The N=4 effective action of type IIA supergravity compactified on SU(2)-structure manifolds

We study compactifications of type IIA supergravity on six-dimensional manifolds with SU(2) structure and compute the low-energy effective action in terms of the non-trivial intrinsic torsion. The consistency with gauged N=4 supergravity is established and the gauge group is determined. Depending on the structure of the intrinsic torsion, antisymmetric tensor fields can become massive.Comment: 29 pages, latex, v2: minor corrections, added references, published versio

Amplitude and phase effects on the synchronization of delay-coupled oscillators

We consider the behavior of Stuart–Landau oscillators as generic limit-cycle oscillators when they are interacting with delay. We investigate the role of amplitude and phase instabilities in producing symmetry-breaking/restoring transitions. Using analytical and numerical methods we compare the dynamics of one oscillator with delayed feedback, two oscillators mutually coupled with delay, and two delay-coupled elements with self-feedback. Taking only the phase dynamics into account, no chaotic dynamics is observed, and the stability of the identical synchronization solution is the same in each of the three studied networks of delay-coupled elements. When allowing for a variable oscillation amplitude, the delay can induce amplitude instabilities. We provide analytical proof that, in case of two mutually coupled elements, the onset of an amplitude instability always results in antiphase oscillations, leading to a leader-laggard behavior in the chaotic regime. Adding selffeedback with the same strength and delay as the coupling stabilizes the system in the transverse direction and, thus, promotes the onset of identically synchronized behaviorWe would like to thank T. Erneux, E. Schöll, S. Yanchuk, and P. Perlikowski for helpful discussions. O.D. acknowledges the Research Foundation Flanders FWO-Vlaanderen for a fellowship and for project support. This work was partially supported by the Interuniversity Attraction Poles program of the Belgian Science Policy Office, under Grant No. IAP VI-10 “photonics@be,” by MICINN Spain under project DeCoDicA Grant No. TEC2009- 14101 ,, and by the project PHOCUS EU FET Open Grant No. 240763 .Peer reviewe

Role of delay for the symmetry in the dynamics of networks

PACS number(s): 05.45.Xt, 89.75.Kd, 89.75.Hc, 02.30.KsThe symmetry in a network of oscillators determines the spatiotemporal patterns of activity that can emerge. We study how a delay in the coupling affects symmetry-breaking and -restoring bifurcations. We are able to draw general conclusions in the limit of long delays. For one class of networks we derive a criterion that predicts that delays have a symmetrizing effect. Moreover, we demonstrate that for any network admitting a steady-state solution, a long delay can solely advance the first bifurcation point as compared to the instantaneous-coupling regime.This work was partially supported by the Interuniversity Attraction Poles program Photonics@be of the Belgian Science Policy Office under Grant No. IAP VI-10 by MICINN (Spain) under Project No. DeCoDicA (TEC2009-14101) and by the project PHOCUS (EU FET-Open Grant No. 240763). S. Yanchuk and P. Perlikowski are gratefully acknowledged for fruitful discussions.Peer reviewe

Tunable semiconductor ring laser with filtered optical feedback: Traveling wave description and experimental validation

We study experimentally and theoretically a semiconductor ring laser with four filtering channels providing filtered delayed optical feedback. To describe and analyze the wavelength selection and tuning in this device, we exploit the traveling-wave model determining the evolution of optical fields and carrier density along the ring cavity and filtering branches. The numerical results agree with the experimental observations: we can reproduce the wavelength tuning, the multiple wavelength emission, and the wavelength switching speed measured in these devices. The traveling-wave model allows us to study in detail the effect of the different laser parameters and can be useful for designing the future devices

LUCID-GAN: Conditional Generative Models to Locate Unfairness

Most group fairness notions detect unethical biases by computing statistical parity metrics on a model's output. However, this approach suffers from several shortcomings, such as philosophical disagreement, mutual incompatibility, and lack of interpretability. These shortcomings have spurred the research on complementary bias detection methods that offer additional transparency into the sources of discrimination and are agnostic towards an a priori decision on the definition of fairness and choice of protected features. A recent proposal in this direction is LUCID (Locating Unfairness through Canonical Inverse Design), where canonical sets are generated by performing gradient descent on the input space, revealing a model's desired input given a preferred output. This information about the model's mechanisms, i.e., which feature values are essential to obtain specific outputs, allows exposing potential unethical biases in its internal logic. Here, we present LUCID-GAN, which generates canonical inputs via a conditional generative model instead of gradient-based inverse design. LUCID-GAN has several benefits, including that it applies to non-differentiable models, ensures that canonical sets consist of realistic inputs, and allows to assess proxy and intersectional discrimination. We empirically evaluate LUCID-GAN on the UCI Adult and COMPAS data sets and show that it allows for detecting unethical biases in black-box models without requiring access to the training data.Comment: 24 pages, 6 figures, 1st World Conference on eXplainable Artificial Intelligenc

