Convex Geometry Research Papers - Academia.edu (original) (raw)

69 Followers

Most cited papers in Convex Geometry

Top Papers
Most Cited Papers
Most Downloaded Papers
Newest Papers
People
- by W. Schellart and +1
- •
- Convex Geometry, Time Use, Multidisciplinary, Nature

In his work on log-concavity of multiplicities, Okounkov showed in passing that one could associate a convex body to a linear series on a projective variety, and then use convex geometry to study such linear systems. Although Okounkov was essentially working in the classical setting of ample line bundles, it turns out that the construction goes through for an arbitrary big divisor. Moreover, this viewpoint renders transparent many basic facts about asymptotic invariants of linear series, and opens the door to a number of extensions. The purpose of this paper is to initiate a systematic development of the theory, and to give a number of applications and examples.

- by Robert Lazarsfeld
- •
- Algebraic Geometry, Convex Geometry, Linear System
- by Paul Edelman
- •
- Convex Geometry, Pure Mathematics
- by Jonathan Huntington
- •
- Convex Geometry, Geophysics, Algorithms, Statistics

The piece-wise convex multiple model endmember detection algorithm (P-COMMEND) and the Piece-wise Convex End-member detection (PCE) algorithm autonomously estimate many sets of endmembers to represent a hyperspectral image. A piece-wise convex model with several sets of endmembers is more effective for representing non-convex hyperspectral imagery over the standard convex geometry model (or linear mixing model). The terms of the objective function in P-COMMEND are based on geometric properties of the input data and the endmember estimates. In this paper, the P-COMMEND algorithm is extended to autonomously determine the number of sets of endmembers needed. The number of sets of endmembers, or convex regions, is determined by incorporating the competitive agglomeration algorithm into P-COMMEND. Results are shown comparing the Competitive Agglomeration P-COMMEND (CAP) algorithm to results found using the statistical PCE endmember detection method.

- by Alina Zare
- •
- Information Systems, Engineering, Environmental Engineering, Civil Engineering

Convexity in Graphs and Hypergraphs. [SIAM Journal on Algebraic and Discrete Methods 7, 433 (1986)]. Martin Farber, Robert E. Jamison. Abstract. We study several notions of abstract convexity in graphs and hypergraphs. In ...

- by Robert Jamison
- •
- Convex Geometry
- by Kiumars Kaveh
- •
- Algebraic Geometry, Convex Geometry, Large classes, Boolean Satisfiability
- by Magnus M. Halldorsson
- •
- Stochastic Process, Convex Geometry, Graph Theory, Computer Aided Design
- by SÉbastien Boucksom
- •
- Algebraic Geometry, Convex Geometry, Pure Mathematics
- by Alina Zare
- •
- Convex Geometry, Geophysics, Algorithms, Geometry
- by Paul Edelman
- •
- Applied Mathematics, Convex Geometry, Boolean Algebra, Shapley value
- by Peter Butkovic
- •
- Engineering, Convex Geometry, Mathematical Sciences, Nonnegative Matrix Factorization
- by Mokshay Madiman
- •
- Convex Geometry, Entropy, Convex Programming, Euclidean space
- by Sergio Sanchez Sanchez
- •
- Convex Geometry, Parallel Algorithms, Parallel Computing, Image Processing
- by Ari Honda
- •
- Engineering, Convex Geometry, Entropy, Discrete Mathematics
- by Kiumars Kaveh
- •
- Algebraic Geometry, Convex Geometry, Vector Space
- by Baoxin Hu
- •
- Convex Geometry, Geomatic Engineering, Leaf Area Index, Jack Pine
- by Mokshay Madiman
- •
- Convex Geometry, Functional Analysis, Information Theory, Pure Mathematics
- by Jacques-olivier Lachaud
- •
- Applied Mathematics, Convex Geometry, Discrete Geometry, Image segmentation
- by Tigran Melkonyan
- •
- Convex Geometry, Statistics, Approximate Reasoning, Numerical Analysis and Computational Mathematics
- by Paul Edelman
- •
- Convex Geometry, Pure Mathematics, Representation Theory, Order
- by alberto marquez
- •
- Convex Geometry, Pure Mathematics, Convex Hull
- by Juan José Jiménez
- •
- Convex Geometry, Collision detection, Barycentric coordinates, Real Time
- by Karl-hermann Neeb
- •
- Lie Algebra, Convex Geometry, Pure Mathematics, Lie Theory
- by Pasquale Lione
- •
- Convex Geometry, Functional Analysis, Pure Mathematics, Mathematical Analysis
- by Sergei Sergeev
- •
- Convex Geometry, Pure Mathematics, Mathematical Sciences, Convex Analysis
- by Sergei Sergeev
- •
- Convex Geometry, Linear Equations, Contemporary Mathematics, Optimal Path
- by Antonio Jimenez
- •
- Convex Geometry, Economics, European Union, Mathematical Models for Social Sciences
- by Christophe Labreuche
- •
- Convex Geometry, Game Theory, Multidisciplinary, Shapley value
- by Kun-Jhih Lin
- •
- Engineering, Convex Geometry, Finite Element Analysis, Lumbar spine
- by Elitza Maneva
- •
- Convex Geometry, Discrete Mathematics
- by Kiumars Kaveh
- •
- Algebraic Geometry, Convex Geometry
- by nathalie caspard
- •
- Convex Geometry, Pure Mathematics, Algorithm
- by Michel L Lapidus
- •
- Convex Geometry, Riemann zeta function, Rough Set, Fuzzy Metric Space

