A new scaling algorithm for the maximum mean cut problem

We present a new scaling algorithm for the maximum mean cut problem. The mean of a cut is defined by the cut capacity divided by the number of arcs crossing the cut. The algorithm uses an approximate binary search and solves the circulation feasibility problem with relaxed capacity bounds. The maximum mean cut problem has recently been studied as a dual analogue of the minimum mean cycle problem in the framework of the minimum cost flow problem by Ervolina and McCormick. A networkN=(G, lower, upper) with lower and upper arc capacities is said to be -feasible ifN has a feasible circulation when we relax the capacity bounds by ; that is, we use (lower(a)- , upper(a)+) bounds instead of (lower(a), upper(a)) bounds for each arca A. During an approximate binary search we maintain two bounds,LB andUB, such thatN is LB-infeasible andUB-feasible, and we reduce the interval size (LB, UB) by at least one-third at each iteration. For a graph withn vertices, m arcs, and integer capacities bounded byU, the running time of this algorithm is O(mn log(nU). This time bound is better than the time achieved by McCormick and Ervolina under thesimilarity condition (that is,U=O(n^o(1))). Our algorithm can be naturally used for the circulation feasibility problem, and thus provides a new scaling algorithm for the minimum cut problem.Research supported by a grant-in-aid of the Ministry of Education, Science and Culture of Japan.     

Expression, structure and chromosomal localization of the human cGMP-binding cGMP-specific phosphodiesterase PDE5A gene

1. Nicotinylalanine, an inhibitor of kynurenine metabolism, has been shown to elevate brain levels of endogenous kynurenic acid, an excitatory amino acid receptor antagonist. This study examined the potential of nicotinylalanine to influence excitotoxic damage to striatal NADPH diaphorase (NADPH-d) and gamma-aminobutyric acid (GABA)ergic neurones that are selectively lost in Huntington's disease. 2. A unilateral injection of the N-methyl-D-aspartate (NMDA) receptor agonist, quinolinic acid, into the rat striatum produced an 88% depletion of NADPH-d neurones. Intrastriatal infusion of quinolinic acid also produced a dose-dependent reduction in striatal GABA content. 3. Nicotinylalanine (2.3, 3.2, 4.6, 6.4 nmol 5 microl(-1), i.c.v.) administered with L-kynurenine (450 mg kg(-1)), a precursor of kynurenic acid, and probenecid (200 mg kg(-1)), an inhibitor of organic acid transport, 3 h before the injection of quinolinic acid (15 nmol) produced a dose-related attenuation of the quinolinic acid-induced loss of NADPH-d neurones. Nicotinylalanine (5.6 nmol 5 microl(-1)) in combination with L-kynurenine and probenecid also attenuated quinolinic acid-induced reductions in striatal GABA content. 4. Nicotinylalanine (4.6 nmol, i.c.v.), L-kynurenine alone or L-kynurenine administered with probenecid did not attenuate quinolinic acid-induced depletion of striatal NADPH-d neurones. However, combined administration of kynurenine and probenecid did prevent quinolinic acid-induced reductions in ipsilateral striatal GABA content. 5. Injection of nicotinylalanine, at doses (4.6 nmol and 5.6 nmol i.c.v.) which attenuated quinolinic acid-induced striatal neurotoxicity, when combined with L-kynurenine and probenecid produced increases in both whole brain and striatal kynurenic acid levels. Administration of L-kynurenine and probenecid without nicotinylalanine also elevated kynurenic acid, but to a lesser extent. 6. The results of this study demonstrate that nicotinylalanine has the potential to attenuate quinolinic acid-induced striatal neurotoxicity. It is suggested that nicotinylalanine exerts its effect by increasing levels of endogenous kynurenic acid in the brain. The results of this study suggest that agents which influence levels of endogenous excitatory amino acid antagonists such as kynurenic acid may be useful in preventing excitotoxic damage to neurones in the CNS.     

Phase relations associated with the aluminum blast furnace: Aluminum oxycarbide melts and Al-C-X (X=Fe,Si) liquid alloys

The thermodynamic properties and the phase relations were evaluated and estimated for the Al-O-C, Al-Si-C, and Al-Fe-C systems which are important to understand the chemical behavior in an aluminum blast furnace. The mixing properties of binary liquid alloys, including metal-carbon systems, were represented by the Redlich-Kister equation. The properties of liquid Al−C and Si−C alloys were estimated so as to be consistent with their phase diagrams. The coefficients of Al−Fe and Fe−C liquids were evaluated from reported values for activity and enthalpy. The extrapolation to the higher order systems was made by Maggianu's method. The aluminum oxycarbide melt was represented by a subregular solution model. In the Al-O-C system, liquid alloy/oxycarbide melt equilibria were calculated and compared with earlier experimental results and estimates. Attempts were made to clarify the volatilization of aluminum oxycarbide melts, and also the carbidation of liquid aluminum alloys. An empirical correlation between the first terms of the Redlich-Kister equation for the enthalpies and the excess entropies was discussed.     

