October 04, 2004

A two envelopes puzzle

[Math_] Here is a version of the problem from Bertsekas and Tsitsiklis: "You are handed two envelopes, and you know that each contains a positive integer dollar amount and that the two amounts are different. You select at random one of the two envelopes and after looking at the amount inside, you may switch the envelopes if you wish. Is there a strategy that will increase above 1/2 the probability of ending up with the envelope with the larger amount?"

This is not to be confused with the related and much more popular two envelopes paradox. I first heard this problem in a different form where the two numbers did not have to be positive or integers.

I think it is instructive to look at the different variants of this problem where the two numbers come from: a finite interval, a half open interval, and a circular structure like hours or angles.

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July 21, 2004

Some experiments with a Naive Bayes WSD system

Deniz Yuret. In Proceedings of SENSEVAL-3, the Third International Workshop on the Evaluation of Systems for the Semantic Analysis of Text

Abstract: This document describes the architecture of a WSD system that participated in the SENSEVAL-3 English all words evaluation exercise. The system uses two independent statistical models, one based on local collocations and another based on a bag of words around the target. The model with the higher confidence provides the final answer for each instance. Both models use Naive Bayes and supervised training with different feature sets. The experiments using this system indicate that the specific smoothing parameters used for Naive Bayes make a big impact on the performance, smaller context sizes give better accuracy, and that the bag of words model adds little to the performance.

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April 02, 2004

Relationships Between Amino Acid Sequence and Backbone Torsion Angle Preferences

Özlem Keskin, Deniz Yuret, Attila Gürsoy, Metin Türkay and Burak Erman. In Proteins: Structure, Function, and Bioinformatics. 55(4):992-8. (PDF)

Abstract: Statistical averages and correlations for backbone torsion angles of chymotrypsin inhibitor 2 are calculated by using the Rotational Isomeric States model of chain statistics. Statistical weights of torsional states of phi-psi pairs, needed for the statistics of the full chain, are obtained in two different ways: 1) by using knowledge-based pairwise dependent phi-psi energy maps from Protein Data Bank (PDB) and 2) by collecting torsion angle data from a large number of random coil configurations of an all-atom protein model with volume exclusion. Results obtained by using PDB data show strong correlations between adjacent torsion angle pairs belonging to both the same and different residues. These correlations favor the choice of the nativestate torsion angles, and they are strongly context dependent, determined by the specific amino acid sequence of the protein. Excluded volume or steric clashes, only, do not introduce context-dependent phi-psi correlations into the chain that would affect the choice of native-state torsional angles.

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