Structure of trajectories of complex-matrix eigenvalues in the Hermitian-non-Hermitian transition

The statistical properties of trajectories of eigenvalues of Gaussian complex matrices whose Hermitian condition is progressively broken are investigated. It is shown how the ordering on the real axis of the real eigenvalues is reflected in the structure of the trajectories and also in the final distribution of the eigenvalues in the complex plane.

Average control of Markov decision processes with Feller transition probabilities and general action spaces

This paper studies the average control problem of discrete-time Markov Decision Processes (MDPs for short) with general state space, Feller transition probabilities, and possibly non-compact control constraint sets A(x). Two hypotheses are considered: either the cost function c is strictly unbounded or the multifunctions A(r)(x) = {a is an element of A(x) : c(x, a) <= r} are upper-semicontinuous and compact-valued for each real r. For these two cases we provide new results for the existence of a solution to the average-cost optimality equality and inequality using the vanishing discount approach. We also study the convergence of the policy iteration approach under these conditions. It should be pointed out that we do not make any assumptions regarding the convergence and the continuity of the limit function generated by the sequence of relative difference of the alpha-discounted value functions and the Poisson equations as often encountered in the literature. (C) 2012 Elsevier Inc. All rights reserved.

Using a matrix in life transition research

Life transitions can be planned or can occur unexpectedly. They can cause a major change to a person's life patterns and well-being. Older adulthood is a time for many life transitions as a result of changes in life roles and health status. In this exploratory study, the authors investigate the transition involved in driving cessation for older people. In analyzing and organizing the data, they develop a matrix that incorporated descriptive and temporal factors associated with the transition. This matrix is useful in organizing and communicating the findings as a whole and could be used in describing individual experiences. It might be of use for the organization of qualitative data about other life transitions such as illness, retirement, and the development and adoption of new behaviors.

Uniqueness criteria for continuous-time Markov chains with general transition structures

We derive necessary and sufficient conditions for the existence of bounded or summable solutions to systems of linear equations associated with Markov chains. This substantially extends a famous result of G. E. H. Reuter, which provides a convenient means of checking various uniqueness criteria for birth-death processes. Our result allows chains with much more general transition structures to be accommodated. One application is to give a new proof of an important result of M. F. Chen concerning upwardly skip-free processes. We then use our generalization of Reuter's lemma to prove new results for downwardly skip-free chains, such as the Markov branching process and several of its many generalizations. This permits us to establish uniqueness criteria for several models, including the general birth, death, and catastrophe process, extended branching processes, and asymptotic birth-death processes, the latter being neither upwardly skip-free nor downwardly skip-free.

The Cratylia Mollis Seed Lectin Induces Membrane Permeability Transition In Isolated Rat Liver Mitochondria And A Cyclosporine A-insensitive Permeability Transition In Trypanosoma Cruzi Mitochondria.

Previous results provided evidence that Cratylia mollis seed lectin (Cramoll 1,4) promotes Trypanosoma cruzi epimastigotes death by necrosis via a mechanism involving plasma membrane permeabilization to Ca(2+) and mitochondrial dysfunction due to matrix Ca(2+) overload. In order to investigate the mechanism of Ca(2+) -induced mitochondrial impairment, experiments were performed analyzing the effects of this lectin on T. cruzi mitochondrial fraction and in isolated rat liver mitochondria (RLM), as a control. Confocal microscopy of T. cruzi whole cell revealed that Cramoll 1,4 binding to the plasma membrane glycoconjugates is followed by its internalization and binding to the mitochondrion. Electrical membrane potential (∆Ψm ) of T. cruzi mitochondrial fraction suspended in a reaction medium containing 10 μM Ca(2+) was significantly decreased by 50 μg/ml Cramoll 1,4 via a mechanism insensitive to cyclosporine A (CsA, membrane permeability transition (MPT) inhibitor), but sensitive to catalase or 125 mM glucose. In RLM suspended in a medium containing 10 μM Ca(2+) this lectin, at 50 μg/ml, induced increase in the rate of hydrogen peroxide release, mitochondrial swelling, and ∆Ψm disruption. All these mitochondrial alterations were sensitive to CsA, catalase, and EGTA. These results indicate that Cramoll 1, 4 leads to inner mitochondrial membrane permeabilization through Ca(2+) dependent mechanisms in both mitochondria. The sensitivity to CsA in RLM characterizes this lectin as a MPT inducer and the lack of CsA effect identifies a CsA-insensitive MPT in T. cruzi mitochondria.

