117 research outputs found
The complexity of dynamics in small neural circuits
Mean-field theory is a powerful tool for studying large neural networks.
However, when the system is composed of a few neurons, macroscopic differences
between the mean-field approximation and the real behavior of the network can
arise. Here we introduce a study of the dynamics of a small firing-rate network
with excitatory and inhibitory populations, in terms of local and global
bifurcations of the neural activity. Our approach is analytically tractable in
many respects, and sheds new light on the finite-size effects of the system. In
particular, we focus on the formation of multiple branching solutions of the
neural equations through spontaneous symmetry-breaking, since this phenomenon
increases considerably the complexity of the dynamical behavior of the network.
For these reasons, branching points may reveal important mechanisms through
which neurons interact and process information, which are not accounted for by
the mean-field approximation.Comment: 34 pages, 11 figures. Supplementary materials added, colors of
figures 8 and 9 fixed, results unchange
Computational Methods for Cognitive and Cooperative Robotics
In the last decades design methods in control engineering made substantial progress in
the areas of robotics and computer animation. Nowadays these methods incorporate the
newest developments in machine learning and artificial intelligence. But the problems
of flexible and online-adaptive combinations of motor behaviors remain challenging for
human-like animations and for humanoid robotics. In this context, biologically-motivated
methods for the analysis and re-synthesis of human motor programs provide new insights
in and models for the anticipatory motion synthesis.
This thesis presents the authorâs achievements in the areas of cognitive and developmental robotics, cooperative and humanoid robotics and intelligent and machine learning methods in computer graphics. The first part of the thesis in the chapter âGoal-directed Imitation for Robotsâ considers imitation learning in cognitive and developmental robotics.
The work presented here details the authorâs progress in the development of hierarchical
motion recognition and planning inspired by recent discoveries of the functions of mirror-neuron cortical circuits in primates. The overall architecture is capable of âlearning for
imitationâ and âlearning by imitationâ. The complete system includes a low-level real-time
capable path planning subsystem for obstacle avoidance during arm reaching. The learning-based path planning subsystem is universal for all types of anthropomorphic robot arms, and is capable of knowledge transfer at the level of individual motor acts.
Next, the problems of learning and synthesis of motor synergies, the spatial and spatio-temporal combinations of motor features in sequential multi-action behavior, and the
problems of task-related action transitions are considered in the second part of the thesis
âKinematic Motion Synthesis for Computer Graphics and Roboticsâ. In this part, a new
approach of modeling complex full-body human actions by mixtures of time-shift invariant
motor primitives in presented. The online-capable full-body motion generation architecture
based on dynamic movement primitives driving the time-shift invariant motor synergies
was implemented as an online-reactive adaptive motion synthesis for computer graphics
and robotics applications.
The last chapter of the thesis entitled âContraction Theory and Self-organized Scenarios
in Computer Graphics and Roboticsâ is dedicated to optimal control strategies in multi-agent scenarios of large crowds of agents expressing highly nonlinear behaviors. This last
part presents new mathematical tools for stability analysis and synthesis of multi-agent
cooperative scenarios.In den letzten Jahrzehnten hat die Forschung in den Bereichen der Steuerung und Regelung
komplexer Systeme erhebliche Fortschritte gemacht, insbesondere in den Bereichen
Robotik und Computeranimation. Die Entwicklung solcher Systeme verwendet heutzutage
neueste Methoden und Entwicklungen im Bereich des maschinellen Lernens und der
kßnstlichen Intelligenz. Die flexible und echtzeitfähige Kombination von motorischen Verhaltensweisen
ist eine wesentliche Herausforderung fßr die Generierung menschenähnlicher
Animationen und in der humanoiden Robotik. In diesem Zusammenhang liefern biologisch
motivierte Methoden zur Analyse und Resynthese menschlicher motorischer Programme
neue Erkenntnisse und Modelle fĂźr die antizipatorische Bewegungssynthese.
Diese Dissertation präsentiert die Ergebnisse der Arbeiten des Autors im Gebiet der
kognitiven und Entwicklungsrobotik, kooperativer und humanoider Robotersysteme sowie
intelligenter und maschineller Lernmethoden in der Computergrafik. Der erste Teil der
Dissertation im Kapitel âZielgerichtete Nachahmung fĂźr Roboterâ behandelt das Imitationslernen
in der kognitiven und Entwicklungsrobotik. Die vorgestellten Arbeiten beschreiben
neue Methoden fĂźr die hierarchische Bewegungserkennung und -planung, die durch
Erkenntnisse zur Funktion der kortikalen Spiegelneuronen-Schaltkreise bei Primaten inspiriert
wurden. Die entwickelte Architektur ist in der Lage, âdurch Imitation zu lernenâ
und âzu lernen zu imitierenâ. Das komplette entwickelte System enthält ein echtzeitfähiges
Pfadplanungssubsystem zur Hindernisvermeidung während der Durchfßhrung von Armbewegungen.
