Robert Talbert RobertTalbert

Generosity: Give wealth, time, and attention when and where others can be well served by it.
Charity: Look out not only for your own interests, but also the interests of others.
Leadership: Build your influence and use it to make a positive difference.
Balance: Live as a whole person with a multifaceted, multidimensional life.
Health: Build and maintain your physical, emotional, and spiritual self.
Curiosity: Seek out and pursue interesting things and never stop learning.
Adventure: Take risks, seek out new experiences, and pursue growth without fear.
Humor: Keep perspective, don't take yourself too seriously, and have fun.
Persistence: Honor your commitments, finish what you start, and don't give up.
Faith: Love God with all your heart, sould, mind, and strength -- and respond to Him with trust.

Weekly Review

This is a running list of graph isomorphism invariants, that is, properties of graphs such that...

If $G$ and $H$ are isomorphic and $G$ has the property, then $H$ also has the property.

A logically equivalent way to say this is:

If $G$ has the property but $H$ does not, then $G$ and $H$ are not isomorphic.

	# Individual Collatz computation
	def f(n):
	if n % 2 == 0:
	return n//2
	else:
	return 3*n+1

	# Create sequence of integers from the Collatz function
	# This assumes the Collatz conjecture is true LOL
	def collatz(n):

	from sympy import *

	def niceEigs(e1,e2):
	M = Matrix([[e1,0],[0,e2]])
	P = randMatrix(2,2,-3,3)
	while P.det() == 0:
	# Change the -3 and 3 if you want more variety in the entries
	P = randMatrix(2,2,-3,3)
	return PMP.inv()

	# Function to create a random nxn upper triangular matrix
	def randUT(n,lower,upper):
	A = randMatrix(n,n,lower,upper)
	for j in range(n-1):
	for i in range(j+1,n):
	A[i,j] = 0
	return A

	# Code to test this out
	A = randUT(5,-10,10)

	import networkx as nx
	import matplotlib as plt

	# Generate the edge list using a list comprehension that invokes the actual relation you want.
	# For example, here is the relation of "divides", on the set {0,1,2,..., 20}.
	# We know a divides b if b mod a = 0.

	divides_edges = [(a,b) for a in range(21) for b in range(21) if b % a == 0]
	divides_graph = nx.DiGraph(divides_edges)

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	# Code for generating random weighted graphs in networkX and printing off the edges

	import networkx as nx
	import matplotlib.pyplot as plt

	from random import *

	# Create a random graph with 10 nodes and a 50% chance of connection.
	# Change the 10 and 0.5 for graphs with more/fewer nodes and more/fewer connections.
	G = nx.random_graphs.gnp_random_graph(10,.5)