## Archive for the ‘mathematics’ tag

## More free Stanford Online classes beginning in Jan.

Human Computer Interfaces

Game Theory

Probabilistic Graphical Models

Computer Science 101

Software as a Service

Machine Learning

Natural Language Processing

Cryptography

Design and Analysis of Algorithms I

and

Lean Launchpad

Technology Entrepreneurship

I can’t recommend these classes enough. I’ve taken the iPhone Development, Intro to Artificial Intelligence, Intro to Databases, and Machine Learning classes.

It’s my thought that the future of education will not be 4 year degrees on site, but life long learning at home.

If you need to brush up on some math first try Khan Academy, Wolfram Math World.

## How to get Octave and GNUPlot working on OSX

Install Octave per directions.

To start Octave from a command line create the following file and place it with permissions 755 in /user/local/bin

file name: Octave

#!/bin/bash

open /Applications/Octave.app

Next edit /Applications/Octave.app/Contents/Resources/bin/mkoctfile

Add these lines to the bottom of the file:

# fixes to make gnuplot behave

CFLAGS=”-m32 ${CFLAGS}”

FFLAGS=”-m32 ${FFLAGS}”

CPPFLAGS=”-m32 ${CPPFLAGS}”

CXXFLAGS=”-m32 ${CXXFLAGS}”

LDFLAGS=”-m32 ${LDFLAGS}”

Install per directions.

Edit the file /Applications/Gnuplot.app/Contents/Resources/bin/gnuplot

Edit the 5th and 6th lines below and save

# Setting up various path information variables that are needed to

# startup the Gnuplot program.

GNUPLOT_HOME=”${ROOT}”

PATH=”${ROOT}/bin:${PATH}”

# DYLD_LIBRARY_PATH=”${ROOT}/lib:${DYLD_LIBRARY_PATH}”

DYLD_LIBRARY_PATH=”${ROOT}/lib”

DYLD_FRAMEWORK_PATH=”${ROOT}/lib:${DYLD_FRAMEWORK_PATH}”

More information:

Stack Overflow directions to fix GNUPlot to work with Octave on OSX

## Cuckoo Search Algorithm

Cuckoos have an aggressive reproduction strategy that involves the female laying her fertilised eggs in the nest of another species so that the surrogate parents unwittingly raise her brood. Sometimes the cuckoo’s egg in the nest is discovered and the surrogate parents throw it out or abandon the nest and start their own brood elsewhere.

The team base their design search on three simple principles that emerge from the cuckoo’s strategy:

* First, each cuckoo lays one egg (a design solution) at a time, and dumps it in a randomly chosen nest.

* Second, the best nests with a high quality egg (better solution) carry over to the next generation.

* Third, the number of available host nests is fixed, and a host and there is a finite probability of the cuckoo in the nest being discovered.The team have encapsulated these three principles in a mathematical formula that they then converted to computer software code. The various design parameters and constraints are fed to the software, which tests each “egg” discarding some based on lack of fitness and sending the successful solutions through a second round and so on until an optimal solution emerges.

The team has carried out standard mathematical design tests on their cuckoo search, which itself has now been optimised and also compared it with particle swarm optimisation and other techniques to show that it is more efficient than these other approaches to engineering design of a welded beam and a spring, two key engineering components of many structures. Read more

More information:

Engineering Optimisation by Cuckoo Search ( arXiv paper )

Other papers by Xin-She Yang

## Lecture notes on Network Information Theory

If you are interested in network information theory you might want to check out this pdf of combined lecture notes from several graduate classes.

Network information theory deals with the fundamental limits on information flow in networks and optimal coding techniques and protocols that achieve these limits. It extends Shannon’s point-to-point information theory and the Ford–Fulkerson max-flow min-cut theorem to networks with multiple sources and destinations, broadcasting, interference, relaying, distributed compression and computing. Although a complete theory is yet to be developed, several beautiful results and techniques have been developed over the past forty years with potential applications in wireless communication, the Internet, and other networked systems.

This set of lecture notes, which is a much expanded version of lecture notes used in graduate courses over the past eight years at Stanford, UCSD, CUHK, UC Berkeley, and EPFL, aims to provide a broad coverage of key results, techniques, and open problems in network information theory. The lectures are organized in a “top-down” manner into four parts: background, single-hop networks, multi-hop networks, and extensions. The organization attempts to balance the introduction of new techniques and new models. Extensions (if any) to many users and large networks are discussed throughout. The lectures notes provide a unified, simplified, and formalized treatment of achievability using a few basic lemmas. The proofs in the lecture notes use elementary tools and techniques, which should make them accessible to graduate students in EE, CS, Statistics, and related fields as well as to researchers and practitioners in industry.

More Information:

First improvement to max flow algorithm in 10 years announced by MIT

## Yet another computing language, R the language of statistics

Yet another year, yet another dozen languages. Some times it seems as if all my time gets sapped up learning new languages. R is growing rapidly in popularity making news on Slashdot and the NYT late last year.

R provides a graphics package for visualizing your data, a data editor, data manipulation and has C/C++ interfaces. When R is open it provides a set of windows allowing you to interact with your data. The instruction manuals, tutorials, source code for Linux, OSX and Windows are available for free at the R Project site

R is also the name of a popular programming language used by a growing number of data analysts inside corporations and academia. It is becoming their lingua franca partly because data mining has entered a golden age, whether being used to set ad prices, find new drugs more quickly or fine-tune financial models. Companies as diverse as Google, Pfizer, Merck, Bank of America, the InterContinental Hotels Group and Shell use it.

But R has also quickly found a following because statisticians, engineers and scientists without computer programming skills find it easy to use.

“R is really important to the point that it’s hard to overvalue it,” said Daryl Pregibon, a research scientist at Google, which uses the software widely. “It allows statisticians to do very intricate and complicated analyses without knowing the blood and guts of computing systems.”

It is also free. R is an open-source program, and its popularity reflects a shift in the type of software used inside corporations. Open-source software is free for anyone to use and modify. I.B.M., Hewlett-Packard and Dell make billions of dollars a year selling servers that run the open-source Linux operating system, which competes with Windows from Microsoft. Most Web sites are displayed using an open-source application called Apache, and companies increasingly rely on the open-source MySQL database to store their critical information. Many people view the end results of all this technology via the Firefox Web browser, also open-source software. R, the software, finds fans in data analysts read more . . .

See also:

@RStats tips and examples

An Introduction to R

The R Project for Statistical Computing

Revolutions: How R is disrupting a billion dollar market

The iGraph Library for Complex Network Research

SPOT: An R Package for Automatic and Interactive Tuning of Optimization Algorithms by Sequential Parameter Optimization (Download SPOT)