Consistent Recovery of Sensory Stimuli Encoded with MIMO Neural Circuits

We consider the problem of reconstructing finite energy stimuli encoded with a population of spiking leaky integrate-and-fire neurons. The reconstructed signal satisfies a consistency condition: when passed through the same neuron, it triggers the same spike train as the original stimulus. The recovered stimulus has to also minimize a quadratic smoothness optimality criterion. We formulate the reconstruction as a spline interpolation problem for scalar as well as vector valued stimuli and show that the recovery has a unique solution. We provide explicit reconstruction algorithms for stimuli encoded with single as well as a population of integrate-and-fire neurons. We demonstrate how our reconstruction algorithms can be applied to stimuli encoded with ON-OFF neural circuits with feedback. Finally, we extend the formalism to multi-input multi-output neural circuits and demonstrate that vector-valued finite energy signals can be efficiently encoded by a neural population provided that its size is beyond a threshold value. Examples are given that demonstrate the potential applications of our methodology to systems neuroscience and neuromorphic engineering

Bayesian spike inference from calcium imaging data

We present efficient Bayesian methods for extracting neuronal spiking information from calcium imaging data. The goal of our methods is to sample from the posterior distribution of spike trains and model parameters (baseline concentration, spike amplitude etc) given noisy calcium imaging data. We present discrete time algorithms where we sample the existence of a spike at each time bin using Gibbs methods, as well as continuous time algorithms where we sample over the number of spikes and their locations at an arbitrary resolution using Metropolis-Hastings methods for point processes. We provide Rao-Blackwellized extensions that (i) marginalize over several model parameters and (ii) provide smooth estimates of the marginal spike posterior distribution in continuous time. Our methods serve as complements to standard point estimates and allow for quantification of uncertainty in estimating the underlying spike train and model parameters

Multi input multi output neural population encoding

A formal mathematical model for representing neural stimuli is presented. The model enables the investigation of stimulus representation by spiking neurons, and provides algorithms that under certain conditions can recover the stimuli with no error, by knowing only the time of the spike trains. In our model, we assume that N bandlimited input stimuli approach the dendritic trees of M spiking neurons. Each stimulus comes to a different branch of each dendritic tree, and each dendritic tree is modeled as a linear time invariant (LTI) filter. The outputs of all dendritic branches are summed together with a background current (bias), and this sum enters the soma of each neuron, which is modeled as an Integrate-and-Fire neuron. We prove that under certain conditions, it is possible to recover all N input spike trains, by knowing only the M spike trains, and provide an algorithm for that purpose. The proof comes from the mathematical theory of frames and the conditions require a minimum average spike density from the neurons and some mild conditions in the impulse responses of the dendritic branches/filters. We illustrate this algorithm with an example that recovers the stimuli when the dendritic branches perform arbitrary but known time-shifts to the signal. This particular example is important as it illustrates how information from sensory neurons that respond with different latencies, can be combined together. Finally, the model points to the significance of neural population codes, as it shows that data from a single neuron can be misleading in terms of what the input stimulus is. We illustrate this significant observation with an example

