Category Archive Workshops

The meeting aims at discussing advances in different topics of Dynamical System ranging from randomness to bifurcations aspects. Renowned researchers will give lectures on their expertise addressed to students and professors who are interested in the subject.

Date and Venue

Invited Speakers

Mini courses

Schedule

Click on the speaker’s name below to see more details

The Auditorium’s locations at the ICMC building are shown below. Note that the scientific program above displays different colors in respect to the Auditorium selected for the day.

(Adapted from RECEPÇÃO 2016)

Dinner

The dinner will be held at Espaço Múltiplo

The location and route to the bar is shown at the Additional information below (inside the google maps you will be able to visualize the route).

Participation

How to apply

There is available poster presentation:

• • 1. Posters: Occurring simultaneously to the Coffee Break. It should be indicated the title of poster in the form below.

Limited financial support may be available for students, which must be indicated in the form.

Additional information

Restaurants and hotels at the ICMC surroundings

Organizers

Support

Greg Pavliotis

Abstract:

Sampling from a probability distribution in a high dimensional spaces is a standard problem in computational statistical mechanics, Bayesian statistics and other applications. A standard approach for doing this is by constructing an appropriate Markov process that is ergodic with respect to the measure from which we wish to sample. In this talk we will present a class of sampling schemes based on Langevin-type stochastic differential equations. We will show, in particular, nonreversible Langevin samplers, i.e. stochastic dynamics that do not satisfy detailed balance, have, in general, better properties than their reversible counterparts, in the sense of accelerating convergence to equilibrium and of reducing the asymptotic variance. Numerical schemes for such nonreversible samplers will be discussed and the connection with nonequilibrium statistical mechanics will be made.

Hayriye Cagnan

Abstract:

Our everyday actions, from decision making to motor control, are thought to involve information exchange through transient neural synchrony across multiple brain regions. Emerging evidence suggests that a range of neurological disorders such as Parkinson’s disease and essential tremor could be attributed to dysfunction of this fundamental neural property. Deep brain stimulation is commonly used to reduce disease symptoms by delivering high frequency electrical pulses to key brain regions. A new stimulation strategy, called phase-specific deep brain stimulation, aims to selectively regulate neural synchrony. I will highlight some experimental results which show the effect of phase-specific deep brain stimulation for the treatment of patients with pathological tremor and discuss how dynamic causal modelling could be used to infer effect of stimulation on disease circuit.

Jeroen Lamb

Abstract:

Despite the broad interest in probabilistic processes in  applied mathematics and the popularity of including “noise” or uncertainty as a modelling assumption, our understanding of the dynamics of random  systems is predominantly statistical and static, revealing little or  nothing about the actual “random dynamics”. In this talk I will discuss this assertion and give examples of open question and a few partial answers.

Matteo Tanzi

Abstract:

Networks of interacting systems with heterogeneous degrees and community structures are ubiquitously found in natural and artificial systems such as, among others, neuronal networks, gene-regulatory networks, and power grids. Recovering the characteristics of the networks and of the dynamics from observations of the systems is a crucial problem that has attracted a lot of attention. In this talk, I will present an approach to reconstruct the statistical properties of the connectivity structure of the network when the interaction strength between units is weak and the isolated dynamics of the nodes is chaotic. With relatively short time-series, our method can recover the degree distribution, the community structures, and build a model for the isolated dynamics and the interactions. The approach combines machine learning techniques with recent results on the ergodic theory of high-dimensional coupled systems. The procedure is able to accurately reconstruct the characteristic of simulated dynamics when tested on Scale-Free networks and graphs presenting Rich-Club motifs. We then used the results to predict the transitions to collective behaviour of the system from a single multivariate timeseries, observed in a state far from the transition.

Nick Jones

Abstract:

We develop a Bayesian hierarchical model to identify communities of time series. Fitting the model provides an end-to-end community detection algorithm that does not extract information as a sequence of point estimates but propagates uncertainties from the raw data to the community labels. Our approach naturally supports multiscale community detection as well as the selection of an optimal scale using model comparison. We study the properties of the algorithm using synthetic data and apply it to daily returns of constituents of the S&P100 index to identify salient communities of similar stocks.

