Dynamical principles in neuroscience

Dynamical modeling of neural systems and brain functions has a history of success over the last half century. This includes, for example, the explanation and prediction of some features of neural rhythmic behaviors. Many interesting dynamical models of learning and memory based on physiological experiments have been suggested over the last two decades. Dynamical models even of consciousness now exist. Usually these models and results are based on traditional approaches and paradigms of nonlinear dynamics including dynamical chaos. Neural systems are, however, an unusual subject for nonlinear dynamics for several reasons: (i) Even the simplest neural network, with only a few neurons and synaptic connections, has an enormous number of variables and control parameters. These make neural systems adaptive and flexible, and are critical to their biological function. (ii) In contrast to traditional physical systems described by well-known basic principles, first principles governing the dynamics of neural systems are unknown. (iii) Many different neural systems exhibit similar dynamics despite having different architectures and different levels of complexity. (iv) The network architecture and connection strengths are usually not known in detail and therefore the dynamical analysis must, in some sense, be probabilistic. (v) Since nervous systems are able to organize behavior based on sensory inputs, the dynamical modeling of these systems has to explain the transformation of temporal information into combinatorial or combinatorial-temporal codes, and vice versa, for memory and recognition. In this review these problems are discussed in the context of addressing the stimulating questions: What can neuroscience learn from nonlinear dynamics, and what can nonlinear dynamics learn from neuroscience?This work was supported by NSF Grant No. NSF/EIA-0130708, and Grant No. PHY 0414174; NIH Grant No. 1 R01 NS50945 and Grant No. NS40110; MEC BFI2003-07276, and Fundación BBVA

Robust Transient Dynamics and Brain Functions

In the last few decades several concepts of dynamical systems theory (DST) have guided psychologists, cognitive scientists, and neuroscientists to rethink about sensory motor behavior and embodied cognition. A critical step in the progress of DST application to the brain (supported by modern methods of brain imaging and multi-electrode recording techniques) has been the transfer of its initial success in motor behavior to mental function, i.e., perception, emotion, and cognition. Open questions from research in genetics, ecology, brain sciences, etc., have changed DST itself and lead to the discovery of a new dynamical phenomenon, i.e., reproducible and robust transients that are at the same time sensitive to informational signals. The goal of this review is to describe a new mathematical framework – heteroclinic sequential dynamics – to understand self-organized activity in the brain that can explain certain aspects of robust itinerant behavior. Specifically, we discuss a hierarchy of coarse-grain models of mental dynamics in the form of kinetic equations of modes. These modes compete for resources at three levels: (i) within the same modality, (ii) among different modalities from the same family (like perception), and (iii) among modalities from different families (like emotion and cognition). The analysis of the conditions for robustness, i.e., the structural stability of transient (sequential) dynamics, give us the possibility to explain phenomena like the finite capacity of our sequential working memory – a vital cognitive function –, and to find specific dynamical signatures – different kinds of instabilities – of several brain functions and mental diseases

Linear and nonlinear approaches to unravel dynamics and connectivity in neuronal cultures

