Natural variability of atmospheric temperatures and geomagnetic intensity over a wide range of time scales

The majority of numerical models in climatology and geomagnetism rely on deterministic finite-difference techniques and attempt to include as many empirical constraints on the many processes and boundary conditions applicable to their very complex systems. Despite their sophistication, many of these models are unable to reproduce basic aspects of climatic or geomagnetic dynamics. We show that a simple stochastic model, which treats the flux of heat energy in the atmosphere by convective instabilities with random advection and diffusive mixing, does a remarkable job at matching the observed power spectrum of historical and proxy records for atmospheric temperatures from time scales of one day to one million years (Myr). With this approach distinct changes in the power-spectral form can be associated with characteristic time scales of ocean mixing and radiative damping. Similarly, a simple model of the diffusion of magnetic intensity in Earth's core coupled with amplification and destruction of the local intensity can reproduce the observed 1/f noise behavior of Earth's geomagnetic intensity from time scales of 1 (Myr) to 100 yr. In addition, the statistics of the fluctuations in the polarity reversal rate from time scales of 1 Myr to 100 Myr are consistent with the hypothesis that reversals are the result of variations in 1/f noise geomagnetic intensity above a certain threshold, suggesting that reversals may be associated with internal fluctuations rather than changes in mantle thermal or magnetic boundary conditions.     

Force fluctuations and polymerization dynamics of intracellular microtubules

Microtubules are highly dynamic biopolymer filaments involved in a wide variety of biological processes including cell division, migration, and intracellular transport. Microtubules are very rigid and form a stiff structural scaffold that resists deformation. However, despite their rigidity, inside of cells they typically exhibit significant bends on all length scales. Here, we investigate the origin of these bends using a Fourier analysis approach to quantify their length and time dependence. We show that, in cultured animal cells, bending is suppressed by the surrounding elastic cytoskeleton, and even large intracellular forces only cause significant bending fluctuations on short length scales. However, these lateral bending fluctuations also naturally cause fluctuations in the orientation of the microtubule tip. During growth, these tip fluctuations lead to microtubule bends that are frozen-in by the surrounding elastic network. This results in a persistent random walk of the microtubule, with a small apparent persistence length of approximately 30 microm, approximately 100 times smaller than that resulting from thermal fluctuations alone. Thus, large nonthermal forces govern the growth of microtubules and can explain the highly curved shapes observed in the microtubule cytoskeleton of living cells.     

Nonstationary increments, scaling distributions, and variable diffusion processes in financial markets

Fat-tailed distributions have been reported in fluctuations of financial markets for more than a decade. Sliding interval techniques used in these studies implicitly assume that the underlying stochastic process has stationary increments. Through an analysis of intraday increments, we explicitly show that this assumption is invalid for the Euro-Dollar exchange rate. We find several time intervals during the day where the standard deviation of increments exhibits power law behavior in time. Stochastic dynamics during these intervals is shown to be given by diffusion processes with a diffusion coefficient that depends on time and the exchange rate. We introduce methods to evaluate the dynamical scaling index and the scaling function empirically. In general, the scaling index is significantly smaller than previously reported values close to 0.5. We show how the latter as well as apparent fat-tailed distributions can occur only as artifacts of the sliding interval analysis.     

Glass-like dynamics of collective cell migration

Collective cell migration in tissues occurs throughout embryonic development, during wound healing, and in cancerous tumor invasion, yet most detailed knowledge of cell migration comes from single-cell studies. As single cells migrate, the shape of the cell body fluctuates dramatically through cyclic processes of extension, adhesion, and retraction, accompanied by erratic changes in migration direction. Within confluent cell layers, such subcellular motions must be coupled between neighbors, yet the influence of these subcellular motions on collective migration is not known. Here we study motion within a confluent epithelial cell sheet, simultaneously measuring collective migration and subcellular motions, covering a broad range of length scales, time scales, and cell densities. At large length scales and time scales collective migration slows as cell density rises, yet the fastest cells move in large, multicell groups whose scale grows with increasing cell density. This behavior has an intriguing analogy to dynamic heterogeneities found in particulate systems as they become more crowded and approach a glass transition. In addition we find a diminishing self-diffusivity of short-wavelength motions within the cell layer, and growing peaks in the vibrational density of states associated with cooperative cell-shape fluctuations. Both of these observations are also intriguingly reminiscent of a glass transition. Thus, these results provide a broad and suggestive analogy between cell motion within a confluent layer and the dynamics of supercooled colloidal and molecular fluids approaching a glass transition.     

