A Separation Principle for the Continuous-Time LQ-Problem With Markovian Jump Parameters

In this paper, we devise a separation principle for the finite horizon quadratic optimal control problem of continuous-time Markovian jump linear systems driven by a Wiener process and with partial observations. We assume that the output variable and the jump parameters are available to the controller. It is desired to design a dynamic Markovian jump controller such that the closed loop system minimizes the quadratic functional cost of the system over a finite horizon period of time. As in the case with no jumps, we show that an optimal controller can be obtained from two coupled Riccati differential equations, one associated to the optimal control problem when the state variable is available, and the other one associated to the optimal filtering problem. This is a separation principle for the finite horizon quadratic optimal control problem for continuous-time Markovian jump linear systems. For the case in which the matrices are all time-invariant we analyze the asymptotic behavior of the solution of the derived interconnected Riccati differential equations to the solution of the associated set of coupled algebraic Riccati equations as well as the mean square stabilizing property of this limiting solution. When there is only one mode of operation our results coincide with the traditional ones for the LQG control of continuous-time linear systems.

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.

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.

Anomalous diffusion in non-Markovian walks having amnestically induced persistence

We report numerically and analytically estimated values for the Hurst exponent for a recently proposed non-Markovian walk characterized by amnestically induced persistence. These results are consistent with earlier studies showing that log-periodic oscillations arise only for large memory losses of the recent past. We also report numerical estimates of the Hurst exponent for non-Markovian walks with diluted memory. Finally, we study walks with a fractal memory of the past for a Thue-Morse and Fibonacci memory patterns. These results are interpreted and discussed in the context of the necessary and sufficient conditions for the central limit theorem to hold.

Non-Markovian dynamics of quantum discord

We evaluate the quantum discord dynamics of two qubits in independent and common non-Markovian environments. We compare the dynamics of entanglement with that of quantum discord. For independent reservoirs the quantum discord vanishes only at discrete instants whereas the entanglement can disappear during a finite time interval. For a common reservoir, quantum discord and entanglement can behave very differently with sudden birth of the former but not of the latter. Furthermore, in this case the quantum discord dynamics presents sudden changes in the derivative of its time evolution which is evidenced by the presence of kinks in its behavior at discrete instants of time.

A Markovian model market-Akerlof`s lemons and the asymmetry of information

In this work we study an agent based model to investigate the role of asymmetric information degrees for market evolution. This model is quite simple and may be treated analytically since the consumers evaluate the quality of a certain good taking into account only the quality of the last good purchased plus her perceptive capacity beta. As a consequence, the system evolves according to a stationary Markov chain. The value of a good offered by the firms increases along with quality according to an exponent alpha, which is a measure of the technology. It incorporates all the technological capacity of the production systems such as education, scientific development and techniques that change the productivity rates. The technological level plays an important role to explain how the asymmetry of information may affect the market evolution in this model. We observe that, for high technological levels, the market can detect adverse selection. The model allows us to compute the maximum asymmetric information degree before the market collapses. Below this critical point the market evolves during a limited period of time and then dies out completely. When beta is closer to 1 (symmetric information), the market becomes more profitable for high quality goods, although high and low quality markets coexist. The maximum asymmetric information level is a consequence of an ergodicity breakdown in the process of quality evaluation. (C) 2011 Elsevier B.V. All rights reserved.

A Fault-Tolerant Manipulator Robot Based on H(2), H(infinity), and Mixed H(2)/H(infinity) Markovian Controls

This paper develops a Markovian jump model to describe the fault occurrence in a manipulator robot of three joints. This model includes the changes of operation points and the probability that a fault occurs in an actuator. After a fault, the robot works as a manipulator with free joints. Based on the developed model, a comparative study among three Markovian controllers, H(2), H(infinity), and mixed H(2)/H(infinity) is presented, applied in an actual manipulator robot subject to one and two consecutive faults.

Information Filtering and Array Algorithms for Discrete-Time Markovian Jump Linear Systems

This technical note develops information filter and array algorithms for a linear minimum mean square error estimator of discrete-time Markovian jump linear systems. A numerical example for a two-mode Markovian jump linear system, to show the advantage of using array algorithms to filter this class of systems, is provided.

