Construction of Nth-order rogue wave solutions for Hirota equation by means of bilinear method

In this work, we focus on the construction of Nth-rouge wave solutions for the Hirota equation by utilizing the bilinear method. The formula can be represented in terms of determinants. In addition, some interesting dynamic patterns of rogue waves are exhibited.Comment: 10 pages, 2 figure

Initial-boundary value problems for the defocusing nonlinear Schr\"odinger equation in the semiclassical limit

Initial-boundary value problems for integrable nonlinear partial differential equations have become tractable in recent years due to the development of so-called unified transform techniques. The main obstruction to applying these methods in practice is that calculation of the spectral transforms of the initial and boundary data requires knowledge of too many boundary conditions, more than are required make the problem well-posed. The elimination of the unknown boundary values is frequently addressed in the spectral domain via the so-called global relation, and types of boundary conditions for which the global relation can be solved are called \emph{linearizable}. For the defocusing nonlinear Schr\"odinger equation, the global relation is only known to be explicitly solvable in rather restrictive situations, namely homogeneous boundary conditions of Dirichlet, Neumann, and Robin (mixed) type. General nonhomogeneous boundary conditions are not known to be linearizable. In this paper, we propose an explicit approximation for the nonlinear Dirichlet-to-Neumann map supplied by the defocusing nonlinear Schr\"odinger equation and use it to provide approximate solutions of general nonhomogeneous boundary value problems for this equation posed as an initial-boundary value problem on the half-line. Our method sidesteps entirely the solution of the global relation. The accuracy of our method is proven in the semiclassical limit, and we provide explicit asymptotics for the solution in the interior of the quarter-plane space-time domain.Comment: 56 pages, 13 figures. To appear in Stud. Appl. Mat

Application acceleration for wireless and mobile data networks

This work studies application acceleration for wireless and mobile data networks. The problem of accelerating application can be addressed along multiple dimensions. The first dimension is advanced network protocol design, i.e., optimizing underlying network protocols, particulary transport layer protocol and link layer protocol. Despite advanced network protocol design, in this work we observe that certain application behaviors can fundamentally limit the performance achievable when operating over wireless and mobile data networks. The performance difference is caused by the complex application behaviors of these non-FTP applications. Explicitly dealing with application behaviors can improve application performance for new environments. Along this overcoming application behavior dimension, we accelerate applications by studying specific types of applications including Client-server, Peer-to-peer and Location-based applications. In exploring along this dimension, we identify a set of application behaviors that significantly affect application performance. To accommodate these application behaviors, we firstly extract general design principles that can apply to any applications whenever possible. These design principles can also be integrated into new application designs. We also consider specific applications by applying these design principles and build prototypes to demonstrate the effectiveness of the solutions. In the context of application acceleration, even though all the challenges belong to the two aforementioned dimensions of advanced network protocol design and overcoming application behavior are addressed, application performance can still be limited by the underlying network capability, particularly physical bandwidth. In this work, we study the possibility of speeding up data delivery by eliminating traffic redundancy present in application traffics. Specifically, we first study the traffic redundancy along multiple dimensions using traces obtained from multiple real wireless network deployments. Based on the insights obtained from the analysis, we propose Wireless Memory (WM), a two-ended AP-client solution to effectively exploit traffic redundancy in wireless and mobile environments. Application acceleration can be achieved along two other dimensions: network provision ing and quality of service (QoS). Network provisioning allocates network resources such as physical bandwidth or wireless spectrum, while QoS provides different priority to different applications, users, or data flows. These two dimensions have their respective limitations in the context of application acceleration. In this work, we focus on the two dimensions of overcoming application behavior and Eliminating traffic redundancy to improve application performance. The contribution of this work is as follows. First, we study the problem of application acceleration for wireless and mobile data networks, and we characterize the dimensions along which to address the problem. Second, we identify that application behaviors can significantly affect application performance, and we propose a set of design principles to deal with the behaviors. We also build prototypes to conduct system research. Third, we consider traffic redundancy elimination and propose a wireless memory approach.Ph.D.Committee Chair: Sivakumar, Raghupathy; Committee Member: Ammar, Mostafa; Committee Member: Fekri, Faramarz; Committee Member: Ji, Chuanyi; Committee Member: Ramachandran, Umakishor

A logistic regression model for microalbuminuria prediction in overweight male population

Background: Obesity promotes progression to microalbuminuria and increases the risk of chronic kidney disease. Current protocols of screening microalbuminuria are not recommended for the overweight or obese.

Design and Methods: A cross-sectional study was conducted. The relationship between metabolic risk factors and microalbuminuria was investigated. A regression model based on metabolic risk factors was developed and evaluated for predicting microalbuminuria in the overweight or obese.

Results: The prevalence of MA reached up to 17.6% in Chinese overweight men. Obesity, hypertension, hyperglycemia and hyperuricemia were the important risk factors for microalbuminuria in the overweight. The area under ROC curves of the regression model based on the risk factors was 0.82 in predicting microalbuminuria, meanwhile, a decision threshold of 0.2 was found for predicting microalbuminuria with a sensitivity of 67.4% and specificity of 79.0%, and a global predictive value of 75.7%. A decision threshold of 0.1 was chosen for screening microalbuminuria with a sensitivity of 90.0% and specificity of 56.5%, and a global predictive value of 61.7%.

Conclusions: The prediction model was an effective tool for screening microalbuminuria by using routine data among overweight populations

Quasi-B-mode generated by high-frequency gravitational waves and corresponding perturbative photon fluxes

Interaction of very low-frequency primordial(relic) gravitational waves(GWs) to cosmic microwave background(CMB) can generate B-mode polarization. Here, for the first time we point out that the electromagnetic(EM) response to high-frequency GWs(HFGWs) would produce quasi-B-mode distribution of the perturbative photon fluxes, and study the duality and high complementarity between such two B-modes. Based on this quasi-B-mode in HFGWs, it is shown that the distinguishing and observing of HFGWs from the braneworld would be quite possible due to their large amplitude, higher frequency and very different physical behaviors between the perturbative photon fluxes and background photons, and the measurement of relic HFGWs may also be possible though face to enormous challenge.Comment: 22 pages, 6 figures, research articl

Image Based Hair Segmentation Algorithm for the Application of Automatic Facial Caricature Synthesis

Hair is a salient feature in human face region and are one of the important cues for face analysis. Accurate detection and presentation of hair region is one of the key components for automatic synthesis of human facial caricature. In this paper, an automatic hair detection algorithm for the application of automatic synthesis of facial caricature based on a single image is proposed. Firstly, hair regions in training images are labeled manually and then the hair position prior distributions and hair color likelihood distribution function are estimated from these labels efficiently. Secondly, the energy function of the test image is constructed according to the estimated prior distributions of hair location and hair color likelihood. This energy function is further optimized according to graph cuts technique and initial hair region is obtained. Finally, K-means algorithm and image postprocessing techniques are applied to the initial hair region so that the final hair region can be segmented precisely. Experimental results show that the average processing time for each image is about 280 ms and the average hair region detection accuracy is above 90%. The proposed algorithm is applied to a facial caricature synthesis system. Experiments proved that with our proposed hair segmentation algorithm the facial caricatures are vivid and satisfying