Coherent orthogonal polynomials

We discuss a fundamental characteristic of orthogonal polynomials, like the existence of a Lie algebra behind them, which can be added to their other relevant aspects. At the basis of the complete framework for orthogonal polynomials we include thus–in addition to differential equations, recurrence relations, Hilbert spaces and square integrable functions–Lie algebra theory.     

Detecting community structure using label propagation with weighted coherent neighborhood propinquity

Community detection has become an important methodology to understand the organization and function of various real-world networks. The label propagation algorithm (LPA) is an almost linear time algorithm proved to be effective in finding a good community structure. However, LPA has a limitation caused by its one-hop horizon. Specifically, each node in LPA adopts the label shared by most of its one-hop neighbors; much network topology information is lost in this process, which we believe is one of the main reasons for its instability and poor performance. Therefore in this paper we introduce a measure named weighted coherent neighborhood propinquity (weighted-CNP) to represent the probability that a pair of vertices are involved in the same community. In label update, a node adopts the label that has the maximum weighted-CNP instead of the one that is shared by most of its neighbors. We propose a dynamic and adaptive weighted-CNP called entropic-CNP by using the principal of entropy to modulate the weights. Furthermore, we propose a framework to integrate the weighted-CNP in other algorithms in detecting community structure. We test our algorithm on both computer-generated networks and real-world networks. The experimental results show that our algorithm is more robust and effective than LPA in large-scale networks.     

Characterizing neural activities evoked by manual acupuncture through spiking irregularity measures

The neural system characterizes information in external stimulations by different spiking patterns. In order to examine how neural spiking patterns are related to acupuncture manipulations, experiments are designed in such a way that different types of manual acupuncture （MA） manipulations are taken at the ＇Zusanli＇ point of experimental rats, and the induced electrical signals in the spinal dorsal root ganglion are detected and recorded. The interspike interval （ISI） statistical histogram is fitted by the gamma distribution, which has two parameters： one is the time-dependent firing rate and the other is a shape parameter characterizing the spiking irregularities. The shape parameter is the measure of spiking irregularities and can be used to identify the type of MA manipulations. The coefficient of variation is mostly used to measure the spike time irregularity, but it overestimates the irregularity in the case of pronounced firing rate changes. However, experiments show that each acupuncture manipulation will lead to changes in the firing rate. So we combine four relatively rate- independent measures to study the irregularity of spike trains evoked by different types of MA manipulations. Results suggest that the MA manipulations possess unique spiking statistics and characteristics and can be distinguished according to the spiking irregularity measures. These studies have offered new insights into the coding processes and information transfer of acupuncture.     

Steepest-descent method-based adaptive frequency domain equalizer in coherent optical orthogonal frequency division multiplexing with quadrature phase shift keying modulation

An adaptive frequency domain equalizer (A-FDE) in quadrature phase shift keying-coherent optical-orthogonal frequency division multiplexing (QPSK-CO-OFDM) system is proposed in this paper. A-FDE uses steepest descent method to search the optimal equalization parameters. And through applying the adaptive control factor (ACF) to monitor the state of A-FDE, the interference from phase noise (PN) and chromatic dispersion (CD) can be mitigated. The numerical simulation shows that the performance of A-FDE has a remarkable improvement on combating PN and CD comparing with the conventional decision-directed equalizer (DDE). And the A-FDE can achieve the forward-error-correction (FEC) threshold in noisier scenario. Furthermore, because the calculation of ACF only bases on valid data instead of pilot symbols (PSs), A-FDE has low PS overhead merit.     

Study on an optical system with coherent laser array source and phase optimization in turbulent atmosphere

Model of an optical system with coherent laser array source and the piston phase optimized by the stochastic parallel gradient descent algorithm is established. With this model, theory of beam propagation through the optical system in turbulent atmosphere is analyzed, and the analytical formulas of the beam average intensity along the propagation path are derived. Strehl ratio of the received beam induced by intensity disorderly distribution and power efficiency of the received beam are introduced to evaluate performance of the optical system. Under the H-V 5/7 atmospheric turbulent model, performance of an optical system with determinate parameters was calculated, and the influences of the propagation distance and the laser wavelength were numerically analyzed, respectively.     

An improved least square channel estimation algorithm for coherent optical OFDM system

This paper presents an improved processing added to conventional least square (LS) channel estimation to modify its performance for coherent optical orthogonal frequency division multiplexing (CO-OFDM) system. By testing selected limitation factors of the existing algorithms, the influence of our improved algorithm to the performance of CO-OFDM system were studied and compared with other published algorithms. The simulation results of the study demonstrated that the proposed approaches achieved better channel estimation performance and are considered as a more appropriate alternative for CO-OFDM system with the tradeoff between complexity and performance.     

Projective Relativity: Present Status and Outlook

We give a critical analysis of projective relativity theory. Examining Kaluza's own intention and the following development by Klein, Jordan, Pauli, Thiry, Ludwig and others, we conclude that projective relativity was abused in its own terms and much more in the case of newer higher dimensional Kaluza–Klein theories with non-Abelian gauge groups. Reviewing the projective formulation of the Jordan isomorphy theorem yields some hints how one can proceed in a different direction. We can interpret the condition not as a field equation in a 5-dimensional Riemannian space, e.g. as vacuum Einstein-Hilbert equation, but can (or should) interpret it as a geometrical object, a null-quadric. Projective aspects of quantum (field) theory are discussed under this viewpoint.     

Long distance atomic teleportation with as good success as desired

Long distance atomic teleportation (LDAT) is of prime importance in long distance quantum communication. Scheme proposed by Bose et al. (1999) in principle enables us to have LDAT using cavity decay. However it gives message state dependent fidelity and success rate. Here, using interaction of entangled coherent states with atom–cavity systems and a two-step measurement, we show how, LDAT can be achieved with unit fidelity and as good success as desired under ideal conditions. The scheme is unique in that, the first measurement predicts success or failure. If success is predicted then second measurement gives perfect teleportation. If failure is predicted the message-qubit remains conserved therefore a second attempt may be started. We found that even in presence of decoherence due to dissipation of energy our scheme gives message state independent success rate and almost perfect teleportation in single attempt with mean fidelity of teleportation equal to 0.9 at long distances. However if first attempt fails, unlike ideal case where message-qubit remains conserved with unit fidelity, in presence of decoherence the message-qubit remains conserved to some degree, therefore mean fidelity of teleportation can be increased beyond 0.9 by repeating the process.     

Control of Two-photon Fluorescence of Common Dyes and Conjugated Dyes

We present a comprehensive study of the selective excitation of two-photon fluorescence from various pairs of dyes and dyes in different conjugation states with tailored pulse shapes found with a genetic algorithm (GA). We investigate a number of biologically important dyes, and include dyes conjugated to trastuzumab (Herceptin®) and to a poly(amidoamine) dendrimer. We consider in detail the ability of tailored pulse shaping to discriminate dyes with significant spectral overlap. Our procedure for adaptive pulse shaping includes power-law and chirp-scaling checks to prevent trivial convergences. The GA uses a multiplicative fitness parameter in a graded search method that converges on pulse shapes that not only differentiate two-photon processes, but do so in a high signal regime. We consider the results in terms of not only the absolute maximum ratio of discrimination achieved, but also present the evolutionary course of the GA and compare the improvement to a quantitative measure of the noise level. We also implement a time-domain acousto-optic measurement of two-photon excitation cross-section spectra. The results show that the ability to discriminate dyes is determined almost entirely by their differences in two-photon excitation cross section.