# Progress Blog Post 3

In this blog post, we represent better assigned weighting for data reconstruction, also we provide representation of splined raw and reconstructed data and the same two representation for fitted data.

Finally, we have optimized weighting of function according to different events occurring in the past, such as wars, plagues, etc. To explain again, we have took known data and supposed that population between have changed linearly. In unknown periods, in years of great importance , such as plague, we have decreased the population to a certain level (weight). This was done in previous blog for some dates on linear line, yielding unrealistic data. During last few weeks, the data was optimized, in a way that we have corrected a function including a previous correction(weighting). Obtained data is presented below.

We wanted to see how would look like functions and we used method of fitting data to be able to have insight into it. First we applied it to raw data of population, and we got unrealistic polynomial function. We tested it for orders between 1 and 15 and for raw data we got the best solution for 7th order, however we concluded there was a problem with fact that we had too few data points. Also, we did for reconstructed data with same range of orders, and here we ended up with 10th order as the best result. We can notice that fitting is more precise than for raw data. Still, order of polynomial is a consequence of highly dispersed data on short range.

As well, we tried to get better representation of the raw data and reconstructed data by applying spline interpolation between know values. For raw data case, we got function that had too big ‘hills’ or ‘valleys’ in the places with deficit of data about population, while for reconstructed data function looked more realistic, since there were larger supply of intermediate points that we reconstructed. Those intermediate points are main factor for better spline representation.

On the end, all historical events which were used in estimating the population of Venice are presented by timeline which was done on website(http://www.timetoast.com). Since timeline is based on Flash platform, and only Java script representations are possible to post, timeline is provided as link below. Every dot on timeline is including a picture which describes an event. One should note that some old events did not have a direct picture to be described, thus we used our creativity. As add-on, a sentence or two was added as description of event. For events that we didn’t know which day or month happened we assigned date the 5th of May to them. This timeline has purpose of helping people to realise what was an event and to be able to get a new knowledge presented on it. We want to use it as a demo in our final representation since it would be much easier to comprehend whole historical events flow and population state over the time.

For remaining period to finish our project we will dedicate our effort to further development of represented data and to try new better visualisation of timeline as a demo for final presentation.