A tractable method for describing complex couplings between neurons and population rate

Neurons within a population are strongly correlated, but how to simply capture these correlations is still a matter of debate. Recent studies have shown that the activity of each cell is influenced by the population rate, defined as the summed activity of all neurons in the population. However, an explicit, tractable model for these interactions is still lacking. Here we build a probabilistic model of population activity that reproduces the firing rate of each cell, the distribution of the population rate, and the linear coupling between them. This model is tractable, meaning that its parameters can be learned in a few seconds on a standard computer even for large population recordings. We inferred our model for a population of 160 neurons in the salamander retina. In this population, single-cell firing rates depended in unexpected ways on the population rate. In particular, some cells had a preferred population rate at which they were most likely to fire. These complex dependencies could not be explained by a linear coupling between the cell and the population rate. We designed a more general, still tractable model that could fully account for these non-linear dependencies. We thus provide a simple and computationally tractable way to learn models that reproduce the dependence of each neuron on the population rate

Blindfold learning of an accurate neural metric

The brain has no direct access to physical stimuli, but only to the spiking activity evoked in sensory organs. It is unclear how the brain can structure its representation of the world based on differences between those noisy, correlated responses alone. Here we show how to build a distance map of responses from the structure of the population activity of retinal ganglion cells, allowing for the accurate discrimination of distinct visual stimuli from the retinal response. We introduce the Temporal Restricted Boltzmann Machine to learn the spatiotemporal structure of the population activity, and use this model to define a distance between spike trains. We show that this metric outperforms existing neural distances at discriminating pairs of stimuli that are barely distinguishable. The proposed method provides a generic and biologically plausible way to learn to associate similar stimuli based on their spiking responses, without any other knowledge of these stimuli

Closed-loop estimation of retinal network sensitivity reveals signature of efficient coding

According to the theory of efficient coding, sensory systems are adapted to represent natural scenes with high fidelity and at minimal metabolic cost. Testing this hypothesis for sensory structures performing non-linear computations on high dimensional stimuli is still an open challenge. Here we develop a method to characterize the sensitivity of the retinal network to perturbations of a stimulus. Using closed-loop experiments, we explore selectively the space of possible perturbations around a given stimulus. We then show that the response of the retinal population to these small perturbations can be described by a local linear model. Using this model, we computed the sensitivity of the neural response to arbitrary temporal perturbations of the stimulus, and found a peak in the sensitivity as a function of the frequency of the perturbations. Based on a minimal theory of sensory processing, we argue that this peak is set to maximize information transmission. Our approach is relevant to testing the efficient coding hypothesis locally in any context where no reliable encoding model is known

A deep neural network for 12-lead electrocardiogram interpretation outperforms a conventional algorithm, and its physician overread, in the diagnosis of atrial fibrillation

Background: Automated electrocardiogram (ECG) interpretations may be erroneous, and lead to erroneous overreads, including for atrial fibrillation (AF). We compared the accuracy of the first version of a new deep neural network 12-Lead ECG algorithm (Cardiologs®) to the conventional Veritas algorithm in interpretation of AF. Methods: 24,123 consecutive 12-lead ECGs recorded over 6 months were interpreted by 1) the Veritas® algorithm, 2) physicians who overread Veritas® (Veritas® + physician), and 3) Cardiologs® algorithm. We randomly selected 500 out of 858 ECGs with a diagnosis of AF according to either algorithm, then compared the algorithms' interpretations, and Veritas® + physician, with expert interpretation. To assess sensitivity for AF, we analyzed a separate database of 1473 randomly selected ECGs interpreted by both algorithms and by blinded experts. Results: Among the 500 ECGs selected, 399 had a final classification of AF; 101 (20.2%) had ≥1 false positive automated interpretation. Accuracy of Cardiologs® (91.2%; CI: 82.4–94.4) was higher than Veritas® (80.2%; CI: 76.5–83.5) (p < 0.0001), and equal to Veritas® + physician (90.0%, CI:87.1–92.3) (p = 0.12). When Veritas® was incorrect, accuracy of Veritas® + physician was only 62% (CI 52–71); among those ECGs, Cardiologs® accuracy was 90% (CI: 82–94; p < 0.0001). The second database had 39 AF cases; sensitivity was 92% vs. 87% (p = 0.46) and specificity was 99.5% vs. 98.7% (p = 0.03) for Cardiologs® and Veritas® respectively. Conclusion: Cardiologs® 12-lead ECG algorithm improves the interpretation of atrial fibrillation

