Fuzzy minimum weight edge covering problem

Minimum weight edge covering problem, known as a classic problem in graph theory, is employed in many scientific and engineering applications. In the applications, the weight may denote cost, time, or opponent’s payoff, which can be vague in practice. This paper considers the edge covering problem under fuzzy environment, and formulates three models which are expected minimum weight edge cover model, α-minimum weight edge cover model, and the most minimum weight edge cover model. As an extension for the models, we respectively introduce the crisp equivalent of each model in the case that the weights are independent trapezoidal fuzzy variables. Due to the complexity of the problem, a hybrid intelligent algorithm is employed to solve the models, which can deal with the problem with any type of fuzzy weights. At last, some numerical experiments are given to show the application of the models and the robustness of the algorithm.     

Crown reductions for the Minimum Weighted Vertex Cover problem

The paper studies crown reductions for the Minimum Weighted Vertex Cover problem introduced recently in the unweighted case by Fellows et al. [Blow-Ups, Win/Win's and crown rules: some new directions in FPT, in: Proceedings of the 29th International Workshop on Graph Theoretic Concepts in Computer Science (WG’03), Lecture notes in computer science, vol. 2880, 2003, pp. 1-12, Kernelization algorithms for the vertex cover problem: theory and experiments, in: Proceedings of the Workshop on Algorithm Engineering and Experiments (ALENEX), New Orleans, Louisiana, January 2004, pp. 62-69]. We describe in detail a close relation of crown reductions to Nemhauser and Trotter reductions that are based on the linear programming relaxation of the problem. We introduce and study the so-called strong crown reductions, suitable for finding (or counting) all minimum vertex covers, or finding a minimum vertex cover under some additional constraints. It is described how crown decompositions and strong crown decompositions suitable for such problems can be computed in polynomial time. For weighted König-Egerváry graphs (G,w) we observe that the set of vertices belonging to all minimum vertex covers, and the set of vertices belonging to no minimum vertex covers, can be efficiently computed.Further, for some specific classes of graphs, simple algorithms for the MIN-VC problem with a constant approximation factor r<2 are provided. On the other hand, we conclude that for the regular graphs, or for the Hamiltonian connected graphs, the problem is as hard to approximate as for general graphs.It is demonstrated how the results about strong crown reductions can be used to achieve a linear size problem kernel for some related vertex cover problems.     

罗尔中值定理的一些新证法(英文)

给出了罗尔微分中值定理的三种新的证明方法,其中第二种很简便的方法仅依赖于大家熟知的Heine-Borel有限覆盖定理.由此可见罗尔微分中值定理可以是实数的完备性的直接推论.     

Variable Selection and Regularization in Quantile Regression via Minimum Covariance Determinant Based Weights

The importance of variable selection and regularization procedures in multiple regression analysis cannot be overemphasized. These procedures are adversely affected by predictor space data aberrations as well as outliers in the response space. To counter the latter, robust statistical procedures such as quantile regression which generalizes the well-known least absolute deviation procedure to all quantile levels have been proposed in the literature. Quantile regression is robust to response variable outliers but very susceptible to outliers in the predictor space (high leverage points) which may alter the eigen-structure of the predictor matrix. High leverage points that alter the eigen-structure of the predictor matrix by creating or hiding collinearity are referred to as collinearity influential points. In this paper, we suggest generalizing the penalized weighted least absolute deviation to all quantile levels, i.e., to penalized weighted quantile regression using the RIDGE, LASSO, and elastic net penalties as a remedy against collinearity influential points and high leverage points in general. To maintain robustness, we make use of very robust weights based on the computationally intensive high breakdown minimum covariance determinant. Simulations and applications to well-known data sets from the literature show an improvement in variable selection and regularization due to the robust weighting formulation.     

Minimum Divergence Estimators,Maximum Likelihood and the Generalized Bootstrap

This paper states that most commonly used minimum divergence estimators are MLEs for suited generalized bootstrapped sampling schemes. Optimality in the sense of Bahadur for associated tests of fit under such sampling is considered.     

Global X2A′ potential energy surface of Li2H and quantum dynamics of H + Li2 (X1Σg+) → Li + LiH (X1Σ+) reaction

A global potential energy surface (PES) for the electronic ground state of Li₂H system is constructed over a large configuration space. About 30 000 ab initio energy points have been calculated by MRCI‐F12 method with aug‐cc‐pVTZ basis set. The neural network method is applied to fit the PES and the root mean square error of the current PES is only 1.296 meV. The reaction dynamics of the title reaction has been carried out by employing time‐dependent wave packet approach with second order split operator on the new PES. The reaction probability, integral cross section and thermal rate constant are obtained from the dynamics calculation. In most of the collision energy regions, the integral cross sections are in well agreement with the results reported by Gao et al. The rate constant calculated from the new PES increases in the temperature range of present investigation.     

Some features of the buckling of stringer shells

A technique for stability analysis of stringer shells is proposed. It is used to analyze the minimum critical stresses. The dependence of the dimensionless parameters σ_cr/σ_cl on the number of stringers is plotted. The linear and nonlinear theories of ribbed shells are used to examine the features of how stringer shells lose stability. It is shown that the minimum critical stresses determined using the theory of ribbed shells and a structurally orthotropic model are close within the range of stiffness parameters considered __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 2, pp. 59–64, February 2006.     

浅谈电子天平的选择和使用

针对电子天平的选择、使用和维护中容易忽视的问题进行分析和阐述,并提出了解决办法和正确的操作规程。     

Optimal paths for a light-driven engine with a linear phenomenological heat transfer law

An irreversible light-driven engine is described in this paper, in which the heat transfer between the working fluid and the environment obeys a linear phenomenological heat transfer law [ q ∝Δ(T -1)], with a working fluid composed of the bimolecular reacting system 2SO 3 F■S 2 O 6 F2. Piston trajectories maximizing work output and minimizing entropy generation are determined for such an engine with rate-dependent loss mechanisms of friction and heat leakage. The optimal control theory is applied to determi...     

Generation and characterization of low‐energy structures in atomic clusters

Factors relevant for controlling the structures determined in the local optimization of argon clusters are investigated. In particular, the role of volume and shape for the box where initial structures are generated is assessed. A thorough characterization of the optimization is also presented, based on a nearest‐neighbor analysis, in clusters ranging from 30 to 55 atoms. This includes the assessment of the degree of preservation of aspects of the initial randomly generated structure in the final optimized counterpart, and the correlation between optimized energy and the number of nearest neighbors and average departure from the diatomic reference distance. The usefulness of this analysis to explore the energy landscape of atomic clusters is also highlighted. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010