On the Triality Theory for a Quartic Polynomial Optimization Problem

This paper presents a detailed proof of the triality theorem for a class of fourth-order polynomial optimization problems. The method is based on linear algebra but it solves an open problem on the double-min duality left in 2003. Results show that the triality theory holds strongly in a tri-duality form if the primal problem and its canonical dual have the same dimension; otherwise, both the canonical min-max duality and the double-max duality still hold strongly, but the double-min duality holds weakly in a symmetrical form. Four numerical examples are presented to illustrate that this theory can be used to identify not only the global minimum, but also the largest local minimum and local maximum.Comment: 16 pages, 1 figure; J. Industrial and Management Optimization, 2011. arXiv admin note: substantial text overlap with arXiv:1104.297

Opportunistic Relaying in Time Division Broadcast Protocol with Incremental Relaying

In this paper, we investigate the performance of time division broadcast protocol (TDBC) with incremental relaying (IR) when there are multiple available relays. Opportunistic relaying (OR), i.e., the “best” relay is select for transmission to minimize the system’s outage probability, is proposed. Two OR schemes are presented. The first scheme, termed TDBC-OIR-I, selects the “best” relay from the set of relays that can decode both flows of signal from the two sources successfully. The second one, termed TDBC-OIR-II, selects two “best” relays from two respective sets of relays that can decode successfully each flow of signal. The performance, in terms of outage probability, expected rate (ER), and diversity-multiplexing tradeoff (DMT), of the two schemes are analyzed and compared with two TDBC schemes that have no IR but OR (termed TDBC-OR-I and TDBC-OR-II accordingly) and two other benchmark OR schemes that have no direct link transmission between the two sources

Acoustic detection of air shower cores

At an altitude of 1890m, a pre-test with an Air shower (AS) core selector and a small acoustic array set up in an anechoic pool with a volume of 20x7x7 cu m was performed, beginning in Aug. 1984. In analyzing the waveforms recorded during the effective working time of 186 hrs, three acoustic signals which cannot be explained as from any source other than AS cores were obtained, and an estimation of related parameters was made

Self-organizing nonlinear output (SONO): A neural network suitable for cloud patch-based rainfall estimation at small scales

Accurate measurement of rainfall distribution at various spatial and temporal scales is crucial for hydrological modeling and water resources management. In the literature of satellite rainfall estimation, many efforts have been made to calibrate a statistical relationship (including threshold, linear, or nonlinear) between cloud infrared (IR) brightness temperatures and surface rain rates (RR). In this study, an automated neural network for cloud patch-based rainfall estimation, entitled self-organizing nonlinear output (SONO) model, is developed to account for the high variability of cloud-rainfall processes at geostationary scales (i.e., 4 km and every 30 min). Instead of calibrating only one IR-RR function for all clouds the SONO classifies varied cloud patches into different clusters and then searches a nonlinear IR-RR mapping function for each cluster. This designed feature enables SONO to generate various rain rates at a given brightness temperature and variable rain/no-rain IR thresholds for different cloud types, which overcomes the one-to-one mapping limitation of a single statistical IR-RR function for the full spectrum of cloud-rainfall conditions. In addition, the computational and modeling strengths of neural network enable SONO to cope with the nonlinearity of cloud-rainfall relationships by fusing multisource data sets. Evaluated at various temporal and spatial scales, SONO shows improvements of estimation accuracy, both in rain intensity and in detection of rain/no-rain pixels. Further examination of the SONO adaptability demonstrates its potentiality as an operational satellite rainfall estimation system that uses the passive microwave rainfall observations from low-orbiting satellites to adjust the IR-based rainfall estimates at the resolution of geostationary satellites. Copyright 2005 by the American Geophysical Union