Functional It\^{o} calculus and stochastic integral representation of martingales

We develop a nonanticipative calculus for functionals of a continuous semimartingale, using an extension of the Ito formula to path-dependent functionals which possess certain directional derivatives. The construction is based on a pathwise derivative, introduced by Dupire, for functionals on the space of right-continuous functions with left limits. We show that this functional derivative admits a suitable extension to the space of square-integrable martingales. This extension defines a weak derivative which is shown to be the inverse of the Ito integral and which may be viewed as a nonanticipative "lifting" of the Malliavin derivative. These results lead to a constructive martingale representation formula for Ito processes. By contrast with the Clark-Haussmann-Ocone formula, this representation only involves nonanticipative quantities which may be computed pathwise.Comment: Published in at http://dx.doi.org/10.1214/11-AOP721 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Statistical data mining for symbol associations in genomic databases

A methodology is proposed to automatically detect significant symbol associations in genomic databases. A new statistical test is proposed to assess the significance of a group of symbols when found in several genesets of a given database. Applied to symbol pairs, the thresholded p-values of the test define a graph structure on the set of symbols. The cliques of that graph are significant symbol associations, linked to a set of genesets where they can be found. The method can be applied to any database, and is illustrated MSigDB C2 database. Many of the symbol associations detected in C2 or in non-specific selections did correspond to already known interactions. On more specific selections of C2, many previously unkown symbol associations have been detected. These associations unveal new candidates for gene or protein interactions, needing further investigation for biological evidence

Convergence of a high-order compact finite difference scheme for a nonlinear Black-Scholes equation

A high-order compact finite difference scheme for a fully nonlinear parabolic differential equation is analyzed. The equation arises in the modeling of option prices in financial markets with transaction costs. It is shown that the finite difference solution converges locally uniformly to the unique viscosity solution of the continuous equation. The proof is based on a careful study of the discretization matrices and on an abstract convergence result due to Barles and Souganides.High-order compact finite differences, numerical convergence, viscosity solution, financial derivatives

High order compact finite difference schemes for a nonlinear Black-Scholes equation

A nonlinear Black-Scholes equation which models transaction costs arising in the hedging of portfolios is discretized semi-implicitly using high order compact finite difference schemes. In particular, the compact schemes of Rigal are generalized. The numerical results are compared to standard finite difference schemes. It turns out that the compact schemes have very satisfying stability and non-oscillatory properties and are generally more e±cient than the considered classical schemes.Option pricing, transaction costs, parabolic equations, compact finite difference discretizations

Rediscovering the Walisongo, Indonesia: A potential new destination for international pilgrimage

The current paper explores the tradition of Walisongo, the nine saints or nine friends of God, that according to tradition initiated the islamisation of Java in the XV and XVI centuries. Largely unknown outside of Indonesia, the Wali Songo pilgrimage remains unfamiliar in the archipelago as well. Besides allowing a deeper understanding of the roots of Indonesian religious history and of the spread and acceptance of Islam, rediscovering the Wali Songo may help to reintroduce a peaceful image of the Muslim world. In such a way, reactivating the tradition of Wali Songo outside of the country but also inside, may support the idea of a peaceful religion of traders, of scholars and culture lovers open and able to integrate the traditions of other cultural groups. The Wali Songo are said to be at the origin of pesantren (Muslim religious schools) and largely used local arts and culture in their teachings. In an area of Central and East Java where minority groups may tend to impose the views of a reformist not to say a rigorist Islam, the Wali Songo teachings may offer a ‘new common vehicle’, a synonym of understanding, peace and cultural respect. If the development of international pilgrimage activity would suppose the setting up of proper infrastructures, to do so, may also boost new areas of services that would definitely support regional developments in the largest archipelago of the world and in a country that, besides being laic and governed by the principles of Pancasila, is before all the country worldwide with the largest number of Muslim citizens. In a planet currently governed by globalization, the origins of the Wali Songo, which are still relevant, if discussed, would demonstrate that ideas and religions can be shared, peacefully, across the land and seas

Large scale statistical analysis of GEO datasets

The problem addressed here is that of simultaneous treatment of several gene expression datasets, possibly collected under different experimental conditions and/or platforms. Using robust statistics, a large scale statistical analysis has been conducted over $20$ datasets downloaded from the Gene Expression Omnibus repository. The differences between datasets are compared to the variability inside a given dataset. Evidence that meaningful biological information can be extracted by merging different sources is provided