How market ecology explains market malfunction

Standard approaches to the theory of financial markets are based on equilibrium and efficiency. Here we develop an alternative based on concepts and methods developed by biologists, in which the wealth invested in a financial strategy is like the abundance of a species. We study a toy model of a market consisting of value investors, trend followers, and noise traders. We show that the average returns of strategies are strongly density dependent; that is, they depend on the wealth invested in each strategy at any given time. In the absence of noise, the market would slowly evolve toward an efficient equilibrium, but the statistical uncertainty in profitability (which is calibrated to match real markets) makes this noisy and uncertain. Even in the long term, the market spends extended periods of time away from perfect efficiency. We show how core concepts from ecology, such as the community matrix and food webs, give insight into market behavior. For example, at the efficient equilibrium, all three strategies have a mutualistic relationship, meaning that an increase in the wealth of one increases the returns of the others. The wealth dynamics of the market ecosystem explain how market inefficiencies spontaneously occur and gives insight into the origins of excess price volatility and deviations of prices from fundamental values.

Why do markets malfunction? According to the theory of market efficiency, markets always function perfectly. Prices always reflect fundamental values and change only when new information affects fundamental values. Thus, by definition, any problems with price setting are caused by factors outside the market. Empirical evidence suggests otherwise. Large price movements occur even when there is very little new information (1), and prices often deviate substantially from fundamental values (2). This means that we need to go beyond the theory of market efficiency to understand how and why markets malfunction.Here we build on earlier work (3–7)^* and develop the theory of market ecology, which provides the necessary alternative. This approach borrows concepts and methods from biology and applies them to financial markets. Financial trading strategies are analogous to biological species. Plants and animals are specialists that evolve to fill niches that provide food; similarly, financial trading strategies are specialists that evolve to exploit market inefficiencies. Trading strategies can be classified into distinct categories, such as technical trading, value investing, market making, statistical arbitrage, and many others. The capital invested in a strategy is like the population of a species. Trading strategies interact with one another via price setting, and the market evolves as the wealth invested in each strategy changes through time, as regulations change, and as old strategies fail and new strategies appear.The theory of market ecology emerges from the inherent contradictions in the theory of market efficiency. A standard argument used to justify market efficiency is that competition for profits by arbitrageurs should cause markets to rapidly evolve to an equilibrium where it is not possible to make excess profits based on publicly available information. But, if there are no profits to be made, there are no incentives for arbitrageurs, so there is no mechanism to make markets efficient. This paradox suggests that, while markets may be efficient in some approximate sense, they cannot be perfectly efficient (8). In contrast, under the theory of market ecology, trading strategies exploit market inefficiencies, but, as new strategies appear and as the wealth invested in each strategy changes, the inefficiencies change as well. To understand how the market functions, it is necessary to understand how each strategy affects the market and how the interactions between strategies cause market inefficiencies to change with time. The theory of market ecology naturally addresses a different set of problems than the theory of market efficiency and can be viewed as a complement rather than a substitute.Our study here builds on a large body of work on agent-based models of financial markets (e.g. refs. 9–12). The theory of market ecology provides a conceptual framework for understanding such models. Our goal is not to construct a better model of financial markets, but rather to show how ideas from ecology can be used to interpret market phenomena and predict market behavior.Here we study a stylized toy market model with three trading strategies. We approach the problem in the same way that an ecologist would study three interacting species. We study how the average returns of the strategies depend on the wealth invested in each strategy, how their wealth evolves through time under reinvestment, and how their endogenous time evolution causes the market to malfunction.We show that, with realistic parameters, evolution toward market efficiency is very slow. The expected deviations from efficiency are, in some sense, small, but they persist even in the long term, and cause extended deviations from fundamental values and excess volatility (which, in extreme cases, becomes market instability). Our study provides a simple example of how analyzing markets in these terms and tracking market ecosystems through time could give regulators and practitioners better insight into market behavior.     

