A Catalan triangle

AbstractWe develop an arithmetic triangle similar to Pascal's triangle. The entries are interpreted in terms of numbers of pairs of nonintersecting paths in the first quadrant. The main applications are results about the Catalan numbers and various random walk problems

Fermat-linked relations for the Boubaker polynomial sequences via Riordan matrices analysis

The Boubaker polynomials are investigated in this paper. Using Riordan matrices analysis, a sequence of relations outlining the relations with Chebyshev and Fermat polynomials have been obtained. The obtained expressions are a meaningful supply to recent applied physics studies using the Boubaker polynomials expansion scheme (BPES).Comment: 12 pages, LaTe

On γ\gamma-vectors satisfying the Kruskal-Katona inequalities

We present examples of flag homology spheres whose $\gamma$-vectors satisfy the Kruskal-Katona inequalities. This includes several families of well-studied simplicial complexes, including Coxeter complexes and the simplicial complexes dual to the associahedron and to the cyclohedron. In these cases, we construct explicit simplicial complexes whose $f$-vectors are the $\gamma$-vectors in question. In another direction, we show that if a flag $(d-1)$-sphere has at most $2d+2$ vertices its $\gamma$-vector satisfies the Kruskal-Katona inequalities. We conjecture that if $\Delta$ is a flag homology sphere then $\gamma(\Delta)$ satisfies the Kruskal-Katona inequalities. This conjecture is a significant refinement of Gal's conjecture, which asserts that such $\gamma$-vectors are nonnegative.Comment: 18 pages; Our main result and conjectures have been strengthened. Also we now have explicit constructions of simplicial complexes whose $f$-vectors are the $\gamma$-vectors in questio

Tidal Dwarf Galaxies at Intermediate Redshifts

We present the first attempt at measuring the production rate of tidal dwarf galaxies (TDGs) and estimating their contribution to the overall dwarf population. Using HST/ACS deep imaging data from GOODS and GEMS surveys in conjunction with photometric redshifts from COMBO-17 survey, we performed a morphological analysis for a sample of merging/interacting galaxies in the Extended Chandra Deep Field South and identified tidal dwarf candidates in the rest-frame optical bands. We estimated a production rate about 1.4 {\times} 10^{-5} per Gyr per comoving volume for long-lived TDGs with stellar mass 3 {\times} 10^{8-9} solar mass at 0.5<z<1.1. Together with galaxy merger rates and TDG survival rate from the literature, our results suggest that only a marginal fraction (less than 10%) of dwarf galaxies in the local universe could be tidally-originated. TDGs in our sample are on average bluer than their host galaxies in the optical. Stellar population modelling of optical to near-infrared spectral energy distributions (SEDs) for two TDGs favors a burst component with age 400/200 Myr and stellar mass 40%/26% of the total, indicating that a young stellar population newly formed in TDGs. This is consistent with the episodic star formation histories found for nearby TDGs.Comment: 9 pages, 5 figures, Accepted for publication in Astrophysics & Space Scienc

Acute biphenotypic leukaemia: immunophenotypic and cytogenetic analysis

The incidence of acute biphenotypic leukaemia has ranged from less than 1% to almost 50% in various reports in the literature. This wide variability may be attributed to a number of reasons including lack of consistent diagnostic criteria, use of various panels of antibodies, and the failure to recognize the lack of lineage specificity of some of the antibodies used. The morphology, cytochemistry, immunophenotype and cytogenetics of acute biphenotypic leukaemias from our institution were studied. The diagnostic criteria took into consideration the morphology of the analysed cells, light scatter characteristics, and evaluation of antibody fluorescence histograms in determining whether the aberrant marker expression was arising from leukaemic blasts or differentiated bone marrow elements. Fifty-two of 746 cases (7%) fulfilled our criteria for acute biphenotypic leukaemias. These included 30 cases of acute lymphoblastic leukaemia (ALL) expressing myeloid antigens, 21 cases of acute myelogenous leukaemia (AML) expressing lymphoid markers, and one case of ALL expressing both B- and T-cell associated antigens. The acute biphenotypic leukaemia cases consisted of four major immunophenotypic subgroups: CD2± AML (11), CD19± AML (8), CD13 and/or CD33± ALL (24), CD11b± ALL (5) and others (4). Chromosomal analysis was carried out in 42/52 of the acute biphenotypic leukaemia cases; a clonal abnormality was found in 31 of these 42 cases. This study highlights the problems encountered in the diagnosis of acute biphenotypic leukaemia, some of which may be reponsible for the wide variation in the reported incidence of this leukaemia. We suggest that the use of strict, uniform diagnostic criteria may help in establishing a more consistent approach towards diagnosis of this leukaemic entity. We also suggest that biphenotypic leukaemia is comprised of biologically different groups of leukaemia based on immunophenotypic and cytogenetic findings.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/73301/1/j.1365-2141.1993.tb03024.x.pd

Learning from multimedia and hypermedia

Computer-based multimedia and hypermedia resources (e.g., the world wide web) have become one of the primary sources of academic information for a majority of pupils and students. In line with this expansion in the field of education, the scientific study of learning from multimedia and hypermedia has become a very active field of research. In this chapter we provide a short overview with regard to research on learning with multimedia and hypermedia. In two review sections, we describe the educational benefits of multiple representations and of learner control, as these are the two defining characteristics of hypermedia. In a third review section we describe recent scientific trends in the field of multimedia/hypermedia learning. In all three review sections we will point to relevant European work on multimedia/hypermedia carried out within the last 5 years, and often carried out within the Kaleidoscope Network of Excellence. According to the interdisciplinary nature of the field this work might come not only from psychology, but also from technology or pedagogy. Comparing the different research activities on multimedia and hypermedia that have dominated the international scientific discourse in the last decade reveals some important differences. Most important, a gap seems to exist between researchers mainly interested in a “serious” educational use of multimedia/ hypermedia and researchers mainly interested in “serious” experimental research on learning with multimedia/hypermedia. Recent discussions about the pros and cons of “design-based research” or “use-inspired basic research” can be seen as a direct consequence of an increasing awareness of the tensions within these two different cultures of research on education

Size Doesn't Matter: Towards a More Inclusive Philosophy of Biology

notes: As the primary author, O’Malley drafted the paper, and gathered and analysed data (scientific papers and talks). Conceptual analysis was conducted by both authors.publication-status: Publishedtypes: ArticlePhilosophers of biology, along with everyone else, generally perceive life to fall into two broad categories, the microbes and macrobes, and then pay most of their attention to the latter. ‘Macrobe’ is the word we propose for larger life forms, and we use it as part of an argument for microbial equality. We suggest that taking more notice of microbes – the dominant life form on the planet, both now and throughout evolutionary history – will transform some of the philosophy of biology’s standard ideas on ontology, evolution, taxonomy and biodiversity. We set out a number of recent developments in microbiology – including biofilm formation, chemotaxis, quorum sensing and gene transfer – that highlight microbial capacities for cooperation and communication and break down conventional thinking that microbes are solely or primarily single-celled organisms. These insights also bring new perspectives to the levels of selection debate, as well as to discussions of the evolution and nature of multicellularity, and to neo-Darwinian understandings of evolutionary mechanisms. We show how these revisions lead to further complications for microbial classification and the philosophies of systematics and biodiversity. Incorporating microbial insights into the philosophy of biology will challenge many of its assumptions, but also give greater scope and depth to its investigations