[eng] In the present thesis, we propose to explore neuronal circuits at the mesoscale, an approach in which one monitors small populations of few thousand neurons and concentrates in the emergence of collective behavior. In our case, we carried out such an exploration both experimentally and numerically, and by adopting an analysis perspective centered on time series analysis and dynamical systems. Experimentally, we used neuronal cultures and prepared more than 200 of them, which were monitored using fluorescence calcium imaging. By adjusting the experimental conditions, we could set two basic arrangements of neurons, namely homogeneous and aggregated. In the experiments, we carried out two major explorations, namely development and disintegration. In the former we investigated changes in network behavior as it matured; in the latter we applied a drug that reduced neuronal interconnectivity. All the subsequent analyses and modeling along the thesis are based on these experimental data. Numerically, the thesis comprised two aspects. The first one was oriented towards a simulation of neuronal connectivity and dynamics. The second one was oriented towards the development of linear and nonlinear analysis tools to unravel dynamic and connectivity aspects of the measured experimental networks. For the first aspect, we developed a sophisticated software package to simulate single neuronal dynamics using a quadratic integrate–and–fire model with adaptation and depression. This model was plug into a synthetic graph in which the nodes of the network are neurons, and the edges connections. The graph was created using spatial embedding and realistic biology. We carried out hundreds of simulations in which we tuned the density of neurons, their spatial arrangement and the characteristics of the fluorescence signal. As a key result, we observed that homogeneous networks required a substantial number of neurons to fire and exhibit collective dynamics, and that the presence of aggregation significantly reduced the number of required neurons. For the second aspect, data analysis, we analyzed experiments and simulations to tackle three major aspects: network dynamics reconstruction using linear descriptions, dynamics reconstruction using nonlinear descriptors, and the assessment of neuronal connectivity from solely activity data. For the linear study, we analyzed all experiments using the power spectrum density (PSD), and observed that it was sufficiently good to describe the development of the network or its disintegration. PSD also allowed us to distinguish between healthy and unhealthy networks, and revealed dynamical heterogeneities across the network. For the nonlinear study, we used techniques in the context of recurrence plots. We first characterized the embedding dimension m and the time delay δ for each experiment, built the respective recurrence plots, and extracted key information of the dynamics of the system through different descriptors. Experimental results were contrasted with numerical simulations. After analyzing about 400 time series, we concluded that the degree of dynamical complexity in neuronal cultures changes both during development and disintegration. We also observed that the healthier the culture, the higher its dynamic complexity. Finally, for the reconstruction study, we first used numerical simulations to determine the best measure of ‘statistical interdependence’ among any two neurons, and took Generalized Transfer Entropy. We then analyzed the experimental data. We concluded that young cultures have a weak connectivity that increases along maturation. Aggregation increases average connectivity, and more interesting, also the assortativity, i.e. the tendency of highly connected nodes to connect with other highly connected node. In turn, this assortativity may delineates important aspects of the dynamics of the network. Overall, the results show that spatial arrangement and neuronal dynamics are able to shape a very rich repertoire of dynamical states of varying complexity.[cat] L’habilitat dels teixits neuronals de processar i transmetre informació de forma eficient depèn de les propietats dinàmiques intrínseques de les neurones i de la connectivitat entre elles. La present tesi proposa explorar diferents tècniques experimentals i de simulació per analitzar la dinàmica i connectivitat de xarxes neuronals corticals de rata embrionària. Experimentalment, la gravació de l’activitat espontània d’una població de neurones en cultiu, mitjançant una càmera ràpida i tècniques de fluorescència, possibilita el seguiment de forma controlada de l’activitat individual de cada neurona, així com la modificació de la seva connectivitat. En conjunt, aquestes eines permeten estudiar el comportament col.lectiu emergent de la població neuronal. Amb l’objectiu de simular els patrons observats en el laboratori, hem implementat un model mètric aleatori de creixement neuronal per simular la xarxa física de connexions entre neurones, i un model quadràtic d’integració i dispar amb adaptació i depressió per modelar l’ampli espectre de dinàmiques neuronals amb un cost computacional reduït. Hem caracteritzat la dinàmica global i individual de les neurones i l’hem correlacionat amb la seva estructura subjacent mitjançant tècniques lineals i no–lineals de series temporals. L’anàlisi espectral ens ha possibilitat la descripció del desenvolupament i els canvis en connectivitat en els cultius, així com la diferenciació entre cultius sans dels patològics. La reconstrucció de la dinàmica subjacent mitjançant mètodes d’incrustació i l’ús de gràfics de recurrència ens ha permès detectar diferents transicions dinàmiques amb el corresponent guany o pèrdua de la complexitat i riquesa dinàmica del cultiu durant els diferents estudis experimentals. Finalment, a fi de reconstruir la connectivitat interna hem testejat, mitjançant simulacions, diferents quantificadors per mesurar la dependència estadística entre neurona i neurona, seleccionant finalment el mètode de transferència d’entropia gereralitzada. Seguidament, hem procedit a caracteritzar les xarxes amb diferents paràmetres. Malgrat presentar certs tres de xarxes tipus ‘petit món’, els nostres cultius mostren una distribució de grau ‘exponencial’ o ‘esbiaixada’ per, respectivament, cultius joves i madurs. Addicionalment, hem observat que les xarxes homogènies presenten la propietat de disassortativitat, mentre que xarxes amb un creixent nivell d’agregació espaial presenten assortativitat. Aquesta propietat impacta fortament en la transmissió, resistència i sincronització de la xarxa

Information processing in biological complex systems: a view to bacterial and neural complexity

