Persistent Chaos in High Dimensions

An extensive statistical survey of universal approximators shows that as the dimension of a typical dissipative dynamical system is increased, the number of positive Lyapunov exponents increases monotonically and the number of parameter windows with periodic behavior decreases. A subset of parameter space remains in which topological change induced by small parameter variation is very common. It turns out, however, that if the system's dimension is sufficiently high, this inevitable, and expected, topological change is never catastrophic, in the sense chaotic behavior is preserved. One concludes that deterministic chaos is persistent in high dimensions.Comment: 4 pages, 3 figures; Changes in response to referee comment

Description of stochastic and chaotic series using visibility graphs

Nonlinear time series analysis is an active field of research that studies the structure of complex signals in order to derive information of the process that generated those series, for understanding, modeling and forecasting purposes. In the last years, some methods mapping time series to network representations have been proposed. The purpose is to investigate on the properties of the series through graph theoretical tools recently developed in the core of the celebrated complex network theory. Among some other methods, the so-called visibility algorithm has received much attention, since it has been shown that series correlations are captured by the algorithm and translated in the associated graph, opening the possibility of building fruitful connections between time series analysis, nonlinear dynamics, and graph theory. Here we use the horizontal visibility algorithm to characterize and distinguish between correlated stochastic, uncorrelated and chaotic processes. We show that in every case the series maps into a graph with exponential degree distribution P (k) ~ exp(-{\lambda}k), where the value of {\lambda} characterizes the specific process. The frontier between chaotic and correlated stochastic processes, {\lambda} = ln(3/2), can be calculated exactly, and some other analytical developments confirm the results provided by extensive numerical simulations and (short) experimental time series

Chaos-driven dynamics in spin-orbit coupled atomic gases

The dynamics, appearing after a quantum quench, of a trapped, spin-orbit coupled, dilute atomic gas is studied. The characteristics of the evolution is greatly influenced by the symmetries of the system, and we especially compare evolution for an isotropic Rashba coupling and for an anisotropic spin-orbit coupling. As we make the spin-orbit coupling anisotropic, we break the rotational symmetry and the underlying classical model becomes chaotic; the quantum dynamics is affected accordingly. Within experimentally relevant time-scales and parameters, the system thermalizes in a quantum sense. The corresponding equilibration time is found to agree with the Ehrenfest time, i.e. we numerically verify a ~log(1/h) scaling. Upon thermalization, we find the equilibrated distributions show examples of quantum scars distinguished by accumulation of atomic density for certain energies. At shorter time-scales we discuss non-adiabatic effects deriving from the spin-orbit coupled induced Dirac point. In the vicinity of the Dirac point, spin fluctuations are large and, even at short times, a semi-classical analysis fails.Comment: 11 pages, 10 figure

Unified functional network and nonlinear time series analysis for complex systems science: The pyunicorn package

We introduce the \texttt{pyunicorn} (Pythonic unified complex network and recurrence analysis toolbox) open source software package for applying and combining modern methods of data analysis and modeling from complex network theory and nonlinear time series analysis. \texttt{pyunicorn} is a fully object-oriented and easily parallelizable package written in the language Python. It allows for the construction of functional networks such as climate networks in climatology or functional brain networks in neuroscience representing the structure of statistical interrelationships in large data sets of time series and, subsequently, investigating this structure using advanced methods of complex network theory such as measures and models for spatial networks, networks of interacting networks, node-weighted statistics or network surrogates. Additionally, \texttt{pyunicorn} provides insights into the nonlinear dynamics of complex systems as recorded in uni- and multivariate time series from a non-traditional perspective by means of recurrence quantification analysis (RQA), recurrence networks, visibility graphs and construction of surrogate time series. The range of possible applications of the library is outlined, drawing on several examples mainly from the field of climatology.Comment: 28 pages, 17 figure

Prospective Epidemiological Observations on the Course of the Disease in Fibromyalgia Patients

OBJECTIVES: The aim of the study was to carry out a survey in patients with fibromyalgia (FM), to examine their general health status and work incapacity (disability-pension status), and their views on the effectiveness of therapy received, over a two-year observation period. METHODS: 48 patients diagnosed with FM, according to the American College of Rheumatology (ACR) criteria, took part in the study. At baseline, and on average two years later, the patients underwent clinical investigation (dolorimetry, laboratory diagnostics, medical history taking) and completed the Fibromyalgia questionnaire (Dettmer and Chrostek [1]). RESULTS: 27/48 (56%) patients participated in the two-year follow-up. In general, the patients showed no improvement in their symptoms over the observation period, regardless of the type of therapy they had received. General satisfaction with quality of life improved, as did satisfaction regarding health status and the family situation, although the degree of pain experienced remain unchanged. In comparison with the initial examination, there was no change in either work-capacity or disability-pension status. CONCLUSIONS: The FM patients showed no improvement in pain, despite the many various treatments received over the two-year period. The increase in general satisfaction over the observation period was believed to be the result of patient instruction and education about the disease. To what extent a population of patients with FM would show similar outcomes if they did not receive any instruction/education about their disorder, cannot be ascertained from the present study; and, indeed, the undertaking of a study to investigate this would be ethically questionable. As present, no conclusions can be made regarding the influence of therapy on the primary and secondary costs associated with FM

