Dynamical Systems on Networks: A Tutorial

We give a tutorial for the study of dynamical systems on networks. We focus especially on "simple" situations that are tractable analytically, because they can be very insightful and provide useful springboards for the study of more complicated scenarios. We briefly motivate why examining dynamical systems on networks is interesting and important, and we then give several fascinating examples and discuss some theoretical results. We also briefly discuss dynamical systems on dynamical (i.e., time-dependent) networks, overview software implementations, and give an outlook on the field.Comment: 39 pages, 1 figure, submitted, more examples and discussion than original version, some reorganization and also more pointers to interesting direction

Optimal regulation of flow networks with transient constraints

This paper investigates the control of flow networks, where the control objective is to regulate the measured output (e.g. storage levels) towards a desired value. We present a distributed controller that dynamically adjusts the inputs and flows, to achieve output regulation in the presence of unknown constant disturbances, while satisfying given input and flow constraints. Optimal coordination among the controllers minimizing a suitable cost function of the inputs at the nodes, is achieved by exchanging information over a communication network. Exploiting an incremental passivity property, the desired steady state is proven to be globally asymptotically attractive under the closed loop dynamics. Two case studies (a district heating system and a super-conducting DC network) show the effectiveness of the proposed solution. (C) 2019 Elsevier Ltd. All rights reserved

A system-theoretic approach to global and local regulation in neuron morphologies

Synaptic plasticity is a crucial neuronal mechanism for learning and memory. It allows synapses to change their strength over time. This dissertation focuses on a particular form of synaptic plasticity called synaptic scaling, a homeostatic mechanism that preserves relative synaptic strengths in an activity-dependent manner. Synaptic scaling is fundamental for neuronal stability, regulating other plasticity mechanisms like Hebbian plasticity or long-term potentiation (LTP). The aims of this dissertation are to explore the implications of synaptic scaling (and other forms of plasticity, such as structural plasticity) on the overall behavior of neurons. This is done using system-theoretic tools and feedback control. We first formulate a biophysical closed loop model of synaptic scaling. We then study how synaptic scaling affect neurons’ behavior in both abstract and reconstructed morphologies. This study reveals important tradeoffs between robustness, convergence rate, and accuracy of scaling. We first look at synaptic scaling as a “global control action” whose main role is to guarantee a steady level of neural activity. We then consider activity-dependent degradation as a “local control action” whose role is to assist the neuron in fine-tuning different desirable spatial concentration profiles. We show that, in extreme scenarios, it can promote a level of competition between synapses that has a destabilizing effect on the overall behavior. At the methodological level, we use compartmental modeling and we focus on the in- teraction between feedback and transport, in linear and nonlinear settings. Using classical system-theoretic tools like Bode and Nyquist analysis and singular perturbation arguments, and more recent tools like contraction and dominance theory, we derive parameter ranges under which synaptic scaling is stable and well-behaved (slow regulation), stable and oscilla- tory (aggressive regulation), and unstable (pathological regulation). We also study the system robustness against static and dynamics uncertainties. Finally, to understand how different plasticity mechanisms simultaneously affect the neuron behavior, we study synaptic scaling in the presence of activity-dependent growth (mimicking a structural plasticity mechanism). This is a third layer of control action shaping the neuron morphology. We find that activity-dependent growth improves the neuron’s performance when synaptic scaling is insufficient

Implications of Potassium Channel Heterogeneity for Model Vestibulo-Ocular Reflex Response Fidelity

The Vestibulo-Ocular Reflex (VOR) produces compensatory eye movements in response to head and body rotations movements, over a wide range of frequencies and in a variety of dimensions. The individual components of the VOR are separated into parallel pathways, each dealing with rotations or movements in individual planes or axes. The Horizontal VOR (hVOR) compensates for eye movements in the Horizontal plane, and comprises a linear and non-linear pathway. The linear pathway of the hVOR provides fast and accurate compensation for rotations, the response being produced through 3-neuron arc, producing a direct translation of detected head velocity to compensatory eye velocity. However, single neurons involved in the middle stage of this 3-neuron arc cannot account for the wide frequency over which the reflex compensates, and the response is produced through the population response of the Medial Vestibular Nucleus (MVN) neurons involved. Population Heterogeneity likely plays a role in the production of high fidelity population response, especially for high frequency rotations. Here we present evidence that, in populations of bio-physical compartmental models of the MVN neurons involved, Heterogeneity across the population, in the form of diverse spontaneous firing rates, improves the response fidelity of the population over Homogeneous populations. Further, we show that the specific intrinsic membrane properties that give rise to this Heterogeneity may be the diversity of certain slow voltage activated Potassium conductances of the neurons. We show that Heterogeneous populations perform significantly better than Homogeneous populations, for a wide range of input amplitudes and frequencies, producing a much higher fidelity response. We propose that variance of Potassium conductances provides a plausible biological means by which Heterogeneity arises, and that the Heterogeneity plays an important functional role in MVN neuron population responses. We discuss our findings in relation to the specific mechanism of Desynchronisation through which the benfits of Heterogeneity may arise, and place those findings in the context of previous work on Heterogeneity both in general neural processing, and the VOR in particular. Interesting findings regarding the emergence of phase leads are also discussed, as well as suggestions for future work, looking further at Heterogeneity of MVN neuron populations