Oxidative Stress And Susceptibility To Mitochondrial Permeability Transition Precedes The Onset Of Diabetes In Autoimmune Non-obese Diabetic Mice.

Beta cell destruction in type 1 diabetes (TID) is associated with cellular oxidative stress and mitochondrial pathway of cell death. The aim of this study was to determine whether oxidative stress and mitochondrial dysfunction are present in T1D model (non-obese diabetic mouse, NOD) and if they are related to the stages of disease development. NOD mice were studied at three stages: non-diabetic, pre-diabetic, and diabetic and compared with age-matched Balb/c mice. Mitochondria respiration rates measured at phosphorylating and resting states in liver and soleus biopsies and in isolated liver mitochondria were similar in NOD and Balb/c mice at the three disease stages. However, NOD liver mitochondria were more susceptible to calcium-induced mitochondrial permeability transition as determined by cyclosporine-A-sensitive swelling and by decreased calcium retention capacity in all three stages of diabetes development. Mitochondria H2O2 production rate was higher in non-diabetic, but unaltered in pre-diabetic and diabetic NOD mice. The global cell reactive oxygen species (ROS), but not specific mitochondria ROS production, was significantly increased in NOD lymphomononuclear and stem cells in all disease stages. In addition, marked elevated rates of 2',7'-dichlorodihydrofluorescein (H2DCF) oxidation were observed in pancreatic islets from non-diabetic NOD mice. Using matrix-assisted laser desorption/ionization (MALDI) mass spectrometry (MS) and lipidomic approach, we identified oxidized lipid markers in NOD liver mitochondria for each disease stage, most of them being derivatives of diacylglycerols and phospholipids. These results suggest that the cellular oxidative stress precedes the establishment of diabetes and may be the cause of mitochondrial dysfunction that is involved in beta cell death.

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.

Isotropic and anisotropic spin-spin interactions and a quantum phase transition in a dinuclear Cu(II) compound

We report electron-paramagnetic resonance (EPR) studies at similar to 9.5 GHz (X band) and similar to 34 GHz (Q band) of powder and single-crystal samples of the compound Cu(2)[TzTs](4) [N-thiazol-2-yl-toluenesulfonamidatecopper(II)], C(40)H(36)Cu(2)N(8)O(8)S(8), having copper(II) ions in dinuclear units. Our data allow determining an antiferromagnetic interaction J(0)=(-113 +/- 1) cm(-1) (H(ex)=-J(0)S(1)center dot S(2)) between Cu(II) ions in the dinuclear unit and the anisotropic contributions to the spin-spin coupling matrix D (H(ani)=S(1)center dot D center dot S(2)), a traceless symmetric matrix with principal values D/4=(0.198 +/- 0.003) cm(-1) and E/4=(0.001 +/- 0.003) cm(-1) arising from magnetic dipole-dipole and anisotropic exchange couplings within the units. In addition, the single-crystal EPR measurements allow detecting and estimating very weak exchange couplings between neighbor dinuclear units, with an estimated magnitude parallel to J(')parallel to=(0.060 +/- 0.015) cm(-1). The interactions between a dinuclear unit and the ""environment"" of similar units in the structure of the compound produce a spin dynamics that averages out the intradinuclear dipolar interactions. This coupling with the environment leads to decoherence, a quantum phase transition that collapses the dipolar interaction when the isotropic exchange coupling with neighbor dinuclear units equals the magnitude of the intradinuclear dipolar coupling. Our EPR experiments provide a new procedure to follow the classical exchange-narrowing process as a shift and collapse of the line structure (not only as a change of the resonance width), which is described with general (but otherwise simple) theories of magnetic resonance. Using complementary procedures, our EPR measurements in powder and single-crystal samples allow measuring simultaneously three types of interactions differing by more than three orders of magnitude (between 113 cm(-1) and 0.060 cm(-1)).

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.

