Directed Abelian algebras and their application to stochastic models

With each directed acyclic graph (this includes some D-dimensional lattices) one can associate some Abelian algebras that we call directed Abelian algebras (DAAs). On each site of the graph one attaches a generator of the algebra. These algebras depend on several parameters and are semisimple. Using any DAA, one can define a family of Hamiltonians which give the continuous time evolution of a stochastic process. The calculation of the spectra and ground-state wave functions (stationary state probability distributions) is an easy algebraic exercise. If one considers D-dimensional lattices and chooses Hamiltonians linear in the generators, in finite-size scaling the Hamiltonian spectrum is gapless with a critical dynamic exponent z=D. One possible application of the DAA is to sandpile models. In the paper we present this application, considering one- and two-dimensional lattices. In the one-dimensional case, when the DAA conserves the number of particles, the avalanches belong to the random walker universality class (critical exponent sigma(tau)=3/2). We study the local density of particles inside large avalanches, showing a depletion of particles at the source of the avalanche and an enrichment at its end. In two dimensions we did extensive Monte-Carlo simulations and found sigma(tau)=1.780 +/- 0.005.

Using ant colonies for solve the multiprocessor task graph scheduling

The problem of scheduling a parallel program presented by a weighted directed acyclic graph (DAG) to the set of homogeneous processors for minimizing the completion time of the program has been extensively studied as academic optimization problem which occurs in optimizing the execution time of parallel algorithm with parallel computer.In this paper, we propose an application of the Ant Colony Optimization (ACO) to a multiprocessor scheduling problem (MPSP). In the MPSP, no preemption is allowed and each operation demands a setup time on the machines. The problem seeks to compose a schedule that minimizes the total completion time.We therefore rely on heuristics to find solutions since solution methods are not feasible for most problems as such. This novel heuristic searching approach to the multiprocessor based on the ACO algorithm a collection of agents cooperate to effectively explore the search space.A computational experiment is conducted on a suit of benchmark application. By comparing our algorithm result obtained to that of previous heuristic algorithm, it is evince that the ACO algorithm exhibits competitive performance with small error ratio.

PARALLEL ALGORITHMS FOR MAXIMAL CLIQUES IN CIRCLE GRAPHS AND UNRESTRICTED DEPTH SEARCH

We present parallel algorithms on the BSP/CGM model, with p processors, to count and generate all the maximal cliques of a circle graph with n vertices and m edges. To count the number of all the maximal cliques, without actually generating them, our algorithm requires O(log p) communication rounds with O(nm/p) local computation time. We also present an algorithm to generate the first maximal clique in O(log p) communication rounds with O(nm/p) local computation, and to generate each one of the subsequent maximal cliques this algorithm requires O(log p) communication rounds with O(m/p) local computation. The maximal cliques generation algorithm is based on generating all maximal paths in a directed acyclic graph, and we present an algorithm for this problem that uses O(log p) communication rounds with O(m/p) local computation for each maximal path. We also show that the presented algorithms can be extended to the CREW PRAM model.

BEE COLONIES APPLIED TO MULTIPROCESSOR SCHEDULING

In order to achieve the high performance, we need to have an efficient scheduling of a parallelprogram onto the processors in multiprocessor systems that minimizes the entire executiontime. This problem of multiprocessor scheduling can be stated as finding a schedule for ageneral task graph to be executed on a multiprocessor system so that the schedule length can be minimize [10]. This scheduling problem is known to be NP- Hard.In multi processor task scheduling, we have a number of CPU’s on which a number of tasksare to be scheduled that the program’s execution time is minimized. According to [10], thetasks scheduling problem is a key factor for a parallel multiprocessor system to gain betterperformance. A task can be partitioned into a group of subtasks and represented as a DAG(Directed Acyclic Graph), so the problem can be stated as finding a schedule for a DAG to beexecuted in a parallel multiprocessor system so that the schedule can be minimized. Thishelps to reduce processing time and increase processor utilization. The aim of this thesis workis to check and compare the results obtained by Bee Colony algorithm with already generatedbest known results in multi processor task scheduling domain.

gems: An R Package for Simulating from Disease Progression Models

Mathematical models of disease progression predict disease outcomes and are useful epidemiological tools for planners and evaluators of health interventions. The R package gems is a tool that simulates disease progression in patients and predicts the effect of different interventions on patient outcome. Disease progression is represented by a series of events (e.g., diagnosis, treatment and death), displayed in a directed acyclic graph. The vertices correspond to disease states and the directed edges represent events. The package gems allows simulations based on a generalized multistate model that can be described by a directed acyclic graph with continuous transition-specific hazard functions. The user can specify an arbitrary hazard function and its parameters. The model includes parameter uncertainty, does not need to be a Markov model, and may take the history of previous events into account. Applications are not limited to the medical field and extend to other areas where multistate simulation is of interest. We provide a technical explanation of the multistate models used by gems, explain the functions of gems and their arguments, and show a sample application.

A framework for the analysis and optimization of encoding latency for multiview video

We present a novel framework for the analysis and optimization of encoding latency for multiview video. Firstly, we characterize the elements that have an influence in the encoding latency performance: (i) the multiview prediction structure and (ii) the hardware encoder model. Then, we provide algorithms to find the encoding latency of any arbitrary multiview prediction structure. The proposed framework relies on the directed acyclic graph encoder latency (DAGEL) model, which provides an abstraction of the processing capacity of the encoder by considering an unbounded number of processors. Using graph theoretic algorithms, the DAGEL model allows us to compute the encoding latency of a given prediction structure, and determine the contribution of the prediction dependencies to it. As an example of DAGEL application, we propose an algorithm to reduce the encoding latency of a given multiview prediction structure up to a target value. In our approach, a minimum number of frame dependencies are pruned, until the latency target value is achieved, thus minimizing the degradation of the rate-distortion performance due to the removal of the prediction dependencies. Finally, we analyze the latency performance of the DAGEL derived prediction structures in multiview encoders with limited processing capacity.

