Department of Computer Science

University of Crete

Maria Papadopouli (Department of Computer Science, University of Crete)

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__ Introduction: __ We live in the age of networks. The importance of networks has become of central intest in the natural sciences, particularly in the study of complex biological systems including the brain. Modern network approaches are beginning to reveal fundamental principles of brain architercture and function. Connectivity plays an important role in neuroanatomy, neurodevelopment, electrophysiology, functional brain imaging, neural basis of cognition.The analysis of network architecture and connectivity illuminates various problems related to integrative brain functions, e.g., the interaction of neurons in complex physiological responses, the integration of sensory features within and across modalities in cerebral cortex, the changes in sensory input or cognitive tasks, effects of brain trauma or disease, variations in cognitive performance.

This new pilot advanced undergraduate-/graduate- level course is an introductory course that will aim to highlight some of the emerging points of contact between neuroscience and network theory and analysis.

To understand the structure, behaviour and evolution of a complex system, such as brain, we require not only knowledge of elementary system components but also knowledge of the ways in which these components interact and the emergent properties of their interactions. The increasing availability of large datasets, powerful computers, and statistical analysis methods make it easier than before to record, analyze, and model the behaviour of such systems.

Neocortex is a six-layered, folded, sheet-like structure that consists of billions of heavily interconnected neurons. It is the interlaced activity patterns across the neocortical populations of neurons which bestow the capacity to interact intelligently with the environment. Over time much has been learned about the computational properties of single neurons. However, we remain far from understanding how networks of cortical cells coordinate and interact with each other in order to process information and to allow cortical circuits to be modified during learning.

Prof. Stelios Smirnakis (Brigham Women's Hospital and Department of Neurology, Harvard Medical School) and Prof. Maria Papadopouli (Department of Computer Science, University of Crete) will discuss the functional sub-network architecture of the neocortex. To better illustrate the main issues, the course will focus on the primary visual cortex of the mouse. There are a lot of experimental data collected from the primary visual cortex of the mouse. Dr. Anna Palagina (Harvard Medical School) collected GCaMP6- and OGB -based datasets using 2-photon imaging from the V1 area (layers 3/4) from mice. These datasets will be employed to present some important concepts and they will be used for analysis in several assignments and projects. The course's aim is to introduce students to the basic biology of the mouse neocortex and it will present graph-theoretical and statistical analysis tools for analyzing experimental data. It will demonstrate different types of networks and their properties.

**Course Description**

The course's aim is to introduce students to the basic biology of the neocortex and present its functional network architecture. To better illustrate the main issues, the course will focus on the primary visual cortex of the mouse. In the first part of the course, it will overview the principles of brain organization, neurophysiology and biophysics of excitable cells, synaptic transmission, network anatopy and physiology and canonical circuits in mouse neocortex. It will then focus on the multi-neuronal computations. The second part will present graph-theoretical and statistical analysis tools for analyzing functional networks. In the third part of the course, experimental methods for probing circuit function using 2 photo imaging, optgenetics, patch clamping in vivo, in vitro will be discussed. An important part of the course will be the project identification and implementation. During the last week, the students will present their project.

Week |
Short description |

1 | Introduction of the course Basic concepts on neurons Introductory session for the CS students without a background in neuroscience/biology Slides Prof Maria Papadopouli |

2 | Fundamentals in neuroscience Principles of brain organization, structures of neurons, Neurophysiology and biophysics of excitable cells; synaptic transmission; Network Anatomy, physiology and canonical circuits in mouse neocortex Focus on visual cortex of the mouse - layers - description Functional vs. Anatomical vs. Effective connectivity Slides Early Visual System Biological_Networks, monitoring methods, 2-photon_imaging Prof Stelios Smirnakis |

3 | Multi-neuronal computations Desirable Computational properties of biological circuits Sensory representations and shannon information theory (To be decided) Prof Stelios Smirnakis |

4 | Graph-theoretical methods of analysis Graph theory, Graph-theoretical properties: path length, degree of connectivity, diameter, clustering coefficient Network architectures: lattice/regular graphs, random graphs, small world, scale-free networks Slides Graph Theory Prof Maria Papadopouli |

