On the fluid limit of the continuous-time random walk with general Lévy jump distribution functions

The continuous time random walk (CTRW) is a natural generalization of the Brownian random walk that allows the incorporation of waiting time distributions psi(t) and general jump distribution functions eta(x). There are two well-known fluid limits of this model in the uncoupled case. For exponential decaying waiting times and Gaussian jump distribution functions the fluid limit leads to the diffusion equation. On the other hand, for algebraic decaying waiting times psi approximately t(-(1+beta)) and algebraic decaying jump distributions eta approximately x(-(1+alpha)) corresponding to Lévy stable processes, the fluid limit leads to the fractional diffusion equation of order alpha in space and order beta in time. However, these are two special cases of a wider class of models. Here we consider the CTRW for the most general Lévy stochastic processes in the Lévy-Khintchine representation for the jump distribution function and obtain an integrodifferential equation describing the dynamics in the fluid limit. The resulting equation contains as special cases the regular and the fractional diffusion equations. As an application we consider the case of CTRWs with exponentially truncated Lévy jump distribution functions. In this case the fluid limit leads to a transport equation with exponentially truncated fractional derivatives which describes the interplay between memory, long jumps, and truncation effects in the intermediate asymptotic regime. The dynamics exhibits a transition from superdiffusion to subdiffusion with the crossover time scaling as tauc approximately lambda(-alpha/beta), where 1/lambda is the truncation length scale. The asymptotic behavior of the propagator (Green's function) of the truncated fractional equation exhibits a transition from algebraic decay for t>tauc

Black swans or dragon kings? A simple test for deviations from the power law

We develop a simple test for deviations from power law tails, which is based on the asymptotic properties of the empirical distribution function. We use this test to answer the question whether great natural disasters, financial crashes or electricity price spikes should be classified as dragon kings or 'only' as black swans

Media(ted) discourses and climate change : a focus on political subjectivity and (dis)engagement

Research has shown that the media are the main source of information and the main factor shaping people’s awareness and concern in relation to climate change and therefore have an important role in setting the public agenda. As a key forum for the production, reproduction and transformation of the meaning of public issues, the media influence understandings of risks, responsibilities, as well as of the functioning of democratic politics. This article argues that the media also matter to citizens’ perception of their (potential) political agency or their political subjectivity. Media representations construct particular ‘subject positions’ for individuals and cultivate dispositions to action or inaction. The article discusses the importance of citizens’ political engagement with climate change and points out some aspects of media(ted) discourses that may constrain the perceived possibilities of participation in the politics of climate change. While engagement with climate change has multiple dimensions and a number of barriers have been identified through empirical studies, this article offers a critique of the role of the media in political engagement with the problem and suggests avenues for future research.The author is grateful to the Portuguese Funda A, o para a CiIncia e a Tecnologia for funding the project 'The Politics of Climate Change: Discourses and Representations' (POCI/COM56973/2004), to Jan Zienkowski for relevant comments on this paper, and to the reviewers who provided detailed feedback

A finite difference method for pricing European and American options under a geometric Lévy process

In this paper we develop a numerical approach to a fractional-order differential Linear Complementarity Problem (LCP) arising in pricing European and American options under a geometric Lévy process. The LCP is first approximated by a nonlinear penalty fractional Black-Scholes (fBS) equation. We then propose a finite difference scheme for the penalty fBS equation. We show that both the continuous and the discretized fBS equations are uniquely solvable and establish the convergence of the numerical solution to the viscosity solution of the penalty fBS equation by proving the consistency, stability and monotonicity of the numerical scheme. We also show that the discretization has the 2nd-order truncation error in both the spatial and time mesh sizes. Numerical results are presented to demonstrate the accuracy and usefulness of the numerical method for pricing both European and American options under the geometric Lévy process

Antibacterial activity and mode of action of selected glucosinolate hydrolysis products against bacterial pathogens

Plants contain numerous components that are important sources of new bioactive molecules with antimicrobial properties. Isothiocyanates (ITCs) are plant secondary metabolites found in cruciferous vegetables that are arising as promising antimicrobial agents in food industry. The aim of this study was to assess the antibacterial activity of two isothiocyanates (ITCs), allylisothiocyanate (AITC) and 2-phenylethylisothiocyanate (PEITC) against Escherichia coli, Pseudomonas aeruginosa, Staphylococcus aureus and Listeria monocytogenes. The antibacterial mode of action was also characterized by the assessment of different physiological indices: membrane integrity, intracellular potassium release, physicochemical surface properties and surface charge. The minimum inhibitory concentration (MIC) of AITC and PEITC was 100 g/mL for all bacteria. The minimum bactericidal concentration (MBC) of the ITCs was at least 10 times higher than the MIC. Both AITC and PEITC changed the membrane properties of the bacteria decreasing their surface charge and compromising the integrity of the cytoplasmatic membrane with consequent potassium leakage and propidium iodide uptake. The surface hydrophobicity was also non-specifically altered (E. coli and L. monocytogenes become less hydrophilic; P. aeruginosa and S. aureus become more hydrophilic). This study shows that AITC and PEITC have strong antimicrobial potential against the bacteria tested, through the disruption of the bacterial cell membranes. Moreover, phytochemicals are highlighted as a valuable sustainable source of new bioactive products.This work was supported by the Operational Programme for Competitiveness Factors - COMPETE and by the Portuguese Foundation for Science and Technology through Project Phytodisinfectants - PTDC/DTP-SAP/1078/2012 (COMPETE: FCOMP-01-0124-FEDER-028765), the PhD grant awarded to Ana Abreu (SFRH/BD/84393/2012), and the post-doctoral grants awarded to Anabela Borges (SFRH/BPD/98684/2013) and Lucia C. Simoes (SFRH/BPD/81982/2011). Also, this work was undertaken as part of the European Research Project SUSCLEAN (Contract no FP7-KBBE-2011-5, project number: 287514) and the COST Action FA1202. The authors are solely responsible for this work. It does not represent the opinion of the European Community, and the Community is not responsible for any use that might be made of data appearing herein

Glucosinolates, myrosinase hydrolysis products, and flavonols found in rocket (Eruca sativa and Diplotaxis tenuifolia)

Rocket species have been shown to have very high concentrations of glucosinolates and flavonols, which have numerous positive health benefits with regular consumption. In this review we highlight how breeders and processors of rocket species can utilize genomic and phytochemical research to improve varieties and enhance the nutritive benefits to consumers. Plant breeders are increasingly looking to new technologies such as HPLC, UPLC, LC-MS and GC-MS to screen populations for their phytochemical content to inform plant selections. Here we collate the research that has been conducted to-date in rocket, and summarise all glucosinolate and flavonol compounds identified in the species. We emphasize the importance of the broad screening of populations for phytochemicals and myrosinase degradation products, as well as unique traits that may be found in underutilized gene bank resources. We also stress that collaboration with industrial partners is becoming essential for long-term plant breeding goals through research