Generalized Coupled Algebraic Riccati Equations for Discrete-time Markov Jump with Multiplicative Noise Systems

In this paper we consider the existence of the maximal and mean square stabilizing solutions for a set of generalized coupled algebraic Riccati equations (GCARE for short) associated to the infinite-horizon stochastic optimal control problem of discrete-time Markov jump with multiplicative noise linear systems. The weighting matrices of the state and control for the quadratic part are allowed to be indefinite. We present a sufficient condition, based only on some positive semi-definite and kernel restrictions on some matrices, under which there exists the maximal solution and a necessary and sufficient condition under which there exists the mean square stabilizing solution fir the GCARE. We also present a solution for the discounted and long run average cost problems when the performance criterion is assumed be composed by a linear combination of an indefinite quadratic part and a linear part in the state and control variables. The paper is concluded with a numerical example for pension fund with regime switching.

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.

A generalized multi-period mean-variance portfolio optimization with Markov switching parameters

In this paper, we deal with a generalized multi-period mean-variance portfolio selection problem with market parameters Subject to Markov random regime switchings. Problems of this kind have been recently considered in the literature for control over bankruptcy, for cases in which there are no jumps in market parameters (see [Zhu, S. S., Li, D., & Wang, S. Y. (2004). Risk control over bankruptcy in dynamic portfolio selection: A generalized mean variance formulation. IEEE Transactions on Automatic Control, 49, 447-457]). We present necessary and Sufficient conditions for obtaining an optimal control policy for this Markovian generalized multi-period meal-variance problem, based on a set of interconnected Riccati difference equations, and oil a set of other recursive equations. Some closed formulas are also derived for two special cases, extending some previous results in the literature. We apply the results to a numerical example with real data for Fisk control over bankruptcy Ill a dynamic portfolio selection problem with Markov jumps selection problem. (C) 2008 Elsevier Ltd. All rights reserved.

Neuropharmacological effects in mice of Lychnophora species (Vernonieae, Asteraceae) and anticonvulsant activity of 4,5-di-O-[E]-caffeoylquinic acid isolated from the stem of L-rupestris and L-staavioides

Aiming at contributing with the search for neuroactive substances from natural sources, we report for the first time antinociceptive and anticonvulsant effects of some Lychnophora species. We verify the protective effects of polar extracts (600 mg/kg, intraperitoneally), and methanolic fractions of L. staavioides and L. rupestris (100 mg/kg, intraperitoneally) in pentylenetetrazole-induced seizures on mice. Previously, a screening was accomplished, evaluating the antinociceptive central activity (hot plate test), with different extracts of L. rupestris, L. staavioides and L. diamantinana. It was possible to select the possible extracts of Lychnophora with central nervous system activity. Some of the active extracts were submitted to fractionation and purification process and the methanolic fractions of L. rupestris (stem) and L. staavioides (stem), with anticonvulsant properties (100 mg/kg, intraperitoneally), yielded 4,5-di-O-[E]-caffeoylquinic acid. This substance was injected intraperitoneally in mice and showed anticonvulsant effect against pentylenetetrazole-induced seizures at doses of 25 and 50 mg/kg. It has often been shown that seizures induced by pentylenetetrazole are involved in inhibition and/or attenuation of GABAergic neurotransmission. However, other systems of the central nervous system such as adenosinergic and glutamatergic could be involved in the caffeoylquinic acid effects. Further studies should be conducted to verify that the target receptor could be participating in this anticonvulsant property. Although other investigations have reported a series of biological activities from Lychnophora species, this is the first report of central analgesic and anticonvulsant activity in species of this genus.

Copper(II) complexes of mono- and di-nucleating hexaamines

The potentially hexadentate polyamines N,N,N',N'-tetrakis(2-aminoethyl)ethane-1,2-diamine (L-1) and the octamethylated analogue N,N,N',N'-tetrakis(2-dimethylaminoethyl)ethane 1,2-diamine (L-2) have been complexed with copper(II) and the crystal structures of their complexes determined. A trigonal-bipyramidal co-ordination geometry for [Cu(HL1)][ClO4](3) was found where one aminoethyl arm is not co-ordinated. By contrast, a dinuclear structure of formula [(H2O)Cu(L-2)Cu(OH)](3+) was determined for the N-methylated analogue, where the hexaamine acts as a bridging ligand between the two square-pyramidal metal centres. Electronic and EPR spectroscopy are both consistent with these structures being maintained in solution.

