A modified greedy algorithm for dispersively weighted 3-set cover

The set cover problem is that of computing a minimum weight subfamily F^′, given a family F of weighted subsets of a base set U, such that every element of U is covered by some subset in F^′. The k-set cover problem is a variant in which every subset is of size at most k. It has been long known that the problem can be approximated within a factor of by the greedy heuristic, but no better bound has been shown except for the case of unweighted subsets. In this paper we consider approximation of a restricted version of the weighted 3-set cover problem, as a first step towards better approximation of general k-set cover problem, where any two distinct subset costs differ by a multiplicative factor of at least 2. It will be shown, via LP duality, that an improved approximation bound of H(3)-1/6 can be attained, when the greedy heuristic is suitably modified for this case. A key to our algorithm design and analysis is the Gallai-Edmonds structure theorem for maximum matchings.     

Global analysis of single nucleotide polymorphisms in the exons of human deoxyribonuclease I-like 1 and 2 genes

Several SNPs in the deoxyribonuclease I-like 1 (DNase 1L1) and DNase 1L2 were investigated. In the present study, the genotype distributions of three synonymous SNPs (V59V, rs1050095; P67P, rs1130929; A277A, rs17849495) in the DNase 1L1 gene and four non-synonymous SNPs, V122I (rs34952165), Q170H (rs6643670), and D227A (rs5987256) in the DNase 1L1 gene, as well as D197A (rs62621282) in the DNase 1L2 gene were investigated in 13 populations. In all the populations, no variation was found in four SNPs (V59V, Q170H, D227A, and A277A) in DNASE1L1 or in D197A in DNASE1L2. As for V122I, only the German population showed a low degree of polymorphism. The SNP V122I in DNASE1L1 was monoallelic for the G-allele in all of the Asian and African populations examined, with no polymorphism being evident. Since the A-allele in SNP V122I was distributed in only the Caucasian populations, not in the other ethnic groups, it was confirmed that the A-allele in SNP V122I was Caucasian-specific. On the other hand, only P67P in DNASE1L1 was polymorphic among three synonymous SNPs. The effect of nucleotide substitution corresponding to polymorphic SNP P67P on DNase 1L1 activity was examined: the corresponding nucleotide substitution in polymorphic SNP P67P has little effect on the DNase activity.     

Networks with time structure from time series

We propose a method of constructing a network, in which its time structure is directly incorporated, based on a deterministic model from a time series. To construct such a network, we transform a linear model containing terms with different time delays into network topology. The terms in the model are translated into temporal nodes of the network. On each link connecting these nodes, we assign a positive real number representing the strength of relationship, or the “distance,” between nodes specified by the parameters of the model. The method is demonstrated by a known system and applied to two actual time series.     

The falling cat as a port-controlled Hamiltonian system

In this article, the falling cat is modeled as two jointed axial symmetric cylinders with arbitrary twist under the constraint of the vanishing total angular momentum. As a control system with the constraint taken into account, this model is formulated as a port-controlled Hamiltonian system defined on the cotangent bundle of the shape space for the jointed cylinders. A control is then designed as a function on the cotangent bundle, according to a standard procedure. Thus, the equations of motion are determined on the cotangent bundle together with the control. The whole motion as a vibrational motion of the falling cat is obtained after integrating the constraint equation of the vanishing total angular momentum. An example of the falling cat is given in which the model turns a somersault to approach a target state in equilibrium with an expected rotation after finishing a vibrational motion.     

Glass‐bead/X‐ray fluorescence analysis of earthenware body – sampling from heterogeneous earthenware

Samples of ancient earthenware were prepared in 1 : 10 glass beads for the X‐ray fluorescence quantitation of 10 major elements (Na, Mg, Al, Si, P, K, Ca, Ti, Mn, and Fe). Calibration standards of the glass beads were used with a mixture of reagents in an arbitrary ratio instead of rock standards. The calibration curves were constructed using the reported values of Japanese wares and clay materials. The adequacy of conventional sampling methods was statistically evaluated by examining the homogeneities of two shards (112 g of Jomon ware and 92 g of Yayoi ware) with respect to their crystalline phases and 10 major constituents. Both shards were found to be heterogeneous. An important finding is that in the sampling from a shard, unless at least half of the shard is homogenized, small sampling cannot represent the whole shard. The sampling was found to be only marginally reliable because the K/Ca scatter diagram for determination of provenance showed regional characteristics, and the measured analytical values showed normal (or Gaussian) distributions. Furthermore, taking eight samples or above from a shard enhances the reliability of small sampling. Copyright © 2011 John Wiley & Sons, Ltd.     

