This paper introduces an extension of recurrence analysis to symbolic sequences. Heuristic arguments based on Shannon-McMillan-Breiman theorem suggest several relations between the statistical features of ‘symbolic’ recurrence plots and the entropy per unit time of the dynamics; their practical efficiency for experimental sequences of finite length is checked numerically on two paradigmatic mod...

Process monitoring is an important research problem in numerous areas. This paper proposes a novel process monitoring scheme by integrating the recurrence plot (RP) method and the control chart technique. Recently, the RP method has emerged as an effective tool to analyze waveform signals. However, unlike the existing RP methods that employ recurrence quantification analysis (RQA) to quantify t...

An elementary approach is given to studying the recurrence relations associated with generalized heaps (or d-heaps), cost of optimal merge, and generalized divide-and-conquer minimization problems. We derive exact formulae for the solutions of all such recurrences and give some applications. In particular, we present a precise probabilistic analysis of Floyd’s algorithm for constructing d-heaps...

To improve the performances of parallelizing compilers, one must detect recurrences in scientiic programs and subject them to special parallelization methods. We present a method for detecting recurrences which is based on the analysis of Systems of Recurrence Equations. This method identiies recurrences on arrays, recurrences of arbitrary order and multi-equations recurrences. We explain how t...

The classical approach to automatic cost analysis consists of two phases. Given a program and some measure of cost, we first produce recurrence relations (RRs) which capture the cost of our program in terms of the size of its input data. Second, we convert such RRs into closed form (i.e., without recurrences). Whereas the first phase has received considerable attention, with a number of cost an...

In this paper we consider second order recurrences {Vk} and {Un} . We give second order linear recurrences for the sequences {V±kn} and {U±kn}. Using these recurrence relations, we derive relationships between the determinants of certain matrices and these sequences. Further, as generalizations of the earlier results, we give representations and trigonometric factorizations of these sequences b...

In [Koepf (1992)] it was shown how for a given holonomic function a representation as a formal power series of hypergeometric type can be determined algorithmically. This algorithm – that we call FPS algorithm (Formal Power Series) – combines three steps to obtain the desired representation. The authors implemented this algorithm in the computer algebra system Maple as c̀onvert/FormalPowerSeries...

In this paper, we propose a discussion on the robustness and performance properties of a proportional-derivative controller applied to a very flexible joint. Because of the flexible mode due to in-joint compliance, the classical collocated control does not allow to obtain good rigid mode dynamics with a correct phase margin in low and high frequency, and the non-collocated control does not allo...

Minimal solutions of three-term recurrence relations can be computed accurately by various algorithms based on the theory of continued fractions . These algorithms may be adapted to computing solutions which, though not minimal, do initially behave like a minimal solution and only later, for large arguments, diverge away from the minimal solution . This note exhibits a nontrivial example of a s...

We discuss massive scalar perturbations of a Schwarzschild black hole. We argue that quantum effects alter the effective potential near the horizon resulting in Poincaré recurrences in Green functions. Results at the semi-classical level are independent of the details of the modification of the potential provided its minimum near the horizon is inversely proportional to the square of the Poinca...