Similar Markov chains

enin et al. (2000) recently introduced the idea of similarity in the context of birth-death processes. This paper examines the extent to which their results can be extended to arbitrary Markov chains. It is proved that, under a variety of conditions, similar chains are strongly similar in a sense which is described, and it is shown that minimal chains are strongly similar if and only if the corresponding transition-rate matrices are strongly similar. A general framework is given for constructing families of strongly similar chains; it permits the construction of all such chains in the irreducible case.

Fluorescence spectrum of a two-level atom driven by a multiple modulated field

We investigate the fluorescence spectrum of a two-level atom driven by a multiple amplitude-modulated field. The driving held is modeled as a polychromatic field composed of a strong central (resonant) component and a large number of symmetrically detuned sideband fields displaced from the central component by integer multiples of a constant detuning. Spectra obtained here differ qualitatively from those observed for a single pair of modulating fields [B. Blind, P.R. Fontana, and P. Thomann, J. Phys. B 13, 2717 (1980)]. In the case of a small number of the modulating fields, a multipeaked spectrum is obtained with the spectral features located at fixed frequencies that are independent of the number of modulating fields and their Rabi frequencies. As the number of the modulating fields increases, the spectrum ultimately evolves to the well-known Mellow triplet with the sidebands shifted from the central component by an effective Rabi frequency whose magnitude depends on the initial relative phases of the components of the driving held. For equal relative phases, the effective Rabi frequency of the driving field can be reduced to zero resulting in the disappearance of fluorescence spectrum, i.e., the atom can stop interacting with the field. When the central component and the modulating fields are 180 degrees out of phase, the spectrum retains its triplet structure with the sidebands located at frequencies equal to the sum of the Rabi frequencies of the component of the driving field. Moreover, we shaw that the frequency of spontaneous emission can be controlled and switched from one frequency to another when the Rabi frequency or initial phase of the modulating fields are varied.

Path integrals for continuous-time Markov chains

This note presents a method of evaluating the distribution of a path integral for Markov chains on a countable state space.

Set-valued Markov chains and negative semitrajectories of discretized dynamical systems

Computer simulation of dynamical systems involves a phase space which is the finite set of machine arithmetic. Rounding state values of the continuous system to this grid yields a spatially discrete dynamical system, often with different dynamical behaviour. Discretization of an invertible smooth system gives a system with set-valued negative semitrajectories. As the grid is refined, asymptotic behaviour of the semitrajectories follows probabilistic laws which correspond to a set-valued Markov chain, whose transition probabilities can be explicitly calculated. The results are illustrated for two-dimensional dynamical systems obtained by discretization of fractional linear transformations of the unit disc in the complex plane.

Integrals for continuous-time Markov chains

This paper presents a method of evaluating the expected value of a path integral for a general Markov chain on a countable state space. We illustrate the method with reference to several models, including birth-death processes and the birth, death and catastrophe process. (C) 2002 Elsevier Science Inc. All rights reserved.

The left ventricular contractility of the rat heart is modulated by changes in flow and a1-adrenoceptor stimulation

Myocardial contractility depends on several mechanisms such as coronary perfusion pressure (CPP) and flow as well as on a1-adrenoceptor stimulation. Both effects occur during the sympathetic stimulation mediated by norepinephrine. Norepinephrine increases force development in the heart and produces vasoconstriction increasing arterial pressure and, in turn, CPP. The contribution of each of these factors to the increase in myocardial performance needs to be clarified. Thus, in the present study we used two protocols: in the first we measured mean arterial pressure, left ventricular pressure and rate of rise of left ventricular pressure development in anesthetized rats (N = 10) submitted to phenylephrine (PE) stimulation before and after propranolol plus atropine treatment. These observations showed that in vivo a1-adrenergic stimulation increases left ventricular-developed pressure (P<0.05) together with arterial blood pressure (P<0.05). In the second protocol, we measured left ventricular isovolumic systolic pressure (ISP) and CPP in Langendorff constant flow-perfused hearts. The hearts (N = 7) were perfused with increasing flow rates under control conditions and PE or PE + nitroprusside (NP). Both CPP and ISP increased (P<0.01) as a function of flow. CPP changes were not affected by drug treatment but ISP increased (P<0.01). The largest ISP increase was obtained with PE + NP treatment (P<0.01). The results suggest that both mechanisms, i.e., direct stimulation of myocardial a1-adrenoceptors and increased flow, increased cardiac performance acting simultaneously and synergistically.