This thesis is a study of information processing of biological complex systems seen from the perspective of dynamical complexity (the degree of statistical independence of a system as a whole with respect to its components due to its causal structure). In particular, we investigate the influence of signaling functions in cell-to-cell communication in bacterial and neural systems. For each case, we determine the spatial and causal dependencies in the system dynamics from an information-theoretic point of view and we relate it with their physiological capabilities. The main research content is presented into three main chapters. First, we study a previous theoretical work on synchronization, multi-stability, and clustering of a population of coupled synthetic genetic oscillators via quorum sensing. We provide an extensive numerical analysis of the spatio-temporal interactions, and determine conditions in which the causal structure of the system leads to high dynamical complexity in terms of associated metrics. Our results indicate that this complexity is maximally receptive at transitions between dynamical regimes, and maximized for transient multi-cluster oscillations associated with chaotic behaviour. Next, we introduce a model of a neuron-astrocyte network with bidirectional coupling using glutamate-induced calcium signaling. This study is focused on the impact of the astrocyte-mediated potentiation on synaptic transmission. Our findings suggest that the information generated by the joint activity of the population of neurons is irreducible to its independent contribution due to the role of astrocytes. We relate these results with the shared information modulated by the spike synchronization imposed by the bidirectional feedback between neurons and astrocytes. It is shown that the dynamical complexity is maximized when there is a balance between the spike correlation and spontaneous spiking activity. Finally, the previous observations on neuron-glial signaling are extended to a large-scale system with community structure. Here we use a multi-scale approach to account for spatiotemporal features of astrocytic signaling coupled with clusters of neurons. We investigate the interplay of astrocytes and spiking-time-dependent-plasticity at local and global scales in the emergence of complexity and neuronal synchronization. We demonstrate the utility of astrocytes and learning in improving the encoding of external stimuli as well as its ability to favour the integration of information at synaptic timescales to exhibit a high intrinsic causal structure at the system level. Our proposed approach and observations point to potential effects of the astrocytes for sustaining more complex information processing in the neural circuitry

Stochastic neural network dynamics: synchronisation and control

Biological brains exhibit many interesting and complex behaviours. Understanding of the mechanisms behind brain behaviours is critical for continuing advancement in fields of research such as artificial intelligence and medicine. In particular, synchronisation of neuronal firing is associated with both improvements to and degeneration of the brain’s performance; increased synchronisation can lead to enhanced information-processing or neurological disorders such as epilepsy and Parkinson’s disease. As a result, it is desirable to research under which conditions synchronisation arises in neural networks and the possibility of controlling its prevalence. Stochastic ensembles of FitzHugh-Nagumo elements are used to model neural networks for numerical simulations and bifurcation analysis. The FitzHugh-Nagumo model is employed because of its realistic representation of the flow of sodium and potassium ions in addition to its advantageous property of allowing phase plane dynamics to be observed. Network characteristics such as connectivity, configuration and size are explored to determine their influences on global synchronisation generation in their respective systems. Oscillations in the mean-field are used to detect the presence of synchronisation over a range of coupling strength values. To ensure simulation efficiency, coupling strengths between neurons that are identical and fixed with time are investigated initially. Such networks where the interaction strengths are fixed are referred to as homogeneously coupled. The capacity of controlling and altering behaviours produced by homogeneously coupled networks is assessed through the application of weak and strong delayed feedback independently with various time delays. To imitate learning, the coupling strengths later deviate from one another and evolve with time in networks that are referred to as heterogeneously coupled. The intensity of coupling strength fluctuations and the rate at which coupling strengths converge to a desired mean value are studied to determine their impact upon synchronisation performance. The stochastic delay differential equations governing the numerically simulated networks are then converted into a finite set of deterministic cumulant equations by virtue of the Gaussian approximation method. Cumulant equations for maximal and sub-maximal connectivity are used to generate two-parameter bifurcation diagrams on the noise intensity and coupling strength plane, which provides qualitative agreement with numerical simulations. Analysis of artificial brain networks, in respect to biological brain networks, are discussed in light of recent research in sleep theor

Continuity in categorization and theoretical implications

sorry for the silly error. hopefully this'll do the trick. --rickTraditional theories of cognition assume that motor action is executed in an all-or-none fashion, and has little importance for understanding cognitive representation and processing. A series of experiments and simulations presented here challenges this assumption. A relatively higher-order cognitive process, categorization, is shown to have graded effects that are reflected in manual motor output, measured through streaming x-y coordinates from mouse trajectories. Two simulations show that these effects are likely generated from a system in which cognition and action interact fluidly. Finally, theoretical implications of these experiments are drawn out. Symbolic dynamics is introduced, a potential means for reconciling both traditional and continuous accounts of cognition. A broad philosophical discussion follows, in which an integrative and pluralistic approach to cognition is proposed and briefly discussed

