School on Complex Networks and Applications to Neuroscience


Start time: September 28, 2015

Ends on: October 16, 2015

Location: São Paulo, Brazil



  • Stefano Boccaletti (CNR- Institute of Complex Systems – Florence -Italy, and the Italian Embassy in Israel) (by SKYPE)The Master Stability Function
  • Javier M. Buldú (Center for Biomedical Technology  & U.R.J.C., Madrid, Spain): Applications to Biology: from RNA to Brain Networks
  • Hilda Cerdeira (Instituto de Física Teórica, UNESP, São Paulo, Brazil)
  • Jesús Gómez Gardeñes (Universidad de Zaragoza, Spain): Dynamical processes in networks 
  • Claudio Mirasso (IFISC, Universitat de les Illes Balears, Spain): 
    1. Zero-lag and anticipated synchronization in neuronal circuits
    2. Information Processing with neuro-inspired delay-based nonlinear systems
  • Antonio Roque (Universidade de São Paulo at Ribeirão Preto, Brazil): An overview of single-cell and neural network models  

Invited lecturers:

  • Edson Amaro Jr (Hospital Israelita Albert Einstein, Brazil): Neuroimages techniques and mental illnesses
  • Nuno M. de Araujo (Universidade de Lisboa):
    1. Percolation theory in complex networks
    2. Synchronization transitions in the Kuramoto model
    3. Structure and robustness of network infrastructures
  • Mauro Copelli (Universidade Federal de Pernambuco, Brazil): Collective neuronal phenomena
  • Ernesto Estrada (University of Strathclyde, U.K.): Structure of Complex Networks: From Graphs to Real Networks
  • Vincenzo Nicosia (Queen Mary University of London, UK): Multilayer Networks 
  • Adriano Tort (Universidade Federal do Rio Grande do Norte, Brazil):
    1. Detecting and tracking cell assemblies
    2. Cross-frequency coupling between brain rhythms
  • Raúl Vicente (University of Tartu, Estonia): Analysis of neuronal data

Invited speakers:

  • Syamal Dana (Indian Institute of Chemical Biology – Kolkata, India): Chimera states in globally coupled network of oscillators
  • Tiago Pereira (Imperial College London): Synchronization in Complex Networks: Structure and Dynamics
  • Roberto Andrade (Universidade Federal da Bahia, Brazil): Recovering evolutionary history by complex network modularity analysis
  • Ricardo Barros Sampaio (Fundação Oswaldo Cruz – Brasília, Brazil): Complex Network Analysis on Neglected Diseases: A Solution for Public Health

The School on Complex Networks and Applications to Neurosciences will cover theoretical aspects and current trends in the Theory of Complex Networks including their structural properties, dynamical processes, and multiplex networks with applications to social, technological and biological systems. The second half of the school will provide a detailed course on Neurosciences focused on the physiology of the cell and neuronal models, time series analysis and characterization, complex brain networks, collective phenomena and information processing in the brain, and neuroimage techniques and mental diseases. There is no registration fee and limited funds are available for local and travel support of participants.

This school is part of the Topics in Nonlinear Science: Fundamentals and Applications.



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List of confirmed participants: Updated on Sept 23

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Lectures Summary:

Complex Networks

Roberto Andrade (Universidade Federal da Bahia, Brazil): Recovering evolutionary history by complex network modularity analysis
Complex networks have been applied to uncover organizing principles of biological, technological, and social systems. Here we consider networks based on the similarity index of proteins to determine the phylogeny of groups of organisms and evolutionary relationships between them. The used methodology, which consists of several steps based solely on the protein similarity index and complex network properties, leads to a classification scheme that does not requires any previous biological knowledge of the organisms in the set. We illustrate the reliability of the used framework by discussing results related to the origins of mitochondria, the classification of fungi, the origin of FstH protein in Cianobacteria. In an attempt to proceed with a controlled comparison of recovered phylogenies, we used a simplified random evolutionary model to simulate the evolution of a population of haploid organisms. The computational realization of this model keeps track of the complete evolutionary history. It also provides, at the end of the process, the protein structure of all organisms that were created by random mutations. The same network method is then used to classify the organisms that are present in the system at end of the evolutionary history. Despite the fact that no information about the evolutionary history is used in the classification process, our method is able to recover the known phylogeny to very high degree of accuracy.

