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We employed high-density microelectrode arrays to investigate spontaneous firing patterns of neurons in brain circuits of the primary somatosensory cortex (S1) in mice. We recorded from over 150 neurons for 10min in each of eight different experiments, identified their location in S1, sorted their action potentials (spikes), and computed their power spectra and inter-spike interval (ISI) statistics. Of all persistently active neurons, 92% fired with a single dominant frequency — regularly firing neurons (RNs) — from 1 to 8Hz while 8% fired in burst with two dominant frequencies — bursting neurons (BNs) — corresponding to the inter-burst (2–6Hz) and intra-burst intervals (20–160Hz). RNs were predominantly located in layers 2/3 and 5/6 while BNs localized to layers 4 and 5. Across neurons, the standard deviation of ISI was a power law of its mean, a property known as fluctuation scaling, with a power law exponent of 1 for RNs and 1.25 for BNs. The power law implies that firing and bursting patterns are scale invariant: the firing pattern of a given RN or BN resembles that of another RN or BN, respectively, after a time contraction or dilation. An explanation for this scale invariance is discussed in the context of previous computational studies as well as its potential role in information processing.

Time series corresponding to nominal exchange rates between the US dollar and Argentina, Brazil and European Economic Community currencies; different financial indexes as the Industrial Dow Jones, the British Footsie, the German DAX Composite, the Australian Share Price and the Nikkei Cash and also different Argentine local tax revenues, are analyzed looking for the appearance of simple patterns and the possible definition of forecast evaluators. In every case, the statistical fractal dimensions are obtained from the behavior of the corresponding variance of increments at a given lag. The detrended fluctuation analysis of the data in terms of the corresponding exponent in the resulting power law is carried out. Finally, the frequency power spectra of all the time series considered are computed and compared

Price changes of the primary index of the Australian Stock Market are analyzed over a period of about 20 years. The probability distribution of the relative changes in the index (returns) satisfies a distribution which is almost independent of the time interval chosen to measure the change. The distribution is consistent with the analysis of New York and other stock exchanges and also seems to satisfy a power law with exponent consistent with an inverse cubic law. If the data are separated into positive and negative returns this conclusion is not justified, particularly for the rising market. Thus there seems to be a significant asymmetry in the distribution.

A new method, based on the original theory of conservation of sum of kinetic and potential energy defined for prices is proposed and applied on the Dow Jones Industrials Average (DJIA). The general trends averaged over months or years gave a roughly conserved total energy, with three different potential energies, i.e., positive definite quadratic, negative definite quadratic and linear potential energy for exponential rises (and falls), sinusoidal oscillations and parabolic trajectories, respectively. Corresponding expressions for force (impact) are also given.

An agent-based model was built representing an economic environment in which m brands are competing for a product market. These agents represent companies that interact within a social network in which a certain agent persuades others to update or shift their brands; the brands of the products they are using. Decision rules were established that caused each agent to react according to the economic benefits it would receive; they updated/shifted only if it was beneficial. Each agent can have only one of the m possible brands, and she can interact with its two nearest neighbors and another set of agents which are chosen according to a particular set of rules in the network topology. An absorbing state was always reached in which a single brand monopolized the network (known as condensation). The condensation time varied as a function of model parameters is studied including an analysis of brand competition using different networks.

We investigate how humans visually perceive and approximate area or space allocation through visual area experiments. The participants are asked to draw a circle concentric to the reference circle on the monitor screen using a computer mouse with area measurements relative to the area of the reference circle. The activity is repeated for triangle, square and hexagon. The area estimated corresponds to the area estimates of a participant (perceived) for a corresponding requested area to be drawn (stimulus). The area estimated fits very well (goodness of fit R² > 0.97) to a power law given by r^2α where r is the radius of the circle or the distance of the edge for triangle, square and hexagon. The power law fit demonstrates that for all shapes sampled, participants underestimated area for stimulus that are less than ~100% of the reference area and overestimated area for stimulus greater than ~100% of the reference area. The value of α is smallest for the circle (α_∘ ≈ 1.33) and largest for triangle (α_△ ≈ 1.56) indicating that in the presence of a reference area with the same shape, circle is perceived to be smallest among the figures considered when drawn bigger than the reference area, but largest when drawn smaller than the reference area. We also conducted experiments on length estimation and consistent with the results of Dehaene et al., Science 2008, we recover a linear relationship between the perceived length and the stimulus. We show that contrary to number mapping into space and/or length perception, human's perception of area is not corrected by the introduction of cultural interventions such as formal education.

