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

Texas Brazos River Flow and Mussel Growth Reconstructions Using Stable Oxygen, Hydrogen, and Carbon Isotopes and Trace Elements

The interaction between drought and river regulation is monitored to better understand river flow mixing, evaporation, and surface-groundwater exchange in changing regional climates and in increasingly regulated waterways. I compared Brazos River stable isotope (δ^18O and δD) and electrical conductivity values with reservoir, creek, and aquifer samples in the Brazos watershed, the largest watershed in Texas. Shells from two common species of Brazos River mussel, Amblema plicata and Cyrtonaias tampicoensis, were serially-sampled in the inner and outer shell layers for δ^18O, δ^13C, and trace elements to examine the isotopic and chemical signatures of the 2011-2014 drought. Predicted aragonite δ^18O for the 2012-13 study interval has an irregular pattern that complicates development of growth chronologies in modern shells. To circumvent this problem, clumped isotope (Δ47) temperature measurements were used for interpreting segments of shell growth chronologies. To characterize the influence that biological and environmental variables have on shell chemistry, one specimen from each of the above two mussel species were studied using paired isotope-trace element analyses and cathodoluminescence. The Brazos River Alluvium Aquifer and the Lake Whitney reservoir, both on the main river channel, represent water source endmembers of dilute runoff water and evaporated saline water, respectively. The difference between river and precipitation Δ^18O, or Δ^18ORIV-PPT, a measurement of degree of evaporation, ranged from 0.9‰ for a small creek, to 2.7‰ for the Brazos River, to at least 3.7‰ in Lake Whitney. Δ^18O values and trends were similar in coeval shell transects, indicating that δ^18O is a valid chronometer when calibrated, although all shell had winter growth cessations. Δ^13C trends were similar between shells, suggesting strong environmental control influenced by upstream dam releases. The shell isotope chronologies can be used to reconstruct variation in river discharge, flow source, and salinity. Shell δ^13C, Sr/Ca, and Mn/Ca generally covaried in the shell regions sampled, and shell δ^13C is thought to be controlled by upstream dam releases based on previous work. Relationships between Sr/Ca and temperature are consistent with temperature-paced metabolic control on shell Sr/Ca as in other studies

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

Visual attention in violent offenders: Susceptibility to distraction.

Impairments in executive functioning give rise to reduced control of behavior and impulses, and are therefore a risk factor for violence and criminal behavior. However, the contribution of specific underlying processes remains unclear. A crucial element of executive functioning, and essential for cognitive control and goaldirected behavior, is visual attention. To further elucidate the importance of attentional functioning in the general offender population, we employed an attentional capture task to measure visual attention. We expected offenders to have impaired visual attention, as revealed by increased attentional capture, compared to healthy controls. When comparing the performance of 62 offenders to 69 healthy community controls, we found our hypothesis to be partly confirmed. Offenders were more accurate overall, more accurate in the absence of distracting information, suggesting superior attention. In the presence of distracting information offenders were significantly less accurate compared to when no distracting information was present. Together, these findings indicate that violent offenders may have superior attention, yet worse control over attention. As such, violent offenders may have trouble adjusting to unexpected, irrelevant stimuli, which may relate to failures in selfregulation and inhibitory control

ADI splitting schemes for a fourth-order nonlinear partial differential equation from image processing

We present directional operator splitting schemes for the numerical solution of a fourth-order, nonlinear partial differential evolution equation which arises in image processing. This equation constitutes the H−1-gradient flow of the total variation and represents a prototype of higher-order equations of similar type which are popular in imaging for denoising, deblurring and inpainting problems. The efficient numerical solution of this equation is very challenging due to the stiffness of most numerical schemes. We show that the combination of directional splitting schemes with implicit time-stepping provides a stable and computationally cheap numerical realisation of the equation

Irish general practitioner attitudes toward decriminalisation and medical use of cannabis: results from a national survey.

BACKGROUND: Governmental debate in Ireland on the de facto decriminalisation of cannabis and legalisation for medical use is ongoing. A cannabis-based medicinal product (Sativex®) has recently been granted market authorisation in Ireland. This unique study aimed to investigate Irish general practitioner (GP) attitudes toward decriminalisation of cannabis and assess levels of support for use of cannabis for therapeutic purposes (CTP). METHODS: General practitioners in the Irish College of General Practitioner (ICGP) database were invited to complete an online survey. Anonymous data yielded descriptive statistics (frequencies, percentages) to summarise participant demographic information and agreement with attitudinal statements. Chi-square tests and multi-nominal logistic regression were included. RESULTS: The response rate was 15% (n = 565) which is similar to other Irish national GP attitudinal surveys. Over half of Irish GPs did not support the decriminalisation of cannabis (56.8%). In terms of gender, a significantly higher proportion of males compared with females (40.6 vs. 15%; p < 0.0001) agreed or strongly agreed with this drug policy approach. A higher percentage of GPs with advanced addiction specialist training (level 2) agreed/strongly agreed that cannabis should be decriminalised (54.1 vs. 31.5%; p = 0.021). Over 80% of both genders supported the view that cannabis use has a significant effect on patients' mental health and increases the risk of schizophrenia (77.3%). Over half of Irish GPs supported the legalisation of cannabis for medical use (58.6%). A higher percentage of those who were level 1-trained (trained in addiction treatment but not to an advanced level) agreed/strongly agreed cannabis should be legalised for medical use (p = 0.003). Over 60% agreed that cannabis can have a role in palliative care, pain management and treatment of multiple sclerosis (MS). In the regression response predicator analysis, females were 66.2% less likely to agree that cannabis should be decriminalised, 42.5% less likely to agree that cannabis should be legalised for medical use and 59.8 and 37.6% less likely to agree that cannabis has a role in palliative care and in the treatment of multiple sclerosis (respectively) than males. CONCLUSIONS: The majority of Irish GPs do not support the present Irish governmental drug policy of decriminalisation of cannabis but do support the legalisation of cannabis for therapeutic purposes. Male GPs and those with higher levels of addiction training are more likely to support a more liberal drug policy approach to cannabis for personal use. A clear majority of GPs expressed significant concerns regarding both the mental and physical health risks of cannabis use. Ongoing research into the health and other effects of drug policy changes on cannabis use is required

Psychopathic Traits and Their Relationship with the Cognitive Costs and Compulsive Nature of Lying in Offenders

The cognitive view on deception holds that lying typically requires additional mental effort as compared to truth telling. Psychopathy, however, has been associated with swift and even compulsive lying, leading us to explore the ease and compulsive nature of lying in psychopathic offenders. We explored the costs of instructed lying versus truth telling through RTs and error rates in 52 violent male offenders, who were assessed with the Youth Psychopathic Traits Inventory (YPI). Our deception paradigm also included trials with the free choice to lie or tell the truth. By coupling monetary loss to slow and erroneous responding, we hypothesized that the frequency of lying despite likely negative consequences, would provide an index of compulsive lying. Offenders were slower and erred more often when lying than when telling the truth, and there was no robust association between psychopathy and the cognitive cost of lying. From an applied perspective, this suggests that psychopathy may not threaten the validity of computerized cognition-based lie detection. In the face of probable negative consequences, high grandiose-manipulative offenders chose to lie three times as often as low grandiose-manipulative offenders. Our new lying frequency index is a first attempt to create a much needed tool to empirically examine compulsive lying, and provides preliminary support for the compulsive nature of lying in grandiose-manipulative offenders. Alternative interpretation of the findings are discussed