Integrable dispersionless KdV hierarchy with sources

An integrable dispersionless KdV hierarchy with sources (dKdVHWS) is derived. Lax pair equations and bi-Hamiltonian formulation for dKdVHWS are formulated. Hodograph solution for the dispersionless KdV equation with sources (dKdVWS) is obtained via hodograph transformation. Furthermore, the dispersionless Gelfand-Dickey hierarchy with sources (dGDHWS) is presented.Comment: 15 pages, to be published in J. Phys. A: Math. Ge

Deriving N-soliton solutions via constrained flows

The soliton equations can be factorized by two commuting x- and t-constrained flows. We propose a method to derive N-soliton solutions of soliton equations directly from the x- and t-constrained flows.Comment: 8 pages, AmsTex, no figures, to be published in Journal of Physics

Constructing N-soliton solution for the mKdV equation through constrained flows

Based on the factorization of soliton equations into two commuting integrable x- and t-constrained flows, we derive N-soliton solutions for mKdV equation via its x- and t-constrained flows. It shows that soliton solution for soliton equations can be constructed directly from the constrained flows.Comment: 10 pages, Latex, to be published in "J. Phys. A: Math. Gen.

Wearable Sensor Data Based Human Activity Recognition using Machine Learning: A new approach

Recent years have witnessed the rapid development of human activity recognition (HAR) based on wearable sensor data. One can find many practical applications in this area, especially in the field of health care. Many machine learning algorithms such as Decision Trees, Support Vector Machine, Naive Bayes, K-Nearest Neighbor, and Multilayer Perceptron are successfully used in HAR. Although these methods are fast and easy for implementation, they still have some limitations due to poor performance in a number of situations. In this paper, we propose a novel method based on the ensemble learning to boost the performance of these machine learning methods for HAR

Generalized Darboux transformations for the KP equation with self-consistent sources

The KP equation with self-consistent sources (KPESCS) is treated in the framework of the constrained KP equation. This offers a natural way to obtain the Lax representation for the KPESCS. Based on the conjugate Lax pairs, we construct the generalized binary Darboux transformation with arbitrary functions in time $t$ for the KPESCS which, in contrast with the binary Darboux transformation of the KP equation, provides a non-auto-B\"{a}cklund transformation between two KPESCSs with different degrees. The formula for N-times repeated generalized binary Darboux transformation is proposed and enables us to find the N-soliton solution and lump solution as well as some other solutions of the KPESCS.Comment: 20 pages, no figure

SVD-Based Evaluation of Multiplexing in Multipinhole SPECT Systems

Multipinhole SPECT system design is largely a trial-and-error process. General principles can give system designers a general idea of how a system with certain characteristics will perform. However, the specific performance of any particular system is unknown before the system is tested. The development of an objective evaluation method that is not based on experimentation would facilitate the optimization of multipinhole systems. We derive a figure of merit for prediction of SPECT system performance based on the entire singular value spectrum of the system. This figure of merit contains significantly more information than the condition number of the system, and is therefore more revealing of system performance. This figure is then compared with simulated results of several SPECT systems and is shown to correlate well to the results of the simulations. The proposed figure of merit is useful for predicting system performance, but additional steps could be taken to improve its accuracy and applicability. The limits of the proposed method are discussed, and possible improvements to it are proposed

On the Toda Lattice Equation with Self-Consistent Sources

The Toda lattice hierarchy with self-consistent sources and their Lax representation are derived. We construct a forward Darboux transformation (FDT) with arbitrary functions of time and a generalized forward Darboux transformation (GFDT) for Toda lattice with self-consistent sources (TLSCS), which can serve as a non-auto-Backlund transformation between TLSCS with different degrees of sources. With the help of such DT, we can construct many type of solutions to TLSCS, such as rational solution, solitons, positons, negetons, and soliton-positons, soliton-negatons, positon-negatons etc., and study properties and interactions of these solutions.Comment: 20 page