Statistical deviation and dispersion
In bioinformatics, the root-mean-square deviation of atomic positions, or simply root-mean-square deviation (RMSD), is the measure of the average distance between the atoms (usually the backbone atoms) of superimposed proteins. Note that RMSD calculation can be applied to other, non-protein molecules, such as small organic molecules. In the study of globular protein conformations, one customarily measures the similarity in three-dimensional structure by the RMSD of the Cα atomic coordinates after optimal rigid body superposition. When a dynamical system fluctuates about some well-defined average position, the RMSD from the average over time can be referred to as the RMSF or root mean square fluctuation. The size of this fluctuation can be measured, for example using Mössbauer spectroscopy or nuclear magnetic resonance, and can provide important physical information. The Lindemann index is a method of placing the RMSF in the context of the parameters of the system. A widely used way to compare the structures of biomolecules or solid bodies is to translate and rotate one structure with respect to the other to minimize the RMSD. Coutsias, et al. presented a simple derivation, based on quaternions, for the optimal solid body transformation (rotation-translation) that minimizes the RMSD between two sets of vectors. They proved that the quaternion method is equivalent to the well-known Kabsch algorithm. The solution given by Kabsch is an instance of the solution of the d-dimensional problem, introduced by Hurley and Cattell. The quaternion solution to compute the optimal rotation was published in the appendix of a paper of Petitjean. This quaternion solution and the calculation of the optimal isometry in the d-dimensional case were both extended to infinite sets and to the continuous case in the appendix A of another paper of Petitjean. (Wikipedia).
Ex 2: Determine Function Values Given a Square Root Function
This video provides three examples of how to determine function values given a square root function. Complete Library: http://www.mathispower4u.com Search Library: http://www.mathispower4u.wordpress.com
From playlist Determining Function Values
Determine Approximate Values of Square Roots (Irrational Values)
This video explains how to determine what integer values a square root is between. Then it explains how to use a calculator to approximate square roots. http://mathispower4u.com
From playlist Geometry and Measurement
How to find the height of a tree given the angle of elevation
👉 Learn how to solve the word problems with trigonometry. Word problems involving angles, including but not limited to: bearings, angle of elevations and depressions, triangles problems etc are solved using trigonometry. To be able to solve these problems it is important that you have a gr
From playlist Evaluate Inverse Trigonometric Functions
Trig Function Values of Inverse Trig Function Values Using Reference Triangles (Q1)
This video explains how to evaluate expressions that are in the form of trigonometric function values of inverse trigonometric function values using reference triangles. http://mathispower4u.com
From playlist Inverse Trigonometric Functions
Explain how to take the root of a number even or odd using prime factorization, root
👉 Learn how to find the square root of a number. To find the square root of a number, we identify whether that number which we want to find its square root is a perfect square. This is done by identifying a number which when raised to the 2nd power gives the number which we want to find it
From playlist How to Simplify the Square Root of a Number
7B. Protein 1: 3D Structural Genomics, Homology, Catalytic and Regulatory Dynamics, Fun...
MIT HST.508 Genomics and Computational Biology, Fall 2002 Instructor: George Church View the complete course: https://ocw.mit.edu/courses/hst-508-genomics-and-computational-biology-fall-2002/ YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP61gaHWysmlYNeGsuUI8y5GV We'll
From playlist HST.508 Genomics and Computational Biology, Fall 2002
How to take the square root of three different types of numbers, root(4), root(18)
👉 Learn how to find the square root of a number. To find the square root of a number, we identify whether that number which we want to find its square root is a perfect square. This is done by identifying a number which when raised to the 2nd power gives the number which we want to find it
From playlist How to Simplify the Square Root of a Number
What is the Schrödinger Equation? A basic introduction to Quantum Mechanics
This video provides a basic introduction to the Schrödinger equation by exploring how it can be used to perform simple quantum mechanical calculations. After explaining the basic structure of the equation, the infinite square well potential is used as a case study. The separation of variab
From playlist Quantum Physics
Evaluate Inverse Cosine Expressions Using the Reference Triangles
This video explains how to use the reference triangles to evaluate inverse trigonometric expressions. http://mathispower4u.com
From playlist Inverse Trigonometric Functions
Kinetic Molecular Theory of Gases - Practice Problems
This chemistry video tutorial explains the concept of the kinetic molecular theory of gases. It contains a few multiple choice practice problems as well. The assumptions of this model states that the volume of gas particles are negligible. Gas molecules do not exert forces on each other
From playlist New AP & General Chemistry Video Playlist
Quantum Physics Full Course | Quantum Mechanics Course
Quantum physics also known as Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all #quantum #physics including quantum chemistry, quantum field theory
From playlist Quantum Mechanics
Joscha Prochno: The large deviations approach to high-dimensional convex bodies, Lecture I
Given any isotropic convex body in high dimension, it is known that its typical random projections will be approximately standard Gaussian. The universality in this central limit perspective restricts the information that can be retrieved from the lower-dimensional projections. In contrast
From playlist Workshop: High dimensional spatial random systems
Large deviations for non-interacting trapped fermions by Gregory Schehr
Large deviation theory in statistical physics: Recent advances and future challenges DATE: 14 August 2017 to 13 October 2017 VENUE: Madhava Lecture Hall, ICTS, Bengaluru Large deviation theory made its way into statistical physics as a mathematical framework for studying equilibrium syst
From playlist Large deviation theory in statistical physics: Recent advances and future challenges
Top eigenvalue of a Gaussian random matrix: Large Deviations by Satya Majumdar
Large deviation theory in statistical physics: Recent advances and future challenges DATE: 14 August 2017 to 13 October 2017 VENUE: Madhava Lecture Hall, ICTS, Bengaluru Large deviation theory made its way into statistical physics as a mathematical framework for studying equilibrium syst
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Advanced Quantum Mechanics Lecture 3
(October 7, 2013) Leonard Susskind derives the energy levels of electrons in an atom using the quantum mechanics of angular momentum, and then moves on to describe the quantum mechanics of the harmonic oscillator. Originally presented by the Stanford Continuing Studies Program. Stanford
From playlist Lecture Collection | Advanced Quantum Mechanics
Square Root App: Find the Side Length of a Square Given the Area
This video explains how to use a square root to determine the side length of a square given the area of the square. http://mathispower4u.com
From playlist Square Roots
Optimal Transportation and Applications - 16 November 2018
http://crm.sns.it/event/436 It is the ninth edition of this "traditional'' meeting in Pisa, after the ones in 2001, 2003, 2006, 2008, 2010, 2012, 2014 and 2016. Organizing Committee Luigi Ambrosio, Scuola Normale Superiore, Pisa Giuseppe Buttazzo, Dipartimento di Matematica, Università
From playlist Centro di Ricerca Matematica Ennio De Giorgi
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From playlist Arithmetic and Pre-Algebra: Number Sense and Properties