14862024
Exact certification of global optimality of approximate factorizations via rationalizing sums-of-squares with floating point scalars
We generalize the technique by Peyrl and Parillo [Proc. SNC 2007] to computing lower bound certificates for several well-known factorization problems in hybrid symbolic-numeric computation. The idea is to transform a numerical sum-of-squares (SOS) representation of a positive polynomial into an exact rational identity. Our algorithms successfully certify accurate rational lower bounds near the irrational global optima for benchmark approximate polynomial greatest common divisors and multivariate polynomial irreducibility radii from the literature, and factor coefficient bounds in the setting of a model problem by Rump (up to n = 14, factor degree = 13.
 The numeric SOSes produced by the current fixed precision semi-definite programming (SDP) packages (SeDuMi, SOSTOOLS, YALMIP) are usually too coarse to allow successful projection to exact SOSes via Maple 11's exact linear algebra. Therefore, before projection we refine the SOSes by rank-preserving Newton iteration. For smaller problems the starting SOSes for Newton can be guessed without SDP ("SDP-free SOS"), but for larger inputs we additionally appeal to sparsity techniques in our SDP formulation.
10784212
Approximate GCDs of polynomials and SOS relaxation
min p,u1,...,us ‖f1−p·u1‖2+‖f2−p·u2‖2+· · ·+‖fs−p·us‖2 (1) where p, u1, . . . , us are polynomials such that deg(p) ≤ k, deg(p · ui) ≤ di = deg fi for 1 ≤ i ≤ s. Here ‖f‖2 denotes the norm of the coefficient vector of polynomial f . The minimization problem has many different formulations and various numeric optimization strategies have been proposed, see [1, 3] and references therein. In particular, Karmarkar and Lakshman [4] proposed an algorithm based on the global minimization of a rational function to compute the approximate GCD of univariate polynomials. The most expensive part of their algorithm is to find all the real solutions of two bivariate polynomials with high degrees. It has been shown in [8] that sum of squares (SOS) relaxation[5, 9] can be used to find the global minimum of the rational function arising from the approximate GCD computation. The SOS relaxation can be solved by reformulating them as semidefinite programs (SDPs), which in turn are solved efficiently by using interior point methods [7]. Motivated by the interesting results obtained in [8], we show how to apply SOS relaxation to solve different optimization problems formulated in [1, 3, 4]. Let fi,ui,p be coefficient vectors corresponding to polynomials fi, ui, p respectively, and Ai = Ai(p) be convolution ∗ This research was partially supported by NKBRPC (2004CB318000) and the Chinese National Natural Science Foundation under Grant 10401035 (Li and Zhi).
709845
Supporting Live Video on Ad Hoc Wireless Networks: Unbalanced Multiple Description Coding, Single Path Transport and Recursive Error Concealment
Robust transmission of live video over ad hoc wireless networks presents new challenges: high bandwidth requirements are coupled with delay constraints; nodes are constrained in processing power and storage capacity; ad hoc wireless networks suffer from bursty packet losses that drastically degrade the viewing experience. Accordingly, we propose a simple, but practical unbalanced multiple description (UMD) codec that uses single path transport only. At the UMD decoder, the lost Low- Resolution (LR) frames can be receded from the corresponding ones of the correctly received High- Resolution (HR) stream. This makes LR more robust to packet losses and ensures continuous video playback. The simulation results show that the proposed UMD codec has higher decoded quality, smaller quality fluctuation and lower probability of pause than other error resilience techniques, especially when channel burstiness becomes large. We also propose a novel sequence-based error concealment (EC) algorithm for our UMD decoder. It recursively uses multi-frame recovery principle to frame-by-frame reduce error drift in the HR description with respect to the LR description. In fact, the algorithm can be applied to most UMD schemes. It has the advantage of working on integer-, half- or quarter- pixel precision and looking backward without buffering future frames. Experimental results show that error decreases the fastest if the UMD decoder uses our EC algorithm. It can provide satisfactory performance on both objective and subjective evaluation.
15998088
Understand behavior and performance of Real Coded Optimization Algorithms via NK-linkage model
Classical NK-landcape model was designed for analyzing optimization and evolution process in binary solution space, so it can not be used to analyze real coded optimization algorithms (RCOAs) directly, which work in continuous solution space directly. In this paper, the concept of NK-landscape model is extended to the continuous space, and a new NK-landscape model with continuous space is proposed. The new model is powerful and comprehensive with simple structure and flexible formula. Therefore, it can be used to construct test functions of various types of linkages for analyzing various performances of RCOAs. The feasibility of the proposed model is testified via experiments with 3 well-known RCOAs, ( i.e. covariance matrix adapting evolutionary strategy (CMA-ES), differential evolution (DE), neighborhood search differential evolution (NSDE)). The results show that the new model can reveal the merits and demerits of RCOAs effectively.
14221074
Accurate and efficient processor performance prediction via regression tree based modeling
Computer architects usually evaluate new designs using cycle-accurate processor simulation. This approach provides a detailed insight into processor performance, power consumption and complexity. However, only configurations in a subspace can be simulated in practice due to long simulation time and limited resource, leading to suboptimal conclusions which might not be applied to a larger design space. In this paper, we propose a performance prediction approach which employs state-of-the-art techniques from experiment design, machine learning and data mining. According to our experiments on single and multi-core processors, our prediction model generates highly accurate estimations for unsampled points in the design space and show the robustness for the worst-case prediction. Moreover, the model provides quantitative interpretation tools that help investigators to efficiently tune design parameters and remove performance bottlenecks.
16775013
A Dynamic Trust Model for the Multi-agent Systems
Internet provides a fertile medium for new breeds of computer viruses. Many people who have access to a wealth of information via Internet are attacked by more computer viruses than they can effectively process. We present a dynamic computer virus detection model that can detect known viruses and previously unknown viruses to prevent information systems from damage. This model is inspired by biological immune systems that protect the body against damage from pathogens. The architecture of this model, the formal definitions of self nonself antigen, antibody, and vaccine gene library are introduced. Furthermore, the evolution of self and nonself, the generation of the antibody, the evolution of the virus vaccine gene, and the detection of the antigen are depicted. Experiment results show that this model has better capacity of self-adaptability and self-learning in detecting unknown viruses than traditional models.
14995264
A mixed-signal simulator for VHDL-AMS