Regular Walks Research Articles

Biharmonic functions on groups and limit theorems for quasimorphisms along random walks

We show for very general classes of measures on locally compact second countable groups that every Borel measurable quasimorphism is at bounded distance from a quasi-biharmonic one. This allows us to deduce non-degenerate central limit theorems and laws of the iterated logarithm for such quasimorphisms along regular random walks on topological groups using classical martingale limit theorems of Billingsley and Stout. For quasi-biharmonic quasimorphism on countable groups we also obtain integral representations using martingale convergence.

Exercising the embryo

Lifestyle factors and choices are likely to emerge as the most interesting aetiological and confounding variables in the many causes of infertility and the success or failure of fertility treatment. The big three; obesity, cigarette smoking and recreational drugs are now joined by age especially of the woman, as the variables, which health care professionals struggle to influence. Helpful strategies for overweight women intending to conceive and achieve a sustainable normal weight exist but are undervalued or underutilised in favour of ‘quick-fix’ empirical fertility treatment rather than addressing obesity first. Kucuk and colleagues in this issue of Reproductive BioMedicine Online add further evidence of the beneficial effects of moderate levels of exercise for women undergoing assisted reproductive technology (ART), reporting substantially higher implantation and live birth rates than if there was a low level of exercise. Given that ART involves minor surgery for the oocyte retrieval, it is not a surprise that high levels of activity are not undertaken, but it is clear that immobilisation or reduced physical activity should not be advised. It is notable that the study groups here did not seem to include women at the extremes of BMI ranges, so one may speculate about how beneficial dietary advice for the underweight and dietary advice as well as exercise for the overweight might be. No doubt there are complex mechanisms involved, which are unlikely to be measurable using existing scientific tools, but this is no reason to doubt the findings in this well designed study. It is notable that none of the women undergoing ART had a high level of activity, so an enquiry about physical activity and reinforcing/advising women to maintain their normal moderate level of activity makes complete sense. Whether the benefits come from exercise induced factors acting directly on the implantation process or via complex neuroendocrine pathways is of secondary relevance, if any. As ‘research on the welfare of the human embryo’ is part of this journal’s mission statement we welcome studies such as Kucuk and colleagues have conducted. So if taking the embryo for regular walks or other forms of moderate exercise will lead to a higher chance of live birth then women should be encouraged to do so, but tread (mill) moderately.

Fatores de risco para nascimentos pré-termo em Londrina, Paraná, Brasil

The objective of this study was to identify risk factors associated with pre-term birth among live births in a hospital in Londrina, Paraná State, Brazil. Cases consisted of 328 pre-term births, and controls were 369 births with gestational age greater than 37 weeks. A multiple hierarchical logistic regression analysis was carried out. There was a significant correlation (p < 0.05) between pre-term birth and the following variables: socioeconomic status (slum residence); low age of head-of-family; maternal BMI < 19 or > 30 kg/m2; history of prematurity; history of assisted reproduction; mothers in a relationship for less than two years; maternal stress; weekly maternal alcohol consumption; insufficient prenatal care; gestational complications such as bleeding, genital tract infection, altered amniotic fluid volume, high blood pressure, and hospital admission; and twin pregnancy. Regular walks during pregnancy were a protective factor. Improved quality of prenatal care and the identification of the above factors during pregnancy may help reduce premature birth.

Animal Behavior Case of the Month

Animal Behavior Case of the Month

Regular walks slow decline in peripheral arterial function

Regular walks slow decline in peripheral arterial function

Study of the non-linear autocorrelations within the Gaussian regime

In this work we extend the recently considered toy model of Weierstrass or Levy walks with varying velocity of the walker [1] by introducing a more realistic possibility that the walk can be occasionally intermitted by its momentary localization; the localizations themselves are again described by the Weierstrass or Levy process. The direct empirical motivation for developing this combined model is, for example, the dynamics of financial high-frequency time series or hydrological and even meteorological ones where variations of the index are randomly intermitted by flat intervals of different length exhibiting no changes in the activity of the system. This combined Weierstrass walks was developed in the framework of the non-separable generalized continuous-time random walk (GCTRW) formalism developed recently [2]. This approach makes it possible to study by stochastic simulations the whole spatial-temporal range while analytically we can study only the initial, pre-asymptotic and asymptotic regions (but not the intermediate one). Our approach is possible since the Weierstrass walks is a geometric superposition of regular random walks each of which can be simply treated by stochastic simulations. This non-Markovian two-state (walking-localization) model makes possible to cover by the unified treatment a broad band of known up to now types of non-biased diffusion from the dispersive one over the normal, enhanced, ballistic, and hyperdiffusion up to the Richardson law of diffusion which defines here a part of the borderline which separates the latter from the `Levy ocean' where the total mean-square displacement of the walker diverges. We observed that anomalous diffusion is characterized here by three fractional exponents: temporal one characterizing the localized state and two, temporal and spatial ones, characterizing the walking state. By considering successive dynamic (even) exponents we constructed a series of different diffusion phase diagrams on the plane defined by the spatial and temporal fractional dimensions of the walking state. To adapt the model to the description of empirical data (or discrete time series) which are collected with a discrete time-step we used in the continuous-time series produced by the model a discretization procedure. We observed that such a procedure generates, in general, long-range non-linear autocorrelations even in the Gaussian regime, which appear to be similar to those observed, e.g., in the financial time series [3–6], although single steps of the walker within continuous time are, by definition, uncorrelated. This suggests a surprising explanation alternative to the one proposed very recently (cf. [7] and Refs. therein) although both approaches involve related variants of the well-known CTRW formalism applied yet in many different branches of knowledge [8–10].