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Regression and Algorithmic Information Theory
Samuel Epstein
In this paper we prove a theorem about regression, in that the shortest description of a function consistent with a finite sample of data is less than the combined conditional Kolm…
A Quantum Outlier Theorem
Samuel Epstein
In recent results, it has been proven that all sampling methods produce outliers. In this paper, we extend these results to quantum information theory. Projectors of large rank mus…
On the Algorithmic Information Between Probabilities
Samuel Epstein
We extend algorithmic conservation inequalities to probability measures. The amount of self information of a probability measure cannot increase when submitted to randomized proces…
Uniform Tests and Algorithmic Thermodynamic Entropy
Samuel Epstein
We prove that given a computable metric space and two computable measures, the set of points that have high universal uniform test scores with respect to the first measure will hav…
How to Compress the Solution
Samuel Epstein
Using derandomization, we provide an upper bound on the compression size of solutions to the graph coloring problem. In general, if solutions to a combinatorial problem exist with…
On the Existence of Anomalies, The Reals Case
Samuel Epstein
The Independence Postulate (IP) is a finitary Church-Turing Thesis, saying mathematical sequences are independent from physical ones. Modelling observations as infinite sequences o…
On the Existence of Anomalies
Samuel Epstein
The Independence Postulate (IP) is a finitary Church-Turing Thesis, saying mathematical sequences are independent from physical ones. IP implies the existence of anomalies.
Some Implications of the Independence Postulate for Physics
Samuel Epstein
The Many Worlds Theory and Constructor Theory are in conflict with the Independence Postulate. The conflict with the Many Worlds Theory is shown through the existence of a finite e…
A Quantum EL Theorem
Samuel Epstein
In this paper, we prove a quantum version of the EL Theorem. It states that non-exotic projections of large rank must have simple quantum states in their images. A consequence to t…