From rough path estimates to multilevel Monte Carlo

New classes of stochastic differential equations can now be studied using rough path theory (e.g. Lyons et al. [LCL07] or Friz--Hairer [FH14]). In this paper we investigate, from a numerical analysis point of view, stochastic differential equations driven by Gaussian noise in the aforementioned sense. Our focus lies on numerical implementations, and more specifically on the saving possible via multilevel methods. Our analysis relies on a subtle combination of pathwise estimates, Gaussian concentration, and multilevel ideas. Numerical examples are given which both illustrate and confirm our findings.Comment: 34 page

From rough path estimates to multilevel Monte Carlo

Discrete approximations to solutions of stochastic differential equations are well-known to converge with strong rate 1/2. Such rates have played a key-role in Giles' multilevel Monte Carlo method [Giles, Oper. Res. 2008] which gives a substantial reduction of the computational effort necessary for the evaluation of diffusion functionals. In the present article similar results are established for large classes of rough differential equations driven by Gaussian processes (including fractional Brownian motion with H>1/4 as special case)

Complex Politics: A Quantitative Semantic and Topological Analysis of UK House of Commons Debates

This study is a first, exploratory attempt to use quantitative semantics techniques and topological analysis to analyze systemic patterns arising in a complex political system. In particular, we use a rich data set covering all speeches and debates in the UK House of Commons between 1975 and 2014. By the use of dynamic topic modeling (DTM) and topological data analysis (TDA) we show that both members and parties feature specific roles within the system, consistent over time, and extract global patterns indicating levels of political cohesion. Our results provide a wide array of novel hypotheses about the complex dynamics of political systems, with valuable policy applications

Identification and characterisation of a hyper-variable apoplastic effector gene family of the potato cyst nematodes.

Sedentary endoparasitic nematodes are obligate biotrophs that modify host root tissues, using a suite of effector proteins to create and maintain a feeding site that is their sole source of nutrition. Using assumptions about the characteristics of genes involved in plant-nematode biotrophic interactions to inform the identification strategy, we provide a description and characterisation of a novel group of hyper-variable extracellular effectors termed HYP, from the potato cyst nematode Globodera pallida. HYP effectors comprise a large gene family, with a modular structure, and have unparalleled diversity between individuals of the same population: no two nematodes tested had the same genetic complement of HYP effectors. Individuals vary in the number, size, and type of effector subfamilies. HYP effectors are expressed throughout the biotrophic stages in large secretory cells associated with the amphids of parasitic stage nematodes as confirmed by in situ hybridisation. The encoded proteins are secreted into the host roots where they are detectable by immunochemistry in the apoplasm, between the anterior end of the nematode and the feeding site. We have identified HYP effectors in three genera of plant parasitic nematodes capable of infecting a broad range of mono- and dicotyledon crop species. In planta RNAi targeted to all members of the effector family causes a reduction in successful parasitism

Measurement of left ventricular dimensions with contrast-enhanced three-dimensional cine imaging facilitated by k-t SENSE

AIM: To compare three-dimensional (3D) k-t sensitivity encoded (k-t SENSE) cine cardiovascular magnetic resonance (CMR), before and after contrast administration, against standard 2D imaging for the assessment of left ventricular volumes and mass. METHOD: Twenty-six subjects (14 volunteers, 12 patients) underwent multiple breathhold 2D balanced turbo-field echo cine CMR in addition to k-t SENSE accelerated 3D imaging (acceleration factor 5; 5x k-t SENSE), performed before and after administration of a high-relaxivity gadolinium-based contrast agent (Gadobutrolum). k-t acceleration factors of 7 and 10 were also assessed in six volunteers. Left ventricular end diastolic volume (EDV), end systolic volume (ESV), mass, and ejection fraction (EF) were calculated for each method. RESULTS: There was at least moderate agreement between the EDV, ESV, mass and EF calculated by 2D and 3D 5x k-t SENSE methods before contrast (concordance coefficients 0.92, 0.95, 0.97, 0.92, respectively). Agreement improved following contrast (concordance coefficients 0.97, 0.99, 0.98, 0.93, respectively). The 3D method underestimated all parameters compared to 2D (mean bias pre-contrast 6.1 ml, 0.6 ml, 3.5 g, 2.0% respectively). 3D image quality scores were significantly poorer than 2D, showing a non-significant trend to improvement following contrast administration. Parameters derived with k-t acceleration factors of 7 and 10 showed poorer agreement with 2D values. CONCLUSION: Left ventricular volumes and mass are reliably assessed using 3D 5x k-t SENSE accelerated CMR. Contrast administration further improves agreement between 5x k-t SENSE and 2D-derived measurements. k-t acceleration factors greater than 5, though feasible, produce poorer agreement with 2D values

