Related papers: Rosenbrock-Wanner Methods: Construction and Missio…
We prove that we can identify three types of pointwise behaviour in the regularity of the (generalized) Rosenblatt process. This extends to a non Gaussian setting previous results known for the (fractional) Brownian motion. On this purpose,…
We attempt to trace the history and development of Markov chain Monte Carlo (MCMC) from its early inception in the late 1940s through its use today. We see how the earlier stages of Monte Carlo (MC, not MCMC) research have led to the…
In this issue we demonstrate the very inspiring role of the continuous-time random walk (CTRW) formalism and its numerous modifications thanks to their flexibility and various applications as well its promising perspectives in different…
This article summarizes the various ways one may use to construct the Skew Brownian motion, and shows their connections. Recent applications of this process in modelling and numerical simulation motivates this survey. This article ends with…
We review the history of the development of the Chandra X-ray Observatory from our personal perspective. This review is necessarily biased and limited by space since it attempts to cover a time span approaching 5 decades.
In the last two decades recurrence plots (RPs) were introduced in many different scientific disciplines. It turned out how powerful this method is. After introducing approaches of quantification of RPs and by the study of relationships…
Since its original formulation by Isaac Newton in 1685, the problem of determining bodies of minimal resistance moving through a fluid has been one of the classical problems in the calculus of variations. Initially posed for cylindrically…
The work done by Isaac Newton more than three hundred years ago, continues being a path to increase our knowledge of Nature. To better understand all the ideas behind it, one of the finest ways is to generalize them to wider situations. In…
Generalized Robertson-Walker spacetimes extend the notion of Robertson-Walker spacetimes, by allowing for spatial non-homogeneity. A survey is presented, with main focus on Chen's characterization in terms of a timelike concircular vector.…
In this paper, we present a general theory of motion planning for kinematic systems. This theory has been developed for long by one of the authors in a previous series of papers. It is mostly based upon concepts from subriemannian geometry.…
The aim of this article is twofold. First, we shall review and analyse the Neo-Kantian justification for the application of probabilistic concepts in physics that was defended by Hans Reichenbach early in his career, notably in his…
In this work (PartI) the qualitative analysis of statics and dynamics of defects and textures in liquid crystals is performed with help of meanders and train tracks. It is argued that similar analysis can be applied to 2+1 gravity. More…
The aim of this paper is to discuss the constructivity of the method originally introduced by U. Bessi to approach the phenomenon of topological instability commonly known as Arnold's Diffusion. By adapting results and proofs from existing…
Markov Chain Monte Carlo (MCMC) methods have become a cornerstone of many modern scientific analyses by providing a straightforward approach to numerically estimate uncertainties in the parameters of a model using a sequence of random…
In this article we consider importance sampling (IS) and sequential Monte Carlo (SMC) methods in the context of 1-dimensional random walks with absorbing barriers. In particular, we develop a very precise variance analysis for several IS…
In this paper, we propose several solutions to guide an older adult along a safe path using a robotic walking assistant (the c-Walker). We consider four different possibilities to execute the task. One of them is mechanical, with the…
Although RNNs have been shown to be powerful tools for processing sequential data, finding architectures or optimization strategies that allow them to model very long term dependencies is still an active area of research. In this work, we…
Heisenberg's breakthrough in his July 1925 paper that set in motion the development of Quantum Mechanics through subsequent papers by Born, Jordan, Heisenberg and also Dirac (from 1925 to 1927) is reexamined through a modern lens. In this…
One of the first fully quantitative distance matrix visualization methods was proposed by Jan Czekanowski at the beginning of the previous century. Recently, a software package, RMaCzek, was made available that allows for producing such…
In the year 1905 Albert Einstein published four papers that raised him to a giant in the history of science of all times. These works encompass the photon hypothesis (for which he obtained the Nobel prize in 1921), his first two papers on…