Geometric Stable Laws Through Series Representations

Let (Xi ) be a sequence of i.i.d. random variables, and let N be a geometric random variable independent of (Xi ). Geometric stable distributions are weak limits of (normalized) geometric compounds, SN = X1 + · · · + XN , when the mean of N converges to infinity. By an appropriate representation of the individual summands in SN we obtain series representation of the limiting geometric stable distribution. In addition, we study the asymptotic behavior of the partial sum process SN (t) = ⅀( i=1 ... [N t] ) Xi , and derive series representations of the limiting geometric stable process and the corresponding stochastic integral. We also obtain strong invariance principles for stable and geometric stable laws

Certain bivariate distributions and random processes connected with maxima and minima

It is well-known that [S(x)]^n and [F(x)]^n are the survival function and the distribution function of the minimum and the maximum of n independent, identically distributed random variables, where S and F are their common survival and distribution functions, respectively. These two extreme order statistics play important role in countless applications, and are the central and well-studied objects of extreme value theory. In this work we provide stochastic representations for the quantities [S(x)]^alpha and [F(x)]^beta, where alpha> 0 is no longer an integer, and construct a bivariate model with these margins. Our constructions and representations involve maxima and minima with a random number of terms. We also discuss generalizations to random process and further extensions

A novel weighted likelihood estimation with empirical Bayes flavor

We propose a novel approach to estimation, where each individual observation in a random sample is used to derive an estimator of an unknown parameter using the maximum likelihood principle. These individual estimators are then combined as a weighted average to produce the final estimator. The weights are chosen to be proportional to the likelihood function evaluated at the estimators based on each observation. The method can be related to a Bayesian approach, where the prior distribution is data driven. In case of estimating a location parameter of a unimodal density, the prior distribution is the empirical distribution of the sample, and converges to the true distribution that generated the data as the sample size increases. We provide several examples illustrating the new method, argue for its consistency, and conduct simulation studies to assess the performance of the estimators. It turns out that this straightforward methodology produces consistent estimators, which seem to be comparable with those obtained by the maximum likelihood method

Money as a fictitious commodity – liberal utopia according to Karl Polanyi

This article concerns Karl Polanyi’s theory of money as a fictitious commodity and its importance for understanding liberal ideology. According to the Hungarian economist, money is not a commodity but a social relation between the debtor and the creditor. Therefore, the complete commodification of money is part of a liberal utopia, as it is associated with a counter-movement and an economic crisis, two processes that make impossible the constitution of a market society. The author analyzes the problem of counter-movement through the prism of Karl Mannheim’s theory of utopia and ideology. The final part of the article deals with the problem of economic crises, Polanyi’s views on the nature of economic breakdown are compared with contemporary reflection on the role of money in financial markets

Advances in Plant-Derived Scaffold Proteins

Scaffold proteins form critical biomatrices that support cell adhesion and proliferation for regenerative medicine and drug screening. The increasing demand for such applications urges solutions for cost effective and sustainable supplies of hypoallergenic and biocompatible scaffold proteins. Here, we summarize recent efforts in obtaining plant-derived biosynthetic spider silk analogue and the extracellular matrix protein, collagen. Both proteins are composed of a large number of tandem block repeats, which makes production in bacterial hosts challenging. Furthermore, post-translational modification of collagen is essential for its function which requires co-transformation of multiple copies of human prolyl 4-hydroxylase. We discuss our perspectives on how the GAANTRY system could potentially assist the production of native-sized spider dragline silk proteins and prolyl hydroxylated collagen. The potential of recombinant scaffold proteins in drug delivery and drug discovery is also addressed

Generalized Mittag-Leffler Distributions and Processes for Applications in Astrophysics and Time Series Modeling

