相关论文: Cycles and Circles in Roundoff Errors

This paper is devoted to a systematic study of a class of binary trees encoding the structure of rational numbers both from arithmetic and dynamical point of view. The paper is divided into two parts. The first one is a critical review of…

Due to the limited number of bits in floating-point or fixed-point arithmetic, rounding is a necessary step in many computations. Although rounding methods can be tailored for different applications, round-off errors are generally…

In this paper, we investigate temporal clusters of extremes defined as subsequent exceedances of high thresholds in a stationary time series. Two meaningful features of these clusters are the probability distribution of the cluster size and…

Sequences have become first class citizens in supervised learning thanks to the resurgence of recurrent neural networks. Many complex tasks that require mapping from or to a sequence of observations can now be formulated with the…

Asymmetric systematic errors arise when there is a non-linear dependence of a result on a nuisance parameter. Their combination is traditionally done by adding positive and negative deviations separately in quadrature. There is no sound…

A new family of error-correcting codes, called Fourier codes, is introduced. The code parity-check matrix, dimension and an upper bound on its minimum distance are obtained from the eigenstructure of the Fourier number theoretic transform.…

We report an inconsistency found in probability theory (also referred to as measure-theoretic probability). For probability measures induced by real-valued random variables, we deduce an "equality" such that one side of the "equality" is a…

Fracterms are introduced as a proxy for fractions. A precise definition of fracterms is formulated and on that basis reasonably precise definitions of various classes of fracterms are given. In the context of the meadow of rational numbers…

A few years ago we identified a recursion that works directly with the gaps among the generators in each stage of Eratosthenes sieve. This recursion provides explicit enumerations of sequences of gaps among the generators, which are known…

Chaos is widely understood as being a consequence of sensitive dependence upon initial conditions. This is the result of an instability in phase space, which separates trajectories exponentially. Here, we demonstrate that this criterion…

After Boltzmann and Gibbs, the notion of disorder in statistical physics relates to ensembles, not to individual states. This disorder is measured by the logarithm of ensemble volume, the entropy. But recent results about measure…

Although a system is described by a well-known set of equations leading to a deterministic behavior, in the real world the value of a measurand obtained by an experiment will mostly scatter. Accordingly, an uncertainty is associated with…

Cycling chaos is a heteroclinic connection between several chaotic attractors, at which switching between the chaotic sets occur at growing time intervals. Here we characterize the coherence properties of these switchings, considering…

As a contribution to the inverse scattering problem for classical chaotic systems, we show that one can select sequences of intervals of continuity, each of which yields the information about period, eigenvalue and symmetry of one unstable…

This paper considers the joint distribution of elements of a random sample and an order statistic of the same sample. \ The motivation for this work stems from the important problem in reliability analysis, to estimate the number of…

In a stationary ergodic process, clustering is defined as the tendency of events to appear in series of increased frequency separated by longer breaks. Such behavior, contradicting the theoretical "unbiased behavior" with exponential…

Over the past two decades, several consistent procedures have been designed to infer causal conclusions from observational data. We prove that if the true causal network might be an arbitrary, linear Gaussian network or a discrete Bayes…

We analyze record-breaking events in time series of continuous random variables that are subsequently discretized by rounding down to integer multiples of a discretization scale $\Delta>0$. Rounding leads to ties of an existing record,…

The notion of drift refers to the phenomenon that the distribution, which is underlying the observed data, changes over time. Albeit many attempts were made to deal with drift, formal notions of drift are application-dependent and…

The goals of this paper are to obtain theoretical models of what happens when a computer calculates the rotation set of a homeomorphism, and to find a good algorithm to perform simulations of this rotation set. To do that we introduce the…