On the mechanisms of phenothiazine-induced mitochondrial permeability transition: Thiol oxidation, strict Ca(2+) dependence, and cyt c release

Phenothiazines (PTZ) are drugs widely used in the treatment of schizophrenia. Trifluoperazine, a piperazinic PTZ derivative, has been described as inhibitor of the mitochondrial permeability transition (MPT). We reported previously the antioxidant activity of thioridazine at relatively low concentrations associated to the inhibition of the MPT (Brit. J. Pharmacol., 2002;136:136-142). In this study, it was investigated the induction of MPT by PTZ derivatives at concentrations higher than 10 mu M focusing on the molecular mechanism involved. PTZ promoted a dose-response mitochondrial swelling accompanied by mitochondrial transmembrane potential dissipation and calcium release, being thioridazine the most potent derivative. PTZ-induced MPT was partially inhibited by CsA or Mg(2+) and completely abolished by the abstraction of calcium. The oxidation of reduced thiol group of mitochondrial membrane proteins by PTZ was upstream the VIP opening and it was not sufficient to promote the opening of PTP that only occurred when calcium was present in the mitochondrial matrix. EPR experiments using DMPO as spin trapping excluded the participation of reactive oxygen species on the PTZ-induced MPT. Since 117 give rise to cation radicals chemically by the action of peroxidases and cyanide inhibited the PTZ-induced swelling, we propose that VIZ bury in the inner mitochondrial membrane and the chemically generated 117 cation radicals modify specific thiol groups that in the presence of Ca(2+) result in MPT associated to cytochrome c release. These findings contribute for the understanding of mechanisms of MET induction and may have implications for the cell death induced by PTZ. (C) 2010 Elsevier Inc. All rights reserved.

Impact of adenosine nucleotide translocase (ANT) proline isomerization on Ca(2+)-induced cysteine relative mobility/mitochondrial permeability transition pore

Mitochondrial membrane carriers containing proline and cysteine, such as adenine nucleotide translocase (ANT), are potential targets of cyclophilin D (CyP-D) and potential Ca(2+)-induced permeability transition pore (PTP) components or regulators; CyP-D, a mitochondrial peptidyl-prolyl cis-trans isomerase, is the probable target of the PTP inhibitor cyclosporine A (CsA). In the present study, the impact of proline isomerization (from trans to cis) on the mitochondrial membrane carriers containing proline and cysteine was addressed using ANT as model. For this purpose, two different approaches were used: (i) Molecular dynamic (MD) analysis of ANT-Cys(56) relative mobility and (ii) light scattering techniques employing rat liver isolated mitochondria to assess both Ca(2+)-induced ANT conformational change and mitochondrial swelling. ANT-Pro(61) isomerization increased ANT-Cys(56) relative mobility and, moreover, desensitized ANT to the prevention of this effect by ADP. In addition, Ca(2+) induced ANT ""c"" conformation and opened PTP; while the first effect was fully inhibited, the second was only attenuated by CsA or ADP. Atractyloside (ATR), in turn, stabilized Ca(2+)-induced ANT ""c"" conformation, rendering the ANT conformational change and PTP opening less sensitive to the inhibition by CsA or ADP. These results suggest that Ca(2+) induces the ANT ""c"" conformation, apparently associated with PTP opening, but requires the CyP-D peptidyl-prolyl cis-trans isomerase activity for sustaining both effects.

Entanglement in a simple quantum phase transition

What entanglement is present in naturally occurring physical systems at thermal equilibrium? Most such systems are intractable and it is desirable to study simple but realistic systems that can be solved. An example of such a system is the one-dimensional infinite-lattice anisotropic XY model. This model is exactly solvable using the Jordan-Wigner transform, and it is possible to calculate the two-site reduced density matrix for all pairs of sites. Using the two-site density matrix, the entanglement of formation between any two sites is calculated for all parameter values and temperatures. We also study the entanglement in the transverse Ising model, a special case of the XY model, which exhibits a quantum phase transition. It is found that the next-nearest-neighbor entanglement (though not the nearest-neighbor entanglement) is a maximum at the critical point. Furthermore, we show that the critical point in the transverse Ising model corresponds to a transition in the behavior of the entanglement between a single site and the remainder of the lattice.

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.