Pouzat, Christophe

Reynaud-Bouret, Patricia

Numérisation de Documents Anciens Mathématiques

Journal de la Société Française de StatistiqueVol. 157 No. 1 (2016)Editorial for the special issue on Statistics andNeurosciencesTitre: Éditorial du numéro spécial sur la statistique et les neurosciencesChristophe Pouzat1 and Patricia Reynaud-Bouret2The neurosciences are nowadays undergoing a fast development driven mainly by new experimen-tal techniques (Luo, 2015, Chap. 13). Large data sets containing the simultaneous activities ofmany (10 - 1000) neurons are becoming common. Anatomical data revealing the morphologytogether with part of the expressed genes at the single neuron level but for large brain regionsare produced every day. Such data are clearly presenting attractive challenges for statisticians,probabilists and any mathematically oriented scientists. The problems range from experimentalmethods improvement–something falling into the category of pre-processing for experimentalists–to stochastic model formulation and exploration / resolution not to speak of more classicalexperimental design.In the large realm of neuroscience, we have chosen to focus on problems taking the neuronas the elementary level of analysis in a given small population of neurons, in contrast to moremacroscopic approaches where neuronal populations are taken as elementary–as is frequently donewhen analyzing electroencephalographic (EEG) or functional magnetic resonance imaging (fMRI)data or more microscopic levels such as gene or synapses. This choice was clearly not motivatedby a lack of interesting statistical questions at the other levels–far from that!–but as editors, weaimed at giving a unity to the present opus as well as at focusing on our present area of expertise.We have also chosen topics that would most readily appeal to neurobiologists, or people interestedin theoretical models in neuroscience as well as statisticians, hoping that some of them will ventureinto these pages, as opposed to topics dealing with specific experimental recording techniquesand the data processing problems they generate. In other words, the stochastic modeling–in timeor space–was privileged over the "pre-processing" issues despite of the fundamental importanceof the latter.The first two articles, Samson and Ditlevsen and Galves and Löcherbach are motivated by the"stochastic" or "irregular" behavior of neurons embedded in a network. Samson ans Ditlevsen con-sider a single neuron and model a two dimensional process with a stochastic differential equation(SDE) – a stochastic version of the Morris-Lecar model. One component of the 2D process can beidentified with a membrane potential, a quantity familiar to cellular neurophysiologists. Stochastic1 MAP5, Université Paris-Descartes et UMR 8145, 45, rue des Saints-Pères, 75006 Paris, France.E-mail: christophe.pouzat@parisdescartes.fr2 Laboratoire J. A. Dieudonné, Université Nice Sophia Antipolis, CNRS, LJAD, UMR 7351, 06100 Nice, France.E-mail: reynaudb@unice.frJournal de la Société Française de Statistique, Vol. 157 No. 1 1-2http://www.sfds.asso.fr/journal© Société Française de Statistique et Société Mathématique de France (2016) ISSN: 2102-62382 C. Pouzat, P. Reynaud-Bouretmodeling of membrane potential can be traced back to Gerstein and Mandelbrot (1964), but thevast majority of the literature in this domain does not explicitly model the action potential: a SDEis used below a threshold and every time the threshold is reached an action potential is emittedand the membrane potential is reset to a "resting" level, this is the now classical integrate-and-firemodel, see Burkitt (2006a,b) for a review. Samson ans Ditlevsen are presenting a richer butmore complex model with the inference challenges it generates. Galves and Löcherbach tacklethe next level: given a large population of coupled stochastic neurons, what can be said andanalytically computed about its macroscopic properties? This is obviously a typical issue intheoretical / computational neuroscience; the originality of the Galves and Löcherbach model isthat by imposing a small restriction–the relevant history for the prediction of the action potentialoccurrence for a given neuron goes back to the last action potential of that neuron–they are gettinga variable-order Markov model from which many properties can be analytically derived. Theythen review many classical macroscopic properties of neural networks from the viewpoint of theirmodel. As mentioned this is a vast topic than cannot possibly be covered in a single review andthe interested reader looking for another "popular" approach in that field can start with Coccoet al. (2009).The last article by S. Eglen presents–at the editors’ request–two topics: a spatial stochasticmodel for photo-receptor types localization in the retina together with a fully reproducibledescription of the analysis. These two topics are currently actively explored in neuroscience.A good introduction to the known quantitative aspects of neuro-anatomy is the the book ofBraitenberg and Schüz (1998). Until recently, anatomical data have mainly been used to constraintnetwork models (like the one of Galves and Löcherbach), Eglen article presents a new trend inthe field were generative models are considered. This approach presents clearly natural bridgeswith dynamic–like developmental (Luo, 2015, Chap. 5 and 7) and memory / plasticity (Luo,2015, Chap. 10)–issues making it particularly attractive. The second topic, the explicit descriptionof the analysis with all the codes in R and access to the data, addresses a pressing issue forany "outsider", like a statistician, interested by new scientific problems. It is all too often verylong–and painful–to figure out what was precisely done to the data and to compare a too vaguelydescribed analysis with a newly proposed method. By advertising an approach, reproducibleresearch, that is making progress in neuroscience, we hope to convince data eager statisticians thatcontemporary neuroscience has lot of fascinating and challenging problems to offer, on which it isactually possible to work. It is definitely a great time to work at neuroscience / statistics interface!ReferencesBraitenberg, V. and Schüz, A. (1998). Cortex: Statistics and Geometry of Neuronal Connectivity. Studies BrainFunction Series. Springer.Burkitt, A. N. (2006a). A Review of the Integrate-and-fire Neuron Model: I. Homogeneous Synaptic Input. BiologicalCybernetics, 95(1):1–19.Burkitt, A. N. (2006b). A review of the integrate-and-fire neuron model: II. Inhomogeneous synaptic input and networkproperties. Biological Cybernetics, pages 1–16.Cocco, S., Leibler, S., and Monasson, R. (2009). Neuronal couplings between retinal ganglion cells inferred by efficientinverse statistical physics methods. Proceedings of the National Academy of Sciences, 106(33):14058–14062.Gerstein, G. L. and Mandelbrot, B. (1964). Random Walk Models for the Spike Activity of a Single Neuron. BiophysJ., 4(1):41–68.Luo, L. (2015). Principles of Neurobiology. Garland Science.Journal de la Société Française de Statistique, Vol. 157 No. 1 1-2http://www.sfds.asso.fr/journal© Société Française de Statistique et Société Mathématique de France (2016) ISSN: 2102-6238

Editorial for the special issue on Statistics and Neurosciences

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Editorial for the special issue on Statistics and Neurosciences

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Numérisation de Documents Anciens Mathématiques