Criticality of mostly informative samples: A Bayesian model selection approach

We discuss a Bayesian model selection approach to high dimensional data in the deep under sampling regime. The data is based on a representation of the possible discrete states $s$, as defined by the observer, and it consists of $M$ observations of the state. This approach shows that, for a given sample size $M$, not all states observed in the sample can be distinguished. Rather, only a partition of the sampled states $s$ can be resolved. Such partition defines an {\em emergent} classification $q_s$ of the states that becomes finer and finer as the sample size increases, through a process of {\em symmetry breaking} between states. This allows us to distinguish between the $resolution$ of a given representation of the observer defined states $s$, which is given by the entropy of $s$, and its $relevance$ which is defined by the entropy of the partition $q_s$. Relevance has a non-monotonic dependence on resolution, for a given sample size. In addition, we characterise most relevant samples and we show that they exhibit power law frequency distributions, generally taken as signatures of "criticality". This suggests that "criticality" reflects the relevance of a given representation of the states of a complex system, and does not necessarily require a specific mechanism of self-organisation to a critical point.Comment: 31 pages, 7 figure

Towards a statistical mechanics of macroscopic brain states

Esta tesis estudia la naturaleza de las fluctuaciones espontáneas de la actividadcerebral humana, medida a gran escala. Dichas fluctuaciones se organizan enun repertorio de patrones espacio temporales que se repiten en diversas condiciones,tanto en la ejecución de tareas como en reposo y tanto en el sueño como enla vigilia. La relación entre los "estados físicos", definidos por las interaccionesneuronales que forman estos patrones, y los "estados mentales" asociados a cambiosen la consciencia, el procesamiento de información y los diferentes procesoscognitivos que realiza el cerebro, es una pregunta abierta y fundamental en laneurociencia. Desde un punto de vista físico, el problema consiste en entender los mecanismosdinámicos responsables de la emergencia de dichos patrones. En este trabajo,usamos herramientas de la mecánica estadística para describir y modelar la actividadcerebral espontánea, en experimentos de resonancia magnética funcional enestado de reposo. Nuestra hipótesis principal es que la complejidad observada sepuede entender por analogía a los fenómenos críticos observados en sistemas físicosque presentan una transición de fase de segundo orden. En el caso particulardel cerebro, con sus cientos de miles de millones de neuronas interactuando, resultaimportante determinar qué relación existe entre la complejísima estructurade conexiones y la dinámica colectiva que de ellas emerge. Aquí abordamos esteproblema mediante la construcción de un modelo híbrido basado en conexionesaxonales empíricas y una dinámica de masas neuronales. Desde el punto de vista de la neurociencia, la pregunta más interesante está relacionadacon la naturaleza funcional de los patrones espacio temporales observados. Es decir, tratar de entender la relación entre los estados físicos y los estadosmentales mencionados previamente. En este trabajo presentamos una conexiónentre ambos niveles de descripción al estudiar los cambios en la dinámica cerebralde sujetos al quedarse dormidos. De esta manera exploramos la hipótesisde que el origen neurobiológico de las uctuaciones espontáneas de la actividadesté relacionado con cambios en el estado de vigilia de los sujetos. Tanto en la neurociencia como en cualquier disciplina que estudie sistemascomplejos, el problema de modelado tiene una dificultad inherente y es que, dadala alta dimensionalidad del sistema, los datos experimentales se encuentraninevitablemente subsampleados. Por este motivo, resulta necesario definir representacionesreducidas del sistema que al mismo tiempo resulten informativas. Enesta tesis incluimos una discusión teórica sobre este problema general, usandoelementos de la teoría de la información para cuantificar la relevancia de distintasrepresentaciones de los datos experimentales y su relación con la hipótesis decriticalidad.In this thesis we study the nature of spontaneous large scale fluctuations ofhuman brain activity. These fluctuations are organised into a set of spatiotemporalpatterns that emerge in different conditions, such as during a task or at rest,and during wakefulness and sleep. The relationship between the "physical states"of the brain, dfined by the interacting neurons forming these patterns, and the 'mental states' associated with changes in consciousness, information processingand cognitive processes, is a fundamental open question in neuroscience. From a physicist point of view, the problem lies in understanding the dynamicalmechanisms responsible for the emergence of the aforementioned patterns. We approach this problem using tools from statistical mechanics to describe andmodel the spontaneous fluctuations of brain activity, measured with functionalmagnetic resonance imaging (fMRI) in resting state experiments. Our main hypothesisis that the observed complexity can be explained by analogy with criticalphenomena, known in physical systems undergoing a second order phase transition. In the particular case of the brain, with its hundred billion neurons interacting,it is important to determine the relationship between the complex structureof connections and the collective dynamics that emerge from them. Here we studythis using a hybrid model based on an empirical structure of axonal connectionsand neural mass dynamics. From the point of view of neuroscience, the most interesting question is relatedto the functional nature of the observed spatiotemporal patterns. Thatmeans understanding the relation between the aforementioned physical and mentalstates. In this work we present a connection between both levels of descriptionby studying the changes in the brain dynamics when subjects fall asleep. In thisway we explored the hypothesis that the neurobiological origin of spontaneousactivity fluctuations is related with changes in the state of sleep or wakefulnessof the subjects. In neuroscience as in any other complex system science, the problem of buildingmodels from the data has a fundamental difficulty which comes from thefact that complex systems are extremely high dimensional and therefore the relevantvariables for their description are usually strongly under sampled in theexperiments. Thus, in order to get a meaningful model one has to find reducedrepresentations while keeping relevant information about the system. We discussa general framework to choose between different representations of the limiteddata, using information theoretical measures to quantify their relevance, andanalyse how this affects the hypothesis of criticality.Fil: Haimovici, Ariel. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina

