I am interested in finding out more about Poisson processes, like the arrival of cars at a toll booth. I do not have much experience with discrete event systems, so this is a learning experience for me.
There is a parking garage near an office building with an electronic sign outside it that displays how many spaces are available. I went there at 6:00 on a Friday and saw there were 635 empty spaces.
I recorded the number of space available every 5 minutes until 9:40. This does not give an exact count of the number of cars arriving, since some cars arrive, drop someone off and then leave, and similar other exceptions. But, the parking garage and building are at the end of a dead-end road, so there is little other traffic at that time of day except people going to that garage.
The graph below shows the observed number of spaces available over time, as well as a piecewise function that attempts to model the net arrival rate of cars to the parking garage.
Taking the difference in number of spaces available at each 5 minute interval gives the net arrival rate of cars. You can see this in the graph below.
I have attempted to represent the arrival rate using the Erlang distribution, which is related to the expected time between events.
The specific parameter values I used were k=79 and lambda=9. I then multiplied this entire distribution by a factor of 70 to fit it to the net total number of cars that arrived.
This does not seem to work well after 9:00 am, so after that point I have simply modeled the arrival rate with a downward sloping line with a slope of -1, since I did not have enough data to make anything meaningful from this time interval.
A couple of years ago I proposed a simple model of Spain’s future numbers of unemployed people in the post ‘Spanish Unemployment – No Rapid Road Down‘.
The Spanish government has recently posted updated quarterly unemployment figures, so I decided to update the graphs from my previous post.
Below you can see the actual figures (bold lines) and the estimates derived from my model (thin lines) in the scenario where Spain’s economy makes a gradual restoration to pre-crisis levels in the monthly probability of an unemployed person finding work and the monthly probability of an employed person losing their job.
You can see that the number of people unemployed in each category (unemployed 0-6 months, unemployed 6-12 months, etc.) seems to roughly be following the gradual restoration scenario. The model estimated that, for this scenario, the number of long-term unemployed (that is, people unemployed for 2+ years) would peak in late 2014 or early 2015 and then slowly decline over the 3 or 4 years. This estimation was made at a time when the number of long-term unemployed was still rising rapidly.
The graph below shows the overall unemployment figure (red line) and the estimates according to the ‘gradual restoration’ scenario (blue line) and ‘current conditions persist’ scenario (green line). Again, the actual figures look more like the gradual restoration case than that things are staying as bad as they were in 2013.
I would like to stress that the scenarios I published in 2013 were in no way predictions of what I thought would happen. One was simply the case of Spain’s economy slowly getting better and the other was the case where 2013 conditions persisted indefinitely.
And, from looking at only this one metric, it seems that the employment situation might be slowly improving.
I have become enamored by this silver box that was discovered at Jamestown: 3D view of Jamestown reliquary from the Smithsonian.
There are a lot of good articles about it. Here is one from The Atlantic. The box belonged to Gabriel Archer, who died in the early 1600s.
Scans have shown that the box contains bone fragments and archaeologists think it is a reliquary – a container that Catholics use to keep holy items. Below is an image I’ve stolen from the Web:
This is surprising to me since, when I visited Jamestown, I was told that this colony was established by the British in part to keep the Spanish from settling the rest of North America. The Spanish, of course, were Catholic, and one of the cornerstones of British nationalism, at the time, was fierce opposition to anything Catholic.
I was especially impressed by the door, which is fitted extremely well despite its irregular shape and has an enigmatic ‘M’ scratched into.
To the best of my knowledge, the archaeologists have not opened the box, so there are no images of the inside.
I wanted to figure how it might have been constructed, so I decided to build one for myself from 22-gauge sterling silver.
I measured the proportions from the Smithsonian’s 3D scan. I have changed the design of the door somewhat, because this is the first time I have made a door like this, so I did not want to have to deal with the tapered shape that only covers a portion of the surface. Instead, my has parallel edges and extends the length of the face.
I have not yet fully polished and cleaned it. There is still some firescale to remove before I might try to scratch and ‘M’ into it.
Inside I put four pieces of silver leftover from a previous project and held them in place with vitreous enamel.
Overall, I am happy with the results so far and have only grown more impressed by what people were able to accomplish 400 years ago without modern equipment.
More about this reliquary and other artifacts
Sterling silver (7g). 18K gold wire.
The idea here was to take the C-shaped ring format from the flip ring and bridge the gap with gold wire.
The silver band was made from an old project where I etched text onto a silver sheet, so you can see some of the letters on the inside of the band.
Here was my first effort at the rotating decoration (now melted). I tried to put too much enamel into the silver form I made and ended up melting the decoration. I had a similar problem with the stock-and-flow cufflinks. More practice with enamel is needed, I guess. Here is the inspiration for the flip ring, which a friend bought in the Dominican.
I found this bit of amber for sale loose in a shop in Gdansk, Poland, and decided to make a ring for it from a block of sterling silver that I worked down into sheet and wire by hand. This ring took a bit more work and re-work than I anticipated and the result includes a defect at the side of the ring opposite the amber, though this is noticeable mostly from the inside of the ring and much less from the outside.
I went through several iterations on the design of the setting. I first considered a standard bezel cup (a flat silver plate with a ridge around it), but wanted a more-open design that would allow more light in. I also considered flat plate with tabs around it that would fold up around the amber (essentially, a bezel cup with only multiple short sections of the ridge, instead of the entire ridge).
Eventually, I settled on the design above. The setting is made from two square wires joined to the ring at their mid-points. The amber is placed atop the wires and the four ends of the wires bent up and over the amber to hold it securely. The ends of the wires are filed and shaped a bit so that they are rounded, instead of being sharp. Overall, I am happy with how the setting turned out and would use this style again if I ever have a similar stone to work with.
I put a small piece of 24K gold leaf on the ring itself, under the setting that holds the amber, to make the underside of the setting yellow in color. (This is similar to how I added gilding to the center of the head of the fasola pin). This piece is very small though and I do not think it really does anything to affect the piece. So, next time I would leave that out.