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We are interested in the existence of depolarization waves in the human brain. These waves propagate in the grey matter and are absorbed in the white matter. We consider a two-dimensional model $u_t=\Delta u + f(u) \1_{|y|\leq R} - \alpha u…
We investigate in detail two models describing how stresses propagate and fluctuate in granular media. The first one is a scalar model where only the vertical component of the stress tensor is considered. In the continuum limit, this model…
The frequent emergence of diseases with the potential to become threats at local and global scales, such as influenza A(H1N1), SARS, MERS, and recently COVID-19 disease, makes it crucial to keep designing models of disease propagation and…
In real social networks, person-to-person interactions are known to be heterogeneous, which can affect the way a disease spreads through a population, reaches a tipping point in the fraction of infected individuals, and becomes an epidemic.…
We study the paraxial wave equation with a randomly perturbed index of refraction, which can model the propagation of a wave beam in a turbulent medium. The random perturbation is a stationary and isotropic process with a general form of…
We describe the development of a model to detect user-level clinical depression based on a user's temporal social media posts. Our model uses a Depression Symptoms Detection (DSD) classifier, which is trained on the largest existing samples…
Information, ideas, and diseases, or more generally, contagions, spread over space and time through individual transmissions via social networks, as well as through external sources. A detailed picture of any diffusion process can be…
Several differential equation models have been proposed to explain the formation of patterns characteristic of the grid cell network. Understanding the effect of noise on these models is one of the key open questions in computational…
Static or frozen disorder, characterised by spatial heterogeneities, influences diverse complex systems, encompassing many-body systems, equilibrium and nonequilibrium states of matter, intricate network topologies, biological systems, and…
In this paper, we characterize major depression (MD) as a complex dynamical system in which symptoms (e.g., insomnia and fatigue) are directly connected to one another in a network structure. We hypothesize that individuals can be…
We study shock propagation in a system of initially stationary hard-spheres that is driven by a continuous injection of particles at the origin. The disturbance created by the injection of energy spreads radially outwards through collision…
Modeling and simulating how oxygen supply shapes neuronal excitability is crucial for advancing the understanding of brain function in pathological scenarios, such as ischemia. This condition is caused by a reduced blood supply, leading to…
While the physics of disordered packing in non-growing systems is well understood, unexplored phenomena can emerge when packing takes place in growing domains. We study the arrangements of pigment cells (chromatophores) on squid skin as a…
Epidemic spreading often occurs in spatially heterogeneous environments, yet how quenched heterogeneity reshapes its onset and critical dynamics remains poorly understood. The diffusive epidemic process, a minimal reaction-diffusion model…
Significance: The depolarization of circularly polarized light caused by scattering in turbid media reveals structural information about the dispersed particles, such as their size, density, and distribution, which is useful for…
Deep brain stimulation(DBS)has become an effective intervention for advanced Parkinson's disease, but the exact mechanism of DBS is still unclear. In this review, we discuss the history of DBS, the anatomy and internal architecture of the…
We investigate the spread complexity of a generic two-level subsystem of a larger system to analyze the influence of energy level statistics, comparing chaotic and integrable systems. Initially focusing on the nearest-neighbor level…
Diffusion is a fundamental phenomenon that occurs ubiquitously in nature and remains the subject of continuous research interest. Understanding diffusion is a key to understanding leaving systems. In this Chapter, I discuss diffusion of…
Foam is an industrially important form of matter, commonly deployed to clean objects and even our own skin, thanks to its ability to absorb oil and particles into its interior. To clean a large area, a foam is spread over a substrate, but…
The spreading of misfolded proteins is a known hallmark in some neurodegenerative diseases, known as proteinopathies. A significant example is the tau protein, associated with many pathologies, such as Alzheimer's. In this work, we discuss…