This article reviews the application of various notions from the theory of dy-namical systems to the analysis of numerical approximation of initial value problems over long time intervals. Standard error estimates comparing individual trajectories are of no direct use in this context since the error constant typically grows like the exponential of the time interval under consideration. Instead ...

In this opening introductory paper, we discuss the possibility that scaleinvariant correlations may be a feature of biological and possibly even social systems. We illustrate this possibility by reviewing recent work at Boston University. Speci® cally, we focus ® rst on the apparent scale-invariant correlations in non-coding deoxyribonucleic acid (DNA) and show that this feature can be used to ...

Computer-based assessment of many cognitive processes (eg, anticipatory and response readiness processes) requires the use of invariant stimulus display times (SDT) and intertrial intervals (ITI). Although designs with invariant SDTs and ITIs have been used in functional magnetic resonance imaging (fMRI) research, such designs are problematic for fMRI studies because of collinearity issues. Thi...

We construct a data-driven dynamical system model for macroscopic variable the Reynolds number of high-dimensionally chaotic fluid flow by training its scalar time-series data. use machine-learning approach, reservoir computing construction model, and do not knowledge physical process dynamics in procedure. It is confirmed that an inferred obtained from approximates actual one each various time...

Abstract The fine-tuning of the universe for life, idea that constants nature (or ratios between them) must belong to very small intervals in order life exist, has been debated by scientists several decades. Several criticisms have emerged concerning probabilistic measurement life-permitting intervals. Herein, a Bayesian statistical approach is used assign an upper bound probability tuning, whi...

For a quadratic Thurston map having two distinct critical points and $n$ postcritical points, we count the number of possible dynamical portraits. We associate elastic graph spines to several hyperbolic rational functions. These functions have four real coefficients, invariant intervals. The are constructed such that each has embedding energy less than one. supporting examples Dylan Thurston's ...

For a separable rearrangement invariant space X on $$(0,\infty )$$ of fundamental type we identify the set all $$p\in [1,\infty ]$$ such that $$\ell ^p$$ is finitely represented in way unit basis vectors ( $$c_0$$ if $$p=\infty $$ ) correspond to pairwise disjoint and equimeasurable functions. This characterization hinges upon description approximate eigenvalues doubling operator $$x(t)\mapsto ...

in this paper, we give connection between the order of the generalized baer-invariant of a pair of finite groups and its factor groups, when ? is considered to be the specific variety. moreover, we give a necessary and sufficient condition in which the generalized baer-invariant of a pair of groups can be embedded into the generalized baer-invariant of pair of its factor groups.

We present an angular analysis of the $B^{+}\rightarrow K^{\ast+}(\rightarrow K_{S}^{0}\pi^{+})\mu^{+}\mu^{-}$ decay using 9$\,\mbox{fb}^{-1}$ $pp$ collision data collected with LHCb experiment. For first time, full set CP-averaged observables is measured in intervals dimuon invariant mass squared. Local deviations from Standard Model predictions are observed, similar to those previous analyses...

In this article we consider the -stabilization of nth-order linear time-invariant dynamical systems using multiplicity-induced-dominancy-based controller design in presence delays input or output channels. A sufficient condition is given for dominancy a real root with multiplicity at least and n an integral factorization corresponding characteristic function. necessary -stabilizability analyzed...