Stage-specific proteophosphoglycan from Leishmania mexicana amastigotes - Structural characterization of novel mono-, di-, and triphosphorylated phosphodiester-linked oligosaccharides

Intracellular amastigotes of the protozoan parasite Leishmania mexicana secrete a macromolecular proteophosphoglycan (aPPG) into the phagolysosome of their host cell, the mammalian macrophage. The structures of aPPG glycans were analyzed by a combination of high pH anion exchange high pressure liquid chromatography, gas chromatography-mass spectrometry, enzymatic digestions, electrospray-mass spectrometry as well as H-1 and P-31 NMR spectroscopy. Some glycans are identical to oligosaccharides known from Leishmania mexicana promastigote lipophosphoglycan and secreted acid phosphatase, However, the majority of the aPPG glycans represent amastigote stage-specific and novel structures. These include neutral glycans ([Glc beta(1-3)](1-2)Gal beta 1-4Man, Gal beta 1-3Gal beta 1-4Man, Gal beta 1-3Glc beta 1-3Gal beta 1-4Man), several monophosphorylated glycans containing the conserved phosphodisaccharide backbone (R-3-[PO4-6-Gal]beta 1-4Man) but carrying stage-specific modifications (R = Gal beta 1-, [Glc beta 1-3](1-2)Glc beta 1-), and monophosphorylated aPPG tri- and tetrasaccharides that are uniquely phosphorylated on the terminal hexose (PO4-6-Glc beta 1-3Gal beta 1-4Man, PO4-6-Glc beta 1-3Glc beta 1-3Gal beta 1-4Man, PO4-6-Gal beta 1-3Glc beta 1-3Gal beta 1-4Man), In addition aPPG contains highly unusual di- and triphosphorylated glycans whose major species are PO4-6-Glc beta 1-3Glc beta 1-3[PO4-6-Gal]beta 1-4Man, PO4-6-Gal beta 1-3Glc beta 1-3 [PO4-6-Gal]beta 1-4Man, PO4-6-GaL beta 1-3Glc beta 1-3Glc beta 1-3[PO4-6-Gal]beta 1-4Man, PO4-6-Glc beta 1-3[PO4-6-Glc]beta 1-3[PO4-6-Gal]beta 1-4Man, PO4-6Gal beta 1-3[PO4-6-Glc]beta 1-3Glc beta 1-3[PO4-6-Gal]beta 1-4Man, and PO4-6-Glc beta 1-3[PO4-6-Glc]beta 1-3Glc beta 1-3[PO4-6-Gal]beta 1-4Man. These glycans are linked together by the conserved phosphodiester R-Man alpha 1-PO4-6-Gal-R or the novel phosphodiester R-Man alpha 1-PO4-6-Glc-R and are connected to Ser(P) of the protein backbone most likely via the linkage R-Man alpha 1-PO4-Ser. The variety of stage-specific glycan structures in Leishmania mexicana aPPG suggests the presence of developmentally regulated amastigote glycosyltransferases which may be potential anti-parasite drug targets.

A numerical study of large sparse matrix exponentials arising in Markov chains

Krylov subspace techniques have been shown to yield robust methods for the numerical computation of large sparse matrix exponentials and especially the transient solutions of Markov Chains. The attractiveness of these methods results from the fact that they allow us to compute the action of a matrix exponential operator on an operand vector without having to compute, explicitly, the matrix exponential in isolation. In this paper we compare a Krylov-based method with some of the current approaches used for computing transient solutions of Markov chains. After a brief synthesis of the features of the methods used, wide-ranging numerical comparisons are performed on a power challenge array supercomputer on three different models. (C) 1999 Elsevier Science B.V. All rights reserved.AMS Classification: 65F99; 65L05; 65U05.

Quasistationarity of continuous-time Markov chains with positive drift

We shall study continuous-time Markov chains on the nonnegative integers which are both irreducible and transient, and which exhibit discernible stationarity before drift to infinity sets in. We will show how this 'quasi' stationary behaviour can be modelled using a limiting conditional distribution: specifically, the limiting state probabilities conditional on not having left 0 for the last time. By way of a dual chain, obtained by killing the original process on last exit from 0, we invoke the theory of quasistationarity for absorbing Markov chains. We prove that the conditioned state probabilities of the original chain are equal to the state probabilities of its dual conditioned on non-absorption, thus allowing us to establish the simultaneous existence and then equivalence, of their limiting conditional distributions. Although a limiting conditional distribution for the dual chain is always a quasistationary distribution in the usual sense, a similar statement is not possible for the original chain.

