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Related Concept Videos

Introduction to Scalers01:21

Introduction to Scalers

Many familiar physical quantities can be specified completely by giving a single number and the appropriate unit. For example, "a class period lasts 50 min," or "the gas tank in my car holds 65 L," or "the distance between the two posts is 100 m." A physical quantity that can be specified completely in this manner is called a scalar quantity. The word "scalar" is a synonym for "number." Time, mass, distance, length, volume, temperature, and energy are some examples of scalar quantities.
Scalar...
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
Collisions in Multiple Dimensions: Problem Solving01:06

Collisions in Multiple Dimensions: Problem Solving

In multiple dimensions, the conservation of momentum applies in each direction independently. Hence, to solve collisions in multiple dimensions, we should write down the momentum conservation in each direction separately. To help understand collisions in multiple dimensions, consider an example.
A small car of mass 1,200 kg traveling east at 60 km/h collides at an intersection with a truck of mass 3,000 kg traveling due north at 40 km/h. The two vehicles are locked together. What is the...
Scaling01:26

Scaling

In designing and analyzing filters, resonant circuits, or circuit analysis at large, working with standard element values like 1 ohm, 1 henry, or 1 farad can be convenient before scaling these values to more realistic figures. This approach is widely utilized by not employing realistic element values in numerous examples and problems; it simplifies mastering circuit analysis through convenient component values. The complexity of calculations is thereby reduced, with the understanding that...
Scale-Up Processes01:14

Scale-Up Processes

The scale-up of microbial fermentation processes is essential in industrial biotechnology, allowing the transition from laboratory-scale experiments to commercial-scale production while aiming to maintain product yield and quality. This process requires meticulous adjustment of equipment design, process parameters, and contamination control strategies to accommodate increasing culture volumes.At the laboratory scale, cultures are typically maintained in 1 to 10-liter glass or autoclavable...
Collisions in Multiple Dimensions: Introduction01:05

Collisions in Multiple Dimensions: Introduction

It is far more common for collisions to occur in two dimensions; that is, the initial velocity vectors are neither parallel nor antiparallel to each other. Let's see what complications arise from this. The first idea is that momentum is a vector. Like all vectors, it can be expressed as a sum of perpendicular components (usually, though not always, an x-component and a y-component, and a z-component if necessary). Thus, when the statement of conservation of momentum is written for a problem,...

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Related Experiment Videos

How Fitch-Margoliash Algorithm can Benefit from Multi Dimensional Scaling.

Sylvain Lespinats1, Delphine Grando, Eric Maréchal

  • 1UMR INSERM unité U722 and Université Denis Diderot-Paris 7, Faculté de médecine, site Xavier Bichat, 16 rue Henri Huchard, 75870 Paris cedex 18, France.

Evolutionary Bioinformatics Online
|June 24, 2011
PubMed
Summary
This summary is machine-generated.

This study explores how high-dimensional spaces affect phylogenetic reconstructions using the Fitch-Margoliash algorithm. New criteria improve distance preservation and robustness in evolutionary tree building.

Keywords:
Fitch-MargoliashLeast Square methodsMulti Dimensional ScalingSammon’s mappingmolecular phylogeny

Related Experiment Videos

Area of Science:

  • Bioinformatics
  • Computational Biology
  • Evolutionary Biology

Background:

  • Phylogenetic methods often represent genetic sequences as points in high-dimensional space.
  • Studying evolutionary processes in these spaces involves challenges like the concentration of measured phenomena.

Purpose of the Study:

  • To investigate the influence of high-dimensional space properties on phylogenetic reconstruction.
  • To evaluate the Fitch-Margoliash algorithm, a Least Squares method, in this context.

Main Methods:

  • Examined the relationship between Least Squares methods (Fitch-Margoliash) and Multi-Dimensional Scaling (MDS).
  • Introduced concepts of "continuity" and "trustworthiness" to mitigate risks like "false neighborhoods" and "tears" in dimensionality reduction.
  • Proposed new criteria for phylogeny construction.

Main Results:

  • Least Squares methods for phylogeny are closely related to MDS.
  • Identified "false neighborhood" and "tears" as key risks in dimensionality reduction for phylogenetics.
  • Demonstrated that new criteria enhance distance preservation and robustness in phylogenetic trees.

Conclusions:

  • Improvements in MDS can benefit Least Squares-based phylogenetic methods.
  • Addressing dimensionality reduction risks is crucial for accurate evolutionary inference.
  • The proposed criteria offer a more robust approach to building phylogenies, honoring Professor W.M. Fitch's legacy.