Ecohydrodynamics of Cold-Water Coral Reefs:A Case Study of the Mingulay Reef Complex (Western Scotland)

Ecohydrodynamics investigates the hydrodynamic constraints on ecosystems across different temporal and spatial scales. Ecohydrodynamics play a pivotal role in the structure and functioning of marine ecosystems, however the lack of integrated complex flow models for deep-water ecosystems beyond the coastal zone prevents further synthesis in these settings. We present a hydrodynamic model for one of Earth's most biologically diverse deep-water ecosystems, cold-water coral reefs. The Mingulay Reef Complex (western Scotland) is an inshore seascape of cold-water coral reefs formed by the scleractinian coral Lophelia pertusa. We applied single-image edge detection and composite front maps using satellite remote sensing, to detect oceanographic fronts and peaks of chlorophyll a values that likely affect food supply to corals and other suspension-feeding fauna. We also present a high resolution 3D ocean model to incorporate salient aspects of the regional and local oceanography. Model validation using in situ current speed, direction and sea elevation data confirmed the model's realistic representation of spatial and temporal aspects of circulation at the reef complex including a tidally driven current regime, eddies, and downwelling phenomena. This novel combination of 3D hydrodynamic modelling and remote sensing in deep-water ecosystems improves our understanding of the temporal and spatial scales of ecological processes occurring in marine systems. The modelled information has been integrated into a 3D GIS, providing a user interface for visualization and interrogation of results that allows wider ecological application of the model and that can provide valuable input for marine biodiversity and conservation applications

High spatial resolution myocardial perfusion cardiac magnetic resonance for the detection of coronary artery disease

Aims To evaluate the feasibility and diagnostic performance of high spatial resolution myocardial perfusion cardiac magnetic resonance (perfusion-CMR). Methods and results Fifty-four patients underwent adenosine stress perfusion-CMR. An in-plane spatial resolution of 1.4 × 1.4 mm2 was achieved by using 5× k-space and time sensitivity encoding (k-t SENSE). Perfusion was visually graded for 16 left ventricular and two right ventricular (RV) segments on a scale from 0 = normal to 3 = abnormal, yielding a perfusion score of 0-54. Diagnostic accuracy of the perfusion score to detect coronary artery stenosis of >50% on quantitative coronary angiography was determined. Sources and extent of image artefacts were documented. Two studies (4%) were non-diagnostic because of k-t SENSE-related and breathing artefacts. Endocardial dark rim artefacts if present were small (average width 1.6 mm). Analysis by receiver-operating characteristics yielded an area under the curve for detection of coronary stenosis of 0.85 [95% confidence interval (CI) 0.75-0.95] for all patients and 0.82 (95% CI 0.65-0.94) and 0.87 (95% CI 0.75-0.99) for patients with single and multi-vessel disease, respectively. Seventy-four of 102 (72%) RV segments could be analysed. Conclusion High spatial resolution perfusion-CMR is feasible in a clinical population, yields high accuracy to detect single and multi-vessel coronary artery disease, minimizes artefacts and may permit the assessment of RV perfusio

Functional C-terminally Encoded Peptide (CEP) plant hormone domains evolved de novo in the plant parasite Rotylenchulus reniformis

