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record breaking consider keeping track of the world record for some quantity x say earthquake magnitude or longjump
a pin is thrown tumbling in the air what is the probability distribution of the angle theta1 between the pin and the
1 implement the covariant ica algorithm and apply it to toy data2 create algorithms appropriate for the situations a x
four points are selected at random on the surface of a sphere what is the probability that all of them lie on a single
if the top row of pascals triangle which contains the single number lsquo1 is denoted row zero what is the sum of all
can a finite set of 2n distinct points in a two-dimensional space be split in half by a straight linebull if the points
consider the binary threshold neuron in k 3 dimensions and the set of points x 1 0 00 1 00 0 11 1 1 find a parameter
in this chapter we constrained all our hyperplanes to go through the origin in this exercise we remove this
what is the capacity of the axon of a spiking neuron viewed as a communication channel in bits per second see mackay
is the gaussian approximation to pw d alpha too heavy-tailed or too light-tailed or both it may help to consider pw d
how to measure a classifiers quality youve just written a new classification algorithm and want to measure how well it
eriks puzzle in a stripped-down version of conways game of life cells are arranged on a square grid each cell is either
implement this learning rule and investigate empirically its capacity for memorizing random patterns also compare its
explain why the value of eta is not important for the hopfield network defined aboveactivity rule a hopfield networks
adaptive basis functions alternatively we might make a function yx from basis functions that depend on additional
let the power spectrum be a gaussian function of frequency since the fourier transform of a gaussian is a gaussian the
1 what is the input to the recursive filter such that its state sequence and the transmission are the same as those of
investigate these power laws does density evolution predict them can the design of a code be used to manipulate the
derive the ideal soliton distribution at the first iteration t 0 let the number of packets of degree d be h0d show
fill in the details in the proof of lubys main theorem that receiving k k 2 lnsdeltas checks ensures that all the
optimize the degree distribution of a digital fountain code for a file of k 10 000 packets pick a sensible objective
construct a simple example to illustrate the fact that the digital fountain decoder of section 502 is suboptimal - it
f every transmitted packet were created by adding together source packets at random with probability 12 of each source
implement an optimal digital fountain decoder that uses the method of richardson and urbanke 2001b derived for fast
a heavy string is tied at one end to a movable support and to a light thread at the other end as shown in figure 15-e12