Further results on the relationship between mu-invariant measures and quasi-stationary distributions for absorbing continuous-time Markov chains

This note considers continuous-time Markov chains whose state space consists of an irreducible class, C, and an absorbing state which is accessible from C. The purpose is to provide results on mu-invariant and mu-subinvariant measures where absorption occurs with probability less than one. In particular, the well-known premise that the mu-invariant measure, m, for the transition rates be finite is replaced by the more natural premise that m be finite with respect to the absorption probabilities. The relationship between mu-invariant measures and quasi-stationary distributions is discussed. (C) 2000 Elsevier Science Ltd. All rights reserved.

New methods for determining quasi-stationary distributions for Markov chains

We shall be concerned with the problem of determining quasi-stationary distributions for Markovian models directly from their transition rates Q. We shall present simple conditions for a mu-invariant measure m for Q to be mu-invariant for the transition function, so that if m is finite, it can be normalized to produce a quasi-stationary distribution. (C) 2000 Elsevier Science Ltd. All rights reserved.

Neighborhood and Efficiency in Manufacturing in Brazilian Regions: A Spatial Markov Chain Analysis

This paper analyzes the geography of regional competitiveness in manufacturing in Brazil. The authors estimate stochastic frontiers to calculate regional efficiency of representative firms in 137 regions in the period 2000-2006, in four sectors defined by technological intensity. The efficiency results are analyzed using Markov Spatial Transition Matrices to provide insights into the transition of regions between efficiency levels, considering their local spatial context. The results indicate that geography plays an important role in manufacturing competitiveness. In particular, regions with more competitive neighbors are more likely to improve their relative efficiency (pull effect) over time, and regions with less competitive neighbors are more likely to lose relative efficiency (drag effect). The authors find that the pull effect is stronger than the drag effect.

Synthesis and electrochemical properties of vanadyl phosphate di-hydrate/polyaniline derivatives hybrid films

Vanadyl phosphate and its hybrid compounds have proven to undergo electrochemical intercalation and de-intercalation of lithium ions, which enables its use as cathode material for Li ion rechargeable batteries. In this context, vanadyl phosphate di-hydrate/polyaniline derivatives hybrid films were synthesized via the exfoliation and reconstruction approach in order to evaluate their potential use as cathode in ion lithium batteries. X-ray diffraction patterns indicate that the lamellar structure of the inorganic matrix is maintained, consistent with the topotactic process. In the scanning electron micrographs, hybrid films exhibit rough surface consisting of warped and cracked crystallites, quite different from vanadyl phosphate di-hydrate square platelets crystallites. Electrochemical evaluation using cyclic voltammetry and charge-discharge galvanostatic techniques shows small differences between the charge and the discharge curves, indicating an irreversibility of the hybrid systems. (C) 2009 Elsevier B.V. All rights reserved.

Characterization of the rat exploratory behavior in the elevated plus-maze with Markov chains

The elevated plus-maze is an animal model of anxiety used to study the effect of different drugs on the behavior of the animal It consists of a plus-shaped maze with two open and two closed arms elevated 50 cm from the floor The standard measures used to characterize exploratory behavior in the elevated plus-maze are the time spent and the number of entries in the open arms In this work we use Markov chains to characterize the exploratory behavior of the rat in the elevated plus-maze under three different conditions normal and under the effects of anxiogenic and anxiolytic drugs The spatial structure of the elevated plus-maze is divided into squares which are associated with states of a Markov chain By counting the frequencies of transitions between states during 5-min sessions in the elevated plus-maze we constructed stochastic matrices for the three conditions studied The stochastic matrices show specific patterns which correspond to the observed behaviors of the rat under the three different conditions For the control group the stochastic matrix shows a clear preference for places in the closed arms This preference is enhanced for the anxiogenic group For the anxiolytic group the stochastic matrix shows a pattern similar to a random walk Our results suggest that Markov chains can be used together with the standard measures to characterize the rat behavior in the elevated plus-maze (C) 2010 Elsevier B V All rights reserved

Reproductive development and function of female rats exposed to di-eta-butyl-phthalate (DBP) in utero and during lactation

Phthalates are environmental contaminants used in the production of plastics, cosmetics and medical devices. Studies on the effects of phthalates on female reproductive health are particularly sparse and mostly restricted to high-dose exposure in rats. In the present study, pregnant rats were treated with 100 mg/kg-d of di-eta-butyl-phthalate (DBP) or only the vehicle (control group), from GD 12 to GD 20 for evaluation of reproductive outcomes and fetal gonads analysis (F0), and from GD 12 to PND 21 to evaluate reproductive development and function on F1 female offspring. Results showed that all parameters were comparable between groups, although there was a significant increase in the fetal weight after DBP exposure. However, the body weight at birth was normal. Based on these data we can conclude that, in these experimental conditions, DBP did not disturb the reproductive development or function of female rats. (C) 2009 Elsevier Inc. All rights reserved.