We introduce a new class of problems called network information flow which is inspired by computer network applications. Consider a point-to-point communication network on which a number of information sources are to be mulitcast to certain sets of destinations. We assume that the information sources are mutually independent. The problem is to characterize the admissible coding rate region. This model subsumes all previously studied models along the same line. In this paper, we study the problem with one information source, and we have obtained a simple characterization of the admissible coding rate region. Our result can be regarded as the Max-flow Min-cut Theorem for network information flow. Contrary to one’s intuition, our work reveals that it is in general not optimal to regard the information to be multicast as a “fluid” which can simply be routed or replicated. Rather, by employing coding at the nodes, which we refer to as network coding, bandwidth can in general be saved. This finding may have significant impact on future design of switching systems.

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Fitness landscapes are an important concept in molecular evolution. Many important examples of landscapes in physics and combinatorial optimation, which are widely used as model landscapes in simulations of molecular evolution and adaptation, are "elementary", i.e., they are (up to an additive constant) eigenfuctions of a graph Laplacian. It is shown that elementary landscapes are characterized by their correlation functions. The correlation functions are in turn uniquely determined by the geometry of the underlying configuration space and the nearest neighbor correlation of the elementary landscape. Two types of correlation functions are investigated here: the correlation of a time series sampled along a random walk on the landscape and the correlation function with respect to a partition of the set of all vertex pairs.

Figure 1: A synthetically distorted Horse model (left) containing numerous self-intersecting polygons, gaps and holes, and the repaired model (right) with a closed surface. We present a robust method for repairing arbitrary polygon models. The method is guaranteed to produce a closed surface that partitions the space into disjoint internal and external volumes. Given any model represented as a polygon soup, we construct an inside/outside volume using an octree grid, and reconstruct the surface by contouring. Our novel algorithm can efficiently process large models containing millions of polygons and is capable of reproducing sharp features in the original geometry. CR Categories: I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling—Boundary representations; Curve, surface, solid, and object representations; Geometric algorithms, languages, and systems

Highly accurate surface models of the cerebral cortex are becoming increasingly important as tools in the investigation of the functional organization of the human brain. The construction of such models is difficult using current neuroimaging technology due to the high degree of cortical folding. Even single voxel misclassifications can result in erroneous connections being created between adjacent banks of a sulcus, resulting in a topologically inaccurate model. These topological defects cause the cortical model to no longer be homeomorphic to a sheet, preventing the accurate inflation, flattening, or spherical morphing of the reconstructed cortex. Surface deformation techniques can guarantee the topological correctness of a model, but are time-consuming and may result in geometrically inaccurate models. In order to address this need we have developed a technique for taking a model of the cortex, detecting and fixing the topological defects while leaving that majority of the model intact, resulting in a surface that is both geometrically accurate and topologically correct.

This paper presents a calculus for mereotopological reasoning in which two-dimensional spatial regions are treated as primitive entities. A first order predicate language L with a distinguished unary predicate c(x), function-symbols +; : and \Gamma and constants 0 and 1 is defined. An interpretation R for L is provided in which polygonal open subsets of the real plane serve as elements of the domain. Under this interpretation the predicate c(x) is read as "region x is connected" and the function-symbols and constants are given their meaning in terms of a Boolean algebra of polygons. We give an alternative interpretation S based on the real closed plane which turns out to be isomorphic to R. A set of axioms and a rule of inference are introduced. We prove the soundness and completeness of the calculus with respect to the given interpretation.

Several authors have suggested that a more parsimonious and conceptually elegant treatment of everyday mereological and topological reasoning can be obtained by adopting a spatial ontology in which regions, not points, are the primitive entities. This paper challenges this suggestion for mereotopological reasoning in 2-dimensional space. Our strategy is to define a mereotopological language together with a familiar, point-based interpretation. It is proposed that, to be practically useful, any alternative region-based spatial ontology must support the same sentences in our language as this familiar interpretation. This proposal has the merit of transforming a vague, open-ended question about ontologies for "practical" mereotopological reasoning into a precise question in model theory. We show that (a version of) the familiar interpretation is countable and atomic, and therefore prime. We conclude that useful alternative ontologies of the plane are, if anything, less parsimonious than the one which they are supposed to replace.

A quantitative comparison of the BSP and LogP models of parallel computation is developed. We concentrate on a variant of LogP that disallows the so-called stalling behavior, although issues surrounding the stalling phenomenon are also explored. Very efficient cross simulations between the two models are derived, showing their substantial equivalence for algorithmic design guided by asymptotic analysis. It is also shown that the two models can be implemented with similar performance on most point-to-point networks. In conclusion, within the limits of our analysis that is mainly of an asymptotic nature, BSP and (stall-free) LogP can be viewed as closely related variants within the bandwidth-latency framework for modeling parallel computation. BSP seems somewhat preferable due to its greater simplicity and portability, and slightly greater power. LogP lends itself more naturally to multiuser mode.

The notion of one-dimensional one-way cellular automata has been introduced to model cellular automata with only a oneway communication between two neighbor cells. In this paper, we generalize this notion to cellular automata working on different communication graphs. We present some necessary and/or sufficient conditions for a cellular automaton to be simulated by a one-way cellular automaton having the same underlying graph, and we give some bounds on the simulation-time of this mimic.

Abstract not found