Computing with the Integrate and Fire Neuron: Weber's Law, Multiplication and Phase Detection

The integrate and fire model (Stein, 1967) provides an analytically tractable formalism of neuronal firing rate in terms of a neuron's membrane time constant, threshold and refractory period. Integrate and fire (IAF) neurons have mainly been used to model physiologically realistic spike trains but little application of the IAF model appears to have been made in an explicitly computational context. In this paper we show that the transfer function of an IAF neuron provides, over a wide parameter range, a compressive nonlinearity sufficiently close to that of the logarithm so that IAF neurons can be used to multiply neural signals by mere addition of their outputs. Thus, although the IAF transfer function is not explicitly logarithmic, its compressive parameter regime supports a simple, single neuron model for multiplication. A simulation of the IAF multiplier shows that under a wide choice of parameters, the IAF neuron can multiply its inputs to within a 5% relative error. We also show that an IAF neuron under a different, yet biologically reasonable, parameter regime can have a quasi-linear transfer function, acting as an adder or a gain node. We then show an application in which the compressive transfer function of the IAF model provides a simple mechanism for phase-detection: multiplication of 40Hz phasic inputs followed by low-pass filtering yields an output that is a quasi-linear function of the relative phase of the inputs. This is a neural version of the heterodyne phase detection principle. Finally, we briefly discuss the precision and dynamic range of an IAF multiplier that is restricted to reasonable firing rates (in the range of 10-300 Hz) and reasonable computation time (in the range of 25-200 milliseconds).National Institute of Mental Health (5R01MH45969-04); Office of Naval Research (N00014-95-1-0409

Pattern formation in a ring cavity with temporally incoherent feedback

We present a theoretical and experimental study of modulation instability and pattern formation in a passive nonlinear optical cavity that is longer than the coherence length of the light circulating in it. Pattern formation in this cavity exhibits various features of a second-order phase transition, closely resembling laser action

On the importance of experimental details: A Comment on "Non-Polaritonic Effects in Cavity-Modified Photochemistry"

Recently, an article by the Barnes group reported on the experimental study of a photoisomerization reaction inside an optical cavity, claiming to reproduce previous results by Hutchison et al. and making the point that in such setups, changes in the absorption of ultraviolet radiation by the molecules in the cavity can lead to modifications in the photochemical reaction rate. While Hutchison et al. associated such modifications with the emergence of strong light-matter coupling, in their attempt to re-examine these experiments, Barnes et al. did not find any evidence that strong coupling needs to be invoked to explain the observed effects. In response to this publication, we herein highlight the main differences between the two experimental studies, and explain why the results of Barnes et al. are irrelevant to the former study and have no bearing on its conclusions. Specifically, we show that under the experimental conditions used by Hutchison et al. such intensity-modification effects are negligible and can therefore be ruled out

Data-guided statistical sparse measurements modeling for compressive sensing

Digital image acquisition can be a time consuming process for situations where high spatial resolution is required. As such, optimizing the acquisition mechanism is of high importance for many measurement applications. Acquiring such data through a dynamically small subset of measurement locations can address this problem. In such a case, the measured information can be regarded as incomplete, which necessitates the application of special reconstruction tools to recover the original data set. The reconstruction can be performed based on the concept of sparse signal representation. Recovering signals and images from their sub-Nyquist measurements forms the core idea of compressive sensing (CS). In this work, a CS-based data-guided statistical sparse measurements method is presented, implemented and evaluated. This method significantly improves image reconstruction from sparse measurements. In the data-guided statistical sparse measurements approach, signal sampling distribution is optimized for improving image reconstruction performance. The sampling distribution is based on underlying data rather than the commonly used uniform random distribution. The optimal sampling pattern probability is accomplished by learning process through two methods - direct and indirect. The direct method is implemented for learning a nonparametric probability density function directly from the dataset. The indirect learning method is implemented for cases where a mapping between extracted features and the probability density function is required. The unified model is implemented for different representation domains, including frequency domain and spatial domain. Experiments were performed for multiple applications such as optical coherence tomography, bridge structure vibration, robotic vision, 3D laser range measurements and fluorescence microscopy. Results show that the data-guided statistical sparse measurements method significantly outperforms the conventional CS reconstruction performance. Data-guided statistical sparse measurements method achieves much higher reconstruction signal-to-noise ratio for the same compression rate as the conventional CS. Alternatively, Data-guided statistical sparse measurements method achieves similar reconstruction signal-to-noise ratio as the conventional CS with significantly fewer samples

Incoherent solitons in instantaneous nonlocal nonlinear media

We predict random-phase spatial solitons in instantaneous nonlocal nonlinear media. The key mechanism responsible for self-trapping of such incoherent wave packets is played by the nonlocal (rather than the traditional noninstantaneous) nature of the nonlinearity. This kind of incoherent soliton has profoundly different features than other incoherent solitons