Search for: All records

Datasets involving multivariate event streams are prevalent in numerous applications. We present a novel framework for modeling temporal point processes called clock logic neural networks (CLNN) which learn weighted clock logic (wCL) formulas as interpretable temporal rules by which some events promote or inhibit other events. Specifically, CLNN models temporal relations between events using conditional intensity rates informed by a set of wCL formulas, which are more expressive than related prior work. Unlike conventional approaches of searching for generative rules through expensive combinatorial optimization, we design smooth activation functions for components of wCL formulas that enable a continuous relaxation of the discrete search space and efficient learning of wCL formulas using gradient-based methods. Experiments on synthetic datasets manifest our model's ability to recover the ground-truth rules and improve computational efficiency. In addition, experiments on real-world datasets show that our models perform competitively when compared with state-of-the-art models. 

Finding strongly connected components (SCCs) and the diameter of a directed network play a key role in a variety of discrete optimization problems, and subsequently, machine learning and control theory problems. On the one hand, SCCs are used in solving the 2-satisfiability problem, which has applications in clustering, scheduling, and visualization. On the other hand, the diameter has applications in network learning and discovery problems enabling efficient internet routing and searches, as well as identifying faults in the power grid. In this paper, we leverage consensus-based principles to find the SCCs in a scalable and distributed fashion with a computational complexity of O(Ddmaxin−degree) , where D is the (finite) diameter of the network and dmaxin−degree is the maximum in-degree of the network. Additionally, we prove that our algorithm terminates in D+1 iterations, which allows us to retrieve the diameter of the network. We illustrate the performance of our algorithm on several random networks, including Erdö-Rényi, Barabási-Albert, and Watts-Strogatz networks. 

A fundamental challenge in neuroscience is to uncover the principles governing how the brain interacts with the external environment. However, assumptions about external stimuli fundamentally constrain current computational models. We show in silico that unknown external stimulation can produce error in the estimated linear time-invariant dynamical system. To address these limitations, we propose an approach to retrieve the external (unknown) input parameters and demonstrate that the estimated system parameters during external input quiescence uncover spatiotemporal profiles of external inputs over external stimulation periods more accurately. Finally, we unveil the expected (and unexpected) sensory and task-related extra-cortical input profiles using functional magnetic resonance imaging data acquired from 96 subjects (Human Connectome Project) during the resting-state and task scans. This dynamical systems model of the brain offers information on the structure and dimensionality of the BOLD signal’s external drivers and shines a light on the likely external sources contributing to the BOLD signal’s non-stationarity. Our findings show the role of exogenous inputs in the BOLD dynamics and highlight the importance of accounting for external inputs to unravel the brain’s time-varying functional dynamics. 

Resting-state blood-oxygen-level-dependent (BOLD) signal acquired through functional magnetic resonance imaging is a proxy of neural activity and a key mechanism for assessing neurological conditions. Therefore, practical tools to filter out artefacts that can compromise the assessment are required. On the one hand, a variety of tailored methods to preprocess the data to deal with identified sources of noise (e.g., head motion, heart beating, and breathing, just to mention a few) are in place. But, on the other hand, there might be unknown sources of unstructured noise present in the data. Therefore, to mitigate the effects of such unstructured noises, we propose a model-based filter that explores the statistical properties of the underlying signal (i.e., long-term memory). Specifically, we consider autoregressive fractional integrative process filters. Remarkably, we provide evidence that such processes can model the signals at different regions of interest to attain stationarity. Furthermore, we use a principled analysis where a ground-truth signal with statistical properties similar to the BOLD signal under the injection of noise is retrieved using the proposed filters. Next, we considered preprocessed (i.e., the identified sources of noise removed) resting-state BOLD data of 98 subjects from the Human Connectome Project. Our results demonstrate that the proposed filters decrease the power in the higher frequencies. However, unlike the low-pass filters, the proposed filters do not remove all high-frequency information, instead they preserve process-related higher frequency information. Additionally, we considered four different metrics (power spectrum, functional connectivity using the Pearson’s correlation, coherence, and eigenbrains) to infer the impact of such filter. We provided evidence that whereas the first three keep most of the features of interest from a neuroscience perspective unchanged, the latter exhibits some variations that could be due to the sporadic activity filtered out. 

Assessing the stability of biological system models has aided in uncovering a plethora of new insights in genetics, neuroscience, and medicine. In this paper, we focus on analyzing the stability of neurological signals, including electroencephalogram (EEG) signals. Interestingly, spatiotemporal discrete-time linear fractional-order systems (DTLFOS) have been shown to accurately and efficiently represent a variety of neurological and physiological signals. Here, we leverage the conditions for stability of DTLFOS to assess a real-world EEG data set. By analyzing the stability of EEG signals during movement and rest tasks, we provide evidence of the usefulness of the quantification of stability as a bio-marker for cognitive motor control.