Quasiperiodic time dependent current in driven superlattices: distorted Poincare maps and strange attractors

Intriguing routes to chaos have been experimentally observed in semiconductor superlattices driven by an ac field. In this work, a theoretical model of time dependent transport in ac driven superlattices is numerically solved. In agreement with experiments, distorted Poincare maps in the quasiperiodic regime are found. They indicate the appearance of very complex attractors and routes to chaos as the amplitude of the AC signal increases. Distorted maps are caused by the discrete well-to-well jump motion of a domain wall during spiky high-frequency self-sustained oscillations of the current.Comment: 10 pages, 4 figure

Estimating Mutual Information

We present two classes of improved estimators for mutual information $M(X,Y)$, from samples of random points distributed according to some joint probability density $\mu(x,y)$. In contrast to conventional estimators based on binnings, they are based on entropy estimates from $k$-nearest neighbour distances. This means that they are data efficient (with $k=1$ we resolve structures down to the smallest possible scales), adaptive (the resolution is higher where data are more numerous), and have minimal bias. Indeed, the bias of the underlying entropy estimates is mainly due to non-uniformity of the density at the smallest resolved scale, giving typically systematic errors which scale as functions of $k/N$ for $N$ points. Numerically, we find that both families become {\it exact} for independent distributions, i.e. the estimator $\hat M(X,Y)$ vanishes (up to statistical fluctuations) if $\mu(x,y) = \mu(x) \mu(y)$. This holds for all tested marginal distributions and for all dimensions of $x$ and $y$. In addition, we give estimators for redundancies between more than 2 random variables. We compare our algorithms in detail with existing algorithms. Finally, we demonstrate the usefulness of our estimators for assessing the actual independence of components obtained from independent component analysis (ICA), for improving ICA, and for estimating the reliability of blind source separation.Comment: 16 pages, including 18 figure

Postmortem metabolomics: influence of time since death on the level of endogenous compounds in human femoral blood. Necessary to be considered in metabolome study planning?

Introduction The (un)targeted analysis of endogenous compounds has gained interest in the field of forensic postmortem investigations. The blood metabolome is influenced by many factors, and postmortem specimens are considered particularly challenging due to unpredictable decomposition processes. Objectives This study aimed to systematically investigate the influence of the time since death on endogenous compounds and its relevance in designing postmortem metabolome studies. Methods Femoral blood samples of 427 authentic postmortem cases, were collected at two time points after death (854 samples in total; t1: admission to the institute, 1.3–290 h; t2: autopsy, 11–478 h; median ∆t = 71 h). All samples were analyzed using an untargeted metabolome approach, and peak areas were determined for 38 compounds (acylcarnitines, amino acids, phospholipids, and others). Differences between t2 and t1 were assessed by Wilcoxon signed-ranked test (p < 0.05). Moreover, all samples (n = 854) were binned into time groups (6 h, 12 h, or 24 h intervals) and compared by Kruskal–Wallis/Dunn’s multiple comparison tests (p < 0.05 each) to investigate the effect of the estimated time since death. Results Except for serine, threonine, and PC 34:1, all tested analytes revealed statistically significant changes between t1 and t2 (highest median increase 166%). Unpaired analysis of all 854 blood samples in-between groups indicated similar results. Significant differences were typically observed between blood samples collected within the first and later than 48 h after death, respectively. Conclusions To improve the consistency of comprehensive data evaluation in postmortem metabolome studies, it seems advisable to only include specimens collected within the first 2 days after death

Temperature dependence of current self-oscillations and electric field domains in sequential tunneling doped superlattices

We examine how the current--voltage characteristics of a doped weakly coupled superlattice depends on temperature. The drift velocity of a discrete drift model of sequential tunneling in a doped GaAs/AlAs superlattice is calculated as a function of temperature. Numerical simulations and theoretical arguments show that increasing temperature favors the appearance of current self-oscillations at the expense of static electric field domain formation. Our findings agree with available experimental evidence.Comment: 7 pages, 5 figure