Antimalarial drug use in general populations of tropical Africa

<p>Abstract</p> <p>Background</p> <p>The burden of <it>Plasmodium falciparum </it>malaria has worsened because of the emergence of chloroquine resistance. Antimalarial drug use and drug pressure are critical factors contributing to the selection and spread of resistance. The present study explores the geographical, socio-economic and behavioural factors associated with the use of antimalarial drugs in Africa.</p> <p>Methods</p> <p>The presence of chloroquine (CQ), pyrimethamine (PYR) and other antimalarial drugs has been evaluated by immuno-capture and high-performance liquid chromatography in the urine samples of 3,052 children (2–9 y), randomly drawn in 2003 from the general populations at 30 sites in Senegal (10), Burkina-Faso (10) and Cameroon (10). Questionnaires have been administered to the parents of sampled children and to a random sample of households in each site. The presence of CQ in urine was analysed as dependent variable according to individual and site characteristics using a random – effect logistic regression model to take into account the interdependency of observations made within the same site.</p> <p>Results</p> <p>According to the sites, the prevalence rates of CQ and PYR ranged from 9% to 91% and from 0% to 21%, respectively. In multivariate analysis, the presence of CQ in urine was significantly associated with a history of fever during the three days preceding urine sampling (OR = 1.22, p = 0.043), socio-economic level of the population of the sites (OR = 2.74, p = 0.029), age (2–5 y = reference level; 6–9 y OR = 0.76, p = 0.002), prevalence of anti-circumsporozoite protein (CSP) antibodies (low prevalence: reference level; intermediate level OR = 2.47, p = 0.023), proportion of inhabitants who lived in another site one year before (OR = 2.53, p = 0.003), and duration to reach the nearest tarmacked road (duration less than one hour = reference level, duration equal to or more than one hour OR = 0.49, p = 0.019).</p> <p>Conclusion</p> <p>Antimalarial drug pressure varied considerably from one site to another. It was significantly higher in areas with intermediate malaria transmission level and in the most accessible sites. Thus, <it>P. falciparum </it>strains arriving in cross-road sites or in areas with intermediate malaria transmission are exposed to higher drug pressure, which could favour the selection and the spread of drug resistance.</p

Structure and sensitivity of neural population responses in the retina

Les cellules ganglionnaires transfèrent l'information visuelle de l’œil au cerveau, sous une forme encore débattue. Leurs réponses aux stimuli visuels sont non-linéaires, corrélées entre neurones, et une partie de l'information est présente au niveau de la population seulement. J'étudie d'abord la structure des réponses de population. Les cellules du cortex sont influencées par l'activité globale des neurones avoisinants, mais ces interactions manquaient encore de modèle. Je décris un modèle de population qui reproduit le couplage entre neurones et activité globale. Je montre que les neurones de la rétine de salamandre dépendent de l'activité globale de manière surprenante. Je décris ensuite une méthode pour caractériser la sensibilité de populations de neurones de la rétine de rat à des perturbations d'un stimulus. J'utilise des expériences en boucle fermée pour explorer sélectivement l'espace des perturbations autour d'un stimulus donné. Je montre que les réponses à de petites perturbations peuvent être décrites par une linéarisation de leur probabilité. Leur sensibilité présente des signes de codage efficace. Enfin, je montre comment estimer la sensibilité des réponses d'une population de neurones à partir de leur structure. Je montre que les machines de Boltzmann restreintes (RBMs) sont des modèles précis des corrélations neurales. Pour mesurer le pouvoir de discrimination des neurones, je cherche une métrique neurale telle que les réponses à des stimuli différents soient éloignées, et celles à un même stimulus soient proches. Je montre que les RBMs fournissent des métriques qui surpassent les métriques classiques pour discriminer de petites perturbations du stimulus.Ganglion cells form the output of the retina: they transfer visual information from the eye to the brain. How they represent information is still debated. Their responses to visual stimuli are highly nonlinear, exhibit strong correlations between neurons, and some information is only present at the population level. I first study the structure of population responses. Recent studies have shown that cortical cells are influenced by the summed activity of neighboring neurons. However, a model for these interactions was still lacking. I describe a model of population activity that reproduces the coupling between each cell and the population activity. Neurons in the salamander retina are found to depend in unexpected ways on the population activity. I then describe a method to characterize the sensitivity of rat retinal neurons to perturbations of a stimulus. Closed-loop experiments are used to explore selectively the space of perturbations around a given stimulus. I show that responses to small perturbations can be described by a local linearization of their probability, and that their sensitivity exhibits signatures of efficient coding. Finally, I show how the sensitivity of neural populations can be estimated from response structure. I show that Restricted Boltzmann Machines (RBMs) are accurate models of neural correlations. To measure the discrimination power of neural populations, I search for a neural metric such that responses to different stimuli are far apart and responses to the same stimulus are close. I show that RBMs provide such neural metrics, and outperform classical metrics at discriminating small stimulus perturbations

