using mock magnitude-limited and volume-limited SDSS redshift surveys, obtained on the basis of the Millennium simulation. We investigate error trends, biases and the topological structure of the resulting fields, concentrating on the void population identified by the Watershed Void Finder. Environmental effects are addressed by evaluating the density fields on a range of ...
Segmentation of Three Dimensional Cell Culture Models from aSingle Focal Plane
Chang, Hang; Parvin, Bahram
2006-11-01
Three dimensional cell culture models offer new opportunities for development of computational techniques for segmentation and localization. These assays have a unique signature of a clump of cells that correspond to a functioning colony. Often the nuclear compartment is labeled and then imaged with fluorescent microscopy to provide context for protein localization. These colonies are first delineated from background using the level set method. Within each colony, nuclear regions are then bounded by their center of mass through radial voting, and a local neighborhood for each nucleus is established through Voronoi tessellation. Finally, the level set method is applied again within each Voronoi region to delineate the nuclear compartment. The paper concludes with the application of the proposed method to a dataset of experimental data demonstrating a stable solution when iterative radial voting and level set methods are used synergistically.
Subsurface Grain Morphology Reconstruction by Differential Aperture X-ray Microscopy
Eisenlohr, Philip; Shanthraj, Pratheek; Vande Kieft, Brendan R.; Bieler, Thomas R.; Liu, Wenjun; Xu, Ruqing
2017-04-27
A multistep, non-destructive grain morphology reconstruction methodology that is applicable to near-surface volumes is developed and tested on synthetic grain structures. This approach probes the subsurface crystal orientation using differential aperture X-ray microscopy (DAXM) on a sparse grid across the microstructure volume of interest. Resulting orientation data is clustered according to proximity in physical and orientation space and used as seed points for an initial Voronoi tessellation to (crudely) approximate the grain morphology. Curvature-driven grain boundary relaxation, simulated by means of the Voronoi Implicit Interface Method (VIIM), progressively improves the reconstruction accuracy. The similarity between bulk and readily accessible surface reconstruction error provides an objective termination criterion for boundary relaxation.
Korneta, W.; Pytel, Z.
1988-07-01
The random walk of a particle on a three-dimensional semi-infinite lattice is considered. In order to study the effect of the surface on the random walk, it is assumed that the velocity of the particle depends on the distance to the surface. Moreover it is assumed that at any point the particle may be absorbed with a certain probability. The probability of the return of the particle to the starting point and the average time of eventual return are calculated. The dependence of these quantities on the distance to the surface, the probability of absorption and the properties of the surface is discussed. The method of generating functions is used.
Shapes of randomly placed droplets
Panchagnula, Mahesh; Janardan, Nachiketa; Deevi, Sri Vallabha
2016-11-01
Surface characterization is essential for many industrial applications. Surface defects result in a range of contact angles, which lead to Contact Angle Hysteresis (CAH). We use shapes of randomly shaped drops on surfaces to study the family of shapes that may result from CAH. We image the triple line from these drops and extract additional information related to local contact angles as well as curvatures from these images. We perform a generalized extreme value analysis (GEV) on this microscopic contact angle data. From this analysis, we predict a range for extreme contact angles that are possible for a sessile drop. We have also measured the macroscopic advancing and receding contact angles using a Goniometer. From the extreme values of the contact line curvature, we estimate the pinning stress distribution responsible for the random shapes. It is seen that this range follows the same trend as the macroscopic CAH measured using a Goniometer, and can be used as a method of characterizing the surface.
Optimal randomized scheduling by replacement
Saias, I.
1996-05-01
In the replacement scheduling problem, a system is composed of n processors drawn from a pool of p. The processors can become faulty while in operation and faulty processors never recover. A report is issued whenever a fault occurs. This report states only the existence of a fault but does not indicate its location. Based on this report, the scheduler can reconfigure the system and choose another set of n processors. The system operates satisfactorily as long as, upon report of a fault, the scheduler chooses n non-faulty processors. We provide a randomized protocol maximizing the expected number of faults the system can sustain before the occurrence of a crash. The optimality of the protocol is established by considering a closely related dual optimization problem. The game-theoretic technical difficulties that we solve in this paper are very general and encountered whenever proving the optimality of a randomized algorithm in parallel and distributed computation.