Sudden onset of log-periodicity and superdiffusion in non-Markovian random walks with amnestically induced persistence: exact results

Random walks can undergo transitions from normal diffusion to anomalous diffusion as some relevant parameter varies, for instance the L,vy index in L,vy flights. Here we derive the Fokker-Planck equation for a two-parameter family of non-Markovian random walks with amnestically induced persistence. We investigate two distinct transitions: one order parameter quantifies log-periodicity and discrete scale invariance in the first moment of the propagator, whereas the second order parameter, known as the Hurst exponent, describes the growth of the second moment. We report numerical and analytical results for six critical exponents, which together completely characterize the properties of the transitions. We find that the critical exponents related to the diffusion-superdiffusion transition are identical in the positive feedback and negative feedback branches of the critical line, even though the former leads to classical superdiffusion whereas the latter gives rise to log-periodic superdiffusion.

Complex rearrangements in patients with duplications of MECP2 can occur by fork stalling and template switching

Duplication at the Xq28 band including the MECP2 gene is one of the most common genomic rearrangements identified in neurodevelopmentally delayed males. Such duplications are non-recurrent and can be generated by a non-homologous end joining (NHEJ) mechanism. We investigated the potential mechanisms for MECP2 duplication and examined whether genomic architectural features may play a role in their origin using a custom designed 4-Mb tiling-path oligonucleotide array CGH assay. Each of the 30 patients analyzed showed a unique duplication varying in size from similar to 250 kb to similar to 2.6 Mb. Interestingly, in 77% of these non-recurrent duplications, the distal breakpoints grouped within a 215 kb genomic interval, located 47 kb telomeric to the MECP2 gene. The genomic architecture of this region contains both direct and inverted low-copy repeat (LCR) sequences; this same region undergoes polymorphic structural variation in the general population. Array CGH revealed complex rearrangements in eight patients; in six patients the duplication contained an embedded triplicated segment, and in the other two, stretches of non-duplicated sequences occurred within the duplicated region. Breakpoint junction sequencing was achieved in four duplications and identified an inversion in one patient, demonstrating further complexity. We propose that the presence of LCRs in the vicinity of the MECP2 gene may generate an unstable DNA structure that can induce DNA strand lesions, such as a collapsed fork, and facilitate a Fork Stalling and Template Switching event producing the complex rearrangements involving MECP2.

Switching control of sympathetic activity from forebrain to hindbrain in chronic dehydration

We investigated the mechanisms responsible for increased blood pressure and sympathetic nerve activity (SNA) caused by 2-3 days dehydration (DH) both in vivo and in situ preparations. In euhydrated (EH) rats, systemic application of the AT(1) receptor antagonist Losartan and subsequent pre-collicular transection (to remove the hypothalamus) significantly reduced thoracic (t) SNA. In contrast, in DH rats, Losartan, followed by pre-collicular and pontine transections, failed to reduce tSNA, whereas transection at the medulla-spinal cord junction massively reduced tSNA. In DH but not EH rats, selective inhibition of the commissural nucleus tractus solitarii (cNTS) significantly reduced tSNA. Comparable data were obtained in both in situ and in vivo (anaesthetized/conscious) rats and suggest that following chronic dehydration, the control of tSNA transfers from supra-brainstem structures (e. g. hypothalamus) to the medulla oblongata, particularly the cNTS. As microarray analysis revealed up-regulation of AP1 transcription factor JunD in the dehydrated cNTS, we tested the hypothesis that AP1 transcription factor activity is responsible for dehydration-induced functional plasticity. When AP1 activity was blocked in the cNTS using a viral vector expressing a dominant negative FosB, cNTS inactivation was ineffective. However, tSNA was decreased after pre-collicular transection, a response similar to that seen in EHrats. Thus, the dehydration-induced switch in control of tSNA from hypothalamus to cNTS seems to be mediated via activation of AP1 transcription factors in the cNTS. If AP1 activity is blocked in the cNTS during dehydration, sympathetic activity control reverts back to forebrain regions. This unique reciprocating neural structure-switching plasticity between brain centres emphasizes the multiple mechanisms available for the adaptive response to dehydration.

