Scale-free Power Research Articles

The visibility graph analysis of heart rate variability during chi meditation and Kundalini Yoga techniques

The human heartbeat reflects one of the most crucial types of complex physiologic fluctuations. The purpose of this study is to study and evaluate the complexity of heart rate time series to capture its intrinsic multiscale dynamics based on the concept of fractality and complexity. The visibility graph (VG) of the heart rate series is proposed as a quantitative method to differentiate subjects in rest and meditation periods of two techniques: Chi meditation and Kundalini Yoga meditation. Differential complexities between the two mentioned states are quantified using the power of scale-freeness (PS) and the graph index complexity (GIC) in VG. The model is applied to available heart rate signals in the PhysioBank. The results reveal the promising ability of PS and GIC to assess the distinction between the two states. However, in both meditation techniques, the complexities of heart rate signals are increased during meditation. The results also show all heart rate series have visibility graphs with a power-law topology, and fractality in the heart rate series is dictated by a mechanism associated with the chaotic nature of the biological signals that could be useful to evaluate heart rate signals during meditation.

Indices from visibility graph complexity of spontaneous speech signal: An efficient nonlinear tool for Alzheimer's disease diagnosis

Interest in dynamical data analytics of human speech related to the diagnosis of Alzheimer's disease (AD) has recently risen. This study aims to scrutinize the dynamic variations in AD speech based on concepts called complexity and fractality. Towards this goal, the visibility graph (VG) of the spontaneous speech time series as a quantitative approach is proposed to distinguish healthy subjects from those with Alzheimer's. The dynamical patterns of the speech signals are analyzed between three stages of AD and healthy subjects by examining some specific kinds of these measures, known as graph index complexity (GIC) and power of scale-freeness (PS) in VG. The results show the practical ability of the GIC and PS to detect the underlying pathological mechanism of Alzheimer's disease. In addition, it is found that all speech series have visibility graphs with a power-law topology, and fractality in them is reflected by a mechanism related to the brain system pathology, which affects the language skills of people.

Neuronal avalanches: Sandpiles of self-organized criticality or critical dynamics of brain waves?

Analytical expressions for scaling of brain wave spectra derived from the general nonlinear wave Hamiltonian form show excellent agreement with experimental "neuronal avalanche" data. The theory of the weakly evanescent nonlinear brain wave dynamics [Phys. Rev. Research 2, 023061 (2020); J. Cognitive Neurosci. 32, 2178 (2020)] reveals the underlying collective processes hidden behind the phenomenological statistical description of the neuronal avalanches and connects together the whole range of brain activity states, from oscillatory wave-like modes, to neuronal avalanches, to incoherent spiking, showing that the neuronal avalanches are just the manifestation of the different nonlinear side of wave processes abundant in cortical tissue. In a more broad way these results show that a system of wave modes interacting through all possible combinations of the third order nonlinear terms described by a general wave Hamiltonian necessarily produces anharmonic wave modes with temporal and spatial scaling properties that follow scale free power laws. To the best of our knowledge this has never been reported in the physical literature and may be applicable to many physical systems that involve wave processes and not just to neuronal avalanches.

Critical brain wave dynamics of neuronal avalanches.

Analytical expressions for scaling of brain wave spectra derived from the general non-linear wave Hamiltonian form show excellent agreement with experimental "neuronal avalanche" data. The theory of the weakly evanescent non-linear brain wave dynamics reveals the underlying collective processes hidden behind the phenomenological statistical description of the neuronal avalanches and connects together the whole range of brain activity states, from oscillatory wave-like modes, to neuronal avalanches, to incoherent spiking, showing that the neuronal avalanches are just the manifestation of the different non-linear side of wave processes abundant in cortical tissue. In a more broad way these results show that a system of wave modes interacting through all possible combinations of the third order non-linear terms described by a general wave Hamiltonian necessarily produces anharmonic wave modes with temporal and spatial scaling properties that follow scale free power laws. To the best of our knowledge this has never been reported in the physical literature and may be applicable to many physical systems that involve wave processes and not just to neuronal avalanches.

