How to calculate the barycenter of a weighted graph

Discrete structures like graphs make it possible to naturally and exibly model complex phenomena. Since graphs that represent various types of information are increasingly available today, their analysis has become a popular subject of research. The graphs studied in the field of data science at this time generally have a large number of nodes that are not fairly weighted and connected to each other, translating a structural specification of the data. Yet, even an algorithm for locating the average position in graphs is lacking although this knowledge would be of primary interest for statistical or representation problems. In this work, we develop a stochastic algorithm for finding the Fréchet mean of weighted undirected metric graphs. This method relies on a noisy simulated annealing algorithm dealt with using homogenization. We then illustrate our algorithm with two examples (subgraphs of a social network and of a collaboration and citation network)

How to calculate the barycenter of a weighted graph

Discrete structures like graphs make it possible to naturally and exibly model complex phenomena. Since graphs that represent various types of information are increasingly available today, their analysis has become a popular subject of research. The graphs studied in the field of data science at this time generally have a large number of nodes that are not fairly weighted and connected to each other, translating a structural specification of the data. Yet, even an algorithm for locating the average position in graphs is lacking although this knowledge would be of primary interest for statistical or representation problems. In this work, we develop a stochastic algorithm for finding the Fréchet mean of weighted undirected metric graphs. This method relies on a noisy simulated annealing algorithm dealt with using homogenization. We then illustrate our algorithm with two examples (subgraphs of a social network and of a collaboration and citation network)

Socio-Cognitive and Affective Computing

Social cognition focuses on how people process, store, and apply information about other people and social situations. It focuses on the role that cognitive processes play in social interactions. On the other hand, the term cognitive computing is generally used to refer to new hardware and/or software that mimics the functioning of the human brain and helps to improve human decision-making. In this sense, it is a type of computing with the goal of discovering more accurate models of how the human brain/mind senses, reasons, and responds to stimuli. Socio-Cognitive Computing should be understood as a set of theoretical interdisciplinary frameworks, methodologies, methods and hardware/software tools to model how the human brain mediates social interactions. In addition, Affective Computing is the study and development of systems and devices that can recognize, interpret, process, and simulate human affects, a fundamental aspect of socio-cognitive neuroscience. It is an interdisciplinary field spanning computer science, electrical engineering, psychology, and cognitive science. Physiological Computing is a category of technology in which electrophysiological data recorded directly from human activity are used to interface with a computing device. This technology becomes even more relevant when computing can be integrated pervasively in everyday life environments. Thus, Socio-Cognitive and Affective Computing systems should be able to adapt their behavior according to the Physiological Computing paradigm. This book integrates proposals from researchers who use signals from the brain and/or body to infer people's intentions and psychological state in smart computing systems. The design of this kind of systems combines knowledge and methods of ubiquitous and pervasive computing, as well as physiological data measurement and processing, with those of socio-cognitive and affective computing

Investigating reward-based motor performance in volatile environments using computational modelling and electroencephalography

Motor improvements have been linked to reward magnitude in deterministic contexts. Nevertheless, it remains unclear whether individual inferences about reward probability dynamically influence motor vigour. Moreover, how factors such as age, Parkinson’s disease or anxiety affect the modulation of motor vigour by predictions of reward probability remains unexplored. This thesis, across four experiments, investigates how inferences about the volatile action-reward contingencies modulate motor performance on a trial-by-trial basis. We employed a reward-based motor decision-making task and modelled the behavioural data using the Hierarchical Gaussian Filter (HGF). In the final two studies, we also recorded the brain electrical activity through electroencephalography and used convolution models for oscillatory responses to delve into the neural underpinnings of motor decisions. The results revealed that stronger predictions about action-reward probabilities led to faster performance tempo on a trial-by-trial basis in healthy participants. This effect was preserved in older adults and medicated Parkinson’s disease patients. Furthermore, the invigoration of motor responses extended to explicit beliefs (confidence) about reward tendencies. Trait anxiety did not modulate the association between predictions and motor performance but affected practice effects over time. Analyses of the time-frequency representation of HGF computational quantities describing decision making unveiled increased alpha/beta correlates of different types of uncertainty among high trait anxiety individuals. Finally, we found that state anxiety dampened the invigoration effect previously discussed. This manifested as longer reaction time for actions that were highly anticipated to yield rewards. Moreover, state anxiety led to reduced theta oscillatory responses during processing win/lose outcomes. In conclusion, this thesis integrates computational modelling, Bayesian statistics, and electrophysiological approaches to explore motor decision-making behaviour under volatility. It provides novel evidence for an invigoration of motor performance by predictions about the action-reward contingency and sheds light on the modulation of this effect by age, Parkinson’s disease, trait and state anxiety

A Study of Biomedical Time Series Using Empirical Mode Decomposition : Extracting event-related modes from EEG signals recorded during visual processing of contour stimuli

