Order Statistics and Benford's Law

Fix a base B and let zeta have the standard exponential distribution; the distribution of digits of zeta base B is known to be very close to Benford's Law. If there exists a C such that the distribution of digits of C times the elements of some set is the same as that of zeta, we say that set exhibits shifted exponential behavior base B (with a shift of log_B C \bmod 1). Let X_1, >..., X_N be independent identically distributed random variables. If the X_i's are drawn from the uniform distribution on [0,L], then as N\to\infty the distribution of the digits of the differences between adjacent order statistics converges to shifted exponential behavior (with a shift of \log_B L/N \bmod 1). By differentiating the cumulative distribution function of the logarithms modulo 1, applying Poisson Summation and then integrating the resulting expression, we derive rapidly converging explicit formulas measuring the deviations from Benford's Law. Fix a delta in (0,1) and choose N independent random variables from any compactly supported distribution with uniformly bounded first and second derivatives and a second order Taylor series expansion at each point. The distribution of digits of any N^\delta consecutive differences \emph{and} all N-1 normalized differences of the order statistics exhibit shifted exponential behavior. We derive conditions on the probability density which determine whether or not the distribution of the digits of all the un-normalized differences converges to Benford's Law, shifted exponential behavior, or oscillates between the two, and show that the Pareto distribution leads to oscillating behavior.Comment: 14 pages, 2 figures, version 4: Version 3: most of the numerical simulations on shifted exponential behavior have been suppressed (though are available from the authors upon request). Version 4: a referee pointed out that we need epsilon > 1/3 - delta/2 in the proof of Theorem 1.5; this has now been adde

RAS Mutations and Oncogenesis: Not all RAS Mutations are Created Equally

Mutation in RAS proteins is one of the most common genetic alterations observed in human and experimentally induced rodent cancers. In vivo, oncogenic mutations have been shown to occur at exons 12, 13, and 61, resulting in any 1 of 19 possible point mutations in a given tumor for a specific RAS isoform. While some studies have suggested a possible role of different mutant alleles in determining tumor severity and phenotype, no general consensus has emerged on the oncogenicity of different mutant alleles in tumor formation and progression. Part of this may be due to a lack of a single, signature pathway that shows significant alterations between different mutations. Rather, it is likely that subtle differences in the activation, or lack thereof, of downstream effectors by different RAS mutant alleles may determine the eventual outcome in terms of tumor phenotype. This paper reviews our current understanding of the potential role of different RAS mutations on tumorigenesis, highlights studies in model cell culture and in vivo systems, and discusses the potential of expression array and computational network modeling to dissect out differences in activated RAS genes in conferring a transforming phenotype

The future of work now: The multi-faceted mall security guard at a multi-faceted Jewel

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Modelling loanword success – a sociolinguistic quantitative study of Māori loanwords in New Zealand English

Loanword use has dominated the literature on language contact and its salient nature continues to draw interest from linguists and non-linguists. Traditionally, loanwords were investigated by means of raw frequencies, which are at best uninformative and at worst misleading. Following a new wave of studies which look at loans from a quantitatively more informed standpoint, modelling “success” by taking into account frequency of the counterparts available in the language adopting the loanwords, we propose a similar model of loan-use and demonstrate its benefits in a case study of loanwords from Māori into (New Zealand) English. Our model contributes to previous work in this area by combining both the success measure mentioned above with a rich range of linguistic characteristics of the loanwords (such as loan length and word class), as well as a similarly detailed group of sociolinguistic characteristics of the speakers using them (gender, age and ethnicity of both, speakers and addresses). Our model is unique in bringing together of all these factors at the same time. The findings presented here illustrate the benefit of a quantitatively balanced approach to modelling loanword use. Furthermore, they illustrate the complex interaction between linguistic and sociolinguistic factors in such language contact scenarios

Multiple Spatial Scale Assessment of Coral Reef and Hard-Bottom Community Structure in the Florida Keys National Marine Sanctuary

The zoning plan for the Florida Keys National Marine Sanctuary (FKNMS) established 23 relatively small no-fishing zones distributed mostly along the offshore reef tract in 1997. In 1999, a two-stage, stratified random sampling design based on the proportion of coral reef and hard-bottom types within the FKNMS was conducted. Our study focused on differences in coverage, density, and condition of benthic organisms with respect to habitat type, regional variations, and differences between no-fishing zones and reference sites at 80 locations spanning 200 km. Most variables exhibited significant spatial differences by habitat type or between individual no-fishing zones and reference sites (e.g. species richness, coral density, gorgonian density, and recruitment), although some regional differences were also apparent. Many of the differences among the no-fishing zones and reference sites reflect the placement of the zones in well-developed offshore reefs, and for many of the variables targeted, individual zones are as different from one another as from reference sites. These results emphasize the need to address spatial variations at multiple scales, and to consider a range of variables beyond common metrics such as coral cover

Sampling methods for Acropora corals, other benthic coral reef organisms, and marine debris in the Florida Keys: Field protocol manual for 2011-2012 assessments

The 2011-2012 sampling of Acropora corals, other coral reef benthic invertebrates, and marine debris in the Florida Keys National Marine Sanctuary (FKNMS) is being undertaken as a spatially intensive effort to provide updated population distribution and abundance information. The particular focus of surveys in the Florida Keys, as well as in the U.S. Caribbean (Puerto Rico and the U.S.V.I.), concerns the habitat distribution, colony density, size, condition, and population abundance of Acropora corals. Surveys in the Florida Keys also include assessments of urchins, mollusks, anemones, corallimorpharians, and marine debris. These additional assessments are relatively fast and easy to perform. Annual surveys for Acropora corals began in 2006 in the Florida Keys in response to their listing on the Federal Endangered Species List, as well as the paucity of large-scale information on habitat distribution, abundance, and condition in the Florida Keys. Periodic surveys for Acropora corals as part of our long-term monitoring and assessment program date back to 1999. The purpose of this field protocol manual is to outline the Acropora sampling procedures used in the Florida Keys and to standardize survey methods for the Florida and U.S. Caribbean regional population assessments planned for 2012. A previous draft of this manual was prepared for Florida Keys National Marine Sanctuary personnel in June 2011 to help guide the field sampling in 2011

