Composite MR image reconstruction and unaliasing for general trajectories using neural networks

In rapid parallel magnetic resonance imaging, the problem of image reconstruction is challenging. Here, a novel image reconstruction technique for data acquired along any general trajectory in neural network framework, called “Composite Reconstruction And Unaliasing using Neural Networks” (CRAUNN), is proposed. CRAUNN is based on the observation that the nature of aliasing remains unchanged whether the undersampled acquisition contains only low frequencies or includes high frequencies too. Here, the transformation needed to reconstruct the alias-free image from the aliased coil images is learnt, using acquisitions consisting of densely sampled low frequencies. Neural networks are made use of as machine learning tools to learn the transformation, in order to obtain the desired alias-free image for actual acquisitions containing sparsely sampled low as well as high frequencies. CRAUNN operates in the image domain and does not require explicit coil sensitivity estimation. It is also independent of the sampling trajectory used, and could be applied to arbitrary trajectories as well. As a pilot trial, the technique is first applied to Cartesian trajectory-sampled data. Experiments performed using radial and spiral trajectories on real and synthetic data, illustrate the performance of the method. The reconstruction errors depend on the acceleration factor as well as the sampling trajectory. It is found that higher acceleration factors can be obtained when radial trajectories are used. Comparisons against existing techniques are presented. CRAUNN has been found to perform on par with the state-of-the-art techniques. Acceleration factors of up to 4, 6 and 4 are achieved in Cartesian, radial and spiral cases, respectively.     

Effects of indium doping on the superconducting properties of YBa2Cu3Oy sintered compounds and thin films

We investigated the effects of indium doping on the superconducting properties of YBCO sintered samples and thin films. In₂O₃-doped YBCO and YBa₂Cu_3−xIn_xO_y sintered samples showed a gradual decrease in the critical temperature (T_c) with increasing indium content; however, a T_c value above 80 K was maintained even up to 30 vol.% addition and x = 0.4, respectively. Ba₃Cu₃In₄O₁₂ was detected by X-ray diffractometry and energy-dispersive X-ray spectroscopy as a reaction product for both sintered samples. The normalized J_c under a magnetic field of 0.1 T showed a maximum at x = 0.3. Indium-doped YBCO films prepared by pulsed laser deposition showed a similar dependence of T_c on indium content as the sintered samples.     

40 MCi tritium source for experiments with low energy neutrino

The artificial tritium source of 40 MCi activity was developed for the scattering experiment to measure the electron antineutrino magnetic moment. We present R&D results which specify source design and physical parameters, its experimental effectiveness and guarantee safety during its life-cycle. Relevant technological issues are featured.     

Stability of bumps in piecewise smooth neural fields with nonlinear adaptation

We study the linear stability of stationary bumps in piecewise smooth neural fields with local negative feedback in the form of synaptic depression or spike frequency adaptation. The continuum dynamics is described in terms of a nonlocal integrodifferential equation, in which the integral kernel represents the spatial distribution of synaptic weights between populations of neurons whose mean firing rate is taken to be a Heaviside function of local activity. Discontinuities in the adaptation variable associated with a bump solution means that bump stability cannot be analyzed by constructing the Evans function for a network with a sigmoidal gain function and then taking the high-gain limit. In the case of synaptic depression, we show that linear stability can be formulated in terms of solutions to a system of pseudo-linear equations. We thus establish that sufficiently strong synaptic depression can destabilize a bump that is stable in the absence of depression. These instabilities are dominated by shift perturbations that evolve into traveling pulses. In the case of spike frequency adaptation, we show that for a wide class of perturbations the activity and adaptation variables decouple in the linear regime, thus allowing us to explicitly determine stability in terms of the spectrum of a smooth linear operator. We find that bumps are always unstable with respect to this class of perturbations, and destabilization of a bump can result in either a traveling pulse or a spatially localized breather.     

The weakly nonlocal limit of a one-population Wilson-Cowan model

We derive the weakly nonlocal limit of a one-population neuronal field model of the Wilson-Cowan type in one spatial dimension. By transforming this equation to an equation in the firing rate variable, it is shown that stationary periodic solutions exist by appealing to a pseudo-potential analysis. The solutions of the full nonlocal equation obey a uniform bound, and the stationary periodic solutions in the weakly nonlocal limit satisfying the same uniform bound are characterized by finite ranges of pseudo energy constants. The time dependent version of the model is reformulated as a Ginzburg-Landau-Khalatnikov type of equation in the firing rate variable where the maximum (minimum) points correspond stable (unstable) homogeneous solutions of the weakly nonlocal limit. Based on this formulation it is also conjectured that the stationary periodic solutions are unstable. We implement a numerical method for the weakly nonlocal limit of the Wilson-Cowan type of model based on the wavelet-Galerkin approach. We perform some numerical tests to illustrate the stability of homogeneous solutions and the evolution of the bumps.     

A canonical model for gradient frequency neural networks

We derive a canonical model for gradient frequency neural networks (GFNNs) capable of processing time-varying external stimuli. First, we employ normal form theory to derive a fully expanded model of neural oscillation. Next, we generalize from the single oscillator model to heterogeneous frequency networks with an external input. Finally, we define the GFNN and illustrate nonlinear time-frequency transformation of a time-varying external stimulus. This model facilitates the study of nonlinear time-frequency transformation, a topic of critical importance in auditory signal processing.     

Singular Hopf bifurcations and mixed-mode oscillations in a two-cell inhibitory neural network

Recent studies of a firing rate model for neural competition as observed in binocular rivalry and central pattern generators [R. Curtu, A. Shpiro, N. Rubin, J. Rinzel, Mechanisms for frequency control in neuronal competition models, SIAM J. Appl. Dyn. Syst. 7 (2) (2008) 609-649] showed that the variation of the stimulus strength parameter can lead to rich and interesting dynamics. Several types of behavior were identified such as: fusion, equivalent to a steady state of identical activity levels for both neural units; oscillations due to either an escape or a release mechanism; and a winner-take-all state of bistability. The model consists of two neural populations interacting through reciprocal inhibition, each endowed with a slow negative-feedback process in the form of spike frequency adaptation. In this paper we report the occurrence of another complex oscillatory pattern, the mixed-mode oscillations (MMOs). They exist in the model at the transition between the relaxation oscillator dynamical regime and the winner-take-all regime. The system distinguishes itself from other neuronal models where MMOs were found by the following interesting feature: there is no autocatalysis involved (as in the examples of voltage-gated persistent inward currents and/or intrapopulation recurrent excitation) and therefore the two cells in the network are not intrinsic oscillators; the oscillations are instead a combined result of the mutual inhibition and the adaptation. We prove that the MMOs are due to a singular Hopf bifurcation point situated in close distance to the transition point to the winner-take-all case. We also show that in the vicinity of the singular Hopf other types of bifurcations exist and we construct numerically the corresponding diagrams.     

一类具分布时滞神经网络的全局指数稳定性

本文讨论了一类具分布时滞神经网络的稳定性.利用广义Dahlquist数和广义Halanay不等式,我们得到了该神经网络平衡点存在、唯一且全局指数稳定的充分条件.此外,我们的方法还估计出了神经网络指数收敛到平衡点的速度.由于我们的方法去除了关于激活函数的有界性、可微性和单调性的常用假设,因此我们的结果是某些现有结果的推广和改进.     

变时滞细胞神经网络的全局指数稳定性研究

本文采用Lyapunov-Krasovskii泛函方法对一类变时滞细胞神经网络的全局指数稳定性进行了研究,得出了一些关于DCNN全局指数稳定性的充分条件。