On q-Gaussians and Exchangeability

The q-Gaussians are discussed from the point of view of variance mixtures of normals and exchangeability. For each q< 3, there is a q-Gaussian distribution that maximizes the Tsallis entropy under suitable constraints. This paper shows that q-Gaussian random variables can be represented as variance mixtures of normals. These variance mixtures of normals are the attractors in central limit theorems for sequences of exchangeable random variables; thereby, providing a possible model that has been extensively studied in probability theory. The formulation provided has the additional advantage of yielding process versions which are naturally q-Brownian motions. Explicit mixing distributions for q-Gaussians should facilitate applications to areas such as option pricing. The model might provide insight into the study of superstatistics.Comment: 14 page

Transcriptomic assessment of resistance to effects of an aryl hydrocarbon receptor (AHR) agonist in embryos of Atlantic killifish (Fundulus heteroclitus) from a marine Superfund site

© The Author(s), 2011. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in BMC Genomics 12 (2011): 263, doi:10.1186/1471-2164-12-263.Populations of Atlantic killifish (Fundulus heteroclitus) have evolved resistance to the embryotoxic effects of polychlorinated biphenyls (PCBs) and other halogenated and nonhalogenated aromatic hydrocarbons that act through an aryl hydrocarbon receptor (AHR)-dependent signaling pathway. The resistance is accompanied by reduced sensitivity to induction of cytochrome P450 1A (CYP1A), a widely used biomarker of aromatic hydrocarbon exposure and effect, but whether the reduced sensitivity is specific to CYP1A or reflects a genome-wide reduction in responsiveness to all AHR-mediated changes in gene expression is unknown. We compared gene expression profiles and the response to 3,3',4,4',5-pentachlorobiphenyl (PCB-126) exposure in embryos (5 and 10 dpf) and larvae (15 dpf) from F. heteroclitus populations inhabiting the New Bedford Harbor, Massachusetts (NBH) Superfund site (PCB-resistant) and a reference site, Scorton Creek, Massachusetts (SC; PCB-sensitive). Analysis using a 7,000-gene cDNA array revealed striking differences in responsiveness to PCB-126 between the populations; the differences occur at all three stages examined. There was a sizeable set of PCB-responsive genes in the sensitive SC population, a much smaller set of PCB-responsive genes in NBH fish, and few similarities in PCB-responsive genes between the two populations. Most of the array results were confirmed, and additional PCB-regulated genes identified, by RNA-Seq (deep pyrosequencing). The results suggest that NBH fish possess a gene regulatory defect that is not specific to one target gene such as CYP1A but rather lies in a regulatory pathway that controls the transcriptional response of multiple genes to PCB exposure. The results are consistent with genome-wide disruption of AHR-dependent signaling in NBH fish.This work was supported in part by National Institutes of Health grants P42ES007381 (Superfund Basic Research Program at Boston University) and by a grant from the WHOI Ocean Life Institute

\u3ci\u3eFundulus\u3c/i\u3e as the premier teleost model in environmental biology: Opportunities for new insights using genomics

A strong foundation of basic and applied research documents that the estuarine fish Fundulus heteroclitus and related species are unique laboratory and field models for understanding how individuals and populations interact with their environment. In this paper we summarize an extensive body of work examining the adaptive responses of Fundulus species to environmental conditions, and describe how this research has contributed importantly to our understanding of physiology, gene regulation, toxicology, and ecological and evolutionary genetics of teleosts and other vertebrates. These explorations have reached a critical juncture at which advancement is hindered by the lack of genomic resources for these species. We suggest that a more complete genomics toolbox for F. heteroclitus and related species will permit researchers to exploit the power of this model organism to rapidly advance our understanding of fundamental biological and pathological mechanisms among vertebrates, as well as ecological strategies and evolutionary processes common to all living organisms

Fundulus as the premier teleost model in environmental biology : opportunities for new insights using genomics

Author Posting. © Elsevier B.V., 2007. This is the author's version of the work. It is posted here by permission of Elsevier B.V. for personal use, not for redistribution. The definitive version was published in Comparative Biochemistry and Physiology Part D: Genomics and Proteomics 2 (2007): 257-286, doi:10.1016/j.cbd.2007.09.001.A strong foundation of basic and applied research documents that the estuarine fish Fundulus heteroclitus and related species are unique laboratory and field models for understanding how individuals and populations interact with their environment. In this paper we summarize an extensive body of work examining the adaptive responses of Fundulus species to environmental conditions, and describe how this research has contributed importantly to our understanding of physiology, gene regulation, toxicology, and ecological and evolutionary genetics of teleosts and other vertebrates. These explorations have reached a critical juncture at which advancement is hindered by the lack of genomic resources for these species. We suggest that a more complete genomics toolbox for F. heteroclitus and related species will permit researchers to exploit the power of this model organism to rapidly advance our understanding of fundamental biological and pathological mechanisms among vertebrates, as well as ecological strategies and evolutionary processes common to all living organisms.This material is based on work supported by grants from the National Science Foundation DBI-0420504 (LJB), OCE 0308777 (DLC, RNW, BBR), BES-0553523 (AW), IBN 0236494 (BBR), IOB-0519579 (DHE), IOB-0543860 (DWT), FSML-0533189 (SC); National Institute of Health NIEHS P42-ES007381(GVC, MEH), P42-ES10356 (RTD), ES011588 (MFO); and NCRR P20 RR-016463 (DWT); Natural Sciences and Engineering Research Council of Canada Discovery (DLM, TDS, WSM) and Collaborative Research and Development Programs (DLM); NOAA/National Sea Grant NA86RG0052 (LJB), NA16RG2273 (SIK, MEH,GVC, JJS); Environmental Protection Agency U91620701 (WSB), R82902201(SC) and EPA’s Office of Research and Development (DEN)

Empirical central limit theorems for exchangeable random variables

This paper provides an empirical central limit theorem (CLT) for exchangeable random variables when the norming constants in the regular CLT are with h(n) a slowly varying function. The situation with norming constants of the form nh(n) is also discussed.Empirical central limit theorem Exchangeable random variable

Limit theorems for the logarithm of sample spacings

Many statistical problems can be reformulated in terms of tests of uniformity. Some strong laws of large numbers and a central limit theorem for the logarithm of transformed spacings are obtained. These theorems provide a characterization of the uniform distribution. A general information-type inequality is deduced which gives a quantitative measurement (using the Kullback-Leibler number) of the discrepancy between an arbitrary distribution and the uniform distribution.Sample spacings Strong laws of large numbers Central limit theorems Information-type inequalities Entropy

Existence and strong consistency of maximum likelihood estimates for 1-dimensional exponential families

The paper focuses on existence, in the sense of Hoffmann-Jørgensen, of the maximum likelihood estimate (MLE) of the parameter for 1-dimensional exponential families. It is established that the MLE exists in most cases.Maximum likelihood Strong consistency Exponential families Steep exponential families