International trade distributions and their relation with random fragmentation processes

A study of the distribution of the value of traded goods under the Harmonized System is presented. The ramifications of this classification system are found to exhibit an approximate power law decay, indicating complexity and self-organization in the nomenclature of traded merchandises. For almost all countries with available data, log-values of annually imported and exported goods are well described by three-parameter Weibull distributions. This distribution commonly appears in particles size distributions, suggesting a connection between random fragmentation processes and the mechanisms behind the international trade of merchandises. Analysis of the resulting values for the fitting parameters from 1995 to 2018 shows a nearly constant linear relationship between the parameters of the Weibull distributions, so that, for each country, the distribution of log-values can be approximately characterized by a single shape parameter [Formula: see text]. The empirical findings of this paper suggest that specialization on trading a constant set of goods prevents the values of all traded merchandises from growing/decreasing simultaneously.

Experimental Study on the Relationship Between Capillary Pressure and Resistivity Index in Tight Sandstone Rocks

To further understand the relationship between the capillary pressure and resistivity index of tight reservoir sandstones, we measured these parameters using the semiporous plate method in four tight clayey sandstones from the Junggar Basin, China. To provide a benchmark for analyzing our results, we applied the same experimental procedures to four clay-free, tight Fontainebleau sandstones from the Paris Basin, France. We observed approximate power law relationships between the resistivity index and water saturation for Fontainebleau sandstones and Junggar Basin sandstones, in agreement with the Archie’s equation and Waxman-Smits equation, respectively. The capillary pressure and resistivity index data were differently related in the two types of sandstones. We observed a power law correlation for the Fontainebleau sandstones, whereas the Junggar sandstones showed a linear relationship. These differences in behavior appear to be primarily linked to the presence of clays in the Junggar sandstones but not in the Fontainebleau sandstone, and the difference in pore structure between the two types of sandstones.

Die hard holographic phenomenology of cuprates

We discuss the attempts of fitting a number of the approximate power-law dependences observed in the cuprates into one consistent holographic or holographically inspired hydrodynamic framework. Contrary to the expectations, the goal of reproducing as many as possible of the established behaviours of the thermodynamic and transport coefficients appears to be achievable within the picture of a non-degenerate fermion fluid with quadratic dispersion. While not immediately elucidating the essential physics of the cuprates, this observation suggests a possible reason for which the previous attempts towards that goal have so far remained inconclusive.

Market instability and the size-variance relationship

We show that some key features of the behavior of mutual funds is accounted for by a stochastic model of proportional growth. We find that the negative dependence of the variance of funds’ growth rates on size is well described by an approximate power law. We discover that during periods of crisis the volatility of the largest funds’ growth rates increases with respect to mid-sized funds. Our result reveals that a lower and flatter slope provides relevant information on the structure of the system. We find that growth rates volatility poorly depends on the size of the funds, thus questioning the benefits of diversification achieved by larger funds. Our findings show that the slope of the size-variance relationship can be used as a synthetic indicator to monitor the intensity of instabilities and systemic risk in financial markets.

Numerical Analysis for the Fractional Ambartsumian Equation via the Homotopy Herturbation Method

The fractional calculus is useful in describing the natural phenomena with memory effect. This paper addresses the fractional form of Ambartsumian equation with a delay parameter. It may be a challenge to obtain accurate approximate solution of such kinds of fractional delay equations. In the literature, several attempts have been conducted to analyze the fractional Ambartsumian equation. However, the previous approaches in the literature led to approximate power series solutions which converge in subdomains. Such difficulties are solved in this paper via the Homotopy Perturbation Method (HPM). The present approximations are expressed in terms of the Mittag-Leffler functions which converge in the whole domain of the studied model. The convergence issue is also addressed. Several comparisons with the previous published results are discussed. In particular, while the computed solution in the literature is physical in short domains, with our approach it is physical in the whole domain. The results reveal that the HPM is an effective tool to analyzing the fractional Ambartsumian equation.

The spectrum of covariance matrices of randomly connected recurrent neuronal networks

A key question in theoretical neuroscience is the relation between connectivity structure and collective dynamics of a network of neurons. Here we study the connectivity-dynamics relation as reflected in the distribution of eigenvalues of the covariance matrix of the dynamic fluctuations of the neuronal activities, which is closely related to the network’s Principal Component Analysis (PCA) and the associated effective dimensionality. We consider the spontaneous fluctuations around a steady state in randomly connected recurrent network of spiking neurons. We derive an exact analytical expression for the covariance eigenvalue distribution in the large network limit. We show analytically that the distribution has a finitely supported smooth bulk spectrum, and exhibits an approximate power law tail for coupling matrices near the critical edge. Effects of adding connectivity motifs and extensions to EI networks are also discussed. Our results suggest that the covariance spectrum is a robust feature of population dynamics in recurrent neural circuits and provide a theoretical predictions for this spectrum in simple connectivity models that can be compared with experimental data.

A new radio catalogue for M83: supernova remnants and H ii regions

ABSTRACT We present a new catalogue of radio sources in the face-on spiral galaxy M83. Radio observations taken in 2011, 2015, and 2017 with the Australia Telescope Compact Array at 5.5 and 9 GHz have detected 270 radio sources. Although a small number of these sources are background extragalactic sources, most are either H ii regions or supernova remnants (SNRs) within M83 itself. Three of the six historical supernovae are detected, as is the very young remnant that had been identified in a recent study, which is likely the result of a supernova that exploded in the last ∼100 yr but was missed. All of these objects are generally fading with time. Confusion limits our ability to measure the radio emission from a number of the SNRs in M83, but 64 were detected in unconfused regions, and these have the approximate power-law luminosity function that has been observed in other galaxies. The SNRs in M83 are systematically smaller in diameter and brighter than those that have been detected at radio wavelengths in M33. A number of the radio sources are coincident with X-ray sources in M83; most of these coincident sources turn out to be SNRs. Our dual frequency observations are among the most sensitive to date for a spiral galaxy outside the Local Group; despite this we were not able to place realistic constraints on the spectral indices, and as a result, it was not possible to search for SNRs based on their radio properties alone.