Tunable semiconductor ring laser with filtered optical feedback: Traveling wave description and experimental validation

We study experimentally and theoretically a semiconductor ring laser with four filtering channels providing filtered delayed optical feedback. To describe and analyze the wavelength selection and tuning in this device, we exploit the traveling-wave model determining the evolution of optical fields and carrier density along the ring cavity and filtering branches. The numerical results agree with the experimental observations: we can reproduce the wavelength tuning, the multiple wavelength emission, and the wavelength switching speed measured in these devices. The traveling-wave model allows us to study in detail the effect of the different laser parameters and can be useful for designing the future devices

Solitary and Coupled Semiconductor Ring Lasers as Optical Spiking Neurons

We theoretically investigate the possibility of generating pulses in an excitable (asymmetric) semiconductor ring laser (SRL) using optical trigger pulses. We show that the phase difference between the injected field and the electric field inside the SRL determines the direction of the perturbation in phase space. Due to the folded shape of the excitability threshold, this has an important influence on the ability to cross it. A mechanism for exciting multiple consecutive pulses using a single trigger pulse (i.e. multi pulse excitability) is revealed. We furthermore investigate the possibility of using asymmetric SRLs in a coupled configuration, which is a first step toward an all-optical neural network using SRLs as building blocks.Comment: 9 pages, 7 figure

bunpogakushu ni yakudatsu goikyoiku -imirontekihyogenbunpo no shuppatsuten-

We study the synchronization behavior of Stuart-Landau oscillators coupled with delay, using analytical and numerical methods. We compare the dynamics of one oscillator with delayed feedback, two mutually oscillators coupled with delay, and two delay-coupled elements with feedback. Taking only the phase dynamics into account, no chaotic dynamics has been observed. Moreover, the stability of the symmetric (identical synchronization) solution is the same in each of the three studied networks of delay-coupled elements. When allowing variable oscillation amplitude, the delay can induce amplitude instabilities. We provide analytical proof that, in case of two mutually coupled elements, the onset of an amplitude instability is accompanied by a symmetry breaking, leading to the in lasers observed leader-laggard behavior in the chaotic regime. Adding self-feedback (with the same strength and delay as the coupling), stabilizes the system in transverse directionO.D. acknowledges the Research Foundation Flanders (FWO-Vlaanderen) for a fellowship and for project support. R.V. acknowledges the support of the Hertie Foundation. This work was partially supported by the Interuniversity Attraction Poles program of the Belgian Science Policy Office, under grant IAP VI-10 ”photonics@ be” and by the European Community Project GABA (FP6-NEST contract 043309).Peer reviewe

Do Optomechanical Metasurfaces Run Out of Time?

Artificially structured metasurfaces make use of specific configurations of subwavelength resonators to efficiently manipulate electromagnetic waves. Additionally, optomechanical metasurfaces have the desired property that their actual configuration may be tuned by adjusting the power of a pump beam, as resonators move to balance pump-induced electromagnetic forces with forces due to elastic filaments or substrates. Although the reconfiguration time of optomechanical metasurfaces crucially determines their performance, the transient dynamics of unit cells from one equilibrium state to another is not understood. Here, we make use of tools from nonlinear dynamics to analyze the transient dynamics of generic optomechanical metasurfaces based on a damped-resonator model with one configuration parameter. We show that the reconfiguration time of optomechanical metasurfaces is not only limited by the elastic properties of the unit cell but also by the nonlinear dependence of equilibrium states on the pump power. For example, when switching is enabled by hysteresis phenomena, the reconfiguration time is seen to increase by over an order of magnitude. To illustrate these results, we analyze the nonlinear dynamics of a bilayer cross-wire metasurface whose optical activity is tuned by an electromagnetic torque. Moreover, we provide a lower bound for the configuration time of generic optomechanical metasurfaces. This lower bound shows that optomechanical metasurfaces cannot be faster than state-of-the-art switches at reasonable powers, even at optical frequencies

Excitability in optical systems close to Z2-symmetry

We report theoretically and experimentally on excitability in semiconductor ring lasers in order to reveal a mechanism of excitability, general for systems close to Z2-symmetry. The global shapes of the invariant manifolds of a saddle in the vicinity of a homoclinic loop determine the origin of excitability and the fea- tures of the excitable pulses. We show how to experimentally make a semiconductor ring laser excitable by breaking the Z2-symmetry in a controlled way. The experiments confirm the theoretical predictions.Comment: 4 pages, 4 figure