Practical Model-Based Diagnosis with Qualitative Possibilistic Uncertainty

An approach to fault isolation that exploits vastly incomplete models is presented. It relies on separate descriptions of each component behavior, together with the links between them, which enables focusing of the reasoning to the relevant part of the system. As normal observations do not need explanation, the behavior of the components is limited to anomaly propagation. Diagnostic solutions are disorders (fault modes or abnormal signatures) that are consistent with the observations, as well as abductive explanations. An ordinal representation of uncertainty based on possibility theory provides a simple exception-tolerant description of the component behaviors. We can for instance distinguish between effects that are more or less certainly present (or absent) and effects that are more or less certainly present (or absent) when a given anomaly is present. A realistic example illustrates the benefits of this approach.Comment: Appears in Proceedings of the Eleventh Conference on Uncertainty in Artificial Intelligence (UAI1995

Efficient resolution of the Colebrook equation

A robust, fast and accurate method for solving the Colebrook-like equations is presented. The algorithm is efficient for the whole range of parameters involved in the Colebrook equation. The computations are not more demanding than simplified approximations, but they are much more accurate. The algorithm is also faster and more robust than the Colebrook solution expressed in term of the Lambert W-function. Matlab and FORTRAN codes are provided

On semidefinite representations of plane quartics

This note focuses on the problem of representing convex sets as projections of the cone of positive semidefinite matrices, in the particular case of sets generated by bivariate polynomials of degree four. Conditions are given for the convex hull of a plane quartic to be exactly semidefinite representable with at most 12 lifting variables. If the quartic is rationally parametrizable, an exact semidefinite representation with 2 lifting variables can be obtained. Various numerical examples illustrate the techniques and suggest further research directions

Non linear eigenvalue problems

In this paper we consider generalized eigenvalue problems for a family of operators with a polynomial dependence on a complex parameter. This problem is equivalent to a genuine non self-adjoint operator. We discuss here existence of non trivial eigenstates for models coming from analytic theory of smoothness for P.D.E. We shall review some old results and present recent improvements on this subject

Time Evolution of States for Open Quantum Systems. The quadratic case

Our main goal in this paper is to extend to any system of coupled quadratic Hamiltonians some properties known for systems of quantum harmonic oscillators related with the Brownian Quantum Motion model. In a first part we get a rather general formula for the purity (or the linear entropy) in a short time approximation. In a second part we establish a master equation (or a Fokker-Planck type equation) for the time evolution of the reduced matrix density for bilinearly coupled quadratic Hamiltonians. The Hamiltonians and the bilinear coupling can be time dependent. Moreover we give an explicit formula for the solution of this master equation so that the time evolution of the reduced density at time $t$ is connected with the reduced density at initial time $t_0$ for $t_0 \leq t <t_0 +t_c$ where $t_c\in ]0, \infty]$ is a critical time but reversibility is lost for $t \geq t_0 +t_c$

Lisp, Jazz, Aikido -- Three Expressions of a Single Essence

The relation between Science (what we can explain) and Art (what we can't) has long been acknowledged and while every science contains an artistic part, every art form also needs a bit of science. Among all scientific disciplines, programming holds a special place for two reasons. First, the artistic part is not only undeniable but also essential. Second, and much like in a purely artistic discipline, the act of programming is driven partly by the notion of aesthetics: the pleasure we have in creating beautiful things. Even though the importance of aesthetics in the act of programming is now unquestioned, more could still be written on the subject. The field called "psychology of programming" focuses on the cognitive aspects of the activity, with the goal of improving the productivity of programmers. While many scientists have emphasized their concern for aesthetics and the impact it has on their activity, few computer scientists have actually written about their thought process while programming. What makes us like or dislike such and such language or paradigm? Why do we shape our programs the way we do? By answering these questions from the angle of aesthetics, we may be able to shed some new light on the art of programming. Starting from the assumption that aesthetics is an inherently transversal dimension, it should be possible for every programmer to find the same aesthetic driving force in every creative activity they undertake, not just programming, and in doing so, get deeper insight on why and how they do things the way they do. On the other hand, because our aesthetic sensitivities are so personal, all we can really do is relate our own experiences and share it with others, in the hope that it will inspire them to do the same. My personal life has been revolving around three major creative activities, of equal importance: programming in Lisp, playing Jazz music, and practicing Aikido. But why so many of them, why so different ones, and why these specifically? By introspecting my personal aesthetic sensitivities, I eventually realized that my tastes in the scientific, artistic, and physical domains are all motivated by the same driving forces, hence unifying Lisp, Jazz, and Aikido as three expressions of a single essence, not so different after all. Lisp, Jazz, and Aikido are governed by a limited set of rules which remain simple and unobtrusive. Conforming to them is a pleasure. Because Lisp, Jazz, and Aikido are inherently introspective disciplines, they also invite you to transgress the rules in order to find your own. Breaking the rules is fun. Finally, if Lisp, Jazz, and Aikido unify so many paradigms, styles, or techniques, it is not by mere accumulation but because they live at the meta-level and let you reinvent them. Working at the meta-level is an enlightening experience. Understand your aesthetic sensitivities and you may gain considerable insight on your own psychology of programming. Mine is perhaps common to most lispers. Perhaps also common to other programming communities, but that, is for the reader to decide..

On convexity of the frequency response of a stable polynomial

In the complex plane, the frequency response of a univariate polynomial is the set of values taken by the polynomial when evaluated along the imaginary axis. This is an algebraic curve partitioning the plane into several connected components. In this note it is shown that the component including the origin is exactly representable by a linear matrix inequality if and only if the polynomial is stable, in the sense that all its roots have negative real parts