Dynamics of Neural Networks with Continuous Attractors

We investigate the dynamics of continuous attractor neural networks (CANNs). Due to the translational invariance of their neuronal interactions, CANNs can hold a continuous family of stationary states. We systematically explore how their neutral stability facilitates the tracking performance of a CANN, which is believed to have wide applications in brain functions. We develop a perturbative approach that utilizes the dominant movement of the network stationary states in the state space. We quantify the distortions of the bump shape during tracking, and study their effects on the tracking performance. Results are obtained on the maximum speed for a moving stimulus to be trackable, and the reaction time to catch up an abrupt change in stimulus.Comment: 6 pages, 7 figures with 4 caption

Phantom Mimicry on the Normal Branch of a DGP-inspired Braneworld Scenario with Curvature Effect

It has been shown recently that phantom-like effect can be realized on the normal branch of the DGP setup without introduction of any phantom matter neither in the bulk nor on the brane and therefore without violation of the null energy condition. It has been shown also that inclusion of the Gauss-Bonnet term in the bulk action modifies this picture via curvature effects. Here, based on the Lue-Starkman conjecture on the dynamical screening of the brane cosmological constant in the DGP setup, we extend this proposal to a general DGP-inspired $f(R,\phi)$ model that stringy effects in the ultra-violet sector of the theory are taken into account by inclusion of the Gauss-Bonnet term in the bulk action. We study cosmological dynamics of this setup, especially its phantom-like behavior and possible crossing of the phantom divide line especially with a non-minimally coupled quintessence field on the brane. In this setup, scalar field and curvature quintessence are treated in a unified framework.Comment: 25 Figures, To appear in MPL

Remarks on hard Lefschetz conjectures on Chow groups

We propose two conjectures of Hard Lefschetz type on Chow groups and prove them for some special cases. For abelian varieties, we shall show they are equivalent to well-known conjectures of Beauville and Murre.Comment: to appear in Sciences in China, Ser. A Mathematic

Semi-leptonic and Non-leptonic BB meson decays to charmed mesons

We study the semi-leptonic and non-leptonic $B$ weak decays which are governed by the $B\rightarrow D^{(*)}$ transitions. The branching ratios, CP asymmetries (CPA) and polarization fractions (FA) of non-leptonic decays are investigated in the factorization approximation. The $B\rightarrow D^{(*)}$ form factors are estimated in the Salpeter method. Our estimation on branching ratios generally agree with the existent experimental data. For CPA and polarizations, comparisons among the FA results, the perturbative QCD predictions and experimental data are made.Comment: 8 pages, 1 figures, 5 table

Two Dimensional Quantum Mechanical Modeling of Nanotransistors

Quantization in the inversion layer and phase coherent transport are anticipated to have significant impact on device performance in 'ballistic' nanoscale transistors. While the role of some quantum effects have been analyzed qualitatively using simple one dimensional ballistic models, two dimensional (2D) quantum mechanical simulation is important for quantitative results. In this paper, we present a framework for 2D quantum mechanical simulation of a nanotransistor / Metal Oxide Field Effect Transistor (MOSFET). This framework consists of the non equilibrium Green's function equations solved self-consistently with Poisson's equation. Solution of this set of equations is computationally intensive. An efficient algorithm to calculate the quantum mechanical 2D electron density has been developed. The method presented is comprehensive in that treatment includes the three open boundary conditions, where the narrow channel region opens into physically broad source, drain and gate regions. Results are presented for (i) drain current versus drain and gate voltages, (ii) comparison to results from Medici, and (iii) gate tunneling current, using 2D potential profiles. Methods to reduce the gate leakage current are also discussed based on simulation results.Comment: 12 figures. Journal of Applied Physics (to appear

Phase diagram of Eu magnetic ordering in Sn-flux-grown Eu(Fe1−x_{1-x}Cox_{x})2_{2}As2_{2} single crystals

The magnetic ground state of the Eu$^{2+}$ moments in a series of Eu(Fe$_{1-x}$Co$_{x}$)$_{2}$As$_{2}$ single crystals grown from the Sn flux has been investigated in detail by neutron diffraction measurements. Combined with the results from the macroscopic properties (resistivity, magnetic susceptibility and specific heat) measurements, a phase diagram describing how the Eu magnetic order evolves with Co doping in Eu(Fe$_{1-x}$Co$_{x}$)$_{2}$As$_{2}$ is established. The ground-state magnetic structure of the Eu$^{2+}$ spins is found to develop from the A-type antiferromagnetic (AFM) order in the parent compound, via the A-type canted AFM structure with some net ferromagnetic (FM) moment component along the crystallographic $\mathit{c}$ direction at intermediate Co doping levels, finally to the pure FM order at relatively high Co doping levels. The ordering temperature of Eu declines linearly at first, reaches the minimum value of 16.5(2) K around $\mathit{x}$ = 0.100(4), and then reverses upwards with further Co doping. The doping-induced modification of the indirect Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between the Eu$^{2+}$ moments, which is mediated by the conduction $\mathit{d}$ electrons on the (Fe,Co)As layers, as well as the change of the strength of the direct interaction between the Eu$^{2+}$ and Fe$^{2+}$ moments, might be responsible for the change of the magnetic ground state and the ordering temperature of the Eu sublattice. In addition, for Eu(Fe$_{1-x}$Co$_{x}$)$_{2}$As$_{2}$ single crystals with 0.10 $\leqslant$ $\mathit{x}$ $\leqslant$ 0.18, strong ferromagnetism from the Eu sublattice is well developed in the superconducting state, where a spontaneous vortex state is expected to account for the compromise between the two competing phenomena.Comment: 10 pages, 9 figure