A simple spiking retina model for exact video stimulus representation

A computational model for the representation of visual stimuli with a population of spiking neurons is presented. We show that under mild conditions it is possible to faithfully represent an analog video stream into a sequence of spike trains and provide an algorithm that recovers the video input by using only the spike times of the population. In our model an analog, bandlimited in time, video stream approaches the dendritic trees of a neural population. At each neuron, the multi-dimensional video input is filtered by the neuron's spatiotemporal receptive field, and the one-dimensional output dendritic current enters the soma of the neuron (see Figure 1). The set of the spatial receptive fields is modeled as a Gabor filterbank. The spike generation mechanism is threshold based: Each time the dendritic current exceeds a threshold a spike is fired and the membrane potential is reset by a negative potential through a negative feedback loop that gets triggered by the spike. This simple spike mechanism has been shown to accurately model the responses of various neurons in the early visual system 1. Figure 1 Encoding and decoding mechanisms for video stimuli: The stimulus is filtered by the receptive fields of the neurons and enters the soma Encoding and decoding mechanisms for video stimuli: The stimulus is filtered by the receptive fields of the neurons and enters the soma. Spike generation is threshold based and a negative feedback mechanism resets the membrane potential after each spike. In the decoding part each spike, represented by a delta pulse, is weighted by an appropriate coefficient and then filtered from the same receptive field for stimulus reconstruction. The total sum is passed from a low pass filter to recover the original input stimulus. We prove and demonstrate that we can recover the whole video stream based only on the knowledge of the spike times, provided that the size of the neural population is sufficiently big. Increasing the number of neurons to achieve better representation is consistent with basic neurobiological thought 2. Although very precise, the responses of visual neurons show some variability between subsequent stimulus repeats, which can be attributed to various noise sources 1. We examine the effect of noise on our algorithm and show that the reconstruction quality gracefully degrades when white noise is present at the input or at the feedback loop

Phases of two-dimensional spinless lattice fermions with first-quantized deep neural-network quantum states

First-quantized deep neural network techniques are developed for analyzing strongly coupled fermionic systems on the lattice. Using a Slater-Jastrow inspired ansatz which exploits deep residual networks with convolutional residual blocks, we approximately determine the ground state of spinless fermions on a square lattice with nearest-neighbor interactions. The flexibility of the neural-network ansatz results in a high level of accuracy when compared to exact diagonalization results on small systems, both for energy and correlation functions. On large systems, we obtain accurate estimates of the boundaries between metallic and charge ordered phases as a function of the interaction strength and the particle density

Efficient and accurate extraction of in vivo calcium signals from microendoscopic video data

In vivo calcium imaging through microendoscopic lenses enables imaging of previously inaccessible neuronal populations deep within the brains of freely moving animals. However, it is computationally challenging to extract single-neuronal activity from microendoscopic data, because of the very large background fluctuations and high spatial overlaps intrinsic to this recording modality. Here, we describe a new constrained matrix factorization approach to accurately separate the background and then demix and denoise the neuronal signals of interest. We compared the proposed method against previous independent components analysis and constrained nonnegative matrix factorization approaches. On both simulated and experimental data recorded from mice, our method substantially improved the quality of extracted cellular signals and detected more well-isolated neural signals, especially in noisy data regimes. These advances can in turn significantly enhance the statistical power of downstream analyses, and ultimately improve scientific conclusions derived from microendoscopic data

Einheit von Park und Architektur : der Park am IG Hochhaus

Cerebellar granule cells, which constitute half the brain's neurons, supply Purkinje cells with contextual information necessary for motor learning, but how they encode this information is unknown. Here we show, using two-photon microscopy to track neural activity over multiple days of cerebellum-dependent eyeblink conditioning in mice, that granule cell populations acquire a dense representation of the anticipatory eyelid movement. Initially, granule cells responded to neutral visual and somatosensory stimuli as well as periorbital airpuffs used for training. As learning progressed, two-thirds of monitored granule cells acquired a conditional response whose timing matched or preceded the learned eyelid movements. Granule cell activity covaried trial by trial to form a redundant code. Many granule cells were also active during movements of nearby body structures. Thus, a predictive signal about the upcoming movement is widely available at the input stage of the cerebellar cortex, a

An inpainting system for automatic image structure - texture restoration with text removal

In this paper we deal with the inpainting problem and with the problem of finding text in images. We first review many of the methods used for structure and texture inpaintings. The novel contribution of the paper is the combination of the inpainting techniques with the techniques of finding text in images and a simple morphological algorithm that links them. This combination results in an automatic system for text removal and image restoration that requires no user interface at all. Examples on real images show very good performance of the proposed system and the importance of the new linking algorithm. Index Terms — inpainting, texture synthesis, text detection, mathematical morphology. 1