Coarse-grained stochastic processes for microscopic lattice systems

Diverse scientific disciplines ranging from materials science to catalysis to biomolecular dynamics to climate modeling involve nonlinear interactions across a large range of physically significant length scales. Here a class of coarse-grained stochastic processes and corresponding Monte Carlo simulation methods, describing computationally feasible mesoscopic length scales, are derived directly from microscopic lattice systems. It is demonstrated below that the coarse-grained stochastic models can capture large-scale structures while retaining significant microscopic information. The requirement of detailed balance is used as a systematic design principle to guarantee correct noise fluctuations for the coarse-grained model. The coarse-grained stochastic algorithms provide large computational savings without increasing programming complexity or computer time per executive event compared to microscopic Monte Carlo simulations.     

Evidence for a diffusion-controlled mechanism for fluorescence blinking of colloidal quantum dots

Fluorescence blinking in nanocrystal quantum dots is known to exhibit power-law dynamics, and several different mechanisms have been proposed to explain this behavior. We have extended the measurement of quantum-dot blinking by characterizing fluctuations in the fluorescence of single dots over time scales from microseconds to seconds. The power spectral density of these fluctuations indicates a change in the power-law statistics that occurs at a time scale of several milliseconds, providing an important constraint on possible mechanisms for the blinking. In particular, the observations are consistent with the predictions of models wherein blinking is controlled by diffusion of the energies of electron or hole trap states.     

Microdynamics in stationary complex networks

Many complex systems, including networks, are not static but can display strong fluctuations at various time scales. Characterizing the dynamics in complex networks is thus of the utmost importance in the understanding of these networks and of the dynamical processes taking place on them. In this article, we study the example of the US airport network in the time period 1990–2000. We show that even if the statistical distributions of most indicators are stationary, an intense activity takes place at the local (“microscopic”) level, with many disappearing/appearing connections (links) between airports. We find that connections have a very broad distribution of lifetimes, and we introduce a set of metrics to characterize the links'' dynamics. We observe in particular that the links that disappear have essentially the same properties as the ones that appear, and that links that connect airports with very different traffic are very volatile. Motivated by this empirical study, we propose a model of dynamical networks, inspired from previous studies on firm growth, which reproduces most of the empirical observations both for the stationary statistical distributions and for the dynamical properties.     

Self-organized complexity in economics and finance

This article discusses some of the similarities between work being done by economists and by physicists seeking to contribute to economics. We also mention some of the differences in the approaches taken and seek to justify these different approaches by developing the argument that by approaching the same problem from different points of view, new results might emerge. In particular, we review two newly discovered scaling results that appear to be universal, in the sense that they hold for widely different economies as well as for different time periods: (i) the fluctuation of price changes of any stock market is characterized by a probability density function, which is a simple power law with exponent -4 extending over 10(2) SDs (a factor of 10(8) on the y axis); this result is analogous to the Gutenberg--Richter power law describing the histogram of earthquakes of a given strength; and (ii) for a wide range of economic organizations, the histogram shows how size of organization is inversely correlated to fluctuations in size with an exponent approximately 0.2. Neither of these two new empirical laws has a firm theoretical foundation. We also discuss results that are reminiscent of phase transitions in spin systems, where the divergent behavior of the response function at the critical point (zero magnetic field) leads to large fluctuations.     

The fractal nature of blood glucose fluctuations

AimsFluctuations of blood glucose are generated by multiple external and internal factors continuously modifying glucose concentrations through complex feedback loops. This equilibrium may be perturbed during physiological or pathological conditions. The traditional theory suggests that physiological systems achieve homeostasis when disturbed and restore equilibrium through linear feedback loops. Complex systems on the other hand, may function nonlinearly with feedback loops that operate at different time scales, exhibiting chaotic or fractal behavior. We hypothesized that blood glucose fluctuations recorded for prolonged time periods show chaotic, fractal-like behavior that may be altered in diabetes.MethodsWe applied nonlinear analytical methods such as detrended fluctuation analysis to glucose data derived from continuous glucose monitoring devices for prolonged time periods in healthy volunteers, diabetes type 1 and pregnant diabetes type 1 patients.ResultsGlucose fluctuations extracted for prolonged time periods show fractal-like behavior and power law behavior of the system.ConclusionsHidden features underlying glucose fluctuations in health and in disease were revealed by using dynamic nonlinear analyses methods to discrete glucose readings extracted from continuous glucose monitoring devices. By using such methods we can enhance our understanding of the dynamics of blood glucose fluctuations in health and disease.     

