Evaluation of binomial double sums involving absolute values

We show that double sums of the form $$\sum_{i,j=-n} ^{n} |i^sj^t(i^k-j^k)^\beta| \binom {2n} {n+i} \binom {2n} {n+j}$$ can always be expressed in terms of a linear combination of just four functions, namely $\binom {4n}{2n}$, ${\binom {2n}n}^2$, $4^n\binom {2n}n$, and $16^n$, with coefficients that are rational in $n$. We provide two different proofs: one is algorithmic and uses the second author's computer algebra package Sigma; the second is based on complex contour integrals. In many instances, these results are extended to double sums of the above form where $\binom {2n}{n+j}$ is replaced by $\binom {2m}{m+j}$ with independent parameter $m$.Comment: AmS-LaTeX, 42 pages; substantial revision: several additional and more general results, see Proposition 11 and Theorems 15-1

A generalization of the q-Saalschutz sum and the Burge transform

A generalization of the q-(Pfaff)-Saalschutz summation formula is proved. This implies a generalization of the Burge transform, resulting in an additional dimension of the ``Burge tree''. Limiting cases of our summation formula imply the (higher-level) Bailey lemma, provide a new decomposition of the q-multinomial coefficients, and can be used to prove the Lepowsky and Primc formula for the A_1^{(1)} string functions.Comment: 18 pages, AMSLaTe

The spectra of lifted digraphs

We present a method to derive the complete spectrum of the lift \mathrm{\Gamma\alpha} of a base digraph \mathrm{\Gamma}, with voltage assignment α on a (finite) group $\textit{G}$. The method is based on assigning to \mathrm{\Gamma} a quotient-like matrix whose entries are elements of the group algebra \mathds{C}[$\textit{G}$], which fully represents \mathrm{\Gamma\alpha}. This allows us to derive the eigenvectors and eigenvalues of the lift in terms of those of the base digraph and the irreducible characters of G. Thus, our main theorem generalizes some previous results of Lovász and Babai concerning the spectra of Cayley digraphs

Autonomy support, basic need satisfaction and the optimal functioning of adult male and female sport participants: A test of basic needs theory

Grounded in Basic Needs Theory (BNT; Ryan and Deci, American Psychologist, 55, 68–78, 2000a), the present study aimed to: (a) test a theoretically-based model of coach autonomy support, motivational processes and well-/ill being among a sample of adult sport participants, (b) discern which basic psychological need(s) mediate the link between autonomy support and well-/ill-being, and (c) explore gender invariance in the hypothesized model. Five hundred and thirty nine participants (Male = 271;Female = 268; Mage = 22.75) completed a multi-section questionnaire tapping the targeted variables. Structural Equation Modeling (SEM) analysis revealed that coach autonomy support predicted participants’ basic need satisfaction for autonomy, competence and relatedness. In turn, basic need satisfaction predicted greater subjective vitality when engaged in sport. Participants with low levels of autonomy were more susceptible to feeling emotionally and physically exhausted from their sport investment. Autonomy and competence partially mediated the path from autonomy support to subjective vitality. Lastly, the results supported partial invariance of the model with respect to gender

Rising from the Sea: Correlations between Sulfated Polysaccharides and Salinity in Plants

High salinity soils inhibit crop production worldwide and represent a serious agricultural problem. To meet our ever-increasing demand for food, it is essential to understand and engineer salt-resistant crops. In this study, we evaluated the occurrence and function of sulfated polysaccharides in plants. Although ubiquitously present in marine algae, the presence of sulfated polysaccharides among the species tested was restricted to halophytes, suggesting a possible correlation with salt stress or resistance. To test this hypothesis, sulfated polysaccharides from plants artificially and naturally exposed to different salinities were analyzed. Our results revealed that the sulfated polysaccharide concentration, as well as the degree to which these compounds were sulfated in halophytic species, were positively correlated with salinity. We found that sulfated polysaccharides produced by Ruppia maritima Loisel disappeared when the plant was cultivated in the absence of salt. However, subjecting the glycophyte Oryza sativa Linnaeus to salt stress did not induce the biosynthesis of sulfated polysaccharides but increased the concentration of the carboxylated polysaccharides; this finding suggests that negatively charged cell wall polysaccharides might play a role in coping with salt stress. These data suggest that the presence of sulfated polysaccharides in plants is an adaptation to high salt environments, which may have been conserved during plant evolution from marine green algae. Our results address a practical biological concept; additionally, we suggest future strategies that may be beneficial when engineering salt-resistant crops

