Put  some dots randomly on a piece of paper and draw the smallest possible circle around them. Recently I have been struggling with this little problem. Finally I understood that my solution was wrong and the follwoing algorithm was correct:

1. Choose any two points, Pi and Pj

2. Construct the circle whose center is at the midpoint of the line connecting Pi and Pj and which passes through Pi and Pj.  If this circle contains all points, then the center of the circle is the optimal X. Otherwise, choose a point Pk outside the circle.

3. If the triangle determined by Pi, Pj and Pk is a right triangle or an obtuse triangle, rename the two points opposite the right angle or the obtuse angle as Pi and Pj  and go to step 2.  Otherwise, the three points determine an acute triangle. Construct the circle passing through the three points. (The center is the intersection of the perpendicular bisectors of two sides of the triangle.) If the circle contains all the points, stop,else, go to 4.

4. Choose some point Pl not in the circle, and let Q be the point among {Pi, Pj, Pk} that is greatest distance from Pl. Extend the diameter (from the circle center) through the point Q into a line that divides the plane into two half planes. Let the point R be the point among {Pi, Pj, Pk} that is in the half plane opposite Pl. With the points Q, R, and Pl, go to step 3.

D. Jack Elzinga, Donald W. Hearn, “Geometrical Solutions for some minimax location problems,”  Transportation Science, 6, (1972), pp 379 – 394.[url]

Lately, I have been poking around to group a list of resources for those that wants to code using python, but for their sake have decided to buy a mac. I have to admit that I did this many times already, but this was the first time during an operating system change (10.3 -> 10.4).

What I have understood can be summarized as follows:

1. there is a huge mess of distributions for python for mac; Usually the OSX system comes with an already-out-dated version of python. For instance the 10.4 comes with the python 2.3.5 while there is already the 2.4.1. Developers around the globe offer their replacement package for the official version: [1]. [2].

2. If you look for an IDE there are only a few possibilities: [1] (commercial); and [2] which requires the PyObjC, which is stuck at OSX 10.3.

3. An alternative may be to use Eclipse with a specific plugin.

4. The official page of pythonmac.org contains a list of packages that are ported to the OSX platform and that allows to integrate more deeply some coding functionalities. Additionally using PyObjC is possible to package a script in a standalone cocoa application.

5. Rui Carmo maintain also a good resource page with pointers, as for the integration with Tiger, the only good pointer I found is here. Too many hacks though, so I will stay with the official distribution for now and try to make things simple as far as I can.

This might be one of the research direction to where the topic of my thesis can lead me. Different problem can emerge from this approach:

defining the semantic similarities of different messages, maybe using a markov model; categorise and tag each message to correspond to a spatial/cognitive criteria; create a convergence from the folksonomies to the categories of the messages.

Two problems might be interesting:

– define the size of the cluster of aggregation

– attribute a descriptor to the cluster

NB I have to check Amy Soller work with Markov models.

Today, with Alessandro, we spent some time discussing a cheap and simple euristic that can make us smart in approximating the positions of the GSM antennas. Patrick pointed us to this web page that explain a nice  and simple method. In the mean time we came out with an alternative that I am hoping to implement in the next couple of days …

Here’s a simple problem for you: “Put  some dots randomly on a piece of paper and draw the smallest possible circle around them.”  How hard can that be?

I found this nice java applet to understand in two seconds what exactly is the last square method. It is a nice example of microworld.

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I am interested in how to combine the hidden markov model technique with the transversal analysis of the posted messages on the ShoutSpace/STAMPS environment.

I have to find some more papers on HMM and natural language processing.

N. Eagle and A. Pentland. Reality mining: Sensing complex social systems. Journal of Personal and Ubiquitous Computing, June 2005. [url]

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This paper report the analysis of the mobile usage patterns of 100 users which have been loged during the period of 9 months. The subjects were equipped with a mobile phone hacked with a logging software (the same of the context project of the university of helsinki) that could record all the activity on the phone, plus the bluetooth proxemics with other devices and the cell id information.

The authors developed two techniques of datamining with complex method, namely a hidden Markov Model and a Gaussian mixture model, using which they obtained interesting results in patter recognition.

One of the interesting results was the ability to stimulate serendipidity of encounters, informing the users of the structure of the other’s pattern of interaction. The authors rely in this a great value for collaborative work.

Overall the paper contains a good overview of the statistical methods used to analyse and infer the pattern from the dataset.

(via)

This is a nice example of Italian technology that can be useful, patented and sold abroad. I wonder why the medical field is one of the only context where international results are produced.

The probing device emits radio waves similar to the cell phones that are reflected by the body, returning a signal that indicated the health state of the tissues.

I have been testing the GSM Tracker build by our students for the semester project. Apparently it work well on the series 60 and 40. I tested it with the Nokia 3660 and the Nokia 6630. There seems to be still a little glitch with the signal strength.

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People can be divided in two categories: chocolate eaters and chocolate buyers. To survive in this world one should try hard in not falling in any of these two.

Mauro Cherubini, 28-04-2005