Power-law Characteristics Research Articles

Spectrum Degradation of Hippocampal LFP During Euthanasia.

The hippocampal local field potential (LFP) exhibits a strong correlation with behavior. During rest, the theta rhythm is not prominent, but during active behavior, there are strong rhythms in the theta, theta harmonics, and gamma ranges. With increasing running velocity, theta, theta harmonics and gamma increase in power and in cross-frequency coupling, suggesting that neural entrainment is a direct consequence of the total excitatory input. While it is common to study the parametric range between the LFP and its complementing power spectra between deep rest and epochs of high running velocity, it is also possible to explore how the spectra degrades as the energy is completely quenched from the system. Specifically, it is unknown whether the 1/f slope is preserved as synaptic activity becomes diminished, as low frequencies are generated by large pools of neurons while higher frequencies comprise the activity of more local neuronal populations. To test this hypothesis, we examined rat LFPs recorded from the hippocampus and entorhinal cortex during barbiturate overdose euthanasia. Within the hippocampus, the initial stage entailed a quasi-stationary LFP state with a power-law feature in the power spectral density. In the second stage, there was a successive erosion of power from high- to low-frequencies in the second stage that continued until the only dominant remaining power was <20 Hz. This stage was followed by a rapid collapse of power spectrum toward the absolute electrothermal noise background. As the collapse of activity occurred later in hippocampus compared with medial entorhinal cortex, it suggests that the ability of a neural network to maintain the 1/f slope with decreasing energy is a function of general connectivity. Broadly, these data support the energy cascade theory where there is a cascade of energy from large cortical populations into smaller loops, such as those that supports the higher frequency gamma rhythm. As energy is pulled from the system, neural entrainment at gamma frequency (and higher) decline first. The larger loops, comprising a larger population, are fault-tolerant to a point capable of maintaining their activity before a final collapse.

Bright soliton dynamics in higher-dimensional system with power-law nonlinearity

For power-law nonlinear system in higher-dimensional setting like the three-dimensional case, we derived its bright soliton solution with specific power-law feature based on the self-similar method. The dynamical evolution pattern of the derived solution is pictorially demonstrated which illustrates the typical bright soliton feature. The theoretical results presented in this work can be used to guide experimental observation of soliton behavior in higher-dimensional system with power-law nonlinearity.

Identifying Geomorphic Process Domains in the Synthetic Landscapes of West Virginia, USA

AbstractHuman activities such as mining, agriculture, and urbanization have resulted in severe, large‐scale alteration to landform organization and associated geomorphic processes. The mountaintop mining (MTM) region of West Virginia, USA has experienced dramatic topographic alteration, by removing steep slopes and introducing plateau‐like areas at ridgelines and benches on valley fills. The resulting engineered landforms create synthetic landscapes, disconnected from previous geomorphic processes. Invoking the process domain concept, we compare differences in slope‐area relations, cumulative area distributions (CADs), elevation, slope, upslope accumulated area, and a slope*area product before and after mining to adjacent unmined sub‐catchments in five study basins. Differences in the slope‐area relation include a 42% slope reduction in low drainage areas, corresponding to hillslopes, unchanneled valleys, and debris flow dominated channels, which may fall below thresholds required for debris flow processes. The curved slope‐area relation that represents valley incision by debris flows is replaced by slope‐area relations that resemble basins where gullying and the stream power law dominate. Extremely high chemical weathering of unconsolidated valley fills materials may facilitate process domain shifts from debris flows to gullying and fluvial erosion. The characteristic power law scaling break in CADs that represents the headward limit of the channelized network is subdued in post‐mined sites and may reflect headward channelized network extension in mined basins. Slope‐area relations and CADs present a unique topographic signature of MTM activity, potentially providing an analytical approach to assess impacts on underlying geomorphic processes for other synthetic landscapes such as cities or large‐scale agricultural production.

Revisiting the Power Law Characteristics of the Plastic Shock Front under Shock Loading.

