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• This study presents a practical optimization framework of elastic motion estimation. It employs the Levenberg-Marquardt method to facilitate fast gradient descent speed at early stage of iteration by introducing a diagonal matrix into the Gauss-Newton's Hessian matrix. Thus, the slow convergence of conventional Gauss-Newton's optimization method can be efficiently dealt with, especially when the initial solution is far from the optimum. • We prove that the Gauss-Newton's Hessian matrix is positive semi-definite with a probability of 0.6951 on average, by discussing the convexity of the motion-compensated error function. Such an observation lays a theoretical foundation for us that we can adopt a sign-alternating factor, instead of a positive constant used in the traditional L-M method, to update iteratively the diagonal matrix coefficient. This strategy guarantees that our method searches for the optimal motion vector in a much bigger parameter space. • To avoid a negative diagonal matrix coefficient producing a singular or ill-conditioned Hessian matrix, we further determine an upper bound and a lower bound for the diagonal matrix coefficient, with whose constraints we propose an adaptive method to compute the sign-alternating factor to restrict the update process into a reasonable range. • The proposed elastic motion estimation algorithm explores simultaneously a bigger parameter space and a more suitable update manner which effectively adapts to the distribution of the motion-compensated error function. Therefore, it outperforms the full search based on block-wise translational model and the elastic motion estimation based on Gauss-Newton's method in terms of the motion-compensated peak signal-to-noise ratio (PSNR). Furthermore, our method needs only 1–2 iterations before it achieves higher PSNR than conventional elastic motion estimation and the block-wise translational full search. The elastic motion estimation is an efficient temporal predictive coding tool for predicting complex motions including zooming, shearing and twisting. However, its optimization solution still suffers from high computational complexity and unstable convergence yet. We thus present a novel optimization framework to improve the elastic motion estimation efficiency. By introducing a diagonal matrix into the Gauss-Newton's Hessian matrix, we employ the Levenberg-Marquardt optimization to compute the elastic motion vectors. It obtains superior convergence to the conventional Gauss-Newton's method, especially when the starting point is far away from the globally/locally optimum. Furthermore, we prove that the Gauss-Newton's Hessian matrix for elastic motion estimation is positive semi-definite by discussing the convexity of the motion-compensated error function. Such a finding allows us to adopt a sign-alternating factor, instead of a positive constant used in the traditional L-M method, to update iteratively the diagonal matrix coefficient. And a bound is determined for the diagonal matrix coefficient to guarantee the non-singularity of the Hessian matrix, with whose constraints we propose an adaptive method to compute the sign-alternating factor to restrict the iterative process into a reasonable motion vector space. Finally, a novel elastic motion estimation algorithm is presented based on the modified Levenberg-Marquardt optimization. Experimental results show that the proposed algorithm gains higher motion-compensated peak signal-to-noise ratio (PSNR) than several benchmark methods. Moreover, our algorithm converges fast which needs only 1–2 iterations before it achieves higher PSNR than conventional elastic motion estimation. [ABSTRACT FROM AUTHOR]

We study the instanton partition functions of two well-known superconformai field theories with mass deformations. Two types of anomaly equations, namely, the modular anomaly and holomorphic anomaly, have been discovered in the literature. We provide a clean solution to the long standing puzzle about their precise relation, and obtain some universal formulas. We show that the partition function is invariant under the SL(2,Z) duality which exchanges theories at strong coupling with those of weak coupling. [ABSTRACT FROM AUTHOR]

Recently, an ultra-wideband (UWB) system with frequency-modulated differential chaos shift keying (FM-DCSK) modulation has attracted increasing interest for its many distinctive superiorities over its conventional counterparts, especially in low-rate and low-power wireless personal area network (WPAN) applications. However, some of its drawbacks, such as low energy efficiency, complex implementation and weak multiaccess capacity, have also been noticed, which restrict its further acceptance and applications. To overcome these problems, an architecture, named single-input and multiple-output (SIMO) FM-DCSK UWB system, is introduced in this paper. With chaotic transmitted signals based on a high-order Walsh function and multiple antennas diversity reception, this paper demonstrates the superiorities of the new system in bit error rate (BER) performance as well as in moderation complexity. Furthermore, by transmitting chaotic pulse cluster signals, an improved emission signal structure of the SIMO FM-DCSK UWB system is proposed so as to overcome the delay line implementation constraints and to further enhance the BER performance. Based on this new signal format, a method of combining time division and Walsh function division is introduced into the existing Walsh function division scheme, thereby resolving the inherent obstacle in user capability which was known to be limited by the order of the Walsh function. [ABSTRACT FROM PUBLISHER]

In a previous paper, we proposed a probability interpretation for higher genus amplitudes of BMN (Berenstein-Maldacena-Nastase) strings in a pp-wave background with infinite negative curvature. This provides a natural definition of the entropy of a BMN string as the Shannon entropy of its corresponding probability distribution. We prove a universal upper bound that the entropy grows at most logarithmically in the strong string coupling limit. We also study the entropy by numerical methods and discuss some interesting salient features. [ABSTRACT FROM AUTHOR]

In a previous paper we proposed a factorization principle for the correlation functions of Berenstein-Maldacena-Nastase (BMN) operators in free N=4 super-Yang-Mills theory. These correlators are conjectured to described physical string amplitudes in an infinitely curved Ramond-Ramond pp-wave background. There was a puzzle that the factorization seems to break down for the S channel in the 2 2 scattering process. Here we resolve this puzzle by including some diagrams missed in the previous paper. We also observe some interesting relations which further support the interpretation of higher genus correlators as physical string loop amplitudes. [ABSTRACT FROM AUTHOR]