Let G be a graph with vertex set V = V (G) and edge set E = E(G). The cardinalities of these sets are denoted by |V (G)| = n and |E(G)| = e. Let u and v be two distinct vertices of G. A path from u to v, also called an uv-path in G, is a subgraph P with vertex set V (P ) = {u = x0, x1, . . . , xr = v} and it is usually denoted by P : x0x1 · · ·xr. Two uv-paths P and Q are said to be internally ...

This work presents a contribution to the solution of the average agreement problem on a network with quantized links. Starting from the well-known linear diffusion algorithm, we propose a simple and effective adaptation which is able to preserve the average of states and to drive the system near to the consensus value, when a uniform quantization is applied to communication between agents. The ...

We discuss a method to estimate the confidence bounds for average economic growth, which is robust to misspecification of the unit root property of a given time series. We derive asymptotic theory for the consequences of such misspecification. Our empirical method amounts to an implementation of the bootstrapping procedure advocated in Romano and Wolf (2001). Simulation evidence supports the th...

The properties of spatial distribution of luminous matter are investigated analysing all the available three dimensional catalogues of galaxies. In standard view, galaxies are believed to have a fractal distribution at small scale with a crossover to an homogeneous one at large scale. However up to now, the quantitative determination of this presumed homogeneity scale is still lacking. Contrary...

The usual definition of average degree for a non-regular lattice has the disadvantage that it takes the same value for many lattices with clearly different connectivity. We introduce an alternative definition of average degree, which better separates different lattices. These measures are compared on a class of lattices and are analyzed using a Markov chain describing a random walk on the latti...