Structure et sensibilité des réponses de populations de neurones dans la rétine

Ganglion cells form the output of the retina: they transfer visual information from the eye to the brain. How they represent information is still debated. Their responses to visual stimuli are highly nonlinear, exhibit strong correlations between neurons, and some information is only present at the population level. I first study the structure of population responses. Recent studies have shown that cortical cells are influenced by the summed activity of neighboring neurons. However, a model for these interactions was still lacking. I describe a model of population activity that reproduces the coupling between each cell and the population activity. Neurons in the salamander retina are found to depend in unexpected ways on the population activity. I then describe a method to characterize the sensitivity of rat retinal neurons to perturbations of a stimulus. Closed-loop experiments are used to explore selectively the space of perturbations around a given stimulus. I show that responses to small perturbations can be described by a local linearization of their probability, and that their sensitivity exhibits signatures of efficient coding. Finally, I show how the sensitivity of neural populations can be estimated from response structure. I show that Restricted Boltzmann Machines (RBMs) are accurate models of neural correlations. To measure the discrimination power of neural populations, I search for a neural metric such that responses to different stimuli are far apart and responses to the same stimulus are close. I show that RBMs provide such neural metrics, and outperform classical metrics at discriminating small stimulus perturbations.Les cellules ganglionnaires transfèrent l'information visuelle de l’œil au cerveau, sous une forme encore débattue. Leurs réponses aux stimuli visuels sont non-linéaires, corrélées entre neurones, et une partie de l'information est présente au niveau de la population seulement. J'étudie d'abord la structure des réponses de population. Les cellules du cortex sont influencées par l'activité globale des neurones avoisinants, mais ces interactions manquaient encore de modèle. Je décris un modèle de population qui reproduit le couplage entre neurones et activité globale. Je montre que les neurones de la rétine de salamandre dépendent de l'activité globale de manière surprenante. Je décris ensuite une méthode pour caractériser la sensibilité de populations de neurones de la rétine de rat à des perturbations d'un stimulus. J'utilise des expériences en boucle fermée pour explorer sélectivement l'espace des perturbations autour d'un stimulus donné. Je montre que les réponses à de petites perturbations peuvent être décrites par une linéarisation de leur probabilité. Leur sensibilité présente des signes de codage efficace. Enfin, je montre comment estimer la sensibilité des réponses d'une population de neurones à partir de leur structure. Je montre que les machines de Boltzmann restreintes (RBMs) sont des modèles précis des corrélations neurales. Pour mesurer le pouvoir de discrimination des neurones, je cherche une métrique neurale telle que les réponses à des stimuli différents soient éloignées, et celles à un même stimulus soient proches. Je montre que les RBMs fournissent des métriques qui surpassent les métriques classiques pour discriminer de petites perturbations du stimulus

Modeling the Correlated Activity of Neural Populations: A Review

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Closed-loop experiment in the retina

