Dynamical model and nonextensive statistical mechanics of a market index on large time windows

The shape and tails of partial distribution functions (PDF) for a financial signal, i.e. the S&P500 and the turbulent nature of the markets are linked through a model encompassing Tsallis nonextensive statistics and leading to evolution equations of the Langevin and Fokker-Planck type. A model originally proposed to describe the intermittent behavior of turbulent flows describes the behavior of normalized log-returns for such a financial market index, for small and large time windows, both for small and large log-returns. These turbulent market volatility (of normalized log-returns) distributions can be sufficiently well fitted with a $\chi^2$-distribution. The transition between the small time scale model of nonextensive, intermittent process and the large scale Gaussian extensive homogeneous fluctuation picture is found to be at $ca.$ a 200 day time lag. The intermittency exponent ($\kappa$) in the framework of the Kolmogorov log-normal model is found to be related to the scaling exponent of the PDF moments, -thereby giving weight to the model. The large value of $\kappa$ points to a large number of cascades in the turbulent process. The first Kramers-Moyal coefficient in the Fokker-Planck equation is almost equal to zero, indicating ''no restoring force''. A comparison is made between normalized log-returns and mere price increments.Comment: 40 pages, 14 figures; accepted for publication in Phys Rev

Non-Visual Effects of Light on Melatonin, Alertness and Cognitive Performance: Can Blue-Enriched Light Keep Us Alert?

Light exposure can cascade numerous effects on the human circadian process via the non-imaging forming system, whose spectral relevance is highest in the short-wavelength range. Here we investigated if commercially available compact fluorescent lamps with different colour temperatures can impact on alertness and cognitive performance

Effect of Trends on Detrended Fluctuation Analysis

Detrended fluctuation analysis (DFA) is a scaling analysis method used to estimate long-range power-law correlation exponents in noisy signals. Many noisy signals in real systems display trends, so that the scaling results obtained from the DFA method become difficult to analyze. We systematically study the effects of three types of trends -- linear, periodic, and power-law trends, and offer examples where these trends are likely to occur in real data. We compare the difference between the scaling results for artificially generated correlated noise and correlated noise with a trend, and study how trends lead to the appearance of crossovers in the scaling behavior. We find that crossovers result from the competition between the scaling of the noise and the ``apparent'' scaling of the trend. We study how the characteristics of these crossovers depend on (i) the slope of the linear trend; (ii) the amplitude and period of the periodic trend; (iii) the amplitude and power of the power-law trend and (iv) the length as well as the correlation properties of the noise. Surprisingly, we find that the crossovers in the scaling of noisy signals with trends also follow scaling laws -- i.e. long-range power-law dependence of the position of the crossover on the parameters of the trends. We show that the DFA result of noise with a trend can be exactly determined by the superposition of the separate results of the DFA on the noise and on the trend, assuming that the noise and the trend are not correlated. If this superposition rule is not followed, this is an indication that the noise and the superimposed trend are not independent, so that removing the trend could lead to changes in the correlation properties of the noise.Comment: 20 pages, 16 figure

Common Scaling Patterns in Intertrade Times of U. S. Stocks

We analyze the sequence of time intervals between consecutive stock trades of thirty companies representing eight sectors of the U. S. economy over a period of four years. For all companies we find that: (i) the probability density function of intertrade times may be fit by a Weibull distribution; (ii) when appropriately rescaled the probability densities of all companies collapse onto a single curve implying a universal functional form; (iii) the intertrade times exhibit power-law correlated behavior within a trading day and a consistently greater degree of correlation over larger time scales, in agreement with the correlation behavior of the absolute price returns for the corresponding company, and (iv) the magnitude series of intertrade time increments is characterized by long-range power-law correlations suggesting the presence of nonlinear features in the trading dynamics, while the sign series is anti-correlated at small scales. Our results suggest that independent of industry sector, market capitalization and average level of trading activity, the series of intertrade times exhibit possibly universal scaling patterns, which may relate to a common mechanism underlying the trading dynamics of diverse companies. Further, our observation of long-range power-law correlations and a parallel with the crossover in the scaling of absolute price returns for each individual stock, support the hypothesis that the dynamics of transaction times may play a role in the process of price formation.Comment: 8 pages, 5 figures. Presented at The Second Nikkei Econophysics Workshop, Tokyo, 11-14 Nov. 2002. A subset appears in "The Application of Econophysics: Proceedings of the Second Nikkei Econophysics Symposium", editor H. Takayasu (Springer-Verlag, Tokyo, 2003) pp.51-57. Submitted to Phys. Rev. E on 25 June 200

Scaling of the distribution of fluctuations of financial market indices

We study the distribution of fluctuations over a time scale $\Delta t$ (i.e., the returns) of the S&P 500 index by analyzing three distinct databases. Database (i) contains approximately 1 million records sampled at 1 min intervals for the 13-year period 1984-1996, database (ii) contains 8686 daily records for the 35-year period 1962-1996, and database (iii) contains 852 monthly records for the 71-year period 1926-1996. We compute the probability distributions of returns over a time scale $\Delta t$, where $\Delta t$ varies approximately over a factor of 10^4 - from 1 min up to more than 1 month. We find that the distributions for $\Delta t \leq$ 4 days (1560 mins) are consistent with a power-law asymptotic behavior, characterized by an exponent $\alpha \approx 3$, well outside the stable L\'evy regime $0 < \alpha < 2$. To test the robustness of the S&P result, we perform a parallel analysis on two other financial market indices. Database (iv) contains 3560 daily records of the NIKKEI index for the 14-year period 1984-97, and database (v) contains 4649 daily records of the Hang-Seng index for the 18-year period 1980-97. We find estimates of $\alpha$ consistent with those describing the distribution of S&P 500 daily-returns. One possible reason for the scaling of these distributions is the long persistence of the autocorrelation function of the volatility. For time scales longer than $(\Delta t)_{\times} \approx 4$ days, our results are consistent with slow convergence to Gaussian behavior.Comment: 12 pages in multicol LaTeX format with 27 postscript figures (Submitted to PRE May 20, 1999). See http://polymer.bu.edu/~amaral/Professional.html for more of our work on this are

