Filed under: education

Pluralism for the win!

http://plato.stanford.edu/entries/relativism/

Biology:

http://en.wikipedia.org/wiki/Sex-determination_system

http://www.sciencedaily.com/releases/2008/01/080121112642.htm

Math:

http://en.wikipedia.org/wiki/Product_%28category_theory%29

http://en.wikipedia.org/wiki/Multinomial_distribution

http://en.wikipedia.org/wiki/Orthogonal_coordinates

http://en.wikipedia.org/wiki/Fa%C3%A0_di_Bruno%27s_formula

http://en.wikipedia.org/wiki/Table_of_Newtonian_series

http://en.wikipedia.org/wiki/Hyperfactorial#Factorial-like_products

http://en.wikipedia.org/wiki/Function_space

http://en.wikipedia.org/wiki/Symmetric_polynomial

Filed under: math

dummit foote prove that a+bSqrt[-5] is not euclidean domain merely by proving it is not PID. (sufficient but not necessary)

all euclidean domains must be PIDs.

http://www.math.ucsb.edu/~mckernan/Teaching/05-06/Winter/220B/l_3.pdf

Filed under: math

The fundamental assumption in the paper is that the source information is ergodic. With this

assumption, the paper proved the AEP property and capacity theorems. Therefore, one curiosity

is arisen that “what happens if the source is not ergodic?”. If the information is not ergodic, it

is reducible or periodic. If AEP property holds with this source(not ergodic), shannon’s capacity

theorem also satis¯es in this case because capacity theorem is not based on ergodic source but on

AEP property. Therefore, to ¯nd a source that is not ergodic and holds AEP property is one of

meaningful works. Following example is one of these sources.

Definition A stochastic process is said to be stationary if the joint

distribution of any subset of the sequence of random variables is invariant

with respect to shifts in the time index; that is,

Pr{X1 = x1,X2 = x2, . . . , Xn = xn}

= Pr{X1+l = x1,X2+l = x2, . . . , Xn+l = xn} (4.1)

for every n and every shift l and for all x1, x2, . . . , xn ∈ X.