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We study the Integrated Density of States (IDS) of the random Schr\"odinger operator appearing in the study of certain reinforced random processes in connection with a supersymmetric sigma-model. We rely on previous results on the…
Gene expression patterns (GEPs) are established by cross-regulating target genes that interpret morphogen gradients. However, as development progresses, morphogen activity is reduced, leaving the emergent GEP without stabilizing positional…
Objective. The distribution of equal states (DES) quantifies amplitude fluctuations in biomedical signals. However, under certain conditions, such as a high resolution of data collection or special signal processing techniques, equal states…
Considerable evidence suggests that anticipating sudden shifts from one state to another in bistable dynamical systems is a challenging task, examples include ecosystems, financial markets, complex diseases, etc. In this paper, we…
Intracranial EEG (iEEG) provides high-fidelity neural recordings essential for clinical and brain-computer interface applications, but acquiring these signals requires invasive surgery. While recent studies have attempted to estimate iEEG…
In this work we identify and investigate a novel bifurcation in conserved systems. This secondary bifurcation stops active phase separation in its nonlinear regime. It is then either replaced by an extended, system-filling, spatially…
Electroencephalography (EEG) motor imagery (MI) classification is a fundamental, yet challenging task due to the variation of signals between individuals i.e., inter-subject variability. Previous approaches try to mitigate this using…
Sudden Unexpected Death in Epilepsy (SUDEP) and acute ischemic stroke are life-threatening conditions involving complex interactions across cortical, brainstem, and autonomic systems. We present a unified geometric-stochastic multimodal…
The generalized phase retrieval problem over compact groups aims to recover a set of matrices -- representing an unknown signal -- from their associated Gram matrices. This framework generalizes the classical phase retrieval problem, which…
Electroencephalography has been established as an effective method for detecting Parkinson's disease, typically diagnosed early.Current Parkinson's disease detection methods have shown significant success within individual datasets,…
In electronic health records (EHRs), irregular time-series (ITS) occur naturally due to patient health dynamics, reflected by irregular hospital visits, diseases/conditions and the necessity to measure different vitals signs at each visit…
Modern electronic health records (EHRs) hold immense promise in tracking personalized patient health trajectories through sequential deep learning, owing to their extensive breadth, scale, and temporal granularity. Nonetheless, how to…
Current studies about motor imagery based rehabilitation training systems for stroke subjects lack an appropriate analytic method, which can achieve a considerable classification accuracy, at the same time detects gradual changes of imagery…
Self-supervised approaches for electroencephalography (EEG) representation learning face three specific challenges inherent to EEG data: (1) The low signal-to-noise ratio which challenges the quality of the representation learned, (2) The…
The effect of demographic stochasticity, in the form of Gaussian white noise, in a predator-prey model with one fast and two slow variables is studied. We derive the stochastic differential equations (SDEs) from a discrete model. For…
Generalised hyperbolic (GH) processes are a class of stochastic processes that are used to model the dynamics of a wide range of complex systems that exhibit heavy-tailed behavior, including systems in finance, economics, biology, and…
The present study introduces an innovative approach to the synthesis of Electroencephalogram (EEG) signals by integrating diffusion models with reinforcement learning. This integration addresses key challenges associated with traditional…
Electromigration-induced step bunching in the presence of sublimation or deposition is studied theoretically in the attachment-limited regime. We predict a phase transition as a function of the relative strength of kinetic asymmetry and…
A person tends to generate dynamic attention towards speech under complicated environments. Based on this phenomenon, we propose a framework combining dynamic attention and recursive learning together for monaural speech enhancement. Apart…
Effective metabolic waste clearance and maintaining ionic homeostasis are essential for the health and normal function of the central nervous system. To understand its mechanism and the role of fluid flow, we develop a multidomain…