The results of R dynamical random surface model (2-dimensional quantum gravity with a R term) are applied to explain the personal income distribution. A scale invariance exists if there is not the R term in the action. The R term provides a typical scale and breaks the scale invariance explicitly in the low and middle income range. A new distribution, Weibull distribution, is deduced from the a...

Phase separation and coarsening is a phenomenon commonly seen in binary physical and chemical systems that occur in nature. Often, thermal fluctuations, modelled as stochastic noise, are present in the system and the phase segregation process occurs on a surface. In this work, the segregation process is modelled via the Cahn-Hilliard-Cook model, which is a fourth-order parabolic stochastic syst...

We describe and analyze a new algorithm for agnostically learning half-spaces with respect to the margin error rate. Roughly speaking, this corre-sponds to the worst-case error rate after each point is perturbed by a noisevector of length at most μ. Margin based analysis is widely used in learningtheory and is considered the most successful theoretical explanation for thesta...

In describing the first-order properties of laser speckle under polarized illumination conditions, it is almost an article of faith that the contrast is unity. In many processing schemes, however, the contrast defined as the quotient of the standard deviation and the mean is calculated over a localized spatial region. In such cases, this local contrast displays a distribution of values that can...

We prove fourteen equivalent conditions for a set of time-frequency shifts on a lattice Λ, {e2g(t − λ1) : (λ1, λ2) ∈ Λ} ⊆ L (R), to be a frame for L(R). Remarkably, several of these conditions can be formulated without an inequality. In particular, instead of checking the invertibility of the frame operator on L(R), it suffices to verify that it is one-to-one on a certain subspace of tempered d...

[This corrects the article DOI: 10.1186/s40064-016-2868-z.].

We analyze a sample of bright long bursts and find that the pulses duration have a lognormal distribution while the intervals between pulses have an excess of long intervals (relative to lognormal distribution). This excess can be explained by the existence of quiescent times, long periods with no signal above the background. The lognormal distribution of the intervals (excluding the quiescent ...

Pearson differential equation‎. ‎This distribution is also obtained from a compounding mixture of‎ ‎distributions‎. ‎Moments‎, ‎inequality measures‎, ‎uncertainty measures and reliability measures are theoretically established‎. ‎Characterizations of MLBXII distribution are also studied via different techniques‎. ‎Parameters of MLBXII dist...

Tthe Zografos–Balakrishnan-log-logistic (ZBLL) distribution is a new distribution of three parameters that has been introduced by Ramos et el. [1], and They presented some properties of the new distribution such as its probability density function, The cumulative distribution function, The  moment generating function, its hazard (failure) rate function, quantiles and moments, Rényi and Shannon ...

Though commonly used, the unigram is widely known as being a poor model of term frequency; it assumes that term occurrences are independent, whereas many words, especially topic-oriented ones, tend to occur in bursts. Herein, we propose a model of term frequency that treats words independently, but allows for much higher variance in frequency values than does the unigram. Although it has valuab...