Spatial Logics for Bigraphs

Bigraphs are emerging as an interesting model for concurrent calculi, like CCS, pi-calculus, and Petri nets. Bigraphs are built orthogonally on two structures: a hierarchical place graph for locations and a link (hyper-)graph for connections. With the aim of describing bigraphical structures, we introduce a general framework for logics whose terms represent arrows in monoidal categories. We then instantiate the framework to bigraphical structures and obtain a logic that is a natural composition of a place graph logic and a link graph logic. We explore the concepts of separation and sharing in these logics and we prove that they generalise some known spatial logics for trees, graphs and tree contexts

Bigraphical Logics for XML

Bigraphs have been recently proposed as a meta-model for global computing resources; they are built orthogonally on two structures: a hierarchical ‘place’ graph for locations and a ‘link’ (hyper-)graph for connections. XML is now the standard meta-language for the data exchange and storage on the web. In this paper we address the similarities between bigraphs and XML and we propose bigraphs as a rich model for XML (and XML contexts). Building on this idea we proceed by investigating how the recently proposed logic of BiLog can be instantiated to describe, query and reason about web data (and web contexts)

Static BiLog: a Unifying Language for Spatial Structures

Aiming at a unified view of the logics describing spatial structures, we introduce a general framework, BiLog, whose formulae characterise monoidal categories. As a first instance of the framework we consider bigraphs, which are emerging as a an interesting (meta-)model for spatial structures and distributed calculi. Since bigraphs are built orthogonally on two structures, a hierarchical place graph for locations and a link (hyper-)graph for connections, we obtain a logic that is a natural composition of other two instances of BiLog: a Place Graph Logic and a Link Graph Logic. We prove that these instances generalise the spatial logics for trees, for graphs and for tree contexts. We also explore the concepts of separation and sharing in these logics. We note that both the operator * of Separation Logic and the operator | of spatial logics do not completely separate the underlying structures. These two different forms of separation can be naturally derived as instances of BiLog by using the complete separation induced by the tensor product of monoidal categories along with some form of sharing

BiLog: Spatial Logics for Bigraphs

Bigraphs are emerging as a (meta-)model for concurrent calculi, like CCS, ambients, $\pi$-calculus, and Petri nets. They are built orthogonally on two structures: a hierarchical place graph for locations and a link (hyper-)graph for connections. Aiming at describing bigraphical structures, we introduce a general framework, BiLog, whose formulae describe arrows in monoidal categories. We then instantiate the framework to bigraphical structures and we obtain a logic that is a natural composition of a place graph logic and a link graph logic. We explore the concepts of separation and sharing in these logics and we prove that they generalise well known spatial logics for trees, graphs and tree contexts. As an application, we show how XML data with links and web services can be modelled by bigraphs and described by BiLog. The framework can be extended by introducing dynamics in the model and a standard temporal modality in the logic. However, in some cases, temporal modalities can be already expressed in the static framework. To testify this, we show how to encode a minimal spatial logic for CCS in an instance of BiLog

Modulational instability in dispersion-kicked optical fibers

We study, both theoretically and experimentally, modulational instability in optical fibers that have a longitudinal evolution of their dispersion in the form of a Dirac delta comb. By means of Floquet theory, we obtain an exact expression for the position of the gain bands, and we provide simple analytical estimates of the gain and of the bandwidths of those sidebands. An experimental validation of those results has been realized in several microstructured fibers specifically manufactured for that purpose. The dispersion landscape of those fibers is a comb of Gaussian pulses having widths much shorter than the period, which therefore approximate the ideal Dirac comb. Experimental spontaneous MI spectra recorded under quasi continuous wave excitation are in good agreement with the theory and with numerical simulations based on the generalized nonlinear Schr\"odinger equation

Heteroclinic structure of parametric resonance in the nonlinear Schr\"odinger equation

We show that the nonlinear stage of modulational instability induced by parametric driving in the {\em defocusing} nonlinear Schr\"odinger equation can be accurately described by combining mode truncation and averaging methods, valid in the strong driving regime. The resulting integrable oscillator reveals a complex hidden heteroclinic structure of the instability. A remarkable consequence, validated by the numerical integration of the original model, is the existence of breather solutions separating different Fermi-Pasta-Ulam recurrent regimes. Our theory also shows that optimal parametric amplification unexpectedly occurs outside the bandwidth of the resonance (or Arnold tongues) arising from the linearised Floquet analysis

