→ study of elastic-plastic oscillators with noise 2 References in Engineering literature: → an elasto-plastic model with noise (Karnopp & Scharton, 1966) → estimation of the variance of the deformation (Feau, 2007) 2 / 44 Motivation: risk analysis of failure for mechanical structures under random forcing

We develop a mathematical framework of continuum neural field theory as the beginning point for an analysis of the global brain. Arguments for and against this approach are developed. Applications to cortical dynamics and learning in somato-sensory cortex, visual cortex and motor control

the semantic web formalisms nor the Conceptual Graphs Formalism are suitable for this task, and we justify the introduction of the new Unit Graphs (UGs) framework. We introduce the fundamental concepts of the UGs mathematical framework: the Unit Types hierarchy and the Unit Graphs. We then show how they may

Learning, planning, and representing knowledge at multiple levels of temporal abstraction are key, longstanding challenges for AI. In this paper we consider how these challenges can be addressed within the mathematical framework of reinforcement learning and Markov decision processes (MDPs). We

A mathematical framework for steganalysis is presented in this paper with linear steganography being the main focus. A mathematically formal definition of steganalysis is given. Then, active steganalysis defined as the extraction of a hidden message with little or no a priori information

We develop a mathematical framework allowing to study anomalous transport in homogeneous solids. The main tools characterizing the anomalous transport properties are spectral and diffusion exponents associated to the covariant Hamiltonians describing these media. The diffusion exponents

The development of autonomous agents, such as mobile robots and software agents, has generated considerable research in recent years. Robotic systems, which are usually built from a mixture of continuous (analog) and discrete (digital) components, are often referred to as hybrid dynamical systems. Traditional approaches to real-time hybrid systems usually define behaviors purely in terms of determinism or sometimes non-determinism. However, this is insufficient as real-time dynamical systems very often exhibit uncertain behaviour. To address this issue, we develop a semantic model, Probabilistic Constraint Nets (PCN), for probabilistic hybrid systems.

linear feedback systems using distributions

This work has been performed in collaboration with Simon K.

-sessment task, the current methodologies rely on the quantitative evalu-ations of experts in a substantial way. This paper addresses the problem of detaching the methodology results from the subjective judgements of experts, by formalising a risk assessment methodology in an appropriate mathematical framework