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 $_1\psi_1$ summation, Bailey's $_2\psi_2$ transformations, and Bailey's $_6\psi_6$ 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 $a+b, a+2b, ..., a+nb$ is a polynomial in $na+n(n+1)b/2$. 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 $r$-fold sums of powers without resorting to the notion of $r$-reflexive functions. We also provide formulas for the $r$-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

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