Exact Spin and Pseudo-Spin Symmetric Solutions of the Dirac-Kratzer Problem with a tensor potential via Laplace Transform Approach

Exact bound state solutions of the Dirac equation for the Kratzer potential in the presence of a tensor potential are studied by using the Laplace transform approach for the cases of spin- and pseudo-spin symmetry. The energy spectra is obtained in the closed form for the relativistic as well as non-relativistic cases including the Coulomb potential. It is seen that our analytical results are in agrement with the ones given in literature. The numerical results are also given in a table for different parameter values.Comment: 8 page

Building Extraction from Very High Resolution Aerial Imagery Using Joint Attention Deep Neural Network

Automated methods to extract buildings from very high resolution (VHR) remote sensing data have many applications in a wide range of fields. Many convolutional neural network (CNN) based methods have been proposed and have achieved significant advances in the building extraction task. In order to refine predictions, a lot of recent approaches fuse features from earlier layers of CNNs to introduce abundant spatial information, which is known as skip connection. However, this strategy of reusing earlier features directly without processing could reduce the performance of the network. To address this problem, we propose a novel fully convolutional network (FCN) that adopts attention based re-weighting to extract buildings from aerial imagery. Specifically, we consider the semantic gap between features from different stages and leverage the attention mechanism to bridge the gap prior to the fusion of features. The inferred attention weights along spatial and channel-wise dimensions make the low level feature maps adaptive to high level feature maps in a target-oriented manner. Experimental results on three publicly available aerial imagery datasets show that the proposed model (RFA-UNet) achieves comparable and improved performance compared to other state-of-the-art models for building extraction

Role of axin in nerve growth factor-stimulated neurite outgrowth

The role of integrin-linked kinase (ILK), a kinase that is involved in various cellular processes, including adhesion and migration, has not been studied in primary neurons. Using mRNA dot blot and Western blot analysis of ILK in rat and human brain tissue, we found that ILK is expressed in various regions of the CNS. Immunohistochemical and immunocytochemical techniques revealed granular ILK staining that is enriched in neurons and colocalizes with the 1 integrin subunit. The role of ILK in neurite growth promotion by NGF was studied in rat pheochromocytoma cells and dorsal root ganglion neurons using a pharmacological inhibitor of ILK (KP-392) or after overexpres-sion of dominant-negative ILK (ILK-DN). Both molecular and pharmacological inhibition of ILK activity significantly reduced NGF-induced neurite outgrowth. Survival assays indicate that KP-392-induced suppression of neurite outgrowth occurred in the absence of cell death. ILK kinase activity was stimulated by NGF. NGF-mediated stimulation of phosphorylation of both AKT and the Taukinase glycogen synthase kinase-3 (GSK-3) was inhibited in the presence of KP-392 and after overexpression of ILK-DN. Consequently, ILKinhibition resulted in an increase in the hyperphosphorylation of Tau , a substrate of GSK-3. Together these findings indicate that ILK is an important effector in NGF-mediated neurite outgrowth. The role of integrin-linked kinase (ILK), a kinase that is involved in various cellular processes, including adhesion and migration, has not been studied in primary neurons. Using mRNA dot blot and Western blot analysis of ILK in rat and human brain tissue, we found that ILK is expressed in various regions of the CNS. Immunohistochemical and immunocytochemical techniques revealed granular ILK staining that is enriched in neurons and colocalizes with the 1 integrin subunit. The role of ILK in neurite growth promotion by NGF was studied in rat pheochromocytoma cells and dorsal root ganglion neurons using a pharmacological inhibitor of ILK (KP-392) or after overexpres- sion of dominant-negative ILK (ILK-DN). Both molecular and pharmacological inhibition of ILK activity significantly reduced NGF- induced neurite outgrowth. Survival assays indicate that KP-392-induced suppression of neurite outgrowth occurred in the absence of cell death. ILK kinase activity was stimulated by NGF. NGF-mediated stimulation of phosphorylation of both AKT and the Tau kinase glycogen synthase kinase-3 (GSK-3) was inhibited in the presence of KP-392 and after overexpression of ILK-DN. Consequently, ILK inhibition resulted in an increase in the hyperphosphorylation of Tau , a substrate of GSK-3. Together these findings indicate that ILK is an important effector in NGF-mediated neurite outgrowth