The numerical solution of fractional differential equations: Speed versus accuracy

This paper discusses the development of efficient algorithms for a certain fractional differential equation.Manchester Centre for Computational Mathematic

The numerical solution of linear multi-term fractional differential equations: Systems of equations

This is a PDF version of a preprint submitted to Elsevier. The definitive version was published in the Journal of computational and applied mathematics and is available at www.elsevier.comThis article discusses how the numerical approximation of a linear multi-term fractional differential equation can be calculated by the reduction of the problem to a system of ordinary and fractional differential equations each of order at most unity.This article was submitted to the RAE2008 for the University of Chester - Applied Mathematics

Stably non-synchronizable maps of the plane

Pecora and Carroll presented a notion of synchronization where an (n-1)-dimensional nonautonomous system is constructed from a given $n$-dimensional dynamical system by imposing the evolution of one coordinate. They noticed that the resulting dynamics may be contracting even if the original dynamics are not. It is easy to construct flows or maps such that no coordinate has synchronizing properties, but this cannot be done in an open set of linear maps or flows in $\R^n$, $n\geq 2$. In this paper we give examples of real analytic homeomorphisms of $\R^2$ such that the non-synchronizability is stable in the sense that in a full $C^0$ neighborhood of the given map, no homeomorphism is synchronizable

Covalent targeting of the vacuolar H+-ATPase activates autophagy via mTORC1 inhibition.

Autophagy is a lysosomal degradation pathway that eliminates aggregated proteins and damaged organelles to maintain cellular homeostasis. A major route for activating autophagy involves inhibition of the mTORC1 kinase, but current mTORC1-targeting compounds do not allow complete and selective mTORC1 blockade. Here, we have coupled screening of a covalent ligand library with activity-based protein profiling to discover EN6, a small-molecule in vivo activator of autophagy that covalently targets cysteine 277 in the ATP6V1A subunit of the lysosomal v-ATPase, which activates mTORC1 via the Rag guanosine triphosphatases. EN6-mediated ATP6V1A modification decouples the v-ATPase from the Rags, leading to inhibition of mTORC1 signaling, increased lysosomal acidification and activation of autophagy. Consistently, EN6 clears TDP-43 aggregates, a causative agent in frontotemporal dementia, in a lysosome-dependent manner. Our results provide insight into how the v-ATPase regulates mTORC1, and reveal a unique approach for enhancing cellular clearance based on covalent inhibition of lysosomal mTORC1 signaling

The Photon Underproduction Crisis

We examine the statistics of the low-redshift Lyman-alpha forest from smoothed particle hydrodynamic simulations in light of recent improvements in the estimated evolution of the cosmic ultraviolet background (UVB) and recent observations from the Cosmic Origins Spectrograph (COS). We find that the value of the metagalactic photoionization rate required by our simulations to match the observed properties of the low-redshift Lyman-alpha forest is a factor of 5 larger than the value predicted by state-of-the art models for the evolution of this quantity. This mismatch results in the mean flux decrement of the Lyman-alpha forest being underpredicted by at least a factor of 2 (a 10-sigma discrepancy with observations) and a column density distribution of Lyman-alpha forest absorbers systematically and significantly elevated compared to observations over nearly two decades in column density. We examine potential resolutions to this mismatch and find that either conventional sources of ionizing photons (galaxies and quasars) must be significantly elevated relative to current observational estimates or our theoretical understanding of the low-redshift universe is in need of substantial revision.Comment: Submitted to ApJ Letters; 6 pages including 3 figure

The Design and Development of Interactive Multimedia Conference Proceedings

Many conferences are now providing electronic proceedings. Often, these proceedings are little more than electronic collections of documents put together in a standard software package, such as SuperBook or Acrobat. This means that few of these proceedings incorporate the full range of materials that a conference generates. Furthermore, because these general interfaces are not designed for conference proceedings, they do not provide all the features a conference warrants. The interactive multimedia proceedings for the DAGS\u2792 Institute on Parallel Computation used an interface designed specifically for presenting conference materials and provided both talks (audio, video, and slides) and papers (in hypertext form) along with an extensive set of features for navigating and using the proceedings. This interface provided the basis for further work on the design and creation of electronic proceedings. As we developed the electronic proceedings for DAGS\u2793 and DAGS\u2794 we surveyed users of the prior proceedings and reevaluated this interface. This evaluation suggested many alternatives and extensions to the interface and led us to redesign and reimplement the DAGS interactive proceedings interface. In this paper, we summarize the materials and features that comprise conference proceedings, describe and evaluate the DAGS\u2792 interface and detail the changes and decisions made in developing the new interface used for DAGS\u2793 and DAGS\u2794