This work was supported by the Biotechnology and Biological Sciences Research Council (BBSRC) and The James Hutton Institute through a PhD studentship to SE-vdA. The James Hutton Institute receives funding from the Scottish Government Rural and Environment Science and Analytical Services division. SE-vdA is supported by BBSRC grant BB/M014207/1.Sedentary Plant-Parasitic Nematodes (PPNs) induce and maintain an intimate relationship with their host, stimulating cells adjacent to root vascular tissue to re-differentiate into unique and metabolically active “feeding sites”. The interaction between PPNs and their host is mediated by nematode effectors. We describe the discovery of a large and diverse family of effector genes, encoding C-terminally Encoded Peptide (CEP) plant hormone mimics (RrCEPs), in the syncytia-forming plant-parasite Rotylenchulus reniformis. The particular attributes of RrCEPs distinguish them from all other CEPs, regardless of origin. Together with the distant phylogenetic relationship of R. reniformis to the only other CEP-encoding nematode genus identified to date (Meloidogyne), this suggests CEPs likely evolved de novo in R. reniformis. We have characterised the first member of this large gene family (RrCEP1), demonstrating its significant upregulation during the plant-nematode interaction and expression in the effector-producing pharyngeal gland cell. All internal CEP domains of multi-domain RrCEPs are followed by di-basic residues, suggesting a mechanism for cleavage. A synthetic peptide corresponding to RrCEP1 domain 1 is biologically active and capable of upregulating plant nitrate transporter (AtNRT2.1) expression, while simultaneously reducing primary root elongation. When a non-CEP containing, syncytia-forming PPN species (Heterodera schachtii) infects Arabidopsis in a CEP-rich environment a smaller feeding site is produced. We hypothesise that CEPs of R. reniformis represent a two-fold adaptation to sustained biotrophy in this species; 1) increasing host nitrate uptake while 2) limiting the size of the syncytial feeding site produced.Publisher PDFPeer reviewe

Evidence for electronically-driven ferroelectricity in the family of strongly correlated dimerized BEDT-TTF molecular conductors

By applying measurements of the dielectric constants and relative length changes to the dimerized molecular conductor $\kappa$-(BEDT-TTF)$_2$Hg(SCN)$_2$Cl, we provide evidence for order-disorder type electronic ferroelectricity which is driven by charge order within the (BEDT-TTF)$_2$ dimers and stabilized by a coupling to the anions. According to our density functional theory calculations, this material is characterized by a moderate strength of dimerization. This system thus bridges the gap between strongly dimerized materials, often approximated as dimer-Mott systems at 1/2 filling, and non- or weakly dimerized systems at 1/4 filling exhibiting charge order. Our results indicate that intra-dimer charge degrees of freedom are of particular importance in correlated $\kappa$-(BEDT-TTF)$_2$X salts and can create novel states, such as electronically-driven multiferroicity or charge-order-induced quasi-1D spin liquids.Comment: 6 pages, 4 figures + Supplementary Information (8 pages, 8 figures

P-and N-Depletion Trigger Similar Cellular Responses to Promote Senescence in Eukaryotic Phytoplankton

Global change will affect multiple physico-chemical parameters of the oceans, amongst them also the abundances of macronutrients like phosphorus and nitrogen that are critical for phytoplankton growth. Here, we assessed the transcriptomic responses to phosphorus (P) depletion in the haploid and diploid life-cycle stage of the coccolithophore Emiliania huxleyi (RCC1217/1216) and compared the results with an existing dataset on nitrogen (N) depletion. The responses to the two depletion scenarios within one particular life-cycle stage were more similar at the transcriptome level than the responses of the two stages toward only one particular depletion scenario, emphasizing the tripartite nature of the coccolithophore genome. When cells senesced in both scenarios, they applied functionally similar programs to shut down cell-cycling, re-adjust biochemical pathways, and increase metabolic turnover to efficiently recycle elements. Those genes that exclusively responded to either P- or N-depletion modulated the general response to enhance scavenging, uptake, and attempted storage of the limiting nutrient. The metabolic adjustments during senescence involved conserved and ancient pathways (e.g., proline oxidation or the glycolytic bypass) that prolong survival on the one hand, but on the other hand give rise to toxic messengers (e.g., reactive oxygen species or methylglyoxal). Continued senescence thus promotes various processes that lead to cell death, which can be delayed only for a limited time. As a consequence, the interplay of the involved processes determines how long cells can endure severe nutrient depletion before they lyse and provide their constituent nutrients to the more viable competitors in their environment. These responses to nutrient depletion are observable in other phytoplankton, but it appears that E. huxleyi's outstanding endurance under nutrient deficiency is due to its versatile high-affinity uptake systems and an efficient, NAD-independent malate oxidation that is absent from most other taxa