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Intractable phase dynamics often challenge our understanding of complex oscillatory systems, hindering the exploration of synchronisation, chaos, and emergent phenomena across diverse fields. We introduce a novel conceptual framework for…
We study synchronization of locally coupled noisy phase oscillators which move diffusively in a one-dimensional ring. Together with the disordered and the globally synchronized states, the system also exhibits several wave-like states which…
We consider evolution of initial disturbances in spatially extended systems with autonomous rhythmic activity, such as the heart. We consider the case when the activity is stable with respect to very smooth (changing little across the…
In phase retrieval, the goal is to recover a complex signal from the magnitude of its linear measurements. While many well-known algorithms guarantee deterministic recovery of the unknown signal using i.i.d. random measurement matrices,…
Dynamical control of biological systems is often restricted by the practical constraint of unidirectional parameter perturbations. We show that such a restriction introduces surprising complexity to the stability of one-dimensional map…
This paper introduces a novel technique for reconstructing the phase of modified spectrograms of audio signals. From the analysis of mixtures of sinusoids we obtain relationships between phases of successive time frames in the…
Spiral waves are self-repeating waves that can form in excitable media, propagating outward from their center in a spiral pattern. Spiral waves have been observed in different natural phenomena and have been linked to medical conditions…
Ensembles of phase-oscillators are known to exhibit a variety of collective regimes. Here, we show that a simple mean-field model involving two heterogenous populations of pulse-coupled oscillators, exhibits, in the strong-coupling limit, a…
In the past decade, synchronization on complex networks has attracted increasing attentions from various research disciplines. Most previous works, however, focus only on the dynamic behaviors of synchronization process in the stable…
We consider networks of coupled stochastic oscillators. When coupled we find strong collective oscillations, while each unit remains stochastic. In the limit (N\to \infty) we derive a system of integro-delay equations and show analytically…
Spatial variations in the electrical properties of cardiac tissue can occur because of cardiac diseases. We introduce such gradients into mathematical models for cardiac tissue and then study, by extensive numerical simulations, their…
Experimental studies of synchronization properties on networks with controlled connection topology can provide powerful insights into the physics of complex networks. Here, we report experimental results on the influence of connection…
The heart exhibits complex systems behaviors during atrial fibrillation (AF), where the macroscopic collective behavior of the heart causes the microscopic behavior. However, the relationship between the downward causation and scale is…
Time-varying graph signal recovery has been widely used in many applications, including climate change, environmental hazard monitoring, and epidemic studies. It is crucial to choose appropriate regularizations to describe the…
Our work aims at using quantitative imaging tools to complement the limitation of noise encountered by high resolution fluorescence microscopy methods. Several cycles of fluorophore activation, imaging and deactivation produce a sequence of…
Biological systems can rely on collective formation of a metachronal wave in an ensemble of oscillators for locomotion and for fluid transport. We consider one-dimensional chains of phase oscillators with nearest neighbor interactions,…
We present a novel mechanism for resolving the mechanical rigidity of nanoscopic circular polymers that flow in a complex environment. The emergence of a regime of negative differential mobility induced by topological interactions between…
Rotating spiral waves with a central core composed of phase-randomized oscillators can arise in reaction-diffusion systems if some of the chemical components involved are diffusion-free. This peculiar phenomenon is demonstrated for a…
Cardiac blood flow patterns contain rich information about disease severity and clinical interventions, yet current imaging and computational methods fail to capture underlying relational structures of coherent flow features. We propose a…
Generic wave dislocations (phase singularities, optical vortices) in three dimensions have anisotropic local structure, which is analysed, with emphasis on the twist of surfaces of equal phase along the singular line, and the rotation of…