Beer brewing using a fusant between a sake yeast and a brewer's yeast

Beer brewing using a fusant between a sake yeast (a lysine auxotrophic mutant of sake yeast K-14) and a brewer's yeast (a respiratory-deficient mutant of the top fermentation yeast NCYC1333) was performed to take advantage of the beneficial characteristics of sake yeasts, i.e., the high productivity of esters, high tolerance to ethanol, and high osmotolerance. The fusant (F-32) obtained was different from the parental yeasts regarding, for example, the assimilation of carbon sources and tolerance to ethanol. A brewing trial with the fusant was carried out using a 100-l pilot-scale plant. The fusant fermented wort more rapidly than the parental brewer's yeast. However, the sedimentation capacity of the fusant was relatively low. The beer brewed using the fusant contained more ethanol and esters compared to that brewed using the parental brewer's yeast. The fusant also obtained osmotolerance in the fermentation of maltose and fermented high-gravity wort well.     

Zonotopes and the LP-Newton method

Although linear programming problems can be solved in polynomial time by the ellipsoid method and interior-point algorithms, there still remains a long-standing open problem of devising a strongly polynomial algorithm for linear programming (or of disproving the existence of such an algorithm). The present work is motivated by an attempt toward solving this problem. Linear programming problems can be formulated in terms of a zonotope, a kind of greedy polyhedron, on which linear optimization is made easily. We propose a method, called the LP-Newton method, for linear programming that is based on the zonotope formulation and the minimum-norm-point algorithm of Philip Wolfe. The LP-Newton method is a finite algorithm even for real-number input data with exact arithmetic computations. We show some preliminary computational results to examine the behavior of the LP-Newton method. Major part of this paper was presented as a plenary talk with the same title at ICOTA7 (December 12–15, 2007, Kobe, Japan) by the first author. The fourth author’s research was carried out while visiting RIMS in August 2007.     

Remarks on “optimal stochastic control for discrete-time linear system with interrupted observations”

In the paper by Fujita and Fukao [1], a proof of the separation theorem for discrete-time linear systems with interrupted observations was presented. The theorem is based heavily on [1, Lemma]. This note points out errors of the proof of [1, Lemma] and disproves the separation theorem.     

Minimum Cost Source Location Problems with Flow Requirements

In this paper, we consider source location problems and their generalizations with three connectivity requirements (arc-connectivity requirements λ and two kinds of vertex-connectivity requirements κ and ), where the source location problems are to find a minimum-cost set S⊆V in a given graph G=(V,A) with a capacity function u:A→ℝ₊ such that for each vertex v∈V, the connectivity from S to v (resp., from v to S) is at least a given demand d ⁻(v) (resp., d ⁺(v)). We show that the source location problem with edge-connectivity requirements in undirected networks is strongly NP-hard, which solves an open problem posed by Arata et al. (J. Algorithms 42: 54–68, 2002). Moreover, we show that the source location problems with three connectivity requirements are inapproximable within a ratio of cln D for some constant c, unless every problem in NP has an O(N ^{log log N} )-time deterministic algorithm. Here D denotes the sum of given demands. We also devise (1+ln D)-approximation algorithms for all the extended source location problems if we have the integral capacity and demand functions. By the inapproximable results above, this implies that all the source location problems are Θ(ln ∑ _v∈V (d ⁺(v)+d ⁻(v)))-approximable. An extended abstract of this paper appeared in Sakashita et al. (Proceedings of LATIN 2006, Chile, LNCS, vol. 3887, pp. 769–780, March 2006).     

Living polymerization of hexaethylcyclotrisiloxane

Summary Living polymerization of hexaethylcyclotrisiloxane was achieved with nBuLi-(nBuO)₃PO at room temperature to produce living poly(diethylsiloxane). The molecular weight of the polymer increased in direct proportion to monomer conversion and to the reciprocal to the initial nBuLi concentration. Molecular weight distribution remained 1.1–1.2 during the polymerization. The polymerization was completed only after 1 day despite no solvent was used. When a compound containing SiOH groups was added to the polymerization system, the number of polymer chain agreed with a sum of nBuLi and SiOH groups. Received: 29 June 1999/Revised version: 23 August 1999/Accepted: 25 August 1999