5-6 | Statistical Analysis: Correlations, Null Hypothesis Testing, Regression and Clustering Statistics: Hypothesis testing, probabilities, CDFs Temporal correlation measures: Pearson correlation, autocorrelation, periodograms, STTC Kolmogorov-Smirnov test, clustering, linear regression Clustering (K-means) Slides Modeling Tools, Null Hypothesis, Temporal Correlation Modeling Temporal Correlation, STTC, Kolmogorov Smirnov test K-means-Linear Regression-Lasso-Ridge Prof Maria Papadopouli |

7 | Group meetings - Break 1 week Identification and start of the implementation of the project from 1) literature review, or 2) a small data analysis laboratory project on two photon data that will be provided. Such projects could involve the graph-theoretical analysis and pattern discovery of neuronal circuits in absence epilepsy, under spontaneous conditions, etc Team work under the supervision of Stelios Smirnakis & Maria Papadopouli |

8 | Machine-learning methods of analysis Machine-learning algorithms basics, feature extraction, SVD Deep learning Relation of biological networks to computational networks Slides Artificial Neural Networks - Convolutional Neural Networks - Recurrent Neural Networks Dr. Greg Tsagkatakis |

9-10 | Group meetings - Implementation & discussions of the projectTeam work under the supervision of Stelios Smirnakis & Maria Papadopouli Invited Lecture (Prof Kiki Sidiropoulou) Slides Networks Lecture |

11 | Experimental methods for probing circuit function 2 photon imaging; optogenetics etc; patch clamping in vivo, in vitro Learning in neuronal networks Hebbian plasticity Prof Stelios Smirnakis |

12 |
Douglas Martin - Requirements of circuit code Jiang paper circuit connectivity Ensembles ala Yuste - future questions/ experimental approaches - bottom up vs top-down - how to best decipher circuit function Neuroscience vs. Deep Learning Slides Cortical Circuits Prof Stelios Smirnakis |

12-13 | Reconvene for project presentation Workshop |

Date |
Material |

13/10 | Probability Theory Basics (Eirini Troullinou) |

20/10 | ReadMe_Graph, Plot_Graph_Matlab Code (Maria Plakia) |

3/11 | Linear Regression, Linear Regression Examples_Matlab Code (Evripides Tzamousis) |

15/11 | Dictionary Learning - KSVD (Eirini Troullinou), Decision Trees (Maria Plakia) |

1/12 | Hypothesis Testing_Clustering_Linear Regression_Matlab Code (Evripides Tzamousis) |

19/12 | Tutorial on Deep Learning, Deep Learning Examples_Matlab Code (Evripides Tzamousis) |

__Grading Formula__

Στο report/meeting συμπεριλαμβάνεται όχι μονο η τελική αναφορά, αλλά συνεκτιμάται και η συνέπεια/εργατικότητα στην παράδοση αναφορών και συναντήσεις κατά τη διάρκεια του εξαμήνου.

__Announcements__

__Suggested Reading__

** Main textbook:**

Networks of the Brain by Olaf Sporns, The MIT Press ISBN 978-0-262-01469-4

** Supplementary textbooks:**

Νευροεπιστήμη και συμπεριφορά. Eric Kandel, James Schwartz, and Thomas Jessell (Μετάφραση στα ελληνικά, Χάρης Καζλαρής και άλλοι, Πανεπιστημιακές Εκδόσεις Κρήτης)

Βασικές αρχές λειτουργίας του νευρικού συστήματος. Kiki Sidiropoulou

**References - Papers (to be extended)**

Internally Mediated Developmental Desynchronization of Neocortical Network Activty. Golshani P., Goncalves J.T. , Khoshkhoo S., Mostany R, Smirnakis S. and Portera-Cailliau C.

Attractor dynamics of network UP states in the neocortex. Cossart R., Aronov D., and Yuste R.

Detecting pairwise correlations in spike trains: an objective comparison of methods and application to the study of retinal waves. Cutts, C.S. and S.J. Eglen. J Neurosci, 2014. 34(43): p. 14288-303.

Anatomy and function of an excitatory network in the visual cortex. R. Clay Reed. Nature 532: 370-374 (2016).

Functional organization of excitatory synaptic strength in primary visualcortex. Cossell, L., et al. Nature 518.7539 (2015): 399.

Nature. 2015 May 28;521(7553):436-44. doi: 10.1038/nature14539

A functional microcircuit for cat visual cortex. Douglas RJ, Martin KA. J Physiol. 1991;440:735-69.