Dynamical transition and proteinquake in photoactive yellow protein

Conformational dynamics in protein functioning covers a wide range of time scales from nanosecond fluctuations around a conformation to the large-amplitude conformational changes of milliseconds or longer. We illustrate a picture of cooperative coupling among such motions of different time scales in a model protein, photoactive yellow protein, by proposing a model that can consistently explain the experimental results on the photocycle of photoactive yellow protein. The model provides a scenario in which the global collective motion induced by the unfolding of the N-terminal domain promotes the loosening of the atomistic packing around the chromophore, which produces the favorable molecular environment for the photoexcited chromophore, thereby stabilizing the partially unfolded intermediate in the photocycle. The proteinquake, the large conformational change triggered by the local structural disturbance, plays a decisive role in controlling the kinetics of functioning.     

Protein dynamics-induced variation of excitation energy transfer pathways

Strong anticorrelation between the fluorescence emission of different emitters is observed by employing single-molecule fluorescence spectroscopy on photosystem I at cryogenic temperatures. This anticorrelation demonstrates a time-dependent interaction between pigments participating in the exciton transfer chain, implying that uniquely defined energy transfer pathways within the complex do not exist. Fluctuations of the chromophores themselves or their immediate protein surroundings induce changes in their site energy, and, as a consequence, these fluctuations change the coupling within the excitation transfer pathways. The time scales of the site energy fluctuations of the individual emitters do not meet the time scales of the observed correlated emission behavior. Therefore, the emitters must be fed individually by energetically higher lying states, causing the observed intensity variations. This phenomenon is shown for photosystem I pigment–protein complexes from 2 different cyanobacteria (Thermosynechococcus elongatus and Synechocystis sp. PCC 6803) with strongly different spectral properties underlining the general character of the findings. The variability of energy transfer pathways might play a key role in the extreme robustness of light-harvesting systems in general.     

Trends in financial satisfaction among middle-age and old-age Americans, 1972-1996

Using data from the General Social Surveys (1972-1996), this study decomposes the trends in financial satisfaction into intercohort and intracohort patterns to assess the intracohort change and cohort replacement effects on financial satisfaction. The results suggest that a positive intracohort component of financial satisfaction trends, indicating more financial satisfaction with time; and a negative intercohort component, indicating that younger cohorts are less satisfied financially. The multivariate analysis further suggests that the change in financial satisfaction trends is mostly due to a strong intercohort replacement effect. That is, the change in financial satisfaction trends can be largely accounted for by the intercohort replacement effect of younger cohorts' being less satisfied financially.     

Direct observation of fast protein conformational switching

Folded proteins can exist in multiple conformational substates. Each substate reflects a local minimum on the free-energy landscape with a distinct structure. By using ultrafast 2D-IR vibrational echo chemical-exchange spectroscopy, conformational switching between two well defined substates of a myoglobin mutant is observed on the approximately 50-ps time scale. The conformational dynamics are directly measured through the growth of cross peaks in the 2D-IR spectra of CO bound to the heme active site. The conformational switching involves motion of the distal histidine/E helix that changes the location of the imidazole side group of the histidine. The exchange between substates changes the frequency of the CO, which is detected by the time dependence of the 2D-IR vibrational echo spectrum. These results demonstrate that interconversion between protein conformational substates can occur on very fast time scales. The implications for larger structural changes that occur on much longer time scales are discussed.     

Control of time-dependent biological processes by temporally patterned input

Temporal patterning of biological variables, in the form of oscillations and rhythms on many time scales, is ubiquitous. Altering the temporal pattern of an input variable greatly affects the output of many biological processes. We develop here a conceptual framework for a quantitative understanding of such pattern dependence, focusing particularly on nonlinear, saturable, time-dependent processes that abound in biophysics, biochemistry, and physiology. We show theoretically that pattern dependence is governed by the nonlinearity of the input–output transformation as well as its time constant. As a result, only patterns on certain time scales permit the expression of pattern dependence, and processes with different time constants can respond preferentially to different patterns. This has implications for temporal coding and decoding, and allows differential control of processes through pattern. We show how pattern dependence can be quantitatively predicted using only information from steady, unpatterned input. To apply our ideas, we analyze, in an experimental example, how muscle contraction depends on the pattern of motorneuron firing.     

