The problem of biclustering consists of the simultaneous clustering of rows and columns of a matrix such that each of the submatrices induced by a pair of row and column clusters is as uniform as possible. In this paper we approximate the optimal biclustering by applying one-way clustering algorithms independently on the rows and on the columns of the input matrix. We show that such a solution ...

Let Ω be a convex domain with smooth boundary in Rd. It has been shown recently that the semigroup generated by the discrete Laplacian for quasi-uniform families of piecewise linear finite element spaces on Ω is analytic with respect to the maximum-norm, uniformly in the mesh-width. This implies a resolvent estimate of standard form in the maximum-norm outside some sector in the right halfplane...

In this paper, we study a free boundary problem for compressible spherically symmetric Navier-Stokes equations without a solid core. Under certain assumptions imposed on the initial data, we obtain the global existence and uniqueness of the weak solution, give some uniform bounds (with respect to time) of the solution and show that it converges to a stationary one as time tends to infinity. Mor...

In this paper, we present a new optimal interpolation error estimate in Lp norm (1 ≤ p ≤ ∞) for finite element simplicial meshes in any spatial dimension. A sufficient condition for a mesh to be nearly optimal is that it is quasi-uniform under a new metric defined by a modified Hessian matrix of the function to be interpolated. We also give new functionals for the global moving mesh method and ...

For a nonlinear optimal control problem with state constraints, we give conditions under which the optimal control depends Lipschitz continuously in the L2 norm on a parameter. These conditions involve smoothness of the problem data, uniform independence of active constraint gradients, and a coercivity condition for the integral functional. Under these same conditions, we obtain a new nonoptima...

In this paper, we present a new optimal interpolation error estimate in Lp norm (1 ≤ p ≤ ∞) for finite element simplicial meshes in any spatial dimension. A sufficient condition for a mesh to be nearly optimal is that it is quasi-uniform under a new metric defined by a modified Hessian matrix of the function to be interpolated. We also give new functionals for the global moving mesh method and ...

This paper presents a simple and efficient tracking algorithm based on representing the appearance of objects using learned linear subspaces. The tracker updates this subspace and maintains an updated appearance model of the object making the tracking problem simpler. Using the L2 reconstruction norm in this framework we provide a simple algorithm for finding a subspace whose uniform Lreconstru...

Existing control theory for linear parameter-varying systems uses a uniform-in-the-parameters upper bound (a constant scalar) on the induced-L 2 norm. In this paper, this constant is generalized to a function of the parameters; the performance criterion generalizes to an integral quadratic constraint and implies a norm bound that depends naturally on the real-time parameter trajectory. As in ex...

We consider the generalized Cesàro sequence spaces defined by Suantai (2003) and consider it equipped with the Amemiya norm. The main purpose of this paper is to show that ces (p) equipped with the Amemiya norm is rotund and has uniform Kadec-Klee property. 1. Introduction. In the whole paper, N and R stand for the sets of natural numbers and real numbers, respectively. Let (X, · ·) be a real n...

We provide rigorous guarantees on learning with the weighted trace-norm under arbitrarysampling distributions. We show that the standard weighted trace-norm might fail when thesampling distribution is not a product distribution (i.e. when row and column indexes arenot selected independently), present a corrected variant for which we establish strong learningguarantees, and demon...