No-arbitrage conditions and absolutely continuous changes of measure

We study the stability of several no-arbitrage conditions with respect to absolutely continuous, but not necessarily equivalent, changes of measure. We first consider models based on continuous semimartingales and show that no-arbitrage conditions weaker than NA and NFLVR are always stable. Then, in the context of general semimartingale models, we show that an absolutely continuous change of measure does never introduce arbitrages of the first kind as long as the change of measure density process can reach zero only continuously.Comment: 14 pages. Arbitrage, Credit and Informational Risks (C. Hillairet, M. Jeanblanc and Y. Jiao, eds.), Peking University Series in Mathematics, Vol. 6, World Scientific, 201

Random Latin squares and Sudoku designs generation

Uniform random generation of Latin squares is a classical problem. In this paper we prove that both Latin squares and Sudoku designs are maximum cliques of properly defined graphs. We have developed a simple algorithm for uniform random sampling of Latin squares and Sudoku designs. It makes use of recent tools for graph analysis. The corresponding SAS code is annexed

Why we live in the Computational Universe

To better understand the deep significance of our best physical theories it could be interesting to compare our Universe with its models. It may happen that the differences between the model and reality can be made indistinguishable, to the point that it may seem acceptable to consider reality as a gigantic program, a 'mother computation' running in a Universal Computer. The computational interpretation of reality is here adopted for introducing concepts that are common in computer science, they may offer a new insight. For instance, code and memory usage optimization techniques are common in computer science because they improve the performances at a reduced hardware cost. According to the concepts discussed in this paper, the possibility of recognizing the effects of optimization rules in a physical reality will allow us to discriminate if our reality is fundamental or the result of a large computation. Conversely, code and memory optimization has side effects, if it is present in our Universe it can produce many interesting phenomena, some seem readily recognizable, others only wait to be discovered.Comment: This is an excerpt from an article accepted by Space Technology and Applications International Forum (STAIF 2006) February 12-16, 2006, Albuquerque Hilton Hotel. Space applications omitted. Title changed accordingly. 6 pages with 1 figure added for version

Epigenetic Tracking: Implementation Details

"Epigenetic Tracking" is the name of a model of cellular development that, coupled with an evolutionary technique, becomes an evo-devo (or "artificial embryology", or "computational development") method to generate 2d or 3d sets of artificial cells arbitrarily shaped. 'In silico' experiments have proved the effectiveness of the method in devo-evolving any kind of shape, of any complexity (in terms of number of cells, number of colours, etc.); being shape complexity a metaphor for organismal complexity, such simulations established its potential to generate the complexity typical of biological systems. Moreover, it has also been shown how the underlying model of cellular development is able to produce the artificial version of key biological phenomena such as embryogenesis, the presence of "junk DNA", the phenomenon of ageing and the process of carcinogenesis. The objective of this document is not to provide new material (most of the material presented here has already been published elsewhere): rather, it is to provide all details that, for lack of space, could not be provided in the published papers and in particular to give all technical details necessary to re-implement the method.Comment: 26 pages, 20 figure