Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Frustration and Conflict: Avoidance-Avoidance, Double-Approach Avoidance01:14

Frustration and Conflict: Avoidance-Avoidance, Double-Approach Avoidance

188
Avoidance-avoidance conflict refers to a psychological situation where a person must choose between two or more unpleasant alternatives. These conflicts are particularly stressful because neither option is desirable. This dilemma is often expressed in sayings like "caught between a rock and a hard place" or "between the devil and the deep blue sea." For instance, individuals who fear dental procedures may find themselves torn between enduring a painful toothache or facing the...
188
Alternative Sets of Equilibrium Equations01:31

Alternative Sets of Equilibrium Equations

490
When analyzing the behavior of structures, engineers often rely on the concept of equilibrium. This refers to the state where all forces and moments acting on a system balance each other, resulting in no net movement or rotation. In many cases, equilibrium can be described by a set of standard equations. However, in some situations, alternative sets of equilibrium equations must be used to describe the system's behavior accurately.
One example of such a situation can be observed in a...
490
Reduced Mass Coordinates: Isolated Two-body Problem01:12

Reduced Mass Coordinates: Isolated Two-body Problem

1.6K
In classical mechanics, the two-body problem is one of the fundamental problems describing the motion of two interacting bodies under gravity or any other central force. When considering the motion of two bodies, one of the most important concepts is the reduced mass coordinates, a quantity that allows the two-body problem to be solved like a single-body problem. In these circumstances, it is assumed that a single body with reduced mass revolves around another body fixed in a position with an...
1.6K
Factors Influencing Attraction I: Proximity01:22

Factors Influencing Attraction I: Proximity

17
Proximity plays a fundamental role in shaping interpersonal attraction by increasing opportunities for interaction and fostering familiarity. Research consistently demonstrates that individuals are more likely to form social bonds with those who are physically closer to them, whether in residential settings, workplaces, or educational institutions. This effect is largely driven by the increased frequency of encounters, which facilitates the development of friendships and romantic...
17
Routh-Hurwitz Criterion I01:15

Routh-Hurwitz Criterion I

353
Consider an electrical power grid, where stability is essential to prevent blackouts. The Routh-Hurwitz criterion is a valuable tool for assessing system stability under varying load conditions or faults. By analyzing the closed-loop transfer function, the Routh-Hurwitz criterion helps determine whether the system remains stable.
To apply the Routh-Hurwitz criterion, a Routh table is constructed. The table's rows are labeled with powers of the complex frequency variable s, starting from the...
353
Routh-Hurwitz Criterion II01:19

Routh-Hurwitz Criterion II

452
In the application of the Routh-Hurwitz criterion, two specific scenarios can arise that complicate stability analysis.
The first scenario occurs when a singular zero appears in the first column of the Routh table. This situation creates a division by zero issues. To resolve this, a small positive or negative number, denoted as epsilon (∈), is substituted for the zero. The stability analysis proceeds by assuming a sign for ∈. If ∈ is positive, any sign change in the first...
452

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

A milestone for the solution to the lattice sphere covering problem in dimension n = 6.

Acta crystallographica. Section A, Foundations and advances·2024
Same journal

A better-than-1.6-approximation for prize-collecting TSP.

Mathematical programming·2026
Same journal

A <math><mrow><mfrac><mn>4</mn> <mn>3</mn></mfrac></mrow></math> -approximation for the maximum leaf spanning arborescence problem in DAGs.

Mathematical programming·2026
Same journal

An FPTAS for Connectivity Interdiction.

Mathematical programming·2026
Same journal

A first order method for linear programming parameterized by circuit imbalance.

Mathematical programming·2026
Same journal

Tight lower bounds for block-structured integer programs.

Mathematical programming·2026
Same journal

Accelerated first-order optimization under nonlinear constraints.

Mathematical programming·2026
See all related articles

Related Experiment Video

Updated: Oct 1, 2025

Straightforward Assay for Quantification of Social Avoidance in Drosophila melanogaster
08:08

Straightforward Assay for Quantification of Social Avoidance in Drosophila melanogaster

Published on: December 13, 2014

11.4K

Complete positivity and distance-avoiding sets.

Evan DeCorte1, Fernando Mário de Oliveira Filho2, Frank Vallentin3

  • 1Mathematics and Statistics, McGill University, 805 Sherbrooke W., Montreal, QC H3A 0B9 Canada.

Mathematical Programming
|March 7, 2022
PubMed
Summary
This summary is machine-generated.

We introduce a new mathematical concept, the cone of completely positive functions, to precisely define maximum-density distance-avoiding sets. This allows for improved proofs and results regarding these sets in various spaces.

Keywords:
Chromatic number of Euclidean spaceCopositive programmingHadwiger-Nelson problemHarmonic analysisSemidefinite programming

More Related Videos

Investigating Pain-Related Avoidance Behavior using a Robotic Arm-Reaching Paradigm
09:00

Investigating Pain-Related Avoidance Behavior using a Robotic Arm-Reaching Paradigm

Published on: October 3, 2020

4.1K
Setting Limits on Supersymmetry Using Simplified Models
07:46

Setting Limits on Supersymmetry Using Simplified Models

Published on: November 15, 2013

8.7K

Related Experiment Videos

Last Updated: Oct 1, 2025

Straightforward Assay for Quantification of Social Avoidance in Drosophila melanogaster
08:08

Straightforward Assay for Quantification of Social Avoidance in Drosophila melanogaster

Published on: December 13, 2014

11.4K
Investigating Pain-Related Avoidance Behavior using a Robotic Arm-Reaching Paradigm
09:00

Investigating Pain-Related Avoidance Behavior using a Robotic Arm-Reaching Paradigm

Published on: October 3, 2020

4.1K
Setting Limits on Supersymmetry Using Simplified Models
07:46

Setting Limits on Supersymmetry Using Simplified Models

Published on: November 15, 2013

8.7K

Area of Science:

  • Mathematics
  • Optimization Theory
  • Geometric Analysis

Background:

  • Distance-avoiding sets are fundamental in various mathematical fields.
  • Existing methods for characterizing these sets have limitations.
  • Convex optimization problems offer a powerful framework for analysis.

Purpose of the Study:

  • To introduce the cone of completely positive functions.
  • To fully characterize maximum-density distance-avoiding sets using convex optimization.
  • To provide a unified approach for reproving and improving existing results.

Main Methods:

  • Definition and analysis of the cone of completely positive functions.
  • Formulation of a convex optimization problem for distance-avoiding sets.
  • Application of optimization theory to derive properties of these sets.

Main Results:

  • The cone of completely positive functions is introduced as a subset of positive-type functions.
  • Maximum-density distance-avoiding sets are characterized as optimal solutions to a convex optimization problem.
  • New proofs and improved results for distance-avoiding sets on spheres and in Euclidean space are established.

Conclusions:

  • The cone of completely positive functions provides a novel and effective tool for studying distance-avoiding sets.
  • Convex optimization offers a powerful framework for understanding the properties and optimality of these sets.
  • This work unifies and advances the study of distance-avoiding sets across different mathematical domains.