Falsification Of The Atmospheric CO2 Greenhouse Effects Within The Frame Of Physics

The atmospheric greenhouse effect, an idea that many authors trace back to the traditional works of Fourier (1824), Tyndall (1861), and Arrhenius (1896), and which is still supported in global climatology, essentially describes a fictitious mechanism, in which a planetary atmosphere acts as a heat pump driven by an environment that is radiatively interacting with but radiatively equilibrated to the atmospheric system. According to the second law of thermodynamics such a planetary machine can never exist. Nevertheless, in almost all texts of global climatology and in a widespread secondary literature it is taken for granted that such mechanism is real and stands on a firm scientific foundation. In this paper the popular conjecture is analyzed and the underlying physical principles are clarified. By showing that (a) there are no common physical laws between the warming phenomenon in glass houses and the fictitious atmospheric greenhouse effects, (b) there are no calculations to determine an average surface temperature of a planet, (c) the frequently mentioned difference of 33 degrees Celsius is a meaningless number calculated wrongly, (d) the formulas of cavity radiation are used inappropriately, (e) the assumption of a radiative balance is unphysical, (f) thermal conductivity and friction must not be set to zero, the atmospheric greenhouse conjecture is falsified.Comment: 115 pages, 32 figures, 13 tables (some typos corrected

Hidden attractors in fundamental problems and engineering models

Recently a concept of self-excited and hidden attractors was suggested: an attractor is called a self-excited attractor if its basin of attraction overlaps with neighborhood of an equilibrium, otherwise it is called a hidden attractor. For example, hidden attractors are attractors in systems with no equilibria or with only one stable equilibrium (a special case of multistability and coexistence of attractors). While coexisting self-excited attractors can be found using the standard computational procedure, there is no standard way of predicting the existence or coexistence of hidden attractors in a system. In this plenary survey lecture the concept of self-excited and hidden attractors is discussed, and various corresponding examples of self-excited and hidden attractors are considered

An Intact Kidney Slice Model to Investigate Vasa Recta Properties and Function in situ

Background: Medullary blood flow is via vasa recta capillaries, which possess contractile pericytes. In vitro studies using isolated descending vasa recta show that pericytes can constrict/dilate descending vasa recta when vasoactive substances are present. We describe a live kidney slice model in which pericyte-mediated vasa recta constriction/dilation can be visualized in situ. Methods: Confocal microscopy was used to image calcein, propidium iodide and Hoechst labelling in ‘live’ kidney slices, to determine tubular and vascular cell viability and morphology. DIC video-imaging of live kidney slices was employed to investigate pericyte-mediated real-time changes in vasa recta diameter. Results: Pericytes were identified on vasa recta and their morphology and density were characterized in the medulla. Pericyte-mediated changes in vasa recta diameter (10–30%) were evoked in response to bath application of vasoactive agents (norepinephrine, endothelin-1, angiotensin-II and prostaglandin E2) or by manipulating endogenous vasoactive signalling pathways (using tyramine, L-NAME, a cyclo-oxygenase (COX-1) inhibitor indomethacin, and ATP release). Conclusions: The live kidney slice model is a valid complementary technique for investigating vasa recta function in situ and the role of pericytes as regulators of vasa recta diameter. This technique may also be useful in exploring the role of tubulovascular crosstalk in regulation of medullary blood flow

Ground, Proximal, and Satellite Remote Sensing of Soil Moisture

Soil moisture (SM) is a key hydrologic state variable that is of significant importance for numerous Earth and environmental science applications that directly impact the global environment and human society. Potential applications include, but are not limited to, forecasting of weather and climate variability; prediction and monitoring of drought conditions; management and allocation of water resources; agricultural plant production and alleviation of famine; prevention of natural disasters such as wild fires, landslides, floods, and dust storms; or monitoring of ecosystem response to climate change. Because of the importance and wide‐ranging applicability of highly variable spatial and temporal SM information that links the water, energy, and carbon cycles, significant efforts and resources have been devoted in recent years to advance SM measurement and monitoring capabilities from the point to the global scales. This review encompasses recent advances and the state‐of‐the‐art of ground, proximal, and novel SM remote sensing techniques at various spatial and temporal scales and identifies critical future research needs and directions to further advance and optimize technology, analysis and retrieval methods, and the application of SM information to improve the understanding of critical zone moisture dynamics. Despite the impressive progress over the last decade, there are still many opportunities and needs to, for example, improve SM retrieval from remotely sensed optical, thermal, and microwave data and opportunities for novel applications of SM information for water resources management, sustainable environmental development, and food security