Shapes From Echoes: Uniqueness From Point-to-Plane Distance Matrices

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We show that for m points and n lines in R-2, the number of distinct distances between the points and the lines is Omega(m(1/5)n(3/5)), as long as m(1/2)

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n\ge 3

, we define

e(n)

to be the minimum positive integer such that an ...

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Let S be a set of n points in R-2 contained in an algebraic curve C of degree d. We prove that the number of distinct distances determined by S is at least c(d)n(4/3), unless C contains a line or a circle. We also prove the lower bound c(d)' min{m(2/3)n(2/ ...

Any symmetric matrix can be reduced to antitriangular form in finitely many steps by orthogonal similarity transformations. This form reveals the inertia of the matrix and has found applications in, e.g., model predictive control and constraint preconditio ...

The most basic form of the max-sum dispersion problem (MSD) is as follows: given n points in R^q and an integer k, select a set of k points such that the sum of the pairwise distances within the set is maximal. This is a prominent diversity problem, with w ...

Direct methods that transform the geometry of a structure and conserve its static equilibrium are of particular interest for designers. They allow the exploration of alternative solutions at minimum computational cost. While parallel transformations (stret ...

Let B-M : C x C -> C be a bilinear form B-M(p, q) - p(T)Mq, with an invertible matrix M is an element of C-2x2. We prove that any finite set S contained in an irreducible algebraic curve C of degree d in C determines Omega(d)(vertical bar S vertical bar(4/ ...

Symmetries are omnipresent and play a fundamental role in the description of Nature. Thanks to them, we have at our disposal nontrivial selection rules that dictate how a theory should be constructed. This thesis, which is naturally divided into two parts, ...

The characterization of images by geometric features facilitates the precise analysis of the structures found in biological micrographs such as cells, proteins, or tissues. In this thesis, we study image representations that are adapted to local geometric ...

Shapes From Echoes: Uniqueness From Point-to-Plane Distance Matrices

Chattez avec Graph Search

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