This study examined the determinants of foreign bank location decisions in Shanghai markets over the period of 1990 to 2009. The growing foreign presence in Shanghai was found to be related to two different policy regimes: Pudong development area foreign enterprise clustering period after China opened Pudong, and "deposit-loan-match principle" implementing period after China joined WTO. The current location pattern was found to be correlated to deposit potential in each district. It is evident that the foreign bank location decisions were influenced by those of domestic banks while the reverse did not hold. These findings provide a valuable platform for theoretical modeling and further analysis.

The spread and burned areas of wildfires in Alberta, Canada during a 50 year period, from 1961 through 2010 are studied here. Meteorological factors that control the spread and burn area have been discussed for a long time. In this paper, we analyze the temperature rise that could drastically enhance the spread and average burned area of wildfires. A simple lattice model that mimics meteorological factors is also introduced to simulate the temperature effect on the spread and burned areas of wildfires. The numerical results demonstrate the temperature effects on wildfires when compared to the empirical data.

Several deterministic and stochastic multi-variable global optimization algorithms (Conjugate Gradient, Nelder–Mead, Quasi-Newton and global) are investigated in conjunction with energy minimization principle to resolve the pressure and volumetric flow rate fields in single ducts and networks of interconnected ducts. The algorithms are tested with seven types of fluid: Newtonian, power law, Bingham, Herschel–Bulkley, Ellis, Ree–Eyring and Casson. The results obtained from all those algorithms for all these types of fluid agree very well with the analytically derived solutions as obtained from the traditional methods which are based on the conservation principles and fluid constitutive relations. The results confirm and generalize the findings of our previous investigations that the energy minimization principle is at the heart of the flow dynamics systems. The investigation also enriches the methods of computational fluid dynamics for solving the flow fields in tubes and networks for various types of Newtonian and non-Newtonian fluids.

Remittances, as money or goods that people send to families and friends, are very important social and economic phenomenon at local, national, regional and international levels. In the year 2017, total international remittances were at levels around USD 613 billion. From World Bank bilateral remittances and migration matrixes, we calculate for each country and territory its aggregated or total amount of remittances inflow (TRI) coming from the rest of the world, its total remittances outflow (TRO) extracted from that country and sent to all other countries, its total emigrant stock (TEMI) living overseas, and its total number of foreign-world immigrants (TIMM) living in that country. For each of these quantities, its highest-ranked countries follow an approximate Pareto power law distribution. Remittances and migrants flow in opposite directions, the statistical correlation $R^2$ between TRI and TEMI is 0.79, and between TRO and TIMM is 0.97. Both inflowing remittances per emigrant TRI/TEMI and outflowing remittances per immigrant TRO/TIMM fluctuate approximately around 3100 USD per year.

Public opinion quickly generated and propagated on online social networks brings huge influences on society and state security. Previous studies mostly analyze its snapshot in a short-term time interval to predict and control the explosive size, but neglect its long-term evolutionary process. In this paper, based on the online social network of Sina Weibo, we trace nine public opinion events in the nearly two-year duration to comprehensively observe the long-term evolutionary processes and characterize the temporal dynamics and propagating networks. The long-term evolutionary processes of public opinion are constructed by quantitatively measuring forwarding sizes at a daily scale. We show their non-Markov temporal dynamics by autocorrelation analysis, which is verified by the heavy-tail interval time distribution of individual forwarding behaviors. Also, the temporally propagating networks are abstracted from individual forwarding behaviors to represent the microcosmic organization of forming public opinion. The topological analysis of aggregating propagating networks shows that the microcosmic organization is generally constructed by a giant connected component and amounts of small connected components with strongly heterogeneous cascade sizes, and the corresponding degree distributions obeys a power law which is shaped by the giant connected component. Furthermore, we compare the follower–followee (i.e. friendship) network with the propagating network to unveil their potential correlation, and find that at large scale they behave a similar connection pattern. This work first projects public opinion into a process-based model to study its temporal dynamics and helps us to better understand the underlying mechanics of forming public opinion.