Optimized gamma synchronization enhances functional binding of fronto-parietal cortices in mathematically gifted adolescents during deductive reasoning

As enhanced fronto-parietal network has been suggested to support reasoning ability of math-gifted adolescents, the main goal of this EEG source analysis is to investigate the temporal binding of the gamma-band (30-60Hz) synchronization between frontal and parietal cortices in adolescents with exceptional mathematical ability, including the functional connectivity of gamma neurocognitive network, the temporal dynamics of fronto-parietal network (phase-locking durations and network lability in time domain), and the self-organized criticality of synchronizing oscillation. Compared with the average-ability subjects, the math-gifted adolescents show a highly integrated fronto-parietal network due to distant gamma phase-locking oscillations, which is indicated by lower modularity of the global network topology, more ?connector bridges? between the frontal and parietal cortices and less ?connector hubs? in the sensorimotor cortex. The time-domain analysis finds that, while maintaining more stable phase dynamics of the fronto-parietal coupling, the math-gifted adolescents are characterized by more extensive fronto-parietal connection reconfiguration. The results from sample fitting in the power-law model further find that the phase-locking durations in the math-gifted brain abides by a wider interval of the power-law distribution. This phase-lock distribution mechanism could represent a relatively optimized pattern for the functional binding of frontal-parietal network, which underlies stable fronto-parietal connectivity and increases flexibility of timely network reconfiguration

Constraints-led approach and synergetic behaviour in volleyball performance

O objetivo desta tese foi investigar a Abordagem Baseada nos Constrangimentos (ABC) e comportamento sinergético no voleibol. Enquadrados pela dinâmica ecológica investigámos conceitos teóricos relacionados com o comportamento sinergético individual e coletivo e aplicamos a ABC em equipas de voleibol. Inicialmente, apresentámos uma revisão narrativa dos princípios da ABC e pedagogia não-linear sugerindo dois exemplos para aplicação em treino. De seguida, produzimos dois artigos de opinião sobre o papel das estruturas de biotensegridade no comportamento sinergético individual e coletivo. Nos estudos experimentais implementámos a ABC para guiar os atletas através das fases de “Search”, “Discover” e “Exploit”. Primeiro, numa equipa de cadetes feminina manipulámos os constrangimentos da tarefa de forma a respeitar as diferenças individuais e comparar a precisão no remate após o treino, assim como, analisar a estratégia temporal na estrutura coordenativa da corrida e chamada de remate. Os resultados mostram que respeitar as diferenças individuais promovem melhor performance (i.e., na precisão do remate) e que congelar os graus de liberdade numa componente da estrutura coordenativa da chamada foi a estratégia associada com mais precisão no remate. De seguida, implementámos um estudo com jogadoras peritas para comparar frequências de contacto na defesa entre o jogo formal, a estratégia tradicional de defesa e a estratégia de coletivamente atender a variáveis especificadoras no decorrer da jogada. Adicionalmente, medimos a sincronização da defesa em situações de sucesso e insucesso defensivo. Resultados mostram que coletivamente atender a variáveis especificadoras no decorrer da jogada promove maior frequência de contactos e que as jogadas de sucesso defensivo estão associadas a alterações na sincronização no decorrer da jogada. Por último, com jogadores jovens de elite comparámos os efeitos na performance de ataque entre treinar de acordo com os princípios da ABC e com uma abordagem tradicional. Também tivemos como objetivo predizer quais as variáveis espácio-temporais que foram exploradas pelos jogadores nos ataques com sucesso. Resultados mostram um aumento da performance com a ABC e que variabilidade na chamada e consistência no ponto de contacto da bola aumenta a probabilidade de atacar com sucesso.The aim of this thesis was to research the Constraints-led Approach (CLA) and synergetic behaviour in volleyball performance. Grounded on ecological dynamics framework we researched theoretically concepts related to individual and collective synergetic behaviour and experimentally implemented the CLA with volleyball teams. First, we presented a narrative review on the principles of CLA and nonlinear pedagogy providing two practical examples to apply to the sub-phase of volleyball attack. Next, we advanced a position statement and a novel hypothesis on the crucial role of biotensegrity structures in individual and collective coordinative structurers (i.e., synergies). In the experimental studies we implemented CLA to guide the performers trough the phases of “Search”, “Discover” and “Exploit”. First, with a team of young female volleyball players we manipulate task constraints to accommodate individual differences and compare spike accuracy after training as well as understand time strategies in the coordinative structure of the horizontal approach. Results show that accommodating individual differences enhances performance (i.e., spike accuracy) and freezing degrees of freedom maintaining high variability in a component of the coordinative structure of the horizontal approach was the strategy of movement re-organization associated with higher spike accuracy. Next, we implemented a study with expert female volleyball players to compare frequencies of defensive ball contacts between real game, traditional defense strategy and “online” attunement to specifying variables. Additionally, we measure group synchronization in successful and unsuccessful defense situations. Results show that collectively attuning to relevant information promotes significant higher frequencies of defense ball contact than pre-determined strategies of action and successful defensive plays are associated with “online” significant changes in group synchronization. Finally, with young male elite volleyball players we aimed to compare the effects of training based on CLA principles to a traditional approach on attack performance. Also, aimed to predict what spatial temporal variables were exploited by the players to achieve successful attacks. Results showed a significant improvement in attack performance for CLA, and we found that variability at the end of the planting step and consistency at ball contact increased the chances of a successful attack