Dynamic programming for a Markov-switching jump–diffusion

We consider an optimal control problem with a deterministic finite horizon and state variable dynamics given by a Markov-switching jump–diffusion stochastic differential equation. Our main results extend the dynamic programming technique to this larger family of stochastic optimal control problems. More specifically, we provide a detailed proof of Bellman’s optimality principle (or dynamic programming principle) and obtain the corresponding Hamilton–Jacobi–Belman equation, which turns out to be a partial integro-differential equation due to the extra terms arising from the Lévy process and the Markov process. As an application of our results, we study a finite horizon consumption– investment problem for a jump–diffusion financial market consisting of one risk-free asset and one risky asset whose coefficients are assumed to depend on the state of a continuous time finite state Markov process. We provide a detailed study of the optimal strategies for this problem, for the economically relevant families of power utilities and logarithmic utilities.

S100A6 Amyloid Fibril Formation Is Calcium-modulated and Enhances Superoxide Dismutase-1 (SOD1) Aggregation

S100A6 is a small EF-hand calcium- and zinc-binding protein involved in the regulation of cell proliferation and cytoskeletal dynamics. It is overexpressed in neurodegenerative disorders and a proposed marker for Amyotrophic Lateral Sclerosis (ALS). Following recent reports of amyloid formation by S100 proteins, we investigated the aggregation properties of S100A6. Computational analysis using aggregation predictors Waltz and Zyggregator revealed increased propensity within S100A6 helices HI and HIV. Subsequent analysis of Thioflavin-T binding kinetics under acidic conditions elicited a very fast process with no lag phase and extensive formation of aggregates and stacked fibrils as observed by electron microscopy. Ca2+ exerted an inhibitory effect on the aggregation kinetics, which could be reverted upon chelation. An FT-IR investigation of the early conformational changes occurring under these conditions showed that Ca2+ promotes anti-parallel β-sheet conformations that repress fibrillation. At pH 7, Ca2+ rendered the fibril formation kinetics slower: time-resolved imaging showed that fibril formation is highly suppressed, with aggregates forming instead. In the absence of metals an extensive network of fibrils is formed. S100A6 oligomers, but not fibrils, were found to be cytotoxic, decreasing cell viability by up to 40%. This effect was not observed when the aggregates were formed in the presence of Ca2+. Interestingly, native S1006 seeds SOD1 aggregation, shortening its nucleation process. This suggests a cross-talk between these two proteins involved in ALS. Overall, these results put forward novel roles for S100 proteins, whose metal-modulated aggregation propensity may be a key aspect in their physiology and function.

Modelos de previsão de deterioração de pontes existentes: processos de Markov

Dissertação apresentada na Faculdade de Ciências e Tecnologia da Universidade Nova de Lisboa para obtenção do grau de Mestre em Engenharia Civil

Explosion of smoothness from a point to everywhere for conjugacies between Markov families

For uniformly asymptotically affine (uaa) Markov maps on train tracks, we prove the following type of rigidity result: if a topological conjugacy between them is (uaa) at a point in the train track then the conjugacy is (uaa) everywhere. In particular, our methods apply to the case in which the domains of the Markov maps are Canter sets. We also present similar statements for (uaa:) and C-r Markov families. These results generalize the similar ones of Sullivan and de Faria for C-r expanding circle maps with r > 1 and have useful applications to hyperbolic dynamics on surfaces and laminations.

Estudo dosimétrico para implementação da técnica radioterapêutica volumetric modulated arc therapy (VMAT)

Dissertação para obtenção do Grau de Mestre em Engenharia Biomédica

Candida glabrata susceptibility to antifungals and phagocytosis is modulated by acetate

Candida glabrata is considered a major opportunistic fungal pathogen of humans. The capacity of this yeast species to cause infections is dependent on the ability to grow within the human host environment and to assimilate the carbon sources available. Previous studies have suggested that C. albicans can encounter glucose-poor microenvironments during infection and that the ability to use alternative non-fermentable carbon sources, such as carboxylic acids, contributes to the virulence of this fungus. Transcriptional studies on C. glabrata cells identified a similar response, upon nutrient deprivation. In this work, we aimed at analyzing biofilm formation, antifungal drug resistance, and phagocytosis of C. glabrata cells grown in the presence of acetic acid as an alternative carbon source. C. glabrata planktonic cells grown in media containing acetic acid were more susceptible to fluconazole and were better phagocytosed and killed by macrophages than when compared to media lacking acetic acid. Growth in acetic acid also affected the ability of C. glabrata to form biofilms. The genes ADY2a, ADY2b, FPS1, FPS2, and ATO3, encoding putative carboxylate transporters, were upregulated in C. glabrata planktonic and biofilm cells in the presence of acetic acid. Phagocytosis assays with fps1 and ady2a mutant strains suggested a potential role of FPS1 and ADY2a in the phagocytosis process. These results highlight how acidic pH niches, associated with the presence of acetic acid, can impact in the treatment of C. glabrata infections, in particular in vaginal candidiasis.

The role of Rac1-modulated gene transcription in tumorigenesis

Dissertation presented to obtain the Ph.D degree in Biology