Mixed-integer vertex covers on bipartite graphs

Let $A$ be the edge-node incidence matrix of a bipartite graph \n$G = (U, V ; E)$, $I$ be a subset of the nodes of $G$, and $b$ be a vector such \nthat $2b$ is integral. We consider the following mixed-integer set: \n X(G, b, I) = {x : Ax ≥ b, x ≥ 0, x_i integer for all i ∈ I}. \nWe characterize conv$(X(G, b, I))$ in its original space. That is, we describe a matrix $(C, d)$ such that conv(X(G, b, I)) = {x : Cx ≥ d}. This \nis accomplished by computing the projection onto the space of the $x$-variables of an extended formulation, given in [1], for $conv(X(G, b, I))$. \nWe then give a polynomial-time algorithm for the separation problem for conv$(X(G, b, I))$, thus showing that the problem of optimizing a linear \nfunction over the set $X(G, b, I)$ is solvable in polynomial time. \

Vibrated and self-compacting fibre reinforced concrete: experimental investigation on the fibre orientation

In addition to the fibre type and content, the residual properties of fibre reinforced concrete are influenced by fibre orientation. Consequently, the performance fibre reinforced concrete can be affected by its fresh properties (workability, flowing capacity) and by casting and compaction processes adopted. This paper focuses on the study of the orientation of steel or macro-synthetic fibres in two materials characterized by very different fresh properties: vibrated and self-compacting concrete. Four rectangular slabs 1800 mm long, 925 mm wide and 100 mm high were produced changing concrete and fibre type. From each slab, eighteen small prisms (550 mm long) were firstly cut either orthogonal or parallel to casting direction and, secondly, notched and tested in bending according to EN 14651. Experimental results showed that the toughness properties of a thin slab significantly varies both in vibrated and self-compacting concrete, even if in case of self-compacting concrete this variation resulted higher. Steel fibres led to greater variability of results compared to polymer one, underlining a different fibre orientation. A discussion on the relative residual capacity measured on the prisms sawn from the slabs and the parameters obtained from standard specimens is performed.Facultad de Ingenierí

PARISROC, a Photomultiplier Array Integrated Read Out Chip

PARISROC is a complete read out chip, in AMS SiGe 0.35 !m technology, for photomultipliers array. It allows triggerless acquisition for next generation neutrino experiments and it belongs to an R&D program funded by the French national agency for research (ANR) called PMm2: ?Innovative electronics for photodetectors array used in High Energy Physics and Astroparticles? (ref.ANR-06-BLAN-0186). The ASIC (Application Specific Integrated Circuit) integrates 16 independent and auto triggered channels with variable gain and provides charge and time measurement by a Wilkinson ADC (Analog to Digital Converter) and a 24-bit Counter. The charge measurement should be performed from 1 up to 300 photo- electrons (p.e.) with a good linearity. The time measurement allowed to a coarse time with a 24-bit counter at 10 MHz and a fine time on a 100ns ramp to achieve a resolution of 1 ns. The ASIC sends out only the relevant data through network cables to the central data storage. This paper describes the front-end electronics ASIC called PARISROC.Comment: IEEE Nuclear Science Symposium an Medical Imaging Conference (2009 NSS/MIC

Approximation of corner polyhedra with families of intersection cuts

We study the problem of approximating the corner polyhedron using intersection cuts derived from families of lattice-free sets in $\mathbb{R}^n$. In particular, we look at the problem of characterizing families that approximate the corner polyhedron up to a constant factor, which depends only on $n$ and not the data or dimension of the corner polyhedron. The literature already contains several results in this direction. In this paper, we use the maximum number of facets of lattice-free sets in a family as a measure of its complexity and precisely characterize the level of complexity of a family required for constant factor approximations. As one of the main results, we show that, for each natural number $n$, a corner polyhedron with $n$ basic integer variables and an arbitrary number of continuous non-basic variables is approximated up to a constant factor by intersection cuts from lattice-free sets with at most $i$ facets if $i> 2^{n-1}$ and that no such approximation is possible if $i \leq 2^{n-1}$. When the approximation factor is allowed to depend on the denominator of the fractional vertex of the linear relaxation of the corner polyhedron, we show that the threshold is $i > n$ versus $i \leq n$. The tools introduced for proving such results are of independent interest for studying intersection cuts