Related papers: A Dynamical Systems and System Identification Fram…
Phase-amplitude coupling (PAC) describes the phenomenon where the power of a high-frequency oscillation evolves with the phase of a low-frequency one. We propose a model that explains the emergence of PAC in two commonly-accepted…
Background: In electrical brain signals such as Local Field Potential (LFP) and Electroencephalogram (EEG), oscillations emerge as a result of neural network activity. The oscillations extend over several frequency bands. Between their…
Recent evidence has revealed cross-frequency coupling and, particularly, phase-amplitude coupling (PAC) as an important strategy for the brain to accomplish a variety of high-level cognitive and sensory functions. However, decoding PAC is…
Several methods have been developed to extract information from electroencephalograms (EEG). One of them is Phase-Amplitude Coupling (PAC) which is a type of Cross-Frequency Coupling (CFC) method, consisting in measure the synchronization…
Combining machine clustering with deep models has shown remarkable superiority in deep clustering. It modifies the data processing pipeline into two alternating phases: feature clustering and model training. However, such alternating…
We present a data-driven framework for reachability analysis of nonlinear dynamical systems that requires no explicit model. A denoising diffusion probabilistic model learns the time-evolving state distribution of a dynamical system from…
Predicting the response of nonlinear dynamical systems subject to random, broadband excitation is important across a range of scientific disciplines, such as structural dynamics and neuroscience. Building data-driven models requires…
We introduce a novel technique for verification and model synthesis of sequential programs. Our technique is based on learning a regular model of the set of feasible paths in a program, and testing whether this model contains an incorrect…
We quantify nonlinear interactions between coupled complex processes, when the system is subject to noise and not all its components are measurable. Our method is applicable even when the system cannot be continuously monitored over time,…
While the identification of nonlinear dynamical systems is a fundamental building block of model-based reinforcement learning and feedback control, its sample complexity is only understood for systems that either have discrete states and…
In this paper we present a novel model checking approach to finite-time safety verification of black-box continuous-time dynamical systems within the framework of probably approximately correct (PAC) learning. The black-box dynamical…
We develop model free PAC performance guarantees for multiple concurrent MDPs, extending recent works where a single learner interacts with multiple non-interacting agents in a noise free environment. Our framework allows noisy and resource…
We propose lacunarity as a novel recurrence quantification measure and illustrate its efficacy to detect dynamical regime transitions which are exhibited by many complex real-world systems. We carry out a recurrence plot based analysis for…
Symbolic control techniques aim to satisfy complex logic specifications. A critical step in these techniques is the construction of a symbolic (discrete) abstraction, a finite-state system whose behaviour mimics that of a given…
We present an approach for the detection of sharp change points (short-lived and persistent) in nonlinear and nonstationary dynamic systems under high levels of noise by tracking the local phase and amplitude synchronization among the…
Spatiotemporal dynamics is central to a wide range of applications from climatology, computer vision to neural sciences. From temporal observations taken on a high-dimensional vector of spatial locations, we seek to derive knowledge about…
When functional data manifest amplitude and phase variations, a commonly-employed framework for analyzing them is to take away the phase variation through a function alignment and then to apply standard tools to the aligned functions. A…
A new method is introduced for analysis of interactions between time-dependent coupled oscillators, based on the signals they generate. It distinguishes unsynchronized dynamics from noise-induced phase slips, and enables the evolution of…
Networked dynamical systems are widely used as formal models of real-world cascading phenomena, such as the spread of diseases and information. Prior research has addressed the problem of learning the behavior of an unknown dynamical system…
In many problems of data-driven modeling for dynamical systems, the governing equations are not known a priori and must be selected phenomenologically from a large set of candidate interactions and basis functions. In such situations, point…