[Forum SIS] Seminario GOLDIN (RGS, ADAMSS, CIMAB & Matematica Applicata)

[Giacomo Aletti]

Con preghiera di diffusione tra tutti i possibili interessati, scusandomi per invii multipli.
Cordialmente,
Giacomo Aletti

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Nell'ambito dei Reading Group Seminars e del Seminario di Matematica Applicata, in collaborazione col centro ADAMSS e il CIMAB, il giorno venerdì 24 Giugno 2016, alle ore 17.00, nell'Aula C (secondo piano) del Dipartimento di Matematica dell'Universita' degli Studi di Milano, Via C. Saldini, 50, Milano,

"Neuronal Classification from Network Connectivity "
Rebecca GOLDIN
George Mason University 

Abstract

The mammalian brain is a large network of neurons (~10^8 in rodents up to 10^11 in humans) sparsely interconnected by synapses (~10^4 per neuron). Most synapses are directional contacts between extensive tree-like structures, namely the axon of the output neuron and the dendrite of the input neuron. The ongoing assembly of complete maps of such circuits (“connectomes”) is crucial to understanding the brain structure-function relationship. Although the exact connectivity pattern of each neuron is unique, the common working assumption posits the existence of distinct “neuronal classes”, such that neurons in the same class share more similar connectivity patterns than neurons in different classes. A rigorous definition of this concept is still lacking, and even the order of magnitude of the number of neuronal classes is source of wide disagreement in neuroscience. 

Connectomic data may become available within the next decade for at least parts of nervous system in animal models, yet the mathematics to analyze these data is still underdeveloped. Indeed, that same mathematics should inform the data collection itself: Should we collect as much data from one animal as possible, or from as many 
animals as possible? Are more data with less precision better or worse than more precision with less data? 

We developed a class of probabilistic models that formalizes the concept of neuronal class based on network connectivity. Given a complete list of all neurons and their connections in a network, the model derives the number of neuronal classes, and an assignment of each neuron to a class. We fit the model using sparse singular value decomposition, and cluster the latent vectors into groups, and infer the neuronal classes. 

We tested the models on neurobiologically realistic simulated data, and found that our approach is robust and computationally tractable. We generated 50 graphs with 32,768 vertices each by stochastically assigning (secret) groups. One model consistently returned 100% correct class assignment, with 2% error in individual neural 
assignment, and reconstructed probability matrices well within the precision specified in the original probability matrix. This method 
provides a practical and theoretical foundation to bridge neuronal- and system-level neuroanatomy. 

Joint work with: Giorgio Ascoli, Carey Priebe, David Marchette, Paul Salomonsky, and Joshua Vogelstein t.



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Reading Group Seminars: The Reading Group Seminars (RGS) are organized within an open community of researchers interested in applying up to date mathematical modeling and data analysis approaches to the study of biological systems. The RGS take place at the Math. Department in Milan (via Saldini). Initiatives and updates are published on the website: http://rgs.mat.unimi.it/.(http://rgs.mat.unimi.it/)

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Giacomo Aletti, Associate Professor


ADAMSS Centre (ex MIRIAM)
Advanced Applied Mathematical and Statistical Sciences


Department of Mathematics (www.mat.unimi.it)
Via Saldini, 50
20133 Milano, Italy
Tel: +39-02-503.16158
Fax:+39-02-503.16090
Cell:+39-340-9739142


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