Continuously heated granular gas of elongated particles

Some years ago, Harth et al. experimentally explored the steady state dynamics of a heated granular gas of rod-like particles in microgravity [K. Harth et al. Phys. Rev. Lett. 110, 144102 (2013)]. Here, we report numerical results that quantitatively reproduce their experimental findings and provide additional insight into the process. A system of sphero-cylinders is heated by the vibration of three flat side walls, resulting in one symmetrically heated direction, one non-symmetrically heated direction, and one non-heated direction. In the non-heated direction, the speed distribution follows a stretched exponential distribution $$p(\upsilon )\, \propto \,{\rm{exp}}\left( { - {{\left( {{{\left| \upsilon \right|} \mathord{\left/ {\vphantom {{\left| \upsilon \right|} C}} \right. \kern-\nulldelimiterspace} C}} \right)}^{1.5}}} \right)$$. In the symmetrically heated direction, the velocity statistics at low speeds is similar but it develops pronounced exponential tails at high speeds. In the non-symmetrically heated direction (not accessed experimentally), the distribution also follows $$p(\upsilon )\, \propto \,{\rm{exp}}\left( { - {{\left( {{{\left| \upsilon \right|} \mathord{\left/ {\vphantom {{\left| \upsilon \right|} C}} \right. \kern-\nulldelimiterspace} C}} \right)}^{1.5}}} \right)$$ , but the velocity statistics of rods moving toward the vibrating wall resembles the indirectly excited direction, whereas the velocity statistics of those moving away from the wall resembles the direct excited direction.

Epigenetic adaptation prolongs photoreceptor survival during retinal degeneration

Neural degenerative diseases often display a progressive loss of cells as a stretched exponential distribution. The mechanisms underlying the survival of a subset of genetically identical cells in a population beyond what is expected by chance alone remains unknown. To gain mechanistic insights underlying prolonged cellular survival, we used Spata7 mutant mice as a model and performed single-cell transcriptomic profiling of retinal tissue along the time course of photoreceptor degeneration. Intriguingly, rod cells that survive beyond the initial rapid cell apoptosis phase progressively acquire a distinct transcriptome profile. In these rod cells, expression of photoreceptor-specific phototransduction pathway genes is downregulated while expression of other retinal cell type-specific marker genes is upregulated. These transcriptomic changes are achieved by modulation of the epigenome and changes of the chromatin state at these loci, as indicated by immunofluorescence staining and single-cell ATAC-seq. Consistent with this model, when induction of the repressive epigenetic state is blocked by in vivo histone deacetylase inhibition, all photoreceptors in the mutant retina undergo rapid degeneration, strongly curtailing the stretched exponential distribution. Our study reveals an intrinsic mechanism by which neural cells progressively adapt to genetic stress to achieve prolonged survival through epigenomic regulation and chromatin state modulation.

An Investigation of Stretched Exponential Function in Quantifying Long-Term Memory of Extreme Events Based on Artificial Data following Lévy Stable Distribution

Extreme events, which are usually characterized by generalized extreme value (GEV) models, can exhibit long-term memory, whose impact needs to be quantified. It was known that extreme recurrence intervals can better characterize the significant influence of long-term memory than using the GEV model. Our statistical analyses based on time series datasets following the Lévy stable distribution confirm that the stretched exponential distribution can describe a wide spectrum of memory behavior transition from exponentially distributed intervals (without memory) to power-law distributed ones (with strong memory or fractal scaling property), extending the previous evaluation of the stretched exponential function using Gaussian/exponential distributed random data. Further deviation and discussion of a historical paradox (i.e., the residual waiting time tends to increase with an increasing elapsed time under long-term memory) are also provided, based on the theoretical analysis of the Bayesian law and the stretched exponential distribution.

