Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Distance Problem

Distance Problem

When an object's velocity changes over time, the total distance traveled can be determined by summing small displacement intervals over short increments. This approach approximates the true distance through numerical summation and the use of integral calculus. An estimate of the total displacement can be obtained by measuring velocity at regular intervals and multiplying each value by the corresponding time step.If a runner accelerates over the first three seconds of a race, speed measurements...

Distance Corrections

Distance Corrections

To achieve precise distance measurements, especially in surveying and construction, certain corrections must be applied to account for potential sources of error like the standardization errors, temperature variations, and slope adjustments.Standardization error emerges when measurement equipment undergoes changes, such as wear, repairs, or weather impacts. To address this, surveyors compare the equipment’s readings to a standard. This process identifies any deviation that might lead to...

The Distance Formula

The Distance Formula

In geometry, measuring the direct distance between two points on a plane is essential in various practical and theoretical applications. Whether in navigation, engineering, or computer graphics, determining the shortest path between two locations involves using the distance formula. This formula is derived from the Pythagorean Theorem, which relates the lengths of the sides of a right triangle. On a coordinate plane, the horizontal and vertical distances between two points serve as the legs of...

Short-distance Transport of Resources

Short-distance Transport of Resources

Short-distance transport refers to transport that occurs over a distance of just 2-3 cells, crossing the plasma membrane in the process. Small uncharged molecules, such as oxygen, carbon dioxide, and water, can diffuse across the plasma membrane on their own. In contrast, ions and larger molecules require the assistance of transport proteins due to their charge or size. Transport across membranes also occurs within individual cells, playing a variety of essential roles for the plant as a whole.

What are Biogeochemical Cycles?

What are Biogeochemical Cycles?

The most common elements in organic molecules, carbon, hydrogen, oxygen, nitrogen, sulfur, and phosphorus, are only available in the ecosystem in limited amounts. Therefore, these nutrients must be recycled through both biotic and abiotic components of the ecosystem, in processes generally called biogeochemical cycles.

The Water Cycle

The Water Cycle

The Earth’s hydrosphere includes all of the areas where the storage and movement of water occurs. Since water is the basis of all living processes, the cycling of water is extremely important to ecosystem dynamics.

You might also read

Related Articles

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

Sort by

Same author

Evaluating the concordance between AI-based and conventional embryo selection: implications for clinical decision-making.

Reproductive biomedicine online·2026

Same author

An artificial intelligence platform for automated measurement and count estimation of ovarian follicles during ovarian stimulation and IVF: a multicenter study.

Journal of assisted reproduction and genetics·2026

Same author

Computing Generalized Convolutions Faster Than Brute Force.

Algorithmica·2024

Same author

Crystal and electronic structure of PbTe/CdTe nanostructures.

Nanoscale research letters·2011

Same journal

FullSynesth: Syntenic Reconciliation of a Set of Consistent Gene Trees.

Theory of computing systems·2026

Same journal

Tight Approximation and Kernelization Bounds for Vertex-Disjoint Shortest Paths.

Theory of computing systems·2026

Same journal

The Ground-Set-Cost Budgeted Maximum Coverage Problem.

Theory of computing systems·2025

Same journal

Rudin-Shapiro Sums Via Automata Theory and Logic.

Theory of computing systems·2025

Same journal

Prediction and MDL for infinite sequences.

Theory of computing systems·2024

Same journal

On Polynomial Recursive Sequences.

Theory of computing systems·2024

See all related articles

Search research articles

Related Experiment Video

Updated: Jan 21, 2026

Rodent Estrous Cycle Monitoring Utilizing Vaginal Lavage: No Such Thing As a Normal Cycle

Rodent Estrous Cycle Monitoring Utilizing Vaginal Lavage: No Such Thing As a Normal Cycle

Published on: August 30, 2021

Improved Distance Queries and Cycle Counting by Frobenius Normal Form.

Piotr Sankowski¹, Karol Węgrzycki¹

¹Institute of Informatics, University of Warsaw, Warsaw, Poland.

Theory of Computing Systems

|August 10, 2019

Summary

This summary is machine-generated.

This study introduces a new framework for efficiently counting cycles and walks in directed graphs. The method utilizes matrix multiplication for faster graph analysis and improved distance queries.

Keywords:

All-nodes shortest cycles Frobenius normal form Graph algorithms

More Related Videos

Fast Colony Forming Unit Counting in 96-Well Plate Format Applied to the Drosophila Microbiome

Fast Colony Forming Unit Counting in 96-Well Plate Format Applied to the Drosophila Microbiome

Published on: January 13, 2023

Isolation of Human Endothelial Cells from Normal Colon and Colorectal Carcinoma - An Improved Protocol

Isolation of Human Endothelial Cells from Normal Colon and Colorectal Carcinoma - An Improved Protocol

Published on: April 4, 2018

Related Experiment Videos

Last Updated: Jan 21, 2026

Rodent Estrous Cycle Monitoring Utilizing Vaginal Lavage: No Such Thing As a Normal Cycle

Rodent Estrous Cycle Monitoring Utilizing Vaginal Lavage: No Such Thing As a Normal Cycle

Published on: August 30, 2021

Fast Colony Forming Unit Counting in 96-Well Plate Format Applied to the Drosophila Microbiome

Fast Colony Forming Unit Counting in 96-Well Plate Format Applied to the Drosophila Microbiome

Published on: January 13, 2023

Isolation of Human Endothelial Cells from Normal Colon and Colorectal Carcinoma - An Improved Protocol

Isolation of Human Endothelial Cells from Normal Colon and Colorectal Carcinoma - An Improved Protocol

Published on: April 4, 2018

Area of Science:

Graph theory
Discrete mathematics
Computer science algorithms

Background:

Analyzing properties of unweighted, directed graphs is fundamental in computer science.
Efficiently counting cycles and walks is crucial for various graph algorithms.
Existing methods may not scale well for large graph structures.

Purpose of the Study:

To introduce a novel framework for counting cycles and walks in directed graphs.
To achieve matrix multiplication time complexity for these counting problems.
To enhance the efficiency of solving related graph problems like All-Nodes Shortest Cycles and All-Pairs All Walks.

Main Methods:

The framework is based on the fast decomposition into Frobenius normal form.
It leverages efficient Hankel matrix-vector multiplication.
The approach enables matrix multiplication time complexity for cycle and walk counting.

Main Results:

Successfully developed a framework for counting cycles and walks of a given length.
Achieved efficient solutions for All-Nodes Shortest Cycles and All-Pairs All Walks problems.
Demonstrated improvements in distance queries for unweighted graphs.

Conclusions:

The proposed framework offers a significant advancement in analyzing directed graphs.
The method provides efficient solutions for fundamental graph traversal and cycle detection problems.
This work contributes to the development of faster graph algorithms.