Emergence of Physiological Oscillation Frequencies in a Computer Model of Neocortex

Coordination of neocortical oscillations has been hypothesized to underlie the “binding” essential to cognitive function. However, the mechanisms that generate neocortical oscillations in physiological frequency bands remain unknown. We hypothesized that interlaminar relations in neocortex would provide multiple intermediate loops that would play particular roles in generating oscillations, adding different dynamics to the network. We simulated networks from sensory neocortex using nine columns of event-driven rule-based neurons wired according to anatomical data and driven with random white-noise synaptic inputs. We tuned the network to achieve realistic cell firing rates and to avoid population spikes. A physiological frequency spectrum appeared as an emergent property, displaying dominant frequencies that were not present in the inputs or in the intrinsic or activated frequencies of any of the cell groups. We monitored spectral changes while using minimal dynamical perturbation as a methodology through gradual introduction of hubs into individual layers. We found that hubs in layer 2/3 excitatory cells had the greatest influence on overall network activity, suggesting that this subpopulation was a primary generator of theta/beta strength in the network. Similarly, layer 2/3 interneurons appeared largely responsible for gamma activation through preferential attenuation of the rest of the spectrum. The network showed evidence of frequency homeostasis: increased activation of supragranular layers increased firing rates in the network without altering the spectral profile, and alteration in synaptic delays did not significantly shift spectral peaks. Direct comparison of the power spectra with experimentally recorded local field potentials from prefrontal cortex of awake rat showed substantial similarities, including comparable patterns of cross-frequency coupling

Small-World Network Analysis of Cortical Connectivity in Chronic Fatigue Syndrome using EEG

The primary aim of this thesis was to explore the relationship between electroencephalography (qEEG) and brain system dysregulation in people with Chronic Fatigue Syndrome (CFS). EEG recordings were taken from an archival dataset of 30 subjects, 15 people with CFS and 15 healthy controls (HCs), evaluated during an eye-closed resting state condition. Exact low resolution electromagnetic tomography (eLORETA) was applied to the qEEG data to estimate cortical sources and perform functional connectivity analysis assessing the strength of time-varying signals between all pairwise cortical regions of interest. To obtain a comprehensive view of local and global processing, eLORETA lagged coherence was computed on 84 regions of interest representing 42 Brodmann areas for the left and right hemispheres of the cortex, for the delta (1-3 Hz) and alpha-1 (8-10 Hz) and alpha-2 (10-12 Hz) frequency bands. Graph theory analysis of eLORETA coherence matrices for each participant was conducted to derive the “small-worldness” index, a measure of the optimal balance between the functional integration (global) and segregation (local) properties known to be present in brain networks. The data were also associated with the cognitive impairment composite score on the DePaul Symptom Questionnaire (DSQ), a patient-reported symptom outcome measure of frequency and severity of cognitive symptoms. Results showed that small-worldness for the delta band was significantly lower for patients with CFS compared to HCs. Small-worldness for delta, alpha-1, and alpha-2 were associated with higher cognitive composite scores on the DSQ. Finally, small-worldness in all 3 frequency bands correctly distinguished those with CFS from HCS with a classification rate of nearly 87 percent. These preliminary findings suggest disease processes in CFS may be functionally disruptive to small-world characteristics, especially in the delta frequency band, resulting in cognitive impairments. In turn, these findings may help to confirm a biological basis for cognitive symptoms, providing clinically relevant diagnostic indicators, and characterizing the neurophysiological status of people with CFS