A recently developed spatial operator algebra for manipulator modeling, control and tra-jectory design is discussed. The elements of this algebra are linear operators whose domain and range spaces consist of forces, moments, velocities, and accelerations. The eeect of these operators is equivalent to a spatial recursion along the span of a manipulator. Inversion of operators can be eeciently ob...

A recently developed spatial operator algebra for manipulator modeling, control and trajectory design is discussed. The elements of this algebra are linear operators whose domain and range spaces consist of forces, moments, velocities, and accelerations. The e ect of these operators is equivalent to a spatial recursion along the span of a manipulator. Inversion of operators can be e ciently obt...

Development systems for deep learning, such as Theano, Torch, TensorFlow, or MXNet, are easyto-use tools for creating complex neural network models. Since gradient computations are automatically baked in, and execution is mapped to high performance hardware, these models can be trained endto-end on large amounts of data. However, it is currently not easy to implement many basic machine learning...

A recently developed spatial operator algebra for manipulator modeling, control, and trajectory design is discussed. The elements of this algebra are linear operators whose domain and range spaces consist of forces, moments, velocities, and accelerations. The effect of these operators is equivalent to a spatial recursion along the span of a manipulator. Inversion of operators can be efficiently...

This paper provides a consistent set of flexible tools to approximate important geometric attributes, including normal vectors and curvatures, on arbitrary 2D and 3D meshes embedded in n dimensions. We present a consistent derivation of these first and second order differential properties using Voronoi cells and the mixed FiniteElement/Finite-Volume method. The new operators are closely related...

‎In this article‎, ‎we develop two nonparametric smoothing estimators for parameter of a time-variant parametric model‎. ‎This parameter can be from any parametric family or from any parametric or semi-parametric regression model‎. ‎Estimation is based on a two-step procedure‎, ‎in which we first get the raw estimate of the parameter at a set of disjoint time...

A. We establish local well-posedness and smoothing results for the Cauchy problem of a degenerate dispersive Navier-Stokes system that arises from kinetic theory. Under assumptions that the initial data satisfy asymptotic flatness and nontrapping conditions, we show there exists a unique classical solution for a finite time. Due to degeneracies in both dissipation and dispersion for the ...

We survey the literature on robust multigrid methods which have been developed in recent years for solving second order elliptic PDEs with nonsmooth coeecients. We highlight the key ideas of designing robust multigrid methods which are able to recover the usual multigrid eeciency for nonsmooth coeecient PDEs on structured or unstructured grids. In particular, we shall describe various approache...

In this contribution we consider the eeect of a class of \averaging op-erators" on isotropic tness landscapes. Explicit expressions for the correlation function of the averaged landscapes are derived. A new class of tunably rugged landscapes, obtained by iterated smoothing of the random energy model, is established. The correlation structure of certain landscapes, among them the Sherrington-Kir...

The stationary fractional advection dispersion equation is discretized by linear finite element scheme, and a full V-cycle multigrid method (FV-MGM) is proposed to solve the resulting system. Some useful properties of the approximation and smoothing operators are proved. Using these properties we derive the convergence results in both L2 norm and energy norm for FV-MGM. Numerical examples are g...