Dear all,
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The INRIA Rhone-Alpes at Grenoble France is looking for two good students wishing to realize their PhD in France and in relation with a LABEX or a Carnot Institute and supported by Conacyt.
Two subjects are proposed by Dr. Emmanuel Mazer at INRIA Rhone Alpes. If you or some of your collegues are interested in one of these proposals (described below) please contact Dr. Emmanuel Mazer as soon as possible at :
The dead line is May 9th, so you must move as fats as possible if you are interested in these scholarship.
General framework Our main objective is to define the basic components of probabilistic computations. We aim to develop a bottom-up hierarchical probability theory based on these components. Finally, we plan to apply this approach to the conception of new computers which could, in the future, outperform classical computers in tasks involving a direct interaction with the physical world. Living organisms have developed highly sophisticated information processing networks, operating at various time/space scales and achieving a variety of specific and adaptive functions. Compared to computers, biological systems exploit completely different substrates: membrane, macromolecules, diffusible messengers living in water environment. Unlike computers, biological systems are massively parallel, highly tolerant to component and signal variability; they do not require an accurate centralized clock. Most of these important features have already been emphasized, and some of them (e.g. parallelism or asynchrony) have been successfully implemented in modern computers and networks. However, the development of modern computers is entirely devoted to the increase in performance without changing a bit to the principles of computation. In particular, all the components must always perform deterministic and exact operations on sets of binary signals. This is a very hard constraint, which strongly impedes progress in terms of speed, miniaturization and energy consumption. Subject 1 : Probabilistic theory of computation The current concept of computation manipulates sets of binary variables using Boolean algebra. It was formally expressed by Alan Turing, and supported the design of memory devices and logical gates. Later, the concept of programmable computing opens the possibility of high-level representations and hierarchies of languages. In essence, these steps constitute our roadmap to develop probabilistic computation as an extension to logic. Our first objective will be to formalize an extension of Boolean algebra which manipulates probability distributions on binary variables. We will define a minimal set of operators, the Bayesian gates, viewed as an extension of logical gates, which, when combined, can generate any type of probabilistic computation on discrete variables. Our second objective will be to extend the notion of program to probabilistic computations. Some classical programming operations have a natural extension in terms of probabilistic computations, e.g. the sequencing of product and marginalization, the probabilistic conditional branching, the notion of sub-program, etc... We will also take benefit of the existence of dedicated software packages allowing to perform probabilistic computation on classical computers. The simulation on conventional computers of a set of Bayesian gates will constitute a proof-of-concept for this axis. Subject 2 Innovative Probabilistic hardware components One striking feature of biological information processing is that main events (molecular reconfiguration, diffusion, neurotransmitter release, ...) occur randomly, due to thermal agitation. This contrasts with digital processors, where events (like a memory flip) are triggered by a central clock. Our first objective will be to study existing nano-components which may behave stochastically when set in unconventional configuration. Though unreliable behavior is the enemy number one for logic circuit designers, it could prove extremely helpful for probabilistic computation, providing that the stochastic characteristics could be somewhat controlled or conditioned. Our objective is to show how such stochastic components could be combined, eventually with more conventional logical circuits, in order to perform basic probabilistic computations. This step constitute proof-of -concept of our project. Finally, we will specify the technical constraints that must be overcome in order to design integrated and programmable architecture dedicated to probabilistic computation.Sincerely yours,
SSIR
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