Das lernbasierte Pfadplanungssubsystem ist universell und fĂźr alle Arten von
anthropomorphen Roboterarmen in der Lage, Wissen auf der Ebene einzelner motorischer
Handlungen zu Ăźbertragen.
Im zweiten Teil der Arbeit âKinematische Bewegungssynthese fĂźr Computergrafik und
Robotikâ werden die Probleme des Lernens und der Synthese motorischer Synergien, d.h.
von räumlichen und räumlich-zeitlichen Kombinationen motorischer Bewegungselemente
bei Bewegungssequenzen und bei aufgabenbezogenen Handlungs ßbergängen behandelt.
Es wird ein neuer Ansatz zur Modellierung komplexer menschlicher GanzkĂśrperaktionen
durch Mischungen von zeitverschiebungsinvarianten Motorprimitiven vorgestellt. Zudem
wurde ein online-fähiger Synthesealgorithmus fßr GanzkÜperbewegungen entwickelt, der
auf dynamischen Bewegungsprimitiven basiert, die wiederum auf der Basis der gelernten
verschiebungsinvarianten Primitive konstruiert werden. Dieser Algorithmus wurde fĂźr
verschiedene Probleme der Bewegungssynthese fĂźr die Computergrafik- und Roboteranwendungen
implementiert.
Das letzte Kapitel der Dissertation mit dem Titel âKontraktionstheorie und selbstorganisierte
Szenarien in der Computergrafik und Robotikâ widmet sich optimalen Kontrollstrategien
in Multi-Agenten-Szenarien, wobei die Agenten durch eine hochgradig nichtlineare
Kinematik gekennzeichnet sind. Dieser letzte Teil präsentiert neue mathematische Werkzeuge
fßr die Stabilitätsanalyse und Synthese von kooperativen Multi-Agenten-Szenarien
Complex Dynamics in Dedicated / Multifunctional Neural Networks and Chaotic Nonlinear Systems
We study complex behaviors arising in neuroscience and other nonlinear systems by combining dynamical systems analysis with modern computational approaches including GPU parallelization and unsupervised machine learning. To gain insights into the behaviors of brain networks and complex central pattern generators (CPGs), it is important to understand the dynamical principles regulating individual neurons as well as the basic structural and functional building blocks of neural networks. In the first section, we discuss how symbolic methods can help us analyze neural dynamics such as bursting, tonic spiking and chaotic mixed-mode oscillations in various models of individual neurons, the bifurcations that underlie transitions between activity types, as well as emergent network phenomena through synergistic interactions seen in realistic neural circuits, such as network bursting from non-intrinsic bursters. The second section is focused on the origin and coexistence of multistable rhythms in oscillatory neural networks of inhibitory coupled cells. We discuss how network connectivity and intrinsic properties of the cells affect the dynamics, and how even simple circuits can exhibit a variety of mono/multi-stable rhythms including pacemakers, half-center oscillators, multiple traveling-waves, fully synchronous states, as well as various chimeras. Our analyses can help generate verifiable hypotheses for neurophysiological experiments on central pattern generators. In the last section, we demonstrate the inter-disciplinary nature of this research through the applications of these techniques to identify the universal principles governing both simple and complex dynamics, and chaotic structure in diverse nonlinear systems. Using a classical example from nonlinear laser optics, we elaborate on the multiplicity and self-similarity of key organizing structures in 2D parameter space such as homoclinic and heteroclinic bifurcation curves, Bykov T-point spirals, and inclination flips. This is followed by detailed computational reconstructions of the spatial organization and 3D embedding of bifurcation surfaces, parametric saddles, and isolated closed curves (isolas). The generality of our modeling approaches could lead to novel methodologies and nonlinear science applications in biological, medical and engineering systems
Investigating the role of fast-spiking interneurons in neocortical dynamics
PhD ThesisFast-spiking interneurons are the largest interneuronal population in neocortex. It is
well documented that this population is crucial in many functions of the neocortex by
subserving all aspects of neural computation, like gain control, and by enabling
dynamic phenomena, like the generation of high frequency oscillations. Fast-spiking
interneurons, which represent mainly the parvalbumin-expressing, soma-targeting
basket cells, are also implicated in pathological dynamics, like the propagation of
seizures or the impaired coordination of activity in schizophrenia. In the present thesis,
I investigate the role of fast-spiking interneurons in such dynamic phenomena by using
computational and experimental techniques.
