Sharp error terms for return time statistics under mixing conditions

We describe the statistics of repetition times of a string of symbols in a stochastic process. Denote by T(A) the time elapsed until the process spells the finite string A and by S(A) the number of consecutive repetitions of A. We prove that, if the length of the string grows unbondedly, (1) the distribution of T(A), when the process starts with A, is well aproximated by a certain mixture of the point measure at the origin and an exponential law, and (2) S(A) is approximately geometrically distributed. We provide sharp error terms for each of these approximations. The errors we obtain are point-wise and allow to get also approximations for all the moments of T(A) and S(A). To obtain (1) we assume that the process is phi-mixing while to obtain (2) we assume the convergence of certain contidional probabilities

Chains of infinite order, chains with memory of variable length, and maps of the interval

We show how to construct a topological Markov map of the interval whose invariant probability measure is the stationary law of a given stochastic chain of infinite order. In particular we caracterize the maps corresponding to stochastic chains with memory of variable length. The problem treated here is the converse of the classical construction of the Gibbs formalism for Markov expanding maps of the interval

Passives and Se Constructions

In this chapter we discuss some of the main properties of constructions involving participial passives, passive se, and impersonal se in Portuguese, focusing on its two main varieties, European and Brazilian Portuguese (henceforth EP and BP, respectively).1 When the two dialects differ, we will provide the relevant judgments each dialect assigns to the data under discussion by using the abbreviations EP and BP. The chapter is organized in five sections. Section 2 deals with participial passives, distinguishing between adjectival and verbal passives and between the participial forms of passives and compound tenses. Section 3 focuses on passive se and impersonal se constructions, comparing them with verbal passives when appropriate. Section 4 concludes the paper.info:eu-repo/semantics/publishedVersio

Failure of Supervised Chloroquine and Primaquine Regimen for the Treatment of Plasmodium vivax in the Peruvian Amazon

The widespread use of primaquine (PQ) and chloroquine (CQ), together, may be responsible for the relatively few, isolated cases of chloroquine-resistant P. vivax (CQRPV) that have been reported from South America. We report here a case of P. vivax from the Amazon Basin of Peru that recurred against normally therapeutic blood levels of CQ. Four out of 540 patients treated with combination CQ and PQ had a symptomatic recurrence of P. vivax parasitemia within 35 days of treatment initiation, possibly indicating CQ failure. Whole blood total CQ level for one of these four subjects was 95 ng/ml on the day of recurrence. Based on published criteria that delineate CQRPV as a P. vivax parasitemia, either recrudescence or relapse, that appears against CQ blood levels >100 ng/mL, we document the occurrence of a P. vivax strain in Peru that had unusually high tolerance to the synergistic combination therapy of CQ + PQ that normally works quite well

The compound Poisson limit ruling periodic extreme behaviour of non-uniformly hyperbolic dynamics

We prove that the distributional limit of the normalised number of returns to small neighbourhoods of periodic points of non-uniformly hyperbolic dynamical systems is compound Poisson. The returns to small balls around a fixed point in the phase space correspond to the occurrence of rare events, or exceedances of high thresholds, so that there is a connection between the laws of Return Times Statistics and Extreme Value Laws. The fact that the fixed point in the phase space is a repelling periodic point implies that there is a tendency for the exceedances to appear in clusters whose average sizes is given by the Extremal Index, which depends on the expansion of the system at the periodic point. We recall that for generic points, the exceedances, in the limit, are singular and occur at Poisson times. However, around periodic points, the picture is different: the respective point processes of exceedances converge to a compound Poisson process, so instead of single exceedances, we have entire clusters of exceedances occurring at Poisson times with a geometric distribution ruling its multiplicity. The systems to which our results apply include: general piecewise expanding maps of the interval (Rychlik maps), maps with indifferent fixed points (Manneville-Pomeau maps) and Benedicks-Carleson quadratic maps.Comment: To appear in Communications in Mathematical Physic