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

Optimization Problems01:26

Optimization Problems

220
Optimization problems often involve identifying maximum or minimum values under specific constraints. A well-known example is determining the longest horizontal pipe that can be moved around a right-angled corner, where a 3-meter-wide hallway meets a 2-meter-wide hallway. This scenario, common in architectural design and industrial transport, can be understood conceptually through geometric and trigonometric reasoning.To visualize the problem, consider the pipe as a straight line that touches...
220
Area Between Curves: Problem Solving01:27

Area Between Curves: Problem Solving

211
A region can be enclosed by three curves: a square root function, a reflected cube root function, and a linear function. The linear function intersects each of the other two curves, and these intersection points determine where the boundary of the enclosed region changes. Because different curves serve as the upper and lower boundaries in different parts of the graph, the area cannot be found using a single setup over the entire interval.To compute the area, the region is first divided into two...
211
Design Example: Measuring Distance Between Two Points with Obstructions01:10

Design Example: Measuring Distance Between Two Points with Obstructions

581
When measuring distances in areas with physical obstructions, such as a lake in a field, surveyors must employ techniques to calculate accurate lengths without direct line measurements. One effective method is the offset technique, which allows for precise distance estimation over inaccessible stretches.In this scenario, a surveyor must measure a side of an area that crosses a lake. Since the measuring tape cannot span the lake, the surveyor begins by establishing a baseline that aligns with...
581
Area Problem01:26

Area Problem

312
Determining the area of a region with straight edges is straightforward, as geometric formulas for rectangles, triangles, and polygons can be applied directly. However, traditional geometric methods are insufficient when a region has a curved boundary, such as the area under a function.fromThe area problem involves finding a systematic way to measure such regions. One approach to solving this problem is through approximation. Instead of attempting to compute the area exactly at the outset, the...
312
Midpoint Rule01:20

Midpoint Rule

251
Approximating areas under curved boundaries is a common problem in applied mathematics, particularly when an exact calculation is difficult or impractical. One effective numerical method for this purpose is the Midpoint Rule, which provides an estimate of the area under a curve by using rectangular approximations over a specified interval.Description of the Midpoint RuleThe Midpoint Rule begins by dividing the given interval into a number of equal subintervals. For each subinterval, the...
251
The Distance Formula01:20

The Distance Formula

804
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...
804

You might also read

Related Articles

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

Sort by
Same author

<i>Special Issue:</i> 13th International Conference on Computational Advances in Bio and Medical Sciences.

Journal of computational biology : a journal of computational molecular cell biology·2026
Same author

Fast Algorithms for Computing Jaro Similarity.

Journal of computational biology : a journal of computational molecular cell biology·2026
Same author

Potent Acridone Antimalarial against All Three Life Stages of <i>Plasmodium</i>.

Research square·2025
Same author

<i>Special Section:</i> 12th International Computational Advances in Bio and Medical Sciences (ICCABS 2023).

Journal of computational biology : a journal of computational molecular cell biology·2025
Same author

Randomized feature selection based semi-supervised latent Dirichlet allocation for microbiome analysis.

Scientific reports·2024
Same author

KE: A Knowledge Enhancing Framework for Machine Learning Models.

The journal of physical chemistry. A·2023
Same journal

GMSA: A Graph Matching and Point Cloud Registration-Based Method for Spatial Transcriptomics Data Alignment.

Journal of computational biology : a journal of computational molecular cell biology·2026
Same journal

Investigations on Multiple Protein Scaffold Filling.

Journal of computational biology : a journal of computational molecular cell biology·2026
Same journal

Cell Type Prediction for Single-Cell RNA Sequencing Utilizing Unsupervised Domain Adaptation and Semi-Supervised Learning.

Journal of computational biology : a journal of computational molecular cell biology·2026
Same journal

PPIGAN: Prediction of Protein-Protein Interactions Using Generative Adversarial Networks.

Journal of computational biology : a journal of computational molecular cell biology·2026
Same journal

Deep Structure-Enhanced Cell Clustering Model for Single-Cell RNA Sequencing Data.

