Galois correspondence for counting quantifiers

We introduce a new type of closure operator on the set of relations, max-implementation, and its weaker analog max-quantification. Then we show that approximation preserving reductions between counting constraint satisfaction problems (#CSPs) are preserved by these two types of closure operators. Together with some previous results this means that the approximation complexity of counting CSPs is determined by partial clones of relations that additionally closed under these new types of closure operators. Galois correspondence of various kind have proved to be quite helpful in the study of the complexity of the CSP. While we were unable to identify a Galois correspondence for partial clones closed under max-implementation and max-quantification, we obtain such results for slightly different type of closure operators, k-existential quantification. This type of quantifiers are known as counting quantifiers in model theory, and often used to enhance first order logic languages. We characterize partial clones of relations closed under k-existential quantification as sets of relations invariant under a set of partial functions that satisfy the condition of k-subset surjectivity. Finally, we give a description of Boolean max-co-clones, that is, sets of relations on {0,1} closed under max-implementations.Comment: 28 pages, 2 figure

Re‐evaluation of celluloses E 460(i), E 460(ii), E 461, E 462, E 463, E 464, E 465, E 466, E 468 and E 469 as food additives

Following a request from the European Commission, the EFSA Panel on Food Additives and Nutrient sources added to Food (ANS) was asked to deliver a scientific opinion on the re-evaluation of microcrystalline cellulose (E 460(i)), powdered cellulose (E 460(ii)), methyl cellulose (E 461), ethyl cellulose (E 462), hydroxypropyl cellulose (E 463), hydroxypropyl methyl cellulose (E 464), ethyl methyl cellulose (E 465), sodium carboxy methyl cellulose (E 466) and enzymatically hydrolysed carboxy methyl cellulose (E 469) as food additives. The Joint FAO/WHO Expert Committee on Food Additives (JECFA) and the Scientific Committee on Food (SCF) established an acceptable daily intake (ADI) ‘not specified’ for unmodified and modified celluloses. Celluloses are not absorbed and are excreted intact in the faeces; in addition, microcrystalline cellulose, powdered and modified celluloses could be fermented by the intestinal flora in animals and humans. Specific toxicity data were not always available for all the celluloses evaluated in the present opinion and for all endpoints. Given their structural, physicochemical and biological similarities, the Panel considered it possible to read-across between all the celluloses. The acute toxicity of celluloses was low and there was no genotoxic concern. Short-term and subchronic dietary toxicity studies performed with E 460(i), E 461, E 462, E 463, E 464, E 466 and E 469 at levels up to 10% did not indicate specific treatment related adverse effects. In chronic toxicity studies performed with E 460(i), E 461, E 463, E 464, E 465 and E 466, the no observed adverse effect level (NOAEL) values reported ranged up to 9,000 mg/kg body weight (bw) per day. No carcinogenic properties were detected for microcrystalline cellulose and modified celluloses. Adverse effects on reproductive performance or developmental effects were not observed with celluloses at doses greater than 1,000 mg/kg bw by gavage (often the highest dose tested). The combined exposure to celluloses (E 460–466, E 468 and E 469) at 95th percentile of the refined (brand-loyal) exposure assessment for the general population was up to 506 mg/kg bw per day. The Panel concluded that there was no need for a numerical ADI and that there would be no safety concern at the reported uses and use levels for the unmodified and modified celluloses (E 460(i); E 460(ii); E 461–466; E 468 and E 469). The Panel considered an indicative total exposure of around 660–900 mg/kg bw per day for microcrystalline, powdered and modified celluloses

Complexity of approximating #CSPs

Constraint satisfactions is a framework to express combinatorial problems. #CSP is the problem of finding the number of solutions for a constraint satisfaction problem instance. In this work, we study complexity of approximately solving the #CSP. We provide several techniques for approximation preserving reductions among counting problems. Most of this work focuses on reduction to #BIS, the problem of finding the number of independent sets in a bipartite graph. We prove that approximately solving #CSP(Γ) over relations which we call monotone, is not harder than #BIS. We also prove that approximately solving #Hom(H) for reflexive oriented graphs is not easier than #BIS. Finally, we investigate monotone reflexive graphs

Touring a Sequence of Weighted Polygons

In this paper we will solve a generalization of the problem “Touring a Sequence of Polygons” where polygons can be concave and a weight is considered when visiting them. The main idea to solve the problem is triangulation of the polygons and adding some Steiner on the edges. We will also use a modified version of BUSHWHACK algorithm to find the shortest path among Steiner points. The running time of the algorithm will be O ( n

Abstract

Given a subdivision of plane into convex polygon regions, a sequence of polygons to meet, a start point s, and a target point t, we are interested in determining the shortest weighted path on this plane which starts at s, visits each of the polygons in the given order, and ends at t. The length of a path in weighted regions is defined as the sum of the lengths of the sub-paths within each region. We will present an approximation algorithm with maximum δ cost additive. Our algorithm is based on the shortest weighted path algorithm proposed by Mata and Mitchel [2]. The algorithm runs in O(((n 3 LW + RW) k δ)3) time, where n is the number of vertices of the region boundaries, L is the longest boundary, W is the maximum weight in the region, R is the sum of the perimeters of the regions, and k is the number of polygons. The main idea in the algorithm is to add Steiner points on the region boundaries and polygon edges. In addition, we will also present a solution to the query version of this problem. We will extend our result in unweighted version of the “Touring a Sequence of Polygons ” problem [3]. We will give an approximation algorithm to solve the general case of the problem (with non-convex intersecting polygons)

Molecular Identification of Candida Albicans Isolated From the Oncology Patients at Four University Hospitals in Mazandaran Province (2005-6)

AbstractBackground and Purpose: Early detection of Candida species in body site could improve the survival of the immunosuppressed patients by allowing the initiation of specific treatment while the fungal biomass is still low. The aim of this study was the identification of Candida albicans isolated from the oncology patients by molecular methods.Materials and Methods: Sixty two of Candida albicans isolated identified by phenotypic methods (color of colony on CHROMagar medium, germ-tube formation in horse serum, chlamydospore formation on Cornmeal agar with 1% Tween 80). DNA was extracted by using a glass bead/phenol- chloroform method. The oligonucleotide primer pairs (NL1/NL4) were used to amplify a 620-bp fragment of D1/D2 region of large submit (26s) ribosomal DNA gene. PCR-products were electrophoresed in a 1.5% agarose gel. Eighteen PCR-amplified products sequenced and results were evaluated by online BLAST software. Multiple sequence alignment was performed by using online CLUSTAL-W (version 1.83) software.Results: The BLAST search revealed that all of products were Candida albicans. All sequences showed >99% similarity when compared with known reference sequences at the Gene-Bank. Four different strains were obtained of albicans species, including: AA 1622b (13 samples), 24698 (3 samples), TA 62 (1samples) and 551 FC (1 sample). A total of 131 nucleotide exchange sites were revealed.Conclusion: The dominant species by phenotypic approaches was Candida albicans. In addition, identification of Candida albicans by (26S) rDNA sequencing was 100% concordant to the results obtained by the phenotypic meth