From the official report of narco-war-related casualties in Mexico from December 2006 to September 2011, we show that the inter-event time distribution (calculated for a range of minimum sizes) approximately obeys simple scaling laws similar to violent conflicts in Iraq (2003–2005), Afghanistan (2008–2010) and Northern Ireland (1969–2001). Furthermore, normalizing deaths by population municipalities (the smallest Mexican political entities) yields even better fitting results.

Samples with the nominal composition Bi₂Sr₂GdCu₂O_y in Bi-2212 where Gd replaces Ca as well as samples without Gd were prepared by solid-state reaction method. From the room temperature X-ray diffraction data, the samples were found to be similar to the single phase Bi-2212 structure. Impedance studies were performed from room temperature to 423 K at different frequencies in the range of 10 to 700 KHz. The AC conductivity increases with temperature and frequency, exhibiting frequency dispersion at low temperature region. The activation energy from AC conductivity in the high temperature region is found to be 0.432 eV. The permitivity increases with the increase in temperature and at 373 K it shows a maximum value exhibiting a dielectric loss. Complex impedance spectra are analyzed in terms of bulk relaxation and interfacial effects. The activation energy of the dipoles involved in the relaxation was estimated to be 0.482 eV. The universal power law of Jonscher is verified in the present system.

We introduce preferential behavior into the study on statistical mechanics of money circulation. The computer simulation results show that the preferential behavior can lead to power laws on distributions over both holding time and amount of money held by agents. However, some constraints are needed in generation mechanism to ensure the robustness of power-law distributions.

A unidirectional coupling method to successfully suppress spiral waves in excitable media is proposed. It is shown that this control method has high control efficiency and is robust. It adapts to control of spiral waves for catalytic CO oxidation on platinum as well as for the FHN model. The power law n ~ c^-k of control time steps n versus the coupling strength c for different models has been obtained.

It has been empirically known that the disordered system exhibits a power-law behavior. We show from calculation the power law t^-1-α for the pausing-time distribution of thermal diffusion of hydrogen in the exponential density of states. This power law of the pausing-time distribution is examined by the Monte Carlo simulation. The results agree with those obtained by analytical calculation. We discuss the power law in terms of random walk in fractal structure (Cantor ensemble).

The pausing-time distribution of thermal diffusion of hydrogen is analytically shown in the Gaussian density of state. The pausing-time distribution exhibits a log-normal distribution. It has been shown that the pausing-time distribution follows approximately power law, i.e., t^-1-α(t: pausing time). The diffusion coefficient of hydrogen is also obtained to be approximately τ^α-1 (τ: diffusion time). The value of α is the ratio of hydrogen temperature T_r to T_2σ, in which T_2σ, is a temperature corresponding to 2σ (σ: standard deviation). Finally, Brownian motion is shown to correspond to the case of σ = 0. The width of the energy distribution play an important role in hydrogen diffusion.

The diffusion coefficient of hydrogen is obtained for exponential energy distribution in hydrogenated amorphous silicon (a-Si:H). It is shown that the diffusion coefficient follows the form of τ^α-1 (τ: diffusion time) in the case of α < 1 and a larger τ, in which α is the ratio of hydrogen temperature to width for energy distribution function. In the case of α ≥ 1, as α reaches infinity at the limit, the hydrogen diffusion approaches Brownian motion.

A distinctive fishtail feature in multifractal spectra derived from heart rate variability (HRV) data closely resembles similar features in plots of the Gibbs free energy versus reduced pressure for a van der Waals fluid below the critical temperature, and, in analogy to the nonideal fluid, signals a phase transition from one multifractal state to another. This fishtail feature, often overlooked or dismissed in previous studies, is observed most prevalently in unhealthy patients and suggests a realignment between multifractal variables and their thermodynamic analogs. The van der Waals analogy and subsequent alternate interpretation of multifractal variables and functions lead one to construct a three-dimensional heart health phase diagram reminiscent of a $P-V-T$ diagram for the van der Waals fluid. The diagram which makes use of the Maxwell width as a measure of heart health produces an orderly progression from healthy to unhealthy.

This paper studies a random differential equation with random switch perturbations. We explore how the maximum displacement from the equilibrium state depends on the statistical properties of time series of the random switches. We show a power law dependence between the upper bound of displacement and the frequency of random perturbation switches, and the slope of power law dependence is dependent on the specific distribution of the intervals between switching times. This result suggests a quantitative connection between frequency modulation and amplitude modulation under random perturbations.