Journal of computational biology : a journal of computational molecular cell biology·2026
Same journal

Asymmetric Drug-Drug Interaction Prediction Based on Generative Adversarial Networks and Knowledge Graph.

Journal of computational biology : a journal of computational molecular cell biology·2026
See all related articles

Related Experiment Video

Updated: May 3, 2026

Author Spotlight: Optimization of Processing Technology for Tiebangchui with Zanba Based on CRITIC Combined with Box-Behnken Response Surface Method
09:16

Author Spotlight: Optimization of Processing Technology for Tiebangchui with Zanba Based on CRITIC Combined with Box-Behnken Response Surface Method

Published on: May 12, 2023

1.6K

Border length minimization problem on a square array.

Vamsi Kundeti1, Sanguthevar Rajasekaran, Hieu Dinh

  • 1Computer Science and Engineering Department, University of Connecticut , Storrs, CT.

Journal of Computational Biology : a Journal of Computational Molecular Cell Biology
|February 18, 2014
PubMed
Summary
This summary is machine-generated.

We proved that the border length minimization problem (BLMP) in peptide microarray fabrication is [Formula: see text]-hard. A new algorithm provides an O(N)-approximation for this optimization challenge, enhancing cancer diagnostics.

Keywords:
DNA self-assemblyalgorithmscombinatorial optimizationgenomicsmachine learning

More Related Videos

Quantifying Intermembrane Distances with Serial Image Dilations
07:45

Quantifying Intermembrane Distances with Serial Image Dilations

Published on: September 28, 2018

8.7K
Magnetic Resonance Derived Myocardial Strain Assessment Using Feature Tracking
07:21

Magnetic Resonance Derived Myocardial Strain Assessment Using Feature Tracking

Published on: February 12, 2011

14.1K

Related Experiment Videos

Last Updated: May 3, 2026

Author Spotlight: Optimization of Processing Technology for Tiebangchui with Zanba Based on CRITIC Combined with Box-Behnken Response Surface Method
09:16

Author Spotlight: Optimization of Processing Technology for Tiebangchui with Zanba Based on CRITIC Combined with Box-Behnken Response Surface Method

Published on: May 12, 2023

1.6K
Quantifying Intermembrane Distances with Serial Image Dilations
07:45

Quantifying Intermembrane Distances with Serial Image Dilations

Published on: September 28, 2018

8.7K
Magnetic Resonance Derived Myocardial Strain Assessment Using Feature Tracking
07:21

Magnetic Resonance Derived Myocardial Strain Assessment Using Feature Tracking

Published on: February 12, 2011

14.1K

Area of Science:

  • Biotechnology
  • Computational Biology
  • Bioinformatics

Background:

  • Protein/peptide microarrays are crucial for cancer diagnosis, aiding in biomarker detection and antibody signature identification.
  • Fabricating high-density peptide arrays efficiently involves solving the complex border length minimization problem (BLMP).

Purpose of the Study:

  • To resolve the 7-year-old open question regarding the tractability of the BLMP.
  • To introduce a novel algorithm for optimizing microarray fabrication.

Main Methods:

  • Proving the BLMP is [Formula: see text]-hard using computational complexity theory.
  • Developing and analyzing a hierarchical refinement algorithm for BLMP heuristic solutions.
  • Establishing an O(N)-approximation for the TSP+1-threading heuristic in BLMP.

Main Results:

  • The border length minimization problem (BLMP) is formally proven to be [Formula: see text]-hard.
  • A hierarchical refinement algorithm is presented to improve heuristic BLMP solutions.
  • The TSP+1-threading heuristic is shown to be an O(N)-approximation algorithm for BLMP.

Conclusions:

  • The computational complexity of BLMP is now definitively established.
  • The developed algorithm and approximation guarantee offer practical improvements for peptide microarray fabrication.
  • These advancements contribute to the more efficient and accurate use of peptide microarrays in cancer diagnostics.