Statistics of Partial Minima

Motivated by multi-objective optimization, we study extrema of a set of N points independently distributed inside the d-dimensional hypercube. A point in this set is k-dominated by another point when at least k of its coordinates are larger, and is a k-minimum if it is not k-dominated by any other point. We obtain statistical properties of these partial minima using exact probabilistic methods and heuristic scaling techniques. The average number of partial minima, A, decays algebraically with the total number of points, A ~ N^{-(d-k)/k}, when 1<=k<d. Interestingly, there are k-1 distinct scaling laws characterizing the largest coordinates as the distribution P(y_j) of the jth largest coordinate, y_j, decays algebraically, P(y_j) ~ (y_j)^{-alpha_j-1}, with alpha_j=j(d-k)/(k-j) for 1<=j<=k-1. The average number of partial minima grows logarithmically, A ~ [1/(d-1)!](ln N)^{d-1}, when k=d. The full distribution of the number of minima is obtained in closed form in two-dimensions.Comment: 6 pages, 1 figur

The transition between stochastic and deterministic behavior in an excitable gene circuit

We explore the connection between a stochastic simulation model and an ordinary differential equations (ODEs) model of the dynamics of an excitable gene circuit that exhibits noise-induced oscillations. Near a bifurcation point in the ODE model, the stochastic simulation model yields behavior dramatically different from that predicted by the ODE model. We analyze how that behavior depends on the gene copy number and find very slow convergence to the large number limit near the bifurcation point. The implications for understanding the dynamics of gene circuits and other birth-death dynamical systems with small numbers of constituents are discussed.Comment: PLoS ONE: Research Article, published 11 Apr 201

Readmission and overstay after day case nasal surgery

BACKGROUND: A readmission is classified as a patient necessitating readmission to hospital due to a post-operative complication following discharge. An overstay however, is classified as a patient having to stay longer than the planned duration in hospital (not having been discharged in the interim) due to a post-operative complication. This study aims to investigate patient-related factors that predispose to readmission or overstay and thus make recommendations to decrease the likelihood of readmission or overstay. METHOD: In this retrospective study 312 'day-case nasal procedures', were selected from a total cohort of 4274 ENT patients over a 17-month period. This sub-group was investigated for a range of demographic factors including, age, gender and ethnicity with regards to their relationship to readmission rates and overstay frequency and duration. RESULTS: The rates were 2.88% and 9.62% for readmission and overstay respectively. The total number of days spent in hospital as a result of readmission was 27. Epistaxis was the leading cause for readmission/overstay (28.9%) followed by high levels of post-operative pain preventing them from being discharged (23.7%). All procedures in this study had readmission rates that were below those recommended in the guidelines set by the Royal College of Surgeons of England. Women overstayed significantly longer (t = 1.65, p < 0.05) than men. CONCLUSIONS: Suitable candidates for day-case ENT surgery highlighted by this study include healthy individuals between the ages of 20 and 60. Operating in the morning would increase the immediate post-operative recovery time, which may reduce the numbers of patients who complain of high levels of pain at the time of discharge. Procedures such as septorhinoplasty being performed routinely in the ambulatory setting require additional research into more effective methods of pain control. Standards need to be improved so that the causes of overstay and readmission are clearly identifiable in patient records

Mutual information rate and bounds for it

The amount of information exchanged per unit of time between two nodes in a dynamical network or between two data sets is a powerful concept for analysing complex systems. This quantity, known as the mutual information rate (MIR), is calculated from the mutual information, which is rigorously defined only for random systems. Moreover, the definition of mutual information is based on probabilities of significant events. This work offers a simple alternative way to calculate the MIR in dynamical (deterministic) networks or between two data sets (not fully deterministic), and to calculate its upper and lower bounds without having to calculate probabilities, but rather in terms of well known and well defined quantities in dynamical systems. As possible applications of our bounds, we study the relationship between synchronisation and the exchange of information in a system of two coupled maps and in experimental networks of coupled oscillators