Power laws

Kleiber's law

Kleiber's law, named after Max Kleiber for his biology work in the early 1930s, is the observation that, for the vast majority of animals, an animal's metabolic rate scales to the 3⁄4 power of the animal's mass. Symbolically: if q0 is the animal's metabolic rate, and M is the animal's mass, then Kleiber's law states that q0~M3/4. Thus, over the same time span, a cat having a mass 100 times that of a mouse will consume only about 32 times the energy the mouse uses. The exact value of the exponent in Kleiber's law is unclear, in part because the law currently lacks a single theoretical explanation that is entirely satisfactory. (Wikipedia).

Kleiber's law
Video thumbnail

The Science of Hobbit Gluttony

Offset your carbon footprint with Wren! They'll plant 10 extra trees for each of the first 100 people who sign up at https://www.wren.co/start/minuteearth. Because smaller animals have to eat more relative to their bodyweight, Tolkein’s hobbits need to eat a lot - not for comfort, but for

From playlist Anatomy & Health

Video thumbnail

The science of symmetry - Colm Kelleher

View full lesson: http://ed.ted.com/lessons/the-science-of-symmetry-colm-kelleher When you hear the word symmetry, you might think generally of triangles, butterflies, or even ballerinas. But defined scientifically, symmetry is "a transformation that leaves an object unchanged." Huh? Colm

From playlist New TED-Ed Originals

Video thumbnail

3/4 and Kleiber's Law - Numberphile

The fraction three quarters has a particular interest to biologists because of its link to the research of Max Kleiber and metabolic rates in animals. More links & stuff in full description below ↓↓↓ This video features Thomas Woolley from the University of Oxford. Tom thanks @gameboygen

From playlist From Numberphile

Video thumbnail

Agnès Desolneux - Maximum Entropy Distributions for Image Synthesis under Statistical Constraints

The question of texture synthesis in image processing is a very challenging problem that can be stated as followed: given an exemplar image, sample a new image that has the same statistical features (empirical mean, empirical covariance, filter responses, neural network responses, etc.). E

From playlist Journée statistique & informatique pour la science des données à Paris-Saclay 2021

Video thumbnail

Shannon 100 - 26/10/2016 - Elisabeth GASSIAT

Entropie, compression et statistique Elisabeth Gassiat (Université de Paris-Sud) Claude Shannon est l'inventeur de la théorie de l'information. Il a introduit la notion d'entropie comme mesure de l'information contenue dans un message vu comme provenant d'une source stochastique et démon

From playlist Shannon 100

Video thumbnail

Bryna Kra : Multiple ergodic theorems: old and new - lecture 2

Abstract : The classic mean ergodic theorem has been extended in numerous ways: multiple averages, polynomial iterates, weighted averages, along with combinations of these extensions. I will give an overview of these advances and the different techniques that have been used, focusing on co

From playlist Dynamical Systems and Ordinary Differential Equations

Video thumbnail

Physics - Mechanics: Gravity (13 of 20) Keppler's 3rd Law

Visit http://ilectureonline.com for more math and science lectures! In this video I will explain and calculate Keppler's 3rd Law.

From playlist PHYSICS 18 GRAVITY

Video thumbnail

Uncertainty Principle - Klim Efremenko

Klim Efremenko Tel-Aviv University; Member, School of Mathematics April 23, 2013 Informally, uncertainty principle says that function and its Fourier transform can not be both concentrated. Uncertainty principle has a lot of applications in areas like compressed sensing, error correcting c

From playlist Mathematics

Video thumbnail

Interpreting nonlinear expressions — Basic example | Math | New SAT | Khan Academy

Watch Sal work through a basic Interpreting nonlinear expressions problem. Watch the next lesson: https://www.khanacademy.org/test-prep/new-sat/new-sat-math/new-sat-passport-advanced-mathematics/v/sat-math-p10-harder?utm_source=YT&utm_medium=Desc&utm_campaign=NewSAT Missed the previous l

From playlist Passport to advanced mathematics | New SAT | Khan Academy

Video thumbnail

Quantum Mechanics 5a - Schrödinger Equation I

Building on Louis de Broglie's hypothesis of "electron waves," Erwin Schrödinger develops a wave equation for electrons. The playlist: http://www.youtube.com/playlist?list=PL193BC0532FE7B02C

From playlist Quantum Mechanics

Video thumbnail

Teach Astronomy - Universal Law of Gravity

http://www.teachastronomy.com/ Newton's master work is the universal law of gravity. Newton's law of gravity states that every object in the universe, every particle, every planet, every star, every galaxy, attracts each other with a force that is proportional to each of the masses of two

From playlist 03. Concepts and History of Astronomy and Physics

Video thumbnail

A quantum particle in a constant magnetic field

This is a first attempt at simulating a quantum particle in a magnetic field. The particle moves in a plane, and the magnetic field is constant, and perpendicular to the plane. The vector potential used in Schrödinger's equation is proportional to the vector (y, -x, 0). I hope to be able t

From playlist Schrödinger's equation

Video thumbnail

Maxwell’s Equations Part 3: Faraday’s Law

With the two forms of Gauss's law understood, we have covered the static aspect of electromagnetism. Now it's time to look at the more dynamic aspect by examining Faraday's law. This is a mathematical formalization of the notion that a changing magnetic flux will induce an electric current

From playlist Classical Physics

Video thumbnail

Statistical Physics and Learning - Florent Krzakala, Sorbonne Université

Recent years have witnessed an increased cross-fertilisation between the fields of statistics and computer science. In the era of Big Data, statisticians are increasingly facing the question of guaranteeing prescribed levels of inferential accuracy within certain time budget. On the other

From playlist Statistics and computation

Video thumbnail

Nelly Pustelnik: Optimization -lecture 2

CIRM HYBRID EVENT Recorded during the meeting "Mathematics, Signal Processing and Learning" the January 27, 2021 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians o

From playlist Virtual Conference

Video thumbnail

Teach Astronomy - Symmetry

http://www.teachastronomy.com/ A lot of fundamental concepts in physics are based on the idea of symmetry. Symmetry is familiar to us in an aesthetic sense. It often means things that have pleasing proportion, or look the same from every direction, or have a harmonious nature about them.

From playlist 23. The Big Bang, Inflation, and General Cosmology 2

Video thumbnail

Lénaïc Chizat: Trajectory inference with Schrödinger bridges - lecture 1

We consider statistical and computation methods to infer trajectories of a stochastic process from snapshots of its temporal marginals. This problem arises in the analysis of single cell RNA-sequencing data. The goal of this mini-course is to present and understand the estimator proposed b

From playlist CEMRACS 2022

Video thumbnail

The Schrodinger Equation is (Almost) Impossible to Solve.

Sure, the equation is easily solvable for perfect / idealized systems, but almost impossible for any real systems. The Schrodinger equation is the governing equation of quantum mechanics, and determines the relationship between a system, its surroundings, and a system's wave function. Th

From playlist Quantum Physics by Parth G

Video thumbnail

Naotoshi Nakamura - LAVENDER extracts individual variability...

Naotoshi Nakamura - LAVENDER extracts individual variability in the response to seasonal influenza vaccination The human immune system is known to be highly variable among individuals, but it is not well understood how the variability changes over time, especially when faced with externa

From playlist From Molecules and Cells to Human Health : Ideas and concepts

Related pages

Surface-area-to-volume ratio | Geometry | Analysis of variance | Fractal | Fractal dimension | Convex combination | Square–cube law