Dissection of complex protein dynamics in human thioredoxin

We report our direct study of complex protein dynamics in human thioredoxin by dissecting into elementary processes and determining their relevant time scales. By combining site-directed mutagenesis with femtosecond spectroscopy, we have distinguished four partly time-overlapped dynamical processes at the active site of thioredoxin. Using intrinsic tryptophan as a molecular probe and from mutation studies, we ascertained the negligible contribution to solvation by protein sidechains and observed that the hydration dynamics at the active site occur in 0.47-0.67 and 10.8-13.2 ps. With reduced and oxidized states, we determined the electron-transfer quenching dynamics between excited tryptophan and a nearby disulfide bond in 10-17.5 ps for three mutants. A robust dynamical process in 95-114 ps, present in both redox states and all mutants regardless of neighboring charged, polar, and hydrophobic residues around the probe, is attributed to the charge transfer reaction with its adjacent peptide bond. Site-directed mutations also revealed the electronic quenching dynamics by an aspartate residue at a hydrogen bond distance in 275-615 ps. The local rotational dynamics determined by the measurement of anisotropy changes with time unraveled a relatively rigid local configuration but implies that the protein fluctuates on the time scale of longer than nanoseconds. These results elucidate the temporal evolution of hydrating water motions, electron-transfer reactions, and local protein fluctuations at the active site, and show continuously synergistic dynamics of biological function over wide time scales.     

Emergence of complex dynamics in a simple model of signaling networks

Various physical, social, and biological systems generate complex fluctuations with correlations across multiple time scales. In physiologic systems, these long-range correlations are altered with disease and aging. Such correlated fluctuations in living systems have been attributed to the interaction of multiple control systems; however, the mechanisms underlying this behavior remain unknown. Here, we show that a number of distinct classes of dynamical behaviors, including correlated fluctuations characterized by 1/f scaling of their power spectra, can emerge in networks of simple signaling units. We found that, under general conditions, complex dynamics can be generated by systems fulfilling the following two requirements, (i) a "small-world" topology and (ii) the presence of noise. Our findings support two notable conclusions. First, complex physiologic-like signals can be modeled with a minimal set of components; and second, systems fulfilling conditions i and ii are robust to some degree of degradation (i.e., they will still be able to generate 1/f dynamics).     

Prospective Measurement of Daily Health Behaviors: Modeling Temporal Patterns in Missing Data,Sexual Behavior,and Substance Use in an Online Daily Diary Study of Gay and Bisexual Men

Daily diary and other intensive longitudinal methods are increasingly being used to investigate fluctuations in psychological and behavioral processes. To inform the development of this methodology, we sought to explore predictors of and patterns in diary compliance and behavioral reports. We used multilevel modeling to analyze data from an online daily diary study of 371 gay and bisexual men focused on sexual behavior and substance use. We found that greater education and older age as well as lower frequency of substance use were associated with higher compliance. Using polynomial and trigonometric functions, we found evidence for circaseptan patterns in compliance, sexual behavior, and substance use, as well as linear declines in compliance and behavior over time. The results suggest potential sources of non-random patterns of missing data and suggest that trigonometric terms provide a similar but more parsimonious investigation of circaseptan rhythms than do third-order polynomial terms.     

Quality of life in patients before and after haematopoietic stem cell transplantation measured with the European Organization for Research and Treatment of Cancer (EORTC) Quality of Life Core Questionnaire QLQ-C30

The EORTC Quality of Life Core Questionnaire QLQ-C30 is widely used, but no reference values are available for patients receiving HSCT. We retrieved data for 38 samples from 33 papers in English and German that provided evaluable information on QLQ-C30 scores (mean, s.d.) covering about 2800 patients. Results are presented as a table that provides reference data that allow QLQ-C30 scores at different points during the disease trajectory to be put in context. With respect to their central tendency and their variance, scores vary over time. Quality of life is lowest during inpatient time. About 1 year after HSCT, the pre-transplant level is reached. Physical functioning is the scale reaching the highest level of all scales. Fatigue, dyspnoea and insomnia are symptoms that remain at an elevated level and should thus be considered as persisting problems after HSCT. For the interpretation of differences between scores, a very conservative recommendation would be to set the s.d. at 30 points. Doing so, one could be quite sure of having found a clinically significant change if the difference of two scores exceeds 15 points. Differences below 5 points should be interpreted with caution.