Don't bleach chaotic data

A common first step in time series signal analysis involves digitally filtering the data to remove linear correlations. The residual data is spectrally white (it is ``bleached''), but in principle retains the nonlinear structure of the original time series. It is well known that simple linear autocorrelation can give rise to spurious results in algorithms for estimating nonlinear invariants, such as fractal dimension and Lyapunov exponents. In theory, bleached data avoids these pitfalls. But in practice, bleaching obscures the underlying deterministic structure of a low-dimensional chaotic process. This appears to be a property of the chaos itself, since nonchaotic data are not similarly affected. The adverse effects of bleaching are demonstrated in a series of numerical experiments on known chaotic data. Some theoretical aspects are also discussed.Comment: 12 dense pages (82K) of ordinary LaTeX; uses macro psfig.tex for inclusion of figures in text; figures are uufile'd into a single file of size 306K; the final dvips'd postscript file is about 1.3mb Replaced 9/30/93 to incorporate final changes in the proofs and to make the LaTeX more portable; the paper will appear in CHAOS 4 (Dec, 1993

Dynamics of a small neutrally buoyant sphere in a fluid and targeting in Hamiltonian systems

We show that, even in the most favorable case, the motion of a small spherical tracer suspended in a fluid of the same density may differ from the corresponding motion of an ideal passive particle. We demonstrate furthermore how its dynamics may be applied to target trajectories in Hamiltonian systems.Comment: See home page http://lec.ugr.es/~julya

Relativistic cosmological perturbation scheme on a general background: scalar perturbations for irrotational dust

In standard perturbation approaches and N-body simulations, inhomogeneities are described to evolve on a predefined background cosmology, commonly taken as the homogeneous-isotropic solutions of Einstein's field equations (Friedmann-Lema\^itre-Robertson-Walker (FLRW) cosmologies). In order to make physical sense, this background cosmology must provide a reasonable description of the effective, i.e. spatially averaged, evolution of structure inhomogeneities also in the nonlinear regime. Guided by the insights that (i) the average over an inhomogeneous distribution of matter and geometry is in general not given by a homogeneous solution of general relativity, and that (ii) the class of FLRW cosmologies is not only locally but also globally gravitationally unstable in relevant cases, we here develop a perturbation approach that describes the evolution of inhomogeneities on a general background being defined by the spatially averaged evolution equations. This physical background interacts with the formation of structures. We derive and discuss the resulting perturbation scheme for the matter model `irrotational dust' in the Lagrangian picture, restricting our attention to scalar perturbations.Comment: 18 pages. Matches published version in CQ

Chaos or Noise - Difficulties of a Distinction

In experiments, the dynamical behavior of systems is reflected in time series. Due to the finiteness of the observational data set it is not possible to reconstruct the invariant measure up to arbitrary fine resolution and arbitrary high embedding dimension. These restrictions limit our ability to distinguish between signals generated by different systems, such as regular, chaotic or stochastic ones, when analyzed from a time series point of view. We propose to classify the signal behavior, without referring to any specific model, as stochastic or deterministic on a certain scale of the resolution $\epsilon$, according to the dependence of the $(\epsilon,\tau)$-entropy, $h(\epsilon, \tau)$, and of the finite size Lyapunov exponent, $\lambda(\epsilon)$, on $\epsilon$.Comment: 24 pages RevTeX, 9 eps figures included, two references added, minor corrections, one section has been split in two (submitted to PRE

Signature of chaos in gravitational waves from a spinning particle

A spinning test particle around a Schwarzschild black hole shows a chaotic behavior, if its spin is larger than a critical value. We discuss whether or not some peculiar signature of chaos appears in the gravitational waves emitted from such a system. Calculating the emitted gravitational waves by use of the quadrupole formula, we find that the energy emission rate of gravitational waves for a chaotic orbit is about 10 times larger than that for a circular orbit, but the same enhancement is also obtained by a regular "elliptic" orbit. A chaotic motion is not always enhance the energy emission rate maximally. As for the energy spectra of the gravitational waves, we find some characteristic feature for a chaotic orbit. It may tell us how to find out a chaotic behavior of the system. Such a peculiar behavior, if it will be found, may also provide us some additional informations to determine parameters of a system such as a spin.Comment: 14 pages, LaTeX, to appear in Phys. Rev.

