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

Quadratic Models01:23

Quadratic Models

Quadratic models are mathematical representations used to describe relationships in which the rate of change changes at a constant rate. These models appear in a wide variety of natural and engineered systems, especially those involving motion, forces, and optimization. One common application is analyzing the vertical motion of objects influenced by gravity, such as a ball thrown into the air.In such scenarios, the object's height changes over time in a curved pattern, rising to a maximum point...
Quadratic Equations01:29

Quadratic Equations

A quadratic equation is an algebraic expression where a variable is raised to the second power and combined with its first power and a constant; all equated to zero. These equations are frequently used to model relationships involving area, motion, and optimization. The general representation of a quadratic equation iswhere a, b, and c are real values, and a is nonzero to ensure the presence of the squared term.One method for solving a quadratic equation involves rewriting it as a product of...
Quadratic Equations in the Complex Number System01:29

Quadratic Equations in the Complex Number System

A quadratic equation in the form ax2+bx+c=0 can have solutions that vary in nature depending on the value of the discriminant, b2−4ac. In this expression, a is the coefficient of the quadratic term x2, b is the coefficient of the linear term x, and c is the constant term. When the discriminant is negative, the equation has no real number solutions. However, by introducing complex numbers through the imaginary unit i, defined by i=-1, these equations can still be solved.The square root of a...
Linearization and Approximation01:26

Linearization and Approximation

Linearization is a mathematical technique used to approximate complex, nonlinear functions with simpler linear models in the vicinity of a chosen reference point. The method is based on the idea that, although a function may be difficult to evaluate exactly, its behavior near a specific input value can often be closely approximated by the tangent line at that point. This approach is particularly useful when small deviations from a known value are involved.Consider the square root function, for...
Equations of Motion: Rectangular Coordinates and Cylindrical Coordinates01:21

Equations of Motion: Rectangular Coordinates and Cylindrical Coordinates

Understanding the motion of particles is a fundamental aspect of classical mechanics, and the choice of the coordinate system plays a pivotal role in unraveling the complexities of their dynamics.
When a particle moves relative to an inertial frame, the equations of motion can be expressed using rectangular components. If the motion is confined to the x-y plane, the equations having the x and y coordinates only can be used to simplify the mathematical representation.
However, when particles...
Coordination Number and Geometry02:57

Coordination Number and Geometry

For transition metal complexes, the coordination number determines the geometry around the central metal ion. Table 1 compares coordination numbers to molecular geometry. The most common structures of the complexes in coordination compounds are octahedral, tetrahedral, and square planar.

You might also read

Related Articles

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

Sort by
Same author

Repurposing homoharringtonine for thyroid cancer treatment through TIMP1/FAK/PI3K/AKT signaling pathway.

iScience·2024
Same author

Corrigendum: Co-treatment of chloroquine and trametinib inhibits melanoma cell proliferation and decreases immune cell infiltration.

Frontiers in oncology·2024
Same author

Inhibition of cIAP1/2 reduces RIPK1 phosphorylation in pulmonary endothelial cells and alleviate sepsis-induced lung injury and inflammatory response.

Immunologic research·2024
Same author

Integrative Genomics and Bioactivity-Guided Isolation of Novel Antimicrobial Compounds from <i>Streptomyces</i> sp. KN37 in Agricultural Applications.

Molecules (Basel, Switzerland)·2024
Same author

Optimization of Composite Enzymatic Extraction, Structural Characterization and Biological Activity of Soluble Dietary Fiber from <i>Akebia trifoliata</i> Peel.

Molecules (Basel, Switzerland)·2024
Same author

iDNA-OpenPrompt: OpenPrompt learning model for identifying DNA methylation.

Frontiers in genetics·2024
Same journal

A Model-Free Reinforcement Learning Implementation of Decision Making Under Uncertainty by Sequential Sampling.

Neural computation·2026
Same journal

DROP: Distributional and Regular Optimism and Pessimism for Reinforcement Learning.

Neural computation·2026
Same journal

Hierarchical Active Inference Using Successor Representations.

Neural computation·2026
Same journal

W-Kernel and Its Principal Space for Frequentist Evaluation of Bayesian Estimators.

Neural computation·2026
Same journal

A Hidden Markov Model-Inspired Sequence Classification Method for Hyperdimensional Computing.

Neural computation·2026
Same journal

Sparse Graphical Modeling for Electrophysiological Phase-Based Connectivity Using Circular Statistics.

Neural computation·2026
See all related articles

Related Experiment Videos

Linear coordinate-descent message passing for quadratic optimization.

Guoqiang Zhang1, Richard Heusdens

  • 1Department of Intelligent Systems, Delft University of Technology, Delft, the Netherlands. g.zhang-1@tudelft.nl

Neural Computation
|September 14, 2012
PubMed
Summary
This summary is machine-generated.

We introduce a new message-passing algorithm for quadratic optimization, linear coordinate-descent (LiCD). This algorithm transmits fewer parameters per message, enhancing efficiency and reducing computational complexity for optimization problems.

Related Experiment Videos

Area of Science:

  • Optimization Algorithms
  • Message Passing
  • Computational Complexity

Background:

  • Quadratic optimization problems are prevalent in various scientific and engineering fields.
  • Existing message-passing algorithms like min-sum can be computationally intensive due to high-dimensional message passing.

Purpose of the Study:

  • To propose a novel message-passing algorithm for quadratic optimization.
  • To reduce the number of parameters transmitted per message and improve computational efficiency.

Main Methods:

  • Developed a new message-passing algorithm based on linear coordinate descent between nodes.
  • Messages are linear functions, unlike the quadratic functions in the min-sum algorithm.
  • Analyzed convergence properties for walk-summable quadratic matrices and addressed convergence for general matrices.

Main Results:

  • The proposed linear coordinate-descent (LiCD) algorithm transmits only one parameter per message, compared to two for the min-sum algorithm.
  • Convergence of the LiCD algorithm is proven for walk-summable quadratic matrices.
  • The LiCD algorithm, used as a subroutine, resolves convergence issues for general quadratic matrices.
  • Experimental results demonstrate comparable convergence speed to the min-sum algorithm on graphs with cycles.

Conclusions:

  • The LiCD algorithm offers a more efficient approach to quadratic optimization through reduced message complexity.
  • This method provides a viable solution for improving the performance of message-passing optimization algorithms.