Category Theory, Entropy and Information Theory

Just for reference, but this looks awfully relevant..

n-Category Cafe May 10, 2011 's entry: Entropies vs. Means (Tom Leinster) as a start, which then takes us to Entropy as a functor and specifically A characterization of entropy in terms of information loss.

This takes us neatly to Reyni's paper A. Rényi, Measures of information and entropy, in Proceedings of the 4th Berkeley Symposium on Mathematics, Statistics and Probability 1960, pp. 547–561.

The thesis being:

Given an ontology, we can calculate the entropy of a set of attributes/classes from that ontology, ie, the entropy of a function that selects a sub-set of that ontology. This is of course complicated by dependencies between attributes within that ontology, eg: star-sign <---> date-of-birth  etc.

For each sub-set we can construct a further set of functions that partition the ontology as above - thus creating a partial ordering of functions (and a semi-lattice where all functions can be ground to a bottom value by a function f O -> _|_ which effectively removes everything giving an entropy of 1, ie: pure randomness and loss of all information.

A privacy preserving function is one that introduces more entropy, ie: obfusicates or anonymised any data passing through. However, There are certain other properties that need to be investigated, such as aspects over the original ontology - not all information is PII etc. Does this imply some weighting in the entropy calculation or something more exotic such as a matrix structure.

This might fit in nicely with some earlier work on trajectories of information....

Dawn

A somewhat forgotten (or badly marketed) mission to investigate asteroids Vesta and Ceres. Anyway, Dawn has captured its first image of Vesta:

NASA's Dawn Captures First Image of Nearing Asteroid

JPL Press Release

This image shows the first, unprocessed image obtained by NASA's Dawn spacecraft of the giant asteroid Vesta in front of a background of stars. Image credit: NASA/JPL-Caltech/UCLA/MPS/DLR/IDA Enlarge Image

May 11, 2011 - PASADENA, Calif. -- NASA's Dawn spacecraft has obtained its first image of the giant asteroid Vesta, which will help fine-tune navigation during its approach. Dawn is expected to achieve orbit around Vesta on July 16, when the asteroid is about 188 million kilometers (117 million miles) from Earth.

Signs of dark matter from Minnesota mine

Signs of dark matter from Minnesota mine

Possible evidence for WIMPs reported, supporting claims of Italy-based experiment

 

By Ron Cowen Web edition : Tuesday, May 3rd, 2011

An experiment in Minnesota is the first to bolster a long-contested claim that detectors a continent away have found evidence of particles called WIMPs.
WIMPs are theorized particles considered to be leading candidates for dark matter, invisible material believed to make up more than 80 percent of the matter in the universe.  In the Minnesota experiment, called COGENT, a hockey puck–sized chunk of germanium deep in a former iron mine attempts to record rare collisions with WIMPS.
In 15 months’ worth of data, COGENT researchers detected a seasonal variation in the collision rate — higher in summer and lower in winter — similar to that seen for 13 years by a larger experiment, using different detectors, in Italy. Researchers with that experiment, DAMA/LIBRA, have attributed the results to the Earth’s motion through a cloud of WIMPs (for weakly interacting massive particles) (SN: 5/10/08, p. 12). But many physicists have doubted that interpretation because, until now, no other experiment had found similar results.

And an earlier article on this from the same author. And the obligatory Wikipedia reference to WIMPs.

Pioneers, Voyagers and New Horizons

Very nice diagram showing the positions of Pioneers 10 and 11, Voyagers 1 and 2 and New Horizons from AOPD (6 May 2011)

Graphs...

Seen this particular structure before somewhere (another story...), but something to keep an eye on:

Enso Introduction by William Cook (via LtU)

Ensō is a theoretically sound and practical reformulation of the concepts of model-driven software development. Ensō is based on first-class structural descriptions, invertable transformations, generic operations and interpretation.


Structures in Ensō are a specialized kind of graph, whose nodes are either primitive data or collections of observable properties, whose values are either nodes or collections of nodes. From a programming language viewpoint this may seem an odd choice for data representation. However, it is essentially the Entity-Relationship (ER) model, also known as Information Models, which is widely used in the design of relational databases and is also the basis for Class Diagrams in the Unified Modeling Language (UML), which describe the structure of networks of objects. The key point is that structures in Ensō are viewed holistically as graphs, not as individual values or traditional sums-and-products data structures.

and...

Peter Hawkins et al, Data Representation Synthesis (also via LtU)

We consider the problem of specifying combinations of data structures
with complex sharing in a manner that is both declarative
and results in provably correct code. In our approach, abstract data
types are specified using relational algebra and functional dependencies.
We describe a language of decompositions that permit the
user to specify different concrete representations for relations, and
show that operations on concrete representations soundly implement
their relational specification. It is easy to incorporate data
representations synthesized by our compiler into existing systems,
leading to code that is simpler, correct by construction, and comparable
in performance to the code it replaces.