Note on Max Lin-2 above Average

In the Max Lin-2 problem we are given a system S of m linear equations in n variables over F₂ in which equation j is assigned a positive integral weight wj for each j. We wish to find an assignment of values to the variables which maximizes the total weight of satisfied equations. This problem generalizes Max Cut. The expected weight of satisfied equations is W/2, where W=w₁+?+wm; W/2 is a tight lower bound on the optimal solution of Max Lin-2.Mahajan et al. (Parameterizing above or below guaranteed values, J. Comput. Syst. Sci. 75 (2009) 137-153) stated the following parameterized version of Max Lin-2: decide whether there is an assignment of values to the variables that satisfies equations of total weight at least W/2+k, where k is the parameter. They asked whether this parameterized problem is fixed-parameter tractable, i.e., can be solved in time f(k)(nm)^O(1), where f(k) is an arbitrary computable function in k only. Their question remains open, but using some probabilistic inequalities and, in one case, a Fourier analysis inequality, Gutin et al. (A probabilistic approach to problems parameterized above tight lower bound, in: Proc. IWPEC'09, in: Lect. Notes Comput. Sci., vol. 5917, 2009, pp. 234-245) proved that the problem is fixed-parameter tractable in three special cases.In this paper we significantly extend two of the three special cases using only tools from combinatorics. We show that one of our results can be used to obtain a combinatorial proof that another problem from Mahajan et al. (Parameterizing above or below guaranteed values, J. Comput. Syst. Sci. 75 (2009) 137-153), Max r-SAT above Average, is fixed-parameter tractable for each r?2. Note that Max r-SAT above Average has been already shown to be fixed-parameter tractable by Alon et al. (Solving MAX-r-SAT above a tight lower bound, in: Proc. SODA 2010, pp. 511-517), but the paper used the approach of Gutin et al. (A probabilistic approach to problems parameterized above tight lower bound, in: Proc. IWPEC'09, in: Lect. Notes Comput. Sci., vol. 5917, 2009, pp. 234-245).     

Saccharomyces cerevisiae protein phosphatase Ppz1 and protein kinases Sat4 and Hal5 are involved in the control of subcellular localization of Gln3 by likely regulating its phosphorylation state

A Saccharomyces cerevisiae mutant lacking PPZ1, encoding a serine/threonine protein phosphatase (PPase), is caffeine-sensitive. To clarify the function of Ppz1 in resistance to caffeine, we attempted systematically to identify protein kinase (PKase) whose disruption lead to suppression of caffeine sensitive phenotype of the ?ppz1 disruptant since disruption of PPZ1 might cause caffeine sensitivity by increasing its phosphorylated substrates and we presumed that disruption of genes for PKase sharing the substrate with Ppz1 could restore the resistance through bypassing necessity for dephosphorylation of substrates. Among the 102 viable pkase disruptions, disruption of either SAT4 or HAL5 suppressed the caffeine sensitivity phenotype and increased expression of ENA1, encoding a P-type ATPase of the ?ppz1 disruptant. Because increased expression of ENA1 in the ?ppz1 disruptant was found to be suppressed by disruption of GLN3, localization and phosphorylation of Gln3 in the ?ppz1 disruptant was compared to that in the ?ppz1?sat4 and ?ppz1?hal5 double disruptants. Gln3 was found to accumulate in the nucleus in the ?ppz1 disruptant, and this nuclear localization was abolished by disruption of either SAT4 or HAL5. Interestingly, the level of Gln3 phosphorylation in the ?ppz1?sat4 and ?ppz1?hal5 disruptants decreased relative to wild type independent of caffeine. From these observations, we conclude that Ppz1 controls Gln3 localization by regulating its phosphorylation state in combination with Sat4 and Hal5.     

在CAD平台上构筑三维实体矿模技术

论述了在Auto CAD平台上用ACIS技术构建三维矿体模型的技术方法,并详细剖析了Sat文件的格式与特点。     

A novel process for the synthesis of unsaturated polyester

Traditionally polyester production is done in a batch reactor equipped with a separation column for a batch distillation. A promising alternative for the intensification of this process is reactive distillation. The aim of this paper is to study the conceptual design of reactive distillation and to find out whether reactive distillation is potentially interesting compared to batch reactor process. Therefore, a reactive distillation model is developed and sensitivity analysis is used to obtain the design and operational parameters for the reactive distillation process. These parameters are the required number of stages, required residence time, feed ratio, reflux ratio and temperature of feed stream. The model predicts the polymer attribute, isomerization and saturation composition of the polymer in the range of industrial polyester production data. The simulation study shows that the total production time of polyester in a continuous reactive distillation system is reduced from 12 h to 1.5-2 h compared to the industrial batch reactor process. The equilibrium conversion is also raised by 7% compared to the conventional process. The model demonstrated that reactive distillation has the potential to intensify the process by factor of 6-8 in comparison to the batch reactor.     

GD-SAT model and crossover line

In the last decade a lot of effort has been invested into both theoretical and experimental analysis of SAT phase transition. However, a deep theoretical understanding of this phenomenon is still lacking. It is still a very challenging problem to determine a relationship between crossover points for different SAT problems. This paper introduces one new class of randomly generated SAT problems, GD-SAT, and we experimentally show there is a phase transition for the problems in this class. On the basis of both analytical and experimental arguments we conjecture that there is a surprisingly simple, linear relationship between crossover points for problems in this class. This relationship is of both theoretical and practical importance.