Under uniaxial shock compression, the steepness of the plastic shock front usually exhibits power law characteristics with the Hugoniot pressure, also known as the "Swegle-Grady law." In this Letter, we show that the Swegle-Grady law can be described better by a third power law rather than the classical fourth power law at the strain rate between 10^{5}-10^{7} s^{-1}. A simple dislocation-based continuum model is developed, which reproduced the third power law and revealed very good agreement with recent experiments of multiple types of metals quantitatively. New insights into this unusual macroscopic phenomenon are presented through quantifying the connection between the macroscopic mechanical response and the collective dynamics of dislocation assembles. It is found that the Swegle-Grady law results from the particular stress dependence of the plasticity behaviors, and that the difference between the third power scaling and the classical fourth power scaling results from different shock dissipative actions.

Fractal derivative fractional grey Riccati model and its application

Fractal geometry methods are widely used to describe the geometric characteristics of complex systems, statistical behaviors, and power-law characteristics of data results. In this study, the fractal derivative and fractional cumulative generating operators are introduced into the grey Riccati model to establish the fractal derivative and fractional grey Riccati model (FDFGRM), and the analytical solution of the model is obtained. At the same time, multi-objective quantum particle swarm optimization algorithm is used for parameter optimization. We consider China's cement production, natural gas production, and primary aluminum production as examples to verify the validity of the model. The results show that the fitting and testing effects of the FDFGRM are better than those of other models. Finally, FDFGRM is used to predict the future trends of these three cases.

A fractional-order SIRD model with time-dependent memory indexes for encompassing the multi-fractional characteristics of the COVID-19.

COVID-19 is a novel coronavirus affecting all the world since December last year. Up to date, the spread of the outbreak continues to complicate our lives, and therefore, several research efforts from many scientific areas are proposed. Among them, mathematical models are an excellent way to understand and predict the epidemic outbreaks evolution to some extent. Due to the COVID-19 may be modeled as a non-Markovian process that follows power-law scaling features, we present a fractional-order SIRD (Susceptible-Infected-Recovered-Dead) model based on the Caputo derivative for incorporating the memory effects (long and short) in the outbreak progress. Additionally, we analyze the experimental time series of 23 countries using fractal formalism. Like previous works, we identify that the COVID-19 evolution shows various power-law exponents (no just a single one) and share some universality among geographical regions. Hence, we incorporate numerous memory indexes in the proposed model, i.e., distinct fractional-orders defined by a time-dependent function that permits us to set specific memory contributions during the evolution. This allows controlling the memory effects of more early states, e.g., before and after a quarantine decree, which could be less relevant than the contribution of more recent ones on the current state of the SIRD system. We also prove our model with Italy’s real data from the Center for Systems Science and Engineering (CSSE) at Johns Hopkins University.

Power law characteristics of trend analysis in Turkey

Trend identification analyses in any hydrometeorological data are necessary and critical for predictions and planning in many disciplines such as atmospheric, environmental, and oceanographic sciences; water engineering; global warming; and climate change applications. In the literature, many researches have employed trend analyses by Mann-Kendall (MK) and innovative trend analysis (ITA) methods. Especially in recent years, the ITA method is preferred in trend identification methodological applications, because it can present trend graphs with visual inspection, verbal inferences, and objective quantitative calculations. In this paper, the trends of sea surface temperature (SST) data are identified by the MK and ITA methods on double logarithmic graphs, which provide fractal geometrical appearances with power law features. The SST data trends are evaluated at 22 coastal area stations of Turkey with monthly records from 1969 to 2014. According to the MK trend test, only 6 of the 22 stations had a significant upward trend at 5% significant level and 4 of these stations are in the Mediterranean Sea coastal area. At 10% significance level increasing trend numbers become 14 stations. According to the MK test results, the data records have been grouped into two parts as warming and cooling periods considering the physical conditions of the SST data. On the other hand, the results of ITA application provide average behavioral form according to the mathematical power law equations.

Generation of 2-mode scale-free graphs for link-level internet topology modeling.

