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We propose a model for combining the Standard Model (SM) with gravity. It relies on a nonminimal coupling of the Higgs field to the Ricci scalar and on the Palatini formulation of gravity. Without introducing any new degrees of freedom in addition to those ...
We describe the first gradient methods on Riemannian manifolds to achieve accelerated rates in the non-convex case. Under Lipschitz assumptions on the Riemannian gradient and Hessian of the cost function, these methods find approximate first-order critical ...
We consider the directed mean curvature flow on the plane in a weak Gaussian random environment. We prove that, when started from a sufficiently flat initial condition, a rescaled and recentred solution converges to the Cole-Hopf solution of the KPZ equati ...
We consider the Allen-Cahn equation ?(t)u - ?u = u - u(3) with a rapidly mixing Gaussian field as initial condition. We show that provided that the amplitude of the initial condition is not too large, the equation generates fronts described by nodal sets o ...
We show that the finite time type II blow up solutions for the energy critical nonlinear wave equation [ \Box u = -u^5 ] on R3+1 constructed in \cite{KST}, \cite{KS1} are stable along a co-dimension one Lipschitz manifold of data perturbations in a ...
In this brief survey we outline the recent advances on the stability issues of certain finite time type II blow-up solutions for the energy critical focusing wave equation □u=−u5 in R3+1. Hereafter we use the convention $\Box=-\parti ...
Objective. Accurate decoding of individual finger movements is crucial for advanced prosthetic control. In this work, we introduce the use of Riemannian-space features and temporal dynamics of electrocorticography (ECoG) signal combined with modern machine ...
Let M be a C-2-smooth Riemannian manifold with boundary and N a complete C-2-smooth Riemannian manifold. We show that each stationary p-harmonic mapping u: M -> N, whose image lies in a compact subset of N, is locally C-1,C-alpha for some alpha is an eleme ...
The predictive control of the self-sustained single spiral vortex breakdown mode is addressed in the three-dimensional flow geometry of Ruith et al. (2003) for a constant swirl number S = 1.095. Based on adjoint optimization algorithms, two different contr ...
In plunging jets and at hydraulic jumps, large amounts of air bubbles are entrained at the impingement of the liquid jet and receiving body (BIN, 1993; ERVINE, 1998; CHANSON, 2009a). Air is entrapped and advected into a turbulent shear layer with strong in ...
