There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Artificial Neural Networks have dramatically improved performance for many machine learning tasks. We demonstrate a new architecture for a fully optical neural network that enables a computational speed enhancement of at least two orders of magnitude and three orders of magnitude in power efficiency over state-of-the-art electronics.

Deep learning with coherent nanophotonic circuits

: This thesis applies neural network feature selection techniques to multivariate time series data to improve prediction of a target time series. Two approaches to feature selection are used. First, a subset enumeration method is used to determine which financial indicators are most useful for aiding in prediction of the S&P 500 futures daily price. The candidate indicators evaluated include RSI, Stochastics and several moving averages. Results indicate that the Stochastics and RSI indicators result in better prediction results than the moving averages. The second approach to feature selection is calculation of individual saliency metrics. A new decision boundary-based individual saliency metric, and a classifier independent saliency metric are developed and tested. Ruck's saliency metric, the decision boundary based saliency metric, and the classifier independent saliency metric are compared for a data set consisting of the RSI and Stochastics indicators as well as delayed closing price values. The decision based metric and the Ruck metric results are similar, but the classifier independent metric agrees with neither of the other metrics. The nine most salient features, determined by the decision boundary based metric, are used to train a neural network and the results are presented and compared to other published results. (AN)

/pdf/nonlinear-time-series-analysis-1j3a35n4y3.pdf

Nonlinear Time Series Analysis.

Recent advances in physical reservoir computing: A review

Neurons in the brain behave as nonlinear oscillators, which develop rhythmic activity and interact to process information. Taking inspiration from this behaviour to realize high-density, low-power neuromorphic computing will require very large numbers of nanoscale nonlinear oscillators. A simple estimation indicates that to fit 108 oscillators organized in a two-dimensional array inside a chip the size of a thumb, the lateral dimension of each oscillator must be smaller than one micrometre. However, nanoscale devices tend to be noisy and to lack the stability that is required to process data in a reliable way. For this reason, despite multiple theoretical proposals and several candidates, including memristive and superconducting oscillators, a proof of concept of neuromorphic computing using nanoscale oscillators has yet to be demonstrated. Here we show experimentally that a nanoscale spintronic oscillator (a magnetic tunnel junction) can be used to achieve spoken-digit recognition with an accuracy similar to that of state-of-the-art neural networks. We also determine the regime of magnetization dynamics that leads to the greatest performance. These results, combined with the ability of the spintronic oscillators to interact with each other, and their long lifetime and low energy consumption, open up a path to fast, parallel, on-chip computation based on networks of oscillators.

/pdf/neuromorphic-computing-with-nanoscale-spintronic-oscillators-3e3rewmz7x.pdf

Neuromorphic computing with nanoscale spintronic oscillators

For a diode laser subjected to filtered feedback from a phase-conjugating mirror, we present the first exact stability analysis and various noise spectra. The stability properties are intermediate between those of the injection laser and the laser with conventional optical feedback. The role of a finite response-time is to drastically enhance the steady-state stability For moderate feedback, the frequency noise is suppressed by several orders of magnitude, and the main relaxation frequency of the laser shows a crossover from the usual relaxation oscillation frequency to a new frequency determined by the amount of feedback. This may be of technological importance since it is expected to improve the modulation bandwidth.

/pdf/stability-and-noise-properties-of-diode-lasers-with-phase-38r3d7s92j.pdf

Stability and noise properties of diode lasers with phase-conjugate feedback

We present experimental and theoretical results of noise-induced attractor hopping between dynamical states found in a single transverse mode vertical-cavity surface-emitting laser (VCSEL) subject to parallel optical injection. These transitions involve dynamical states with different polarizations of the light emitted by the VCSEL. We report an experimental map identifying, in the injected power-frequency detuning plane, regions where attractor hopping between two, or even three, different states occur. The transition between these behaviors is characterized by using residence time distributions. We find multistability regions that are characterized by heavy-tailed residence time distributions. These distributions are characterized by a -1.83±0.17 power law. Between these regions we find coherence enhancement of noise-induced attractor hopping in which transitions between states occur regularly. Simulation results show that frequency detuning variations and spontaneous emission noise play a role in causing switching between attractors. We also find attractor hopping between chaotic states with different polarization properties. In this case, simulation results show that spontaneous emission noise inherent to the VCSEL is enough to induce this hopping.

/pdf/attractor-hopping-between-polarization-dynamical-states-in-a-25qeer69uq.pdf

Attractor hopping between polarization dynamical states in a vertical-cavity surface-emitting laser subject to parallel optical injection

Relative intensity noise spectra of weakly index guided VCSELs in a multitransverse mode regime are analyzedby using a model that takes into account all the transverse modes supported by the waveguide. Several resonancepeaks are obtained in the noise spectra that correspond to the relaxation oscillation frequencies of the transverse modes. In is shown that for low spatially overlapping transverse modes, low RIN operation can be maintained. However, the excitation of transverse modes with a significant mode overlap leads to a clear enhancement of theRIN at low frequencies. Keywords: Semiconductor Lasers, Vertical cavity lasers, Transverse modes, Relative Intensity Noise 1. INTRODUCTION Vertical-cavity surface-emitting lasers (VCSELs) are highly attractive light sources for applications in intercon- nections and optical communications, because of their useful characteristics such as single longitudinal modeoperation, low threshold current, circular output beam, and wafer scale integration.'2 An important consider-ation for such applications of VCSELs is the understanding of their noise characteristics. Several experimentalstudies of the relative intensity noise (RIN) in VCSELs have been performed.39 In general the noise perfor-inance of VCSELs operating in the fundamental mode is comparable to that of edge emitting lasers. However,

Mode partition noise in multi-transverse mode vertical-cavity surface-emitting lasers

A physical scheme based on a single nonlinear dynamical system with delayed feedback has been recently proposed for Reservoir Computing (RC) [1]. In this paper we present a computational implementation of this idea using a simple chain topology with properties derived from its physical counterpart (e.g. the reservoir is defined by two tunable parameters related to feedbackand input-strength terms). An application to time series prediction is described and a comparison with other standard reservoir computing methods is given.

https://www.elen.ucl.ac.be/Proceedings/esann/esannpdf/es2012-142.pdf

Simple reservoirs with chain topology based on a single time-delay nonlinear node.

We demonstrate experimentally the existence of the elliptically polarized injection-locked (EPIL) state. This state is observed when a single-transverse mode VCSEL is subject to orthogonal optical injection. The spectral feature of the EPIL state is verified and the power of each polarization is measured. The regime of the EPIL state is identified in the parameter plane of frequency detuning and injection power for different bias currents. As current decreases the frequency detuning range for the EPIL to exist is narrower and shifts toward the negative frequency detuning. Periodic dynamics of the VCSEL is found in the neighborhood of the EPIL regime.

Luis Pesquera

Papers

Stability and noise properties of diode lasers with phase-conjugate feedback

Attractor hopping between polarization dynamical states in a vertical-cavity surface-emitting laser subject to parallel optical injection

Mode partition noise in multi-transverse mode vertical-cavity surface-emitting lasers

Simple reservoirs with chain topology based on a single time-delay nonlinear node.

Investigation of elliptically polarized injection locked states in VCSELs subject to orthogonal optical injection