Set multi-covering via inclusion-exclusion

Set multi-covering is a generalization of the set covering problem where each element may need to be covered more than once and thus some subset in the given family of subsets may be picked several times for minimizing the number of sets to satisfy the coverage requirement. In this paper, we propose a family of exact algorithms for the set multi-covering problem based on the inclusion-exclusion principle. The presented ESMC (Exact Set Multi-Covering) algorithm takes O* ((2 t)n) time and O* ((t + 1)n) space where t is the maximum value in the coverage requirement set (The O* (f (n)) notation omits a p o l y log (f (n)) factor). We also propose the other three exact algorithms through different tradeoffs of the time and space complexities. To the best of our knowledge, this present paper is the first one to give exact algorithms for the set multi-covering problem with nontrivial time and space complexities. This paper can also be regarded as a generalization of the exact algorithm for the set covering problem given in [A. Björklund, T. Husfeldt, M. Koivisto, Set partitioning via inclusion-exclusion, SIAM Journal on Computing, in: FOCS 2006 (in press, special issue)]. © 2009 Elsevier B.V. All rights reserved.postprin

Dynamic programming based algorithms for set multicover and multiset multicover problems

Given a universe N containing n elements and a collection of multisets or sets over N, the multiset multicover (MSMC) problem or the set multicover (SMC) problem is to cover all elements at least a number of times as specified in their coverage requirements with the minimum number of multisets or sets. In this paper, we give various exact algorithms for these two problems with or without constraints on the number of times a multiset or set may be chosen. First, we show that the MSMC without multiplicity constraints problem can be solved in O* ((b + 1)n | F |) time and polynomial space, where b is the maximum coverage requirement and | F | denotes the total number of given multisets over N. (The O* notation suppresses a factor polynomial in n.) To our knowledge, this is the first known exact algorithm for the MSMC without multiplicity constraints problem. Second, by combining dynamic programming and the inclusion-exclusion principle, we can exactly solve the SMC without multiplicity constraints problem in O ((b + 2)n) time. Compared with two recent results, in [Q.-S. Hua, Y. Wang, D. Yu, F.C.M. Lau, Set multi-covering via inclusion-exclusion, Theoretical Computer Science, 410 (38-40) (2009) 3882-3892] and [J. Nederlof, Inclusion exclusion for hard problems, Master Thesis, Utrecht University, The Netherlands, 2008], respectively, ours is the fastest exact algorithm for the SMC without multiplicity constraints problem. Finally, by directly using dynamic programming, we give the first known exact algorithm for the MSMC or the SMC with multiplicity constraints problem in O ((b + 1)n | F |) time and O* ((b + 1)n) space. This algorithm can also be easily adapted as a constructive algorithm for the MSMC without multiplicity constraints problem. © 2010 Elsevier B.V. All rights reserved.postprin

Isolation of flavonoids from mulberry (Morus alba L.) leaves with macroporous resins

Flavonoids are major active constituents in mulberry (Morus alba L.) leaves and possess various pharmacological activities. In the present study, the extraction technology and preparative separation oftotal flavonoids (TFs) in mulberry leaves extracts by macroporous resins were studied systematically, and the column packed with selected resin was used to perform dynamic adsorption and desorptiontests to optimize the separation process. The research results indicated that the maximal yield of TFs was achieved when mulberry leaves were extracted under the optimized conditions of a pH of 8, asolid-liquid ratio of 1:40, a temperature of 90oC and a time of 4 h. H103 resin is the most appropriate for the separation of TFs from other components in mulberry leaves extracts, which adsorption behavior canbe described with Langmuir and Freundlich isotherms and two-step adsorption kinetics model. The optimum parameters for TFs separation by H103 were achieved, after one run treatment. The recoveryand purity of TFs in the final product were 90.57 and 76.33%, respectively. In conclusion, the preparative separation of TFs in mulberry leaves can be easily and effectively done by H103 resin

