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

Nonlinear Time-Frequency Control Theory with Applications

Nonlinear control is an important subject drawing much attention. When a nonlinear system undergoes route-to-chaos, its response is naturally bounded in the time-domain while in the meantime becoming unstably broadband in the frequency-domain. Control scheme facilitated either in the time- or frequency-domain alone is insufficient in controlling route-to-chaos, where the corresponding response deteriorates in the time and frequency domains simultaneously. It is necessary to facilitate nonlinear control in both the time and frequency domains without obscuring or misinterpreting the true dynamics. The objective of the dissertation is to formulate a novel nonlinear control theory that addresses the fundamental characteristics inherent of all nonlinear systems undergoing route-to-chaos, one that requires no linearization or closed-form solution so that the genuine underlying features of the system being considered are preserved. The theory developed herein is able to identify the dynamic state of the system in real-time and restrain time-varying spectrum from becoming broadband. Applications of the theory are demonstrated using several engineering examples including the control of a non-stationary Duffing oscillator, a 1-DOF time-delayed milling model, a 2-DOF micro-milling system, unsynchronized chaotic circuits, and a friction-excited vibrating disk. Not subject to all the mathematical constraint conditions and assumptions upon which common nonlinear control theories are based and derived, the novel theory has its philosophical basis established in the simultaneous time-frequency control, on-line system identification, and feedforward adaptive control. It adopts multi-rate control, hence enabling control over nonstationary, nonlinear response with increasing bandwidth ? a physical condition oftentimes fails the contemporary control theories. The applicability of the theory to complex multi-input-multi-output (MIMO) systems without resorting to mathematical manipulation and extensive computation is demonstrated through the multi-variable control of a micro-milling system. The research is of a broad impact on the control of a wide range of nonlinear and chaotic systems. The implications of the nonlinear time-frequency control theory in cutting, micro-machining, communication security, and the mitigation of friction-induced vibrations are both significant and immediate

Selecting embedding delays: An overview of embedding techniques and a new method using persistent homology

Delay embedding methods are a staple tool in the field of time series analysis and prediction. However, the selection of embedding parameters can have a big impact on the resulting analysis. This has led to the creation of a large number of methods to optimise the selection of parameters such as embedding lag. This paper aims to provide a comprehensive overview of the fundamentals of embedding theory for readers who are new to the subject. We outline a collection of existing methods for selecting embedding lag in both uniform and non-uniform delay embedding cases. Highlighting the poor dynamical explainability of existing methods of selecting non-uniform lags, we provide an alternative method of selecting embedding lags that includes a mixture of both dynamical and topological arguments. The proposed method, {\em Significant Times on Persistent Strands} (SToPS), uses persistent homology to construct a characteristic time spectrum that quantifies the relative dynamical significance of each time lag. We test our method on periodic, chaotic and fast-slow time series and find that our method performs similar to existing automated non-uniform embedding methods. Additionally, $n$-step predictors trained on embeddings constructed with SToPS was found to outperform other embedding methods when predicting fast-slow time series

Artificial Intelligence empowerment in managerial decision-making

Dissertação de mestrado em Gestão e NegóciosA inteligência artificial (IA) é um dos temas mais interessantes de estudo e desenvolvimento, e fascinante no que às diferentes aplicações e usos diz respeito. O objetivo deste trabalho de pesquisa foi compreender a relação da IA na tomada de decisão na gestão. Assim, a teoria desenvolvida focou-se no crescimento da relação entre tecnologia e a gestão, no que toca à tomada de decisão, salientando a evolução dos sistemas de informação (SI) à IA em termos de tomada de decisões estratégica, tática e operacional. Nesta linha de pensamento, o objetivo era perceber se o uso da tecnologia/IA era condicionado pelas características das empresas, em termos de pequenas, médias ou grandes empresas. Também, analisar o potencial da IA e/ou tecnologias nas empresas, de forma a perceber as mudanças sentidas nas organizações devido às alterações provocadas pela IA/tecnologia. Adicionalmente, passou por perceber o impacto da IA nos gestores, em termos de cooperação, se estavam no peso ideal para trabalhar e para construir o sucesso, e se tinham sugestões para atualizar ou implementar IA nas empresas. A amostra é composta por administradores e CEOs de pequenas, médias e grandes empresas, que foram submetidos a uma entrevista. Os resultados do conteúdo de análise das entrevistas reforçam as ideias exploradas na revisão da literatura, mostrando que o uso da IA na tomada de decisão era maioritariamente presente em grandes empresas, empresas com maiores condições para investir, já em PME notou-se uma maior utilização de SI combinado com a racionalidade humana. A teoria do caos, permitiu perceber que as empresas apresentadas na pesquisa não implementam IA/tecnologias nos processos como uma tentativa de resolver problemas, mas de entender se o seu uso traria benefícios. Além disso, percebeu-se que as empresas não tinham conhecimento das potencialidades da IA para aplicar nas diversas áreas, mas que eram conscientes do seu valor. Por fim, relativamente aos impactos das tecnologias/IA nos trabalhadores, foi sentido pela maioria uma resistência para a sua implementação, vendo-as como uma ameaça, mas aceitando assim que observavam melhores, mais rápidos e precisos resultados. Os entrevistados, conscientes do peso da IA no mundo, mencionaram que o motivo desta resposta era derivado do medo do desconhecido, não os impedindo de crescer, implementar e aprender.Artificial intelligence (AI) is one of the most interesting topics to be studied and developed and fascinating in terms of the different applications and usages. The aim of this research work was to understand the relationship of AI in manage-rial decision-making. Hence, the theory developed was focused on the growth of the rela-tionship between technology and management, specifically in decision-making, noticing the evolution of information systems (IS) to artificial intelligence directed to strategical, tactical, and operational decision-making. This line of thought was followed to understand if the usage of technology and AI was conditioned by firms’ characteristics, in terms of being small, medium, and big firms. The research focused also in analyse the potential of AI and/or technologies in firms, more precisely, understand the changes on organizations due to the alterations provided by AI and technology. Also, understand the impact of AI in managers, in terms of cooperation if it was in the ideal weight to work and build success, and if they had suggestions to upgrade or implement AI within their firms. The sample was composed by administrates and CEOs of small, medium, and big firms, that were sub-mitted to an interview. The results of the content of analysis of the interviews reinforce the ideas exposed in the literature review, showing that the use of AI was most used in big firms, with higher conditions to invest on it, rather than in medium and small firms, that use IS combined with human rationality. With the help of chaos theory, it was perceived that the firms pre-sented in the research do not implement AI/technologies in their processes as an attempt of solve problems but to understand if their usage would bring valuable benefits to them. Additionally, it was observed that the firms were not owning knowledge of the potential-ities of the vast existence of tools with AI to apply in several areas but know that it builds success. Finally, there were quested the impacts of technologies and AI in the workers within firms, demonstrating that most of them offer resistance when implementing AI and technologies, feeling threatened but ends with the acceptance of it by seeing the better, quickly, and accurate results presented by it. The quested people mentioned that most of them fear the unknown, but it does not stop them from growing and working in the pro-cess of implement and know it, being aware of the increase its applications in the world

