Geographic Variation for the Composition of Parrotfish in the South China Sea

Based on the key ecological processes of parrotfish in coral reefs, we compiled species presence-absence data across 51 sites in the South China Sea to identify the distribution and composition of parrotfish and explore the relationship between species distribution and environmental factors, and 50 species (the Pacific: 57 species) of parrotfish were record. Nansha islands had the highest abundance with 41 parrotfish species. Nestedness analysis indicated parrotfish community had statistically significant nested patterns in the South China Sea and Nansha islands was the topmost site of nested matrix rank. Scleractinian coral species richness and Log(reef area) both had a significant effect on sites nested matrix rank (P < 0.05), which supports habitat nestedness hypothesis in the South China Sea. Scrapers were the most important functional group composition while the browser had a greater contribution on species nested matrix rank. Linear regression model showed parrotfish species richness increased with increasing longitude, scleractinian coral species richness and reef area. Variations in the parrotfish species richness in longitude was related to distance from the biodiversity hotspot in the Indo-Australian Archipelago. Parrotfish was mainly distributed in the range of 26-29℃, which was almost the same as the optimum temperature for coral growth. Nansha islands should be as biodiversity conservation priority areas, which could provide important reference significance for conservation efforts of parrotfish in degraded coral reefs habitats, especially in the context of increasing natural variability and anthropogenic disturbance.

Enhancing performance in a LOS MIMO communication using a passive repeater

This paper presents a technique for obtaining a well-conditioned channel matrix in a line of sight multiple input multiple output (MIMO) environment. The technique is based on the implementation of a back-to-back antenna system as a passive repeater to enhance performance in MIMO systems. The flexible configuration with no need for a phase controller allows to spread the proposed repeater in MIMO communications to ensure spatial multiplexing and enhance capacity. A condition number and matrix rank are proposed as metrics to demonstrate the validity of the proposed method.

A Note on Simulating Predecessor-Successor Relationships in Critical Path Models

For any n entities, we exhaust all possible ordered relationships, from rank (or the highest number of connections in a linear chain, comparable to matrix rank) 0 to (n - 1). As an example, we use spreadsheets with the “RAND” function to simulate the case of n = 8 with the order-length = 3, as from a total of 10000possibilities by the number of combinations of selecting 2 (a pair of predecessor-successor) out of 5 (= card{A, B, C, D} + 1) matching- destinations followed by an exponentiation of 4 (= 8 – card{A, B, C, D}). Since the essence of this paper is about ordered structures of networks, our findings here may serve multi-disciplinary interests, in particular, that of the critical path method (CPM) in operations with management. In this connection, we have also included, toward the end of this exposition, a linear algebraic treatment that renders a deterministic mathematical programming for optimal predecessor-successor network structures.

A Note on a Lower Bound on the Minimum Rank of a Positive Semidefinite Hankel Matrix Rank Minimization Problem

This paper investigates the problem of approximating the global minimum of a positive semidefinite Hankel matrix minimization problem with linear constraints. We provide a lower bound on the objective of minimizing the rank of the Hankel matrix in the problem based on conclusions from nonnegative polynomials, semi-infinite programming, and the dual theorem. We prove that the lower bound is almost half of the number of linear constraints of the optimization problem.