Bounded Refinement Types

We present a notion of bounded quantification for refinement types and show how it expands the expressiveness of refinement typing by using it to develop typed combinators for: (1) relational algebra and safe database access, (2) Floyd-Hoare logic within a state transformer monad equipped with combinators for branching and looping, and (3) using the above to implement a refined IO monad that tracks capabilities and resource usage. This leap in expressiveness comes via a translation to "ghost" functions, which lets us retain the automated and decidable SMT based checking and inference that makes refinement typing effective in practice.Comment: 14 pages, International Conference on Functional Programming, ICFP 201

Topological regluing of rational functions

Regluing is a topological operation that helps to construct topological models for rational functions on the boundaries of certain hyperbolic components. It also has a holomorphic interpretation, with the flavor of infinite dimensional Thurston--Teichm\"uller theory. We will discuss a topological theory of regluing, and trace a direction in which a holomorphic theory can develop.Comment: 38 page

Initial distribution spread: A density forecasting approach

Ensemble forecasting of nonlinear systems involves the use of a model to run forward a discrete ensemble (or set) of initial states. Data assimilation techniques tend to focus on estimating the true state of the system, even though model error limits the value of such efforts. This paper argues for choosing the initial ensemble in order to optimise forecasting performance rather than estimate the true state of the system. Density forecasting and choosing the initial ensemble are treated as one problem. Forecasting performance can be quantified by some scoring rule. In the case of the logarithmic scoring rule, theoretical arguments and empirical results are presented. It turns out that, if the underlying noise dominates model error, we can diagnose the noise spread

Homologous Flares and Magnetic Field Topology in Active Region NOAA 10501 on 20 November 2003

We present and interpret observations of two morphologically homologous flares that occurred in active region (AR) NOAA 10501 on 20 November 2003. Both flares displayed four homologous H-alpha ribbons and were both accompanied by coronal mass ejections (CMEs). The central flare ribbons were located at the site of an emerging bipole in the center of the active region. The negative polarity of this bipole fragmented in two main pieces, one rotating around the positive polarity by ~ 110 deg within 32 hours. We model the coronal magnetic field and compute its topology, using as boundary condition the magnetogram closest in time to each flare. In particular, we calculate the location of quasiseparatrix layers (QSLs) in order to understand the connectivity between the flare ribbons. Though several polarities were present in AR 10501, the global magnetic field topology corresponds to a quadrupolar magnetic field distribution without magnetic null points. For both flares, the photospheric traces of QSLs are similar and match well the locations of the four H-alpha ribbons. This globally unchanged topology and the continuous shearing by the rotating bipole are two key factors responsible for the flare homology. However, our analyses also indicate that different magnetic connectivity domains of the quadrupolar configuration become unstable during each flare, so that magnetic reconnection proceeds differently in both events.Comment: 24 pages, 10 figures, Solar Physics (accepted

Apparent-Strain Correction for Combined Thermal and Mechanical Testing

Combined thermal and mechanical testing requires that the total strain be corrected for the coefficient of thermal expansion mismatch between the strain gage and the specimen or apparent strain when the temperature varies while a mechanical load is being applied. Collecting data for an apparent strain test becomes problematic as the specimen size increases. If the test specimen cannot be placed in a variable temperature test chamber to generate apparent strain data with no mechanical loads, coupons can be used to generate the required data. The coupons, however, must have the same strain gage type, coefficient of thermal expansion, and constraints as the specimen to be useful. Obtaining apparent-strain data at temperatures lower than -320 F is challenging due to the difficulty to maintain steady-state and uniform temperatures on a given specimen. Equations to correct for apparent strain in a real-time fashion and data from apparent-strain tests for composite and metallic specimens over a temperature range from -450 F to +250 F are presented in this paper. Three approaches to extrapolate apparent-strain data from -320 F to -430 F are presented and compared to the measured apparent-strain data. The first two approaches use a subset of the apparent-strain curves between -320 F and 100 F to extrapolate to -430 F, while the third approach extrapolates the apparent-strain curve over the temperature range of -320 F to +250 F to -430 F. The first two approaches are superior to the third approach but the use of either of the first two approaches is contingent upon the degree of non-linearity of the apparent-strain curve

Simultaneous Observations of the Chromosphere with TRACE and SUMER

Using mainly the 1600 angstrom continuum channel, and also the 1216 angstrom Lyman-alpha channel (which includes some UV continuum and C IV emission), aboard the TRACE satellite, we observed the complete lifetime of a transient, bright chromospheric loop. Simultaneous observations with the SUMER instrument aboard the SOHO spacecraft revealed interesting material velocities through the Doppler effect existing above the chromospheric loop imaged with TRACE, possibly corresponding to extended non-visible loops, or the base of an X-ray jet.Comment: 14 pages, 10 figures, accepted by Solar Physic

A progressive refinement approach for the visualisation of implicit surfaces

Visualising implicit surfaces with the ray casting method is a slow procedure. The design cycle of a new implicit surface is, therefore, fraught with long latency times as a user must wait for the surface to be rendered before being able to decide what changes should be introduced in the next iteration. In this paper, we present an attempt at reducing the design cycle of an implicit surface modeler by introducing a progressive refinement rendering approach to the visualisation of implicit surfaces. This progressive refinement renderer provides a quick previewing facility. It first displays a low quality estimate of what the final rendering is going to be and, as the computation progresses, increases the quality of this estimate at a steady rate. The progressive refinement algorithm is based on the adaptive subdivision of the viewing frustrum into smaller cells. An estimate for the variation of the implicit function inside each cell is obtained with an affine arithmetic range estimation technique. Overall, we show that our progressive refinement approach not only provides the user with visual feedback as the rendering advances but is also capable of completing the image faster than a conventional implicit surface rendering algorithm based on ray casting

Structures for Interacting Composite Fermions: Stripes, Bubbles, and Fractional Quantum Hall Effect

Much of the present day qualitative phenomenology of the fractional quantum Hall effect can be understood by neglecting the interactions between composite fermions altogether. For example the fractional quantum Hall effect at $\nu=n/(2pn\pm 1)$ corresponds to filled composite-fermion Landau levels,and the compressible state at $\nu=1/2p$ to the Fermi sea of composite fermions. Away from these filling factors, the residual interactions between composite fermions will determine the nature of the ground state. In this article, a model is constructed for the residual interaction between composite fermions, and various possible states are considered in a variational approach. Our study suggests formation of composite-fermion stripes, bubble crystals, as well as fractional quantum Hall states for appropriate situations.Comment: 16 pages, 7 figure