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Low-Rank Matrix Completion By Riemannian Optimization

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Polar Codes: Characterization of Exponent, Bounds, and Constructions

Rüdiger Urbanke, Satish Babu Korada, Eren Sasoglu

Polarization codes were recently introduced by Ar\i kan. They are explicit code constructions which achieve the capacity of arbitrary symmetric binary-input discrete memoryless channels (and even extensions thereof) under a low complexity successive decodi ...

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2009

Optimal control of geodesics in Riemannian manifolds

Roland Rozsnyo

The aim of this dissertation is to solve numerically the following problem, denoted by P : given a Riemannian manifold and two points a and b belonging to that manifold, find a tangent vector T at a, such that expa(T) = b, assuming that T exists. This prob ...

EPFL2007

Recognition of generalized network matrices

Antoine Musitelli

In this thesis, we deal with binet matrices, an extension of network matrices. The main result of this thesis is the following. A rational matrix A of size n×m can be tested for being binet in time O(n6m). If A is binet, our algorithm outputs a nonsingular ...

EPFL2007

Engineered blood and lymphatic capillaries in 3-D VEGF-fibrin-collagen matrices with interstitial flow

Melody Swartz

In vitro endothelial cell organization into capillaries is a long standing challenge of tissue engineering. We recently showed the utility of low level interstitial flow in guiding the organization of endothelial cells through a 3-D fibrin matrix-containin ...

Wiley-Blackwell2007

Orthogonal Neighborhood Preserving Projections: A projection-based dimensionality reduction technique

Effrosyni Kokiopoulou

This paper considers the problem of dimensionality reduction by orthogonal projection techniques. The main feature of the proposed techniques is that they attempt to preserve both the intrinsic neighborhood geometry of the data samples and the global geome ...

2007

Matrix effects on the optical response of silver nanoclusters

Sylvain Lecoultre, Alexandre Rydlo, Fabien Conus

We report absorption spectra for Ag7, Ag9, and Ag11 in an argon matrix grown at a temperature of 28 K and compare them with previous spectra of the same species measured in matrices of argon grown at lower temperatures as well as in neon matrices. We discu ...

2006

Structured Eigenvalue Problems

Daniel Kressner

Most eigenvalue problems arising in practice are known to be structured. Structure is often introduced by discretization and linearization techniques but may also be a consequence of properties induced by the original problem. Preserving this structure can ...

2006

Structured condition numbers for invariant subspaces

Daniel Kressner

Invariant subspaces of structured matrices are sometimes better conditioned with respect to structured perturbations than with respect to general perturbations. Sometimes they are not. This paper proposes an appropriate condition number c(S), for invariant ...

Society for Industrial and Applied Mathematics2006

On Matrix Rigidity and the Complexity of Linear Forms

Mahdi Cheraghchi Bashi Astaneh

The rigidity function of a matrix is defined as the minimum number of its entries that need to be changed in order to reduce the rank of the matrix to below a given parameter. Proving a strong enough lower bound on the rigidity of a matrix implies a nontri ...

2005

Optimal control of geodesics in Riemannian manifolds

Klaus-Dieter Semmler, Roland Rozsnyo

Summary: We present a method based on an optimal control technique for numerical computations of geodesic paths between two fixed points of a Riemannian manifold under the assumption of existence. In this method, the control variable is the tangent vector ...

2004