Two sensors obtain data vectors x and y, respectively, and transmit real vectors mri(z) and rm 2 (y), respectively, to a fusion center. We obtain tight lower bounds on the number of messages (the sumI of the dimensions of mil and r1 2) that have to be transmitted for the fusion center to be able to evaluate a given function fxI, y). When the function f is linear, we show that these bounds are e...

This paper considers a model for cascades on random networks in which the cascade propagation at any node depends on the load at the failed neighbor, the degree of the neighbor as well as the load at that node. Each node in the network bears an initial load that is below the capacity of the node. The trigger for the cascade emanates at a single node or a small fraction of the nodes from some ex...

A few matrix-vector multiplications with random vectors are often sufficient to obtain reasonably good estimates for the norm of a general matrix or trace symmetric positive semi-definite matrix. Several such probabilistic estimators have been proposed and analyzed standard Gaussian Rademacher vectors. In this work, we consider use rank-one vectors, that is, Kronecker products (smaller) It is n...

We discuss in this paper the strong convergence for weighted sums of negatively orthant dependent (NOD) random variables by generalized Gaussian techniques. As a corollary, a Cesaro law of large numbers of i.i.d. random variables is extended in NOD setting by generalized Gaussian techniques.

In this paper, we study a first order random coefficient autoregressive model with Laplace distribution as marginal. A random coefficient moving average model of order one with Laplace as marginal distribution is introduced and its properties are studied. By combining the two models, we develop a first order random coefficient autoregressive moving average model with Laplace marginal and discus...