A Non-Mathematical Introduction to Using Neural Networks
The goal of this article is to help you understand what a neural network is, and how it is used. Most people, even non-programmers, have heard of neural networks. There are many science fiction overtones associated with them. And like many things, sci-fi writers have created a vast, but somewhat inaccurate, public idea of what a neural network is. Most laypeople think of neural networks as a sort of artificial brain. Neural networks are one small part of AI. The human brain really should be called a biological neural network (BNN). There are some basic similarities between biological neural networks and artificial neural networks. Like I said, neural networks are designed to accomplish one small task. The task that neural networks accomplish very well is pattern recognition. Figure 1: A Typical Neural Network As you can see, the neural network above is accepting a pattern and returning a pattern. Neural Network Structure Neural networks are made of layers of similar neurons. Conclusion

New Pattern Found in Prime Numbers
(PhysOrg.com) -- Prime numbers have intrigued curious thinkers for centuries. On one hand, prime numbers seem to be randomly distributed among the natural numbers with no other law than that of chance. But on the other hand, the global distribution of primes reveals a remarkably smooth regularity. This combination of randomness and regularity has motivated researchers to search for patterns in the distribution of primes that may eventually shed light on their ultimate nature. In a recent study, Bartolo Luque and Lucas Lacasa of the Universidad Politécnica de Madrid in Spain have discovered a new pattern in primes that has surprisingly gone unnoticed until now. They found that the distribution of the leading digit in the prime number sequence can be described by a generalization of Benford’s law. “Mathematicians have studied prime numbers for centuries,” Lacasa told PhysOrg.com. The set of all primes - like the set of all integers - is infinite.

PyBrain
Hammack Home
This book is an introduction to the standard methods of proving mathematical theorems. It has been approved by the American Institute of Mathematics' Open Textbook Initiative. Also see the Mathematical Association of America Math DL review (of the 1st edition), and the Amazon reviews. The second edition is identical to the first edition, except some mistakes have been corrected, new exercises have been added, and Chapter 13 has been extended. (The Cantor-Bernstein-Schröeder theorem has been added.) Order a copy from Amazon or Barnes & Noble for $13.75 or download a pdf for free here. Part I: Fundamentals Part II: How to Prove Conditional Statements Part III: More on Proof Part IV: Relations, Functions and Cardinality Thanks to readers around the world who wrote to report mistakes and typos! Instructors: Click here for my page for VCU's MATH 300, a course based on this book.

Connectivism et enaction...mon cheminement
Quand j'ai commencé à travailler sur le concept d'énaction de Francisco Varela, il y a eu un moment de profonds questionnements pour moi...j'ai eu le sentiment que les repères sur lesquels je m'appuyais tombaient les uns après les autres...un peu comme si je vacillais mentalement...presque physiquement d'ailleurs...impossible de dormir pendant près de deux semaines ! Ce qui émergeait pour moi à ce moment là, c'était l'idée qu'aucun modèle pré-existant n'est indispensable à la construction de mes propres représentations....c'était l'idée que l'on peut apprendre de façon autonome dans un couplage permanent au monde...coup de tonnerre dans mon ciel ! Cette idée s'imposait comme une évidence et tous mes repérages se déplaçaient et prenaient sens autour de cette approche...je ne maîtrisais rien et cela se faisait...il faut dire aussi que ce concept résonnait largement avec ma pratique et trouvait là sa cohérence ! Je me suis remise à dormir ! A lire en parallèle :

Brain size and evolution - complexity, "behavioral complexity", and brain size
From Serendip Organisms have indeed gotten more "complex" over evolutionary time, at least on a broad scale Organisms differ in "behavioral complexity" Organisms differ in brain sizeThere is some relation between "behavioral complexity" and brain size, but humans do not have the largest brains. There is a better relation between "behavioral complexity" and brain size in relation to body size. from Harry J. Jerison, Paleoneurology and the Evolution of Mind, Scientific American, January, 1976 Why should such a relation exist? Is the slope of the line 2/3 (surface to volume) or 3/4 (metabolic rate)? I'm still more interested in whether there is life on Mars?.

Connectivism
Editor’s Note: This is a milestone article that deserves careful study. Connectivism should not be con fused with constructivism. George Siemens advances a theory of learning that is consistent with the needs of the twenty first century. His theory takes into account trends in learning, the use of technology and networks, and the diminishing half-life of knowledge. It combines relevant elements of many learning theories, social structures, and technology to create a powerful theoretical construct for learning in the digital age. George Siemens Introduction Behaviorism, cognitivism, and constructivism are the three broad learning theories most often utilized in the creation of instructional environments. Learners as little as forty years ago would complete the required schooling and enter a career that would often last a lifetime. “One of the most persuasive factors is the shrinking half-life of knowledge. Some significant trends in learning: Background An Alternative Theory Connectivism

The human brain can create structures in up to 11 dimensions
Neuroscientists have used a classic branch of maths in a totally new way to peer into the structure of our brains. What they've discovered is that the brain is full of multi-dimensional geometrical structures operating in as many as 11 dimensions. We're used to thinking of the world from a 3-D perspective, so this may sound a bit tricky, but the results of this new study could be the next major step in understanding the fabric of the human brain - the most complex structure we know of. This latest brain model was produced by a team of researchers from the Blue Brain Project, a Swiss research initiative devoted to building a supercomputer-powered reconstruction of the human brain. The team used algebraic topology, a branch of mathematics used to describe the properties of objects and spaces regardless of how they change shape. "We found a world that we had never imagined," says lead researcher, neuroscientist Henry Markram from the EPFL institute in Switzerland.

Max Planck Neuroscience on Nautilus: Surprising Network Activity in the Immature Brain
One of the outstanding mysteries of the cerebral cortex is how individual neurons develop the proper synaptic connections to form large-scale, distributed networks. Now, an international team of scientists have gained novel insights from studying spontaneously generated patterns of activity arising from local connections in the early developing visual cortex. These early activity patterns serve as a template for the subsequent development of the long-range neural connections that are a defining feature of mature distributed networks. In a recently published Nature Neuroscience article, scientists at the Max Planck Florida Institute for Neuroscience, Frankfurt Institute for Advanced Studies, Goethe University of Frankfurt, and the University of Minnesota detail how they investigated the visual cortex of the ferret, an ideal model system to explore the early development of networks in the cortex. Lead image credit: sdecoret / Shutterstock