(Table S2) The reconstructed sea surface temperature (SST) over the eastern equatorial Pacific

Abundant hydroclimatic evidence from western Amazonia and the adjacent Andes documents wet conditions during Heinrich Stadial 1 (HS1, 18-15 ka), a cold period in the high latitudes of the North Atlantic. This precipitation anomaly was attributed to a strengthening of the South American summer monsoon due to a change in the Atlantic interhemispheric sea surface temperature (SST) gradient. However, the physical viability of this mechanism has never been rigorously tested. We address this issue by combining a thorough compilation of tropical South American paleorecords and a set of atmosphere model sensitivity experiments. Our results show that the Atlantic SST variations alone, although leading to dry conditions in northern South America and wet conditions in northeastern Brazil, cannot produce increased precipitation over western Amazonia and the adjacent Andes during HS1. Instead, an eastern equatorial Pacific SST increase (i.e., 0.5-1.5 °C), in response to the slowdown of the Atlantic Meridional Overturning Circulation during HS1, is crucial to generate the wet conditions in these regions. The mechanism works via anomalous low sea level pressure over the eastern equatorial Pacific, which promotes a regional easterly low-level wind anomaly and moisture recycling from central Amazonia towards the Andes.

Detailed analysis of a conservative difference approximation for the time fractional diffusion equation

Diffusion equations that use time fractional derivatives are attractive because they describe a wealth of problems involving non-Markovian Random walks. The time fractional diffusion equation (TFDE) is obtained from the standard diffusion equation by replacing the first-order time derivative with a fractional derivative of order α ∈ (0, 1). Developing numerical methods for solving fractional partial differential equations is a new research field and the theoretical analysis of the numerical methods associated with them is not fully developed. In this paper an explicit conservative difference approximation (ECDA) for TFDE is proposed. We give a detailed analysis for this ECDA and generate discrete models of random walk suitable for simulating random variables whose spatial probability density evolves in time according to this fractional diffusion equation. The stability and convergence of the ECDA for TFDE in a bounded domain are discussed. Finally, some numerical examples are presented to show the application of the present technique.

Implicit difference approximation for the time fractional diffusion equation

In this paper, we consider a time fractional diffusion equation on a finite domain. The equation is obtained from the standard diffusion equation by replacing the first-order time derivative by a fractional derivative (of order $0<\alpha<1$ ). We propose a computationally effective implicit difference approximation to solve the time fractional diffusion equation. Stability and convergence of the method are discussed. We prove that the implicit difference approximation (IDA) is unconditionally stable, and the IDA is convergent with $O(\tau+h^2)$, where $\tau$ and $h$ are time and space steps, respectively. Some numerical examples are presented to show the application of the present technique.

Difference-based meta-analytic procedures for between-participant and/or within-participant designs : a tutorial review for sports and exercise scientists

The aim of this paper is to provide a contemporary summary of statistical and non-statistical meta-analytic procedures that have relevance to the type of experimental designs often used by sport scientists when examining differences/change in dependent measure(s) as a result of one or more independent manipulation(s). Using worked examples from studies on observational learning in the motor behaviour literature, we adopt a random effects model and give a detailed explanation of the statistical procedures for the three types of raw score difference-based analyses applicable to between-participant, within-participant, and mixed-participant designs. Major merits and concerns associated with these quantitative procedures are identified and agreed methods are reported for minimizing biased outcomes, such as those for dealing with multiple dependent measures from single studies, design variation across studies, different metrics (i.e. raw scores and difference scores), and variations in sample size. To complement the worked examples, we summarize the general considerations required when conducting and reporting a meta-analysis, including how to deal with publication bias, what information to present regarding the primary studies, and approaches for dealing with outliers. By bringing together these statistical and non-statistical meta-analytic procedures, we provide the tools required to clarify understanding of key concepts and principles.