Geometric generalized Mittag-Leffler distributions having the Laplace transform $\frac{1}{1+\beta\log(1+t^\alpha)},00$ is introduced and its properties are discussed. Autoregressive processes with Mittag-Leffler and geometric generalized Mittag-Leffler marginal distributions are developed. Haubold and Mathai (2000) derived a closed form representation of the fractional kinetic equation and thermonuclear function in terms of Mittag-Leffler function. Saxena et al (2002, 2004a,b) extended the result and derived the solutions of a number of fractional kinetic equations in terms of generalized Mittag-Leffler functions. These results are useful in explaining various fundamental laws of physics. Here we develop first-order autoregressive time series models and the properties are explored. The results have applications in various areas like astrophysics, space sciences, meteorology, financial modeling and reliability modeling.Comment: 12 pages, LaTe

Probability of ruin in discrete insurance risk model with dependent Pareto claims

Abstract We present basic properties and discuss potential insurance applications of a new class of probability distributions on positive integers with power law tails. The distributions in this class are zero-inflated discrete counterparts of the Pareto distribution. In particular, we obtain the probability of ruin in the compound binomial risk model where the claims are zero-inflated discrete Pareto distributed and correlated by mixture.</jats:p

Ordered kinetochore assembly in the human-pathogenic basidiomycetous yeast Cryptococcus neoformans

Kinetochores facilitate interaction between chromosomes and the spindle apparatus. The formation of a metazoan trilayered kinetochore is an ordered event in which inner, middle, and outer layers assemble during disassembly of the nuclear envelope during mitosis. The existence of a similar strong correlation between kinetochore assembly and nuclear envelope breakdown in unicellular eukaryotes is unclear. Studies in the hemiascomycetous budding yeasts Saccharomyces cerevisiae and Candida albicans suggest that an ordered kinetochore assembly may not be evolutionarily conserved. Here, we utilized high-resolution time-lapse microscopy to analyze the localization patterns of a series of putative kinetochore proteins in the basidiomycetous budding yeast Cryptococcus neoformans, a human pathogen. Strikingly, similar to most metazoa but atypical of yeasts, the centromeres are not clustered but positioned adjacent to the nuclear envelope in premitotic C. neoformans cells. The centromeres gradually coalesce to a single cluster as cells progress toward mitosis. The mitotic clustering of centromeres seems to be dependent on the integrity of the mitotic spindle. To study the dynamics of the nuclear envelope, we followed the localization of two marker proteins, Ndc1 and Nup107. Fluorescence microscopy of the nuclear envelope and components of the kinetochore, along with ultrastructure analysis by transmission electron microscopy, reveal that in C. neoformans, the kinetochore assembles in an ordered manner prior to mitosis in concert with a partial opening of the nuclear envelope. Taken together, the results of this study demonstrate that kinetochore dynamics in C. neoformans is reminiscent of that of metazoans and shed new light on the evolution of mitosis in eukaryotes

Monte Carlo simulation of uncoupled continuous-time random walks yielding a stochastic solution of the space-time fractional diffusion equation

We present a numerical method for the Monte Carlo simulation of uncoupled continuous-time random walks with a Levy alpha-stable distribution of jumps in space and a Mittag-Leffler distribution of waiting times, and apply it to the stochastic solution of the Cauchy problem for a partial differential equation with fractional derivatives both in space and in time. The one-parameter Mittag-Leffler function is the natural survival probability leading to time-fractional diffusion equations. Transformation methods for Mittag-Leffler random variables were found later than the well-known transformation method by Chambers, Mallows, and Stuck for Levy alpha-stable random variables and so far have not received as much attention; nor have they been used together with the latter in spite of their mathematical relationship due to the geometric stability of the Mittag-Leffler distribution. Combining the two methods, we obtain an accurate approximation of space- and time-fractional diffusion processes almost as easy and fast to compute as for standard diffusion processes.Comment: 7 pages, 5 figures, 1 table. Presented at the Conference on Computing in Economics and Finance in Montreal, 14-16 June 2007; at the conference "Modelling anomalous diffusion and relaxation" in Jerusalem, 23-28 March 2008; et