1,321 research outputs found
Semi-Finite Forms of Bilateral Basic Hypergeometric Series
We show that several classical bilateral summation and transformation
formulas have semi-finite forms. We obtain these semi-finite forms from
unilateral summation and transformation formulas. Our method can be applied to
derive Ramanujan's summation, Bailey's transformations,
and Bailey's summation.Comment: 8 pages. accepted by Proc. Amer. Math. So
Faulhaber's Theorem on Power Sums
We observe that the classical Faulhaber's theorem on sums of odd powers also
holds for an arbitrary arithmetic progression, namely, the odd power sums of
any arithmetic progression is a polynomial in
. While this assertion can be deduced from the original
Fauhalber's theorem, we give an alternative formula in terms of the Bernoulli
polynomials. Moreover, by utilizing the central factorial numbers as in the
approach of Knuth, we derive formulas for -fold sums of powers without
resorting to the notion of -reflexive functions. We also provide formulas
for the -fold alternating sums of powers in terms of Euler polynomials.Comment: 12 pages, revised version, to appear in Discrete Mathematic
The Dumont Ansatz for the Eulerian Polynomials, Peak Polynomials and Derivative Polynomials
We observe that three context-free grammars of Dumont can be brought to a
common ground, via the idea of transformations of grammars, proposed by
Ma-Ma-Yeh. Then we develop a unified perspective to investigate several
combinatorial objects in connection with the bivariate Eulerian polynomials. We
call this approach the Dumont ansatz.
As applications, we provide grammatical treatments, in the spirit of the
symbolic method, of relations on the Springer numbers, the Euler numbers, the
three kinds of peak polynomials, an identity of Petersen, and the two kinds of
derivative polynomials, introduced by Knuth-Buckholtz and Carlitz-Scoville, and
later by Hoffman in a broader context. We obtain a convolution formula on the
left peak polynomials, leading to the Gessel formula. In this framework, we are
led to the combinatorial interpretations of the derivative polynomials due to
Josuat-Verg\`es.Comment: 30 pages, 5 figure
MPI Collective Operations over IP Multicast
Many common implementations of Message Passing Inter- face (MPI) implement collective operations over point-to-point operations. This work examines IP multicast as a framework for collective operations. IP multicast is not reliable. If a receiver is not ready when a message is sent via IP multicast, the message is lost. Two techniques for ensuring that a message is not lost due to a slow receiving process are examined. The techniques are implemented and compared experimentally over both a shared and a switched Fast Ethernet. The average performance of collective operations is improved as a function of the number of participating processes and message size for both networks
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Dissecting the regulatory strategies of NF-kB RelA target genes in the inflammatory response reveals differential transactivation logics
Nuclear factor κB (NF-κB) RelA is the potent transcriptional activator of inflammatory response genes. We stringently defined a list of direct RelA target genes by integrating physical (chromatin immunoprecipitation sequencing [ChIP-seq]) and functional (RNA sequencing [RNA-seq] in knockouts) datasets. We then dissected each gene’s regulatory strategy by testing RelA variants in a primary-cell genetic-complementation assay. All endogenous target genes require RelA to make DNA-base-specific contacts, and none are activatable by the DNA binding domain alone. However, endogenous target genes differ widely in how they employ the two transactivation domains. Through model-aided analysis of the dynamic time-course data, we reveal the gene-specific synergy and redundancy of TA1 and TA2. Given that post-translational modifications control TA1 activity and intrinsic affinity for coactivators determines TA2 activity, the differential TA logics suggests context-dependent versus context-independent control of endogenous RelA-target genes. Although some inflammatory initiators appear to require co-stimulatory TA1 activation, inflammatory resolvers are a part of the NF-κB RelA core response
Assessment of the genetic basis of rosacea by genome-wide association study.
Rosacea is a common, chronic skin disease that is currently incurable. Although environmental factors influence rosacea, the genetic basis of rosacea is not established. In this genome-wide association study, a discovery group of 22,952 individuals (2,618 rosacea cases and 20,334 controls) was analyzed, leading to identification of two significant single-nucleotide polymorphisms (SNPs) associated with rosacea, one of which replicated in a new group of 29,481 individuals (3,205 rosacea cases and 26,262 controls). The confirmed SNP, rs763035 (P=8.0 × 10(-11) discovery group; P=0.00031 replication group), is intergenic between HLA-DRA and BTNL2. Exploratory immunohistochemical analysis of HLA-DRA and BTNL2 expression in papulopustular rosacea lesions from six individuals, including one with the rs763035 variant, revealed staining in the perifollicular inflammatory infiltrate of rosacea for both proteins. In addition, three HLA alleles, all MHC class II proteins, were significantly associated with rosacea in the discovery group and confirmed in the replication group: HLA-DRB1*03:01 (P=1.0 × 10(-8) discovery group; P=4.4 × 10(-6) replication group), HLA-DQB1*02:01 (P=1.3 × 10(-8) discovery group; P=7.2 × 10(-6) replication group), and HLA-DQA1*05:01 (P=1.4 × 10(-8) discovery group; P=7.6 × 10(-6) replication group). Collectively, the gene variants identified in this study support the concept of a genetic component for rosacea, and provide candidate targets for future studies to better understand and treat rosacea
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