Studies on Anti-Hepatoma Effect of Gan-Ai-Xiao Decoction

Purpose: To explore the anti-hepatoma effect of Gan-Ai-Xiao Decoction (GAXD), a folk remedy.Methods: High performance liquid chromatography (HPLC) was used to identify the major chemical components of GAXD ethanol extract (EE). The cytotoxic effect of GAXD EE against HepG2 cells was measured by methyl thiazolyl tetrazolium (MTT) assay. Flow cytometry and Western blot were used to study the effect of GAXD EE on apoptosis and apoptotic proteins (Bcl-2, Bax and caspase-3) in HepG2 cells. Xenograft assay was used to evaluate the anti-hepatoma effect of GAXD EE in vivo.Results: Four components were identified in GAXD EE by HPLC. The results of MTT and flow cytometry assays indicated that GAXD EE significantly reduced HepG2 cells viability (p < 0.05) and induced its apoptosis. The results of Western blot assay suggested that GAXD EE down-regulated the expression of anti-apoptotic protein (Bcl-2) and up-regulated the expression of pro-apoptotic proteins (Bax and caspase-3) in HepG2 cells. Furthermore, the results of xenograft assay showed that GAXD EE significantly inhibited the growth of HepG2 cells-induced tumor (p < 0.05) without any effect on the body weight of nude mice.Conclusion: GAXD has anti-hepatoma activity, and the mechanism is associated with apoptosis.Keywords: Gan-Ai-Xiao Decoction, Anti-hepatoma, Flow Cytometry, Western Blot, Xenograft, HepG2 cells, Apoptosi

Insights from Modeling the 3D Structure of New Delhi Metallo-β-Lactamse and Its Binding Interactions with Antibiotic Drugs

New Delhi metallo-beta-lactamase (NDM-1) is an enzyme that makes bacteria resistant to a broad range of beta-lactam antibiotic drugs. This is because it can inactivate most beta-lactam antibiotic drugs by hydrolyzing them. For in-depth understanding of the hydrolysis mechanism, the three-dimensional structure of NDM-1 was developed. With such a structural frame, two enzyme-ligand complexes were derived by respectively docking Imipenem and Meropenem (two typical beta-lactam antibiotic drugs) to the NDM-1 receptor. It was revealed from the NDM-1/Imipenem complex that the antibiotic drug was hydrolyzed while sitting in a binding pocket of NDM-1 formed by nine residues. And for the case of NDM-1/Meropenem complex, the antibiotic drug was hydrolyzed in a binding pocket formed by twelve residues. All these constituent residues of the two binding pockets were explicitly defined and graphically labeled. It is anticipated that the findings reported here may provide useful insights for developing new antibiotic drugs to overcome the resistance problem

Capture barrier of Sn-related DX centers in AlGaAs epilayers

Thermal capture and emission processes of Sn-related DX centers in AlxGa1-xAs (x = 0.26) were measured by a constant capacitance (CC) voltage transient in various temperatures, By employing a Laplace defect spectroscopic (LDS) method, the non-exponential transients were decomposed into several discrete exponential components. The results shown that more exponential components appeared in the small emission rate region as capture period increased. This indicates that electrons preferentially fill shallow energy levels due to their lower capture barriers. Discrete exponential components of the capture process were identified and four of their barriers were preliminarily measured to be about 0.14, 0.15, 0.16, and 0.17 eV, respectively

SIK1/SOS2 networks: decoding sodium signals via calcium-responsive protein kinase pathways

Changes in cellular ion levels can modulate distinct signaling networks aimed at correcting major disruptions in ion balances that might otherwise threaten cell growth and development. Salt-inducible kinase 1 (SIK1) and salt overly sensitive 2 (SOS2) are key protein kinases within such networks in mammalian and plant cells, respectively. In animals, SIK1 expression and activity are regulated in response to the salt content of the diet, and in plants SOS2 activity is controlled by the salinity of the soil. The specific ionic stress (elevated intracellular sodium) is followed by changes in intracellular calcium; the calcium signals are sensed by calcium-binding proteins and lead to activation of SIK1 or SOS2. These kinases target major plasma membrane transporters such as the Na+,K+-ATPase in mammalian cells, and Na+/H+ exchangers in the plasma membrane and membranes of intracellular vacuoles of plant cells. Activation of these networks prevents abnormal increases in intracellular sodium concentration

Graphite flake self-retraction response based on potential seeking

The high elastic modulus and interlayer strengths of graphite flakes make them a durable solid superlubricant. Apart from this, they have configurable electrical properties, exhibit quantum Hall effects, and possess a myriad of useful photonic properties. The self-retraction behavior of graphite flakes can have significant impact on the creation of ordered stacks for various applications because any accidental or intentional displacement of the top flake over the stacks below may result in a misalignment of the carbon-carbon atomic arrangement which, in turn, can have influence over the electrical and photonic properties. It has also been revealed that there was a tendency of the displaced microflake to fail at times to return to its original starting position and orientation. Here, we elucidate this behavior by considering the influence of the interlayer potential forces based on minimal potential energy seeking. The maps of the parameters interrogated here provide the ability for precautions to be undertaken. They also potentially permit the creation of an array of microflake stacks in which the metastable states permit different information to be encoded by virtue of the differentiated photonic or electrical characteristics readable from each array site