On n-sum of an abelian group of order n

Let $G$ be an additive finite abelian group of order $n$, and let $S$ be a sequence of $n+k$ elements in $G$, where $k\geq 1$. Suppose that $S$ contains $t$ distinct elements. Let $\sum_n(S)$ denote the set that consists of all elements in $G$ which can be expressed as the sum over a subsequence of length $n$. In this paper we prove that, either $0\in \sum_n(S)$ or $|\sum_n(S)|\geq k+t-1.$ This confirms a conjecture by Y.O. Hamidoune in 2000

M cells are involved in pathogenesis of human contact lens-associated giant papillary conjunctivitis

INTRODUCTION: The objective was to study the pathogenesis of contact lens-associated giant papillary conjunctivitis (CL-GPC). MATERIALS AND METHODS: Twenty-one biopsies of conjunctival giant papillae were obtained from soft contact lens wearers. The tissues were fixed in 4% paraformaldehyde and embedded in paraffin. Sections of 5 µm thickness were used for studies of histology and immunohistochemistry of pan-B and pan-T cell distributions. RESULTS: Conjunctival epitheliums on the top of conjunctiva-associated lymphoid tissue typically lacked goblet cells. Lymphocytes from underlying lymphoid follicle were pressed into intra-epithelial “pockets” formed through epithelial invagination. Under the follicle-associated epithelium, pan-B cells were mostly gathered in the central folliclar area and intraepithelial pockets, while CD3-positive T cells were predominantly distributed in parafolliclar region, but only a few in the intraepithelial pockets. CONCLUSIONS: Membranous epithelial cells (M cells) play a key role in the pathogenesis of CL-GPC for the binding and translocation of antigen and pathogen

TWO GENERALIZED CONSTANTS RELATED TO ZERO-SUM PROBLEMS FOR TWO SPECIAL SETS

Let n ∈ N and A ⊆ Zn be such that A is non–empty and does not contain 0. Adhikari et al proposed two generalized constants related to the zero-sum problem. One is DA(n), which denotes the least natural number k such that for any sequence (x1, · · · , xk) ∈ Z k, there exists a non-empty subsequence (xj1, · · · , xjl) and (a1, · · · , al) ∈ A l such that � l i=1 aixji ≡ 0 (mod n). The other is EA(n), defined as the smallest t ∈ N such that for all sequences (x1,..., xt) ∈ Z t, there exist indices j1,..., jn ∈ N, 1 ≤ j1 < · · · < jn ≤ t and (ϑ1, · · · , ϑn) ∈ An with �n ϑixji i=1 ≡ 0 (mod n). S. D. Adhikari et al proposed characterizing any other sets for which EA(n) = n + 1 or even those for which EA(n) = n + j for specific small values of j. In this paper we give two kinds of sets, calculate DA(n) and EA(n) for these sets, and partially solve Adhikari’s problem. 1

On n-sums in an Abelian group

Let G be an additive abelian group, let n ≥1 be an integer, let S be a sequence over G of length |S| ≥n + 1, and let (S) denote the maximum multiplicity of a term in S. Let Σ n (S) denote the set consisting of all elements in G which can be expressed as the sum of terms from a subsequence of S having length n. In this paper, we prove that either ng ϵ Σ n(S) for every term g in S whose multiplicity is at least (S) -1 or |Σ n (S)| ≥min{n + 1, |S| -n + | supp (S)| -1}, where |supp(S)| denotes the number of distinct terms that occur in S. When G is finite cyclic and n = |G|, this confirms a conjecture of Y. O. Hamidoune from 2003

Comparative efficacy and safety of thirteen biologic therapies for patients with moderate or severe psoriasis: A network meta-analysis

Purpose: This network meta-analysis was aimed to enhance the corresponding evidence with respect to the efficacy and safety of biologic treatments. Methods: PubMed and EMBASE database searches were conducted. Odds ratios were used to evaluate multi-aspect comparisons. SUCRA was used to analyze the ranking of treatments in each endpoint. Psoriasis Area and Severity Index 50%, 75%, 90%, 100%, PGA, dermatology quality of life index were considered as outcomes while adverse events and discontinuation were adopted to evaluate safety. Results: For safety issues, briakinumab was associated with least headache and itolizumab had the lowest risk of infection. Ustekinumab performed best in discontinuation. SUCRA ranked briakinumab, brodalumab, Infliximab and ixekizumab as the favorable efficacy therapies, while briakinumab and brodalumab seemed to have mild side effects. No heterogeneity was observed between these comparisons. Conclusions: Briakinumab performed relatively stable under efficacy and safety outcome. Infliximab can be a good choice for its lower risk of infection. Brodalumab present very good potential in efficacy outcome like PASI and PGA. More clinical trials are required to supply more data about discontinuation of infliximab and infection of brodalumab and larger RCT for assessment of briakinumab. Keywords: Psoriasis, Network meta-analysis, Antibodies, Monoclonal, PubMed, Biological product

New determination of the position of the pulsar B0329+54 with Chinese VLBI network

We present the first successful CVN (Chinese VLBI Network) phase-referencing observation of the pulsar B0329+54 on October 16, 2008 in S band. A new background source, J0347+5557, 2.5 degrees away from the pulsar was employed as a position reference, which is closer to the pulsar and better for the 'nodding' mode than that used in previous observations. The position by fitting image of the pulsar relative to the calibrator is accurately determined at the level of tens of which is comparable with the present differential VLBI astrometric accuracy, proving that CVN will be a potential powerful tool for astrometry and astrophysics