*coll. *voir pour team. *docs. Untitled. Your brain is an extremely expensive piece of equipment. "The human brain is about 2% of body mass, but it consumes about 20% of the body's energy budget," says Ed Bullmore, Professor of Psychiatry at the Brain Mapping Unit in the University of Cambridge. "It's expensive to build and expensive to keep running. Every time you send a signal down a neuron, it costs quite a lot of metabolic money to reset the neuron after the signal has passed. " Viewed as a network of inter-connected regions, the brain faces a difficult trade-off. On the one hand it needs to be complex to ensure high performance. On the other hand it needs to minimise what you might call wiring cost — the sum of the length of all the connections — because communication over distance is metabolically expensive. In computer chips and in brains wiring is expensive. It's a problem well-known to computer scientists. Small worlds Small world networks have advantages in terms of information transfer.

Russian dolls Rent's rule nodes. Vacuuming the Lungs. By Paul Ford How to breathe deeply when you're nervous. This morning I went to a studio and recorded some writing for eventual radio broadcast. During my readings, I could not get my breath. I sucked in as much air as I could between takes, took off my sweater, wiped my brow, pushed away the chair and knelt on the floor, took a break, and sipped water—but no matter what I tried, I would find myself gasping by the end of every second sentence. Because of this, I couldn't get back to the calm, measured reading I'd rehearsed. The producer was understanding, and I was able to go over many parts of the piece several times, and everything ended up okay.

My girlfriend is an opera singer and performance studies expert who has spent years working on breathing, so I asked her what to do next time. 1. 2. 3. 4. That's it. Phew. Brendel plays Schubert Impromptu Op.90 No.4. Brendel plays Schubert Impromptu Op.90 No.1. Earth's Grid System, Becker-Hagens, Ley Lines, Hartmann Net, Curry Lines - Science and Pseudoscience. Earth's Grid Systems Science and Pseudoscience Topography, is the study of Earth's surface shape and features or those of planets, moons, and asteroids. It is also the description of such surface shapes and features (especially their depiction in maps). The topography of an area can also mean the surface shape and features themselves. Planetary Energetic Grid Theory Planetary Energetic Grid Theory falls under the heading of pseudoscience. Plato recognized grids and their patterns, devising a theory that the Earth's basic structure evolved from a simple geometric shapes to more complex ones.

Becker-Hagens Grid Bill Becker and Bethe Hagens discussed the code of the Platonic Solids' positions on Earth, ascribing this discovery to the work of Ivan P. Becker and Hagens' attention was drawn to this research through the work of Chris Bird, who punished "Planetary Grid" in the New Age Journal in May 1975. South America's grid triangle forms the continent around itself. We see Dr. According to Dr. 21 GIFs That Explain Mathematical Concepts. “Let's face it; by and large math is not easy, but that's what makes it so rewarding when you conquer a problem, and reach new heights of understanding.”

Danica McKellar As we usher in the start of a new school year, it’s time to hit the ground running in your classes! Math can be pretty tough, but since it is the language in which scientists interpret the Universe, there’s really no getting around learning it. Check out these gifs that will help you visualize some tricky aspects of math, so you can dominate your exams this year. Ellipse: Via: giphy Solving Pascal triangles: Via: Hersfold via Wikimedia Commons Use FOIL to easily multiply binomials: Via: mathcaptain Here’s how you solve logarithms: Via: imgur Use this trick so you don’t get mixed up when doing matrix transpositions: Via: Wikimedia Commons What the Pythagorean Theorem is really trying to show you: Via: giphy Exterior angles of polygons will ALWAYS add up to 360 degrees: Via: math.stackexchange Via: imgur Via: Wikimedia Commons Via: reddit.

Muckety - Mapping connections of the rich, famous & influential. Stella - Create Polyhedra and Nets! Platonic, Archimedean, Catalan, Kepler-Poinsot, uniform, and dual polyhedra, their stellations, and polyhedron nets. Hi, and welcome to the Stella home page! Small Stella, Great Stella and Stella4D are computer programs which let you create and view polyhedra on the screen, then print out the nets required to build your own models out of paper.

Small Stella has a fixed list of built-in models and can print out nets for over 300 polyhedra. Great Stella is more advanced, with many more built-in models, and tools for building literally trillions of new ones. Stella4D includes everything from Great Stella, but adds support for 4D polytopes too. 4D models can be projected into 3D, and you can see their 3D cross-sections and nets in real-time. The programs are fun and easy to use.

Click here for feature comparison between products. Small Stella can display and print nets for over 300 polyhedra. Small Stella Features: Rotate polyhedra on the screen by dragging the mouse with the left button down. See screen shots.Download free demo version of Small Stella.Purchase full version of Small Stella. Dissection Fallacy -- from Wolfram MathWorld. A dissection fallacy is an apparent paradox arising when two plane figures with different areas seem to be composed by the same finite set of parts. In order to produce this illusion, the pieces have to be cut and reassembled so skillfully, that the missing or exceeding area is hidden by tiny, negligible imperfections of shape. A strikingly simple and enlightening example can be constructed by dissecting an checkerboard in four pieces as depicted (left figure).

