THE VANISHING DISCOUNT APPROACH FOR THE AVERAGE CONTINUOUS CONTROL OF PIECEWISE DETERMINISTIC MARKOV PROCESSES

This work is concerned with the existence of an optimal control strategy for the long-run average continuous control problem of piecewise-deterministic Markov processes (PDMPs). In Costa and Dufour (2008), sufficient conditions were derived to ensure the existence of an optimal control by using the vanishing discount approach. These conditions were mainly expressed in terms of the relative difference of the alpha-discount value functions. The main goal of this paper is to derive tractable conditions directly related to the primitive data of the PDMP to ensure the existence of an optimal control. The present work can be seen as a continuation of the results derived in Costa and Dufour (2008). Our main assumptions are written in terms of some integro-differential inequalities related to the so-called expected growth condition, and geometric convergence of the post-jump location kernel associated to the PDMP. An example based on the capacity expansion problem is presented, illustrating the possible applications of the results developed in the paper.

Discrete-time mean variance optimal control of linear systems with Markovian jumps and multiplicative noise

In this article, we consider the stochastic optimal control problem of discrete-time linear systems subject to Markov jumps and multiplicative noise under three kinds of performance criterions related to the final value of the expectation and variance of the output. In the first problem it is desired to minimise the final variance of the output subject to a restriction on its final expectation, in the second one it is desired to maximise the final expectation of the output subject to a restriction on its final variance, and in the third one it is considered a performance criterion composed by a linear combination of the final variance and expectation of the output of the system. We present explicit sufficient conditions for the existence of an optimal control strategy for these problems, generalising previous results in the literature. We conclude this article presenting a numerical example of an asset liabilities management model for pension funds with regime switching.

Flatness-based control of a single qubit gate

This work considers the open-loop control problem of steering a two-level quantum system from any initial to any final condition. The model of this system evolves on the state space X = SU(2), having two inputs that correspond to the complex amplitude of a resonant laser field. A symmetry preserving flat output is constructed using a fully geometric construction and quaternion computations. Simulation results of this flatness-based open-loop control are provided.

On recent developments in the theory of abstract differential equations with fractional derivatives

This note is motivated from some recent papers treating the problem of the existence of a solution for abstract differential equations with fractional derivatives. We show that the existence results in [Agarwal et al. (2009) [1], Belmekki and Benchohra (2010) [2], Darwish et al. (2009) [3], Hu et al. (2009) [4], Mophou and N`Guerekata (2009) [6,7], Mophou (2010) [8,9], Muslim (2009) [10], Pandey et al. (2009) [11], Rashid and El-Qaderi (2009) [12] and Tai and Wang (2009) [13]] are incorrect since the considered variation of constant formulas is not appropriate. In this note, we also consider a different approach to treat a general class of abstract fractional differential equations. (C) 2010 Elsevier Ltd. All rights reserved.

Observer agreement of spine stenosis on magnetic resonance imaging analysis of patients with cervical spine myelopathy

Objectives: The purpose of this study was to measure the intraobserver and interobserver reliability of magnetic resonance detection of cervical spondylotic myelopathy with and without operational guidelines. Methods: Seven radiologists examined images from 10 patients with cord signal abnormalities and clinical signs of myelopathy. Radiologist examined films twice, with and without operational guidelines designed to define stenotic changes, while blinded to the clinical findings of the patients. Analyses included a Fleiss kappa assessment of intraobserver and interobserver reliability. Results: Results demonstrated high percentage of agreement and strong intraobserver reliability and variable Fleiss kappa, values for interobserver assessment. Operational guidelines did not improve the intraobserver or interobserver agreement. Conclusion: Although the percentage of agreement was high in some cases, the kappa agreement was low-most likely a result of the base rate problem of a kappa analysis. Sample bias toward severe degenerative changes resulted in highly prevalent selections and kappa adjusted values. Nonetheless, the results do suggest that substantial intraobserver kappa agreement and a wide range of interobserver kappa agreement exists among trained radiologists during detection of stenotic changes associated with cervical spondylotic myelopathy.

Transillumination-guided Study of the Endoscopic Anatomy of the Lacrimal Fossa

Dacryocystorhinostomy is the treatment of choice for the obstruction of the lachrymal apparatus. At the end of last century, the development of the endoscopic instruments for nasosinusal surgery has made it possible to do it through the endoscopic pathway. Nonetheless, anatomical variations make it difficult to have reproducibility endonasaly. Aim: study the endoscopic anatomy of the lachrymal fossa through transillumination of the common canaliculus. Study design: experimental. Materials and Methods: we dissected 40 lachrymal pathways from 20 human cadavers, in three stages: 1. identification and dilation of the lachrymal canaliculus. 2 Optic fiber beam introduction; 3 - endoscopic dissection of the lachrymal sac, describing its position. Results: the most frequent position of the lachrymal sac was between the free border of the middle turbinate and its insertion immediately underneath it. The maxillary line was seen in 95% of the cases. Septoplasty was needed in 12.5%, unicifectomy in 35% and middle turbinectomy in 7.5%. Conclusion: Although the lachrymal sac has a more frequent location, its position varied considerably. The transillumination of the common canaliculus proved useful, solving the problem of the anatomical variability.