Stefano Boccaletti (CNR- Institute of Complex Systems – Florence -Italy, and the Italian Embassy in Israel): The Master Stability Function
The study of synchronization processes on complex networks has received a lot of attention during the last decades. The Master Stability Function (MSF) is a powerful tool to analyse the stability of the synchronization manifold when identical systems of oscillators are diffusively coupled. The MSF allows predicting what dynamical systems are able to synchronize and, more interestingly, which network configurations lead to a stable synchronized state. In this lecture, we will describe the mathematical ground of the MSF together with its main advantages and limitations.

Javier M. Buldú (Center for Biomedical Technology  & U.R.J.C., Madrid, Spain): Applications to Biology: from RNA to Brain Networks
The functioning of many biological systems finds nowadays a suitable framework of representation as the outcome of a network of interconnected dynamical units. We will review the main achievements and ideas developed in recent years that opened a new way to understand and interpret  the functioning of biological systems, starting from the scale of genetic and protein networks, until the larger scale of brain networks.

Ernesto Estrada (University of Strathclyde, U.K.): Structure of Complex Networks: From Graphs to Real Networks
In this part we will review the first steps of modern Network Science highlighting the differences and similarities with Graph Theory. We will show that some of the tools developed in this latter field are useful when analysing real world networks. However, the need of a classification and understanding of the real structural patterns of real complex networks demanded the introduction of new metrics and tools that are more related with the Statistical Physics realm.

Jesús Gómez-Gardeñes (Universidad de Zaragoza, Spain): Dynamical processes in networks
During the last century complex systems research has obtained a variety of interesting results regarding the emergence of collective states from the dynamical rules governing the microscopic interactions among the constituents of the systems. However, most of the times the constituents were assumed to interact in a well-mixed (all-to-all or mean-field) way. One of the most fascinating avenues of research is to unveil what are the effects that the existence of a network of interactions introduces into the emergence of collective states. In many cases, abandoning the well-mixed assumption and considering the explicit network of connections lead to dramatic changes that we will review in this part of the course.

Vicenzo Nicosia (Queen Mary University of London, UK): Multilayer Networks
The fact that real networks do not operate in isolation has introduced a new perspective to study and analyze the structure and dynamics of networks. Within his framework, multilayer networks consist of structured multilevel graphs in which interconnections between layers determine how a given node in a layer and its counterpart in another layer are linked and influence each other. In this lecture, we will review new mathematical methods for the combined analysis of many interacting complex networks working in parallel and influencing each other.


Edson Amaro Jr. (Hospital Israelita Albert Einstein, Brazil): Neurimages techniques and mental illnesses
The progressive development of medical imaging equipment – with new technologies emerging each year – has resulted in increased spatial, contrast, and functional resolution when dealing with medical diagnoses. In parallel, data analysis based on complex models allows a new approach to biology systems dynamics. Today we face a swarm of papers and grant proposal orbiting around big data and potential for mathematical models to unravel neuroscience great questions – pretty much as what we’ll be doing in these days at Botucatu. However, despite the increased capacity to observe biological alterations and process the data in numerous ways, in general, the interpretation of imaging findings is largely conceptual, and only few studies addressed clinical correlations or, notably, histological validation. Diagnosis based on assumption may provide an acceptable sensibility, but certainly compromise the specificity. Validation of these new technologies on both clinical and pathological bases is expected to answer several of questions.
In these three lectures I should cover the basics of medical imaging instrumentation used to probe human brain structure, neurochemistry and function. In particular, I’ll cover principles of image formation in Computed Tomography, Positron Emission Tomography and Magnetic Resonance. Another part of my talk will be dedicated to describe theoretical models – as well as biological evidence – for current medical understanding regarding neurological and psychiatric disease mechanisms. A focus will be given to how imbalances in brain connectivity in various scales are thought to play major role in most prevalent mental diseases. I will briefly mention how we are using techniques (Machine Learning and a few statistical models) to analyse experimental imaging data recorded in MRI scanners. I will also highlight convergent data from Eletrencephalography (EEG), eye-tracking (ET) and Galvanic Skin Conductance (GSK) collected simultaneously with functional MRI data.
Lastly, I’ll comment on a particular project: Platform for Imaging in the Autopsy Room – PISA. This is the core facility in which we have installed the first human 7T whole body MR system in South America. All autopsies performed in non-violent deaths from Great São Paulo (a 23 million inhabitants reference region) take place at the Death Verification Service of the Capital (SVOC). This center performs ~13,000 autopsies/year, making it the largest autopsy service for patients who have died from natural causes in the world. PISA will allow for the development of partnerships with companies that produce new imaging technologies because they can count on a large number and variety of cases for the evaluation of their products. Additionally, countless studies can be developed involving this process in addition to participation in the maintenance and renovation of the equipment in question.At the end of the talk I will give a tour on the website and explain the ways to send a proposal to PISA project.