On intrinsic uncertainties in earth system modelling

Various types of uncertainty plague climate change simulation, which is, in turn, a crucialelement of Earth System modelling. This fact was recognized for example in the Third Assessment Report (TAR) of the Intergovernmental Panel on Climate Change (IPCC, Houghton et al. (2001)), where the authors indicate that for the period between 1990 and 2100 an increase of the global mean temperature around 1.4-5.8°C is to be expected (Houghton et al. 2001). The width of this span as well as the fact that the authors did not give a number concerning the most probable value or a probability distribution shows clearly the large uncertainty. This uncertainty does not only arise due to the different scenarios of future development concerning greenhouse gas emissions for example, but follows to large degree from the wide range of results from different models as well. The chain of these uncertainties of imponderables in the analysis of the Earth System (Schellnhuber and Wenzel 1998), which includes the climate system as well as the anthroposphere, reaches from uncertainties about the existence of critical thresholds, to ignorance of the exact state of today's climate, and ultimately to a lack of knowledge concerning climate-relevant processes, some of which are visible as uncertainties in climate models. Many attempts have been made to reduce these uncertainties by gaining a conceptual understanding of processes, e.g. of El Ni~no / Southern Oscillation (ENSO) (Jin 1997, e.g.) or of the Atlantic overturning (Stommel 1961; Rahmstorf 1996, e.g.), by developing methods to identify critical thresholds in the climate system (Alley et al. 2003; Rial et al. 2004, e.g.), or by implementing an increasing number of processes in a model, resulting in high resolution general circulation models (GCMs), e.g. ECHAM5/MPI-OM (Jungclaus et al. 2006) or HadCM3 (Gordon et al. 2000) and many more. Nevertheless, the much larger part of uncertainties is inevitable in the process of modelling as well as in our understanding of the Earth System. In this thesis we will structure this conglomeration of uncertainties climate research is confronted with. We will address several types of uncertainty and apply methods of dynamical systems theory on a trendsetting field of climate research, i.e. the Indian monsoon ...thesi

Nonlinear Time-Frequency Control Theory with Applications

Nonlinear control is an important subject drawing much attention. When a nonlinear system undergoes route-to-chaos, its response is naturally bounded in the time-domain while in the meantime becoming unstably broadband in the frequency-domain. Control scheme facilitated either in the time- or frequency-domain alone is insufficient in controlling route-to-chaos, where the corresponding response deteriorates in the time and frequency domains simultaneously. It is necessary to facilitate nonlinear control in both the time and frequency domains without obscuring or misinterpreting the true dynamics. The objective of the dissertation is to formulate a novel nonlinear control theory that addresses the fundamental characteristics inherent of all nonlinear systems undergoing route-to-chaos, one that requires no linearization or closed-form solution so that the genuine underlying features of the system being considered are preserved. The theory developed herein is able to identify the dynamic state of the system in real-time and restrain time-varying spectrum from becoming broadband. Applications of the theory are demonstrated using several engineering examples including the control of a non-stationary Duffing oscillator, a 1-DOF time-delayed milling model, a 2-DOF micro-milling system, unsynchronized chaotic circuits, and a friction-excited vibrating disk. Not subject to all the mathematical constraint conditions and assumptions upon which common nonlinear control theories are based and derived, the novel theory has its philosophical basis established in the simultaneous time-frequency control, on-line system identification, and feedforward adaptive control. It adopts multi-rate control, hence enabling control over nonstationary, nonlinear response with increasing bandwidth ? a physical condition oftentimes fails the contemporary control theories. The applicability of the theory to complex multi-input-multi-output (MIMO) systems without resorting to mathematical manipulation and extensive computation is demonstrated through the multi-variable control of a micro-milling system. The research is of a broad impact on the control of a wide range of nonlinear and chaotic systems. The implications of the nonlinear time-frequency control theory in cutting, micro-machining, communication security, and the mitigation of friction-induced vibrations are both significant and immediate