The middle and right figures then seem to demonstrate that the same pieces can give rise to two different polygons having area and , respectively. However, a closer look at the slanted sides of the trapezoidal and triangular pieces shows that they cannot be aligned as implied in the above fallacious illustrations. . , respectively, and hence have distinct slopes.

Versus ) is too small to be perceived by the eye. Note that the dissection cuts the sides of the squares according to the proportion 5:3. List of prime knots. From Wikipedia, the free encyclopedia In the mathematical theory of knots, prime knots are those knots that are indecomposable under the operation of knot sum. They are listed here for quick comparison of their properties and varied naming schemes. Table of prime knots[edit] Six or fewer crossings[edit] Seven crossings[edit] Eight crossings[edit] Nine crossings[edit] Ten crossings[edit] Notes[edit] Jump up ^ Originally listed as both 10161 and 10162 in the Rolfsen table. See also[edit] External links[edit] A Few of My Favorite Spaces: The Topologist's Sine Curve - Roots of Unity - Scientific American Blog Network. There are four basic properties of sets that beginning analysis and topology students see: open, closed, compact, and connected.

Of those properties, it seems like connectedness should be the easiest. Connected has a pretty clear meaning in English. But it's surprisingly difficult to get the mathematical definition just right. The topologist's sine curve is one of the examples that helps illuminate exactly what it means to be connected. As a regular English word, we usually think of connectedness as a property of two things: A and B are connected if they overlap in some way or if you can get from A to B.

In mathematics, connectedness is a property of one set. How do we make the English idea mathematical and apply it to one object? Connectedness is a little more subtle. What was the problem? All that work just to define connectedness! This space is the graph of the function f(x)=sin(1/x) for x in the interval (0,1] joined with the point (0,0). Why is it connected?

The Infinite Earring. The Mathematical Magic of the Fibonacci Numbers. This page looks at some patterns in the Fibonacci numbers themselves, from the digits in the numbers to their factors and multiples and which are prime numbers. There is an unexpected pattern in the initial digits too. We also relate Fibonacci numbers to Pascal's triangle via the original rabbit problem that Fibonacci used to introduce the series we now call by his name. We can also make the Fibonacci numbers appear in a decimal fraction, introduce you to an easily learned number magic trick that only works with Fibonacci-like series numbers, see how Pythagoras' Theorem and right-angled triangles such as 3-4-5 have connections with the Fibonacci numbers and then give you lots of hints and suggestions for finding more number patterns of your own. Take a look at the Fibonacci Numbers List or, better, see this list in another browser window, then you can refer to this page and the list together. 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987 ..More.. 1.1 The Final Digits or.

Classeur : Journals. Folk theorem (game theory) For an infinitely repeated game, any Nash equilibrium payoff must weakly dominate the minmax payoff profile of the constituent stage game. This is because a player achieving less than his minmax payoff always has incentive to deviate by simply playing his minmax strategy at every history. The folk theorem is a partial converse of this: A payoff profile is said to be feasible if it lies in the convex hull of the set of possible payoff profiles of the stage game. The folk theorem states that any feasible payoff profile that strictly dominates the minmax profile can be realized as a Nash equilibrium payoff profile, with sufficiently large discount factor. For example, in the Prisoner's Dilemma, both players cooperating is not a Nash equilibrium. The only Nash equilibrium is given by both players defecting, which is also a mutual minmax profile.

In mathematics, the term folk theorem refers generally to any theorem that is believed and discussed, but has not been published. 1. 2. 3. 2. 3. The Golden Section - the Number and Its Geometry. Contents of this Page The icon means there is a Things to do investigation at the end of the section. The icon means there is an interactive calculator in this section. 1·61803 39887 49894 84820 45868 34365 63811 77203 09179 80576 ..More.. What is the golden section (or Phi)? Also called the golden ratio or the golden mean, what is the value of the golden section? A simple definition of Phi There are just two numbers that remain the same when they are squared namely 0 and 1. One definition of the golden section number is that to square it you just add 1 or, if we let this value be denoted by the upper-case Greek letter Phi Φ in mathematics: Phi2 = Phi + 1 In fact, there are two numbers with this property, one is Phi and another is closely related to it when we write out some of its decimal places.

Here is a mathematical derivation (or proof) of the two values. The two values are : 1/2 + √5/2 and 1/2 – √5/2 or 1·6180339887... and –0·6180339887... A bit of history... <-------- 1 ---------> A G B g 1–g. Game Theory. First published Sat Jan 25, 1997; substantive revision Wed May 5, 2010 Game theory is the study of the ways in which strategic interactions among economic agents produce outcomes with respect to the preferences (or utilities) of those agents, where the outcomes in question might have been intended by none of the agents.

The meaning of this statement will not be clear to the non-expert until each of the italicized words and phrases has been explained and featured in some examples. Doing this will be the main business of this article. First, however, we provide some historical and philosophical context in order to motivate the reader for the technical work ahead. 1. Philosophical and Historical Motivation The mathematical theory of games was invented by John von Neumann and Oskar Morgenstern (1944).

