Fibrational induction rules for initial algebras

This paper provides an induction rule that can be used to prove properties of data structures whose types are inductive, i.e., are carriers of initial algebras of functors. Our results are semantic in nature and are inspired by Hermida and Jacobs’ elegant algebraic formulation of induction for polynomial data types. Our contribution is to derive, under slightly different assumptions, an induction rule that is generic over all inductive types, polynomial or not. Our induction rule is generic over the kinds of properties to be proved as well: like Hermida and Jacobs, we work in a general fibrational setting and so can accommodate very general notions of properties on inductive types rather than just those of particular syntactic forms. We establish the correctness of our generic induction rule by reducing induction to iteration. We show how our rule can be instantiated to give induction rules for the data types of rose trees, finite hereditary sets, and hyperfunctions. The former lies outside the scope of Hermida and Jacobs’ work because it is not polynomial; as far as we are aware, no induction rules have been known to exist for the latter two in a general fibrational framework. Our instantiation for hyperfunctions underscores the value of working in the general fibrational setting since this data type cannot be interpreted as a set

Coarsening Dynamics of Granular Heaplets in Tapped Granular Layers

A semi-continuum model is introduced to study the dynamics of the formation of granular heaplets in tapped granular layers. By taking into account the energy dissipation of collisions and screening effects due to avalanches, this model is able to reproduce qualitatively the pattern of these heaplets. Our simulations show that the granular heaplets are characterised by an effective surface tension which depends on the magnitude of the tapping intensity. Also, we observe that there is a coarsening effect in that the average size of the heaplets, V grows as the number of taps k increases. The growth law at intermediate times can be fitted by a scaling function V ~ k^z but the range of validity of the power law is limited by size effects. The growth exponent z appears to diverge as the tapping intensity is increased.Comment: 4 pages, 4 figure

Engineering Quantum States, Nonlinear Measurements, and Anomalous Diffusion by Imaging

We show that well-separated quantum superposition states, measurements of strongly nonlinear observables, and quantum dynamics driven by anomalous diffusion can all be achieved for single atoms or molecules by imaging spontaneous photons that they emit via resonance florescence. To generate anomalous diffusion we introduce continuous measurements driven by L\'evy processes, and prove a number of results regarding their properties. In particular we present strong evidence that the only stable L\'evy density that can realize a strictly continuous measurement is the Gaussian.Comment: revtex4-1, 17 pages, 7 eps figure

The synthesis of optimal controls for linear problems with retarded controls

Synthesis of optimal controls for linear systems with retarded control

Valley current characterization of high current density resonant tunnelling diodes for terahertz-wave applications

We report valley current characterisation of high current density InGaAs/AlAs/InP resonant tunnelling diodes (RTDs) grown by metal-organic vapour phase epitaxy (MOVPE) for THz emission, with a view to investigate the origin of the valley current and optimize device performance. By applying a dual-pass fabrication technique, we are able to measure the RTD I-V characteristic for different perimeter/area ratios, which uniquely allows us to investigate the contribution of leakage current to the valley current and its effect on the PVCR from a single device. Temperature dependent (20 – 300 K) characteristics for a device are critically analysed and the effect of temperature on the maximum extractable power (PMAX) and the negative differential conductance (NDC) of the device is investigated. By performing theoretical modelling, we are able to explore the effect of typical variations in structural composition during the growth process on the tunnelling properties of the device, and hence the device performance

Radiometric temperature analysis of the Hayabusa spacecraft re-entry

Hayabusa, an unmanned Japanese spacecraft, was launched to study and collect samples from the surface of the asteroid 25143 Itokawa. In June 2010, the Hayabusa spacecraft completed it’s seven year voyage. The spacecraft and the sample return capsule (SRC) re-entered the Earth’s atmosphere over the central Australian desert at speeds on the order of 12 km/s. This provided a rare opportunity to experimentally investigate the radiative heat transfer from the shock-compressed gases in front of the sample return capsule at true-flight conditions. This paper reports on the results of observations from a tracking camera situated on the ground about 100 km from where the capsule experienced peak heating during re-entry

In vivo Detection of Hyperoxia-induced Pulmonary Endothelial Cell Death Using \u3csup\u3e99m\u3c/sup\u3eTc-Duramycin

Introduction 99mTc-duramycin, DU, is a SPECT biomarker of tissue injury identifying cell death. The objective of this study is to investigate the potential of DU imaging to quantify capillary endothelial cell death in rat lung injury resulting from hyperoxia exposure as a model of acute lung injury. Methods Rats were exposed to room air (normoxic) or \u3e 98% O2 for 48 or 60 hours. DU was injected i.v. in anesthetized rats, scintigraphy images were acquired at steady-state, and lung DU uptake was quantified from the images. Post-mortem, the lungs were removed for histological studies. Sequential lung sections were immunostained for caspase activation and endothelial and epithelial cells. Results Lung DU uptake increased significantly (p \u3c 0.001) by 39% and 146% in 48-hr and 60-hr exposed rats, respectively, compared to normoxic rats. There was strong correlation (r2 = 0.82, p = 0.005) between lung DU uptake and the number of cleaved caspase 3 (CC3) positive cells, and endothelial cells accounted for more than 50% of CC3 positive cells in the hyperoxic lungs. Histology revealed preserved lung morphology through 48 hours. By 60 hours there was evidence of edema, and modest neutrophilic infiltrate. Conclusions Rat lung DU uptake in vivo increased after just 48 hours of \u3e 98% O2 exposure, prior to the onset of any substantial evidence of lung injury. These results suggest that apoptotic endothelial cells are the primary contributors to the enhanced DU lung uptake, and support the utility of DU imaging for detecting early endothelial cell death in vivo

Generic Fibrational Induction

This paper provides an induction rule that can be used to prove properties of data structures whose types are inductive, i.e., are carriers of initial algebras of functors. Our results are semantic in nature and are inspired by Hermida and Jacobs' elegant algebraic formulation of induction for polynomial data types. Our contribution is to derive, under slightly different assumptions, a sound induction rule that is generic over all inductive types, polynomial or not. Our induction rule is generic over the kinds of properties to be proved as well: like Hermida and Jacobs, we work in a general fibrational setting and so can accommodate very general notions of properties on inductive types rather than just those of a particular syntactic form. We establish the soundness of our generic induction rule by reducing induction to iteration. We then show how our generic induction rule can be instantiated to give induction rules for the data types of rose trees, finite hereditary sets, and hyperfunctions. The first of these lies outside the scope of Hermida and Jacobs' work because it is not polynomial, and as far as we are aware, no induction rules have been known to exist for the second and third in a general fibrational framework. Our instantiation for hyperfunctions underscores the value of working in the general fibrational setting since this data type cannot be interpreted as a set.Comment: For Special Issue from CSL 201