Brain Organization into Resting State Networks Emerges at Criticality on a Model of the Human Connectome

The relation between large-scale brain structure and function is an outstanding open problem in neuroscience. We approach this problem by studying the dynamical regime under which realistic spatiotemporal patterns of brain activity emerge from the empirically derived network of human brain neuroanatomical connections. The results show that critical dynamics unfolding on the structural connectivity of the human brain allow the recovery of many key experimental findings obtained from functional magnetic resonance imaging, such as divergence of the correlation length, the anomalous scaling of correlation fluctuations, and the emergence of large-scale resting state networks.Fil: Haimovici, Ariel. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Física; Argentina;Fil: Tagliazucchi, Enzo Rodolfo. Brain Imaging Center, Goethe University; Alemania;Fil: Balenzuela, Pablo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires; Argentina;Fil: Chialvo, Dante Renato. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Fisica; Argentina

Beyond pain: modeling decision-making deficits in chronic pain

Risky decision-making seems to be markedly disrupted in patients with chronic pain, probably due to the high cost that impose pain and negative mood on executive control functions. Patients’ behavioral performance on decision-making tasks such as the Iowa Gambling Task (IGT) is characterized by selecting cards more frequently from disadvantageous than from advantageous decks, and by switching often between competing responses in comparison with healthy controls (HCs). In the present study, we developed a simple heuristic model to simulate individuals’ choice behavior by varying the level of decision randomness and the importance given to gains and losses. The findings revealed that the model was able to differentiate the behavioral performance of patients with chronic pain and HCs at the group, as well as at the individual level. The best fit of the model in patients with chronic pain was yielded when decisions were not based on previous choices and when gains were considered more relevant than losses. By contrast, the best account of the available data in HCs was obtained when decisions were based on previous experiences and losses loomed larger than gains. In conclusion, our model seems to provide useful information to measure each individual participant extensively, and to deal with the data on a participant-by-participant basis.Research was supported by a grant from the Spanish Secretary of State for R & D and European regional development funds (ERDF) (#PSI2010-19372)

Dynamical Signatures of Structural Connectivity Damage to a Model of the Brain Posed at Criticality

Synchronization of brain activity fluctuations is believed to represent communication between spatially distant neural processes. These interareal functional interactions develop in the background of a complex network of axonal connections linking cortical and subcortical neurons, termed the human ?structural connectome.? Theoretical considerations and experimental evidence support the view that the human brain can be modeled as a system operating at a critical point between ordered (subcritical) and disordered (supercritical) phases. Here, we explore the hypothesis that pathologies resulting from brain injury of different etiologies are related to this model of a critical brain. For this purpose, we investigate how damage to the integrity of the structural connectome impacts on the signatures of critical dynamics. Adopting a hybrid modeling approach combining an empirical weighted network of human structural connections with a conceptual model of critical dynamics, we show that lesions located at highly transited connections progressively displace the model toward the subcritical regime. The topological properties of the nodes and links are of less importance when considered independently of their weight in the network. We observe that damage to midline hubs such as the middle and posterior cingulate cortex is most crucial for the disruption of criticality in the model. However, a similar effect can be achieved by targeting less transited nodes and links whose connection weights add up to an equivalent amount. This implies that brain pathology does not necessarily arise due to insult targeted at well-connected areas and that intersubject variability could obscure lesions located at nonhub regions. Finally, we discuss the predictions of our model in the context of clinical studies of traumatic brain injury and neurodegenerative disorders.Fil: Haimovici, Ariel. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Física; ArgentinaFil: Balenzuela, Pablo. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Física; ArgentinaFil: Tagliazucchi, Enzo. Netherlands Institute For Neuroscience; Países Bajo

On wakefulness fluctuations as a source of BOLD functional connectivity dynamics

Human brain dynamics and functional connectivity fluctuate over a range of temporal scales in coordination with internal states and environmental demands. However, the neurobiological significance and consequences of functional connectivity dynamics during rest have not yet been established. We show that the coarse-grained clustering of whole-brain dynamic connectivity measured with magnetic resonance imaging reveals discrete patterns (dynamic connectivity states) associated with wakefulness and sleep. We validate this using EEG in healthy subjects and patients with narcolepsy and by matching our results with previous findings in a large collaborative database. We also show that drowsiness may account for previous reports of metastable connectivity states associated with different levels of functional integration. This implies that future studies of transient functional connectivity must independently monitor wakefulness. We conclude that a possible neurobiological significance of dynamic connectivity states, computed at a sufficiently coarse temporal scale, is that of fluctuations in wakefulness.Fil: Haimovici, Ariel. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; ArgentinaFil: Tagliazucchi, Enzo Rodolfo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Física; ArgentinaFil: Balenzuela, Pablo. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; ArgentinaFil: Laufs, Helmut. Brain Imaging Center, Goethe University; Alemani