Almost sure and moment exponential stability in the numerical simulation of stochastic differential equations

Relatively little is known about the ability of numerical methods for stochastic differential equations (SDEs) to reproduce almost sure and small-moment stability. Here, we focus on these stability properties in the limit as the timestep tends to zero. Our analysis is motivated by an example of an exponentially almost surely stable nonlinear SDE for which the Euler-Maruyama (EM)method fails to reproduce this behavior for any nonzero timestep. We begin by showing that EM correctly reproduces almost sure and small-moment exponential stability for sufficiently small timesteps on scalar linear SDEs. We then generalize our results to multidimensional nonlinear SDEs. We show that when the SDE obeys a linear growth condition, EM recovers almost surely exponential stability very well. Under the less restrictive condition that the drift coefficient of the SDE obeys a one-sided Lipschitz condition, where EM may break down, we show that the backward Euler method maintains almost surely exponential stability

Ex-ante measure of patent quality reveals intrinsic fitness for citation-network growth

We have constructed a fitness parameter, characterizing the intrinsic attractiveness for patents to be cited, from attributes of the associated inventions known at the time a patent is granted. This exogenously obtained fitness is shown to determine the temporal growth of the citation network in conjunction with mechanisms of preferential attachment and obsolescence-induced ageing that operate without reference to characteristics of individual patents. Our study opens a window on understanding quantitatively the interplay of the rich-gets-richer and fit-gets-richer paradigms that have been suggested to govern the growth dynamics of real-world complex networks.Comment: 6 pages, 3 figures, RevTex4.1, v2: minor changes, version to appear as a Rapid Communication in Phys. Rev.

Unraveling the dynamics of growth, aging and inflation for citations to scientific articles from specific research fields

We analyze the time evolution of citations acquired by articles from journals of the American Physical Society (PRA, PRB, PRC, PRD, PRE and PRL). The observed change over time in the number of papers published in each journal is considered an exogenously caused variation in citability that is accounted for by a normalization. The appropriately inflation-adjusted citation rates are found to be separable into a preferential-attachment-type growth kernel and a purely obsolescence-related (i.e., monotonously decreasing as a function of time since publication) aging function. Variations in the empirically extracted parameters of the growth kernels and aging functions associated with different journals point to research-field-specific characteristics of citation intensity and knowledge flow. Comparison with analogous results for the citation dynamics of technology-disaggregated cohorts of patents provides deeper insight into the basic principles of information propagation as indicated by citing behavior.Comment: 13 pages, 6 figures, Elsevier style, v2: revised version to appear in J. Informetric

Recalibration effects in judgments of learning: a signal detection analysis

In this study we investigated the influence of list composition on judgments of learning (JOLs). To this end, we compared JOLs assigned in a multi-cycle procedure to a set of moderately difficult word pairs. Experiment 1 revealed that when difficult new pairs were added to the study list, the mean of JOLs assigned to the moderate pairs increased as compared to the baseline. In Experiment 2, we reversed this pattern by including easy new pairs in the study list. By analyzing metacognitive ROCs (MROCs), we demonstrate that these results were caused by criterion shifts, by which participants adjusted the level of evidence needed to assign particular JOL ratings. Changes in the study list composition led to a recalibration of the JOL scale – i.e. resetting of the criteria – in order to accommodate the addition of new items. We discuss the usefulness of MROCs for detecting criterion shifts in rating tasks

Dating the Bronze Age of Southeast Asia: why does it matter?

We have dated human bone, freshwater shell, charcoal and rice grains from key sites in mainland Southeast Asia in order to establish the chronological scaffolding for later prehistory (ca 2500 BC-AD 500). In a recent report on the metal remains from the site of Ban Chiang, however, this chronology has been challenged. Here, we respond to these claims and show that they are unfounded and misleading. We maintain the integrity of the Bayesian-modelled radiocarbon results that identify the arrival of the first rice and millet farmers in mainland Southeast Asia towards the end of the 3rd millennium BC, with the first evidence for the casting of bronze by about 1100 BC. Social change that followed the establishment of metallurgy was rapid and profound

Urinary incontinence in men with Duchenne and Becker muscular dystrophy

© 2020 Morse et al. The prevalence of urinary incontinence in Duchenne and Becker muscular dystrophy (D/ BMD) is reported to be between 15 29%, this however includes ages across the lifespan, and with no description of impact on daily life. The present study, aimed to determine the prevalence of urinary incontinence in men with D/BMD, and to identify which aspects of daily life were impacted by urinary incontinence. Twenty-seven adult males, 11 with BMD and 16 with DMD, aged 20 57 years, volunteered to participate in this study. Six questionnaires were completed to provide an overview of participant mobility, urinary incontinence and distress caused by urinary incontinence. These included: The Barthel index of disability, International Consultation on Incontinence Questionnaire-Urinary Incontinence Form, Incontinence Impact Questionnaire Short Form, The Urogenital Distress Inventory, and the Brooke and Vignos scale. The prevalence of urinary incontinence within the present men with D/BMD was 37%, assessed as urine leakage of once a week or more. Those with urinary incontinence all reported only a "small amount" of urine leakage, with urinary incontinence frequency of once a week in 5/10 participants, two or three times a week in 2/10 participants, and once a day in 3/10 participants. Of those with urinary incontinence 8/10 experienced some impact on their daily life from urine leakage including travel (4/10), social aspects (5/10), and emotional aspects (8/10). All participants with urinary incontinence were bothered by some aspect, including urine leakage (9/10), and frequent urination (4/10). In conclusion, 37% of the present men with D/BMD experience urinary incontinence on a weekly or daily basis and negatively impacted aspects of life related to travel, social and emotional wellbeing. Urine leakage, and frequent urination should be considered a meaningful problem by care providers, and discussed openly with those with D/BMD

Assessing the association between oral hygiene and preterm birth by quantitative light-induced fluorescence

The aim of this study was to investigate the purported link between oral hygiene and preterm birth by using image analysis tools to quantify dental plaque biofilm. Volunteers (η = 91) attending an antenatal clinic were identified as those considered to be “at high risk” of preterm delivery (i.e., a previous history of idiopathic preterm delivery, case group) or those who were not considered to be at risk (control group). The women had images of their anterior teeth captured using quantitative light-induced fluorescence (QLF). These images were analysed to calculate the amount of red fluorescent plaque (ΔR%) and percentage of plaque coverage. QLF showed little difference in ΔR% between the two groups, 65.00% case versus 68.70% control, whereas there was 19.29% difference with regard to the mean plaque coverage, 25.50% case versus 20.58% control. A logistic regression model showed a significant association between plaque coverage and case/control status (Ρ = 0.031), controlling for other potential predictor variables, namely, smoking status, maternal age, and body mass index (BMI)

Stochastic B-series analysis of iterated Taylor methods

For stochastic implicit Taylor methods that use an iterative scheme to compute their numerical solution, stochastic B--series and corresponding growth functions are constructed. From these, convergence results based on the order of the underlying Taylor method, the choice of the iteration method, the predictor and the number of iterations, for It\^o and Stratonovich SDEs, and for weak as well as strong convergence are derived. As special case, also the application of Taylor methods to ODEs is considered. The theory is supported by numerical experiments