Arithmetic progressions consisting of unlike powers

In this paper we present some new results about unlike powers in arithmetic progression. We prove among other things that for given $k\geq 4$ and $L\geq 3$ there are only finitely many arithmetic progressions of the form $(x_0^{l_0},x_1^{l_1},...,x_{k-1}^{l_{k-1}})$ with $x_i\in{\Bbb Z},$ gcd$(x_0,x_1)=1$ and $2\leq l_i\leq L$ for $i=0,1,...,k-1.$ Furthermore, we show that, for L=3, the progression $(1,1,...,1)$ is the only such progression up to sign.Comment: 16 page

An ontological approach to creating an Andean Weaving Knowledge Base

Andean textiles are products of one of the richest, oldest and continuous weaving traditions in the world. Understanding the knowledge and practice of textile production as a form of cultural heritage is particularly relevant in the Andean context due to erosion of clothing traditions, reuse of traditional textiles on commodities targeted at the tourism market, and loss of knowledge embedded in textile production. ``Weaving Communities of Practice'' was a pilot project that aimed to create a knowledge base of Andean weaving designed to contribute to curatorial practice and heritage policy. The research team gathered data on the chain of activities, instruments, resources, peoples, places and knowledge involved in the production of textiles, relating to over 700 textile samples. A major part of the project has been the modelling and representation of the knowledge of domain experts and information about the textile objects themselves in the form of an OWL ontology, and the development of a suite of search facilities to be supported by the ontology. This paper describes the research challenges faced in developing the ontology and search facilities, the methodology adopted, the design and implementation of the system, and the design and outcomes of a user evaluation of the system undertaken with a group of domain experts

Color separation of galaxy types in the Sloan Digital Sky Survey imaging data

We study the optical colors of 147,920 galaxies brighter than g* = 21, observed in five bands by the Sloan Digital Sky Survey (SDSS) over similar to 100 deg(2) of high Galactic latitude sky along the celestial equator. The distribution of galaxies in the g*-r* versus u*-g* color-color diagram is strongly bimodal, with an optimal color separator of u*-r* = 2.22. We use visual morphology and spectral classification of subsamples of 287 and 500 galaxies, respectively, to show that the two peaks correspond roughly to early- (E, S0, and Sa) and late-type (Sb, Sc, and Irr) galaxies, as expected from their different stellar populations. We also find that the colors of galaxies are correlated with their radial profiles, as measured by the concentration index and by the likelihoods of exponential and de Vaucouleurs' profile fits. While it is well known that late-type galaxies are bluer than early-type galaxies, this is the first detection of a local minimum in their color distribution. In all SDSS bands, the counts versus apparent magnitude relations for the two color types are significantly different and demonstrate that the fraction of blue galaxies increases toward the faint end

Recruitment of Histone Deacetylase 3 to the Interferon-A Gene Promoters Attenuates Interferon Expression

Induction of Type I Interferon (IFN) genes constitutes an essential step leading to innate immune responses during virus infection. Sendai virus (SeV) infection of B lymphoid Namalwa cells transiently induces the transcriptional expression of multiple IFN-A genes. Although transcriptional activation of IFN-A genes has been extensively studied, the mechanism responsible for the attenuation of their expression remains to be determined.In this study, we demonstrate that virus infection of Namalwa cells induces transient recruitment of HDAC3 (histone deacetylase 3) to IFN-A promoters. Analysis of chromatin-protein association by Chip-QPCR demonstrated that recruitment of interferon regulatory factor (IRF)3 and IRF7, as well as TBP correlated with enhanced histone H3K9 and H3K14 acetylation, whereas recruitment of HDAC3 correlated with inhibition of histone H3K9/K14 acetylation, removal of IRF7 and TATA-binding protein (TBP) from IFN-A promoters and inhibition of virus-induced IFN-A gene transcription. Additionally, HDAC3 overexpression reduced, and HDAC3 depletion by siRNA enhanced IFN-A gene expression. Furthermore, activation of IRF7 enhanced histone H3K9/K14 acetylation and IFN-A gene expression, whereas activation of both IRF7 and IRF3 led to recruitment of HDAC3 to the IFN-A gene promoters, resulting in impaired histone H3K9 acetylation and attenuation of IFN-A gene transcription.Altogether these data indicate that reversal of histone H3K9/K14 acetylation by HDAC3 is required for attenuation of IFN-A gene transcription during viral infection

Blimp1 Activation by AP-1 in Human Lung Cancer Cells Promotes a Migratory Phenotype and Is Inhibited by the Lysyl Oxidase Propeptide

