A wideband linear tunable CDTA and its application in field programmable analogue array

This document is the Accepted Manuscript version of the following article: Hu, Z., Wang, C., Sun, J. et al. ‘A wideband linear tunable CDTA and its application in field programmable analogue array’, Analog Integrated Circuits and Signal Processing, Vol. 88 (3): 465-483, September 2016. Under embargo. Embargo end date: 6 June 2017. The final publication is available at Springer via https://link.springer.com/article/10.1007%2Fs10470-016-0772-7 © Springer Science+Business Media New York 2016In this paper, a NMOS-based wideband low power and linear tunable transconductance current differencing transconductance amplifier (CDTA) is presented. Based on the NMOS CDTA, a novel simple and easily reconfigurable configurable analogue block (CAB) is designed. Moreover, using the novel CAB, a simple and versatile butterfly-shaped FPAA structure is introduced. The FPAA consists of six identical CABs, and it could realize six order current-mode low pass filter, second order current-mode universal filter, current-mode quadrature oscillator, current-mode multi-phase oscillator and current-mode multiplier for analog signal processing. The Cadence IC Design Tools 5.1.41 post-layout simulation and measurement results are included to confirm the theory.Peer reviewedFinal Accepted Versio

Birth of a Learning Law

Defense Advanced Research Projects Agency; Office of Naval Research (N00014-95-1-0409, N00014-95-1-0657, N00014-92-J-1309

Noncommutative vector bundles over fuzzy CP^N and their covariant derivatives

We generalise the construction of fuzzy CP^N in a manner that allows us to access all noncommutative equivariant complex vector bundles over this space. We give a simplified construction of polarization tensors on S^2 that generalizes to complex projective space, identify Laplacians and natural noncommutative covariant derivative operators that map between the modules that describe noncommuative sections. In the process we find a natural generalization of the Schwinger-Jordan construction to su(n) and identify composite oscillators that obey a Heisenberg algebra on an appropriate Fock space.Comment: 34 pages, v2 contains minor corrections to the published versio

Quantized Nambu-Poisson Manifolds and n-Lie Algebras

We investigate the geometric interpretation of quantized Nambu-Poisson structures in terms of noncommutative geometries. We describe an extension of the usual axioms of quantization in which classical Nambu-Poisson structures are translated to n-Lie algebras at quantum level. We demonstrate that this generalized procedure matches an extension of Berezin-Toeplitz quantization yielding quantized spheres, hyperboloids, and superspheres. The extended Berezin quantization of spheres is closely related to a deformation quantization of n-Lie algebras, as well as the approach based on harmonic analysis. We find an interpretation of Nambu-Heisenberg n-Lie algebras in terms of foliations of R^n by fuzzy spheres, fuzzy hyperboloids, and noncommutative hyperplanes. Some applications to the quantum geometry of branes in M-theory are also briefly discussed.Comment: 43 pages, minor corrections, presentation improved, references adde

Instantons, supersymmetric vacua, and emergent geometries

We study instanton solutions and superpotentials for the large number of vacua of the plane-wave matrix model and a 2+1 dimensional Super Yang-Mills theory on $R\times S^2$ with sixteen supercharges. We get the superpotential in the weak coupling limit from the gauge theory description. We study the gravity description of these instantons. Perturbatively with respect to a background, they are Euclidean branes wrapping cycles in the dual gravity background. Moreover, the superpotential can be given by the energy of the electric charge system characterizing each vacuum. These charges are interpreted as the eigenvalues of matrices from a reduction for the 1/8 BPS sector of the gauge theories. We also discuss qualitatively the emergence of the extra spatial dimensions appeared on the gravity side.Comment: 29 pages, 3 figures, latex. v2: references added, comments added. v3: accepted version in PR

Magnetic operations: a little fuzzy physics?

We examine the behaviour of charged particles in homogeneous, constant and/or oscillating magnetic fields in the non-relativistic approximation. A special role of the geometric center of the particle trajectory is elucidated. In quantum case it becomes a 'fuzzy point' with non-commuting coordinates, an element of non-commutative geometry which enters into the traditional control problems. We show that its application extends beyond the usually considered time independent magnetic fields of the quantum Hall effect. Some simple cases of magnetic control by oscillating fields lead to the stability maps differing from the traditional Strutt diagram.Comment: 28 pages, 8 figure