First, I introduce a neural mass model of the neocortical microcircuit featuring divisive
inhibition, a gain control mechanism, which is thought to be delivered mainly by the
soma-targeting interneurons. Its dynamics were analysed at the onset of chaos and
during the phenomena of entrainment and long-range synchronization. It is
demonstrated that the mechanism of divisive inhibition reduces the sensitivity of the
network to parameter changes and enhances the stability and
exibility of oscillations.
Next, in vitro electrophysiology was used to investigate the propagation of activity in
the network of electrically coupled fast-spiking interneurons. Experimental evidence
suggests that these interneurons and their gap junctions are involved in the propagation
of seizures. Using multi-electrode array recordings and optogenetics, I investigated the
possibility of such propagating activity under the conditions of raised extracellular K+
concentration which applies during seizures. Propagated activity was recorded and the
involvement of gap junctions was con rmed by pharmacological manipulations.
Finally, the interaction between two oscillations was investigated. Two oscillations with di erent frequencies were induced in cortical slices by directly activating the pyramidal
cells using optogenetics. Their interaction suggested the possibility of a coincidence
detection mechanism at the circuit level. Pharmacological manipulations were used to
explore the role of the inhibitory interneurons during this phenomenon. The results,
however, showed that the observed phenomenon was not a result of synaptic activity.
Nevertheless, the experiments provided some insights about the excitability of the
tissue through scattered light while using optogenetics.
This investigation provides new insights into the role of fast-spiking interneurons in the
neocortex. In particular, it is suggested that the gain control mechanism is important
for the physiological oscillatory dynamics of the network and that the gap junctions
between these interneurons can potentially contribute to the inhibitory restraint during
a seizure.Wellcome Trust
Computational study of resting state network dynamics
Lo scopo di questa tesi è quello di mostrare, attraverso una simulazione con il software The Virtual Brain, le piĂš importanti proprietĂ della dinamica cerebrale durante il resting state, ovvero quando non si è coinvolti in nessun compito preciso e non si è sottoposti a nessuno stimolo particolare. Si comincia con lo spiegare cosâè il resting state attraverso una breve revisione storica della sua scoperta, quindi si passano in rassegna alcuni metodi sperimentali utilizzati nellâanalisi dellâattivitĂ cerebrale, per poi evidenziare la differenza tra connettivitĂ strutturale e funzionale. In seguito, si riassumono brevemente i concetti dei sistemi dinamici, teoria indispensabile per capire un sistema complesso come il cervello. Nel capitolo successivo, attraverso un approccio âbottom-upâ, si illustrano sotto il profilo biologico le principali strutture del sistema nervoso, dal neurone alla corteccia cerebrale. Tutto ciò viene spiegato anche dal punto di vista dei sistemi dinamici, illustrando il pionieristico modello di Hodgkin-Huxley e poi il concetto di dinamica di popolazione. Dopo questa prima parte preliminare si entra nel dettaglio della simulazione. Prima di tutto si danno maggiori informazioni sul software The Virtual Brain, si definisce il modello di network del resting state utilizzato nella simulazione e si descrive il âconnettomaâ adoperato. Successivamente vengono mostrati i risultati dellâanalisi svolta sui dati ricavati, dai quali si mostra come la criticitĂ e il rumore svolgano un ruolo chiave nell'emergenza di questa attivitĂ di fondo del cervello. Questi risultati vengono poi confrontati con le piĂš importanti e recenti ricerche in questo ambito, le quali confermano i risultati del nostro lavoro. Infine, si riportano brevemente le conseguenze che porterebbe in campo medico e clinico una piena comprensione del fenomeno del resting state e la possibilitĂ di virtualizzare lâattivitĂ cerebrale
Bessel Functions in Mass Action. Modeling of Memories and Remembrances
Data from experimental observations of a class of neurological processes
(Freeman K-sets) present functional distribution reproducing Bessel function
behavior. We model such processes with couples of damped/amplified oscillators
which provide time dependent representation of Bessel equation. The root loci
of poles and zeros conform to solutions of K-sets. Some light is shed on the
problem of filling the gap between the cellular level dynamics and the brain
functional activity. Breakdown of time-reversal symmetry is related with the
cortex thermodynamic features. This provides a possible mechanism to deduce
lifetime of recorded memory.Comment: 16 pages, 9 figures, Physics Letters A, 2015 in pres
- âŚ