Given a sequence of non-negative real numbers 0 ; 1 ; : : : which sum to 1, we consider random graphs having approximately i n vertices of degree i. Essentially, we show that if P i(i \Gamma 2) i ? 0 then such graphs almost surely have a giant component, while if P i(i \Gamma 2) i ! 0

from this exploratory investigation are: (1) in estimating models of the expected market return, the non-negativity restriction of the expected excess return should be explicitly included as part of the specification; (2) estimators which use realized returns should be adjusted for heteroscedasticity.

with loops (undirected cycles). The algorithm is an exact inference algorithm for singly connected networks -the beliefs converge to the cor rect marginals in a number of iterations equal to the diameter of the graph.1 However, as Pearl noted, the same algorithm will not give the correct beliefs for mul

Turing-computable issue is important in research of Turing Machine and has significant value in both theory and practice. The paper analyzes Turing-computable issue of non-negative numbers by relational operations(includes greater than, less than and equal) and arithmetic operations(includes add

Abstract. If β> 1, then every non-negative number x has a β-expansion, i.e., x = 0(x) +

We present a probabilistic model for learning non-negative tensor factorizations (NTF), in which the tensor factors are latent variables associated with each data dimension. The non-negativity constraint for the latent factors is handled by choosing priors with support on the non-negative numbers

Abstract. Necessary conditions are derived for a rank-r tensor to be a best rank-r approximation of a given tensor. It is shown that a positive tensor with rank> 1 has a unique rank one approximation, and that a non negative tensor generally has a unique low-rank nonnegative approximate. We

1 Introduction Consider a complete graph G(V; E) with node set V = fv1; v2; : : : ; vn g. In the problem which we consider, both edges and nodes are assigned numbers to reflect their lengths and weights. Associated with each edge (vi; vj) is a non-negative number d(i; j) that represents its length

. Assuming that the quadratic module of all such sums is archimedean, we establish a local-global condition for f to have such a representation, vis-à-vis the zero set of f in K. This criterion is most useful when f has only finitely many zeros in K. We present a number of concrete situations where

In this work we apply non-negative matrix factorizations (NMF) to some imaging and inverse problems. We propose a sparse low-rank approximation of big data and images in terms of tensor products, and investigate its effectiveness in terms of the number of tensor products to be used