Study of multiplicity dependence of pion fluctuations in $$\pi ^{-}$$ π - –AgBr collisions at 350 GeV using complex network approach

A complex network and chaos-based method, based on the visibility graph algorithm, is applied to study particle fluctuations in $$\pi ^{-}$$ –AgBr interactions at 350 GeV with respect to the shower multiplicity dependence. The fractal structure of the fluctuations is studied by using the power of scale freeness of visibility graph (PSVG). The selection of visibility graph as the type of complex network for our analysis is justified as this algorithm gives the most precise result with finite number of data points and this experiment has finite number of events. The topological parameters along with PSVG values are extracted and analysed. The analysis shows that the fractality character is weaker for the lowest multiplicity bin and is stronger for the highest multiplicity bin.

Chaos Based Quantitative Risk Assessment of Cardiac Dysfunction

Congestive Heart Failure is a growing menace spreading its jaws worldwide. As for all diseases, early detection of the disease is the key to thwart the rampage caused by the disease. With the existent diagnostic devices and methodologies, cost of diagnosis is high and some are painful due to their invasive nature. This has led us to apply non-linear methods for analysis of ECG signals and formulate biomarkers. Analysis of cardiac signals using fractal analysis has gained sufficient momentum over the past few years. In this article the cardiac dynamics of ECG data are explored with chaos based non-linear time series analysis techniques -- Hurst exponent and Power of scale freeness in Visibility Graph PSVG. The ECG data of normal subjects and CHF subjects are taken from Physionet [1] database and analyzed with these techniques to calculate values of Hurst Exponent and PSVG. The Hurst exponent analysis reflects the chaotic behavior of normal and CHF patients’ heart and the PSVG parameter can significantly differentiate the CHF patients from normal people. The parameters obtained by the non-linear analysis of ECG signals can be used as biomarkers. The biomarkers can be used by clinical laboratories as well as by smart phone users. Clinical software or mobile apps implementing the proposed method can be used for alarm generation during onset of cardiac abnormalities of the CHF patients.

EFFECT OF DARK MATTER HALO SUBSTRUCTURES ON GALAXY ROTATION CURVES

The effect of halo substructures on galaxy rotation curves is investigated in this paper using a simple model of dark matter clustering. A dark matter halo density profile is developed based only on the scale free nature of clustering that leads to a statistically self-similar distribution of the substructures at galactic scale. Semi-analytical method is used to derive rotation curves for such a clumpy dark matter density profile. It is found that the halo substructures significantly affect the galaxy velocity field. Based on the fractal geometry of the halo, this self-consistent model predicts an NFW-like rotation curve and a scale free power spectrum of the rotation velocity fluctuations.

Non-Gaussianities in extendedD-term inflation

We explore extensions of hybrid inflationary models in the context of supersymmetric $D$-term inflation. We point out that a large variety of inflationary scenarios can be encountered when the field content is extended. It is not only possible to get curvaton type models but also scenarios in which different fields, with nontrivial statistical properties, contribute to the primordial curvature fluctuations. We explore more particularly the parameter space of these multiple-field inflationary models. It is shown that there exists a large domain in which significant primordial non-Gaussianities can be produced while preserving a scale free power spectrum for the metric fluctuations. In particular we explicitly compute the expected bispectrum and trispectrum for such models and compared the results to the current and expected observational constraints. It is shown that it is necessary to use both the bispectra and trispectra of cosmic microwave background anisotropies to efficiently reduce their parameter space.

