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Many feedforward neural networks (NNs) generate continuous and piecewise-linear (CPWL) mappings. Specifically, they partition the input domain into regions on which the mapping is affine. The number of these so-called linear regions offers a natural metric ...
We prove global in time well-posedness for perturbations of the 2D stochastic Navier-Stokes equations partial derivative( t)u + u center dot del u = Delta u - del p + sigma + xi, u(0, center dot ) = u(0),div (u) = 0, driven by additive space-time white noi ...
We study the global well-posedness and asymptotic behavior for a semilinear damped wave equation with Neumann boundary conditions, modeling a one-dimensional linearly elastic body interacting with a rigid substrate through an adhesive material. The key fea ...
Spontaneous capillary imbibition is a classical problem in interfacial fluid dynamics with a broad range of applications, from microfluidics to agriculture. Here we study the duration of the cross-over between an initial linear growth of the imbibition fro ...
CAMBRIDGE UNIV PRESS2022
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Bedload transport often exhibits dual-mode behavior due to interactions of spatiotemporal controlling factors with the migrating three-dimensional bedforms (characterized by the fully developed patterns in the bed, such as alternate bars, pools, and cluste ...
AMER GEOPHYSICAL UNION2023
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The 70-kD heat shock protein (Hsp70) chaperone system is a central hub of the proteostasis network that helps maintain protein homeostasis in all organisms. The recruitment of Hsp70 to perform different and specific cellular functions is regulated by the J ...
Washington2023
The synthesis of molecular-sieving two-dimensional zeolitic membranes by the assembly of crystalline building blocks without resorting to the secondary growth process is highly desirable. The precise pore size for molecular sieving, ultrathin thickness, an ...
EPFL2022
In this thesis, we study the stochastic heat equation (SHE) on bounded domains and on the whole Euclidean space Rd. We confirm the intuition that as the bounded domain increases to the whole space, both solutions become arbitrarily close to one another ...
The physical mechanism of Narrow bipolar events (NBEs) has been studied for decades but it still holds many mysteries. Recent observations indicate that the fast breakdown discharges that produce NBEs sometimes contain a secondary fast breakdown that propa ...
Chaotic dynamics in systems ranging from low-dimensional nonlinear differential equations to high-dimensional spatiotemporal systems including fluid turbulence is supported by nonchaotic, exactly recurring time-periodic solutions of the governing equations ...