Theoretical Approaches in Non-Linear Dynamical Systems

From Preface: The 15th International Conference „Dynamical Systems - Theory and Applications” (DSTA 2019, 2-5 December, 2019, Lodz, Poland) gathered a numerous group of outstanding scientists and engineers who deal with widely understood problems of theoretical and applied dynamics. Organization of the conference would not have been possible without great effort of the staff of the Department of Automation, Biomechanics and Mechatronics of the Lodz University of Technology. The patronage over the conference has been taken by the Committee of Mechanics of the Polish Academy of Sciences and Ministry of Science and Higher Education of Poland. It is a great pleasure that our event was attended by over 180 researchers from 35 countries all over the world, who decided to share the results of their research and experience in different fields related to dynamical systems. This year, the DSTA Conference Proceedings were split into two volumes entitled „Theoretical Approaches in Non-Linear Dynamical Systems” and „Applicable Solutions in Non-Linear Dynamical Systems”. In addition, DSTA 2019 resulted in three volumes of Springer Proceedings in Mathematics and Statistics entitled „Control and Stability of Dynamical Systems”, „Mathematical and Numerical Approaches in Dynamical Systems” and „Dynamical Systems in Mechatronics and Life Sciences”. Also, many outstanding papers will be recommended to special issues of renowned scientific journals.Cover design: Kaźmierczak, MarekTechnical editor: Kaźmierczak, Mare

Systems evolution: the conceptual framework and a formal model

This research addresses to some of the fundamental problems in systems science.T he aim of this study is to: (1) provide a general conceptual framework for systems evolution; (2) develop a formal model for evolving systems based on dynamical systems theory; (3) analyse the evolving behaviour of various systems by using the formal model so far developed. First of all, it is argued that a system, which can be recognized by an observer as a system, is characterised by some emergent properties at a certain level of discourse. These properties are the results of the interactions between the system as components but not reducible to the individual or summative properties of those components. Any system is such an emergent and organized whole, and this whole can be defined and described as an emergent attractor. To maintain the wholeness in a changing environment, an open system may undergo radical changes both in its structure and function. The process of change is what is called of systems evolution. On reviewing the existing theories of self-organization, such as "Theory of Dissipative Structure", "Synergetics", "Hypercycle", "Cellular Automata", "Random Boolean Network" et al., a general conceptual framework for systems evolution has been outlined and it is based on the concept of emergent attractor for open systems. The emphasis is placed on the structural aspect of the process of change. Modem mathematical dynamical systems theory, with the study of nonlinear dynamics as its core, can provide (a) the concept of "attractor" to describe a system as an organized whole; (b) simple geometrical models of complex behaviour, (c) a complete taxonomy of attractors and bifurcation patterns; (d) a mathematical rationale for the explanations of evolutionary processes. Based on this belief, a formal model of evolving systems has been developed by using the language of mathematical dynamical systems theory (DST). Attractors and emergent attractors are formally defined. It is argued that the state of any systems can be described by one of the four fundamental types of attractors ( i. e. point attractor, periodic attractor, quasiperiodic attractor, chaotic attractor) at a certain level. The evolving behaviour of open systems can be analyzed by looking at the loss of structural stability in the systems. For a full analysis of systems evolution, the emphasis is put on the nonlinear inner dynamics which governs evolving systems. In trying to apply this conceptual framework and formal model, the evolving behaviour of various systems at different levels have been discussed. Among them are Benard cells in hydrodynamics, Brusselator in chemical systems, replicator systems in biology (hypercycle), predator-prey-food systems in ecology, and artificial neural networks. The complex dynamical behaviour of these systems, like the existence of various types of attractors and the occurrences of bifurcation when the environment changes, have been discussed. In most of the examples, the results in previous studies are cited directly and they are only re-interpreted by using the conceptual framework and the formal model developed in this research. In the study of artificial neural networks, a simple cellular automata network with only three neurons has been constructed and the activation dynamics has been analysed according to the formal model. Different attractors representing different dynamical behaviour of this network have been identified (point, periodic, quasiperiodic, and chaotic attractor). Similar discussions have been applied to a coupled Wilson-Cowan net. It is believed that the study of systems evolution is one of those attempts to bring systems science out of its primitive stage in which it ought not to be