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Say’s Law, also known as the Law of Markets, is an important component of classical economics and formulated thus:
It is worthwhile to remark that a product is no sooner created than it, from that instant, affords a market for other products to the full extent of its own value. When the producer has put the [...]

Say’s Law »

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Lisp Reference

By Kai | Published: March 15, 2010

A collection of lisp snippets I’ll be adding to as I learn more.

Factorial (recursive function)

(defun factorial (n)                                
  (if (= n 0)                                       
    1                                             
    (if (> n 0)                                   
      (* n (factorial (- n 1))))))
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Hidden Layer Neurons

By Kai | Published: October 25, 2009

Neuron

Hidden layer neurons are large groups of neurons between an input layer and output layer– your sensory receptors and your motor actions. Their size, type, and network topology (who connects to who) affect the complexity of problems they solve and decisions they make. Successful networks find solutions because they are statistically favored. Neurons compete for resources. With successful predictions, they grow stronger. Those that fail to make patterns out of chaos weaken. These cells even contain programming to destroy themselves, a process called apoptosis. This occurs at a rapid rate early in life as the brain first organizes itself, then slows down in adulthood.

We seem to be able to direct our own mental processes, somehow– which is absurd to me. One part of the brain exerting control of another? Different patterns resonating in electrochemical waves: metastable yet amplifying. Consciousness subsuming itself with each passing moment. Alive. It seems awfully political: these neurons in such chaotic, demanding labor to produce a transient mind. They are decision-making agents: competing for scarce resources, struggling for strong connections, forming computational alliances. The competition for statistical significance may be experienced as a tug of attention, a drive to act, or a flash of inspiration. The steps neurons take to assemble personal truth are invisible.

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jQuery Rollover Nav Bar

By Kai | Published: August 30, 2009

Here’s a simple jquery nav bar with animated rollover effects. The page titles roll up to reveal page descriptions underneath. This was originally designed for the Amuse Bouche Homepage.

Here’s the jQuery, hover.js:

$(function() {
    var navButtons = '#home, #cast, #pictures, #videos, #mail';
    $(navButtons).hover(function() {
        $(this).stop().animate({'top':'-30px'});
        }, function () {
        $(this).stop().animate({'top':'0px'})
        });
});

Get the code >>

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Simple Matrix Multiplication in Python

By Kai | Published: August 26, 2009

In this tutorial we’ll look at some simple matrix multiplication tools in Python. The arrays are constructed using lists within lists, and the multiplication itself is implemented using for loops. The program works well for small arrays, but really starts bogging down at sizes 500×500 and above. Anyone doing serious work will want to check out NumPy, which has matrix operations built-in and runs several thousand times faster. In Part 2 I’ll compare NumPy’s performance to other optimized methods.

Let’s feast our eyes on the function definitions we’ll be using in matrix.py:

import random
from time import *
import cProfile
 
def zero(m,n):
    # Create zero matrix
    new_matrix = [[0 for row in range(n)] for col in range(m)]
    return new_matrix
 
def rand(m,n):
    # Create random matrix
    new_matrix = [[random.random() for row in range(n)] for col in range(m)]
    return new_matrix
 
def show(matrix):
    # Print out matrix
    for col in matrix:
        print col 
 
def mult(matrix1,matrix2):
    # Matrix multiplication
    if len(matrix1[0]) != len(matrix2):
        # Check matrix dimensions
        print 'Matrices must be m*n and n*p to multiply!'
    else:
        # Multiply if correct dimensions
        new_matrix = zero(len(matrix1),len(matrix2[0]))
        for i in range(len(matrix1)):
            for j in range(len(matrix2[0])):
                for k in range(len(matrix2)):
                    new_matrix[i][j] += matrix1[i][k]*matrix2[k][j]
        return new_matrix
 
def time_mult(matrix1,matrix2):
    # Clock the time matrix multiplication takes
    start = clock()
    new_matrix = mult(matrix1,matrix2)
    end = clock()
    print 'Multiplication took ',end-start,' seconds'
 
def profile_mult(matrix1,matrix2):
    # A more detailed timing with process information
    # Arguments must be strings for this function
    # eg. profile_mult('a','b')
    cProfile.run('matrix.mult(' + matrix1 + ',' + matrix2 + ')')

Go forth and multiply >>

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