Opening the grey box. Douglas RJ, Martin KA.Trends Neurosci. 1991 Jul;14(7):286-93. Review.PMID: 1719675

Mapping the matrix: the ways of neocortex. Douglas RJ, Martin KA.Neuron. 2007 Oct 25;56(2):226-38. Review. PMID: 17964242

Topology and dynamics of the canonical circuit of cat V1. Binzegger T, Douglas RJ, Martin KA. Neural Netw. 2009

Class-specific features of neuronal wiring. Stepanyants A, Tamas G, Chklovskii DB.Neuron. 2004 Jul 22;43(2):251-9.PMID: 15260960

Principles of Connectivity among Morphologically Defined Cell Types in Adult Neocortex. Science. Jiang X, Shen S, Cadwell CR, Berens P, Sinz F, Ecker AS, Patel S & Tolias AS (2015). Vol. 350 no. 6264 DOI: 10.1126 Link

Small-world Propensity and Weighted Brain Networks. Muldoon S., Bridgeford E.W., Bassett D.S.

Collective dynamics of 'small-world' networks. Watts D. J., Strogatz S. H.

Network 'Small-World-Ness': A Quantitative Method for Determining Canonical Network Equivalence. Humphries M.D., Gurney K.

Scale-free characteristics of random networks: the topology of the world-wide web. Barabasi A., Albert R., Jeong H.

Networks Science, The Scale-free Property (section 4), Ablert-Laszlo Barabasi

Collective dynamics of 'small-world' networks. Watts DJ, Strogatz SH. Nature 1998;393(6684):440-2.

Deep learning. LeCun Y1, Bengio Y2, Hinton G3.

Toward an Integration of Deep Learning and Neuroscience. Adam H. Marblestone1, Greg Wayne and Konrad P. Kording

[Note: Historically Friedrich came first, then Vogelstein. Essentially simultaneously with Sang, Pnevmatikakis proposed another method which is now the most currently used method, and which Anna Palagina employed for the datasets of the projects.]

Reconstruction of firing rate changes across neuronal populations by temporally deconvolved Ca2+ imaging. Yaksi E., Friedrich R.W.

Fast Nonnegative Deconvolution for Spike Train Inference From Population Calcium Imaging. Vogelstein J.T., Packer A.M., Machado T.A., et al.

Visually Driven Neuropil Activity and Information Encoding in Mouse Primary Visual Cortex. Sangkyun L., Meyer J., Park J., Smirnakis S.M.

Simultaneous Denoising, Deconvolution, and Demixing of Calcium Imaging Data. Pnevmatikakis E.A., Soudry D., Gao Y., et al.

**Preparation for the final Exam:**

Neuroscience Basics - Questions.

**Datatraces/databases **

BrainMap database of published functional and structural neuroimaging experiments with coordinate-based results (x,y,z) in Talairach or MNI space.
The goal of BrainMap is to develop software and tools to share neuroimaging results
and enable meta-analysis of studies of human brain function and structure in healthy and diseased subjects.

http://brainmap.org

**Tentative Assignments**

Week |
Short description |

1-10 | Reading papers/textbook |

3 | Graph theoretical metrics, simple statistics (CDFs, histograms) |

4 | Reading papers |

5 | Null hypothesis, temporal correlation |

6 | Project |

6-9 | Group meetings - milestones |

10 | Presentations |

Analysis and modeling of the functional networks using data collected from the V1 L2/L3

1. Graph-theoretical analysis

1.1. Estimation of the degree of connectivity, discovering small-worlds

graph_analysis

1st assignment.

The oral examination of the assignment will be held after its submission

To submit the 1st Assignment send an e-mail to troullinou@csd.uoc.gr

2. Estimation of the temporal correlation of the activation patterns of neurons using STTC

STTC_analysis

2nd assignment.

To submit the 2nd Assignment send an e-mail both to troullinou@csd.uoc.gr

Projects Identification and start of the implementation of the project from 1) literature review, or 2) a small data analysis laboratory project on two photon data that will be provided. The project could involve the graph-theoretical analysis and pattern discovery of neuronal circuits in absence epilepsy, under spontaneous conditions, etc Team work under the supervision of Stelios Smirnakis & Maria Papadopouli |

Project Examples

**Marking scheme**

Midterm | N/A |

Assignments | ✔ |

Final exam | ✔ |

Project | Customized to each team |

**Other Sources:**

A journey through the Visual System

Exploring the Visual Brain

Funded by the Greek Diaspora Fellowship Program (Fellow: Prof Stelios Smirnakis, Host: Maria Papadopouli)