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- THOMAS E. CECIL
- 2008

Let M be an isoparametric hypersurface in the sphere S n with four distinct principal curvatures. Münzner showed that the four principal curvatures can have at most two distinct mul-tiplicities m 1 , m 2 , and Stolz showed that the pair (m 1 , m 2) must either be (2, 2), (4, 5), or be equal to the multiplicities of an isopara-metric hypersurface of… (More)

- Chris Murphy, Daniel Lindquist, Ann Marie Rynning, Thomas Cecil, Sarah Leavitt, Mark L. Chang
- 15th Annual IEEE Symposium on Field-Programmable…
- 2007

We present a low-cost stereo vision implementation suitable for use in autonomous vehicle applications and designed with agricultural applications in mind. This implementation utilizes the Census transform algorithm to calculate depth maps from a stereo pair of automotive-grade CMOS cameras. The final prototype utilizes commodity hardware, including a… (More)

In this paper we extend the two dimensional methods set forth in [4], proposing a variational approach to a path planning problem in three dimensions using a level set framework. After defining an energy integral over the path, we use gradient flow on the defined energy and evolve the entire path until a locally optimal steady state is reached. We follow… (More)

- Thomas Cecil
- 2004

In this paper we propose a numerical method for computing minimal surfaces with fixed boundaries. The level set method is used to evolve a codimension-1 surface with fixed codimension-2 boundary in R n under mean curvature flow. The level set method applied to geometrically based motion, materials science, and image processing, UCLA CAM Report, 00-20] using… (More)

In this paper we propose a variational approach to a path planning problem in 2 dimensions using a level set framework. After defining an energy integral over the path, we use gradient flow on the defined energy and evolve the entire path until a locally optimal steady state is reached. Unlike typical level set implementations where the interface being… (More)

- THOMAS E. CECIL
- 2000

If M is an isoparametric hypersurface in a sphere S n with four distrinct principal curvatures, then the principal curvatures κ 1 ,. .. , κ 4 can be ordered so that their multiplicities satisfy m 1 = m 2 and m 3 = m 4 , and the cross-ratio r of the principal curvatures (the Lie curvature) equals −1. In this paper, we prove that if M is an irreducible… (More)

- R Mirnezami, A M Mehta, +6 authors A H Mirnezami
- British journal of cancer
- 2014

BACKGROUND
Colorectal cancer peritoneal metastasis (CPM) confers an exceptionally poor prognosis, and traditional treatment involving systemic chemotherapy (SC) is largely ineffective. Cytoreductive surgery (CRS) combined with hyperthermic intraperitoneal chemotherapy (HIPEC) is increasingly advocated for selected patients with CPM; however, opinions are… (More)

- Thomas E. CECIL
- 2008

A hypersurface M n−1 in a real space-form R n , S n or H n is isoparametric if it has constant principal curvatures. For R n and H n , the classification of isoparametric hypersurfaces is complete and relatively simple, but asÉlie Cartan showed in a series of four papers in 1938–1940, the subject is much deeper and more complex for hypersurfaces in the… (More)

- THOMAS E. CECIL
- 1997

We prove that any connected proper Dupin hypersur-face in R n is analytic algebraic and is an open subset of a connected component of an irreducible algebraic set. We prove the same result for any connected non-proper Dupin hypersurface in R n that satisfies a certain finiteness condition. Hence any taut submani-fold M in R n , whose tube M ǫ satisfies this… (More)