Two main types of subduction zones can be distinguished: (1) those where the subduction hinge migrates away from the upper plate; and (2) those in which the subduction hinge migrates toward the upper plate. Apart from a few exceptions, this distinction seems to apply particularly for W-directed subduction zones and Eor NE-directed subduction zones, respectively. Moreover, the rate of subduction...

We study homogenization by Γ-convergence, with respect to the L1-strong convergence, of periodic multiple integrals in W 1,∞ when the integrand can take infinite values outside of a convex bounded open set of matrices.

0. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1. Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2. Connecting Singularities with Controlled Length . . . . . . . . . . . . . . . . . . . . . ....

In this paper, we explore theoretical properties of training a two-layered ReLU network g(x;w) = ∑K j=1 σ(w T j x) with centered d-dimensional spherical Gaussian input x (σ=ReLU). We train our network with gradient descent on w to mimic the output of a teacher network with the same architecture and fixed parameters w∗. We show that its population gradient has an analytical formula, leading to i...

In this paper, we use dynamical system to analyze the nonlinear weight dynamics of two-layered bias-free networks in the form of g(x;w) = ∑K j=1 σ(w T j x), where σ(·) is ReLU nonlinearity. We assume that the input x follow Gaussian distribution. The network is trained using gradient descent to mimic the output of a teacher network of the same size with fixed parameters w∗ using l2 loss. We fir...

We extend the Lp theory of sparse graph limits, which was introduced in a companion paper, by analyzing different notions of convergence. Under suitable restrictions on node weights, we prove the equivalence of metric convergence, quotient convergence, microcanonical ground state energy convergence, microcanonical free energy convergence, and large deviation convergence. Our theorems extend the...

We study the behavior of oscillatory solutions to convection-diffusion problems, subject to initial and forcing data with modulated oscillations. We quantify the weak convergence in W−1,∞ to the ’expected’ averages and obtain a sharp W−1,∞-convergence rate of order O(ε) – the small scale of the modulated oscillations. Moreover, in case the solution operator of the equation is compact, this weak...

We study the behavior of oscillatory solutions to convection-diiusion problems, subject to initial and forcing data with modulated oscillations. We quantify the weak convergence in W ?1;1 to the 'expected' averages and obtain a sharp W ?1;1-convergence rate of order O(") { the small scale of the modulated oscillations. Moreover, in case the solution operator of the equation is compact, this wea...

In this note we illustrate and develop further with mathematics and examples, the work on successive standardization (or normalization) that is studied earlier by the same authors in [1] and [2]. Thus, we deal with successive iterations applied to rectangular arrays of numbers, where to avoid technical difficulties an array has at least three rows and at least three columns. Without loss, an it...