Communication : where evolutionary linguistics went wrong

In this article we offer a detailed assessment of current approaches to the origins of language, with a special focus on their historical and theoretical underpinnings. It is a widely accepted view within evolutionary linguistics that an account of the emergence of human language necessarily involves paying special attention to its communicative function and its relation to other animal communication systems. Ever since Darwin, some variant of this view has constituted the mainstream version in evolutionary linguistics; however, it is our contention in this article that this approach is seriously flawed, and that "animal communication" does not constitute a natural kind on which a sound theoretical model can be built. As a consequence, we argue that this communicative perspective is better abandoned in favor of a structural/formal approach based on the notion of homology, and that some interesting and unexpected similarities may be found by applying this venerable comparative method founded in the 19th century by Richard Owen

Drosophila Carrying Pex3 or Pex16 Mutations Are Models of Zellweger Syndrome That Reflect Its Symptoms Associated with the Absence of Peroxisomes

The peroxisome biogenesis disorders (PBDs) are currently difficult-to-treat multiple-organ dysfunction disorders that result from the defective biogenesis of peroxisomes. Genes encoding Peroxins, which are required for peroxisome biogenesis or functions, are known causative genes of PBDs. The human peroxin genes PEX3 or PEX16 are required for peroxisomal membrane protein targeting, and their mutations cause Zellweger syndrome, a class of PBDs. Lack of understanding about the pathogenesis of Zellweger syndrome has hindered the development of effective treatments. Here, we developed potential Drosophila models for Zellweger syndrome, in which the Drosophila pex3 or pex16 gene was disrupted. As found in Zellweger syndrome patients, peroxisomes were not observed in the homozygous Drosophila pex3 mutant, which was larval lethal. However, the pex16 homozygote lacking its maternal contribution was viable and still maintained a small number of peroxisome-like granules, even though PEX16 is essential for the biosynthesis of peroxisomes in humans. These results suggest that the requirements for pex3 and pex16 in peroxisome biosynthesis in Drosophila are different, and the role of PEX16 orthologs may have diverged between mammals and Drosophila. The phenotypes of our Zellweger syndrome model flies, such as larval lethality in pex3, and reduced size, shortened longevity, locomotion defects, and abnormal lipid metabolisms in pex16, were reminiscent of symptoms of this disorder, although the Drosophila pex16 mutant does not recapitulate the infant death of Zellweger syndrome. Furthermore, pex16 mutants showed male-specific sterility that resulted from the arrest of spermatocyte maturation. pex16 expressed in somatic cyst cells but not germline cells had an essential role in the maturation of male germline cells, suggesting that peroxisome-dependent signals in somatic cyst cells could contribute to the progression of male germ-cell maturation. These potential Drosophila models for Zellweger syndrome should contribute to our understanding of its pathology

A Single Peroxisomal Targeting Signal Mediates Matrix Protein Import in Diatoms

Peroxisomes are single membrane bound compartments. They are thought to be present in almost all eukaryotic cells, although the bulk of our knowledge about peroxisomes has been generated from only a handful of model organisms. Peroxisomal matrix proteins are synthesized cytosolically and posttranslationally imported into the peroxisomal matrix. The import is generally thought to be mediated by two different targeting signals. These are respectively recognized by the two import receptor proteins Pex5 and Pex7, which facilitate transport across the peroxisomal membrane. Here, we show the first in vivo localization studies of peroxisomes in a representative organism of the ecologically relevant group of diatoms using fluorescence and transmission electron microscopy. By expression of various homologous and heterologous fusion proteins we demonstrate that targeting of Phaeodactylum tricornutum peroxisomal matrix proteins is mediated only by PTS1 targeting signals, also for proteins that are in other systems imported via a PTS2 mode of action. Additional in silico analyses suggest this surprising finding may also apply to further diatoms. Our data suggest that loss of the PTS2 peroxisomal import signal is not reserved to Caenorhabditis elegans as a single exception, but has also occurred in evolutionary divergent organisms. Obviously, targeting switching from PTS2 to PTS1 across different major eukaryotic groups might have occurred for different reasons. Thus, our findings question the widespread assumption that import of peroxisomal matrix proteins is generally mediated by two different targeting signals. Our results implicate that there apparently must have been an event causing the loss of one targeting signal even in the group of diatoms. Different possibilities are discussed that indicate multiple reasons for the detected targeting switching from PTS2 to PTS1