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

Group Polarization01:01

Group Polarization

35.6K
Group polarization is the strengthening of an original group attitude following the discussion of views within a group (Teger & Pruitt, 1967). That is, if a group initially favors a viewpoint, after discussion the group consensus is likely a stronger endorsement of the viewpoint. Conversely, if the group was initially opposed to a viewpoint, group discussion would likely lead to stronger opposition.
35.6K
Potential Due to a Polarized Object01:29

Potential Due to a Polarized Object

472
A neutral atom consists of a positively charged nucleus surrounded by a negatively charged electron cloud. When placed in an external electric field, the external electric force pulls the electrons and nucleus apart, opposite to the intrinsic attraction between the nucleus and the electrons. The opposing forces balance each other with a slight shift between the center of masses of the nucleus and the electron cloud, resulting in a polarized atom. On the other hand, a few molecules, like water,...
472
Curvilinear Motion: Polar Coordinates01:27

Curvilinear Motion: Polar Coordinates

483
In polar coordinates, the motion of a particle follows a curvilinear path. The radial coordinate symbolized as 'r,' extends outward from a fixed origin to the particle, while the angular coordinate, 'θ,' measured in radians, represents the counterclockwise angle between a fixed reference line and the radial line connecting the origin to the particle.
The particle's location is described using a unit vector along the radial direction. Deriving the particle's position...
483
Polar and Cylindrical Coordinates01:22

Polar and Cylindrical Coordinates

15.7K
The Cartesian coordinate system is a very convenient tool to use when describing the displacements and velocities of objects and the forces acting on them. However, it becomes cumbersome when we need to describe the rotation of objects. So, when describing rotation, the polar coordinate system is generally used.
15.7K
Spherical Coordinates01:23

Spherical Coordinates

11.0K
Spherical coordinate systems are preferred over Cartesian, polar, or cylindrical coordinates for systems with spherical symmetry. For example, to describe the surface of a sphere, Cartesian coordinates require all three coordinates. On the other hand, the spherical coordinate system requires only one parameter: the sphere's radius. As a result, the complicated mathematical calculations become simple. Spherical coordinates are used in science and engineering applications like electric and...
11.0K
Frost Circles for Different Conjugated Systems01:18

Frost Circles for Different Conjugated Systems

2.9K
The inscribed polygon method is consistent with Hückel’s 4n + 2 rule and helps to learn whether the given cyclic compound is aromatic or not. The compound is stable and aromatic if every bonding molecular orbital (MO) is completely filled with a pair of electrons. However, if the non-bonding or antibonding orbitals are filled with electrons, the compound is unstable and not aromatic. Consider the Frost circle diagrams for cycloalkenes containing 4 to 8 carbons.
2.9K

You might also read

Related Articles

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

Sort by
Same author

Decision-making tools for healthcare structures in times of pandemic.

Anaesthesia, critical care & pain medicine·2022
Same author

A Universal Approximation Result for Difference of Log-Sum-Exp Neural Networks.

IEEE transactions on neural networks and learning systems·2020
Same author

Log-Sum-Exp Neural Networks and Posynomial Models for Convex and Log-Log-Convex Data.

IEEE transactions on neural networks and learning systems·2019
Same author

Exploration of the role of the virulence factor ElrA during Enterococcus faecalis cell infection.

Scientific reports·2018
Same author

Overexpression of Enterococcus faecalis elr operon protects from phagocytosis.

BMC microbiology·2015
Same author

Discrete limit and monotonicity properties of the Floquet eigenvalue in an age structured cell division cycle model.

Journal of mathematical biology·2015

Related Experiment Video

Updated: Sep 15, 2025

Author Spotlight: Non-Invasive Imaging of Complex Bio-Structures Using Polarization-Sensitive Two-Photon Microscopy
05:54

Author Spotlight: Non-Invasive Imaging of Complex Bio-Structures Using Polarization-Sensitive Two-Photon Microscopy

Published on: September 8, 2023

1.3K

Signed Tropicalization of Polar Cones.

Marianne Akian1, Xavier Allamigeon1, Stéphane Gaubert1

  • 1Inria and CMAP, École polytechnique, IP Paris, CNRS, Paris, France.

Journal of Optimization Theory and Applications
|July 14, 2025
PubMed
Summary

This study introduces tropical polars and their properties over signed tropical numbers. These tropical polars simplify complex matrix cone hierarchies, offering new optimization insights.

Keywords:
Completely positiveCopositivePolar coneSigned tropicalizationSymmetrized tropical semiring

More Related Videos

Observation of Photobehavior in Chlamydomonas reinhardtii
03:54

Observation of Photobehavior in Chlamydomonas reinhardtii

Published on: May 6, 2022

4.0K
Multimodal Optical Microscopy Methods Reveal Polyp Tissue Morphology and Structure in Caribbean Reef Building Corals
10:39

Multimodal Optical Microscopy Methods Reveal Polyp Tissue Morphology and Structure in Caribbean Reef Building Corals

Published on: September 5, 2014

12.4K

Related Experiment Videos

Last Updated: Sep 15, 2025

Author Spotlight: Non-Invasive Imaging of Complex Bio-Structures Using Polarization-Sensitive Two-Photon Microscopy
05:54

Author Spotlight: Non-Invasive Imaging of Complex Bio-Structures Using Polarization-Sensitive Two-Photon Microscopy

Published on: September 8, 2023

1.3K
Observation of Photobehavior in Chlamydomonas reinhardtii
03:54

Observation of Photobehavior in Chlamydomonas reinhardtii

Published on: May 6, 2022

4.0K
Multimodal Optical Microscopy Methods Reveal Polyp Tissue Morphology and Structure in Caribbean Reef Building Corals
10:39

Multimodal Optical Microscopy Methods Reveal Polyp Tissue Morphology and Structure in Caribbean Reef Building Corals

Published on: September 5, 2014

12.4K

Area of Science:

  • Algebraic Geometry
  • Optimization Theory
  • Tropical Algebra

Background:

  • The study of polars of cones is fundamental in convex geometry and optimization.
  • Tropical algebra provides a framework for analyzing algebraic structures over specific semirings.

Purpose of the Study:

  • To define and characterize the tropical analogue of the polar of a cone over the semiring of tropical numbers with signs.
  • To investigate the relationship between tropical polars and classical polars using nonarchimedean valuations.
  • To apply these tropical concepts to analyze classical matrix cones and their hierarchies.

Main Methods:

  • Utilizing the semiring of tropical numbers with signs.
  • Employing a tropical analogue of Fourier-Motzkin elimination for cone characterization.
  • Relating tropical polars to classical polars via nonarchimedean valuation and signed valuation.
  • Analyzing semi-algebraic sets over real closed nonarchimedean fields.

Main Results:

  • Characterization of tropical polars through an invariance property under tropical Fourier-Motzkin elimination.
  • Demonstration that the polar operation commutes with signed valuation for semi-algebraic sets.
  • Identification of the collapse of hierarchies of classical matrix cones (e.g., positive semidefinite, completely positive) under tropicalization.
  • Characterization of images of classical cones and their polars (e.g., co-positive matrices) under signed valuation.

Conclusions:

  • The tropical polar provides a powerful tool for understanding geometric and algebraic structures in tropical algebra.
  • The commutation of polar and signed valuation simplifies analysis of matrix cones over nonarchimedean fields.
  • Tropicalization offers a novel perspective on matrix cone structures and their optimization properties.