In this paper we consider dynamic networks that can change over time. Often, such networks have a repetitive pattern despite constant and otherwise unpredictable changes. Based on this observation, we introduce the notion of a ρ-recurring family of a dynamic network, which has the property that the dynamic network frequently contains a graph in the family, where frequently means at a rate 0<ρ≤1...

Let H = −d/dx + V (x) be a Schrödinger operator on L2(0,∞) with spectral measure ρ, and suppose that the potential V is known on an initial interval [0, N ]. We show that this information yields strong restrictions on ρ(I) for intervals I ⊂ R. More precisely, we prove upper and lower bounds on ρ(I). The upper bound is finite for any I that is bounded above and the lower bound is positive if the...

Abstract We examine the eigenvalue spectrum, ρ(μ), of the adjacency matrix of a random scale-free network with an average of p edges per vertex using the replica method. We show how in the dense limit, when p → ∞, one can obtain two relatively simple coupled equations whose solution yields ρ(μ) for an arbitrary complex network. For scale-free graphs, with degree distribution exponent λ, we obta...

Given a stationary first-order autoregressive process X t (with lag-one correlation ρ satisfying |ρ| < 1), we examine the Central Limit Theorem for 1 n ln |X 1 · · · X n | and compute variances to high precision. Given a nonstationary process X t (with |ρ| > 1), we examine instead

abstract to optimal use of available water, irrigation scheduling is important to over scarcity of water resources in arid and semi-arid area. in this research to estimate of maximum allowable deficit (or: management allowed depletion) and irrigation scheduling of fodder mays based on canopy-air temperature difference, a field study was conducted in agricultural faculty of karaj. the lower limi...

The von Neumann entropy and the subentropy of a mixed quantum state are upper and lower bounds, respectively, on the accessible information of any ensemble consistent with the given mixed state. Here we define and investigate a set of quantities intermediate between entropy and subentropy. PACS numbers: 03.67.-a, 89.70.+c, 65.40.Gr 1 1 Entropy and subentropy The von Neumann entropy of a quantum...