Stability and ergodicity of piecewise deterministic Markov processes

The main goal of this paper is to establish some equivalence results on stability, recurrence, and ergodicity between a piecewise deterministic Markov process ( PDMP) {X( t)} and an embedded discrete-time Markov chain {Theta(n)} generated by a Markov kernel G that can be explicitly characterized in terms of the three local characteristics of the PDMP, leading to tractable criterion results. First we establish some important results characterizing {Theta(n)} as a sampling of the PDMP {X( t)} and deriving a connection between the probability of the first return time to a set for the discrete-time Markov chains generated by G and the resolvent kernel R of the PDMP. From these results we obtain equivalence results regarding irreducibility, existence of sigma-finite invariant measures, and ( positive) recurrence and ( positive) Harris recurrence between {X( t)} and {Theta(n)}, generalizing the results of [ F. Dufour and O. L. V. Costa, SIAM J. Control Optim., 37 ( 1999), pp. 1483-1502] in several directions. Sufficient conditions in terms of a modified Foster-Lyapunov criterion are also presented to ensure positive Harris recurrence and ergodicity of the PDMP. We illustrate the use of these conditions by showing the ergodicity of a capacity expansion model.

AVERAGE CONTINUOUS CONTROL OF PIECEWISE DETERMINISTIC MARKOV PROCESSES

This paper deals with the long run average continuous control problem of piecewise deterministic Markov processes (PDMPs) taking values in a general Borel space and with compact action space depending on the state variable. The control variable acts on the jump rate and transition measure of the PDMP, and the running and boundary costs are assumed to be positive but not necessarily bounded. Our first main result is to obtain an optimality equation for the long run average cost in terms of a discrete-time optimality equation related to the embedded Markov chain given by the postjump location of the PDMP. Our second main result guarantees the existence of a feedback measurable selector for the discrete-time optimality equation by establishing a connection between this equation and an integro-differential equation. Our final main result is to obtain some sufficient conditions for the existence of a solution for a discrete-time optimality inequality and an ordinary optimal feedback control for the long run average cost using the so-called vanishing discount approach. Two examples are presented illustrating the possible applications of the results developed in the paper.

Node-Depth Encoding and Multiobjective Evolutionary Algorithm Applied to Large-Scale Distribution System Reconfiguration

The power loss reduction in distribution systems (DSs) is a nonlinear and multiobjective problem. Service restoration in DSs is even computationally hard since it additionally requires a solution in real-time. Both DS problems are computationally complex. For large-scale networks, the usual problem formulation has thousands of constraint equations. The node-depth encoding (NDE) enables a modeling of DSs problems that eliminates several constraint equations from the usual formulation, making the problem solution simpler. On the other hand, a multiobjective evolutionary algorithm (EA) based on subpopulation tables adequately models several objectives and constraints, enabling a better exploration of the search space. The combination of the multiobjective EA with NDE (MEAN) results in the proposed approach for solving DSs problems for large-scale networks. Simulation results have shown the MEAN is able to find adequate restoration plans for a real DS with 3860 buses and 632 switches in a running time of 0.68 s. Moreover, the MEAN has shown a sublinear running time in function of the system size. Tests with networks ranging from 632 to 5166 switches indicate that the MEAN can find network configurations corresponding to a power loss reduction of 27.64% for very large networks requiring relatively low running time.

Optimization of modal filters based on arrays of piezoelectric sensors

Modal filters may be obtained by a properly designed weighted sum of the output signals of an array of sensors distributed on the host structure. Although several research groups have been interested in techniques for designing and implementing modal filters based on a given array of sensors, the effect of the array topology on the effectiveness of the modal filter has received much less attention. In particular, it is known that some parameters, such as size, shape and location of a sensor, are very important in determining the observability of a vibration mode. Hence, this paper presents a methodology for the topological optimization of an array of sensors in order to maximize the effectiveness of a set of selected modal filters. This is done using a genetic algorithm optimization technique for the selection of 12 piezoceramic sensors from an array of 36 piezoceramic sensors regularly distributed on an aluminum plate, which maximize the filtering performance, over a given frequency range, of a set of modal filters, each one aiming to isolate one of the first vibration modes. The vectors of the weighting coefficients for each modal filter are evaluated using QR decomposition of the complex frequency response function matrix. Results show that the array topology is not very important for lower frequencies but it greatly affects the filter effectiveness for higher frequencies. Therefore, it is possible to improve the effectiveness and frequency range of a set of modal filters by optimizing the topology of an array of sensors. Indeed, using 12 properly located piezoceramic sensors bonded on an aluminum plate it is shown that the frequency range of a set of modal filters may be enlarged by 25-50%.

