Essential spectra and exponential estimates of eigenfunctions of lattice operators of quantum mechanics

This paper is devoted to estimates of the exponential decay of eigenfunctions of difference operators on the lattice Z^n which are discrete analogs of the Schr\"{o}dinger, Dirac and square-root Klein-Gordon operators. Our investigation of the essential spectra and the exponential decay of eigenfunctions of the discrete spectra is based on the calculus of so-called pseudodifference operators (i.e., pseudodifferential operators on the group Z^n) with analytic symbols and on the limit operators method. We obtain a description of the location of the essential spectra and estimates of the eigenfunctions of the discrete spectra of the main lattice operators of quantum mechanics, namely: matrix Schr\"{o}dinger operators on Z^n, Dirac operators on Z^3, and square root Klein-Gordon operators on Z^n

Essential spectra of difference operators on \sZ^n-periodic graphs

Let (\cX, \rho) be a discrete metric space. We suppose that the group \sZ^n acts freely on $X$ and that the number of orbits of $X$ with respect to this action is finite. Then we call $X$ a \sZ^n-periodic discrete metric space. We examine the Fredholm property and essential spectra of band-dominated operators on $l^p(X)$ where $X$ is a \sZ^n-periodic discrete metric space. Our approach is based on the theory of band-dominated operators on \sZ^n and their limit operators. In case $X$ is the set of vertices of a combinatorial graph, the graph structure defines a Schr\"{o}dinger operator on $l^p(X)$ in a natural way. We illustrate our approach by determining the essential spectra of Schr\"{o}dinger operators with slowly oscillating potential both on zig-zag and on hexagonal graphs, the latter being related to nano-structures

Chaotic Dynamics of Spin-Valve Oscillators

Recent experimental and theoretical studies on the magnetization dynamics driven by an electric current have uncovered a number of unprecedented rich dynamic phenomena. We predict an intrinsic chaotic dynamics that has not been previously anticipated. We explicitly show that the transition to chaotic dynamics occurs through a series of period doubling bifurcations. In chaotic regime, two dramatically different power spectra, one with a well-defined peak and the other with a broadly distributed noise, are identified and explained

Can we identify non-stationary dynamics of trial-to-trial variability?"

Identifying sources of the apparent variability in non-stationary scenarios is a fundamental problem in many biological data analysis settings. For instance, neurophysiological responses to the same task often vary from each repetition of the same experiment (trial) to the next. The origin and functional role of this observed variability is one of the fundamental questions in neuroscience. The nature of such trial-to-trial dynamics however remains largely elusive to current data analysis approaches. A range of strategies have been proposed in modalities such as electro-encephalography but gaining a fundamental insight into latent sources of trial-to-trial variability in neural recordings is still a major challenge. In this paper, we present a proof-of-concept study to the analysis of trial-to-trial variability dynamics founded on non-autonomous dynamical systems. At this initial stage, we evaluate the capacity of a simple statistic based on the behaviour of trajectories in classification settings, the trajectory coherence, in order to identify trial-to-trial dynamics. First, we derive the conditions leading to observable changes in datasets generated by a compact dynamical system (the Duffing equation). This canonical system plays the role of a ubiquitous model of non-stationary supervised classification problems. Second, we estimate the coherence of class-trajectories in empirically reconstructed space of system states. We show how this analysis can discern variations attributable to non-autonomous deterministic processes from stochastic fluctuations. The analyses are benchmarked using simulated and two different real datasets which have been shown to exhibit attractor dynamics. As an illustrative example, we focused on the analysis of the rat's frontal cortex ensemble dynamics during a decision-making task. Results suggest that, in line with recent hypotheses, rather than internal noise, it is the deterministic trend which most likely underlies the observed trial-to-trial variability. Thus, the empirical tool developed within this study potentially allows us to infer the source of variability in in-vivo neural recordings

Generalized Chaotic Synchronizationin Coupled Ginzburg-Landau Equations

Generalized synchronization is analyzed in unidirectionally coupled oscillatory systems exhibiting spatiotemporal chaotic behavior described by Ginzburg-Landau equations. Several types of coupling betweenthe systems are analyzed. The largest spatial Lyapunov exponent is proposed as a new characteristic of the state of a distributed system, and its calculation is described for a distributed oscillatory system. Partial generalized synchronization is introduced as a new type of chaotic synchronization in spatially nonuniform distributed systems. The physical mechanisms responsible for the onset of generalized chaotic synchronization in spatially distributed oscillatory systems are elucidated. It is shown that the onset of generalized chaotic synchronization is described by a modified Ginzburg-Landau equation with additional dissipation irrespective of the type of coupling. The effect of noise on the onset of a generalized synchronization regime in coupled distributed systems is analyzed.Comment: 12 page