Generalized Statistical Models of Voids and Hierarchical Structure in Cosmology

Generalized statistical models of voids and hierarchical structure in cosmology are developed. The often quoted negative binomial model and frequently used thermodynamic model are shown to be special cases of a more general distribution which contains a parameter a. The parameter is related to the Levy index alpha and the Fisher critical exponent tau, the latter describing the power law fall off of clumps of matter around a phase transition. The parametera, exponent tau, or index alpha can be obtained from properties of a void scaling function. A stochastic probability variable is introduced into a statistical model which represent the adhesive growth of galaxy structure. For p 1/2, an adhesive growth can go on indefinitely thereby forming an infinite supercluster. At p=1/2 a scale free power law distribution for the galaxy count distribution is present. The stochastic description also leads to consequences that have some parallels with cosmic string results, percolation theory and phase transitions.

Merging history trees for dark matter haloes: tests of the Merging Cell Model in a CDM cosmology

The merging history of dark matter halos is computed with the Merging Cell Model proposed by Rodrigues & Thomas (1996). While originally discussed in the case of scale–free power spectra, it is developed and tested here in the framework of the cold dark matter cosmology. The halo mass function, the mass distribution of progenitors and child halos, as well as the probability distribution of formation times, have been computed and compared to the available analytic predictions. The halo auto– correlation function has also been obtained (a first for a semi–analytic merging tree), and tested against analytic formulae. An overall good agreement is found between results of the model, and the predictions derived from the Press & Schechter theory and its extensions. More severe discrepancies appear when formulae that better describe N-body simulations are used for comparison. In many instances, the model can be a useful tool for following the hierarchical growth of structures. In particular, it is suitable for addressing the issue of the formation and evolution of galaxy clusters, as well as the population of Lyman–break galaxies at high redshift, and their clustering properties.

Steps toward the Power Spectrum of Matter. III. The Primordial Spectrum

We compare the observed power spectrum of matter found in our earlier papers with analytical power spectra. We extrapolate the observed power spectra on small scales to find the linear power spectrum of matter. We consider spatially flat cold and mixed dark matter models with the cosmological constant as well as open models. We fix the Hubble constant and the baryon density in the middle of the allowed range and vary the density parameter and the cosmological constant. We determine the primordial power spectrum of matter using the power spectrum of matter and the transfer functions of analytical models. We take two different spectra suggested by observations: one with a sharp maximum at 120 h-1 Mpc and a second one with a broader maximum, as found for regions with rich and medium-rich superclusters of galaxies, respectively. For both models, the primordial power spectra have a break in amplitude; in the case of the spectrum with a sharp maximum the break is sharp. We conclude that a scale-free primordial power spectrum is excluded if presently available data on the distribution of clusters and galaxies represent the true mass distribution of the universe.

The structure and dynamical evolution of dark matter haloes

(Shortened) We use N-body simulations to investigate the structure and dynamical evolution of dark matter halos in galaxy clusters. Our sample consists of nine massive halos from an EdS universe with scale free power spectrum and n = -1. Halos are resolved by ~20000 particles each, with a dynamical resolution of 20-25 kpc. Large scale tidal fields are included up to L=150 Mpc using background particles. The halo formation process can be characterized by the alternation of two dynamical configurations: a merging phase and a relaxation phase, defined by their signature on the evolution of the total mass and rms velocity. Halos spend on average one 1/3 of their evolution in the merging phase and 2/3 in the relaxation phase. Using this definition, we study the density profiles and their change during the halo history. The average density profiles are fitted by the NFW analytical model with an rms residual of 17% between the virial radius Rv and 0.01 Rv. The Hernquist (1990) profiles fits the same halos with an rms residual of 26%. The trend with mass of the scale radius of these fits is marginally consistent with that found by Cole & Lacey (1996): in comparison our halos are more centrally concentrated, and the relation between scale radius and halo mass is slightly steeper. We find a moderately large scatter in this relation, due both to dynamical evolution within halos and to fluctuations in the halo population. We analyze the dynamical equilibrium of our halos using the Jeans' equation, and find that on average they are approximately in equilibrium within their virial radius. Finally, we find that the projected mass profiles of our simulated halos are in very good agreement with the profiles of three rich galaxy clusters derived from strong and weak gravitational lensing observations.