Dynamic scaling approach to study time series fluctuations

Dynamic scaling of stochastic thermodynamic observables for chemical reactions at and away from equilibrium

Physical kinetic roughening processes are well-known to exhibit universal scaling of observables that fluctuate in space and time. Are there analogous dynamic scaling laws that are unique to the chemical reaction mechanisms available synthetically and occurring naturally? Here, we formulate an approach to the dynamic scaling of stochastic fluctuations in thermodynamic observables at and away from equilibrium. Both analytical expressions and numerical simulations confirm our dynamic scaling ansatz with associated scaling exponents, function, and law. A survey of common chemical mechanisms reveals classes that organize according to the molecularity of the reactions involved, the nature of the reaction vessel and external reservoirs, (non)equilibrium conditions, and the extent of autocatalysis in the reaction network. Varying experimental parameters, such as temperature, can cause coupled reactions capable of chemical feedback to transition between these classes. While path observables, such as the dynamical activity, have scaling exponents that are time-independent, the variance in the entropy production and flow can have time-dependent scaling exponents and self-averaging properties as a result of temporal correlations that emerge during thermodynamically irreversible processes. Altogether, these results establish dynamic universality classes in the nonequilibrium fluctuations of thermodynamic observables for well-mixed chemical reactions.

Non-Parametric Evaluation Methods of the Brain Activity of a Bottlenose Dolphin during an Assisted Therapy

Simple Summary

Dolphin Assisted Therapies (DAT) can be used with any person or group with specific needs and it can be as disparate as people at risk of social exclusion, eating disorders, terminally ill, mental health disorders, among many others. This paper is focused on measuring and analyzing dolphins brain activity when DAT is taking place, in order to identify if there is any differences in female dolphin’s neuronal signal when it is interacting with control or intervention subjects. In addition, we designed a wireless and portable electroencephalographic single-channel signal capture device to monitor the brain activity of a female bottle-nose dolphin. Our findings also validate the evidence that the interaction between a patient with a certain disease or disorder and undergoes to a DAT modifies usual brain activity behavior of a female bottle-nose dolphin.

Abstract

Dolphin-Assisted Therapies (DAT) are alternative therapies aimed to reduce anxiety levels, stress relief and physical benefits. This paper is focused on measuring and analyzing dolphins brain activity when DAT is taking place in order to identify if there is any differences in female dolphin’s neuronal signal when it is interacting with control or intervention subjects, performing our research in Delfiniti, Ixtapa, Mexico facilities. We designed a wireless and portable electroencephalographic single-channel signal capture sensor to acquire and monitor the brain activity of a female bottle-nose dolphin. This EEG sensor was able to show that dolphin activity at rest is characterized by high spectral power at slow-frequencies bands. When the dolphin participated in DAT, a 23.53% increment in the 12–30 Hz frequency band was observed, but this only occurred for patients with some disease or disorder, given that 0.5–4 Hz band keeps it at 17.91% when there is a control patient. Regarding the fractal or Self-Affine Analysis, we found for all samples studied that at the beginning the dolphin’s brain activity behaved as a self-affine fractal described by a power-law until the fluctuations of voltage reached the crossovers, and after the crossovers these fluctuations left this scaling behavior. Hence, our findings validate the hypothesis that the participation in a DAT of a Patient with a certain disease or disorder modifies the usual behavior of a female bottle-nose dolphin.

Neurodynamics of Patients during a Dolphin-Assisted Therapy by Means of a Fractal Intraneural Analysis

The recent proliferation of sensor technology applications in therapies for children’s disabilities to promote positive behavior among such children has produced optimistic results in developing a variety of skills and abilities in them. Dolphin-Assisted Therapy (DAT) has also become a topic of public and research interest for these disorders’ intervention and treatment. This work exposes the development of a system that controls brain–computer interaction when a patient with different abilities undergoes a DAT. To develop the proposed system, TGAM1, i.e., ThinkGear-AM1 series of NeuroSky company, was used, connecting it to an isolated Bluetooth 4.0 communication protocol from a brackish and humid environment, and a Notch Filter was applied to reduce the input noise. In this way, at Definiti Ixtapa-Mexico facilities, we explored the behavior of three children with Infantile Spastic Cerebral Palsy (Experiment 1), as well as the behavior of Obsessive Compulsive Disorder and neurotypic children (Experiment 2). This was done applying the Power Spectrum Density (PSD) and the Self-Affine Analysis (SSA) from Electroencephalogram (EEG) biosignals. The EEG Raw data were time series showing the cerebral brain activity (voltage versus time) before and during DAT for the Experiment 1, and before, during DAT and after for the Experiment 2. Likewise, the EEW RAW data were recorded by the first frontopolar electrode (FP1) by means of an EEG biosensor TGAM1 Module. From the PSD we found that in all child patients a huge increment of brain activity during DAT regarding the before and after therapy periods around 376.28%. Moreover, from the SSA we found that the structure function of the all five child patients displayed an antipersistent behavior, characterized by σ∝δtH, for before, during DAT and after. Nonetheless, we propose that one way to assess whether a DAT is being efficient to the child patients is to increase the during DAT time when the samples are collected, supposing the data fitting by a power law will raise the time, displaying a persistent behavior or positive correlations, until a crossover appears and the curve tends to be horizontal, pointing out that our system has reached a stationary state.