Deterministic polarization chaos from a laser diode

Fifty years after the invention of the laser diode and fourty years after the report of the butterfly effect - i.e. the unpredictability of deterministic chaos, it is said that a laser diode behaves like a damped nonlinear oscillator. Hence no chaos can be generated unless with additional forcing or parameter modulation. Here we report the first counter-example of a free-running laser diode generating chaos. The underlying physics is a nonlinear coupling between two elliptically polarized modes in a vertical-cavity surface-emitting laser. We identify chaos in experimental time-series and show theoretically the bifurcations leading to single- and double-scroll attractors with characteristics similar to Lorenz chaos. The reported polarization chaos resembles at first sight a noise-driven mode hopping but shows opposite statistical properties. Our findings open up new research areas that combine the high speed performances of microcavity lasers with controllable and integrated sources of optical chaos.Comment: 13 pages, 5 figure

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

Risk of Malignant Progression in Barrett’s Esophagus Patients: Results from a Large Population-Based Study

BACKGROUND: Barrett’s esophagus (BE) is a premalignant lesion that predisposes to esophageal adenocarcinoma. However, the reported incidence of esophageal adenocarcinoma in patients with BE varies widely. We examined the risk of malignant progression in patients with BE using data from the Northern Ireland Barrett’s esophagus Register (NIBR), one of the largest population-based registries of BE worldwide, which includes every adult diagnosed with BE in Northern Ireland between 1993 and 2005. SUBJECTS AND METHODS: We followed 8522 patients with BE, defined as columnar lined epithelium of the esophagus with or without specialized intestinal metaplasia (SIM), until the end of 2008. Patients with incident adenocarcinomas of the esophagus or gastric cardia or with high-grade dysplasia of the esophagus were identified by matching the NIBR with the Northern Ireland Cancer Registry, and deaths were identified by matching with records from the Registrar General’s Office. Incidence of cancer outcomes or high-grade dysplasia was calculated as events per 100 person-years (% per year) of follow-up, and Cox proportional hazard models were used to determine incidence by age, sex, length of BE segment, presence of SIM, macroscopic BE, or low-grade dysplasia. All P values were from two-sided tests. RESULTS: After a mean of 7.0 years of follow-up, 79 patients were diagnosed with esophageal cancer, 16 with cancer of the gastric cardia, and 36 with high-grade dysplasia. In the entire cohort, incidence of esophageal or gastric cardia cancer or high-grade dysplasia combined was 0.22% per year (95% confidence interval [CI] = 0.19% to 0.26%). SIM was found in 46.0% of patients. In patients with SIM, the combined incidence was 0.38% per year (95% CI = 0.31 to 0.46%). The risk of cancer was statistically significantly elevated in patients with vs without SIM at index biopsy (0.38% per year vs 0.07% per year; hazard ratio [HR] = 3.54, 95% CI = 2.09 to 6.00, P < .001), in men compared with women (0.28% per year vs 0.13% per year; HR = 2.11, 95% CI = 1.41 to 3.16, P < .001), and in patients with low-grade dysplasia compared with no dysplasia (1.40% per year vs 0.17% per year; HR = 5.67, 95% CI = 3.77 to 8.53, P < .001). CONCLUSION: We found the risk of malignant progression among patients with BE to be lower than previously reported, suggesting that currently recommended surveillance strategies may not be cost-effective

Diffusion-weighted whole-body imaging with background body signal suppression (DWIBS): features and potential applications in oncology

Diffusion-weighted magnetic resonance imaging (DWI) provides functional information and can be used for the detection and characterization of pathologic processes, including malignant tumors. The recently introduced concept of “diffusion-weighted whole-body imaging with background body signal suppression” (DWIBS) now allows acquisition of volumetric diffusion-weighted images of the entire body. This new concept has unique features different from conventional DWI and may play an important role in whole-body oncological imaging. This review describes and illustrates the basics of DWI, the features of DWIBS, and its potential applications in oncology

Uptake of genetic testing by the children of Lynch syndrome variant carriers across three generations

Many Lynch syndrome (LS) carriers remain unidentified, thus missing early cancer detection and prevention opportunities. Tested probands should inform their relatives about cancer risk and options for genetic counselling and predictive gene testing, but many fail to undergo testing. To assess predictive testing uptake and demographic factors influencing this decision in LS families, a cross-sectional registry-based cohort study utilizing the Finnish Lynch syndrome registry was undertaken. Tested LS variant probands (1184) had 2068 children divided among three generations: 660 parents and 1324 children (first), 445 and 667 (second), and 79 and 77 (third). Of children aged 418 years, 801 (67.4%), 146 (43.2%), and 5 (23.8%), respectively, were genetically tested. Together, 539 first-generation LS variant carriers had 2068 children and grandchildren (3.84 per carrier). Of the 1548 (2.87 per carrier) eligible children, 952 (61.5%) were tested (1.77 per carrier). In multivariate models, age (OR 1.08 per year; 95% CI 1.06-1.10), family gene (OR 2.83; 1.75-4.57 for MLH1 and 2.59; 1.47-4.56 for MSH2 compared with MSH6), one or more tested siblings (OR 6.60; 4.82-9.03), no siblings (OR 4.63; 2.64-8.10), and parent under endoscopic surveillance (OR 5.22; 2.41-11.31) were independent predictors of having genetic testing. Examples of parental adherence to regular surveillance and genetically tested siblings strongly influenced children at 50% risk of LS to undergo predictive gene testing. High numbers of untested, adult at-risk individuals exist even among well-established cohorts of known LS families with good adherence to endoscopic surveillance.Peer reviewe