Parallel Dynamic Optimization of Steel Risers

This paper addresses the use of optimization techniques in the design of a steel riser. Two methods are used: the genetic algorithm, which imitates the process of natural selection, and the simulated annealing, which is based on the process of annealing of a metal. Both of them are capable of searching a given solution space for the best feasible riser configuration according to predefined criteria. Optimization issues are discussed, such as problem codification, parameter selection, definition of objective function, and restrictions. A comparison between the results obtained for economic and structural objective functions is made for a case study. Optimization method parallelization is also addressed. [DOI: 10.1115/1.4001955]

Singular Perturbation for the Discounted Continuous Control of Piecewise Deterministic Markov Processes

This paper deals with the expected discounted continuous control of piecewise deterministic Markov processes (PDMP`s) using a singular perturbation approach for dealing with rapidly oscillating parameters. The state space of the PDMP is written as the product of a finite set and a subset of the Euclidean space a""e (n) . The discrete part of the state, called the regime, characterizes the mode of operation of the physical system under consideration, and is supposed to have a fast (associated to a small parameter epsilon > 0) and a slow behavior. By using a similar approach as developed in Yin and Zhang (Continuous-Time Markov Chains and Applications: A Singular Perturbation Approach, Applications of Mathematics, vol. 37, Springer, New York, 1998, Chaps. 1 and 3) the idea in this paper is to reduce the number of regimes by considering an averaged model in which the regimes within the same class are aggregated through the quasi-stationary distribution so that the different states in this class are replaced by a single one. The main goal is to show that the value function of the control problem for the system driven by the perturbed Markov chain converges to the value function of this limit control problem as epsilon goes to zero. This convergence is obtained by, roughly speaking, showing that the infimum and supremum limits of the value functions satisfy two optimality inequalities as epsilon goes to zero. This enables us to show the result by invoking a uniqueness argument, without needing any kind of Lipschitz continuity condition.

Linear minimum mean square filter for discrete-time linear systems with Markov jumps and multiplicative noises

In this paper we obtain the linear minimum mean square estimator (LMMSE) for discrete-time linear systems subject to state and measurement multiplicative noises and Markov jumps on the parameters. It is assumed that the Markov chain is not available. By using geometric arguments we obtain a Kalman type filter conveniently implementable in a recurrence form. The stationary case is also studied and a proof for the convergence of the error covariance matrix of the LMMSE to a stationary value under the assumption of mean square stability of the system and ergodicity of the associated Markov chain is obtained. It is shown that there exists a unique positive semi-definite solution for the stationary Riccati-like filter equation and, moreover, this solution is the limit of the error covariance matrix of the LMMSE. The advantage of this scheme is that it is very easy to implement and all calculations can be performed offline. (c) 2011 Elsevier Ltd. All rights reserved.

S/MIMO MC-CDMA Heuristic Multiuser Detectors Based on Single-Objective Optimization

This paper analyzes the complexity-performance trade-off of several heuristic near-optimum multiuser detection (MuD) approaches applied to the uplink of synchronous single/multiple-input multiple-output multicarrier code division multiple access (S/MIMO MC-CDMA) systems. Genetic algorithm (GA), short term tabu search (STTS) and reactive tabu search (RTS), simulated annealing (SA), particle swarm optimization (PSO), and 1-opt local search (1-LS) heuristic multiuser detection algorithms (Heur-MuDs) are analyzed in details, using a single-objective antenna-diversity-aided optimization approach. Monte- Carlo simulations show that, after convergence, the performances reached by all near-optimum Heur-MuDs are similar. However, the computational complexities may differ substantially, depending on the system operation conditions. Their complexities are carefully analyzed in order to obtain a general complexity-performance framework comparison and to show that unitary Hamming distance search MuD (uH-ds) approaches (1-LS, SA, RTS and STTS) reach the best convergence rates, and among them, the 1-LS-MuD provides the best trade-off between implementation complexity and bit error rate (BER) performance.

