Homotopy continuation is an approach to solving a system of equations by annealing between the solution of a known system and the system of interest.

A two-dimensional Turing machine with a very simple set of rules but complicated emergent behavior.

Tries to provide a unified treatment of analytic methods in combinatorics. Might be important to know how to create "averages" of combinatorially exploding things.

Peter Norvig shows how to achieve 80 to 90% accuracy for English spelling correction in 20 lines of python code.

"This design of a minimalistic universal computer was motivated by my desire to come up with a concrete definition of Kolmogorov Complexity, which studies randomness of individual objects."

Explains Shor’s algorithm (a quantum algorithm for factoring) without using a single ket sign, or for that matter any math beyond arithmetic.

How can we automatically build a problem-specific representation that is more tractable than the general space?

An algorithm M is described that solves any well-defined problem p as quickly as the fastest algorithm computing a solution to p, save for a factor of 5 and low-order additive terms.

Draft of a textbook on computational complexity theory. Basic complexity classes, lower bounds for concrete computational models and more advanced topics.

An upper bound on the speed of evolution is derived. The bound concerns the amount of genetic information which is expressed in observable ways in various aspects of the phenotype. Typically it can't increase faster than a few bits per generation.

A model of self-referential dynamics.

Introduces a general and in a certain sense time-optimal way of solving one problem after another, efficiently searching the space of programs that compute solution candidates.

Alan Turing proved in 1936 that a general algorithm to decide for all program-input pairs whether a program will halt or run forever cannot exist.

A Unified Approach to Problems in Pattern Recognition and Artificial Intelligence.

For any non-trivial property of partial functions, the question of whether a given algorithm computes a partial function with this property is undecidable.

Solomonoff induction is a mathematically rigorous, idealized form of induction, that is, predicting what will happen in the future based on prior experiences.

The VC dimension (for Vapnik Chervonenkis dimension) is a measure of the capacity of a statistical classification algorithm.

New discoveries about algorithms are leading scientists beyond the Church-Turing Thesis. Super-recursive algorithms offer prospects for algorithms of much greater computing power and efficiency.

Market mechanisms suggest how a EURISKO-like system could operate without level boundaries or protected sets of supervisory heuristics.

A filter that detects new or anomalous patterns.

A naive Bayes classifier (also known as Idiot's Bayes) is a simple probabilistic classifier based on applying Bayes' theorem with strong (naive) independence assumptions.

Sequential Decisions based on Algorithmic Probability

An introduction to Shannon information and Shannon entropy