This is an overview of merging the techniques of vector lattice theory and convex geometry.

- by Semen Kutateladze
- •
- Applied Mathematics, Convex Geometry, Functional Analysis
- by nathalie caspard
- •
- Convex Geometry, Mathematical Sciences
- by Miguel Navarro-Cía
- •
- Convex Geometry, Condensed Matter Physics, Quantum Physics, Metamaterial
- by Kira Adaricheva
- •
- Convex Geometry, Pure Mathematics, Dimensional, Boolean Satisfiability
- by Vadim Levit and +1
- •
- Applied Mathematics, Convex Geometry, Computer Science, Social Sciences
- by Károly Bezdek
- •
- Mathematics, Convex Geometry, Pure Mathematics, Primary
- by Gleb Koshevoy
- •
- Convex Geometry, Pure Mathematics, Order, Boolean Satisfiability

We introduce and study a new class of eps\epseps-convex bodies (extending the class of convex bodies) in metric and normed linear spaces. We analyze relations between characteristic properties of convex bodies, demonstrate how eps\epseps-convex bodies connect with some classical results of Convex Geometry, as Helly theorem, and find applications to geometric tomography. We introduce the notion of a circular projection

- by Vladimir Golubyatnikov
- •
- Convex Geometry, Differential Geometry, Euclidean space

An endmember detection and spectral unmixing algorithm that uses both spatial and spectral information is presented. This method, Spatial Piece-wise Convex Multiple Model Endmember Detection (Spatial P-COMMEND), autonomously estimates multiple sets of endmembers and performs spectral unmixing for input hyperspectral data. Spatial P-COMMEND does not restrict the estimated endmembers to define a single convex region during spectral unmixing. Instead, a piece-wise convex representation is used that can effectively represent non-convex hyperspectral data. Spatial P-COMMEND drives neighboring pixels to be unmixed by the same set of endmembers encouraging spatially-smooth unmixing results.

- by Alina Zare
- •
- Convex Geometry, Computational Geometry, Spatial, Spatial Information

In this paper we extend our geometric approach to the theory of evidence
in order to include other important classes of nite fuzzy measures.
In particular we describe the geometric counterparts of possibility measures or fuzzy sets, represented as consonant belief functions.
The correspondence between chains of subsets and convex sets of consonant functions is studied and its properties analyzed, eventually yielding an elegant representation of the region of consonant belief functions
in terms of the notion of simplicial complex.

- by Maitland Wright
- •
- Mathematical Physics, Convex Geometry, Quantum Physics, Pure Mathematics
- by Victor Reiner
- •
- Convex Geometry, Pure Mathematics, Characteristic Polynomial
- by Yoshio Sano
- •
- Applied Mathematics, Convex Geometry, Pure Mathematics, Discrete Mathematics
- by Ansgar Grüne
- •
- Convex Geometry, Computational Geometry, Differential Geometry
- by Sergei Sergeev
- •
- Convex Geometry, Pure Mathematics, Convex Hull

Convex Geometry Research Papers - Academia.edu (original) (raw)

Log In