Discrete-time recurrent neural networks with time-varying delays: Exponential stability analysis

This is the post print version of the article. The official published version can be obtained from the link below - Copyright 2007 Elsevier LtdThis Letter is concerned with the analysis problem of exponential stability for a class of discrete-time recurrent neural networks (DRNNs) with time delays. The delay is of the time-varying nature, and the activation functions are assumed to be neither differentiable nor strict monotonic. Furthermore, the description of the activation functions is more general than the recently commonly used Lipschitz conditions. Under such mild conditions, we first prove the existence of the equilibrium point. Then, by employing a Lyapunov–Krasovskii functional, a unified linear matrix inequality (LMI) approach is developed to establish sufficient conditions for the DRNNs to be globally exponentially stable. It is shown that the delayed DRNNs are globally exponentially stable if a certain LMI is solvable, where the feasibility of such an LMI can be easily checked by using the numerically efficient Matlab LMI Toolbox. A simulation example is presented to show the usefulness of the derived LMI-based stability condition.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, the Nuffield Foundation of the UK under Grant NAL/00630/G, the Alexander von Humboldt Foundation of Germany, the Natural Science Foundation of Jiangsu Education Committee of China (05KJB110154), the NSF of Jiangsu Province of China (BK2006064), and the National Natural Science Foundation of China (10471119)

Nuclear dependence of azimuthal asymmetry in semi-inclusive deep inelastic scattering

Within the framework of a generalized factorization, semi-inclusive deeply inelastic scattering (SIDIS) cross sections can be expressed as a series of products of collinear hard parts and transverse-momentum-dependent (TMD) parton distributions and correlations. The azimuthal asymmetry $of unpolarized SIDIS in the small transverse momentum region will depend on both twist-2 and 3 TMD quark distributions in target nucleons or nuclei. Nuclear broadening of these twist-2 and 3 quark distributions due to final-state multiple scattering in nuclei is investigated and the nuclear dependence of the azimuthal asymmetry$$ is studied. It is shown that the azimuthal asymmetry is suppressed by multiple parton scattering and the transverse momentum dependence of the suppression depends on the relative shape of the twist-2 and 3 quark distributions in the nucleon. A Gaussian ansatz for TMD twist-2 and 3 quark distributions in nucleon is used to demonstrate the nuclear dependence of the azimuthal asymmetry and to estimate the smearing effect due to fragmentation.Comment: 9 pages in RevTex with 2 figure

Exponential stability of delayed recurrent neural networks with Markovian jumping parameters

This is the post print version of the article. The official published version can be obtained from the link below - Copyright 2006 Elsevier Ltd.In this Letter, the global exponential stability analysis problem is considered for a class of recurrent neural networks (RNNs) with time delays and Markovian jumping parameters. The jumping parameters considered here are generated from a continuous-time discrete-state homogeneous Markov process, which are governed by a Markov process with discrete and finite state space. The purpose of the problem addressed is to derive some easy-to-test conditions such that the dynamics of the neural network is stochastically exponentially stable in the mean square, independent of the time delay. By employing a new Lyapunov–Krasovskii functional, a linear matrix inequality (LMI) approach is developed to establish the desired sufficient conditions, and therefore the global exponential stability in the mean square for the delayed RNNs can be easily checked by utilizing the numerically efficient Matlab LMI toolbox, and no tuning of parameters is required. A numerical example is exploited to show the usefulness of the derived LMI-based stability conditions.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, the Nuffield Foundation of the UK under Grant NAL/00630/G, and the Alexander von Humboldt Foundation of Germany

A review of snapshot multidimensional optical imaging: Measuring photon tags in parallel

Multidimensional optical imaging has seen remarkable growth in the past decade. Rather than measuring only the two-dimensional spatial distribution of light, as in conventional photography, multidimensional optical imaging captures light in up to nine dimensions, providing unprecedented information about incident photons’ spatial coordinates, emittance angles, wavelength, time, and polarization. Multidimensional optical imaging can be accomplished either by scanning or parallel acquisition. Compared with scanning-based imagers, parallel acquisition–also dubbed snapshot imaging–has a prominent advantage in maximizing optical throughput, particularly when measuring a datacube of high dimensions. Here, we first categorize snapshot multidimensional imagers based on their acquisition and image reconstruction strategies, then highlight the snapshot advantage in the context of optical throughput, and finally we discuss their state-of-the-art implementations and applications