Solving the Maximum Clique Problem with Symmetric Rank-One Non-negative Matrix Approximation

Finding complete subgraphs in a graph, that is, cliques, is a key problem and has many real-world applications, e.g., finding communities in social networks, clustering gene expression data, modeling ecological niches in food webs, and describing chemicals in a substance. The problem of finding the largest clique in a graph is a well-known difficult combinatorial optimization problem and is called the maximum clique problem. In this paper, we formulate a very convenient continuous characterization of the maximum clique problem based on the symmetric rank-one non-negative approximation of a given matrix and build a one-to-one correspondence between stationary points of our formulation and cliques of a given graph. In particular, we show that the local (resp. global) minima of the continuous problem corresponds to the maximal (resp. maximum) cliques of the given graph. We also propose a new and efficient clique finding algorithm based on our continuous formulation and test it on the DIMACS data sets to show that the new algorithm outperforms other existing algorithms based on the Motzkin–Straus formulation and can compete with a sophisticated combinatorial heuristic.     

Kinetic analysis of dehydroxylation of Ethiopian kaolinite during calcination

Journal of Thermal Analysis and Calorimetry - The calcination process is the dehydroxylation reaction of the kaolinite mineral into the formation of amorphous metakaolinite phase. The...     

Period 2 regulates neural stem/progenitor cell proliferation in the adult hippocampus

Background  

Newborn granule neurons are generated from proliferating neural stem/progenitor cells and integrated into mature synaptic networks in the adult dentate gyrus of the hippocampus. Since light/dark variations of the mitotic index and DNA synthesis occur in many tissues, we wanted to unravel the role of the clock-controlled Period2 gene (mPer2) in timing cell cycle kinetics and neurogenesis in the adult DG.     

Extension of β-chloroenals to ethyl 5-chloro-2,4-pentadienoates using Wadsworth-Emmons reactions: subsequent conversions to 5-aryl-5-chloro-2,4-pentadienoic acids and 5-aryl-2-penten-4-ynoic acids

Convenient routes from (Z)-3-aryl-3-chloroenals to (2E,4Z)-5-aryl-5-chloro-2,4-pentadienoates and (2E)-5-aryl-2-penten-4-ynoates are described. The stereochemical assignments are based on NMR spectral data.