A Krylov subspace algorithm for evaluating the phi-functions appearing in exponential integrators

We develop an algorithm for computing the solution of a large system of linear ordinary differential equations (ODEs) with polynomial inhomogeneity. This is equivalent to computing the action of a certain matrix function on the vector representing the initial condition. The matrix function is a linear combination of the matrix exponential and other functions related to the exponential (the so-called phi-functions). Such computations are the major computational burden in the implementation of exponential integrators, which can solve general ODEs. Our approach is to compute the action of the matrix function by constructing a Krylov subspace using Arnoldi or Lanczos iteration and projecting the function on this subspace. This is combined with time-stepping to prevent the Krylov subspace from growing too large. The algorithm is fully adaptive: it varies both the size of the time steps and the dimension of the Krylov subspace to reach the required accuracy. We implement this algorithm in the Matlab function phipm and we give instructions on how to obtain and use this function. Various numerical experiments show that the phipm function is often significantly more efficient than the state-of-the-art.Comment: 20 pages, 3 colour figures, code available from http://www.maths.leeds.ac.uk/~jitse/software.html . v2: Various changes to improve presentation as suggested by the refere

An exploratory study of image and performance enhancement drug use in a male British South Asian community

Background: Consumerism of image and performance enhancement drugs (IPEDs) is a world-wide public health concern. Given anecdotal reporting of increased normalisation of IPED use and uptake of British South Asian male IPED users at UK needle and syringe exchange services, the study aimed to explore use of IPEDs among this under-researched ethnic group. Methods: 20 in depth interviews were conducted with a purposive sample of British South Asian males attending harm reduction outreach in the North East of England. The interviews explored motives for use of IPEDs, sourcing routes, information seeking, injecting behaviours and cultural and community sensitivities around IPED use among this group. The data was collected and analysed using the Interpretative Phenomenological Analysis approach (IPA). Results: Motives for use centred on the achievement of enhanced definition and density of muscle, and improved recovery from training and injuries. All participants reported initial stimulation of interest and triggers to seek information on IPEDs due to social media, community and peer messages. Diverse forms of IPED use were described, with rational and moderated use common among older participants. In contrast younger participants adopted more excessive use in seeking short cuts to attaining muscle size. Sourcing of androgenic–anabolic steroids (AAS) and growth hormones from originating countries (Pakistan, India) was reported, along with diversification of entrepreneurial activity into IPED dealing networks. Sellers were generally reported to provide effective and reliable products and mentoring to inexperienced users. Group injecting practices were common. IPED use was observed by some as health promotion medium within religious contexts. Crime deterrence and drug abstinence occurred for some while involved in AAS cycles. Conclusions: The study is intended to contribute to health policy and practice debate around the targeting of dedicated education, outreach and harm reduction for ethnic groups engaged in IPED use

Stability of central finite difference schemes for the Heston PDE

This paper deals with stability in the numerical solution of the prominent Heston partial differential equation from mathematical finance. We study the well-known central second-order finite difference discretization, which leads to large semi-discrete systems with non-normal matrices A. By employing the logarithmic spectral norm we prove practical, rigorous stability bounds. Our theoretical stability results are illustrated by ample numerical experiments

Cross-linguistic constraints and lineage-specific developments in the semantics of cutting and breaking in Japonic and Germanic

Semantic variation in the cutting and breaking domain has been shown to be constrained across languages in a previous typological study, but it was unclear whether Japanese was an outlier in this domain. Here we revisit cutting and breaking in the Japonic language area by collecting new naming data for 40 videoclips depicting cutting and breaking events in Standard Japanese, the highly divergent Tohoku dialects, as well as four related Ryukyuan languages (Amami, Okinawa, Miyako and Yaeyama). We find that the Japonic languages recapitulate the same semantic dimensions attested in the previous typological study, confirming that semantic variation in the domain of cutting and breaking is indeed cross-linguistically constrained. We then compare our new Japonic data to previously collected Germanic data and find that, in general, related languages resemble each other more than unrelated languages, and that the Japonic languages resemble each other more than the Germanic languages do. Nevertheless, English resembles all of the Japonic languages more than it resembles Swedish. Together, these findings show that the rate and extent of semantic change can differ between language families, indicating the existence of lineage-specific developments on top of universal cross-linguistic constraints