Loose‐powder technique for X‐ray fluorescence analysis of ancient pottery using a small (100 mg) powdered sample

A molded‐loose‐powder technique using a small powdered sample (100 mg) was developed for the X‐ray fluorescence analysis of 22 components (Na₂O, MgO, Al₂O₃, SiO₂, P₂O₅, K₂O, CaO, TiO₂, MnO, Fe₂O₃, V, Cr, Ni, Cu, Zn, Rb, Sr, Y, Zr, Nb, Ba, and Pb) in ancient pottery. This loose powder specimen was prepared by pressing the small powdered sample into a sample holder, formed from a stainless steel disk (48‐mm diameter × 0.8‐mm height) with a hole (11‐mm diameter), by hand. Calibration standards were prepared by homogenizing chemical reagents containing these 22 analytes using the concentration ranges of 166 ancient potteries and three clay materials from Japan. The calibration curves of these benchmark mixtures exhibited a good linearity (correlation coefficient, r = 0.990–1.000), accuracy, and reproducibility compared with those of other synthesized specimens and three reference standards. The lower limits of detection were less than tens of mg kg^?1 (e.g., 94 mg kg^?1 for Na₂O, 11 mg kg^?1 for P₂O₅, 1.1 mg kg^?1 for Rb, and 0.9 mg kg^?1 for Y). Using the present method, we determined 22 components in two prehistoric potteries from Japan. The advantage of this method is that only a small amount of sample is required, which can be prepared easily and rapidly and reused for other analyses. Copyright © 2012 John Wiley & Sons, Ltd.     

Analysis of vertical coupling between a 2D photonic crystal cavity and a hydrogenated-amorphous-silicon-wire waveguide

We present an efficient means of light extraction from two-dimensional photonic crystal (2D PC) cavities with SiO₂ cladding. We propose a vertically coupled system consisting of a 2D PC cavity and a hydrogenated-amorphous-silicon (a-Si:H)-wire waveguide, which we theoretically investigate using the 3D finite-difference time-domain method. Light can be extracted with an efficiency of greater than 95% to both output ports of the a-Si:H-wire waveguide or extracted with an efficiency of greater than 90% to a single output port of the a-Si:H-wire waveguide with a reflector.     

Thermodynamics of polymeric fluids – effect of volume on the configurational entropy of chain molecules

Various conformation‐dependent properties of chain molecules have been successfully treated within the rotational isomeric state approximation. The conformation entropy is one of such properties which can be readily defined by the partition function, the sum of all possible configurations of the chain. Flexible polymers often exhibit crystallization and in some cases liquid‐crystallization as well. In these first‐order transitions, changes in the spatial arrangement of polymer chains are considered to be a major factor involved. In order to explicitly determine the conformational contribution to the melting entropy, the latent entropy observed under the isobaric condition must be corrected for the volume change. The entropy separation involves a hypothetical assumption that the volume of the isotropic fluid may be compressed to that of the solid state without affecting the configurational part of the entropy of molecules. Finally thermodynamic significance of the conformation entropy in these transitions is emphasized on the basis of the critical studies of the entropy‐volume relation of chain molecules in the liquid state.     

Photoluminescent copolymer-pendant Ru(BPY)32+ grafted onto non-woven silk fabric and its application to oxygen sensor

Copolymer-pendant Ru(bpy)₃²⁺ grafted onto silk fibroin was prepared by at first grafting copoly(4-methyl-4′-vinyl-2,2′-bipyridine - methylmethacrylate) onto non-woven silk fabric, and then by reacting the grafted sample with cis-Ru(bpy)₂Cl₂. Photoluminescence of this silk-poly Ru complex and its quenching by oxygen were studied in gas, methanol and water phases. The relative emission intensity and the emission lifetime of the silk-poly Ru showed that there are two kinds of sites for the Ru complex. The major, longer lifetime component (1070 ns, 77.1%, under Ar gas) is considered to be surrounded by polymer matrices, and the minor, shorter one (288 ns, 22.9%) seems to be exposed and is subjected to concentration quenching. The shorter lifetime species are quenched by oxygen more effectively than the longer ones. The mechanism of the quenching by oxygen and its application to oxygen sensor were discussed.