one of the generalizations of the wiener number to weighted graphs is to assign probabilities to edges, meaning that in nonstatic conditions the edge is present only with some probability. the reliability wiener number is defined as the sum of reliabilities among pairs of vertices, where the reliability of a pair is the reliability of the most reliable path. closed expressions are derived for t...

molecules are the basic and most important players of life. molecules are composed of atoms, and each molecule has two main specifications or inheritances that are structures, and in biomedical applications, biological function. this dichotomy can be compared to living organisms or humans whom possess genotype and phenotype. each of the two main inherited elements contains a variety of feature ...

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Let $A$ and $B$ be two disjoint subsets of the vertex set $V$ of a graph $G$. The set $A$ is said to dominate $B$, denoted by $A rightarrow B$, if for every vertex $u in B$ there exists a vertex $v in A$ such that $uv in E(G)$. For any graph $G$, a partition $pi = {V_1,$ $V_2,$ $ldots,$ $V_p}$ of the vertex set $V$ is an textit{upper domatic partition} if $V_i rightarrow V_j$ or $V_j rightarrow...

case performance bounds for simple one-dimensional packing algorithms. SIAM J. A better algorithm for an ancient scheduling problem. Analysis of several task-scheduling algorithms for a model of multiprogramming computer systems. A new algorithm for on-line bin-packing. 44 43] G. Galambos and J. B. G. Frenk. A simple proof of Liang's lower bound for on-line bin packing and the extension to the ...

dynamical systems [Curto et al., 2009] or probabilistic frameworks in which variability is modelled as stochastic and correlated variability arises through abstract latent variables whose origin is assumed to lie either in unspecified circuit processes [Ecker et al., 2014, Macke et al., 2011, Pachitariu et al., 2013] or elsewhere in the brain [Goris et al., 2014, de la Rocha et al., 2007]. Whil...

It is well known fact that binary relations are generalized mathematical functions. Contrary to functions from domain to range, binary relations may assign to each element of domain two or more elements of range. Some basic operations on functions such as the inverse and composition are applicable to binary relations as well. Depending on the domain or range or both are fuzzy value fuzzy set, i...

One of the generalizations of the Wiener number to weighted graphs is to assign probabilities to edges, meaning that in nonstatic conditions the edge is present only with some probability. The Reliability Wiener number is defined as the sum of reliabilities among pairs of vertices, where the reliability of a pair is the reliability of the most reliable path. Closed expressions are derived for t...

Molecules are the basic and most important players of life. Molecules are composed of atoms, and each molecule has two main specifications or inheritances that are structures, and in biomedical applications, biological function. This dichotomy can be compared to living organisms or humans whom possess genotype and phenotype. Each of the two main inherited elements contains a variety of feat...