A theory of experiment
This article aims at clarifying the language and practice of scientific experiment, mainly by hooking observability on calculability.
cs.AI↗
arXiv subjects
Pierre Albarede
Publications and source records attributed to Pierre Albarede.
Weighing operator perturbation from quasi-critical source system response
In Hilbert space, a linear source-to-flux problem in the critical (zero eigenvalue) limit is ill-posed, but regularized by a constraint on a linear functional, fulfilled by tuning some control variable. For any exciting perturbation, I obtain, by spectral decomposition and perturbation theory, the regularized flux and the regularizing control variable non-linear responses. May the exciting perturbation be obtained, inversely, from observable responses? Yes, in some cases, from the existence of a weight scale, a perturbation series, determined by recursion relations, involving well-posed source problems, and the possibility of obtaining this weight scale from observables of both the unconstrained and constrained systems.
math-ph↗
Fate stochastic management and policy benchmark in 421, a popular game
Using game and probability theories, I study the French popular game 421, a perfect information stochastic stage game. The problem is to find strategies maximizing the probability of some expected utility. I only solve a player's round against providence, a problem of fate stochastic management: beyond the backward induction solution, bounded complexity motivates heuristic policies. For a unique goal utility, a simple optimal policy, ratchet, is obtained. Its result probabilities are compiled and used, for arbitrary utilities, as the logic of goal identification policies. Various policies appear, close to human behavior, and are exactly evaluated by solving the Kolmogorov equation.
math.OC↗