With Till Hoffmann, Renaud Lambiotte, Leto Peel

Xiaogeng Wan, Björn Crütz and Henrik Jeldtoft Jensen

Abstract:

We present an EEG study of two music improvisation experiments. Professional musicians with high level of improvisation skills were asked to perform music either according to notes (composed music) or in improvisation. Each piece of music was performed in two different modes: strict mode and ‘‘let-go’’ mode. Synchronized EEG data was measured from both musicians and listeners. We used one of the most reliable causality measures: conditional Mutual Information from Mixed Embedding (MIME), to analyze directed correlations between different EEG channels, which was combined with network theory to construct both intrabrain and cross-brain networks. Differences were identified in intrabrain neural networks between composed music and improvisation and between strict mode and ‘‘let-go’’ mode. Particular brain regions such as frontal, parietal and temporal regions were found to play a key role in differentiating the brain activities between different playing conditions. By comparing the level of degree centralities in intra-brain neural networks, we found a difference between the response of musicians and the listeners when comparing the different playing conditions.

Reference: PLOS ONE | DOI:10.1371/journal.pone.
0112776 December 9, 2014

Richard Rosch

Abstract:

From fruit flies to humans, epileptic seizures have been described in virtually all known neuronal model systems. They represent hypersynchronous electrical activity that disrupts normal brain function. Whilst an epileptic seizure is a phenomenon of integrated neuronal networks, identified causes for epilepsy range from molecules (‘epilepsy genes’), to whole-brain abnormalities (‘epileptogenic networks’). Computational models can help linking these different levels of explanation by allowing us insights into otherwise unobservable dynamics. One example approach is using Bayesian model inversions to fit interconnected neuronal population models to electroencephalography (EEG) measures of abnormal neuronal dynamics in epilepsy. Here I will illustrate two worked examples of how this approach can be applied to clinically relevant questions: by (1) offering insights into the epileptogenic effects of a specific molecular disruption of neuronal function (NMDAreceptor antibodies), and (2) making predictions of the epileptic brain’s response to perturbations (from intracranial recordings in patients undergoing epilepsy surgery).

Thomas Parr

Abstract:

Recent approaches to theoretical neurobiology assume that the brain possesses a generative model that is used to infer the causes of sensory data. This implies perception is a process of optimising posterior beliefs, while actions represent experiments to disambiguate between perceptual hypotheses. Under this view, neurological and psychiatric syndromes result from ‘broken’ generative models that represent a poor fit to a patient’s environment. In this talk, I will overview some of our recent work using active inference, as formulated for a Markov decision process, to examine the influence of prior beliefs on behaviour – with a focus on the active visual system. This enables a quantitative phenotyping of neuropsychological syndromes in which visuospatial exploration is disrupted. In brief, we can express computational lesions (for example, those that underwrite visual neglect) as alterations in the parameters of prior probability distributions. Doing so allows us to quantify the evidence associated with different plausible explanations for pathological behaviour.

Karl Friston

Abstract:

This overview of the free energy principle offers an account of embodied exchange with the world that associates neuronal operations with actively inferring the causes of our sensations. Its agenda is to link formal (mathematical) descriptions of dynamical systems to a description of perception in terms of beliefs and goals. The argument has two parts: the first calls on the lawful dynamics of any (weakly mixing) system – from a single cell to a human brain. These lawful dynamics suggest that (internal) states can be interpreted as modelling or predicting the (external) causes of sensory fluctuations. In other words, if a system exists, its internal states must encode probabilistic beliefs about external states. Heuristically, this means that if I exist (am) then I must have beliefs (think). The second part of the argument is that the only tenable beliefs I can entertain about myself are that I exist. This may seem rather obvious; however, it transpires that this is equivalent to believing that the world – and the way it is sampled – will resolve uncertainty about the causes of sensations. We will consider the implications for functional anatomy, in terms of predictive coding and hierarchical architectures, and conclude by looking at the epistemic, self-evidencing behaviour that emerges – using simulations of active inference.