Scale invariance and universality of force networks in static granular matter

Force networks form the skeleton of static granular matter. They are the key factor that determines mechanical properties such as stability, elasticity and sound transmission, which are important for civil engineering and industrial processing. Previous studies have focused on investigations of the global structure of external forces (the boundary condition) and on the probability distribution of individual contact forces. So far, however, precise knowledge of the disordered spatial structure of the force network has remained elusive. Here we report that molecular dynamics simulations of realistic granular packings reveal scale invariance of clusters of particles interacting by means of relatively strong forces. Despite visual variation, force networks for various values of the confining pressure and other parameters have identical scaling exponents and scaling function, thereby determining a universality class. Unexpectedly, the flat ensemble of force configurations (a simple generalization of equilibrium statistical mechanics) belongs to this universality class, whereas some widely studied simplified models do not. This implies that the elasticity of the grains and their geometrical disorder do not affect the universal mechanical properties.     

Indexed Dendrograms on random Dissimilarities

This paper studies the random indexed dendograms produced by agglomerative hierarchical algorithms under the non-classifiability hypothesis of independent identically distributed (i.i.d.) dissimilarities. New tests for classifiability are deduced. The corresponding test statistics are random variables attached to the indexed dendrograms, such as the indices, the survival time of singletons, the value of the ultrametric between two given points, or the size of classes in the different levels of the dendogram. For an indexed dendogram produced by the Single Link method on i.i.d. dissimilarities, the distribution of these random variables is computed, thus leading to explicit tests. For the case of the Average and Complete Link methods, some asymptotic results are presented. The proofs rely essentially on the theory of random graphs.     

Iterative Reconstruction for Transmission Tomography on GPU Using Nvidia CUDA

The iterative reconstruction algorithms for X-ray CT image reconstruction suffer from their high computational cost.Recently Nvidia releases common unified device architecture(CUDA),allowing developers to access to the processing power of Nvidia graphical processing units(GPUs),in order to perform general purpose computations.The use of the GPU,as an alternative computation platform,allows decreasing processing times,for parallel algorithms.This paper aims to demonstrate the feasibility of such an implement...     

Direct observation of Anderson localization of matter waves in a controlled disorder

In 1958, Anderson predicted the localization of electronic wavefunctions in disordered crystals and the resulting absence of diffusion. It is now recognized that Anderson localization is ubiquitous in wave physics because it originates from the interference between multiple scattering paths. Experimentally, localization has been reported for light waves, microwaves, sound waves and electron gases. However, there has been no direct observation of exponential spatial localization of matter waves of any type. Here we observe exponential localization of a Bose-Einstein condensate released into a one-dimensional waveguide in the presence of a controlled disorder created by laser speckle. We operate in a regime of pure Anderson localization, that is, with weak disorder-such that localization results from many quantum reflections of low amplitude-and an atomic density low enough to render interactions negligible. We directly image the atomic density profiles as a function of time, and find that weak disorder can stop the expansion and lead to the formation of a stationary, exponentially localized wavefunction-a direct signature of Anderson localization. We extract the localization length by fitting the exponential wings of the profiles, and compare it to theoretical calculations. The power spectrum of the one-dimensional speckle potentials has a high spatial frequency cutoff, causing exponential localization to occur only when the de Broglie wavelengths of the atoms in the expanding condensate are greater than an effective mobility edge corresponding to that cutoff. In the opposite case, we find that the density profiles decay algebraically, as predicted in ref. 13. The method presented here can be extended to localization of atomic quantum gases in higher dimensions, and with controlled interactions.     

Genome sequencing in microfabricated high-density picolitre reactors

The proliferation of large-scale DNA-sequencing projects in recent years has driven a search for alternative methods to reduce time and cost. Here we describe a scalable, highly parallel sequencing system with raw throughput significantly greater than that of state-of-the-art capillary electrophoresis instruments. The apparatus uses a novel fibre-optic slide of individual wells and is able to sequence 25 million bases, at 99% or better accuracy, in one four-hour run. To achieve an approximately 100-fold increase in throughput over current Sanger sequencing technology, we have developed an emulsion method for DNA amplification and an instrument for sequencing by synthesis using a pyrosequencing protocol optimized for solid support and picolitre-scale volumes. Here we show the utility, throughput, accuracy and robustness of this system by shotgun sequencing and de novo assembly of the Mycoplasma genitalium genome with 96% coverage at 99.96% accuracy in one run of the machine.     

On estimating contemporaneous quarterly regional GDP

Subnational regional jurisdictions rarely have at their disposal a reasonable array of timely statistics to monitor their economic condition. In light of this, we develop a procedure that simultaneously estimates a quarterly time series for all regions of a country based upon quarterly national and annual regional data. While other such techniques exist, we suggest a temporal error structure that eliminates possible spurious jumps. Using our approach, regional analysts should now be able to distribute national growth among regions as soon as quarterly national figures are released. In a Spanish application, we detail some practicalities of the process and show that our proposal produces better estimates than the uniregional methods often used. Copyright © 2007 John Wiley & Sons. Ltd.     

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Seriation in the Presence of Errors: NP-Hardness of <Emphasis Type="Italic">l</Emphasis><Subscript><Emphasis Type="Italic">∞</Emphasis></Subscript> -Fitting Robinson Structures to Dissimilarity Matrices

In this paper, we establish that the following fitting problem is NP-hard: given a finite set X and a dissimilarity measure d on X (d is a symmetric function from X ² to the nonnegative real numbers and vanishing on the diagonal), we wish to find a Robinsonian dissimilarity d _R on X minimizing the l _∞ -error ||d − d _R || _∞ = max_x,y ∈X{|d(x, y) − d _R (x, y)|} between d and d _R . Recall that a dissimilarity d _R on X is called monotone (or Robinsonian) if there exists a total order ≺ on X such that x ≺ z ≺ y implies that d(x, y) ≥ max{d(x, z), d(z, y)}. The Robinsonian dissimilarities appear in seriation and clustering problems, in sparse matrix ordering and DNA sequencing.