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81.
Jan Johannsen 《Mathematical Logic Quarterly》1998,44(2):205-215
We define a property of substructures of models of arithmetic, that of being length-initial, and show that sharply bounded formulae are absolute between a model and its length-initial submodels. We use this to prove independence results for some weak fragments of bounded arithmetic by constructing appropriate models as length-initial submodels of some given model. 相似文献
82.
证明了任意2-连通图G,对于其每一个顶点来说,与它距离为2的顶点集在G中的独立数为1,则G是Hamilton图。 相似文献
83.
Jian Xu Qing-Song Xu Chi-On Chan Daniel Kam-Wah Mok Lun-Zhao Yi Foo-Tim Chau 《Analytica chimica acta》2015
Bioactive component identification is a crucial issue in search for new drug leads. We provide a new strategy to search for bioactive components based on Sure Independence Screening (SIS) and interval PLS (iPLS). The method, which is termed as SIS–iPLS, is not only able to find out the chief bioactive components, but also able to judge how many components should be there responsible for the total bioactivity. The method is totally “data-driven” with no need for prior knowledge about the unknown mixture analyzed, therefore especially suitable for effect-directed work like bioassay-guided fractionation. Two data sets, a synthetic mixture system of twelve components and a suite of Radix Puerariae Lobatae extracts samples, are used to test the identification ability of the SIS–iPLS method. 相似文献
84.
85.
86.
Variable neighborhood search for extremal graphs. 21. Conjectures and results about the independence number 总被引:1,自引:0,他引:1
Mustapha Aouchiche Gunnar Brinkmann Pierre Hansen 《Discrete Applied Mathematics》2008,156(13):2530-2542
A set of vertices S in a graph G is independent if no neighbor of a vertex of S belongs to S. The independence number α is the maximum cardinality of an independent set of G. A series of best possible lower and upper bounds on α and some other common invariants of G are obtained by the system AGX 2, and proved either automatically or by hand. In the present paper, we report on such lower and upper bounds considering, as second invariant, minimum, average and maximum degree, diameter, radius, average distance, spread of eccentricities, chromatic number and matching number. 相似文献
87.
《Discrete Mathematics》2019,342(12):111607
We prove an upper bound for the independence number of a graph in terms of the largest Laplacian eigenvalue, and of a certain induced subgraph. Our bound is a refinement of a well-known Hoffman-type bound. 相似文献
88.
Fabio G. Cozman 《International Journal of Approximate Reasoning》2013,54(9):1261-1278
This paper examines concepts of independence for full conditional probabilities; that is, for set-functions that encode conditional probabilities as primary objects, and that allow conditioning on events of probability zero. Full conditional probabilities have been used in economics, in philosophy, in statistics, in artificial intelligence. This paper characterizes the structure of full conditional probabilities under various concepts of independence; limitations of existing concepts are examined with respect to the theory of Bayesian networks. The concept of layer independence (factorization across layers) is introduced; this seems to be the first concept of independence for full conditional probabilities that satisfies the graphoid properties of Symmetry, Redundancy, Decomposition, Weak Union, and Contraction. A theory of Bayesian networks is proposed where full conditional probabilities are encoded using infinitesimals, with a brief discussion of hyperreal full conditional probabilities. 相似文献
89.
Antoni Marczyk 《Discrete Mathematics》2009,309(11):3588-3594
Let G be a graph of order n and r, 1≤r≤n, a fixed integer. G is said to be r-vertex decomposable if for each sequence (n1,…,nr) of positive integers such that n1+?+nr=n there exists a partition (V1,…,Vr) of the vertex set of G such that for each i∈{1,…,r}, Vi induces a connected subgraph of G on ni vertices. G is called arbitrarily vertex decomposable if it is r-vertex decomposable for each r∈{1,…,n}.In this paper we show that if G is a connected graph on n vertices with the independence number at most ⌈n/2⌉ and such that the degree sum of any pair of non-adjacent vertices is at least n−3, then G is arbitrarily vertex decomposable or isomorphic to one of two exceptional graphs. We also exhibit the integers r for which the graphs verifying the above degree-sum condition are not r-vertex decomposable. 相似文献
90.
Denis Cornaz 《Mathematical Programming》2006,105(2-3):329-344
Let G be a simple undirected graph with node set V(G) and edge set E(G). We call a subset independent if F is contained in the edge set of a complete multipartite (not necessarily induced) subgraph of G, F is dependent otherwise. In this paper we characterize the independents and the minimal dependents of G. We note that every minimal dependent of G has size two if and only if G is fan and prism-free. We give a 0-1 linear programming formulation of the following problem: find the maximum weight of
a complete multipartite subgraph of G, where G has nonnegative edge weights. This formulation may have an exponential number of constraints with respect to |V(G)| but we show that the continuous relaxation of this 0-1 program can be solved in polynomial time. 相似文献