Skip-free Markov chains

The aim of this paper is to develop a general theory for the class of skip-free Markov chains on denumerable state space. This encompasses their potential theory via an explicit characterization of their potential kernel expressed in terms of the family of fundamental excessive functions, which are defined by means of the theory of the Martin boundary. We also describe their fluctuation theory generalizing the celebrated fluctuations identities that were obtained by using the Wiener-Hopf factorization for the specific skip-free random walks. We proceed by resorting to the concept of similarity to identify the class of skip-free Markov chains whose transition operator has only real and simple eigenvalues. We manage to find a set of sufficient and easy-to-check conditions on the one-step transition probability for a Markov chain to belong to this class. We also study several properties of this class including their spectral expansions given in terms of a Riesz basis, derive a necessary and sufficient condition for this class to exhibit a separation cutoff, and give a tighter bound on its convergence rate to stationarity than existing results

Analysis of non-reversible Markov chains via similarity orbits

AbstractIn this paper we develop an in-depth analysis of non-reversible Markov chains on denumerable state space from a similarity orbit perspective. In particular, we study the class of Markov chains whose transition kernel is in the similarity orbit of a normal transition kernel, such as that of birth–death chains or reversible Markov chains. We start by identifying a set of sufficient conditions for a Markov chain to belong to the similarity orbit of a birth–death chain. As by-products, we obtain a spectral representation in terms of non-self-adjoint resolutions of identity in the sense of Dunford [21] and offer a detailed analysis on the convergence rate, separation cutoff and L2-cutoff of this class of non-reversible Markov chains. We also look into the problem of estimating the integral functionals from discrete observations for this class. In the last part of this paper we investigate a particular similarity orbit of reversible Markov kernels, which we call the pure birth orbit, and analyse various possibly non-reversible variants of classical birth–death processes in this orbit.</jats:p

Investigating the effects of cholesterol on phospholipid bilayer with molecular dynamics simulations

This PhD project studies the effects of cholesterol in phospholipid bilayer using molecular dynamics (MD) simulations. Dipalmitoylphosphatidylcholine(DPPC) bilayers with cholesterol concentrations between 0% and 40% were simulated using all-­‐atom CHARMM36 force filed. The main concerned aspects of the lipid bilayer with cholesterol include structural properties, the lipid dynamics and mechanical properties of the bilayer. It was found that the lipid bilayer was condensed when it was embedded with cholesterol molecules. Addition of cholesterol in bilayer systems induced a smaller average surface area occupied by DPPC molecules, a more ordered hydrocarbon chains of DPPC molecules, and a thickened bilayer. The effects of cholesterol on dynamics properties of lipid bilayer were also observed as a decrease in the lateral diffusion coefficients for both cholesterol and DPPC in DPPC-­‐cholesterol mixture bilayer. Furthermore, lateral pressure profiles were calculated to look into the local stress distribution along the bilayer norm. It was found that cholesterol introduced extra contraction troughs in the profiles at the position under the head groups of DPPC, which explained the structural changes observed in the study. Bending moduli of the bilayer with and without cholesterol were estimated by calculating the splay modulus of pairs of each bilayer components. It was found that the involvement of cholesterol reduced the splay angles of each pair of bilayer component, resulting in a higher bending modulus of the structure

Strong many-particle localization and quantum computing with perpetually coupled qubits

We demonstrate the onset of strong on-site localization in a one-dimensional many-particle system. The localization is obtained by constructing, in an explicit form, a bounded sequence of on-site energies that eliminates resonant hopping between both nearest and remote sites. This sequence leads to quasi-exponential decay of the single-particle transition amplitude. It also leads to strong localization of stationary many-particle states in a finite-length chain. For an {\it infinite} chain, we instead study the time during which {\it all} many-particle states remain strongly localized. We show that, for any number of particles, this time exceeds the reciprocal frequency of nearest-neighbor hopping by a factor $\sim 10^5$ already for a moderate bandwidth of on-site energies. The proposed energy sequence is robust with respect to small errors. The formulation applies to fermions as well as perpetually coupled qubits. The results show viability of quantum computing with time-independent qubit coupling.Comment: 20 pages, 10 figure

