## convex hull

Overview page. Subjects: Computing — Probability and Statistics.

The convex hull of a set of points in ℝ*
^{n}
* is the smallest convex polyhedron (polygon when

*n*=2) that contains all the points.

**Convex hull**....

## convex hull

in** A Dictionary of Statistics**

January 2008; p ublished online January 2008 .

Reference Entry. Subjects: Probability and Statistics. 48 words.

The convex hull of a set of points in ℝ*
^{n}
* is the smallest *convex polyhedron (polygon when

*n*

## convex hull

in** A Dictionary of Statistics**

January 2014; p ublished online September 2014 .

Reference Entry. Subjects: Probability and Statistics. 50 words.

The convex hull of a set of points in ℝ*
^{n}
* is the smallest *convex polyhedron (polygon when

*n...*

## convex hull

Overview page. Subjects: Computing — Probability and Statistics.

The convex hull of a set of points in ℝ*
^{n}
* is the smallest convex polyhedron (polygon when

*n*=2) that contains all the points.

**Convex hull**....

## convex hull

in** A Dictionary of Computer Science**

January 2016; p ublished online January 2016 .

Reference Entry. Subjects: Computing. 40 words.

The smallest convex set that contains a given set. A set is convex if for any two points in the set, the points on the straight line segment joining the two points are also contained in the...

## convex hull

in** A Dictionary of Computing**

January 2008; p ublished online January 2008 .

Reference Entry. Subjects: Computing. 40 words.

The smallest convex set that contains a given set. A set is convex if for any two points in the

## Convex hull of two quadratic constraints is an LMI set

in** IMA Journal of Mathematical Control and Information**

December 2009; p ublished online October 2009 .

Journal Article. Subjects: Mathematics. 0 words.

In this work, we are interested in the convex hull of the region determined by two quadratic polynomial constraints. The main result is that if this region is not empty, the convex hull is...

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** » ** abstract

## Area and Perimeter of the Convex Hull of Stochastic Points

in** The Computer Journal**

August 2016; p ublished online August 2016 .

Journal Article. Subjects: Computer Science. 7199 words.

Given a set [math] of [math] points in the plane, we study the computation of the probability distribution function of both the area and perimeter of the convex hull of a random subset ...

## Prediction of recursive convex hull class assignments for protein residues

in** Bioinformatics**

April 2008; p ublished online February 2008 .

Journal Article. Subjects: Bioinformatics and Computational Biology. 7142 words.

**Motivation:** We introduce a new method for designating the location of residues in folded protein structures based on the recursive convex hull (RCH) of a point set of atomic...

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** » ** abstract

## Applicability of convex hull in multiple detector response space for neutron dose measurements

in** Radiation Protection Dosimetry**

August 2009; p ublished online July 2009 .

Journal Article. Subjects: Nuclear Chemistry, Photochemistry, and Radiation. 5212 words.

A novel neutron dose measurement method that flexibly responds to variations in the neutron field is being developed by Japan Atomic Energy Agency. This is an implementation of the...

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** » ** abstract

## Using convex hulls to extract interaction interfaces from known structures

in** Bioinformatics**

July 2004; p ublished online July 2004 .

Journal Article. Subjects: Bioinformatics and Computational Biology. 0 words.

**Motivation:** Protein interactions provide an important context for the understanding of function. Experimental approaches have been complemented with computational ones, such as...

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** » ** abstract

## Constrained stabilization: an enlargement technique of positively invariant sets

in** IMA Journal of Mathematical Control and Information**

March 2005; p ublished online March 2005 .

Journal Article. Subjects: Mathematics. 0 words.

This paper presents a new technique of enlargement of positively invariant sets for linear systems with input saturation. This technique is based on the use of the convex hull of the union...

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** » ** abstract

## Root Polytopes and Borel Subalgebras

in** International Mathematics Research Notices**

January 2015; p ublished online May 2014 .

Journal Article. Subjects: Mathematics. 10015 words.

Let *Φ* be a finite crystallographic irreducible root system and [math] be the convex hull of the roots in *Φ*. We give a uniform explicit description of the polytope [math], analyze the...

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** » ** abstract

## Random Polytopes

in** New Perspectives in Stochastic Geometry**

November 2009; p ublished online February 2010 .

Chapter. Subjects: Geometry. 17181 words.

This chapter deals with random polytopes which are the convex hulls of random points. Recent developments concern mainly distributional aspects of functionals of random polytopes: estimates...

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** » ** abstract

##
*Ε*-Fr ´Echet Differentiability

in** Fréchet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces (AM-179)**

February 2012; p ublished online October 2017 .

Chapter. Subjects: Mathematics. 9636 words.

This chapter treats results on ε-Fréchet differentiability of Lipschitz functions in asymptotically smooth spaces. These results are highly exceptional in the sense that they prove almost...

## Unique Sets Oriented Parallelization of Loops with Non-uniform Dependences

in** The Computer Journal**

January 1997; p ublished online January 1997 .

Journal Article. Subjects: Computer Science. 0 words.

Although many methods exist for nested loop partitioning, most of them perform poorly when parallelizing loops with non-uniform dependences. This paper addresses the issue of automatic...

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** » ** abstract

## Minimax Theorem

in** Noncooperative Game Theory**

June 2017; p ublished online May 2018 .

Chapter. Subjects: Logic. 3148 words.

This chapter deals with the Minimax Theorem and its proof, which is based on elementary results from convex analysis. The theorem states that for every matrix *A*, the average security levels...

## A method to search for large-scale concavities in asteroid shape models

in** Monthly Notices of the Royal Astronomical Society**

P ublished online August 2015 .

Journal Article. Subjects: Astronomy and Astrophysics. 6630 words.

Photometric light-curve inversion of minor planets has proven to produce a unique model solution only under the hypothesis that the asteroid is convex. However, it was suggested that the...

## On spectral properties for graph matching and graph isomorphism problems

in** Information and Inference: A Journal of the IMA**

March 2015; p ublished online February 2015 .

Journal Article. Subjects: Science and Mathematics; Mathematics; Applied Mathematics; Computer Science. 5866 words.

Problems related to graph matching and isomorphisms are very important both from a theoretical and practical perspective, with applications ranging from image and video analysis to...

## Stern–Brocot Tree

in** From Christoffel Words to Markoff Numbers**

November 2018; p ublished online January 2019 .

Chapter. Subjects: Pure Mathematics. 7057 words.

Christoffel words have a strong connection with continued fractions of rational numbers, as was recognized by Christoffel. They are in some sense equivalent to them, being a way to encode...

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** » ** abstract

## Containment control of fractional-order nonlinear multi-agent systems under fixed topologies

in** IMA Journal of Mathematical Control and Information**

P ublished online March 2017 .

Journal Article. Subjects: Mathematics. 6877 words.

**Abstract**

This article investigates the containment control problem of fractional-order nonlinear multi-agent systems under fixed topologies. The containment...