A Direct Elliptic Solver Based on Hierarchically Low-rank Schur Complements

A parallel fast direct solver for rank-compressible block tridiagonal linear systems is presented. Algorithmic synergies between Cyclic Reduction and Hierarchical matrix arithmetic operations result in a solver with $O(N \log^2 N)$ arithmetic complexity and $O(N \log N)$ memory footprint. We provide a baseline for performance and applicability by comparing with well known implementations of the $\mathcal{H}$-LU factorization and algebraic multigrid with a parallel implementation that leverages the concurrency features of the method. Numerical experiments reveal that this method is comparable with other fast direct solvers based on Hierarchical Matrices such as $\mathcal{H}$-LU and that it can tackle problems where algebraic multigrid fails to converge

Design of small Stirling dynamic isotope power system for robotic space missions

Design of a multihundred-watt Dynamic Isotope Power System (DIPS) based on the U.S. Department of Energy (DOE) General Purpose Heat Source (GPHS) and small (multihundred-watt) free-piston Stirling engine (FPSE) technology is being pursued as a potential lower cost alternative to radioisotope thermoelectric generators (RTG's). The design is targeted at the power needs of future unmanned deep space and planetary surface exploration missions ranging from scientific probes to Space Exploration Initiative precursor missions. Power level for these missions is less than a kilowatt. Unlike previous DIPS designs which were based on turbomachinery conversion (e.g. Brayton), this small Stirling DIPS can be advantageously scaled down to multihundred-watt unit size while preserving size and mass competitiveness with RTG's. Preliminary characterization of units in the output power ranges 200-600 We indicate that on an electrical watt basis the GPHS/small Stirling DIPS will be roughly equivalent to an advanced RTG in size and mass but require less than a third of the isotope inventory

Climate- and Eustasy-Driven Cyclicity in Pennsylvanian Fusulinid Assemblages, Donets Basin (Ukraine)

A model of cyclic recurrence (~ 0.6–1.2 myr) of three fusulinid assemblages in the Middle Pennsylvanian siliciclastic–carbonate succession of the Donets Basin is proposed. Each cycle records progressive turnover of assemblages in shallow marine environments in response to sea-level and regional climate change. A Hemifusulina-assemblage (A), adapted to cooler and reduced salinity seawater records the onset of sea level rise accompanied by humid climatic conditions. Sea level high stand is captured by the Beedeina–Neostaffella–Ozawainella–Taitzehoella (or Beedeina-dominated) assemblage (B), characteristic of relatively deeper-water environments. The B assemblage is successively replaced by the most diverse population of the warm-water Fusulinella-dominated assemblage (C). This assemblage, which occurs in the upper limestones of each fusulinid cycle records the onset of sea level fall accompanied by a shift to drier conditions and likely increased seawater salinity. The proposed model permits robust interbasinal correlation of the Pennsylvanian successions of the Tethyan realm. Fusulinids of the A and C2 assemblages are the most provincial and therefore the most useful for paleogeographic reconstructions. Specifically, they delineate originally contiguous regions that subsequently were dispersed hundreds to thousands of kilometers, whereas fusulinids of the B assemblage hold the highest potential for global correlation. Extinction at the Moscovian–Kasimovian transition of fusulinid genera of the A and B assemblages, which inhabited predominately cooler and normal salinity (perhaps hyposaline) waters, can be explained by the onset of global warming in the earliest Late Pennsylvanian. Fusulinid assemblages define various types of distribution patterns that differ by tectonic setting of the studied basins suggesting that fusulinid assemblage patterns hold potential for reconstructing the paleogeography and tectonic evolution of Pennsylvanian basins of eastern Laurasia

Complexity Bounds for Ordinal-Based Termination

`What more than its truth do we know if we have a proof of a theorem in a given formal system?' We examine Kreisel's question in the particular context of program termination proofs, with an eye to deriving complexity bounds on program running times. Our main tool for this are length function theorems, which provide complexity bounds on the use of well quasi orders. We illustrate how to prove such theorems in the simple yet until now untreated case of ordinals. We show how to apply this new theorem to derive complexity bounds on programs when they are proven to terminate thanks to a ranking function into some ordinal.Comment: Invited talk at the 8th International Workshop on Reachability Problems (RP 2014, 22-24 September 2014, Oxford

Nonlinear Screening and Effective Electrostatic Interactions in Charge-Stabilized Colloidal Suspensions

A nonlinear response theory is developed and applied to electrostatic interactions between spherical macroions, screened by surrounding microions, in charge-stabilized colloidal suspensions. The theory describes leading-order nonlinear response of the microions (counterions, salt ions) to the electrostatic potential of the macroions and predicts microion-induced effective many-body interactions between macroions. A linear response approximation [Phys. Rev. E 62, 3855 (2000)] yields an effective pair potential of screened-Coulomb (Yukawa) form, as well as a one-body volume energy, which contributes to the free energy. Nonlinear response generates effective many-body interactions and essential corrections to both the effective pair potential and the volume energy. By adopting a random-phase approximation (RPA) for the response functions, and thus neglecting microion correlations, practical expressions are derived for the effective pair and triplet potentials and for the volume energy. Nonlinear screening is found to weaken repulsive pair interactions, induce attractive triplet interactions, and modify the volume energy. Numerical results for monovalent microions are in good agreement with available ab initio simulation data and demonstrate that nonlinear effects grow with increasing macroion charge and concentration and with decreasing salt concentration. In the dilute limit of zero macroion concentration, leading-order nonlinear corrections vanish. Finally, it is shown that nonlinear response theory, when combined with the RPA, is formally equivalent to the mean-field Poisson-Boltzmann theory and that the linear response approximation corresponds, within integral-equation theory, to a linearized hypernetted-chain closure.Comment: 30 pages, 8 figures, Phys. Rev. E (in press

