Two main technologies are available to design and represent freeform surfaces: NonUniform Rational B-Splines (NURBS) and subdivision surfaces. Both representations are built on uniform B-splines, but they extend this foundation in incompatible ways, and different industries have therefore established a preference for one representation over the other. NURBS are the dominant standard for Compute...

Mesh quadrangulation has received increasing attention in the past decade. While previous works have mostly focused on producing a high quality quad mesh of a single model, the connectivity of the quadrangulation is typically difficult to control and varies among models even with similar shapes. In this paper, we propose a novel interactive framework for quadrangulating a set of models collecti...

Clozel, Harris and Taylor have recently proved a modularity lifting theorem of the following general form: if ρ is an l-adic representation of the absolute Galois group of a number field for which the residual representation ρ comes from a modular form then so does ρ. This theorem has numerous hypotheses; a crucial one is that the image of ρ must be “big,” a technical condition on subgroups of ...

For a given point set S (in general position), two pointed pseudo-triangulations are compatible if their union is plane. We show that for any set S there exist two maximally disjoint compatible pointed pseudotriangulations, that is, their union is a triangulation of S. In contrast, we show that there are point sets S and pointed pseudo-triangulations T such that there exists no pointed pseudo-t...

We present a new class of irregular low-density parity-check (LDPC) codes for moderate block lengths (up to a few thousand bits) that are well-suited for rate-compatible puncturing. The proposed codes show good performance under puncturing over a wide range of rates and are suitable for usage in incremental redundancy hybrid-automatic repeat request (ARQ) systems. In addition, these codes are l...

In a quasi-linear environment we characterize the boundaries of the set of transfers which implement a given allocation rule (extremal transfers). Doing so allows us to generalize and unify several existing results of the mechanism design literature. More specifically, our approach delivers a characterization result for the set of implementable allocation rules. Second, we obtain an exact chara...

Formulations of quantum mechanics (QM) can be characterized as realistic, operationalist, or a combination of the two. In this paper a realistic theory is defined as describing a closed system entirely by means of entities and concepts pertaining to the system. An operationalist theory, on the other hand, requires in addition entities external to the system. A realistic formulation comprises an...

E. L. Foster, M. Jekic, J. A. Bender, J. W. Arnold, S. V. Raman, and O. P. Simonetti Dorothy M. Davis Heart and Lung Research Institute, The Ohio State University, Columbus, OH, United States, Biomedical Engineering, The Ohio State University, Agricultural Technical Institute, The Ohio State University, Internal Medicine, The Ohio State University, Internal Medicine and Radiology, The Ohio Stat...

This paper studies power indices based on average representations of a weighted game. If restricted to account for the lack of power of dummy voters, average representations become coherent measures of voting power, with power distributions being proportional to the distribution of weights in the average representation. This makes these indices representationcompatible, a property not fulfilled...