Localization of reinforced random walks
Tarrès, Pierre
2011-01-01
We describe and analyze how reinforced random walks can eventually localize, i.e. only visit finitely many sites. After introducing vertex and edge self-interacting walks on a discrete graph in a general setting, and stating the main results and conjectures so far on the topic, we present martingale techniques that provide an alternative proof of the a.s. localization of vertex-reinforced random walks (VRRWs) on the integers on finitely many sites and, with positive probability, on five consecutive sites, initially proved by Pemantle and Volkov (1999). Next we introduce the continuous time-lines representation (sometimes called Rubin construction) and its martingale counterpart, and explain how it has been used to prove localization of some reinforced walks on one attracting edge. Then we show how a modified version of this construction enables one to propose a new short proof of the a.s. localization of VRRWs on five sites on Z.
Randomized benchmarking of multiqubit gates.
Gaebler, J P; Meier, A M; Tan, T R; Bowler, R; Lin, Y; Hanneke, D; Jost, J D; Home, J P; Knill, E; Leibfried, D; Wineland, D J
2012-06-29
We describe an extension of single-qubit gate randomized benchmarking that measures the error of multiqubit gates in a quantum information processor. This platform-independent protocol evaluates the performance of Clifford unitaries, which form a basis of fault-tolerant quantum computing. We implemented the benchmarking protocol with trapped ions and found an error per random two-qubit Clifford unitary of 0.162±0.008, thus setting the first benchmark for such unitaries. By implementing a second set of sequences with an extra two-qubit phase gate inserted after each step, we extracted an error per phase gate of 0.069±0.017. We conducted these experiments with transported, sympathetically cooled ions in a multizone Paul trap-a system that can in principle be scaled to larger numbers of ions.
Groups, graphs and random walks
Salvatori, Maura; Sava-Huss, Ecaterina
2017-01-01
An accessible and panoramic account of the theory of random walks on groups and graphs, stressing the strong connections of the theory with other branches of mathematics, including geometric and combinatorial group theory, potential analysis, and theoretical computer science. This volume brings together original surveys and research-expository papers from renowned and leading experts, many of whom spoke at the workshop 'Groups, Graphs and Random Walks' celebrating the sixtieth birthday of Wolfgang Woess in Cortona, Italy. Topics include: growth and amenability of groups; Schrödinger operators and symbolic dynamics; ergodic theorems; Thompson's group F; Poisson boundaries; probability theory on buildings and groups of Lie type; structure trees for edge cuts in networks; and mathematical crystallography. In what is currently a fast-growing area of mathematics, this book provides an up-to-date and valuable reference for both researchers and graduate students, from which future research activities will undoubted...
Orientability thresholds for random hypergraphs
Gao, Pu
2010-01-01
Let $h>w>0$ be two fixed integers. Let $\\orH$ be a random hypergraph whose hyperedges are all of cardinality $h$. To {\\em $w$-orient} a hyperedge, we assign exactly $w$ of its vertices positive signs with respect to the hyperedge, and the rest negative. A $(w,k)$-orientation of $\\orH$ consists of a $w$-orientation of all hyperedges of $\\orH$, such that each vertex receives at most $k$ positive signs from its incident hyperedges. When $k$ is large enough, we determine the threshold of the existence of a $(w,k)$-orientation of a random hypergraph. The $(w,k)$-orientation of hypergraphs is strongly related to a general version of the off-line load balancing problem. The graph case, when $h=2$ and $w=1$, was solved recently by Cain, Sanders and Wormald and independently by Fernholz and Ramachandran, which settled a conjecture of Karp and Saks.
Knot probabilities in random diagrams
Cantarella, Jason; Chapman, Harrison; Mastin, Matt
2016-10-01
We consider a natural model of random knotting—choose a knot diagram at random from the finite set of diagrams with n crossings. We tabulate diagrams with 10 and fewer crossings and classify the diagrams by knot type, allowing us to compute exact probabilities for knots in this model. As expected, most diagrams with 10 and fewer crossings are unknots (about 78% of the roughly 1.6 billion 10 crossing diagrams). For these crossing numbers, the unknot fraction is mostly explained by the prevalence of ‘tree-like’ diagrams which are unknots for any assignment of over/under information at crossings. The data shows a roughly linear relationship between the log of knot type probability and the log of the frequency rank of the knot type, analogous to Zipf’s law for word frequency. The complete tabulation and all knot frequencies are included as supplementary data.