B lymphocyte-induced maturation protein 1 (Blimp1) is a master regulator of B cell differentiation, and controls migration of primordial germ cells. Recently we observed aberrant Blimp1 expression in breast cancer cells resulting from an NF-κB RelB to Ras signaling pathway. In order to address the question of whether the unexpected expression of Blimp1 is seen in other epithelial-derived tumors, we selected lung cancers as they are frequently driven by Ras signaling. Blimp1 was detected in all five lung cancer cell lines examined and shown to promote lung cancer cell migration and invasion. Interrogation of microarray datasets demonstrated elevated BLIMP1 RNA expression in lung adenocarcinoma, pancreatic ductal carcinomas, head and neck tumors as well as in glioblastomas. Involvement of Ras and its downstream kinase c-Raf was confirmed using mutant and siRNA strategies. We next addressed the issue of mechanism of Blimp1 activation in lung cancer. Using knockdown and ectopic expression, the role of the Activator Protein (AP)-1 family of transcription factors was demonstrated. Further, chromatin immunoprecipitation assays confirmed binding to identified AP-1 elements in the BLIMP1 promoter of ectopically expressed c-Jun and of endogenous AP-1 subunits following serum stimulation. The propeptide domain of lysyl oxidase (LOX-PP) was identified as a tumor suppressor, with ability to reduce Ras signaling in lung cancer cells. LOX-PP reduced expression of Blimp1 by binding to c-Raf and inhibiting activation of AP-1, thereby attenuating the migratory phenotype of lung cancer cells. Thus, Blimp1 is a mediator of Ras/Raf/AP-1 signaling that promotes cell migration, and is repressed by LOX-PP in lung cancer

Stochastic Modeling of B Lymphocyte Terminal Differentiation and Its Suppression by Dioxin

<p>Abstract</p> <p>Background</p> <p>Upon antigen encounter, naïve B lymphocytes differentiate into antibody-secreting plasma cells. This humoral immune response is suppressed by the environmental contaminant 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD) and other dioxin-like compounds, which belong to the family of aryl hydrocarbon receptor (AhR) agonists.</p> <p>Results</p> <p>To achieve a better understanding of the immunotoxicity of AhR agonists and their associated health risks, we have used computer simulations to study the behavior of the gene regulatory network underlying B cell terminal differentiation. The core of this network consists of two coupled double-negative feedback loops involving transcriptional repressors Bcl-6, Blimp-1, and Pax5. Bifurcation analysis indicates that the feedback network can constitute a bistable system with two mutually exclusive transcriptional profiles corresponding to naïve B cells and plasma cells. Although individual B cells switch to the plasma cell state in an all-or-none fashion when stimulated by the polyclonal activator lipopolysaccharide (LPS), stochastic fluctuations in gene expression make the switching event probabilistic, leading to heterogeneous differentiation response among individual B cells. Moreover, stochastic gene expression renders the dose-response behavior of a population of B cells substantially graded, a result that is consistent with experimental observations. The steepness of the dose response curve for the number of plasma cells formed vs. LPS dose, as evaluated by the apparent Hill coefficient, is found to be inversely correlated to the noise level in Blimp-1 gene expression. Simulations illustrate how, through AhR-mediated repression of the AP-1 protein, TCDD reduces the probability of LPS-stimulated B cell differentiation. Interestingly, stochastic simulations predict that TCDD may destabilize the plasma cell state, possibly leading to a reversal to the B cell phenotype.</p> <p>Conclusion</p> <p>Our results suggest that stochasticity in gene expression, which renders a graded response at the cell population level, may have been exploited by the immune system to launch humoral immune response of a magnitude appropriately tuned to the antigen dose. In addition to suppressing the initiation of the humoral immune response, dioxin-like compounds may also disrupt the maintenance of the acquired immunity.</p

Marine Biodiversity in the Caribbean: Regional Estimates and Distribution Patterns

This paper provides an analysis of the distribution patterns of marine biodiversity and summarizes the major activities of the Census of Marine Life program in the Caribbean region. The coastal Caribbean region is a large marine ecosystem (LME) characterized by coral reefs, mangroves, and seagrasses, but including other environments, such as sandy beaches and rocky shores. These tropical ecosystems incorporate a high diversity of associated flora and fauna, and the nations that border the Caribbean collectively encompass a major global marine biodiversity hot spot. We analyze the state of knowledge of marine biodiversity based on the geographic distribution of georeferenced species records and regional taxonomic lists. A total of 12,046 marine species are reported in this paper for the Caribbean region. These include representatives from 31 animal phyla, two plant phyla, one group of Chromista, and three groups of Protoctista. Sampling effort has been greatest in shallow, nearshore waters, where there is relatively good coverage of species records; offshore and deep environments have been less studied. Additionally, we found that the currently accepted classification of marine ecoregions of the Caribbean did not apply for the benthic distributions of five relatively well known taxonomic groups. Coastal species richness tends to concentrate along the Antillean arc (Cuba to the southernmost Antilles) and the northern coast of South America (Venezuela – Colombia), while no pattern can be observed in the deep sea with the available data. Several factors make it impossible to determine the extent to which these distribution patterns accurately reflect the true situation for marine biodiversity in general: (1) highly localized concentrations of collecting effort and a lack of collecting in many areas and ecosystems, (2) high variability among collecting methods, (3) limited taxonomic expertise for many groups, and (4) differing levels of activity in the study of different taxa