Noninvasive neuroimaging techniques like functional Magnetic Resonance Imaging (fMRI) and/or Electroencephalography (EEG) allow researchers to investigate and analyze brain activities during visual processing. EEG offers a high temporal resolution at a level of submilliseconds which can be combined favorably with fMRI which has a good spatial resolution on small spatial scales in the millimeter range. These neuroimaging techniques were, and still are instrumental in the diagnoses and treatments of neurological disorders in the clinical applications. In this PhD thesis we concentrate on lectrophysiological signatures within EEG recordings of a combined EEG-fMRI data set which where taken while performing a contour integration task. The estimation of location and distribution of the electrical sources in the brain from surface recordings which are responsible for interesting EEG waves has drawn the attention of many EEG/MEG researchers. However, this process which is called brain source localization is still one of the major problems in EEG. It consists of solving two modeling problems: forward and inverse. In the forward problem, one is interested in predicting the expected potential distribution on the scalp from given electrical sources that represent active neurons in the head. These evaluations are necessary to solve the inverse problem which can be defined as the problem of estimating the brain sources that generated the measured electrical potentials. This thesis presents a data-driven analysis of EEG data recorded during a combined EEG/fMRI study of visual processing during a contour integration task. The analysis is based on an ensemble empirical mode decomposition (EEMD) and discusses characteristic features of event related modes (ERMs) resulting from the decomposition. We identify clear differences in certain ERMs in response to contour vs non-contour Gabor stimuli mainly for response amplitudes peaking around 100 [ms] (called P100) and 200 [ms] (called N200) after stimulus onset, respectively. We observe early P100 and N200 responses at electrodes located in the occipital area of the brain, while late P100 and N200 responses appear at electrodes located in frontal brain areas. Signals at electrodes in central brain areas show bimodal early/late response signatures in certain ERMs. Head topographies clearly localize statistically significant response differences to both stimulus conditions. Our findings provide an independent proof of recent models which suggest that contour integration depends on distributed network activity within the brain. Next and based on the previous analysis, a new approach for source localization of EEG data based on combining ERMs, extracted with EEMD, with inverse models has been presented. As the first step, 64 channel EEG recordings are pooled according to six brain areas and decomposed, by applying an EEMD, into their underlying ERMs. Then, based upon the problem at hand, the most closely related ERM, in terms of frequency and amplitude, is combined with inverse modeling techniques for source localization. More specifically, the standardized low resolution brain electromagnetic tomography (sLORETA) procedure is employed in this work. Accuracy and robustness of the results indicate that this approach deems highly promising in source localization techniques for EEG data. Given the results of analyses above, it can be said that EMD is able to extract intrinsic signal modes, ERMs, which contain decisive information about responses to contour and non-contour stimuli. Hence, we introduce a new toolbox, called EMDLAB, which serves the growing interest of the signal processing community in applying EMD as a decomposition technique. EMDLAB can be used to perform, easily and effectively, four common types of EMD: plain EMD, ensemble EMD (EEMD), weighted sliding EMD (wSEMD) and multivariate EMD (MEMD) on the EEG data. The main goal of EMDLAB toolbox is to extract characteristics of either the EEG signal by intrinsic mode functions (IMFs) or ERMs. Since IMFs reflect characteristics of the original EEG signal, ERMs reflect characteristics of ERPs of the original signal. The new toolbox is provided as a plug-in to the well-known EEGLAB which enables it to exploit the advantageous visualization capabilities of EEGLAB as well as statistical data analysis techniques provided there for extracted IMFs and ERMs of the signal

Bayesian inversion in biomedical imaging

Biomedizinische Bildgebung ist zu einer Schlüsseltechnik geworden, Struktur oder Funktion lebender Organismen nicht-invasiv zu untersuchen. Relevante Informationen aus den gemessenen Daten zu rekonstruieren erfordert neben mathematischer Modellierung und numerischer Simulation das verlässliche Lösen schlecht gestellter inverser Probleme. Um dies zu erreichen müssen zusätzliche a-priori Informationen über die zu rekonstruierende Größe formuliert und in die algorithmischen Lösungsverfahren einbezogen werden. Bayesianische Invertierung ist eine spezielle mathematische Methodik dies zu tun. Die vorliegende Arbeit entwickelt eine aktuelle Übersicht Bayesianischer Invertierung und demonstriert die vorgestellten Konzepte und Algorithmen in verschiedenen numerischen Studien, darunter anspruchsvolle Anwendungen aus der biomedizinischen Bildgebung mit experimentellen Daten. Ein Schwerpunkt liegt dabei auf der Verwendung von Dünnbesetztheit/Sparsity als a-priori Information.Biomedical imaging techniques became a key technology to assess the structure or function of living organisms in a non-invasive way. Besides innovations in the instrumentation, the development of new and improved methods for processing and analysis of the measured data has become a vital field of research. Building on traditional signal processing, this area nowadays also comprises mathematical modeling, numerical simulation and inverse problems. The latter describes the reconstruction of quantities of interest from measured data and a given generative model. Unfortunately, most inverse problems are ill-posed, which means that a robust and reliable reconstruction is not possible unless additional a-priori information on the quantity of interest is incorporated into the solution method. Bayesian inversion is a mathematical methodology to formulate and employ a-priori information in computational schemes to solve the inverse problem. This thesis develops a recent overview on Bayesian inversion and exemplifies the presented concepts and algorithms in various numerical studies including challenging biomedical imaging applications with experimental data. A particular focus is on using sparsity as a-priori information within the Bayesian framework. <br