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We propose a general class of co-evolving tree network models driven by local exploration where new vertices attach to the current network via randomly sampling a vertex and then exploring the graph for a random number of steps in the…
The (measure-theoretical) entropy of a diffeomorphism along an expanding invariant foliation is the rate of complexity generated by the diffeomorphism along the leaves of the foliation. We prove that this number varies upper…
Aeolian sand transport is a major process shaping landscapes on Earth and on diverse celestial bodies. Conditions favoring bimodal sand transport, with fine-grain saltation driving coarse-grain reptation, give rise to the evolution of…
Random forests are classical ensemble algorithms that construct multiple randomized decision trees and aggregate their predictions using naive averaging. \citet{zhou2019deep} further propose a deep forest algorithm with multi-layer forests,…
Coastal erosion is a major and growing environmental problem describing the movement of sand caused by tides, waves or currents. Several phenomena contribute to the significant advance of the sea. These include climate change, with rising…
Vegetation in semi-arid environments self-organizes into striking spatial patterns -- bands, spots, labyrinths, and gaps -- with characteristic wavelengths on the order of tens to hundreds of meters. Existing reaction-diffusion models…
The development of low-level mesocyclones in supercell thunderstorms has often been explained via the development of storm-generated streamwise vorticity along a baroclinic gradient in the forward flank of supercells. However, the ambient…
Wind topographically forced by hills and sand dunes accelerates on the upwind (stoss) slopes and reduces on the downwind (lee) slopes. This secondary wind regime, however, possesses a subtle effect, reported here for the first time from…
We tackle the challenging problem of creating full and accurate three dimensional reconstructions of botanical trees with the topological and geometric accuracy required for subsequent physical simulation, e.g. in response to wind forces.…
We examine theoretically the effects of random topographical substrates on the motion of two-dimensional droplets via appropriate statistical approaches. Different random substrate families are represented as stationary random functions.…
The surface of both Jupiter and Saturn has magnificent vortical storms which help shape the dynamic nature of their atmospheres. Land- and space-based observational campaigns over time have established several properties of these vortices,…
Tip-driven growth processes underlie the development of many plants. To date, tip-driven growth processes have been modelled as an elongating path or series of segments without taking into account lateral expansion during elongation.…
We investigate erosion patterns observed in a horizontal granular bed resulting from seepage of water motivated by observation of beach rills and channel growth in larger scale landforms. Our experimental apparatus consists of a wide…
Networks having the geometry and the connectivity of trees are considered as the spatial support of spatiotemporal dynamical processes. A tree is characterized by two parameters: its ramification and its depth. The local dynamics at the…
Viscous and gravitational flow instabilities cause a displacement front to break up into finger-like fluids. The detection and evolutionary analysis of these fingering instabilities are critical in multiple scientific disciplines such as…
We analyze evolutionary dynamics in a confluent, branching cellular population, such as in a growing duct, vasculature, or in a branching microbial colony. We focus on the coarse-grained features of the evolution and build a statistical…
Predicting transport rates of windblown sand is a central problem in aeolian research, with implications for climate, environmental, and planetary sciences. Though studied since the 1930s, the underlying many-body dynamics is still…
We study the morphological evolution of surfaces during ion sputtering and we compare their dynamical roughening with aeolian ripple formation in sandy deserts. We show that, although the two phenomena are physically different, they must…
Recently proposed budding tree is a decision tree algorithm in which every node is part internal node and part leaf. This allows representing every decision tree in a continuous parameter space, and therefore a budding tree can be jointly…
The high reflection of land vegetation in the near-infrared, the vegetation red edge (VRE), is often cited as a spectral biosignature for surface vegetation on exoplanets. The VRE is only a few percent change in reflectivity for a…