Inteligência artificial aplicada à Zootecnia

Os sistemas biológicos são surpreendentemente flexíveis pra processar informação proveniente do mundo real. Alguns organismos biológicos possuem uma unidade central de processamento denominada de cérebro. O cérebro humano consiste de 10(11) neurônios e realiza processamento inteligente de forma exata e subjetiva. A Inteligência Artificial (IA) tenta trazer para o mundo da computação digital a heurística dos sistemas biológicos de várias maneiras, mas, ainda resta muito para que isso seja concretizado. No entanto, algumas técnicas como Redes neurais artificiais e lógica fuzzy tem mostrado efetivas para resolver problemas complexos usando a heurística dos sistemas biológicos. Recentemente o numero de aplicação dos métodos da IA em sistemas zootécnicos tem aumentado significativamente. O objetivo deste artigo é explicar os princípios básicos da resolução de problemas usando heurística e demonstrar como a IA pode ser aplicada para construir um sistema especialista para resolver problemas na área de zootecnia.

Characterization of Hepatitis B virus (HBV) genotypes in patients from Rondonia, Brazil

Background: Hepatitis B virus (HBV) can be classified into nine genotypes (A-I) defined by sequence divergence of more than 8% based on the complete genome. This study aims to identify the genotypic distribution of HBV in 40 HBsAg-positive patients from Rondonia, Brazil. A fragment of 1306 bp partially comprising surface and polymerase overlapping genes was amplified by PCR. Amplified DNA was purified and sequenced. Amplified DNA was purified and sequenced on an ABI PRISM (R) 377 Automatic Sequencer (Applied Biosystems, Foster City, CA, USA). The obtained sequences were aligned with reference sequences obtained from the GenBank using Clustal X software and then edited with Se-Al software. Phylogenetic analyses were conducted by the Markov Chain Monte Carlo (MCMC) approach using BEAST v.1.5.3. Results: The subgenotypes distribution was A1 (37.1%), D3 (22.8%), F2a (20.0%), D4 (17.1%) and D2 (2.8%). Conclusions: These results for the first HBV genotypic characterization in Rondonia state are consistent with other studies in Brazil, showing the presence of several HBV genotypes that reflects the mixed origin of the population, involving descendants from Native Americans, Europeans, and Africans.

Frequency and genotypic distribution of GB virus C (GBV-C) among Colombian population with Hepatitis B (HBV) or Hepatitis C (HCV) infection

Background: GB virus C (GBV-C) is an enveloped positive-sense ssRNA virus belonging to the Flaviviridae family. Studies on the genetic variability of the GBV-C reveals the existence of six genotypes: genotype 1 predominates in West Africa, genotype 2 in Europe and America, genotype 3 in Asia, genotype 4 in Southwest Asia, genotype 5 in South Africa and genotype 6 in Indonesia. The aim of this study was to determine the frequency and genotypic distribution of GBV-C in the Colombian population. Methods: Two groups were analyzed: i) 408 Colombian blood donors infected with HCV (n = 250) and HBV (n = 158) from Bogota and ii) 99 indigenous people with HBV infection from Leticia, Amazonas. A fragment of 344 bp from the 5' untranslated region (5' UTR) was amplified by nested RT PCR. Viral sequences were genotyped by phylogenetic analysis using reference sequences from each genotype obtained from GenBank (n = 160). Bayesian phylogenetic analyses were conducted using Markov chain Monte Carlo (MCMC) approach to obtain the MCC tree using BEAST v. 1.5.3. Results: Among blood donors, from 158 HBsAg positive samples, eight 5.06% (n = 8) were positive for GBV-C and from 250 anti-HCV positive samples, 3.2%(n = 8) were positive for GBV-C. Also, 7.7% (n = 7) GBV-C positive samples were found among indigenous people from Leticia. A phylogenetic analysis revealed the presence of the following GBV-C genotypes among blood donors: 2a (41.6%), 1 (33.3%), 3 (16.6%) and 2b (8.3%). All genotype 1 sequences were found in co-infection with HBV and 4/5 sequences genotype 2a were found in co-infection with HCV. All sequences from indigenous people from Leticia were classified as genotype 3. The presence of GBV-C infection was not correlated with the sex (p = 0.43), age (p = 0.38) or origin (p = 0.17). Conclusions: It was found a high frequency of GBV-C genotype 1 and 2 in blood donors. The presence of genotype 3 in indigenous population was previously reported from Santa Marta region in Colombia and in native people from Venezuela and Bolivia. This fact may be correlated to the ancient movements of Asian people to South America a long time ago.

