Nonuniform tubular neighborhoods of curves in Rn are studied by using weighted distance functions and generalizing the normal exponential map. Different notions of injectivity radii are introduced to investigate singular but injective exponential maps. A generalization of the thickness formula is obtained for nonuniform thickness. All singularities within almost injectivity radius are classifie...

We consider multiscale functions of the type that are studied in averaging and homogenization theory and in multiscale modeling. Typical examples are two-scale functions f(x, x/ ), (0 < << 1) that are periodic in the second variable. We prove that under certain band limiting conditions these multiscale functions can be uniquely and stably recovered from non-uniform samples of optimal rate. The ...

We say that an arbitrary manifold (M,∂M) is topologically rigid relative to its ends if it satisfies the following condition. If (N, ∂N) is any other manifold with a compact subset C ⊂ N for which a proper homotopy equivalence h : (N, ∂N)→ (M,∂M) is a homeomorphism on ∂N ∪ (N\C), then there is a compact subset K ⊂ N and a proper homotopy ht : (N, ∂N) → (M,∂M) from h to a homeomorphism such that...

The purpose of this paper is to develop methods that can reconstruct a bandlimited discrete-time signal from an irregular set of samples at unknown locations. We define a solution to the problem using first a geometric and then an algebraic point of view. We find the locations of the irregular set of samples by treating the problem as a combinatorial optimization problem. We employ an exhaustiv...

Nonuniform traffic patterns can severely degrade the performance of wormhole-routing multistage interconnection networks in multiprocessor systems. A wormhole-routing switch box architecture is proposed that is able to control the degrading effects of saturation trees on the uniform background traffic under nonuniform traffic patterns that are known a priori. An alternating priority mechanism i...

A growable ATM switch architecture is desired for constructing a large scale ATM switch. All the current ATM switch architectures are based on uniform connections of unit switch elements. When the switch size becomes large, the uniform switch architecture is no longer suitable for the nonuniform trafic condition. In this paper, we propose a nonuniform modular growth ATM switch architecture by u...

Biomechanical models generally assume that muscle fascicles shorten uniformly. However, dynamic magnetic resonance (MR) images of the biceps brachii have recently shown nonuniform shortening along some muscle fascicles during low-load elbow flexion (J. Appl. Physiol. 92 (2002) 2381). The purpose of this study was to uncover the features of the biceps brachii architecture and material properties...

This paper provides theoretical guarantees for the recovery of signals from undersampled measurements based on `1-analysis regularization. We provide both nonuniform and stable uniform recovery guarantees for Gaussian random measurement matrices when the rows of the analysis operator form a frame. The nonuniform result relies on a recovery condition via tangent cones and the case of uniform rec...

We investigate the structure and phase behavior of the Stockmayer fluid in the presence of nonuniform electric fields using molecular simulation. We find that an initially homogeneous vapor phase undergoes a local phase separation in a nonuniform field due to the combined effect of the field gradient and the fluid vapor-liquid equilibrium. This results in a high-density fluid condensing in the ...

Let X be a right-angled hyperbolic building. We show that the lattices in Aut(X) share many properties with tree lattices. For example, we characterise the set of covolumes of uniform and of nonuniform lattices in Aut(X), and show that the group Aut(X) admits an infinite ascending tower of uniform and of nonuniform lattices. These results are proved by constructing a functor from graphs of grou...