Validity and responsiveness of the Daily- and Clinical visit-PROactive Physical Activity in COPD (D-PPAC and C-PPAC) instruments

BACKGROUND: The Daily-PROactive and Clinical visit-PROactive Physical Activity (D-PPAC and C-PPAC) instruments in chronic obstructive pulmonary disease (COPD) combines questionnaire with activity monitor data to measure patients' experience of physical activity. Their amount, difficulty and total scores range from 0 (worst) to 100 (best) but require further psychometric evaluation. OBJECTIVE: To test reliability, validity and responsiveness, and to define minimal important difference (MID), of the D-PPAC and C-PPAC instruments, in a large population of patients with stable COPD from diverse severities, settings and countries. METHODS: We used data from seven randomised controlled trials to evaluate D-PPAC and C-PPAC internal consistency and construct validity by sex, age groups, COPD severity, country and language as well as responsiveness to interventions, ability to detect change and MID. RESULTS: We included 1324 patients (mean (SD) age 66 (8) years, forced expiratory volume in 1 s 55 (17)% predicted). Scores covered almost the full range from 0 to 100, showed strong internal consistency after stratification and correlated as a priori hypothesised with dyspnoea, health-related quality of life and exercise capacity. Difficulty scores improved after pharmacological treatment and pulmonary rehabilitation, while amount scores improved after behavioural physical activity interventions. All scores were responsive to changes in self-reported physical activity experience (both worsening and improvement) and to the occurrence of COPD exacerbations during follow-up. The MID was estimated to 6 for amount and difficulty scores and 4 for total score. CONCLUSIONS: The D-PPAC and C-PPAC instruments are reliable and valid across diverse COPD populations and responsive to pharmacological and non-pharmacological interventions and changes in clinically relevant variables

X-ray absorption spectroscopy systematics at the tungsten L-edge

A series of mononuclear six-coordinate tungsten compounds spanning formal oxidation states from 0 to +VI, largely in a ligand environment of inert chloride and/or phosphine, has been interrogated by tungsten L-edge X-ray absorption spectroscopy. The L-edge spectra of this compound set, comprised of [W<sup>0</sup>(PMe<sub>3</sub>)<sub>6</sub>], [W<sup>II</sup>Cl<sub>2</sub>(PMePh<sub>2</sub>)<sub>4</sub>], [W<sup>III</sup>Cl<sub>2</sub>(dppe)<sub>2</sub>][PF<sub>6</sub>] (dppe = 1,2-bis(diphenylphosphino)ethane), [W<sup>IV</sup>Cl<sub>4</sub>(PMePh<sub>2</sub>)<sub>2</sub>], [W<sup>V</sup>(NPh)Cl<sub>3</sub>(PMe<sub>3</sub>)<sub>2</sub>], and [W<sup>VI</sup>Cl<sub>6</sub>] correlate with formal oxidation state and have usefulness as references for the interpretation of the L-edge spectra of tungsten compounds with redox-active ligands and ambiguous electronic structure descriptions. The utility of these spectra arises from the combined correlation of the estimated branching ratio (EBR) of the L<sub>3,2</sub>-edges and the L<sub>1</sub> rising-edge energy with metal Z<sub>eff</sub>, thereby permitting an assessment of effective metal oxidation state. An application of these reference spectra is illustrated by their use as backdrop for the L-edge X-ray absorption spectra of [W<sup>IV</sup>(mdt)<sub>2</sub>(CO)<sub>2</sub>] and [W<sup>IV</sup>(mdt)<sub>2</sub>(CN)<sub>2</sub>]<sup>2–</sup> (mdt<sup>2–</sup> = 1,2-dimethylethene-1,2-dithiolate), which shows that both compounds are effectively W<sup>IV</sup> species. Use of metal L-edge XAS to assess a compound of uncertain formulation requires: 1) Placement of that data within the context of spectra offered by unambiguous calibrant compounds, preferably with the same coordination number and similar metal ligand distances. Such spectra assist in defining upper and/or lower limits for metal Z<sub>eff</sub> in the species of interest; 2) Evaluation of that data in conjunction with information from other physical methods, especially ligand K-edge XAS; 3) Increased care in interpretation if strong π-acceptor ligands, particularly CO, or π-donor ligands are present. The electron-withdrawing/donating nature of these ligand types, combined with relatively short metal-ligand distances, exaggerate the difference between formal oxidation state and metal Z<sub>eff</sub> or, as in the case of [W<sup>IV</sup>(mdt)<sub>2</sub>(CO)<sub>2</sub>], add other subtlety by modulating the redox level of other ligands in the coordination sphere

