The Impact of Sensing Range on Spatial-Temporal Opportunity

In this paper, we study the impact of secondary user (SU) sensing range on spectrum access opportunity in cognitive radio networks. We first derive a closed-form ex- pression of spectrum access opportunity by taking into ac- count the random variations in number, locations and trans- mitted powers of primary users (PUs). Then, we show how SU sensing range affects spectrum access opportunity, and the tradeoff between SU sensing range and spectrum ac- cess opportunity is formulated as an optimization problem to maximize spectrum access opportunity. Furthermore, we prove that there exists an optimal SU sensing range which yields the maximum spectrum access opportunity, and nu- merical results validate our theoretical analysis

Four Variations on Graded Posets

We explore the enumeration of some natural classes of graded posets, including all graded posets, (2+2)- and (3+1)-avoiding graded posets, (2+2)-avoiding graded posets, and (3+1)-avoiding graded posets. We obtain enumerative and structural theorems for all of them. Along the way, we discuss a situation when we can switch between enumeration of labeled and unlabeled objects with ease, generalize a result of Postnikov and Stanley from the theory of hyperplane arrangements, answer a question posed by Stanley, and see an old result of Klarner in a new light.Comment: 28 page

A Comment on "Memory Effects in an Interacting Magnetic Nanoparticle System"

Recently, Sun et al reported that striking memory effects had been clearly observed in their new experiments on an interacting nanoparticle system [1]. They claimed that the phenomena evidenced the existence of a spin-glass-like phase and supported the hierarchical model. No doubt that a particle system may display spin-glass-like behaviors [2]. However, in our opinion, the experiments in Ref. [1] cannot evidence the existence of spin-glass-like phase at all. We will demonstrate below that all the phenomena in Ref. [1] can be observed in a non-interacting particle system with a size distribution. Numerical simulations of our experiments also display the same features.Comment: A comment on "Phys. Rev. Lett. 91, 167206