Comprehensive analysis that aims to understand the topology of real-world networks and the development of algorithms that replicate their characteristics has been significant research issues. Although the accuracy of newly developed network protocols or algorithms does not depend on the underlying topology, the performance generally depends on the topology. As a result, network practitioners have concentrated on generating representative synthetic topologies and utilize them to investigate the performance of their design in simulation or emulation environments. Network generators typically represent the Internet topology as a graph composed of point-to-point links. In this study, we discuss the implications of multi-access links on the synthetic network generation and modeling of the networks as bi-partite graphs to represent both subnetworks and routers. We then analyze the characteristics of sampled Internet topology data sets from backbone Autonomous Systems (AS) and observe that in addition to the commonly recognized power-law node degree distribution, the subnetwork size and the router interface distributions often exhibit power-law characteristics. We introduce a SubNetwork Generator (SubNetG) topology generation approach that incorporates the observed measurements to produce bipartite network topologies. In particular, generated topologies capture the 2-mode relation between the layer-2 (i.e., the subnetwork and interface distributions) and the layer-3 (i.e., the degree distribution) that is missing from the current network generators that produce 1-mode graphs. The SubNetG source code and experimental data is available at https://github.com/netml/sonet.

Research on spatial resilience characteristics and response mechanism of Chengdu-Chongqing urban agglomeration based on power-law

Urban agglomeration is the spatial organization form of urban development and the main carrier of population, economy and information gathering to promote regional coordinated development. Therefore, it is important to research the sustainable development of urban agglomeration. Focus on the scientific issue of the relationship between power-law distribution structure of spatial elements and spatial resilience of urban agglomeration; using the number of urban permanent population and urban built-up area size as the key spatial elements of Chengdu-Chongqing urban agglomeration, firstly, we discussed the spatial-temporal evolution law of power-law characteristics of key spatial elements of Chengdu-Chongqing urban agglomeration. Secondly, we revealed the response mechanism of spatial resilience to power-law distribution of key spatial elements of Chengdu-Chongqing urban agglomeration. The conclusions as following: (1) The spatial resilience of Chengdu-Chongqing urban agglomeration characterized as “concentration” dominated by large cities. (2) The spatial resilience and Pareto distribution of Chengdu-Chongqing urban agglomeration have a remarkable and stable response relationship. (3) In order to maximize the spatial resilience of Chengdu-Chongqing urban agglomeration, it is urgent to control the number of urban permanent population and built-up area scale of large cities.

Unconventional Low-Temperature Luminescence Kinetics in Micro- and Nanopowders of the Anatase Phase of Titanium Dioxide

It is shown that the low-temperature (5 K) decay kinetics of the known luminescence band of titanium dioxide (anatase) in the range of 2.0–2.5 eV has a power-law character. For microcrystals, this behavior is observed in a wide range of delay times from ∼20 ns to 1 ms. The instantaneous luminescence decay time at the end of this range is as long as ∼100 µs. A simple model is proposed to reconstruct the statistics of the lifetime distribution of emitting states using the measured power-law decay curves. Within this model, the observed power-law decay kinetics is associated with radiative recombination mechanisms where a donor-bound electron recombines with an acceptor-bound hole. In crystals with sizes of ∼10 nm, power-law luminescence decay, characteristic of this mechanism, is also observed; however, the luminescence kinetics changes with time, which is explained by the nonradiative recombination of electron—hole pairs via surface states.

CIC-PIM: Trading spare computing power for memory space in graph processing

Shared-memory graph processing is usually more efficient than in a cluster in terms of cost effectiveness, ease of programming and runtime. However, the limited memory capacity of a single machine and the huge sizes of graphs restrains its applicability. Hence, it is imperative to reduce memory footprint. We observe that index compression holds promise and propose CIC-PIM, a lightweight encoding with chunked index compression, to reduce the memory footprint and the runtime of graph algorithms. CIC-PIM aims for significant space saving, real random-access support and high cache efficiency by exploiting the ubiquitous power-law and sparseness features of large scale graphs. The basic idea is to divide index structures into chunks of appropriate size and compress the chunks with our lightweight fixed-length byte-aligned encoding. After CIC-PIM compression, two-fold larger graphs are processed with all data fit in memory, resulting in speedups or fast in-memory processing unattainable previously.