Spaceborne radar observations: A guide for Magellan radar-image analysis

Geologic analyses of spaceborne radar images of Earth are reviewed and summarized with respect to detecting, mapping, and interpreting impact craters, volcanic landforms, eolian and subsurface features, and tectonic landforms. Interpretations are illustrated mostly with Seasat synthetic aperture radar and shuttle-imaging-radar images. Analogies are drawn for the potential interpretation of radar images of Venus, with emphasis on the effects of variation in Magellan look angle with Venusian latitude. In each landform category, differences in feature perception and interpretive capability are related to variations in imaging geometry, spatial resolution, and wavelength of the imaging radar systems. Impact craters and other radially symmetrical features may show apparent bilateral symmetry parallel to the illumination vector at low look angles. The styles of eruption and the emplacement of major and minor volcanic constructs can be interpreted from morphological features observed in images. Radar responses that are governed by small-scale surface roughness may serve to distinguish flow types, but do not provide unambiguous information. Imaging of sand dunes is rigorously constrained by specific angular relations between the illumination vector and the orientation and angle of repose of the dune faces, but is independent of radar wavelength. With a single look angle, conditions that enable shallow subsurface imaging to occur do not provide the information necessary to determine whether the radar has recorded surface or subsurface features. The topographic linearity of many tectonic landforms is enhanced on images at regional and local scales, but the detection of structural detail is a strong function of illumination direction. Nontopographic tectonic lineaments may appear in response to contrasts in small-surface roughness or dielectric constant. The breakpoint for rough surfaces will vary by about 25 percent through the Magellan viewing geometries from low to high Venusian latitudes. Examples of anomalies and system artifacts that can affect image interpretation are described

The Roles of Video in the Design, Development, and Use of Interactive Electronic Conference Proceedings

In this paper, we discuss the design and development of a particular type of electronic publication that has gained recent popularity: electronic conference proceedings. We suggest that modern electronic proceedings should provide a high degree of interactivity. To support such interactivity, proceedings should include an extensive collection of features and diverse multimedia components. Features appropriate for electronic proceedings include annotation, presentation, and retrieval mechanisms. Conference papers and multimedia reproductions of conference presentations with features that allow readers to manipulate these reproductions particularly enhance the interactivity of electronic proceedings. Experience from interactive proceedings the authors have designed is also discussed. Special attention is given to the multiple roles video elements can and should play in interactive proceedings

Heart valve prostheses in pregnancy: Outcomes for women and their babies

Background: As the prognosis of women with prosthetic heart valves improves more of these individuals are contemplating and undertaking pregnancy. Accurate knowledge of perinatal outcomes is essential, assisting counselling and guiding care. The aim of this study was to assess outcomes in a contemporary population of women with heart valve prostheses undertaking pregnancy, and to compare outcomes for women with mechanical and bioprosthetic prostheses. Method and results: Longitudinally-linked population health datasets containing birth and hospital admissions data were obtained for all women giving birth in New South Wales, Australia, 2000-2011. This included information identifying presence of maternal prosthetic heart valve. Cardiovascular and birth outcomes were evaluated. Among 1 144 156 pregnancies, 136 involved women with a heart valve prosthesis (1 in 10 000). No maternal mortality was seen among these women, although the relative risk for an adverse event was higher than the general population, including severe maternal morbidity (13.9% v. 1.4%, RR=9.96, 95% CI 6.32-15.7), major maternal cardiovascular event (4.4% v. 0.1%, RR 34.6, 95% CI 14.6-81.6), preterm birth (18.3% v. 6.6%, RR=2.77, 95% CI 1.88-4.07) and small-for-gestational-age infants (19.3% v. 9.5%, RR=2.12, 95% CI 1.47-3.06). There was a trend towards increased maternal and perinatal morbidity in women with a mechanical valve compared to bioprosthetic. Conclusions: Pregnancies in women with a prosthetic heart valve demonstrate an increased risk of an adverse outcome, for both mothers and babies, compared with pregnancies in the absence of heart valve prostheses. In this contemporary population, the risk was lower than previously reported.NHMRC 1001066, NHMRC 1021025, NHMRC 1062262, ARC FT120100069, Australian Heart Foundatio

Randomized trial comparing proactive, high-dose versus reactive, low-dose intravenous iron supplementation in hemodialysis (PIVOTAL) : Study design and baseline data

Background: Intravenous (IV) iron supplementation is a standard maintenance treatment for hemodialysis (HD) patients, but the optimum dosing regimen is unknown. Methods: PIVOTAL (Proactive IV irOn Therapy in hemodiALysis patients) is a multicenter, open-label, blinded endpoint, randomized controlled (PROBE) trial. Incident HD adults with a serum ferritin 700 μg/L and/or TSAT ≥40%) or a reactive, low-dose IV iron arm (iron sucrose administered if ferritin <200 μg/L or TSAT < 20%). We hypothesized that proactive, high-dose IV iron would be noninferior to reactive, low-dose IV iron for the primary outcome of first occurrence of nonfatal myocardial infarction (MI), nonfatal stroke, hospitalization for heart failure or death from any cause. If noninferiority is confirmed with a noninferiority limit of 1.25 for the hazard ratio of the proactive strategy relative to the reactive strategy, a test for superiority will be carried out. Secondary outcomes include infection-related endpoints, ESA dose requirements, and quality-of-life measures. As an event-driven trial, the study will continue until at least 631 primary outcome events have accrued, but the expected duration of follow-up is 2-4 years. Results: Of the 2,589 patients screened across 50 UK sites, 2,141 (83%) were randomized. At baseline, 65.3% were male, the median age was 65 years, and 79% were white. According to eligibility criteria, all patients were on ESA at screening. Prior stroke and MI were present in 8 and 9% of the cohort, respectively, and 44% of patients had diabetes at baseline. Baseline data for the randomized cohort were generally concordant with recent data from the UK Renal Registry. Conclusions: PIVOTAL will provide important information about the optimum dosing of IV iron in HD patients representative of usual clinical practice. Trial Registration: EudraCT number: 2013-002267-25.Peer reviewedFinal Published versio