Metodología para la determinación de los parámetros de planificación de los nodos e infraestructuras logísticas en un territorio, considerando en su planificación el impacto sobre los diferentes componentes territoriales

Esta tesis presenta el diseño y la aplicación de una metodología que permite la determinación de los parámetros para la planificación de nodos e infraestructuras logísticas en un territorio, considerando además el impacto de estas en los diferentes componentes territoriales, así como en el desarrollo poblacional, el desarrollo económico y el medio ambiente, presentando así un avance en la planificación integral del territorio. La Metodología propuesta está basada en Minería de Datos, que permite el descubrimiento de patrones detrás de grandes volúmenes de datos previamente procesados. Las características propias de los datos sobre el territorio y los componentes que lo conforman hacen de los estudios territoriales un campo ideal para la aplicación de algunas de las técnicas de Minería de Datos, tales como los ´arboles decisión y las redes bayesianas. Los árboles de decisión permiten representar y categorizar de forma esquemática una serie de variables de predicción que ayudan al análisis de una variable objetivo. Las redes bayesianas representan en un grafo acíclico dirigido, un modelo probabilístico de variables distribuidas en padres e hijos, y la inferencia estadística que permite determinar la probabilidad de certeza de una hipótesis planteada, es decir, permiten construir modelos de probabilidad conjunta que presentan de manera gráfica las dependencias relevantes en un conjunto de datos. Al igual que con los árboles de decisión, la división del territorio en diferentes unidades administrativas hace de las redes bayesianas una herramienta potencial para definir las características físicas de alguna tipología especifica de infraestructura logística tomando en consideración las características territoriales, poblacionales y económicas del área donde se plantea su desarrollo y las posibles sinergias que se puedan presentar sobre otros nodos e infraestructuras logísticas. El caso de estudio seleccionado para la aplicación de la metodología ha sido la República de Panamá, considerando que este país presenta algunas características singulares, entra las que destacan su alta concentración de población en la Ciudad de Panamá; que a su vez a concentrado la actividad económica del país; su alto porcentaje de zonas protegidas, lo que ha limitado la vertebración del territorio; y el Canal de Panamá y los puertos de contenedores adyacentes al mismo. La metodología se divide en tres fases principales: Fase 1: Determinación del escenario de trabajo 1. Revisión del estado del arte. 2. Determinación y obtención de las variables de estudio. Fase 2: Desarrollo del modelo de inteligencia artificial 3. Construcción de los ´arboles de decisión. 4. Construcción de las redes bayesianas. Fase 3: Conclusiones 5. Determinación de las conclusiones. Con relación al modelo de planificación aplicado al caso de estudio, una vez aplicada la metodología, se estableció un modelo compuesto por 47 variables que definen la planificación logística de Panamá, el resto de variables se definen a partir de estas, es decir, conocidas estas, el resto se definen a través de ellas. Este modelo de planificación establecido a través de la red bayesiana considera los aspectos de una planificación sostenible: económica, social y ambiental; que crean sinergia con la planificación de nodos e infraestructuras logísticas. The thesis presents the design and application of a methodology that allows the determination of parameters for the planning of nodes and logistics infrastructure in a territory, besides considering the impact of these different territorial components, as well as the population growth, economic and environmental development. The proposed methodology is based on Data Mining, which allows the discovery of patterns behind large volumes of previously processed data. The own characteristics of the territorial data makes of territorial studies an ideal field of knowledge for the implementation of some of the Data Mining techniques, such as Decision Trees and Bayesian Networks. Decision trees categorize schematically a series of predictor variables of an analyzed objective variable. Bayesian Networks represent a directed acyclic graph, a probabilistic model of variables divided in fathers and sons, and statistical inference that allow determine the probability of certainty in a hypothesis. The case of study for the application of the methodology is the Republic of Panama. This country has some unique features: a high population density in the Panama City, a concentration of economic activity, a high percentage of protected areas, and the Panama Canal. The methodology is divided into three main phases: Phase 1: definition of the work stage. 1. Review of the State of the art. 2. Determination of the variables. Phase 2: Development of artificial intelligence model 3. Construction of decision trees. 4. Construction of Bayesian Networks. Phase 3: conclusions 5. Determination of the conclusions. The application of the methodology to the case study established a model composed of 47 variables that define the logistics planning for Panama. This model of planning established through the Bayesian network considers aspects of sustainable planning and simulates the synergies between the nodes and logistical infrastructure planning.

An Algorithmic Approach to Inferring Cross-Ontology Links while Mapping Anatomical Ontologies

ACM Computing Classification System (1998): J.3.

Mapping and Merging of Anatomical Ontologies

This article presents the principal results of the Ph.D. thesis Intelligent systems in bioinformatics: mapping and merging anatomical ontologies by Peter Petrov, successfully defended at the St. Kliment Ohridski University of Sofia, Faculty of Mathematics and Informatics, Department of Information Technologies, on 26 April 2013.

Incomplete pairwise comparison matrices and weighting methods

A special class of preferences, given by a directed acyclic graph, is considered. They are represented by incomplete pairwise comparison matrices as only partial information is available: for some pairs no comparison is given in the graph. A weighting method satisfies the property linear order preservation if it always results in a ranking such that an alternative directly preferred to another does not have a lower rank. We study whether two procedures, the Eigenvector Method and the Logarithmic Least Squares Method meet this axiom. Both weighting methods break linear order preservation, moreover, the ranking according to the Eigenvector Method depends on the incomplete pairwise comparison representation chosen.