Herself’s Artificial Intelligence

I hadn’t heard anything about wavlets in several years and then this news story caught my eye.

. . .Meningiomas are tumours of the brain and nervous system and they account for 20% of all brain tumours. Doctors have a major problem of discriminating between the four different subtypes of meningiomas but doctors face three key problems in making such a diagnois:

– The work can be painstakingly slow requiring up to two hours of analysis and expert consideration of a full “slide” of information.

– The finest tumour specialists (histopathologists) can at times come up with completely contradictory findings based on slight variations in their method of analysis.

– Currently the slides that specialists examine contain a few million pixels of data and the task of tumour diagnosis is painstakingly slow already. This problem is quite literally growing as medical equipment is coming on stream that can produce slides with hundreds of millions pixel resolution.

. . .

Now researchers in the University of Warwick’s Department of Computer Science have devised a method of using “wavelets” to provide an automated analysis of the varying texture of the tumours and guidance to doctor’s within seconds of being presented the data.

[ read more Wavelets crunch through doctor’s day to long struggle to diagnose brain tumors

Maybe wavelets are about to make a bigger splash in the world of artificial intelligence?

Learn more:
An introduction to wavelets
A really friendly guide to wavelets
Tutorial on continuous wavelet analysis
Wavelet ( Wolfram site )
Wavelets
Wavelets for computer graphics

Code:
WAILI – Wavelets C++ library ( open source )
PyWavelets – Python library ( open source )
Wavelets in Java ( source code provided)

Fractals are a fascinating toy, one can easily spend an afternoon lost in Mandelbrot or Julia sets. Mathematicians were aware of fractals as early as the 1700s but it wasn’t until we had computers to do the calculations that we really discovered fractals.

Benoit B. Mandelbrot doing research at IBM was revisiting Gaston Julia’s work with fractals (1917) when he discovered the Mandelbrot set. Fractals are simple equations that are recursively computed. These simple equations create complex shapes.

The Mandelbrot function is z = z^2 + c. z and c are complex numbers, z is set to zero, c is the position on the x ( x, yi ) plane. You recursively compute this function to obtain the Mandelbrot fractal. Black is for the numbers that do not escape to infinity, the other colors represent how many loops it takes to escape.

Fractals have found some use in artificial intelligence. In the world of computer games, fractals create plant life, clouds, mountains and other scenery that would not be possible in such detail. Parkinson’s patients are diagnosed by their gait. In 2004 a sensor was developed that measures the patient’s gait, and analyzes the gait using fractals. 2002 fractals were put to use to help predict natural disasters and better model hurricanes. More recently fractal patterns have been found in solar wind. It is hoped this information will allow us to better predict solar storms.

Fractals have been found in Jackson Pollacks paintings and are being used to try to identify real paintings from fakes. They are also being used in image compression. A more fun way to play with fractals is to use them to predict the stock and commodity markets.

Fractals ( Mandelbrot and Julia in Java – source code )

More information:
Fractal Geometry
Fractals
Math on Display, Science News Online
Genius: Benoit Mandelbrot
3D Mandelbrot images

Papers:
The Fractal Geometry of Nature, Mandelbrot ( pdf/ps )

Can a fringe branch of mathematics forecast the future? A special adviser to the CIA, Fortune 500 companies, and the U.S. Department of Defense certainly thinks so. If you listen to Bruce Bueno de Mesquita, and a lot of people don’t, he’ll claim that mathematics can tell you the future. In fact, the professor says that a computer model he built and has perfected over the last 25 years can predict the outcome of virtually any international conflict, provided the basic input is accurate. What’s more, his predictions are alarmingly specific. His fans include at least one current presidential hopeful, a gaggle of Fortune 500 companies, the CIA, and the Department of Defense. Naturally, there is also no shortage of people less fond of his work. “Some people think Bruce is the most brilliant foreign policy analyst there is,” says one colleague. “Others think he’s a quack.” . . .[ read more Good Magazine - The New Nostradamus ]

Unfortunately none of B de Mesquita’s papers were readily available. You can access several from J Stor if your school or local library has access. So I can’t verify if his predictions do in fact come true. He uses game theory, math and computer simulations to predict political outcomes. Game theory has had quite a bit of success in political predictions so it is entirely possible he has been very successful. According to B de Mesquita 90% of them have come to pass.

More information:
Math Trek: Mathematical Fortune Telling
NYU Faculty – Bruce Bueno De Mesquita

I did find several articles published in political magazines.
How foreign aid can help the poor and why it doesn’t by Bruce Bueno de Mesquita ( National Review )
The political roots of poverty: The economic logic of autocracy (National Interest )
Political Instability as a Source of Growth ( Business Wire )

See also:
Game Theory

If you are in school you should grab one of these packages at the student price:
Mathematica
Maple soft
MathLab

If you have a few dollars
MuPAD is extremely well priced compared to Mathematica, Maple and MathLab.

Following are free and open source versions for those of us no longer getting student discounts.
Sage – installs, extends and provides a front end for Maxima ( It’s a great way to get Maxima installed and running easily on your computer, versions for Win/Linux/OSX )
Maxima has native Windows and Linux Code. ( Instructions for getting it up and running on OS X )
SciLab There are downloads for Windows and Linux and a link to an OSX version.
Axiom has Linux and Windows versions and
OS X instructions
Yacas should word on all operating systems.
Octave has OSX, Linux and Windows versions.
Euler has Linux and Windows versions. It should work on OS X as well.
A link list of other open source computer algebra programs including Jasymca so you can derive and integrate on your mobile smart phone.

Because these software packages are open source you should be able to download and compile any of them for your computer if a binary version is not available.

See also on this site:Useful math websites

If you are confused or unfamiliar with some math you need for AI try these sites. Some have online books, some have examples and explanations, some are online course materials.

Searchable math sites for single topics:
Mathworld ( Wolfram )
MathSearch
Data Analysis Brief Book
MathSciNet
MathPages

Lists of online books:
AMS Books Online by Subject
Mathematics on the Web – Online books

Encyclopedia type sites:
Graph Theory Lessons

Online books and classes:
Free mathematics books
Stanford School of Engineering, online class, Convex Optimization I
Stanford School of Engineering, online class, Convex Optimization II
Stanford School of Engineering, online class, Intro to Linear Dynamical Systems
Stanford School of Engineering Online Course, Fourier Transform and its applications
Introduction to Chaos Theory
Principles of Dynamics, course page
Graph Theory Introduction
Data Analysis Brief Book
MathPages

AMS search for papers:
MathSciNet

Magazines:
+Plus Magazine

See also on this site Free and Open Source Math Software