K终端可靠度分解算法中多边形→链简化定理的完善

无向网络K终端可靠度的分解算法中,包括多边形→链简化在内的等可靠度简化和分解定理结合,可以降低算法的复杂度。本文完善了边随机无向网络和混合随机无向网络的4#,6#,7#型多边形→链简化定理。计算机编程验证了其正确性。     

Improving the training time of support vector regression algorithms through novel hyper-parameters search space reductions

The selection of hyper-parameters in support vector machines (SVM) is a key point in the training process of these models when applied to regression problems. Unfortunately, an exact method to obtain the optimal set of SVM hyper-parameters is unknown, and search algorithms are usually applied to obtain the best possible set of hyper-parameters. In general these search algorithms are implemented as grid searches, which are time consuming, so the computational cost of the SVM training process increases considerably. This paper presents a novel study of the effect of including reductions in the range of SVM hyper-parameters, in order to reduce the SVM training time, but with the minimum possible impact in its performance. The paper presents reduction in parameter C, by considering its relation with the rest of SVM hyper-parameters (γ and ε), through an approximation of the SVM model. On the other hand, we use some characteristics of the Gaussian kernel function and a previous result in the literature to obtain novel bounds for γ and ε hyper-parameters. The search space reductions proposed are evaluated in different regression problems from UCI and StatLib databases. All the experiments carried out applying the popular LIBSVM solver have shown that our approach reduces the SVM training time, maintaining the SVM performance similar to when the complete range in SVM parameters is considered.     

Error function scheme for Burgers' equation

The present paper is devoted to the development of a new scheme to solve the one-dimensional time-dependent Burgers' equation locally on sub-domains, using similarity reductions for partial differential equations. Each sub-domain is divided into three grid points. The ordinary differential equation deduced from the similarity reduction can be integrated and is then used to approximate the flux vector in the Burgers' equation. The arbitrary constants in the analytical solution of the similarity equation can be determined in terms of the dependent variables at the grid points in each sub-domain. This approach eliminates the difficulties associated with boundary conditions for the similarity reductions over the whole solution domain. Numerical results are obtained for two different test cases and are compared with other numerical results.     

未再结晶区控轧工艺对HQ60钢的显微组织与力学性能的影响

研究了未再结晶区的不同压下率对含Ｎｂ－Ｖｉ的ＨＱ６０低合金钢的组织和性能的影响。结果表明，当未再结晶区的累计压下率由４０％提高到７０％时，ＨＱ６０钢的晶粒由４．８５μｍ细化到２．７７μｍ，强度和韧性都有较大提高，使得这种由铁素体、贝氏体和珠光体等复相组织组成的钢的强韧性得到了改善。     

An Explicit Lower Bound for TSP with Distances One and Two

Abstract. We show that, for any ɛ>0 , it is NP-hard to approximate the asymmetric traveling salesman problem with distances one and two within 2805/2804-ɛ . For the special case where the distance function is constrained to be symmetric, we show a lower bound of 5381/5380-ɛ , for any ɛ>0 . While it was previously known that there exists some constant, strictly greater than one, such that it is NP-hard to approximate the traveling salesman problem with distances one and two within that constant, this result is a first step towards the establishment of a good bound. In our proof we develop a new gadget construction to reduce from systems of linear equations mod 2 with two unknowns in each equation and at most three occurrences of each variable. Compared with earlier reductions to the traveling salesman problem with distances one and two, ours reduces the number of cities to less than a tenth of what was previously necessary.     

The problem of guaranteeing the absence of a complete set of reductions

This article is the twelfth of a series of articles discussing various open research problems in automated reasoning. Here we focus on finding criteria for guaranteeing the absence of a complete set of reductions. We include a suggestion for evaluating a proposed solution to this research problem.This work was supported by the Applied Mathematical Sciences subprogram of the Office of Energy Research, U.S. Department of Energy, under Contract W-31-109-Eng-38.     

Saving Space by Fully Exploiting Invisible Transitions

Checking that a given finite state program satisfies a linear temporal logic property suffers from the state explosion problem. Often the resulting lack of available memory is more significant than any time limitations. One way to cope with this is to reduce the state graph used for model checking. We present an algorithm for constructing a state graph that is a projection of the program's state graph. The algorithm maintains the transitions and states that affect the truth of the property to be checked. Especially in conjunction with known partial order reduction algorithms, we show a substantial reduction in memory over using partial order methods alone, both in the precomputation stage, and in the result presented to a model checker. The price of the space reduction is a single additional traversal of the graph obtained with partial order reduction. As part of our space-saving methods, we present a new way to exploit Holzmann's Bit Hash Table, which assists us in solving the revisiting problem.