Random Networks with Preferential Growth and Vertex Death

A dynamic model for a random network evolving in continuous time is defined, where new vertices are born and existing vertices may die. The fitness of a vertex is defined as the accumulated in-degree of the vertex and a new vertex is connected to an existing vertex with probability proportional to a function b of the fitness of the existing vertex. Furthermore, a vertex dies at a rate given by a function d of its fitness. Using results from the theory of general branching processes, an expression for the asymptotic empirical fitness distribution {pk} is derived and analyzed for a number of specific choices of b and d. When b(i) = i + α and d(i) = β, that is, linear preferential attachment for the newborn and random deaths, then pk ∼ k-(2+α). When b(i) = i + 1 and d(i) = β(i + 1), with β < 1, then pk ∼ (1 + β)−k, that is, if the death rate is also proportional to the fitness, then the power-law distribution is lost. Furthermore, when b(i) = i + 1 and d(i) = β(i + 1)γ, with β, γ < 1, then logpk ∼ -kγ, a stretched exponential distribution. The momentaneous in-degrees are also studied and simulations suggest that their behaviour is qualitatively similar to that of the fitnesses.

Random Networks with Preferential Growth and Vertex Death

A dynamic model for a random network evolving in continuous time is defined, where new vertices are born and existing vertices may die. The fitness of a vertex is defined as the accumulated in-degree of the vertex and a new vertex is connected to an existing vertex with probability proportional to a functionbof the fitness of the existing vertex. Furthermore, a vertex dies at a rate given by a functiondof its fitness. Using results from the theory of general branching processes, an expression for the asymptotic empirical fitness distribution {pk} is derived and analyzed for a number of specific choices ofbandd. Whenb(i) =i+ α andd(i) = β, that is, linear preferential attachment for the newborn and random deaths, thenpk∼k-(2+α). Whenb(i) =i+ 1 andd(i) = β(i+ 1), with β &lt; 1, thenpk∼ (1 + β)−k, that is, if the death rate is also proportional to the fitness, then the power-law distribution is lost. Furthermore, whenb(i) =i+ 1 andd(i) = β(i+ 1)γ, with β, γ &lt; 1, then logpk∼ -kγ, a stretched exponential distribution. The momentaneous in-degrees are also studied and simulations suggest that their behaviour is qualitatively similar to that of the fitnesses.

MAXIMIZABLE INFORMATIONAL ENTROPY AS A MEASURE OF PROBABILISTIC UNCERTAINTY

In this work, we consider a recently proposed entropy S defined by a variational relationship [Formula: see text] as a measure of uncertainty of random variable x. The entropy defined in this way underlies an extension of virtual work principle [Formula: see text] leading to the maximum entropy [Formula: see text]. This paper presents an analytical investigation of this maximizable entropy for several distributions such as the stretched exponential distribution, κ-exponential distribution, and Cauchy distribution.

COMPARISON OF DIFFERENT DAILY STREAMFLOW SERIES IN US AND CHINA, UNDER A VIEWPOINT OF COMPLEX NETWORKS

The daily streamflow series of three rivers are analyzed from the view of complex networks, i.e. the Yangtze River in China, the Umpqua River and the Ocmulgee River in the United States. We construct networks from these series by using the visibility graph algorithm respectively. The degree distribution and accumulative degree distribution are investigated. We find that the degree distribution of the Umpqua River series network, the Ocumlgee River series network and the subsequence of the Yangtze River series network can be better fitted by stretched exponential distribution (SED), although the degree distribution curves of these networks in a log–log plot have a linear part. Moreover, the slope α of the linear part and parameters μ in SED have significant meaning in the research of streamflow series properties.

MULTISCALE STATISTICAL MODEL OF FULLY-DEVELOPED TURBULENCE PARTICLE ACCELERATIONS

Based on the experimental measurement results of fluid particle transverse accelerations in fully developed pipe turbulence published in Nature (2001) by La Porta et al, the present authors recently develop a multiscale statistical model which considers both normal diffusion in molecular scale and anomalous diffusion in vortex scale. This model gives rise to a new probability density function, called Power-Stretched Gaussian Distribution model (PSGD). In this study, we make a further comparison of this statistical distribution model with the well-known Lévy distribution, Tsallis distribution and stretched-exponential distribution. Our model is found to have the following merits: 1) fewer parameters, 2) better fitting with experimental data, 3) more explicit physical interpretation.