Kinematic parameters and membership probabilities of open clusters in the Bordeaux PM2000 catalogue

Aims. We derive lists of proper-motions and kinematic membership probabilities for 49 open clusters and possible open clusters in the zone of the Bordeaux PM2000 proper motion catalogue (+ 11 degrees <= delta <= + 18 degrees). We test different parametrisations of the proper motion and position distribution functions and select the most successful one. In the light of those results, we analyse some objects individually. Methods. We differenciate between cluster and field member stars, and assign membership probabilities, by applying a new and fully automated method based on both parametrisations of the proper motion and position distribution functions, and genetic algorithm optimization heuristics associated with a derivative-based hill climbing algorithm for the likelihood optimization. Results. We present a catalogue comprising kinematic parameters and associated membership probability lists for 49 open clusters and possible open clusters in the Bordeaux PM2000 catalogue region. We note that this is the first determination of proper motions for five open clusters. We confirm the non-existence of two kinematic populations in the region of 15 previously suspected non-existent objects.

A simulation-based evolutionary multiobjective approach to manufacturing cell formation

The purpose of this paper is to propose a multiobjective optimization approach for solving the manufacturing cell formation problem, explicitly considering the performance of this said manufacturing system. Cells are formed so as to simultaneously minimize three conflicting objectives, namely, the level of the work-in-process, the intercell moves and the total machinery investment. A genetic algorithm performs a search in the design space, in order to approximate to the Pareto optimal set. The values of the objectives for each candidate solution in a population are assigned by running a discrete-event simulation, in which the model is automatically generated according to the number of machines and their distribution among cells implied by a particular solution. The potential of this approach is evaluated via its application to an illustrative example, and a case from the relevant literature. The obtained results are analyzed and reviewed. Therefore, it is concluded that this approach is capable of generating a set of alternative manufacturing cell configurations considering the optimization of multiple performance measures, greatly improving the decision making process involved in planning and designing cellular systems. (C) 2010 Elsevier Ltd. All rights reserved.

Performance of the Equivalent Reservoir Modelling Technique for Multi-Reservoir Hydropower Systems

This paper investigates the validity of a simplified equivalent reservoir representation of a multi-reservoir hydroelectric system for modelling its optimal operation for power maximization. This simplification, proposed by Arvanitidis and Rosing (IEEE Trans Power Appar Syst 89(2):319-325, 1970), imputes a potential energy equivalent reservoir with energy inflows and outflows. The hydroelectric system is also modelled for power maximization considering individual reservoir characteristics without simplifications. Both optimization models employed MINOS package for solution of the non-linear programming problems. A comparison between total optimized power generation over the planning horizon by the two methods shows that the equivalent reservoir is capable of producing satisfactory power estimates with less than 6% underestimation. The generation and total reservoir storage trajectories along the planning horizon obtained by equivalent reservoir method, however, presented significant discrepancies as compared to those found in the detailed modelling. This study is motivated by the fact that Brazilian generation system operations are based on the equivalent reservoir method as part of the power dispatch procedures. The potential energy equivalent reservoir is an alternative which eliminates problems with the dimensionality of state variables in a dynamic programming model.

Adaptive Approach for a Maximum Entropy Algorithm in Ecological Niche Modeling

This paper presents an Adaptive Maximum Entropy (AME) approach for modeling biological species. The Maximum Entropy algorithm (MaxEnt) is one of the most used methods in modeling biological species geographical distribution. The approach presented here is an alternative to the classical algorithm. Instead of using the same set features in the training, the AME approach tries to insert or to remove a single feature at each iteration. The aim is to reach the convergence faster without affect the performance of the generated models. The preliminary experiments were well performed. They showed an increasing on performance both in accuracy and in execution time. Comparisons with other algorithms are beyond the scope of this paper. Some important researches are proposed as future works.