Finite-temperature critical point of a glass transition

We generalize the simplest kinetically constrained model of a glass-forming liquid by softening kinetic constraints, allowing them to be violated with a small finite rate. We demonstrate that this model supports a first-order dynamical (space-time) phase transition, similar to those observed with hard constraints. In addition, we find that the first-order phase boundary in this softened model ends in a finite-temperature dynamical critical point, which we expect to be present in natural systems. We discuss links between this critical point and quantum phase transitions, showing that dynamical phase transitions in $d$ dimensions map to quantum transitions in the same dimension, and hence to classical thermodynamic phase transitions in $d+1$ dimensions. We make these links explicit through exact mappings between master operators, transfer matrices, and Hamiltonians for quantum spin chains.Comment: 10 pages, 5 figure

The GPRIME approach to finite element modeling

GPRIME, an interactive modeling system, runs on the CDC 6000 computers and the DEC VAX 11/780 minicomputer. This system includes three components: (1) GPRIME, a user friendly geometric language and a processor to translate that language into geometric entities, (2) GGEN, an interactive data generator for 2-D models; and (3) SOLIDGEN, a 3-D solid modeling program. Each component has a computer user interface of an extensive command set. All of these programs make use of a comprehensive B-spline mathematics subroutine library, which can be used for a wide variety of interpolation problems and other geometric calculations. Many other user aids, such as automatic saving of the geometric and finite element data bases and hidden line removal, are available. This interactive finite element modeling capability can produce a complete finite element model, producing an output file of grid and element data

A survey of visual preprocessing and shape representation techniques

Many recent theories and methods proposed for visual preprocessing and shape representation are summarized. The survey brings together research from the fields of biology, psychology, computer science, electrical engineering, and most recently, neural networks. It was motivated by the need to preprocess images for a sparse distributed memory (SDM), but the techniques presented may also prove useful for applying other associative memories to visual pattern recognition. The material of this survey is divided into three sections: an overview of biological visual processing; methods of preprocessing (extracting parts of shape, texture, motion, and depth); and shape representation and recognition (form invariance, primitives and structural descriptions, and theories of attention)

On the relevance of the dam break problem in the context of nonlinear shallow water equations

The classical dam break problem has become the de facto standard in validating the Nonlinear Shallow Water Equations (NSWE) solvers. Moreover, the NSWE are widely used for flooding simulations. While applied mathematics community is essentially focused on developing new numerical schemes, we tried to examine the validity of the mathematical model under consideration. The main purpose of this study is to check the pertinence of the NSWE for flooding processes. From the mathematical point of view, the answer is not obvious since all derivation procedures assumes the total water depth positivity. We performed a comparison between the two-fluid Navier-Stokes simulations and the NSWE solved analytically and numerically. Several conclusions are drawn out and perspectives for future research are outlined.Comment: 20 pages, 15 figures. Accepted to Discrete and Continuous Dynamical Systems. Other author's papers can be downloaded at http://www.lama.univ-savoie.fr/~dutyk

Parallel Algorithms for Geometric Graph Problems

We give algorithms for geometric graph problems in the modern parallel models inspired by MapReduce. For example, for the Minimum Spanning Tree (MST) problem over a set of points in the two-dimensional space, our algorithm computes a $(1+\epsilon)$-approximate MST. Our algorithms work in a constant number of rounds of communication, while using total space and communication proportional to the size of the data (linear space and near linear time algorithms). In contrast, for general graphs, achieving the same result for MST (or even connectivity) remains a challenging open problem, despite drawing significant attention in recent years. We develop a general algorithmic framework that, besides MST, also applies to Earth-Mover Distance (EMD) and the transportation cost problem. Our algorithmic framework has implications beyond the MapReduce model. For example it yields a new algorithm for computing EMD cost in the plane in near-linear time, $n^{1+o_\epsilon(1)}$. We note that while recently Sharathkumar and Agarwal developed a near-linear time algorithm for $(1+\epsilon)$-approximating EMD, our algorithm is fundamentally different, and, for example, also solves the transportation (cost) problem, raised as an open question in their work. Furthermore, our algorithm immediately gives a $(1+\epsilon)$-approximation algorithm with $n^{\delta}$ space in the streaming-with-sorting model with $1/\delta^{O(1)}$ passes. As such, it is tempting to conjecture that the parallel models may also constitute a concrete playground in the quest for efficient algorithms for EMD (and other similar problems) in the vanilla streaming model, a well-known open problem