In this paper, we investigate the sample size requirement for exact recovery of a high order tensor of low rank from a subset of its entries. We show that a gradient descent algorithm with initial value obtained from a spectral method can, in particular , reconstruct a d × d × d tensor of multilinear ranks (r, r, r) with high probability from as few as O(r 7/2 d 3/2 log 7/2 d + r 7 d log 6 d) e...

Path planning belongs to the best-known and well explored problems in computer science. However, in today’s real-time and dynamic applications, such as virtual reality, existing algorithms for static environment are considerably insufficient and, surprisingly, almost no attention is given to techniques for dynamic graphs. This paper introduces two methods to plan a path in an undirected graph w...

In a number of physically important cases, the nonholonomically (nonintegrable) constrained Ricci flows can be modelled by exact solutions of Einstein equations with nonhomogeneous (anisotropic) cosmological constants. We develop two geometric methods for constructing such solutions: The first approach applies the formalism of nonholonomic frame deformations when the gravitational evolution and...

We first review existing sequential methods for estimating a binomial proportion. Afterward, we propose a new family of group sequential sampling schemes for estimating a binomial proportion with prescribed margin of error and confidence level. In particular, we establish the uniform controllability of coverage probability and the asymptotic optimality for such a family of sampling schemes. Our...

We consider a set of electrostatic problems relevant for determining the real-space structure and the groundstate energy of a two-dimensional electron liquid subject to smooth external potentials. Three fundamental geometries are investigated: an elongated metallic island, an antidot, and a constriction. In the first two cases complete closed-form analytical solutions are obtained, despite the ...

The paper studies the solution of stochastic optimization problems in which approximations to the gradient and Hessian are obtained through subsampling. We first consider Newton-like methods that employ these approximations and discuss how to coordinate the accuracy in the gradient and Hessian to yield a superlinear rate of convergence in expectation. The second part of the paper analyzes an in...

We present two algorithms for exact and ap­ proximate inference in causal networks. The first algorithm, dynamic conditioning, is a re­ finement of cutset conditioning that has lin­ ear complexity on some networks for which cutset conditioning is exponential. The sec­ ond algorithm, B-conditioning, is an algo­ rithm for approximate inference that allows one to trade-off the quality of approxima...

This paper argues that many exact and heuristic methods have common structure that permits some degree of unification. It interprets solution algorithms as primal-dual methods in which the primal component searches over problem restrictions, and the dual component obtains bounds on the optimal value. In particular, the concept of an inference dual provides the basis for constraint-directed sear...

In this note is presented a method, given nodal values on multidimensional nonconforming spectral elements, for calculating global Fourier-series coefficients. This method is “exact” in that given the approximation inherent in the spectral-element method (SEM), no further approximation is introduced that exceeds computer round-off error. The method is very useful when the SEM has yielded an ada...

�e �rst review existing sequential methods for estimating a binomial proportion. A�erward, we propose a new family of group sequential sampling schemes for estimating a binomial proportion with prescribed margin of error and con�dence level. In particular, we establish the uniform controllability of coverage probability and the asymptotic optimality for such a family of sampling schemes. Our th...