Using several kinds of coordinate transformations, we standardize the noncanonical symplectic structure Ablowitz–Ladik model (A–L model) nonlinear Schrodinger equation (NLSE), then employ some scheme to simulate solitons motion and test evolution discrete invariants A–L also conserved quantities original NLSE. In comparison with a higher order non-symplectic applied directly model, show overwhelming superiorities method. We compare implementation same different standardized Hamiltonian...

Motivated by applications in nuclear magnetic resonance (NMR) spectroscopy, we introduce a novel blind source separation (BSS) approach to treat nonnegative and correlated data. We consider the (over)-determined case where $n$ sources are be separated from $m$ linear mixtures ($m\geq n$). Among signals, there $n-1$ partially overlapping (Po) one positive everywhere (Pe) source. This condition is applicable for many real-world signals such as NMR spectra of urine blood serum metabolic...

We study the solvability of sparse blind separation n nonnegative sources from m linear mixtures in underdetermined regime $m<n$. The geometric properties mixture matrix and sparseness structure source are closely related to identification mixing matrix. first illustrate establish necessary sufficient conditions for unique case $m+1$ sources, develop a novel algorithm based on data geometry, sparseness, $\ell_1$ minimization. Then we extend results any order $m\times n$, $3\leq m<n$, degree...

The association studies on human complex traits are admittedly propitious to identify deleterious genetic markers. Compared single-trait analyses, multiple-trait analyses can arguably make better use of the information both and markers, thus improve statistical power tests prominently. Principal component analysis (PCA) is a well-known useful tool in multivariate be applied this task. Generally, PCA first performed all then certain number top principal components (PCs) that explain most...

Differential optical absorption spectroscopy (DOAS) is a powerful tool for detecting and quantifying trace gases in atmospheric chemistry [22]. DOAS spectra consist of linear combination complex multi-peak multi-scale structures. Most analysis routines use today are based on least squares techniques, example, the approach developed 1970s [18,19,20,21] uses polynomial fits to remove slowly varying background (broad spectral structures data), known referencespectra retrieve identity...

Because of the existence an exciton-biexciton transition inside optically excited semiconductor, dielectric constant is modified to be a wave-vector-dependent function. The spatial dispersion relation leads three propagating modes polariton, for which two additional boundary conditions will required. In vicinity resonance, mathematical study shows that among dominate, and third wave with large imaginary part can neglected without affecting essential physics. Based on study, criterion...

Substances such as chemical compounds are invisible to human eyes, they usually captured by sensing equipments with their spectral fingerprints. Though spectra of pure chemicals can be identified visual inspection, the mixtures take a variety complicated forms. Given knowledge references constituent chemicals, task data fitting is retrieve weights, and this obtained solving least squares problem. Complications occur if basis functions (reference spectra) may not used directly best fit data....

Given a set of mixtures, blind source separation attempts to retrieve the signals without or with very little information mixing process. We present geometric approach for nonnegative linear mixtures termed {\em facet component analysis} (FCA). The is based on identification underlying cone structure data. Earlier works focus recovering by locating its vertices (vertex analysis VCA) mutual sparsity condition which requires each signal possess stand-alone peak in spectrum. formulate...

Rapid and reliable detection identification of unknown chemical substances is critical to homeland security. It challenging identify components from a wide range explosives. There are two key steps involved. One nondestructive informative spectroscopic technique for data acquisition. The other an associated library reference features along with computational method feature matching meaningful within or beyond the library. Recently several experimental techniques based on Raman scattering...

In this paper, we develop structure assisted nonnegative matrix factorization (NMF) methods for blind source separation of degenerate data. The motivation originates from nuclear magnetic resonance (NMR) spectroscopy, where a multiple mixture NMR spectra are recorded to identify chemical compounds with similar structures. Consider the linear mixing model (LMM), aim involved when process is known be nearly singular. We first consider class data dominant interval(s) (DI) each signals has peaks...