Scaling behavior of the quantum phase transition from a quantum-anomalous-Hall insulator to an axion insulator

The phase transitions from one plateau to the next plateau or to an insulator in quantum Hall and quantum anomalous Hall (QAH) systems have revealed universal scaling behaviors. A magnetic-field-driven quantum phase transition from a QAH insulator to an axion insulator was recently demonstrated in magnetic topological insulator sandwich samples. Here, we show that the temperature dependence of the derivative of the longitudinal resistance on magnetic field at the transition point follows a characteristic power-law that indicates a universal scaling behavior for the QAH to axion insulator phase transition. Similar to the quantum Hall plateau to plateau transition, the QAH to axion insulator transition can also be understood by the Chalker–Coddington network model. We extract a critical exponent κ ~ 0.38 ± 0.02 in agreement with recent high-precision numerical results on the correlation length exponent of the Chalker–Coddington model at ν ~ 2.6, rather than the generally-accepted value of 2.33.

Normal State Properties of Quantum Critical Metals at Finite Temperature

We study the effects of finite temperature on normal state properties of a metal near a quantum critical point to an antiferromagnetic or Ising-nematic state. At $T = 0$ bosonic and fermionic self-energies are traditionally computed within Eliashberg theory and obey scaling relations with characteristic power-laws. Quantum Monte Carlo (QMC) simulations have shown strong systematic deviations from these predictions, casting doubt on the validity of the theoretical analysis. We extend Eliashberg theory to finite $T$ and argue that for the $T$ range accessible in the QMC simulations, the scaling forms for both fermionic and bosonic self energies are quite different from those at $T = 0$. We compare finite $T$ results with QMC data and find good agreement for both systems. This, we argue, resolves the key apparent contradiction between the theory and the QMC simulations.

Implications of Projected Hydroclimatic Change for Tularemia Outbreaks in High-Risk Areas across Sweden.

Hydroclimatic change may affect the range of some infectious diseases, including tularemia. Previous studies have investigated associations between tularemia incidence and climate variables, with some also establishing quantitative statistical disease models based on historical data, but studies considering future climate projections are scarce. This study has used and combined hydro-climatic projection outputs from multiple global climate models (GCMs) in phase six of the Coupled Model Intercomparison Project (CMIP6), and site-specific, parameterized statistical tularemia models, which all imply some type of power-law scaling with preceding-year tularemia cases, to assess possible future trends in disease outbreaks for six counties across Sweden, known to include tularemia high-risk areas. Three radiative forcing (emissions) scenarios are considered for climate change projection until year 2100, incuding low (2.6 Wm−2), medium (4.5 Wm−2), and high (8.5 Wm−2) forcing. The results show highly divergent changes in future disease outbreaks among Swedish counties, depending primarily on site-specific type of the best-fit disease power-law scaling characteristics of (mostly positive, in one case negative) sub- or super-linearity. Results also show that scenarios of steeper future climate warming do not necessarily lead to steeper increase of future disease outbreaks. Along a latitudinal gradient, the likely most realistic medium climate forcing scenario indicates future disease decreases (intermittent or overall) for the relatively southern Swedish counties Örebro and Gävleborg (Ockelbo), respectively, and disease increases of considerable or high degree for the intermediate (Dalarna, Gävleborg (Ljusdal)) and more northern (Jämtland, Norrbotten; along with the more southern Värmland exception) counties, respectively.

Progressive fracture processes around tunnel triggered by blast disturbances under biaxial compression with different lateral pressure coefficients

To investigate the progressive fracture processes around a tunnel triggered by static stress and dynamic disturbance, experiments and numerical simulations were performed. The results show that the spatial distributions of acoustic emission (AE) events become very different as lateral pressure coefficients change. The combined effect of static stress and dynamic disturbance causes the damage around the tunnel, and initial stress conditions control the damage morphology. The blast disturbance cannot fundamentally change the damaged area but will deepen the extent of damage and accelerate the failure speed. The more significant the difference between the vertical and horizontal stresses is, the higher the impact on the tunnel by the dynamic disturbance is. The AE activity recovers to a relatively stable state within a short time after the blast and conforms to power-law characteristics.

Low-frequency vibrations of jammed packings in large spatial dimensions.

