A Comparative Study of Two Real Root Isolation Methods

Recent progress in polynomial elimination has rendered the computation of the real roots of ill-conditioned polynomials of high degree (over 1000) with huge coefficients (several thousand digits) a critical operation in computer algebra. To rise to the occasion, the only method-candidate that has been considered by various authors for modification and improvement has been the Collins-Akritas bisection method [1], which is a based on a variation of Vincent’s theorem [2]. The most recent example is the paper by Rouillier and Zimmermann [3], where the authors present “... a new algorithm, which is optimal in terms of memory usage and as fast as both Collins and Akritas’ algorithm and Krandick variant ...” [3] In this paper we compare our own continued fractions method CF [4] (which is directly based on Vincent’s theorem) with the best bisection method REL described in [3]. Experimentation with the data presented in [3] showed that, with respect to time, our continued fractions method CF is by far superior to REL, whereas the two are about equal with respect to space

Optimal static pricing for a tree network

We study the static pricing problem for a network service provider in a loss system with a tree structure. In the network, multiple classes share a common inbound link and then have dedicated outbound links. The motivation is from a company that sells phone cards and needs to price calls to different destinations. We characterize the optimal static prices in order to maximize the steady-state revenue. We report new structural findings as well as alternative proofs for some known results. We compare the optimal static prices versus prices that are asymptotically optimal, and through a set of illustrative numerical examples we show that in certain cases the loss in revenue can be significant. Finally, we show that static prices obtained using the reduced load approximation of the blocking probabilities can be easily obtained and have near-optimal performance, which makes them more attractive for applications.Massachusetts Institute of Technology. Center for Digital BusinessUnited States. Office of Naval Research (Contract N00014-95-1-0232)United States. Office of Naval Research (Contract N00014-01-1-0146)National Science Foundation (U.S.) (Contract DMI-9732795)National Science Foundation (U.S.) (Contract DMI-0085683)National Science Foundation (U.S.) (Contract DMI-0245352

Improving the Performance of the Continued Fractions Method Using New Bounds of Positive Roots

In this paper we compare four implementations of the Vincent-Akritas-Strzebonski Continued Fractions (VAS-CF) real root isolation method using four different (two linear and two quadratic complexity) bounds on the values of the positive roots of polynomials. The quadratic complexity bounds were included to see if the quality of their estimates compensates for their quadratic complexity. Indeed, experimentation on various classes of special and random polynomials revealed that the VAS-CF implementation using LMQ, the Quadratic complexity variant of our Local Max bound, achieved an overall average speed-up of 40% over the original implementation using Cauchy's linear bound

Multiplexed Detection of Infectious Diseases With Microfluidic Loop-Mediated Isothermal Amplification and a Smartphone

New tools are needed to enable rapid detection, identification, and reporting of infectious viral and microbial pathogens in a wide variety of point-of-care applications that impact human and animal health. We report the design, construction, and characterization of a platform for multiplexed analysis of disease-specific DNA sequences that utilizes a smartphone camera as the sensor in conjunction with a handheld instrument that interfaces the phone with a silicon-based microfluidic chip. Utilizing specific nucleic acid sequences for four equine respiratory pathogens as representative examples, we demonstrated the ability of the system to use a single 15-μL droplet of test sample to perform selective positive/negative determination of target sequences, including integrated experimental controls, in approximately 30 minutes. The system achieves detection limits comparable to those obtained by laboratory-based methods and instruments. © 2017 IEEE