Architecture of optimal transport networks

We analyze the structure of networks minimizing the global resistance to flow (or dissipated energy) with respect to two different constraints: fixed total channel volume and fixed total channel surface area. First, we determine the shape of channels in such optimal networks and show that they must be straight with uniform cross-sectional areas. Then, we establish a relation between the cross-sectional areas of adjoining channels at each junction. Indeed, this relation is a generalization of Murray's law, originally established in the context of local optimization. Moreover, we establish a relation between angles and cross-sectional areas of adjoining channels at each junction, which can be represented as a vectorial force balance equation, where the force weight depends on the channel cross-sectional area. A scaling law between the minimal resistance value and the total volume or surface area value is also derived from the analysis. Furthermore, we show that no more than three or four channels meet in one junction of optimal bi-dimensional networks, depending on the flow profile (e.g.: Poiseuille-like or plug-like) and the considered constraint (fixed volume or surface area). In particular, we show that sources are directly connected to wells, without intermediate junctions, for minimal resistance networks preserving the total channel volume in case of plug flow regime. Finally, all these results are illustrated with a simple example, and compared with the structure of natural networks

Aperiodic tilings and entropy

In this paper we present a construction of Kari-Culik aperiodic tile set - the smallest known until now. With the help of this construction, we prove that this tileset has positive entropy. We also explain why this result was not expected

On the Representation Theory of Orthofermions and Orthosupersymmetric Realization of Parasupersymmetry and Fractional Supersymmetry

We construct a canonical irreducible representation for the orthofermion algebra of arbitrary order, and show that every representation decomposes into irreducible representations that are isomorphic to either the canonical representation or the trivial representation. We use these results to show that every orthosupersymmetric system of order $p$ has a parasupersymmetry of order $p$ and a fractional supersymmetry of order $p+1$.Comment: 13 pages, to appear in J. Phys. A: Math. Ge

5-State Rotation-Symmetric Number-Conserving Cellular Automata are not Strongly Universal

We study two-dimensional rotation-symmetric number-conserving cellular automata working on the von Neumann neighborhood (RNCA). It is known that such automata with 4 states or less are trivial, so we investigate the possible rules with 5 states. We give a full characterization of these automata and show that they cannot be strongly Turing universal. However, we give example of constructions that allow to embed some boolean circuit elements in a 5-states RNCA

Quasiperiodicity and non-computability in tilings

We study tilings of the plane that combine strong properties of different nature: combinatorial and algorithmic. We prove existence of a tile set that accepts only quasiperiodic and non-recursive tilings. Our construction is based on the fixed point construction; we improve this general technique and make it enforce the property of local regularity of tilings needed for quasiperiodicity. We prove also a stronger result: any effectively closed set can be recursively transformed into a tile set so that the Turing degrees of the resulted tilings consists exactly of the upper cone based on the Turing degrees of the later.Comment: v3: the version accepted to MFCS 201

Asymptotic behaviour of the total cross section of p-p scattering and the Akeno cosmic ray data

I present a new determination of the total cross section for proton-proton collisions from the recent Akeno results on absorption of the cosmic ray protons in the p-Air collisions. Extrapolation to the SSC energy suggests $\sigma_{tot}(p-p) \approx (160-170) mb$. I also comment on a possible sensitivity of the p-Air cross section determinations to assumptions on the inelasticity of nuclear collisions at high energy.Comment: . 6 pages, 0 figure

Subshifts, MSO Logic, and Collapsing Hierarchies

We use monadic second-order logic to define two-dimensional subshifts, or sets of colorings of the infinite plane. We present a natural family of quantifier alternation hierarchies, and show that they all collapse to the third level. In particular, this solves an open problem of [Jeandel & Theyssier 2013]. The results are in stark contrast with picture languages, where such hierarchies are usually infinite.Comment: 12 pages, 5 figures. To appear in conference proceedings of TCS 2014, published by Springe

A spatial zero-inflated modelling approach for assessing the H5N1 surveillance system in Thailand

In Thailand, the major epidemic lasted from July 2004 to May 2005. The H5N1 surveillance system has often been assumed to be very efficient during this epidemic. However, no quantitative assessment of the Thai H5N1 surveillance program has been so far undertaken. Here, we propose to use zero-inflated (ZI) models to analyze unilist capture-recapture surveillance data collected during the 2004 epidemic at subdistrict level, to identify the factors driving the presence/absence of the disease and those influencing the detection process. ZI models use the number of detections of infection in the different sites for estimating the total number of infected sites, including those where infection was never detected. We considered each subdistrict of the country as the epidemiological unit (site), and that each H5N1 outbreak notified during the 2004 epidemic constituted a detection of the disease in the site. Therefore, our count dataset focused on the number of detected outbreaks in each subdistrict. To derive the real number of infected sub-districts, we fitted a ZI Poisson model (ZIP) and a ZI negative binomial model (ZINB) to our dataset. We tested the residuals for spatial autocorrelation, proved it was significant and thus added a spatial autocorrelation term in the model. As expected, the spatial ZINB fitted the data better than the spatial ZIP, suggesting the presence of overdispersion in the counts of detections. Derived from the spatial ZINB model, we were able to estimate the real number of infected subdistricts during the epidemic and the sensitivity of detection at sub-district level. We also identified the most important factors that determine the presence/absence of the disease in subdistricts (density of human population and density of free grazing ducks), and influence the detection process (density of free grazing ducks and density of native chicken). (Texte intégral