Amorphous packings prepared in the vicinity of the jamming transition play a central role in theoretical studies of the vibrational spectrum of glasses. Two mean-field theories predict that the vibrational density of states g(ω) obeys a characteristic power law, g(ω)∼ω^{2}, called the non-Debye scaling in the low-frequency region. Numerical studies have, however, reported that this scaling breaks down at low frequencies, due to finite-dimensional effects. In this study, we prepare amorphous packings of up to 128000 particles in spatial dimensions from d=3 to d=9 to characterize the range of validity of the non-Debye scaling. Our numerical results suggest that the non-Debye scaling is obeyed down to a frequency that gradually decreases as d increases, and possibly vanishes for large d, in agreement with mean-field predictions. We also show that the prestress is an efficient control parameter to quantitatively compare packings across different spatial dimensions.

Primordial black holes and secondary gravitational waves from k and G inflation

The possibility that in the mass range around $10^{-12}\ M_\odot$ most of dark matter constitutes of primordial black holes (PBHs) is a very interesting topic. To produce PBHs with this mass, the primordial scalar power spectrum needs to be enhanced to the order of 0.01 at the scale $k\sim 10^{12}\ \text{Mpc}^{-1}$. The enhanced power spectrum also produces large secondary gravitational waves at the mHz band. A phenomenological delta function power spectrum is usually used to discuss the production of PBHs and secondary gravitational waves. Based on G and k inflations, we propose a new mechanism to enhance the power spectrum at small scales by introducing a non-canonical kinetic term $[1-2G(\phi)]X$ with the function $G(\phi)$ having a peak. Away from the peak, $G(\phi)$ is negligible and we recover the usual slow-roll inflation which is constrained by the cosmic microwave background anisotrpy observations. Around the peak, the slow-roll inflation transiently turns to ultra slow-roll inflation. The enhancement of the power spectrum can be obtained with generic potentials, and there is no need to fine tune the parameters in $G(\phi)$. The energy spectrum $\Omega_{GW}(f)$ of secondary gravitational waves have the characteristic power law behaviour $\Omega_{GW}(f)\sim f^{n}$ and is testable by pulsar timing array and space based gravitational wave detectors.

On the temperature and pressure dependences of the effective thermal conductivity of granites

The results of experimental measurements of the temperature dependence of the effective thermal conductivity of various granite samples obtained by the absolute stationary method in the temperature and pressure ranges of 273-523 K and 0.1-400 MPa, respectively, are analyzed. The power-law character of the temperature dependence of the effective thermal conductivity for all measured granite samples at atmospheric pressure is established. We have shown that pressure significantly affects the power law of the temperature dependence of the effective thermal conductivity of granite samples. A low-parameter description of the temperature-pressure behavior of thermal conductivity is proposed. A correlation is established between its components.

A cardiodynamic model for power laws of heartbeats in aging and congestive heart failure

The output of a healthy physiological system exhibits complex fluctuation. Nonlinear analysis, such as power-law characteristics, shows the potential for detecting changes in the biological complexity of disease and aging. This paper characterized the heart rate variability (HRV) of aging and patients with congestive heart failure (CHF) by three types of distribution: Zipf's law, Heaps' law, and frequency distribution. All data analysis and modeling are based on a constructed sequence, that is, the monotonous increase to monotonous decrease amplitude ratios as derived from heartbeat interval data. The experimental result shows a significant decrease of HRV from healthy young people to healthy elderly to CHF patients. We proposed a model by taking account of the “rich-get-richer” theory in experimental observations, which successfully reproduced three types of distribution characterizing the constructed ratio sequences as obtained from the analysis of measured cardiac data. This work provides insight into the dynamic mechanism of cardiac data underlying the regulation of autonomic nerve.

Superexponential self-interacting oscillator

The superexponential self-interacting oscillator (SSO) is introduced and analyzed. Its power law potential is characterized by the dependence of both the base and the exponent on the dynamical variable of the oscillator. Opposite to standard oscillators such as the (an-)harmonic oscillator the SSO combines both scattering and confined periodic motion with an exponentially varying nonlinearity. The SSO potential exhibits a transition point with a hierarchy of singularities of logarithmic and power law character leaving their fingerprints in the agglomeration of its phase space curves. The period of the SSO consequently undergoes a crossover from decreasing linear to a nonlinearly increasing behaviour when passing the transition energy. We explore its dynamics and show that the crossover involves a kick-like behaviour. A symmetric double well variant of the SSO is briefly discussed.