Graphs are fundamental data structures and have been em-ployed for centuries to model real-world systems and phe-nomena. Random walk with restart (RWR) provides a goodproximity score between two nodes in a graph, and it hasbeen successfully used in many applications such as auto-matic image captioning, recommender systems, and link pre-diction. The goal of this work is t...

The most primitive form of a stadium is a circle, say of radius r. If we separate the left and right halves of the circle slightly and connect these two semi circles at the top and bottom by straight lines we have a classical stadium (racetrack). Let a be the horizontal distance from the center of the figure to either the left or right semi circle; that is, the distance of each ‘straightaway’ i...

depiction of a solution space with several clusters Figure 2: Left: recursive counting by partitioning the solution space. Right: fragmentation of solution clusters. away the number of clusters in which x1 takes both values, 0 and 1. Thus, #clusters(F) = #clusters(F)|x1=0 + #clusters(F)|x1=1− #clusters(F)|x!=0&x1=1. The tricky part is to compute #clusters(F)|x1=v1 for any v1, as this no longer ...

We define tensor product decompositions of E0-semigroups with a structure analogous to a classical theorem of Beurling. Such decompositions can be characterized by adaptedness and exactness of unitary cocycles. For CCR-flows we show that such cocycles are convergent.

In the analysis of reactive systems a quantitative objective assigns a real value to every trace of the system. The value decision problem for a quantitative objective requires a trace whose value is at least a given threshold, and the exact value decision problem requires a trace whose value is exactly the threshold. We compare the computational complexity of the value and exact value decision...

It is proved that a discrete group G is exact if and only if its left translation action on the Stone-Čech compactification is amenable. Combining this with an unpublished result of Gromov, we have the existence of non exact discrete groups. In [KW], Kirchberg and Wassermann discussed exactness for groups. A discrete group G is said to be exact if its reduced group C-algebra C λ(G) is exact. Th...

The purpose of this work is to introduce the concept of pseudo-exactness for second-order linear ordinary differential equations (ODEs), and then to try to solve some specific ODEs. © 2011 Elsevier Ltd. All rights reserved.

Abstract Research surveys are important to evaluate fishery resources’ spatial distribution and abundance. Although the underlying sampling is usually conceived with a focus on specific species, efficient designs can also collect data secondary species. We present framework explore adequacy of alternative for research aiming maximize accuracy estimates species abundance while maintaining qualit...

For a class of two-point boundary value problems we prove exactness of S-shaped bifurcation curve. Our result applies to a problem from combustion theory, which involves nonlinearities like e for a > 0.

Mutual localization provides a consensus of reference frame as an essential basis for cooperation in multi-robot systems. Previous works have developed certifiable and robust solvers relative transformation estimation between each pair robots. However, recovering poses robotic swarm with partially mutual observations is still unexploited problem. In this letter, we present complete algorithm it...