Cross-impact analysis is a method for revising estimated probabilities of future events in terms of estimated interactions among those events. This Report presents anelementary cross-impact model where the cross-impacts are formulated as relativeprobabilities. Conditions are derived for the consistency of the matrix of relative probabilities of n events. An extension also provides a nec...

Let G = (V,E) be a connected graph (or hypergraph) and let d(x, y) denote the distance between vertices x, y ∈ V (G). A subset W ⊆ V (G) is called a resolving set for G if for every pair of distinct vertices x, y ∈ V (G), there is w ∈ W such that d(x,w) 6= d(y, w). The minimum cardinality of a resolving set for G is called the metric dimension of G, denoted by β(G). The circulant graph Cn(1, 2,...

A novel phase interferometer method based on virtual baseline is proposed for technical difficulty in resolving angle ambiguity and antenna layout. In this method, only two baselines are set to solve the problem of angle ambiguity. In high noise areas, there are large numbers of outliers which lead to angle error in the measured data, and a way to detect and eliminate the outliers is applied to...

The drive toward more sensitive single-molecule manipulation techniques has led to the recent development of optical tweezers capable of resolving the motions of biological systems at the subnanometer level, approaching the fundamental limit set by Brownian fluctuations. One successful approach has been the dual-trap optical tweezers, in which the system of study is held at both ends by microsp...

A set S ⊆ V (G) is a restrained strong resolving hop dominating in G if for every v ∈ (G)\S, there exists w such that dG(v, w) = 2 and or (G)\S has no isolated vertex. The smallest cardinality of set, denoted by γrsRh(G), called the domination number G. In this paper, we obtained corresponding parameter graphs resulting from join, corona lexicographic product two graphs. Specifically, character...

We show that the greedy spanner algorithm constructs a (1+ )-spanner of weight −O(d)w(MST) for a point set in metrics of doubling dimension d, resolving an open problem posed by Gottlieb [11]. Our result generalizes the result by Narasimhan and Smid [15] who showed that a point set in d-dimension Euclidean space has a (1+ )-spanner of weight at most −O(d)w(MST). Our proof only uses the packing ...

A novel declarative approach of forgetting in answer set programming (ASP) has been proposed recently. In this paper we report a system prototype of forgetting in ASP, called LPForget. It consists of two modules: (1) Forgetting: computing the result of forgetting about certain literals in logic program under the answer set semantics; (2) CRS: application of forgetting in resolving conflict (or ...

We introduce a framework for finding preference information to derive desired conclusions in nonmonotonic reasoning. A new abductive framework called preference abduction enables us to infer an appropriate set of priorities to explain the given observation skeptically, thereby resolving the multiple extension problem in the answer set semantics for extended logic programs. Preference abduction ...

We introduce a new class of rules for resolving quasilinear social choice problems. These rules extend those of Green [6]. We call such rules multi-utilitarian rules. Each multi-utilitarian rule is associated with a probability measure over the set of weighted utilitarian rules, and is derived as the expectation of this probability. These rules are characterized by the axioms efficiency, transl...

Resolving parameters are a fundamental area of combinatorics with applications not only to many branches but also other sciences. In this study, we construct class Toeplitz graphs and will be denoted by T 2 n W ...