For a set Ω of size n ≥ 7 and Ω{3} the set of subsets of Ω of size 3, we examine the binary codes obtained from the adjacency matrix of each of the three graphs with vertex set Ω{3}, with adjacency defined by two vertices as 3-sets being adjacent if they have zero, one or two elements in common, respectively.

Pyoderma Gangrenosum(PG) is an ulcerating neutrophilic dermatosis highly associated with IBD, inflammatory arthritis and monoclonal gammopathy(IgA). Despite linkage systemic disease, limited data on peripheral tissue-specific mediators exist. We prospectively recruited collected biospecimens (blood, skin) over 2 years, from patients ulcers meeting>1 published PG diagnostic framework (Su et al.,...

The Equal Sum Subsets problem, where we are given a set of positive integers and we ask for two nonempty disjoint subsets such that their elements add up to the same total, is known to be NP-hard. In this paper we give (pseudo-)polynomial algorithms and/or (strong) NP-hardness proofs for several natural variations of Equal Sum Subsets. Among others we present (1) a framework for obtaining NP-ha...

background: cd8+ cytotoxic t lymphocytes have been recently divided based on their cytokine expression profile. objective: to evaluate the percentages of cd8+ lymphocytes and their effector subsets including tc1, tc2 and tc17 in the tumor draining lymph nodes (tdlns) of patients with breast cancer. methods: single cell suspensions were obtained from tdlns of 42 patients with breast cancer. stai...

Given a direct product of monoids M = A∗ ×N where A is finite and N is the additive monoid of nonnegative integers, the following problem is recursively decidable: given two rational subsests of M , does there exist a recognizable subset which includes one of the subsets and excludes the other.

In this report a parallel algorithm is presented for unranking k out of n set subsets. The computations run in a specialized architecture that combines some systolic and some associative features. The algorithm has O(k) time complexity and can be applied in specialized systems for parallel adaptive generation of the set of all combinations, its ordered subsets and any random sequences. This pro...

Previous work using a large data set (no. 1, n = 5355) of carcass sponge samples from three large-volume beef abattoirs highlighted the potential use of binary (present or absent) Enterobacteriaceae results for predicting the absence of Salmonella on carcasses. Specifically, the absence of Enterobacteriaceae was associated with the absence of Salmonella. We tested the accuracy of this predictiv...

We prove the following isoperimetric type inequality: Given a finite absolutely continuous Borel measure on ${\mathbb R}^n$, halfspaces have maximal among all subsets with prescribed barycenter. As consequence, we make progress towards solution to problem of Henk and Pollehn, which is equivalent Log-Minkowski inequality for parallelotope centered convex body. Our probabilistic approach also giv...

We provide a new geometric representation of family fragmentation processes by nested laminations which are compact subsets the unit disk made noncrossing chords. specifically consider fragmentation, obtained cutting random stable tree at points, split into smaller subtrees. When coding each these cutpoints chord in disk, we separate connected components, corresponding to subtrees initial tree....

We prove the equidistribution of subsets (R/Z)n defined by fractional parts (Z/qZ)n that are constructed using Chinese Remainder Theorem.