Neutral and Charged Polymers at Interfaces

Chain-like macromolecules (polymers) show characteristic adsorption properties due to their flexibility and internal degrees of freedom, when attracted to surfaces and interfaces. In this review we discuss concepts and features that are relevant to the adsorption of neutral and charged polymers at equilibrium, including the type of polymer/surface interaction, the solvent quality, the characteristics of the surface, and the polymer structure. We pay special attention to the case of charged polymers (polyelectrolytes) that have a special importance due to their water solubility. We present a summary of recent progress in this rapidly evolving field. Because many experimental studies are performed with rather stiff biopolymers, we discuss in detail the case of semi-flexible polymers in addition to flexible ones. We first review the behavior of neutral and charged chains in solution. Then, the adsorption of a single polymer chain is considered. Next, the adsorption and depletion processes in the many-chain case are reviewed. Profiles, changes in the surface tension and polymer surface excess are presented. Mean-field and corrections due to fluctuations and lateral correlations are discussed. The force of interaction between two adsorbed layers, which is important in understanding colloidal stability, is characterized. The behavior of grafted polymers is also reviewed, both for neutral and charged polymer brushes.Comment: a review: 130 pages, 30 ps figures; final form, added reference

Time-frequency investigation of heart rate variability and cardiovascular system modeling of normal and chronic obstructive pulmonary disease (COPD) subjects

A study has been designed to add insight to some questions that have not been fully investigated in the heart rate variability field and the cardiovascular regulation system in normal and Chronic Obstructive Pulmonary Disease (COPD) subjects. It explores the correlations between heart rate variability and cardiovascular regulation, which interact through complex multiple feedback and control loops. This work examines the coupling between heart rate (HR), respiration (RESP), and blood pressure (BP) via closed-loop system identification techniques in order to noninvasively assess the underlying physiology. In the first part of the study, the applications of five different bilinear time-frequency representations are evaluated on modeled HRV test signals, actual electrocardiograms (ECG), BP and RESP signals. Each distribution: the short time Fourier transform (STFT), the smoothed pseudo Wigner-Ville (SPWVD), the ChoiWilliams (CWD), the Bom-Jordan-Cohen (BJC) and wavelet distribution (WL), has unique characteristics which is shown to affect the amount of smoothing and the generation of cross-terms. The CWD and the WL are chosen for further application because of overcoming the drawbacks of other distributions by providing higher resolution in time and frequency while suppressing interferences between the signal components. In the second part of the study, the Morlet, Meyer, Daubechies 4, Mexican Hat and Haar wavelets are used to investigate the heart rate and blood pressure variability from both COPD and normal subjects. The results of wavelet analysis give much more useful information than the Cohen\u27s class representations. Here we are able to quantitatively assess the parasympathetic (HF) and sympatho-vagal balance (LF:HF) changes as a function of time. As a result, COPD subjects breathe faster, have higher blood pressure variability and lower HRV. In the third part of the study, a special class of the exogenous autoregressive (ARX) model is developed as an analytical tool for uncovering the hidden autonomic control processes. Non-parametric relationships between the input and outputs of the ARX model resulting in transfer function estimations of the noise filters and the input filter were used as mechanistic cardiovascular models that have shown to have predictive capabilities for the underlying autonomic nervous system activity of COPD patients. Transfer functions of COPD cardiovascular models have similar DC gains but show a larger lag in phase as compared to the models of normal subjects. Finally, a method of severity classification is presented. This method combines the techniques of principal component analysis (PCA) and cluster analysis (CA) and has been shown to separate the COPD from the normal population with 100% accuracy. It can also classify the COPD population into at risk , mild , moderate and severe stages with 100%, 90%, 88% and 100% accuracy respectively. As a result, cluster and principal component analysis can be used to separate COPD and normal subjects and can be used successfully in COPD severity classification