Early brainstem [18F]THK5351 uptake is linked to cortical hyper-excitability in healthy aging

BACKGROUND: Neuronal hyper-excitability characterizes the early stages of Alzheimer's disease (AD). In animals, early misfolded tau and amyloid-beta (Aβ) protein accumulation, both central to AD neuropathology, promote cortical excitability and neuronal network dysfunction. In healthy humans, misfolded tau and Aβ aggregates are first detected, respectively, in the brainstem and frontomedial and temporobasal cortices, decades prior to the onset of AD cognitive symptoms. Whether cortical excitability is related to early brainstem tau, and its associated neuroinflammation, and cortical Aβ aggregations remains unknown. METHODS: We probed frontal cortex excitability, using transcranial magnetic stimulation combined with electroencephalography, in a sample of 64 healthy late middle-aged individuals (50-69 y; 45 women). We assessed whole-brain [18F]THK5351 positron emission tomography (PET) uptake as a proxy measure of tau/neuroinflammation, and whole-brain Aβ burden with [18F]Flutemetamol or [18F]Florbetapir radiotracers. RESULTS: We find that higher [18F]THK5351 uptake in a brainstem monoaminergic compartment is associated with increased cortical excitability (r = .29, p = .02). By contrast, [18F]THK5351 PET signal in the hippocampal formation, although strongly correlated with brainstem signal in whole-brain voxel-based quantification analyses (pFWE-corrected < .001), was not significantly associated with cortical excitability (r = .14, p = .25). Importantly, no significant association was found between early Aβ cortical deposits and cortical excitability (r = -.20, p = .11). CONCLUSION: These findings reveal potential brain substrates for increased cortical excitability in preclinical AD and may constitute functional in vivo correlates of early brainstem tau accumulation and neuroinflammation in humans. TRIAL REGISTRATION: EudraCT 2016-001436-35. FUNDING: F.R.S.-FNRS Belgium, Wallonie-Bruxelles International, ULiège, Fondation Simone et Pierre Clerdent, European Regional Development Fund

Characterization of Sleep Stages by Correlations of Heartbeat Increments

We study correlation properties of the magnitude and the sign of the increments in the time intervals between successive heartbeats during light sleep, deep sleep, and REM sleep using the detrended fluctuation analysis method. We find short-range anticorrelations in the sign time series, which are strong during deep sleep, weaker during light sleep and even weaker during REM sleep. In contrast, we find long-range positive correlations in the magnitude time series, which are strong during REM sleep and weaker during light sleep. We observe uncorrelated behavior for the magnitude during deep sleep. Since the magnitude series relates to the nonlinear properties of the original time series, while the signs series relates to the linear properties, our findings suggest that the nonlinear properties of the heartbeat dynamics are more pronounced during REM sleep. Thus, the sign and the magnitude series provide information which is useful in distinguishing between the sleep stages.Comment: 7 pages, 4 figures, revte

Circadian dynamics in measures of cortical excitation and inhibition balance

Several neuropsychiatric and neurological disorders have recently been characterized as dysfunctions arising from a ‘final common pathway’ of imbalanced excitation to inhibition within cortical networks. How the regulation of a cortical E/I ratio is affected by sleep and the circadian rhythm however, remains to be established. Here we addressed this issue through the analyses of TMS-evoked responses recorded over a 29h sleep deprivation protocol conducted in young and healthy volunteers. Spectral analyses of TMS-evoked responses in frontal cortex revealed non-linear changes in gamma band evoked oscillations, compatible with an influence of circadian timing on inhibitory interneuron activity. In silico inferences of cell-to-cell excitatory and inhibitory connectivity and GABA/Glutamate receptor time constant based on neural mass modeling within the Dynamic causal modeling framework, further suggested excitation/inhibition balance was under a strong circadian influence. These results indicate that circadian changes in EEG spectral properties, in measure of excitatory/inhibitory connectivity and in GABA/glutamate receptor function could support the maintenance of cognitive performance during a normal waking day, but also during overnight wakefulness. More generally, these findings demonstrate a slow daily regulation of cortical excitation/inhibition balance, which depends on circadian-timing and prior sleep-wake history

Resistance and Resistance Fluctuations in Random Resistor Networks Under Biased Percolation

We consider a two-dimensional random resistor network (RRN) in the presence of two competing biased percolations consisting of the breaking and recovering of elementary resistors. These two processes are driven by the joint effects of an electrical bias and of the heat exchange with a thermal bath. The electrical bias is set up by applying a constant voltage or, alternatively, a constant current. Monte Carlo simulations are performed to analyze the network evolution in the full range of bias values. Depending on the bias strength, electrical failure or steady state are achieved. Here we investigate the steady-state of the RRN focusing on the properties of the non-Ohmic regime. In constant voltage conditions, a scaling relation is found between $/_0$ and $V/V_0$, where $$ is the average network resistance, $_0$ the linear regime resistance and $V_0$ the threshold value for the onset of nonlinearity. A similar relation is found in constant current conditions. The relative variance of resistance fluctuations also exhibits a strong nonlinearity whose properties are investigated. The power spectral density of resistance fluctuations presents a Lorentzian spectrum and the amplitude of fluctuations shows a significant non-Gaussian behavior in the pre-breakdown region. These results compare well with electrical breakdown measurements in thin films of composites and of other conducting materials.Comment: 15 figures, 23 page