Diseño e implementación del kernel de xDEVS, versión distribuida

Para entender nuestro proyecto, debemos comprender DEVS. Dentro de los formalismos más populares de representación de sistemas de eventos discretos se encuentra DES. En la década de los 70, el matemático Bernard Zeigler propuso un formalismo general para la representación de dichos sistemas. Este formalismo denominado DEVS (Discrete EVent System Specification) es el formalismo más general para el tratamiento de DES. DEVS permite representar todos aquellos sistemas cuyo comportamiento pueda describirse mediante una secuencia de eventos discretos. Estos eventos se caracterizan por un tiempo base en el que solo un número de eventos finitos puede ocurrir. DEVS Modelado y Simulación tiene múltiples implementaciones en varios lenguajes de programación como por ejemplo en Java, C# o C++. Pero surge la necesidad de implementar una plataforma distribuida estable para proporcionar la mecánica de interoperabilidad e integrar modelos DEVS diversificados. En este proyecto, se nos dará como código base el core de xDEVS en java, aplicado de forma secuencial y paralelizada. Nuestro trabajo será implementar el core de manera distribuida de tal forma que se pueda dividir un sistema DEVS en diversas máquinas. Para esto hemos utilizado sockets de java para hacer la transmisión de datos lo más eficiente posible. En un principio deberemos especificar el número de máquinas que se conectarán al servidor. Una vez estas se hayan conectado se les enviará el trabajo específico que deberán simular. Cabe destacar que hay dos formas de dividir un sistema DEVS las cuales están implementadas en nuestro proyecto. La primera es dividirlo en módulos atómicos los cuales son subsistemas indivisibles en un sistema DEVS. Y la segunda es dividir las funciones de todos los subsistemas en grupos y repartirlos entre las máquinas. En resumen el funcionamiento de nuestro sistema distribuido será comenzar ejecutando el trabajo asignado al primer cliente, una vez finalizado actualizará la información del servidor y este mandara la orden al siguiente y así sucesivamente.

Egalitarian state-transition systems (extended version)

We argue that considering transitions at the same level as states, as first-class citizens, is advantageous in many cases. Namely, the use of atomic propositions on transitions, as well as on states, allows temporal formulas and strategies to be more powerful, general, and meaningful. We define egalitarian structures and logics, and show how they generalize well-known state-based, event-based, and mixed ones. We present translations from egalitarian to non-egalitarian settings that, in particular, allow the model checking of LTLR formulas using Maude’s LTL model checker. We have implemented these translations as a prototype in Maude itself.

Stenosis triggers spread of helical Pseudomonas biofilms in cylindrical flow systems

Biofilms are multicellular bacterial structures that adhere to surfaces and often endow the bacterial population with tolerance to antibiotics and other environmental insults. Biofilms frequently colonize the tubing of medical devices through mechanisms that are poorly understood. Here we studied the helicoidal spread of Pseudomonas putida biofilms through cylindrical conduits of varied diameters in slow laminar flow regimes. Numerical simulations of such flows reveal vortical motion at stenoses and junctions, which enhances bacterial adhesion and fosters formation of filamentous structures. Formation of long, downstream-flowing bacterial threads that stem from narrowings and connections was detected experimentally, as predicted by our model. Accumulation of bacterial biomass makes the resulting filaments undergo a helical instability. These incipient helices then coarsened until constrained by the tubing walls, and spread along the whole tube length without obstructing the flow. A three-dimensional discrete filament model supports this coarsening mechanism and yields simulations of helix dynamics in accordance with our experimental observations. These findings describe an unanticipated mechanism for bacterial spreading in tubing networks which might be involved in some hospital-acquired infections and bacterial contamination of catheters.

Multivariate orthogonal polynomials and integrable systems

Multivariate orthogonal polynomials in D real dimensions are considered from the perspective of the Cholesky factorization of a moment matrix. The approach allows for the construction of corresponding multivariate orthogonal polynomials, associated second kind functions, Jacobi type matrices and associated three term relations and also Christoffel-Darboux formulae. The multivariate orthogonal polynomials, their second kind functions and the corresponding Christoffel-Darboux kernels are shown to be quasi-determinants as well as Schur complements of bordered truncations of the moment matrix; quasi-tau functions are introduced. It is proven that the second kind functions are multivariate Cauchy transforms of the multivariate orthogonal polynomials. Discrete and continuous deformations of the measure lead to Toda type integrable hierarchy, being the corresponding flows described through Lax and Zakharov-Shabat equations; bilinear equations are found. Varying size matrix nonlinear partial difference and differential equations of the 2D Toda lattice type are shown to be solved by matrix coefficients of the multivariate orthogonal polynomials. The discrete flows, which are shown to be connected with a Gauss-Borel factorization of the Jacobi type matrices and its quasi-determinants, lead to expressions for the multivariate orthogonal polynomials and their second kind functions in terms of shifted quasi-tau matrices, which generalize to the multidimensional realm, those that relate the Baker and adjoint Baker functions to ratios of Miwa shifted tau-functions in the 1D scenario. In this context, the multivariate extension of the elementary Darboux transformation is given in terms of quasi-determinants of matrices built up by the evaluation, at a poised set of nodes lying in an appropriate hyperplane in R^D, of the multivariate orthogonal polynomials. The multivariate Christoffel formula for the iteration of m elementary Darboux transformations is given as a quasi-determinant. It is shown, using congruences in the space of semi-infinite matrices, that the discrete and continuous flows are intimately connected and determine nonlinear partial difference-differential equations that involve only one site in the integrable lattice behaving as a Kadomstev-Petviashvili type system. Finally, a brief discussion of measures with a particular linear isometry invariance and some of its consequences for the corresponding multivariate polynomials is given. In particular, it is shown that the Toda times that preserve the invariance condition lay in a secant variety of the Veronese variety of the fixed point set of the linear isometry.