Parvalbumin interneurons are differentially connected to principal cells in inhibitory feedback microcircuits along the dorso-ventral axis of the medial entorhinal cortex

The medial entorhinal cortex (mEC) shows a high degree of spatial tuning, predominantly grid cell activity, which is reliant on robust, dynamic inhibition provided by local interneurons (INs). In fact, feedback inhibitory microcircuits involving fast-spiking parvalbumin (PV) basket cells (BCs) are believed to contribute dominantly to the emergence of grid cell firing in principal cells (PrCs). However, the strength of PV BC-mediated inhibition onto PrCs is not uniform in this region, but high in the dorsal and weak in the ventral mEC. This is in good correlation with divergent grid field sizes, but the underlying morphologic and physiological mechanisms remain unknown. In this study, we examined PV BCs in layer (L)2/3 of the mEC characterizing their intrinsic physiology, morphology and synaptic connectivity in the juvenile rat. We show that while intrinsic physiology and morphology are broadly similar over the dorsoventral axis, PV BCs form more connections onto local PrCs in the dorsal mEC, independent of target cell type. In turn, the major PrC subtypes, pyramidal cell (PC) and stellate cell (SC), form connections onto PV BCs with lower, but equal probability. These data thus identify inhibitory connectivity as source of the gradient of inhibition, plausibly explaining divergent grid field formation along this dorsoventral axis of the mEC

Development and testing of a predictive traffic safety evaluation tool for road traffic management and ITS impact assessment

In recent research the CONDUITS performance evaluation framework for traffic management and Intelligent Transport Systems (ITS) was developed, consisting of a set of Key Performance Indicators (KPIs) for the strategic themes of traffic efficiency, safety, pollution reduction and social inclusion. Follow-up work has concentrated on integrating the developed CONDUITS KPIs with microscopic traffic simulation. The outcome has been a predictive evaluation tool for traffic management and ITS, called CONDUITS_DST, in which two of the four KPI categories have been integrated to date: pollution and traffic efficiency. The objective of the present study is to further extend the predictive evaluation framework to include the theme of traffic safety. Contributing to the development of the CONDUITS_DST traffic safety module, the paper identifies and proposes relevant models and metrics linking traffic characteristics with road safety impacts. In doing so, it enables the extraction of the necessary input data for each of the three CONDUITS KPIs for traffic safety (accidents, direct impacts, and indirect impacts) directly from microscopic traffic simulation models. The proposed models and metrics are tested in conjunction with the relevant CONDUITS KPIs for safety using data from simulation models before and after the implementation of a bus priority signalling system in Brussels. Testing takes place both at the network level, but also at the level of individual links, and the results show that the framework is able to capture the expected safety impacts adequately well, paving the way towards its implementation is the traffic safety module of CONDUITS_DST

Using Key Performance Indicators for traffic management and Intelligent Transport Systems as a prediction tool

In recent research work (FP7 CONDUITS) a performance evaluation framework for traffic management and Intelligent Transport Systems was developed. The new framework consists of a set of Key Performance Indicators (KPIs) for the strategic themes of traffic efficiency, safety, pollution reduction and social inclusion, and the last stages of the project saw its validation through its application to four case studies. Following up from this work, this paper presents the extension of the framework for use as a prediction tool enabling urban transport authorities to assess the impacts of relevant policies and technologies before implementing them. Focussing on pollution reduction, a tool (CONDUITS-DST) integrating the respective KPIs with microsimulation modelling is developed. The paper describes the integration process, including the model chosen for calculating the emissions levels of a number of scenarios, presents the results of the application to a case study in the city of Brussels, and outlines future developments targeted at broadening the integration of the KPIs into decision-makin

Compton Scattering by the Proton using a Large-Acceptance Arrangement

Compton scattering by the proton has been measured using the tagged-photon facility at MAMI (Mainz) and the large-acceptance arrangement LARA. The new data are interpreted in terms of dispersion theory based on the SAID-SM99K parameterization of photo-meson amplitudes. It is found that two-pion exchange in the t-channel is needed for a description of the data in the second resonance region. The data are well represented if this channel is modeled by a single pole with mass parameter m(sigma)=600 MeV. The asymptotic part of the spin dependent amplitude is found to be well represented by pi-0-exchange in the t-channel. A backward spin-polarizability of gamma(pi)=(-37.1+-0.6(stat+syst)+-3.0(model))x10^{-4}fm^4 has been determined from data of the first resonance region below 455 MeV. This value is in a good agreement with predictions of dispersion relations and chiral pertubation theory. From a subset of data between 280 and 360 MeV the resonance pion-photoproduction amplitudes were evaluated leading to a E2/M1 multipole ratio of the p-to-Delta radiative transition of EMR(340 MeV)=(-1.7+-0.4(stat+syst)+-0.2(model))%. It was found that this number is dependent on the parameterization of photo-meson amplitudes. With the MAID2K parameterization an E2/M1 multipole ratio of EMR(340 MeV)=(-2.0+-0.4(stat+syst)+-0.2(model))% is obtained