Density, Spatial Distribution and Size Structure of Sea Urchins in Florida Keys Coral Reef and Hard-Bottom Habitats

The 1983-84 Caribbean-wide mortality of the long-spined sea urchin Diadema antillarum Philippi was followed by a 2nd mortality event during 1991 in the Florida Keys. Pre-mortality sea urchin densities were up to 5 ind. m-2 and the large scale decline of D. antillarum is considered to be 1 factor affecting community dynamics of Florida Keys reefs. During 1999-2000, we surveyed 125 sites using a stratified random sampling design in shallow-water coral reef and hard-bottom habitats. Strip transects were sampled to assess density, habitat utilization and size structure patterns among habitat types, regional sectors and between fished and protected areas. Nearly 17 yr after the mass mortality, D. antillarum has not recovered to pre-1983 levels, with current densities no greater than 0.05 ind. m-2, and small test sizes (1 to 2 cm) dominate. Other sea urchins such as Eucidaris tribuloides (Lamarck) and Echinometra viridis Agassiz show density and habitat distribution patterns similar to historical observations

Microstimulation of Frontal Cortex Can Reorder a Remembered Spatial Sequence

Complex goal-directed behaviors extend over time and thus depend on the ability to serially order memories and assemble compound, temporally coordinated movements. Theories of sequential processing range from simple associative chaining to hierarchical models in which order is encoded explicitly and separately from sequence components. To examine how short-term memory and planning for sequences might be coded, we used microstimulation to perturb neural activity in the supplementary eye field (SEF) while animals held a sequence of two cued locations in memory over a short delay. We found that stimulation affected the order in which animals saccaded to the locations, but not the memory for which locations were cued. These results imply that memory for sequential order can be dissociated from that of its components. Furthermore, stimulation of the SEF appeared to bias sequence endpoints to converge toward a location in contralateral space, suggesting that this area encodes sequences in terms of their endpoints rather than their individual components

The Octocoral Fishery in the Southeastern U.S. and Gulf of Mexico

Octocorals, also known as gorgonians and soft corals, were previously managed by the U.S. South Atlantic (SAFMC) and Gulf of Mexico (GMFMC) Fishery Management Councils through a joint Coral Fishery Management Plan (FMP). Because octocorals are mostly collected from Florida waters, the Florida Fish and Wildlife Conservation Commission (FWC) is currently tasked with managing octocoral collection, including the monitoring of colony landings, in the Economic Exclusive Zone (EEZ) adjacent to Florida. Collection of 70,000 colonies per year total, which applies to both state and EEZ waters off Florida, is permitted under Rule 68B- 42.006 of the Florida Administrative Code, but has never been exceeded according to available landings data. Before octocoral management responsibility was transferred to the State of Florida, the SAFMC was concerned that octocoral landings data, as opposed to population data, were being used to set Acceptable Biological Catch limits and Overfishing limits under the new Federal fishery management standards. An additional concern with the octocoral fishery and other organisms captured for the marine aquarium and ornamental fisheries is that large taxonomic groups are lumped together, including species with potentially different life histories and ecological functions. This study assessed some of the characteristics of the octocoral fishery by evaluating FWC Trip Ticket data, conducting interviews with octocoral collectors, and analyzing octocoral life history information and available fishery-independent data on population densities and sizes. Based on interviews with collectors, a synthesis of trip ticket results, and population abundance estimates, the long-term stability of the octocoral fishery is not likely to change significantly. The social dynamics of the aquarium industry to seek colorful, rare, and exotic marine species for home aquaria places octocorals at the lower end of the list of desired species. Octocoral distribution and abundance information obtained from an extensive search of the literature, along with available age, growth, and habitat data, suggests that current information is comprehensive and definitive, such that stock assessment or population dynamic modeling could be considered but are probably not required to assess the status of collected octocoral species. For multiple sampling periods, over a decadal period (1999-09) in the Florida Keys, where most octocoral collection occurs, abundance estimates presented for 15 species illustrate that population sizes are large (tens of millions to hundreds of millions of colonies, per species) and abundance is stable or increasing. For example, the numbers of colonies collected in the Florida Keys in two of the collector categories represented \u3c 0.004% of the estimated population sizes. The collectors and aquarium hobbyists interviewed stated that they would welcome and use a field guide to help with octocoral identification, which would ultimately provide better fishery-dependent taxonomic resolution for collected species. The collection of octocorals below the State of Florida quota of 70,000 colonies per year threshold, which has yet to be reached according to landings data, likely does not adversely affect the octocoral populations targeted. This conclusion is based upon the large population estimates determined for octocorals relative to the small number of colonies collected. This conclusion assumes that the distribution and population sizes of targeted species will continue to be relatively stable or increase. Information collected by the State of Florida through trip tickets is probably adequate to understand and manage the octocoral fishery. Minor reporting clarifications and better taxonomic resolution in reporting would help improve the accuracy of collecting data, but improved accuracy is not required to assess the current state of the fishery-the octocoral fishery is sustainable and would likely remain sustainable at colony collection levels orders of magnitude larger