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The theory of non-uniformly hyperbolic diffeomorphisms.

Let L denote the n×n square lattice with wraparound. Call an orientation of L an assignment of a direction to each edge of L, and denote the number of orientations of L such ...

The word "pole" is used prominently in a number of very different branches of mathematics. Perhaps the most important and widespread usage is to denote a singularity of a ...

The mutual information between two discrete random variables X and Y is defined to be I(X;Y)=sum_(x in X)sum_(y in Y)P(x,y)log_2((P(x,y))/(P(x)P(y))) (1) bits. Additional ...

For a given signal, the power spectrum gives a plot of the portion of a signal's power (energy per unit time) falling within given frequency bins. The most common way of ...

A nonlinear deconvolution technique used in deconvolving images from the Hubble Space Telescope before corrective optics were installed.

Predictability at a time tau in the future is defined by (R(x(t),x(t+tau)))/(H(x(t))), and linear predictability by (L(x(t),x(t+tau)))/(H(x(t))), where R and L are the ...

A matrix whose entries are all integers. Special cases which arise frequently are those having only (-1,1) as entries (e.g., Hadamard matrix), (0,1)-matrices having only ...

R(X_1,...X_n)=sum_(i=1)^nH(X_i)-H(X_1,...,X_n), where H(x_i) is the entropy and H(X_1,...,X_n) is the joint entropy. Linear redundancy is defined as ...

A theorem from information theory that is a simple consequence of the weak law of large numbers. It states that if a set of values X_1, X_2, ..., X_n is drawn independently ...