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Mathematical Framework:
"... → study of elasticplastic oscillators with noise 2 References in Engineering literature: → an elastoplastic 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 rando ..."
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→ study of elasticplastic oscillators with noise 2 References in Engineering literature: → an elastoplastic 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
A Mathematical Framework for the
, 2004
"... 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 somatosensory cortex, visual cortex and motor control are briefly ..."
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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 somatosensory cortex, visual cortex and motor control
The Unit Graphs Mathematical Framework
, 2013
"... We are interested in the choice of a graphbased knowledge representation formalism that would allow for the representation, manipulation, query, and reasoning over linguistic knowledge of the Explanatory Combinatorial Dictionary (ECD) of the MeaningText Theory (MTT). We show that neither the seman ..."
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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
Between MDPs and SemiMDPs: A Framework for Temporal Abstraction in Reinforcement Learning
, 1999
"... 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 exte ..."
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Cited by 569 (38 self)
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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 Active Steganalysis
, 2003
"... 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 is formulat ..."
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Cited by 22 (1 self)
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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
Anomalous transport: A mathematical framework
 MR 99b:81046 162
, 1998
"... 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 characterize ..."
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Cited by 18 (8 self)
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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
A Formal Mathematical Framework for
"... 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 syst ..."
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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 realtime hybrid systems usually define behaviors purely in terms of determinism or sometimes nondeterminism. However, this is insufficient as realtime dynamical systems very often exhibit uncertain behaviour. To address this issue, we develop a semantic model, Probabilistic Constraint Nets (PCN), for probabilistic hybrid systems.
Mathematical Framework Feature Vectors
, 2008
"... This work has been performed in collaboration with Simon K. ..."
A mathematical framework for risk assessment
 New Technologies, Mobility and Security, Signals and Communication
, 2007
"... Abstract. Risk assessment is an important step in the development of a secure system: its goal is to identify the possible threats to a system, their impact and, henceforth, to evaluate the connected risks. Although several systematic approaches have been developed to perform a risk assessment task ..."
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Cited by 4 (3 self)
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sessment task, the current methodologies rely on the quantitative evaluations 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
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