Despite the fact that game theory has been rendered mathematically and logically systematic only since 1944, game-theoretic insights can be found among commentators going back to ancient times. Visually stunning math concepts which are easy to explain. Demonstrating the importance of dynamical systems theory -- ScienceDaily. Two new papers demonstrate the successes of using bifurcation theory and dynamical systems approaches to solve biological puzzles.

The articles appear online in the Journal of General Physiology on June 27. In companion papers, Akinori Noma and colleagues from Japan first present computer simulations of a model for bursting electrical activity in pancreatic beta cells, and then use bifurcation diagrams to analyze the behavior of the model. In his Commentary accompanying the articles, Arthur Sherman (National Institutes of Health) proposes that the methods demonstrated in these two papers have broader implications and demonstrate the increasingly important role of dynamical systems approaches in the field of biology.

Mathematical modeling is an important tool in understanding complex cellular processes. Two new papers demonstrate the successes of using bifurcation theory and dynamical systems approaches to solve biological puzzles. Fibonacci Numbers and The Golden Section in Art, Architecture and Music. This section introduces you to some of the occurrences of the Fibonacci series and the Golden Ratio in architecture, art and music. Contents of this page The icon means there is a Things to do investigation at the end of the section. 1·61803 39887 49894 84820 45868 34365 63811 77203 09179 80576 ..More.. The Golden section in architecture The Parthenon and Greek Architecture The ancient Greeks knew of a rectangle whose sides are in the golden proportion (1 : 1.618 which is the same as 0.618 : 1).

The Acropolis (see a plan diagram or Roy George's plan of the Parthenon with active spots to click on to view photographs), in the centre of Athens, is an outcrop of rock that dominates the ancient city. Links Modern Architecture The Eden Project's new Education Building The Eden Project in St. California Polytechnic Engineering Plaza As a guiding element, we selected the Fibonacci series spiral, or golden mean, as the representation of engineering knowledge. The United Nations Building in New York Music Art. 4th Dimension Cube-flatland: Cubes Fall Through Flatland. Untitled. The Tower of Hanoi. Mathematicians and psychologists don't cross paths that often and when they do you wouldn't expect it to involve an (apparently) unassuming puzzle like the Tower of Hanoi.

Yet, the puzzle holds fascination in both fields. In psychology it helps to assess someone's cognitive abilities. In maths it displays a wealth of beautiful features and leads you straight to surprisingly tricky questions that still haven't been answered. The rules of the game are straight-forward. You've got three pegs and a number of discs (eight of them in the original version), stacked up on one of the pegs in order of size, with the biggest disc at the bottom. Your task is to transfer the whole tower onto a different peg, disc by disc, but you're not allowed to ever place a larger disc onto a smaller one.

The mathematician Andreas M. The game plan The best way to see the scope of the game is to draw a network, or graph, that displays all the possible configurations and moves. Connecting the dots. Polyhedra Models. QR Code - Générateur de QR Codes Personnalisés :: QR Codes Jolis :: QR Codes Generator. A Trigonometric Trip Through Time - Introduction. Untitled. Fundamentals of Matrix Algebra. Matrix_algebra.pdf. Cauchy–Riemann equations. Holomorphic function. State-Space Analysis of Time-Varying Higher-Order Spike Correlation for Multiple Neural Spike Train Data. The Maya way of forming a right angle. Universal quantification. Calculus: early transcendentals. 20 awesomely untranslatable words from around the world. VedicMaths.Org - Home. Vedic Maths For All. Contents - The Natural Calculator.

WEB SEMÁNTICA. Protege Ontology Library. Game theory. Normal-form game. Pareto efficiency. Simply me. A Zentangle Spiral Guide. Artistic Line Designs-all free. Bayesian game. Nash equilibrium. Markov decision process. Fictitious play. Minimax. Extensive-form game. Backward induction. Nijikokun/the-zen-approach. Mindfulness and Meditation. Zentangle: Pattern-Drawing as Meditation.

L'oubli épistémologique: les ancrages du savoir dans l'histoire culturelle. Les noeuds marins. Spirograph, spirographs, spirography. Stratégies magiques au pays de Nim. Nombres premiers et cryptologie : l’algorithme RSA. La chronique de Mélisande* Origami Modulaire. Parcours bille - ils sont fort ces japonais - une vidéo Art et Création. Spicynodes : Home. Mind Mapping Finlande. String 090. Katana. Buscar la Vida. Diego Vélasquez. « Unité, dualité, multiplicité. Vers une histoire à la fois globale et plurielle »

L’État social et la mondialisation - La vie des idées. Boston Dynamics: Dedicated to the Science and Art of How Things Move. Jacques Lévy • Les mondes des anti-Monde. Le système national mondial hiérarchisé. Six moments de l'invention du monde. Tangle. Laurent Mucchielli • 1907 : la leçon d’histoire comparée de Gust. Wings 3D. Zoning. Muckety - Mapping connections of the rich, famous & influential. Frédéric Giraut • Révélations et impasses d’une approche radical. La fin de la souveraineté ? - La vie des idées. Intro, regards croisés sur la mondialisation.