Our ability to comprehend and engage with a system hinges on our capacity to address fundamental inquiries. These include determining the minimal set of state variables required for controllability, identifying the minimal set of state variables for observability, and pinpointing which subset of measured state variables, along with specific actuators, is necessary to achieve arbitrary pole placement through decentralized control. Furthermore, these questions can be explored in contexts with privacy constraints and within adversarial environments, giving rise to additional concerns: how to share task-specific data while safeguarding private information, and how to design a resilient sensing infrastructure to protect against malicious adversarial attacks.

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Today's neurostimulation devices have discharging strategies that are determined empirically. Therefore, these devices do not take into consideration the specific brain's dynamics or response to a sequence of discharges. Hence, we seek model-based schemes that enable a personalized discharge scheme that minimizes the interaction with the brain, which leads to better performance and an increase in autonomy for the neurostimulation device.  

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Our approach aims to introduce new models capable of capturing spatiotemporal dependencies, to be later used to determine which regions need to be sensed and which data contains more 'information'. Thus, improving the reliability of the interaction between brain-machine and brain-machine-brain interfaces, with potential applications to neurological disorders (e.g. epilepsy). 

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Understanding the relationship between structural brain connectivity and functional connectivity dictated by blood-oxygenation dependency level (BOLD) across different brain regions is key to understanding the brain in health and disease. The latter may exhibit spatiotemporal fingerprints that are uniquely associated with specific stages of disease that can play a key role in digital pathology and assessing the performance of new therapeutics to mitigate their effects.

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Neurostimulation therapy for neurological diseases and disorders promises to transform the lives of millions suffering from neurological conditions. The challenge is to develop stimulation patterns that interact with the nervous system promptly and precisely, while avoiding abnormal or unwanted activity that can exacerbate the pathology. Current stimulation methods lack predictive models, which makes it difficult to anticipate how the brain will react to a specific stimulus. This can lead to unintended consequences and ineffective treatment.

In this lecture, I will overview how predictive models and approaches from control systems engineering can be used to overcome current limitations in neurostimulation. By implementing these models in the software of neurostimulation devices, we can create stimulation patterns that are more effective and efficient in steering brain activity away from unwanted regimes.

The lecture concludes by highlighting the benefits of the proposed approach, which can potentially improve the quality of life for millions of people who rely on neurostimulation therapy. 

Dynamical networks permeate a vast array of natural and human-engineered systems. Our focus often revolves around ensuring the directed evolution of their states towards desired objectives within predefined temporal constraints. The network topologies at play inherently introduce intricate trade-offs, wherein the interplay between the minimal count of influenced nodes and the time required for control comes to the fore. Intriguingly, our investigation reveals that various measures of centrality and non-centrality lack the capacity to elucidate these trade-offs comprehensively. Consequently, widely employed generative models demonstrate their inadequacy in encapsulating the nuanced dynamics under scrutiny.

Within this seminar, we present an innovative generative model designed to replicate the nuanced trade-offs observed in actual dynamic networks. In essence, we underscore the pivotal role played by the amalgamation of network partitions and degree distributions in shaping the efficacy of our proposed generative framework. We firmly assert that this methodological approach stands as a linchpin when deploying generative models to unravel the dynamic network attributes spanning the realms of science and engineering.

Lastly, our empirical findings substantiate the capacity of the proposed generative model to spawn a diverse spectrum of networks, bearing trade-offs statistically akin to those exhibited by genuine networks. These encompass a range of domains, from neural networks to social networks, wherein the minimum count of manipulated nodes is balanced against the time required to achieve control.