Stochastic modelling and network analysis/Modélisation stochastique et analyse de réseaux

拟议的研究由以下两个统一主题下的几个正在进行的项目组成。** 主要主题是在非线性和随机性影响大量元素行为的情况下进行数学建模，例如金融市场上商品价值的波动。在离散的情况下，我特别感兴趣的战略，导致逆转从一个收集失去的机会，为客户，到一个成功的投资组合，通过使用技术引起的现象称为帕龙多的悖论。在连续的情况下，非线性随机偏微分方程（或一些相关的离散近似方案）的伪装下的适定鞅问题需要建立，模拟和分析通过相互作用的粒子系统。我的目标是在未来几年里，我正在进行的研究项目的基本性质，这些系统，承担潜在的意义，因为它们扩展了经典极限理论的适用性，以新的数学环境的追求。** 补充主题是在某些大数据库，特别是多模式数据的异构信息网络，如社交媒体网络内的知识发现和数据挖掘背景下的统计建模。这些都需要确定的数学特征，最适合的多重比较的框架，链接预测和社区检测的目的。我计划在专门针对这些数据库的估计方法中加入层次结构。这里的新奇来自于使用先进的数据挖掘和分析技术，包括形式概念分析，对这些问题提出新的解决方案。

The proposed research is composed of several ongoing projects, under the following two unifying themes. ******The main theme is mathematical modelling in situations where nonlinearity and randomness affect the behavior of large numbers of elements in an ensemble, such as the fluctuations in value of commodities on the financial markets. In the discrete case I am specifically interested in strategies leading to the reversal from a collection of losing opportunities for the client, into a winning portfolio through the use of techniques giving rise to the phenomenon called Parrondo's paradox. In the continuous case, nonlinear stochastic partial differential equations (or some associated discrete approximation scheme) in the guise of well-posed martingale problems need to be built, simulated and analyzed via interacting particle systems. My objective for the years to come is the pursuit of my ongoing research projects on the fundamental properties of these systems, which bear potential significance as they extend the applicability of classical limit theory to new mathematical contexts. ******The complementary theme is statistical modelling in the context of knowledge discovery and data mining within certain big data bases, notably heterogeneous information networks of multi-modal data such as social media networks. These require the identification of those mathematical characteristics that best suit a framework of multiple comparisons for the purpose of link prediction and community detection. I plan to incorporate hierarchical structures in the estimation methodology specifically destined for these databases. The novelty here comes from the proposal of new solutions to these issues using advanced data mining and analysis techniques, including formal concept analysis.***********