Mauro Copelli (Universidade Federal de Pernambuco, Brazil): Collective neuronal phenomena

Claudio Mirasso (IFISC, Universitat de les Illes Balears, Spain):
1. Zero-lag and anticipated synchronization in neuronal circuits
Understanding how information is processed in the brain is one of the key issues in neuroscience. Among the many possible scenarios, it happens that synchronization among different brain areas might play a significant role. Synchronization has been extensively studied in many systems including the brain, where it has been hypothesized to be relevant to issues such as the binding problem, temporal coding, deployment of spatial attention, higher cognitive functions, and many others. In this talk we will review results obtained in brain circuits where zero-lag and anticipated synchronization can occur. Zero-lag synchronization seems to be essential to explain the coherence perception. In the latter, many different brain areas synchronize at zero, or almost zero, lag despite long conduction delays under certain visual stimuli. Anticipated synchronization is related to the ability of the brain to react faster than normal under certain conditions. Experimental evidence suggests that anticipated synchronization can occur between primary somatosensory cortex and motor cortex in monkeys when performing a visual discrimination task. In this talk we will present and discuss minimal models that accounts for the above-mentioned behaviors.

2. Information Processing with neuro-inspired delay-based nonlinear systems
Inspired by the way the brain processes information the recently introduced paradigm of reservoir computing has been proven to be very successful in solving certain tasks that are inherently difficult for traditional computers. Reservoir computing based on delay-coupled systems has been shown to perform as well as traditional reservoir-computing methods allowing replacing the large networks by a small number of delay-coupled dynamical elements. Its simplest manifestation, a single nonlinear node subject to delayed feedback, already provides excellent performance in certain tasks as spoken digit recognition and time series predictions. In this talk, we will introduce this neuro-inspired approach and present several examples that range from the typical benchmark tasks of machine learning to more sophisticate ones, as the detection of heart arrhythmias.

Antonio C. Roque (Universidade de São Paulo at Ribeirão Preto, Brazil): An overview of single-cell and neural network models
Sustained activity in a layered spiking cortical model. Neurons in the cerebral cortex fire even in the absence of external input. The understanding of the interplay between network topology and neural dynamics in the generation of this self-sustained cortical activity is still an open question. Here I will use a multi-layered cortical microcircuit model to study the effect of layered structure on sustained activity lifetime.

Adriano Tort (Universidade Federal do Rio Grande do Norte, Brazil):
1. Detecting and tracking cell assemblies
Donald Hebb postulated that assemblies of synchronously activated neurons are the elementary units of information processing in the brain. Despite being one of the most influential theories in neuroscience, Hebb’s cell assembly hypothesis only started to become testable in the past two decades due to technological advances. In this lecture we will introduce linear methods for the detection of cell assemblies in large neuronal populations that rely on principal and independent component analysis.

2. Cross-frequency coupling between brain rhythms
Brain oscillations have been classically divided into specific frequency ranges associated with multiple cognitive processes. However, oscillations in different frequency bands may occur simultaneously and interact with each other. In this talk, I will present evidence derived from electrophysiological studies in behaving animals that suggests a functional role for cross-frequency couplings in the execution of cognitive processes.

Raul Vicente (University of Tartu, Estonia): Analysis of neuronal data
Exploring the bridges between the physics of magnets, the complexity of computational problems, artificial neural networks and brain dynamics has led to a better understanding of their complex phenomena. We shall explore these connections and dive in detail into machine learning to explore neuronal data sets. We shall also discuss deep learning, a revolutionary technology with industrial applications which are changing the way to analyze and interact with data.


Additional Information:

Registration: ALL participants should register. The registration will be on September 28 at the institute from 8:00 to 9:00 am. You can find arrival instruction at

BOARDING PASS: All participants, whose travel has been provided or will be reimbursed by the institute, should bring the boarding pass upon registration, and collect an envelope to send the return boarding pass to the institute.

Accommodation: Participants whose accommodation has been provided by the institute will stay at The Universe Flat. Each participant, whose accommodation has been provided by the institute, has received the accommodation details individually by email.

Emergency number: 9 8233 8671 (from São Paulo city); +55 11 9 8233 8671 (from abroad), 11 9 8233 8671 (from outside São Paulo).

Ground transportation instructions: 

Ground transportation from Guarulhos Airport to The Universe Flat

Ground transportation from Congonhas Airport to the Universe Flat

Ground transportation from The Universe Flat to the institute