Maximal Area Triangles in a Convex Polygon

The widely known linear time algorithm for computing the maximum area triangle in a convex polygon was found incorrect recently by Keikha et. al.(arXiv:1705.11035). We present an alternative algorithm in this paper. Comparing to the only previously known correct solution, ours is much simpler and more efficient. More importantly, our new approach is powerful in solving related problems

A Generic Position Based Method for Real Root Isolation of Zero-Dimensional Polynomial Systems

We improve the local generic position method for isolating the real roots of a zero-dimensional bivariate polynomial system with two polynomials and extend the method to general zero-dimensional polynomial systems. The method mainly involves resultant computation and real root isolation of univariate polynomial equations. The roots of the system have a linear univariate representation. The complexity of the method is $\tilde{O}_B(N^{10})$ for the bivariate case, where $N=\max(d,\tau)$, $d$ resp., $\tau$ is an upper bound on the degree, resp., the maximal coefficient bitsize of the input polynomials. The algorithm is certified with probability 1 in the multivariate case. The implementation shows that the method is efficient, especially for bivariate polynomial systems.Comment: 24 pages, 5 figure

Composition and growth effects of the current account: a synthesized portfolio view

This paper analyzes a useful accounting framework that breaks down the current account to two components: a composition effect and a growth effect. We show that past empirical evidence, which strongly supports the growth-eect as the main driver of current account dynamics, is mis- conceived. The remarkable empirical success of the growth eect is driven by the dominance of the cross-sectional variation, which, under conditions met by the data, is generated by an accounting approximation. In contrast to previous ndings that the portfolio share of net foreign assets to total assets is constant in a country, both our theoretical and empirical results support a highly persistent process or a unit root process, with some countries displaying a trend. Finally, we reestablish the composition effect as the quantitatively dominant driving force of current account dynamics in the past data

The Distributed MIMO Scenario: Can Ideal ADCs Be Replaced by Low-resolution ADCs?

This letter considers the architecture of distributed antenna system, which is made up of a massive number of single-antenna remote radio heads (RRHs), some with full-resolution but others with low-resolution analog-to-digital converter (ADC) receivers. This architecture is greatly motivated by its high energy efficiency and low-cost implementation. We derive the worst-case uplink spectral efficiency (SE) of the system assuming a frequency-flat channel and maximum-ratio combining (MRC), and reveal that the SE increases as the number of quantization bits for the low-resolution ADCs increases, and the SE converges as the number of RRHs with low-resolution ADCs grows. Our results furthermore demonstrate that a great improvement can be obtained by adding a majority of RRHs with low-resolution ADC receivers, if sufficient quantization precision and an acceptable proportion of high-to-low resolution RRHs are used.Comment: 4 pages, to be published in IEEE Wireless Communications Letter