Intra- and inter-observer reliability of MRI examination of intervertebral disc abnormalities in patients with cervical myelopathy

Purpose: Intervertebral cervical disc herniation (CDH) is a relatively common disorder that can coexist with degenerative changes to worsen cervicogenic myelopathy. Despite the frequent disc abnormalities found in asymptomatic populations, magnetic resonance imaging (MRI) is considered excellent at detecting cervical spine myelopathy (CSM) associated with disc abnormality. The objective of this study was to investigate the intra- and inter-observer reliability of MRI detection of CSM in subjects who also had co-existing intervertebral disc abnormalities. Materials and methods: Seven experienced radiologists reviewed twice the MRI of 10 patients with clinically and/or imaging determined myelopathy. MRI assessment was performed individually, with and without operational guidelines. A Fleiss Kappa statistic was used to evaluate the intra- and inter-observer agreement. Results: The study found high intra-observer percent agreement but relatively low Kappa values on selected variables. Inter-observer reliability was also low and neither observation was improved with operational guidelines. We believe that those low values may be associated with the base rate problem of Kappa. Conclusion: In conclusion, this study demonstrated high intra-observer percent agreement in MR examination for intervertebral disc abnormalities in patients with underlying cervical myelopathy, but differing levels of intra- and inter-observer Kappa agreement among seven radiologists. (c) 2007 Elsevier Ireland Ltd. All rights reserved.

Continuous and High-Level In Vivo Delivery of Endostatin From Recombinant Cells Encapsulated in TheraCyte (R) Immunoisolation Devices

Endostatin (ES) is a potent inhibitor of angiogenesis and tumor growth. Continuous ES delivery of ES improves the efficacy and potency of the antitumoral therapy. The TheraCyte (R) system is a polytetrafluoroethylene (PTFE) semipermeable membrane macroencapsulation system for implantation of genetically engineered cells specially designed for the in vivo delivery of therapeutic proteins, such as ES, which circumvents the problem of limited half-life and variation in circulating levels. In order to enable neovascularization at the tissues adjacent to the devices prior to ES secretion by the cells inside them, we designed a scheme in which empty TheraCyte (R) devices were preimplanted SC into immunodeficient mice. Only after healing (17 days later) were Chinese hamster ovary cells expressing ES injected into the preimplanted devices. In another model for device implantation, the cells expressing ES where loaded into the immunoisolation devices prior to implantation into the animals, and the TheraCyte (R) were then immediately implanted SC into the mice. Throughout the 2-month study, constant high ES levels of up to 3.7 mu g/ml were detected in the plasma of the mice preimplanted with the devices, while lower but also constant levels of ES (up to 2.1 mu g/ml plasma) were detected in the mice that had received devices preloaded with the ES-expressing cells. Immunohistochemistry using anti-ES antibody showed reaction within the device and outside it, demonstrating that ES, secreted by the confined recombinant cells, permeated through the membrane and reached the surrounding tissues.

Identification and lineage genotyping of South American trypanosomes using fluorescent fragment length barcoding

Trypanosoma cruzi and Trypanosoma rangeli are human-infective blood parasites, largely restricted to Central and South America. They also infect a wide range of wild and domestic mammals and are transmitted by a numerous species of triatomine bugs. There are significant overlaps in the host and geographical ranges of both species. The two species consist of a number of distinct phylogenetic lineages. A range of PCR-based techniques have been developed to differentiate between these species and to assign their isolates into lineages. However, the existence of at least six and five lineages within T. cruzi and T. rangeli, respectively, makes identification of the full range of isolates difficult and time consuming. Here we have applied fluorescent fragment length barcoding (FFLB) to the problem of identifying and genotyping T. cruzi, T. rangeli and other South American trypanosomes. This technique discriminates species on the basis of length polymorphism of regions of the rDNA locus. FFLB was able to differentiate many trypanosome species known from South American mammals: T. cruzi cruzi. T. cruzi marinkellei, T. dionisii-like, T. evansi, T. lewisi, T. rangeli, T. theileri and T. vivax. Furthermore, all five T. rangeli lineages and many T. cruzi lineages could be identified, except the hybrid lineages TcV and TcVI that could not be distinguished from lineages III and II respectively. This method also allowed identification of mixed infections of T. cruzi and T. rangeli lineages in naturally infected triatomine bugs. The ability of FFLB to genotype multiple lineages of T. cruzi and T. rangeli together with other trypanosome species, using the same primer sets is an advantage over other currently available techniques. Overall, these results demonstrate that FFLB is a useful method for species diagnosis, genotyping and understanding the epidemiology of American trypanosomes. (C) 2010 Elsevier B.V. All rights reserved.