Dynamical invariance for random matrices
Unterberger, Jeremie
2016-01-01
We consider a general Langevin dynamics for the one-dimensional N-particle Coulomb gas with confining potential $V$ at temperature $\\beta$. These dynamics describe for $\\beta=2$ the time evolution of the eigenvalues of $N\\times N$ random Hermitian matrices. The equilibrium partition function -- equal to the normalization constant of the Laughlin wave function in fractional quantum Hall effect -- is known to satisfy an infinite number of constraints called Virasoro or loop constraints. We introduce here a dynamical generating function on the space of random trajectories which satisfies a large class of constraints of geometric origin. We focus in this article on a subclass induced by the invariance under the Schr\\"odinger-Virasoro algebra.
Logical independence and quantum randomness
Paterek, T; Kofler, J; Aspelmeyer, M; Zeilinger, A; Brukner, C [Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Boltzmanngasse 3, A-1090 Vienna (Austria); Prevedel, R; Klimek, P [Faculty of Physics, University of Vienna, Boltzmanngasse 5, A-1090 Vienna (Austria)], E-mail: tomasz.paterek@univie.ac.at
2010-01-15
We propose a link between logical independence and quantum physics. We demonstrate that quantum systems in the eigenstates of Pauli group operators are capable of encoding mathematical axioms and show that Pauli group quantum measurements are capable of revealing whether or not a given proposition is logically dependent on the axiomatic system. Whenever a mathematical proposition is logically independent of the axioms encoded in the measured state, the measurement associated with the proposition gives random outcomes. This allows for an experimental test of logical independence. Conversely, it also allows for an explanation of the probabilities of random outcomes observed in Pauli group measurements from logical independence without invoking quantum theory. The axiomatic systems we study can be completed and are therefore not subject to Goedel's incompleteness theorem.
Chakraborty, Soubhik
2009-01-01
This paper has several objectives. First, it separates randomness from lawlessness and shows why even genuine randomness does not imply lawlessness. Second, it separates the question -why should I call a phenomenon random? (and answers it in part one) from the patent question -What is a random sequence? -for which the answer lies in Kolmogorov complexity (which is explained in part two). While answering the first question the note argues why there should be four motivating factors for calling a phenomenon random: ontic, epistemic, pseudo and telescopic, the first two depicting genuine randomness and the last two false. Third, ontic and epistemic randomness have been distinguished from ontic and epistemic probability. Fourth, it encourages students to be applied statisticians and advises against becoming armchair theorists but this is interestingly achieved by a straight application of telescopic randomness. Overall, it tells (the teacher) not to jump to probability without explaining randomness properly first...
True random numbers from amplified quantum vacuum
Jofre, M; Steinlechner, F; Anzolin, G; Torres, J P; Mitchell, M W; Pruneri, V; 10.1364/OE.19.020665
2011-01-01
Random numbers are essential for applications ranging from secure communications to numerical simulation and quantitative finance. Algorithms can rapidly produce pseudo-random outcomes, series of numbers that mimic most properties of true random numbers while quantum random number generators (QRNGs) exploit intrinsic quantum randomness to produce true random numbers. Single-photon QRNGs are conceptually simple but produce few random bits per detection. In contrast, vacuum fluctuations are a vast resource for QRNGs: they are broad-band and thus can encode many random bits per second. Direct recording of vacuum fluctuations is possible, but requires shot-noise-limited detectors, at the cost of bandwidth. We demonstrate efficient conversion of vacuum fluctuations to true random bits using optical amplification of vacuum and interferometry. Using commercially-available optical components we demonstrate a QRNG at a bit rate of 1.11 Gbps. The proposed scheme has the potential to be extended to 10 Gbps and even up t...
Analyzing Walksat on random formulas
Coja-Oghlan, Amin
2011-01-01
Let F be a uniformly distributed random k-SAT formula with n variables and m clauses. We prove that the Walksat algorithm from Papadimitriou (FOCS 1991)/Schoning (FOCS 1999) finds a satisfying assignment of F in polynomial time w.h.p. if m/n0. This is an improvement by a factor of $\\Theta(k)$ over the best previous analysis of Walksat from Coja-Oghlan, Feige, Frieze, Krivelevich, Vilenchik (SODA 2009).