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

Fast, Simple Calcium Imaging Segmentation with Fully Convolutional Networks

Calcium imaging is a technique for observing neuron activity as a series of images showing indicator fluorescence over time. Manually segmenting neurons is time-consuming, leading to research on automated calcium imaging segmentation (ACIS). We evaluated several deep learning models for ACIS on the Neurofinder competition datasets and report our best model: U-Net2DS, a fully convolutional network that operates on 2D mean summary images. U-Net2DS requires minimal domain-specific pre/post-processing and parameter adjustment, and predictions are made on full $512\times512$ images at $\approx$9K images per minute. It ranks third in the Neurofinder competition ($F_1=0.569$) and is the best model to exclusively use deep learning. We also demonstrate useful segmentations on data from outside the competition. The model's simplicity, speed, and quality results make it a practical choice for ACIS and a strong baseline for more complex models in the future.Comment: Accepted to 3rd Workshop on Deep Learning in Medical Image Analysis (http://cs.adelaide.edu.au/~dlmia3/

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

La territorialité de l’Église orthodoxe en France, entre exclusivisme juridictionnel et catholicité locale

Issue de mouvements migratoires liés aux grands bouleversements géopolitiques du 20ème siècle, l’orthodoxie en France est loin de constituer un ensemble culturellement homogène. L’existence de multiples juridictions suivant l’origine nationale, l’Eglise de rattachement et la trajectoire identitaire particulière de chaque communauté est une réalité qui façonne l’organisation territoriale orthodoxe dans la « diaspora ». D’autant plus que cette organisation reflète des rapports de pouvoir entre Eglises et des antagonismes entre différentes acceptations nationales de l’orthodoxie. Et pourtant, selon les règles ecclésiologiques orthodoxes, le territoire, avec sa diversité culturelle, ne devrait pas être un facteur de division mais un principe unificateur.Following migration movements due to the major geopolitical changes of the 20th century, orthodoxy in France is far from being a homogenous cultural ensemble. The existence of multiple jurisdictions based on national origin, the Church of canonical attachment and the particular identity of every community creates a reality that determines the territorial organisation of orthodoxy in the « Diaspora », especially since this type of structure reflects both a certain balance of power between Churches and an antagonism between different national understandings of Orthodoxy. And yet, according to the Orthodox ecclesiology, territory, along with its cultural diversity, should not be a factor of division but rather a unifying principle

L’émigration russe et la naissance d’une orthodoxie française 1925-1953

La révolution d’octobre 1917 et la guerre civile qui s’ensuivit en Russie eut comme conséquence l’émigration de millions d’orthodoxes russes vers les pays de l’Europe occidentale et plus particulièrement la France. Persuadés depuis le début du déracinement que leur exile avait un caractère providentiel, les orthodoxes russes de France ont œuvré pour la réalisation d’une synthèse qui permettrait le rapprochement entre les chrétiens d’Orient et d’Occident et aboutirait au dépassement définitif des dilemmes identitaires historiques. Durant la période 1925-1953, la reconnaissance du français comme langue liturgique orthodoxe, la fondation de la première paroisse orthodoxe de langue française, l’acceptation dans l’orthodoxie d’un groupe chrétien français utilisant une ancienne forme liturgique gallicane, la recherche pour la reconstitution dudit « rite des Gaules » et les efforts pour l’organisation ecclésiastique d’une « orthodoxie française » sous l’obédience du patriarcat de Moscou, sont des exemples montrant l’engagement sincère de certains esprits pionniers au sein de l’émigration russe pour la réalisation d’une orthodoxie authentiquement occidentale

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

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

Excitatory and Inhibitory Subnetworks Are Equally Selective during Decision-Making and Emerge Simultaneously during Learning

Inhibitory neurons, which play a critical role in decision-making models, are often simplified as a single pool of non-selective neurons lacking connection specificity. This assumption is supported by observations in the primary visual cortex: inhibitory neurons are broadly tuned in vivo and show non-specific connectivity in slice. The selectivity of excitatory and inhibitory neurons within decision circuits and, hence, the validity of decision-making models are unknown. We simultaneously measured excitatory and inhibitory neurons in the posterior parietal cortex of mice judging multisensory stimuli. Surprisingly, excitatory and inhibitory neurons were equally selective for the animal’s choice, both at the single-cell and population level. Further, both cell types exhibited similar changes in selectivity and temporal dynamics during learning, paralleling behavioral improvements. These observations, combined with modeling, argue against circuit architectures assuming non-selective inhibitory neurons. Instead, they argue for selective subnetworks of inhibitory and excitatory neurons that are shaped by experience to support expert decision-making