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This paper focuses on analysis and design of timevarying complex networks having fractional order dynamics. These systems are key in modeling the complex dynamical processes arising in several natural and man made systems.Notably, examples include neurophysiological signals such as electroencephalogram (EEG) that captures the variation in potential fields, and blood oxygenation level dependent (BOLD) signal, which serves as a proxy for neuronal activity. Notwithstanding, the complex networks originated by locally measuring EEG and BOLD are often treated as isolated networks and do not capture the dependency from external stimuli, e.g., originated in subcortical structures such as the thalamus and the brain stem. Therefore, we propose a paradigm-shift towards the analysis of such complex networks under unknown unknowns (i.e., excitations). Consequently, the main contributions of the present paper are threefold: (i) we present an alternating scheme that enables to determine the best estimate of the model parameters and unknown stimuli; (ii) we provide necessary and sufficient conditions to ensure that it is possible to retrieve the state and unknown stimuli; and (iii) upon these conditions we determine a small subset of variables that need to be measured to ensure that both state and input can be recovered, while establishing sub-optimality guarantees with respect to the smallest possible subset. Finally, we present several pedagogical examples of the main results using real data collected from an EEG wearable device.

Brain interfaces are cyber-physical systems that aim to harvest information from the (physical) brain through sensing mechanisms, extract information about the underlying processes, and decide/actuate accordingly. Nonetheless, the brain interfaces are still in their infancy, but reaching to their maturity quickly as several initiatives are released to push forward their development (e.g., NeuraLink by Elon Musk and 'typing-by-brain' by Facebook). This has motivated us to revisit the design of EEG-based non-invasive brain interfaces. Specifically, current methodologies entail a highly skilled neurofunctional approach and evidence-based a priori knowledge about specific signal features and their interpretation from a neuro-physiological point of view. Hereafter, we propose to demystify such approaches, as we propose to leverage new time-varying complex network models that equip us with a fractal dynamical characterization of the underlying processes. Subsequently, the parameters of the proposed complex network models can be explained from a system's perspective, and, consecutively, used for classification using machine learning algorithms and/or actuation laws determined using control system's theory. Besides, the proposed system identification methods and techniques have computational complexities comparable with those currently used in EEG-based brain interfaces, which enable comparable online performances. Furthermore, we foresee that the proposed models and approaches are also valid using other invasive and non-invasive technologies. Finally, we illustrate and experimentally evaluate this approach on real EEG-datasets to assess and validate the proposed methodology. The classification accuracies are high even on having less number of training samples.

We present a deep learning approach towards the large-scale prediction and analysis of bird acoustics from 100 different bird species. We use spectrograms constructed on bird audio recordings from the Cornell Bird Challenge (CBC)2020 dataset, which includes recordings of multiple and potentially overlapping bird vocalizations with background noise. Our experiments show that a hybrid modeling approach that involves a Convolutional Neural Network (CNN) for learning the representation for a slice of the spectrogram, and a Recurrent Neural Network (RNN) for the temporal component to combine across time-points leads to the most accurate model on this dataset. We show results on a spectrum of models ranging from stand-alone CNNs to hybrid models of various types obtained by combining CNNs with other CNNs or RNNs of the following types: Long Short-Term Memory (LSTM) networks, Gated Recurrent Units (GRU), and Legendre Memory Units (LMU). The best performing model achieves an average accuracy of 67% over the 100 different bird species, with the highest accuracy of 90% for the bird species, Red crossbill. We further analyze the learned representations visually and find them to be intuitive, where we find that related bird species are clustered close together. We present a novel way to empirically interpret the representations learned by the LMU-based hybrid model which shows how memory channel patterns change over time with the changes seen in the spectrograms.

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