Related papers: Mathematical Encounters
We commend the authors for an exciting paper which provides a strong contribution to the emerging field of probabilistic numerics (PN). Below, we discuss aspects of prior modelling which need to be considered thoroughly in future work.
We study approximations of evolving probability measures by an interacting particle system. The particle system dynamics is a combination of independent Markov chain moves and importance sampling/resampling steps. Under global regularity…
This is a report on a workshop held August 1 to August 5, 2011 at the Institute for Computational and Experimental Research in Mathematics (ICERM) at Brown University, Providence, Rhode Island, organized by Saugata Basu, Joseph M.…
Multi-head finite automata were introduced in (Rabin, 1964) and (Rosenberg, 1966). Since that time, a vast literature on computational and descriptional complexity issues on multi-head finite automata documenting the importance of these…
We study Grothendieck's examples and ideas around complex variables in the years (1949-1957), his references to Riemann, and the influence on the Edinburgh ICM lecture (1958).
Peixoto's structural stability and density theorems represent milestones in the modern theory of dynamical systems and their applications. Despite the importance of these theorems, they are often treated rather superficially, if at all, in…
The idea of the Lehmann Symposia as platforms to encourage a revival of interest in fundamental questions in theoretical statistics, while keeping in focus issues that arise in contemporary interdisciplinary cutting-edge scientific…
Strongly anticipatory systems-that is, systems which use models of themselves for their further development-and which additionally may be able to run hyperincursive routines-that is, develop only with reference to their future states-cannot…
We consider the problem of estimating rare event probabilities, focusing on systems whose evolution is governed by differential equations with uncertain input parameters. If the system dynamics is expensive to compute, standard sampling…
In my lectures at the Les Houches Summer School 2008, I discussed central concepts of computational statistical physics, which I felt would be accessible to the very cross-cultural audience at the school. I started with a discussion of…
Intersection types are a standard tool in operational and semantical studies of the lambda calculus. De Carvalho showed how multi types, a quantitative variant of intersection types providing a handy presentation of the relational…
The talk consisted mainly in commenting in a linear way the seminal paper in 1964 by Michel Henon and graduate student Carl Heiles at Princeton University: "The applicability of the third integral of motion: Some numerical experiments" in…
We recall major findings of a systematic investigation of the mathematization of the individual sciences, conducted by the author in Bielefeld some 35 years ago under the direction of Klaus Krickeberg, and confront them with recent…
Starting from space-discretisation of Maxwell's equations, various classical formulations are proposed for the simulation of electromagnetic fields. They differ in the phenomena considered as well as in the variables chosen for…
The Brazilian National Assessment of Secondary Education (ENEM, Exame Nacional do Ensino M\'edio) has changed in 2009: from a self-assessment of competences at the end of high school to an assessment that allows access to college and…
The history of the development of Monte Carlo methods to solve the many-body problem in quantum mechanics is presented. The survey starts with the early attempts with the first available computers just after the war and extends until the…
I describe some deep-seated problems in higher mathematical education, and give some ideas for their solution -- I advocate a move away from the traditional introduction of mathematics through calculus, and towards computation and discrete…
We deal with the existence of quantitative estimates for solutions of mixed problems to an elliptic second order equation in divergence form with discontinuous coefficient. Our concern is to estimate the solutions with explicit constants,…
Partial differential equation is a powerful tool to characterize various physics systems. In practice, measurement errors are often present and probability models are employed to account for such uncertainties. In this paper, we present a…
Below are the problems that I formulated at Open Problems Session of {\it Workshop on Group Actions on Rational Varieties}, McGill University and University of Montreal, Canada, March 2002. To appear in: "Affine Algebraic Geometry"…