Maximal planar scale-free Sierpinski networks with small-world effect and power-law strength-degree correlation

Many real networks share three generic properties: they are scale-free, display a small-world effect, and show a power-law strength-degree correlation. In this paper, we propose a type of deterministically growing networks called Sierpinski networks, which are induced by the famous Sierpinski fractals and constructed in a simple iterative way. We derive analytical expressions for degree distribution, strength distribution, clustering coefficient, and strength-degree correlation, which agree well with the characterizations of various real-life networks. Moreover, we show that the introduced Sierpinski networks are maximal planar graphs.Comment: 6 pages, 5 figures, accepted by EP

Statistical Mechanics of Two-dimensional Foams

The methods of statistical mechanics are applied to two-dimensional foams under macroscopic agitation. A new variable -- the total cell curvature -- is introduced, which plays the role of energy in conventional statistical thermodynamics. The probability distribution of the number of sides for a cell of given area is derived. This expression allows to correlate the distribution of sides ("topological disorder") to the distribution of sizes ("geometrical disorder") in a foam. The model predictions agree well with available experimental data

Performance Evaluation of Components Using a Granularity-based Interface Between Real-Time Calculus and Timed Automata

To analyze complex and heterogeneous real-time embedded systems, recent works have proposed interface techniques between real-time calculus (RTC) and timed automata (TA), in order to take advantage of the strengths of each technique for analyzing various components. But the time to analyze a state-based component modeled by TA may be prohibitively high, due to the state space explosion problem. In this paper, we propose a framework of granularity-based interfacing to speed up the analysis of a TA modeled component. First, we abstract fine models to work with event streams at coarse granularity. We perform analysis of the component at multiple coarse granularities and then based on RTC theory, we derive lower and upper bounds on arrival patterns of the fine output streams using the causality closure algorithm. Our framework can help to achieve tradeoffs between precision and analysis time.Comment: QAPL 201

Manipulation and removal of defects in spontaneous optical patterns

Defects play an important role in a number of fields dealing with ordered structures. They are often described in terms of their topology, mutual interaction and their statistical characteristics. We demonstrate theoretically and experimentally the possibility of an active manipulation and removal of defects. We focus on the spontaneous formation of two-dimensional spatial structures in a nonlinear optical system, a liquid crystal light valve under single optical feedback. With increasing distance from threshold, the spontaneously formed hexagonal pattern becomes disordered and contains several defects. A scheme based on Fourier filtering allows us to remove defects and to restore spatial order. Starting without control, the controlled area is progressively expanded, such that defects are swept out of the active area.Comment: 4 pages, 4 figure

The Harris-Luck criterion for random lattices

The Harris-Luck criterion judges the relevance of (potentially) spatially correlated, quenched disorder induced by, e.g., random bonds, randomly diluted sites or a quasi-periodicity of the lattice, for altering the critical behavior of a coupled matter system. We investigate the applicability of this type of criterion to the case of spin variables coupled to random lattices. Their aptitude to alter critical behavior depends on the degree of spatial correlations present, which is quantified by a wandering exponent. We consider the cases of Poissonian random graphs resulting from the Voronoi-Delaunay construction and of planar, ``fat'' $\phi^3$ Feynman diagrams and precisely determine their wandering exponents. The resulting predictions are compared to various exact and numerical results for the Potts model coupled to these quenched ensembles of random graphs.Comment: 13 pages, 9 figures, 2 tables, REVTeX 4. Version as published, one figure added for clarification, minor re-wordings and typo cleanu

Why are the equilibrium properties of two-dimensional random cellular structures so similar?

We develop a statistical-mechanics approach for the equilibrium properties of two-dimensional random cellular structures. Determining both one- and two-point correlation functions, the calculation of various experimentally studied quantities is performed. This enables us to compare our results with experimental and simulated data. Our approach is based on a Hamiltonian of interacting topological charges. It turns out that already the simplest construction of this Hamiltonian reproduces the empirically observed topological laws

Analysis of Memory Latencies in Multi-Processor Systems

Predicting timing behavior is key to efficient embedded real-time system design and verification. Current approaches to determine end-to-end latencies in parallel heterogeneous architectures focus on performance analysis either on task or system level. Especially memory accesses, basic operations of embedded application, cannot be accurately captured on a single level alone: While task level methods simplify system behavior, system level methods simplify task behavior. Both perspectives lead to overly pessimistic estimations