Lotka's law, named after Alfred J. Lotka, is one of a variety of special applications of Zipf's law. It describes the frequency of publication by authors in any given field. It states that the number of authors making contributions in a given period is a fraction of the number making a single contribution, following the formula where nearly always equals two, i.e., an approximate inverse-square law, where the number of authors publishing a certain number of articles is a fixed ratio to the number of authors publishing a single article. As the number of articles published increases, authors producing that many publications become less frequent. There are 1/4 as many authors publishing two articles within a specified time period as there are single-publication authors, 1/9 as many publishing three articles, 1/16 as many publishing four articles, etc. Though the law itself covers many disciplines, the actual ratios involved (as a function of 'a') are discipline-specific. The general formula says: or where X is the number of publications, Y the relative frequency of authors with X publications, and n and are constants depending on the specific field. (Wikipedia).
Richard Feynman - The Character of Physical Law - Part4 Symmetry in Physical Law (full version)
Richard Feynman The Character of Physical Law Part4 Symmetry in Physical Law full version
From playlist Feynman's Lectures
Understanding the nature of a force as an interaction between objects is critical to success in a Newton's Laws unit. The What is a Force? Video Tutorial clarifies this concept through several examples. The distinction between contact forces and field forces is discussed. Newton's third la
From playlist Newton's Laws Video Tutorial Series
Set Theory (Part 2): ZFC Axioms
Please feel free to leave comments/questions on the video and practice problems below! In this video, I introduce some common axioms in set theory using the Zermelo-Fraenkel w/ choice (ZFC) system. Five out of nine ZFC axioms are covered and the remaining four will be introduced in their
From playlist Set Theory by Mathoma
The First Law of Thermodynamics: Internal Energy, Heat, and Work
In chemistry we talked about the first law of thermodynamics as being the law of conservation of energy, and that's one way of looking at it, but physicists like doing math more than chemists do, so let's talk about the first law in terms of an equation. You like equations by now, don't yo
From playlist Classical Physics
Set Theory (Part 3): Ordered Pairs and Cartesian Products
Please feel free to leave comments/questions on the video and practice problems below! In this video, I cover the Kuratowski definition of ordered pairs in terms of sets. This will allow us to speak of relations and functions in terms of sets as the basic mathematical objects and will ser
From playlist Set Theory by Mathoma
Roe v. Wade | National Constitution Center | Khan Academy
Keep going! Check out the next lesson and practice what you’re learning: https://www.khanacademy.org/humanities/us-government-and-civics/us-gov-civil-liberties-and-civil-rights/us-gov-due-process-and-the-right-to-privacy/a/lesson-summary-due-process-and-the-right-to-privacy A deep dive in
From playlist The Constitution, Bill of Rights, and Landmark Supreme Court Cases
Principles of Evolution, Ecology and Behavior (EEB 122) Competition among species, or interspecific competition, can have an even greater effect on selection than competition within species (intraspecific competition). This is often the case in lower density populations. Different speci
From playlist Evolution, Ecology and Behavior with Stephen C. Stearns
Follow updates on Twitter: https://twitter.com/eigensteve This video discusses how all exponential growth eventually tapers off, through one mechanism or another. Website: https://www.eigensteve.com/
From playlist Intro to Data Science
Almost Sure and In Probability Convergence in Randomized Urn Model by Krishanu Maulik
PROGRAM: ADVANCES IN APPLIED PROBABILITY ORGANIZERS: Vivek Borkar, Sandeep Juneja, Kavita Ramanan, Devavrat Shah, and Piyush Srivastava DATE & TIME: 05 August 2019 to 17 August 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Applied probability has seen a revolutionary growth in resear
From playlist Advances in Applied Probability 2019
Basics of urban modelling: Professor Sir Alan Wilson, CEO - The Alan Turing Institute
Cities are (nonlinear) complex systems which provide interesting modelling challenges. At the core, is the task of modelling activities at locations and flows between locations (‘spatial interaction’). This can be done on an equilibrium cross-section basis Introduction (no advanced session
From playlist Data science classes
The Sixth Amendment | National Constitution Center | Khan Academy
Keep going! Check out the next lesson and practice what you’re learning: https://www.khanacademy.org/humanities/us-government-and-civics/us-gov-civil-liberties-and-civil-rights/us-gov-due-process-and-the-rights-of-the-accused/v/miranda-v-arizona A deep dive into the Sixth Amendment, which
From playlist The Constitution, Bill of Rights, and Landmark Supreme Court Cases
Symmetries & Conservation Laws: A (Physics) Love Story
There is a deep connection in physics between symmetries of nature and conservation laws, called Noether's theorem. In this physics lesson I'll show you how it works. Get the notes for free here: https://courses.physicswithelliot.com/notes-sign-up The relationship between symmetries and c
From playlist Hamiltonian Mechanics Sequence
Integrating ODEs in MATLAB (Part B) | Lecture 56 | Numerical Methods for Engineers
How to use ode45.m in MATLAB. Join me on Coursera: https://www.coursera.org/learn/numerical-methods-engineers Lecture notes at http://www.math.ust.hk/~machas/numerical-methods-for-engineers.pdf Subscribe to my channel: http://www.youtube.com/user/jchasnov?sub_confirmation=1
From playlist Numerical Methods for Engineers
Winter School on Quantitative Systems Biology DATE:04 December 2017 to 22 December 2017 VENUE:Ramanujan Lecture Hall, ICTS, Bengaluru The International Centre for Theoretical Sciences (ICTS) and the Abdus Salam International Centre for Theoretical Physics (ICTP), are organizing a Winter S
From playlist Winter School on Quantitative Systems Biology
Ch09n1: Geometric Integration: Symplectic method, Hamiltonian preserving method.
Geometric Integration: Symplectic method, Hamiltonian preserving method. Numerical Computation, chapter 9, additional video no 1. To be viewed after the regular videos of chapter 9. Wen Shen, Penn State University, 2018.
From playlist CMPSC/MATH 451 Videos. Wen Shen, Penn State University
Numerical Calculus: Differential Equations, Part 2
Data Science for Biologists Numerical Calculus: Differential Equations Part 2 Course Website: data4bio.com Instructors: Nathan Kutz: faculty.washington.edu/kutz Bing Brunton: faculty.washington.edu/bbrunton Steve Brunton: faculty.washington.edu/sbrunton
From playlist Data Science for Biologists
Cooperation and cheating in microbial populations by Jeff Gore
Winter School on Quantitative Systems Biology DATE:04 December 2017 to 22 December 2017 VENUE:Ramanujan Lecture Hall, ICTS, Bengaluru The International Centre for Theoretical Sciences (ICTS) and the Abdus Salam International Centre for Theoretical Physics (ICTP), are organizing a Winter S
From playlist Winter School on Quantitative Systems Biology
The Fourth Amendment | National Constitution Center | Khan Academy
Keep going! Check out the next lesson and practice what you’re learning: https://www.khanacademy.org/humanities/us-government-and-civics/us-gov-civil-liberties-and-civil-rights/us-gov-balancing-individual-freedom-with-public-order-and-safety/v/the-eighth-amendment A deep dive into the Fou
From playlist The Constitution, Bill of Rights, and Landmark Supreme Court Cases
Mathematical Biology. 15: SIR Model
UCI Math 113B: Intro to Mathematical Modeling in Biology (Fall 2014) Lec 15. Intro to Mathematical Modeling in Biology: SIR Model View the complete course: http://ocw.uci.edu/courses/math_113b_intro_to_mathematical_modeling_in_biology.html Instructor: German A. Enciso, Ph.D. Textbook: Mat
From playlist Math 113B: Mathematical Biology