We study the average consensus problem of multi-agent systems for general network topologies with unidirectional information flow. We propose two (linear) distributed algorithms, deterministic and gossip, respectively for the cases where the inter-agent communication is synchronous and asynchronous. Our contribution is that in both cases, the developed algorithms guarantee state averaging on ar...

The eccentricity of a vertex is the maximum distance from it to another vertex and the average eccentricity ecc(G) of a graph G is the mean value of eccentricities of all vertices of G. In this paper we resolve five conjectures, obtained by the system AutoGraphiX, about the average eccentricity and other graph parameters (independence number, chromatic number and the Randić index), and refute t...

Given a linear system, we consider the expected energy to move from the origin to a uniformly random point on the unit sphere as a function of the set of actuated variables. We show this function is not necessarily supermodular, correcting some claims in the existing literature.

The two-parameter exponential distribution can often be used to describe the lifetime of products for example, electronic components, engines and so on. This paper considers a prediction problem arising in the life test of key parts in high speed trains. Employing the Bayes method, a joint prior is used to describe the variability of the parameters but the form of the prior is not specified and...

For an elliptic curve E over Q and an integer r let πr E(x) be the number of primes p ≤ x of good reduction such that the trace of the Frobenius morphism of E/Fp equals r. We consider the quantity π r E(x) on average over certain sets of elliptic curves. More in particular, we establish the following: If A,B > x1/2+ε and AB > x3/2+ε, then the arithmetic mean of πr E(x) over all elliptic curves ...

It is often claimed that instantaneous frequency, taken as the derivative of the phase of the signal, is appropriate or meaningful only for mono-component signals, and that for multi-component signals a weighted average of individual instantaneous frequencies should be used. In this paper, we show if a signal is decomposed adaptively and we compute the matching pursuit distribution, then the fi...

Not all rational numbers are possibilities for the average genus of an individual graph. The smallest such numbers are determined. and varied examples are constructed to demonstrate that a single value of average genus can be shared by arbitrarily many different graphs. It is proved that the number one is a limit point of the set of possible values for average genus and that the complete graph ...

In this paper, we discuss the complexity and properties of the sets which are computable in polynomial-time on average. This study is motivated by Levin's question of whether all sets in NP are solvable in polynomial-time on average for every reasonable (i.e., polynomial-time computable) distribution on the instances. Let PP-comp denote the class of all those sets which are computable in polyno...

In many practical situations, we know only the intervals which contain the actual (unknown) values of physical quantities. If we know the intervals x for a quantity x and y for another quantity y, then, for every arithmetic operation , the set of possible values of x y also forms an interval; the operations leading from x and y to this new interval are called interval arithmetic operations. For...