Synchronous bursts on scale-free neuronal networks with attractive and repulsive coupling

This paper investigates the dependence of synchronization transitions of bursting oscillations on the information transmission delay over scale-free neuronal networks with attractive and repulsive coupling. It is shown that for both types of coupling, the delay always plays a subtle role in either promoting or impairing synchronization. In particular, depending on the inherent oscillation period of individual neurons, regions of irregular and regular propagating excitatory fronts appear intermittently as the delay increases. These delay-induced synchronization transitions are manifested as well-expressed minima in the measure for spatiotemporal synchrony. For attractive coupling, the minima appear at every integer multiple of the average oscillation period, while for the repulsive coupling, they appear at every odd multiple of the half of the average oscillation period. The obtained results are robust to the variations of the dynamics of individual neurons, the system size, and the neuronal firing type. Hence, they can be used to characterize attractively or repulsively coupled scale-free neuronal networks with delays.Comment: 15 pages, 9 figures; accepted for publication in PLoS ONE [related work available at http://arxiv.org/abs/0907.4961 and http://www.matjazperc.com/

Glycobiology of cell death: when glycans and lectins govern cell fate

Although one typically thinks of carbohydrates as associated with cell growth and viability, glycosylation also has an integral role in many processes leading to cell death. Glycans, either alone or complexed with glycan-binding proteins, can deliver intracellular signals or control extracellular processes that promote initiation, execution and resolution of cell death programs. Herein, we review the role of glycans and glycan-binding proteins as essential components of the cell death machinery during physiologic and pathologic settings.Fil: Lichtenstein, Rachel. Ben-Gurion University of the Negev. Faculty of Engineering. Department of Biotechnology Engineering; IsraelFil: Rabinovich, Gabriel Adrian. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Biología y Medicina Experimental (i); Argentina. Universidad de Buenos Aires. Facultad de Cs.exactas y Naturales. Departamento de Quimica Biologica; Argentin

Physical activity is increased by a 12 week semi-automated telecoaching program in patients with COPD, a multicenter randomized controlled trial

Rationale Reduced physical activity (PA) in patients with COPD is associated with a poor prognosis. Increasing PA is a key therapeutic target, but thus far few strategies have been found effective in this patient group. Objectives To investigate the effectiveness of a 12 week semi-automated telecoaching intervention on PA in COPD patients in a multicenter European RCT. Methods 343 patients from 6 centers, including a wide disease spectrum, were randomly allocated to either a usual care group (UCG) or a telecoaching intervention group (IG) between June and December 2014. This 12 weeks intervention included an exercise booklet and a step counter providing feedback both directly and via a dedicated smartphone application. The latter provided an individualized daily activity goal (steps) revised weekly and text messages as well as allowing occasional telephone contacts with investigators. Physical activity was measured using accelerometry during 1 week preceding randomization and during week 12. Secondary outcomes included exercise capacity and health status. Analyses were based on intention-to-treat. Main results Both groups were comparable at baseline in terms of factors influencing PA. At 12 weeks, the intervention yielded a between group difference of mean, 95% [ll-ul] +1469, 95% [971 – 1965] steps.day-1 and +10.4, 95% [6.1 - 14.7] min.day-1 moderate physical activity; favoring the IG (all p≤0.001). The change in six minute walk distance was significantly different (13.4, 95% [3.40 - 23.5]m, p<0.01), favoring the IG. In IG patients an improvement could be observed in the functional state domain of the CCQ (p=0.03), when compared to UCG. Other health status outcomes did not differ. Conclusions The amount and intensity of PA can be significantly increased in COPD patients using a 12 week semi-automated telecoaching intervention including a stepcounter and an application installed on a smartphone