The theoretical setting of hierarchical Bayesian inference is gaining acceptance as a framework for understanding cortical computation. In this paper, we describe how Bayesian belief propagation in a spatio-temporal hierarchical model, called Hierarchical Temporal Memory (HTM), can lead to a mathematical model for cortical circuits. An HTM node is abstracted using a coincidence detector and a mixture of Markov chains. Bayesian belief propagation equations for such an HTM node define a set of functional constraints for a neuronal implementation. Anatomical data provide a contrasting set of organizational constraints. The combination of these two constraints suggests a theoretically derived interpretation for many anatomical and physiological features and predicts several others. ...

Citation: George D, Hawkins J (2009) Towards a Mathematical Theory of Cortical Micro-circuits. PLoS Comput Biol 5(10): e1000532. doi:10.1371/journal.pcbi.1000532

"Statement: If there exists a walk that starts and ends at the same point without retracing any lines, then each point must be connected to an even number of lines. To see this is true, pick any point with an odd number of lines attached to it. Any walk that traverses every line must, in particular, traverse all the lines attached to this point. The walk visits this point on one bridge, then leaves on another, revisits the point on a different bridge, then leaves on another bridge, and so on (the walk can certainly go elsewhere in between the visits, but we don’t need to know where to make our argument). At some point, because the number of bridges connected to the point is odd, the walk enters the point but can’t leave — unless a bridge is retraced. (If ... the point we picked was the starting point of the walk, the walk would eventually leave the point but couldn’t return without retracing a line.) we can conclude that every each point must be connected to an even number of lines."

"At its heart is a formal Mathematica representation. Its inference engine is basically a large number of individually hand-engineered scripts for tapping into data which he and his team have spent the last several years gathering and "curating". For example, he has assembled tables of historical financial information about countries' GDP's and about companies' stock prices. In a small number of cases, he also connects via API to third party information, but mostly for realtime data such as a current stock price or current temperature. Rather than connecting to and relying on the current or future Semantic Web, Alpha computes its answers primarily from his own curated data to the extent possible; he sees Alpha as the home for almost all the information it needs, and will use to answer users' queries. "

I heard this on Talk of the Nation Science Friday 9/21 while leaving Charleston SC. "features hip, real-world examples, step-by-step instruction, and engaging stories of Danica’s own childhood struggles in math (and stardom). In addition, borrowing from the style of today’s teen magazines, it even includes a Math Horoscope section, Math Personality Quizzes, and Real-Life Testimonials—ultimately revealing why math is easier and cooler than readers think. "

"Using the quite simple momentum theory, we can already deduct important information about the performance of propellers. We can study the influence of the propeller diameter on efficiency as well as how it depends on flight speed or the density of the air (corresponding to a certain altitude). We learn, that an efficient propeller should have a small power loading per disk area, i.e. a large diameter is required. The momentum theory does neither take the planform of the blade into account nor the characteristics of the airfoil sections. For the design or the analysis of a propeller more sophisticated models are necessary, but the momentum theory always gives a good estimate for the maximum efficiency which we can expect. It is possible to extend the momentum theory to include rotational losses, which results in an additional efficiency loss of 2 to 5 percent for typical propellers. These losses depend on the velocity of rotation and favor low torque, high rpm conditions. "

If you have trouble viewing this page, turn style off. This used to be at http://www.well.com/~neal/cypherFAQ.html "It is likely that cypherpunks and other persons interested in crypto will feel some curiosity about my novel CRYPTONOMICON. If so, they will probably find the available information, which is aimed mostly at non-specialists, to be annoyingly long on sales pitch and frustratingly short on technical detail. The purpose of this document is to make available the sort of information that is lacking in sites and PR documents aimed at the general public. "

"The purpose of a propeller is to convert power (delivered by a rotating shaft) into thrust. It does that by accelerating a large mass of air to a higher velocity. The effectiveness with which a propeller performs this conversion is known as "efficiency". As you already know, a propeller blade is a sophisticated whirling airfoil. At a constant RPM and aircraft true airspeed, the speed of the air over any portion of the airfoil varies with the distance from the center of rotation. The maximum velocity occurs at the point of maximum thickness out near the tip. Therefore, in an effort to provide an ideal angle of attack all along the blade, the blade has a "twist" to it which varies the pitch angle of the blade from root to tip. The pitch angle of a blade (ß) is typically the angle measured at 75% of the radial distance from the center of rotation to the prop tip. As aircraft velocity increases, the angle of attack seen by the prop blade of a fixed-pitch prop will decrease. That effect limits the maximum efficiency of a fixed pitch prop to a single airspeed at a given RPM, as shown by the following plot (ref-4:13:149) of efficiency at different blade pitch angles (ß) shows."

"George Price killed himself in a squat near Euston station in the winter of 1974.: William Hamilton, who identified Price’s body, has described the scene: "A mattress on the floor, one chair, a table, and several ammunition boxes made the only furniture. Of all the books and furnishings that I remembered from our first meeting in his fairly luxurious flat near Oxford Circus there remained some cheap clothes, a two-volume copy of Proust, and his typewriter. A cheap suitcase, and some cardboard boxes contained most of his papers, others were scattered about on ammunition chests." The deathbed of an altruist can be a terrible place. Both Price and Hamilton were theoretical biologists, a discipline about as mathematical and abstruse as may be imagined; yet it was Price’s discoveries in the field which had led to his despair and death. He had reformulated a set of mathematical equation that shows how altruism can prosper in a world where it seems that only selfishness is rewarded. The equations had been discovered ten years before by Hamilton, but Price’s reworking was general and more elegant. It provided a general way to measure the direction of any selection process: this ,makes possible, in principle, a Darwinian analysis of any process you can find or imagine."

" Price was the first to show that many unsolved puzzles in animal behavior could be understood by applying the logic of game theory. Price's work stimulated Maynard Smith's interest which eventually led Maynard Smith to develop his concept of the Evolutionarily Stable Strategy (ESS: Maynard Smith & Price, 1973) and to write the classic book Evolution and the Theory of Games (Maynard Smith, 1982) George Price's Contributions to Evolutionary Genetics by Steven A. Frank (pdf) I first became aware of George Price via dear departed lemonyellow. This led me to my first encounter with Andrew Brown and The Darwin Wars. I just learned that Maynard Smith died but none of the obituaries I've seen mention Price."