Transcriptional memory and switching in the Plasmodium falciparum rif gene family

The human malaria parasite Plasmodium falciparum expresses erythrocyte-surface directed variant antigens which are important virulence factors Many are transcribed from multigene families and presumably their mode of expression is strictly controlled to guarantee immune evasion in the human host. In order to elucidate the dynamics of rif transcription and to investigate if rif switching is comparable to var switching we monitored rif variant gene expression in parasites with different cytoadhesive properties as well as after a number of reinvasions. We found identical transcripts in parasite lines with different adhesive phenotypes suggesting that rif genes do not have a critical role in determining the cytoadhesion specificity of infected erythrocytes. We show for the first time that rif genes may show a conserved mode of transcription, maintaining the previously dominant rif transcript in subsequent reinvasions, but also observed rapid switching at rates up to 45% per generation, much higher than for the var gene family. (C) 2009 Elsevier B.V. All rights reserved.

Phylogenetic, morphological and behavioural analyses support host switching of Trypanosoma (Herpetosoma) lewisi from domestic rats to primates

We characterized four Brazilian trypanosomes isolated from domestic rats and three from captive nonhuman primates that were morphologically similar to T. lewisi, a considered non-pathogenic species restricted to rodents and transmitted by fleas, despite its potential pathogenicity for infants. These isolates were identified as T. lewisi by barcoding using V7V8 SSU rDNA sequences. In inferred phylogenetic trees, all isolates clustered tightly with reference T. lewisi and T. lewisi-like trypanosomes from Europe, Asia and Africa and despite their high sequence conservation formed a homogeneous clade separate from other species of the subgenus T. (Herpetosoma). With the aim of clearly resolving the relationships between the Brazilian isolates from domestic rats and primates, we compared sequences from more polymorphic ITS rDNA. Results corroborated that isolates from Brazilian rats and monkeys were indeed of the same species and quite close to T. lewisi isolates of humans and rats from different geographical regions. Morphology of the monkey isolates and their behaviour in culture and in experimentally infected rats were also compatible with T. lewisi. However, infection with T. lewisi is rare among monkeys. We have examined more than 200 free-ranging and 160 captive monkeys and found only three infected individuals among the monkeys held in captivity. The findings of this work suggest that proximity of monkeys and infected rats and their exposure to infected fleas may be responsible for the host switching of T. Iewisi from their natural rodent species to primates. This and previous studies reporting T. lewisi in humans suggest that this trypanosome can cause sporadic and opportunistic fleaborne infection in primates. (C) 2010 Elsevier B.V. All rights reserved.

Semiclassical evolution of dissipative Markovian systems

A semiclassical approximation for an evolving density operator, driven by a `closed` Hamiltonian operator and `open` Markovian Lindblad operators, is obtained. The theory is based on the chord function, i.e. the Fourier transform of the Wigner function. It reduces to an exact solution of the Lindblad master equation if the Hamiltonian operator is a quadratic function and the Lindblad operators are linear functions of positions and momenta. Initially, the semiclassical formulae for the case of Hermitian Lindblad operators are reinterpreted in terms of a (real) double phase space, generated by an appropriate classical double Hamiltonian. An extra `open` term is added to the double Hamiltonian by the non-Hermitian part of the Lindblad operators in the general case of dissipative Markovian evolution. The particular case of generic Hamiltonian operators, but linear dissipative Lindblad operators, is studied in more detail. A Liouville-type equivariance still holds for the corresponding classical evolution in double phase space, but the centre subspace, which supports the Wigner function, is compressed, along with expansion of its conjugate subspace, which supports the chord function. Decoherence narrows the relevant region of double phase space to the neighbourhood of a caustic for both the Wigner function and the chord function. This difficulty is avoided by a propagator in a mixed representation, so that a further `small-chord` approximation leads to a simple generalization of the quadratic theory for evolving Wigner functions.

All-optical switching device for infrared based on PbTe quantum dots

Multilayers of PbTe quantum dots embedded in SiO2 were fabricated by alternate use of Pulsed Laser Deposition (PLD) and Plasma Enhanced Chemical Vapor Deposition (PECVD) techniques. The morphological properties of the nanostructured material were studied by means of High Resolution Transmission Electron Microscopy (HRTEM), Grazing-Incidence Small-Angle X-ray scattering (GISAXS) and X-ray Reflectometry (XRR) techniques. A preliminary analysis of the GISAXS spectra provided information about the multilayer periodicity and its relationship to the size of the deposited PbTe nanoparticles. Finally multilayers were fabricated inside a Fabry-Perot cavity. The device was characterized by means of Scanning Electron Microscopy (SEM). Transmittance measurements show the device functionality in the infrared region. (C) 2007 Elsevier Ltd. All rights reserved.