On the efficiency of evolutionary fuzzy clustering

This paper tackles the problem of showing that evolutionary algorithms for fuzzy clustering can be more efficient than systematic (i.e. repetitive) approaches when the number of clusters in a data set is unknown. To do so, a fuzzy version of an Evolutionary Algorithm for Clustering (EAC) is introduced. A fuzzy cluster validity criterion and a fuzzy local search algorithm are used instead of their hard counterparts employed by EAC. Theoretical complexity analyses for both the systematic and evolutionary algorithms under interest are provided. Examples with computational experiments and statistical analyses are also presented.

Estimating the number of ozone peaks in Mexico City using a non-homogeneous Poisson model

In this paper, we consider the problem of estimating the number of times an air quality standard is exceeded in a given period of time. A non-homogeneous Poisson model is proposed to analyse this issue. The rate at which the Poisson events occur is given by a rate function lambda(t), t >= 0. This rate function also depends on some parameters that need to be estimated. Two forms of lambda(t), t >= 0 are considered. One of them is of the Weibull form and the other is of the exponentiated-Weibull form. The parameters estimation is made using a Bayesian formulation based on the Gibbs sampling algorithm. The assignation of the prior distributions for the parameters is made in two stages. In the first stage, non-informative prior distributions are considered. Using the information provided by the first stage, more informative prior distributions are used in the second one. The theoretical development is applied to data provided by the monitoring network of Mexico City. The rate function that best fit the data varies according to the region of the city and/or threshold that is considered. In some cases the best fit is the Weibull form and in other cases the best option is the exponentiated-Weibull. Copyright (C) 2007 John Wiley & Sons, Ltd.

Genesis of quantum nonlocality

We revisit the problem of an otherwise classical particle immersed in the zero-point radiation field, with the purpose of tracing the origin of the nonlocality characteristic of Schrodinger`s equation. The Fokker-Planck-type equation in the particles phase-space leads to an infinite hierarchy of equations in configuration space. In the radiationless limit the first two equations decouple from the rest. The first is the continuity equation: the second one, for the particle flux, contains a nonlocal term due to the momentum fluctuations impressed by the field. These equations are shown to lead to Schrodinger`s equation. Nonlocality (obtained here for the one-particle system) appears thus as a property of the description, not of Nature. (C) 2011 Elsevier B.V. All rights reserved.

Realistic calculations of carbon-based disordered systems

Carbon nanotubes rank amongst potential candidates for a new family of nanoscopic devices, in particular for sensing applications. At the same time that defects in carbon nanotubes act as binding sites for foreign species, our current level of control over the fabrication process does not allow one to specifically choose where these binding sites will actually be positioned. In this work we present a theoretical framework for accurately calculating the electronic and transport properties of long disordered carbon nanotubes containing a large number of binding sites randomly distributed along a sample. This method combines the accuracy and functionality of ab initio density functional theory to determine the electronic structure with a recursive Green`s functions method. We apply this methodology on the problem of nitrogen-rich carbon nanotubes, first considering different types of defects and then demonstrating how our simulations can help in the field of sensor design by allowing one to compute the transport properties of realistic nanotube devices containing a large number of randomly distributed binding sites.

Path integral representations in noncommutative quantum mechanics and noncommutative version of Berezin-Marinov action

It is known that the actions of field theories on a noncommutative space-time can be written as some modified (we call them theta-modified) classical actions already on the commutative space-time (introducing a star product). Then the quantization of such modified actions reproduces both space-time noncommutativity and the usual quantum mechanical features of the corresponding field theory. In the present article, we discuss the problem of constructing theta-modified actions for relativistic QM. We construct such actions for relativistic spinless and spinning particles. The key idea is to extract theta-modified actions of the relativistic particles from path-integral representations of the corresponding noncommutative field theory propagators. We consider the Klein-Gordon and Dirac equations for the causal propagators in such theories. Then we construct for the propagators path-integral representations. Effective actions in such representations we treat as theta-modified actions of the relativistic particles. To confirm the interpretation, we canonically quantize these actions. Thus, we obtain the Klein-Gordon and Dirac equations in the noncommutative field theories. The theta-modified action of the relativistic spinning particle is just a generalization of the Berezin-Marinov pseudoclassical action for the noncommutative case.

The game of contacts: Estimating the social visibility of groups

Estimating the sizes of hard-to-count populations is a challenging and important problem that occurs frequently in social science, public health, and public policy. This problem is particularly pressing in HIV/AIDS research because estimates of the sizes of the most at-risk populations-illicit drug users, men who have sex with men, and sex workers-are needed for designing, evaluating, and funding programs to curb the spread of the disease. A promising new approach in this area is the network scale-up method, which uses information about the personal networks of respondents to make population size estimates. However, if the target population has low social visibility, as is likely to be the case in HIV/AIDS research, scale-up estimates will be too low. In this paper we develop a game-like activity that we call the game of contacts in order to estimate the social visibility of groups, and report results from a study of heavy drug users in Curitiba, Brazil (n = 294). The game produced estimates of social visibility that were consistent with qualitative expectations but of surprising magnitude. Further, a number of checks suggest that the data are high-quality. While motivated by the specific problem of population size estimation, our method could be used by researchers more broadly and adds to long-standing efforts to combine the richness of social network analysis with the power and scale of sample surveys. (C) 2010 Elsevier B.V. All rights reserved.