Evaluation of dynamic scaling of growing interfaces in EEG fluctuations of seizures in animal model of temporal lobe epilepsy

Epileptic seizures, as a dynamic phenomenon in brain behavior, obey a scale-free behavior, frequently analyzed by electrical activity recording. This recording can be seen as a surface that roughens with time. Dynamic scaling studies roughening processes or growing interfaces. In this theory, a set of exponents -obtained from scale invariance properties- characterize rough interfaces growth. The aim of the present study was to investigate scaling behavior in EEG time series fluctuations of a chemical animal model of temporal lobe epilepsy, with dynamic scaling to detect changes on seizure onset. We analyzed local variables in different sampling intervals and estimated rough, scaling and dynamic exponents. Results exhibited long-range correlations in interictal activity. Results of renormalization and data collapsing confirmed that each epoch of EEG fluctuations for interictal, preictal and postictal collapse in a curve in different scales, each segment independently; remarkably, we found non-scaling behavior in seizures epochs. Data for the different sampling intervals for ictal period do not collapse in one curve, which implies that ictal activity does not exhibit the same scaling behavior than the other epochs. Statistical significant differences of growth exponent were found between interictal and ictal segment, while for scaling exponent, significant differences were found between interictal and postictal segment. These results confirm the potential of scaling exponents as characteristic parameters to detect changes on seizure onset, which suggests their use as inputs for analysis methods for seizure detection in long-term recordings, while changes in growth exponent are potentially useful for prediction purposes.

Nonuniversal effects in mixing correlated-growth processes with randomness: interplay between bulk morphology and surface roughening

To construct continuum stochastic growth equations for competitive nonequilibrium surface-growth processes of the type RD+X that mixes random deposition (RD) with a correlated-growth process X, we use a simplex decomposition of the height field. A distinction between growth processes X that do and do not create voids in the bulk leads to the definition of the effective probability p(eff) of the process X that is a measurable property of the bulk morphology and depends on the activation probability p of X in the competitive process RD+X. The bulk morphology is reflected in the surface roughening via nonuniversal prefactors in the universal scaling of the surface width that scales in p(eff). The equation and the resulting scaling are derived for X in either a Kardar-Parisi-Zhang or Edwards-Wilkinson universality class in (1+1) dimensions and are illustrated by an example of X being a ballistic deposition. We obtain full data collapse on its corresponding universal scaling function for all p∈(0;1]. We outline the generalizations to (1+n) dimensions and to many-component competitive growth processes.

Complete spectral scaling of time series: towards a classification of 1/f noise

The standard spectral scaling, S(f)∼1/f(β), has been traditionally used as a correlation measure characterizing the dynamical behavior of time series. The ubiquity of 1/f and 1/f(2) spectra in many processes certainly suggests the existence of universal mechanisms, but also gives rise to the suspicion that some important features are not included in this scaling. In this paper we argue that a complete spectral scaling, including as a main variable the size of the series, S(f,T)∼T(η)/f(β), which is usually considered irrelevant, gives an insight into this problem. Using synthetically generated series we show that, in general, the scaling exponent β is too generic, while the exponent associated with the size, η, gives a more specific information. Hence, we propose the use of both exponents in a scheme to classify series into different universality classes. In this way many of the processes appearing in the literature could be better identified, and much of the ambiguity that surrounds the standard spectral scaling could be clarified.

Natural time analysis of the Centennial Earthquake Catalog

By using the most recent version (1900-2007) of the Centennial Earthquake Catalog, we examine the properties of the global seismicity. Natural time analysis reveals that the fluctuations of the order parameter κ(1) of seismicity exhibit for at least three orders of magnitude a characteristic feature similar to that of the order parameter for other equilibrium or non-equilibrium critical systems-including self-organized critical systems. Moreover, we find non-trivial magnitude correlations for earthquakes of magnitude greater than or equal to 7.

Nonextensivity and natural time: The case of seismicity

Nonextensive statistical mechanics, pioneered by Tsallis, has recently achieved a generalization of the Gutenberg-Richter law for earthquakes. This remarkable generalization is combined here with natural time analysis, which enables the distinction of two origins of self-similarity, i.e., the process' memory and the process' increments infinite variance. By using also detrended fluctuation analysis for the detection of long-range temporal correlations, we demonstrate the existence of both temporal and magnitude correlations in real seismic data of California and Japan. Natural time analysis reveals that the nonextensivity parameter q , in contrast to some published claims, cannot be considered as a measure of temporal organization, but the Tsallis formulation does achieve a satisfactory description of real seismic data for Japan for q=1.66 when supplemented by long-range temporal correlations.