<p><strong>Data from closed-loop experiment in the retina</strong></p> <p>See the related code on github:</p> <p>https://github.com/ChrisGll/RBM_TRBM</p> <p>This file explains the organization of data recorded in the closed-loop experiment performed by Christophe Gardella and used in the following articles:<br> - Closed-loop estimation of retinal network sensitivity reveals signature of efficient coding, Ferrari, Gardella, Marre and Mora, eNeuro, 2017: http://www.eneuro.org/content/early/2018/01/16/ENEURO.0166-17.2017<br> - Blindfold learning of an accurate neural metric, Gardella, Marre and Mora, PNAS, 2018: http://www.pnas.org/content/early/2018/03/09/1718710115.long<br> The stimulus consists in a series of 0.9 s snippets of bar trajectory. Each snippet is called a sequence. The bar has a smooth random motion, with each sequence trajectory beginning and ending at position 0, the center of the screen.</p> <p>In parentheses are the values specific to our data.</p> <p><strong>Notations :</strong><br> Scalar variables:<br> stim_rate: (=50) binning rate for the stimulus, in Hz</p> <p>Nne: (=60) number of neurons<br> Nseq: (=17034) number of sequences<br> Nb_seq: (=45) number of time bins per sequence</p> <p>Nreftj: (=2) number of reference trajectories<br> Npertdir: (=16) number of perturbation directions per reference trajectory</p> <p><br> Indices:<br> ne_i : index of neuron<br> b_i : index of time bin seq_i : index of sequence (from 1 to Nseq) reftj_i : index of reference trajectory (1 or Nreftj)<br> pertdir_i : index of perturbation direction (1 to Npertdir)</p> <p>In general, in the code:<br> ..._i stands for index:<br> ..._l stands for list<br> ..._il stands for list of indices</p> <p><strong>Stimulus:</strong><br> trajs: cell of size (Nseq,1) with<br> trajs{seq_i}: vector of size (1, Nb_seq) with    trajs{seq_i}(b_i) the bar position in time bin b_i, in µm.</p> <p>rand_seq_il: list of indices of sequences corresponding to random bar trajectories</p> <p>Example: rand_seq_il(1) is the index of the first sequence corresponding to a random trajectory. trajs{rand_seq_il(1)} is the corresponding random trajectory.</p> <p>ref_seq_il: cell of size (1, Nreftj) with ref_seq_il{reftj_i} the list of indices of sequences corresponding to repetitions of reference trajectory reftj_i.</p> <p>pert_seq_il: cell of size (Npertdir, Nreftj) with<br> pert_seq_il{pertdir_i, reftj_i}: list of indices of sequences corresponding to a perturbation of reference trajectory reftj_i in direction pertdir_i. Indices are sorted by increasing perturbation amplitude.</p> <p>Example: All sequence trajectories are either random, a trajectory, or a perturbation. So the intersection between rand_seq_il, any ref_seq_il{reftj_i} or any pert_seq_il{pertdir_i, reftj_i} is always be empty.</p> <p>Example: The union between rand_seq_il, all ref_seq_il{reftj_i} and all pert_seq_il{pertdir_i, reftj_i} is the complete list of indices 1:Nseq.</p> <p>pert_amp_l: cell of size (Npertdir, Nreftj) with<br> pert_amp_l{pertdir_i, reftj_i}: list of amplitudes of corresponding perturbations. pert_amp_l{pertdir_i, reftj_i}(n) is the amplitude of the perturbation in sequence pert_seq_il{pertdir_i, reftj_i}(n).</p> <p><strong>Responses:</strong><br> spkb_rate : (=50) binning rate for the responses, in Hz sparse_spkb_all: cell of size (Nseq,1) with<br> sparse_spkb_all{seq_i}: sparse matrix of size (Nne, Nb_seq): binned response during sequence seq_i. sparse_spkb_all{seq_i}(ne_i,b_i)=1 if neuron ne_i spiked at least once in time bin b_i.</p> <p>sparse_spkb_all is the representation of responses used for computing the linear discriminability and distances with the RBM and TRBM metrics.</p> <p>In order to compute distances, one usually only considers a subset of the Nb_seq time bins of the sequence. We note:<br> b_il_s: (=23:37) list of indices of time bins used for distance computation.</p> <p>If one needs un-binned responses (for some metrics such as the van Rossum metric), spike times can be found in the variable spkt_all:</p> <p>spkt_all: cell of size (Nseq,1) with<br> spkt_all{seq_i}: cell of size (Nne, 1) with<br> spkt_all{seq_i}{ne_i}: list of spike times (in UNIT) of neuron ne_i in sequence seq_i. The list is empty if there is no spike. These times are in s, and are relative, with t=0 the beginning of the sequence.</p> <p>pert_lindiscrim_l: cell of size (Npertdir, Nreftj) with<br> pert_lindiscrim_l{pertdir_i, reftj_i} the linear discriminability of responses to the perturbation of reference trajectory reftj_i in direction pertdir_i. pert_lindiscrim_l{pertdir_i, reftj_i}(n) is the linear discriminability of responses in sequence pert_seq_il{pertdir_i, reftj_i}(n).</p> <p> </p