Automatically proving equivalence by type-safe reflection

We are also grateful for the support of the Scottish Informatics and Computer Science Alliance (SICSA) and EPSRC grant EP/N024222/1.One difficulty with reasoning and programming with dependent types is that proof obligations arise naturally once programs become even moderately sized. For example, implementing an adder for binary numbers indexed over their natural number equivalents naturally leads to proof obligations for equalities of expressions over natural numbers. The need for these equality proofs comes, in intensional type theories, from the fact that the propositional equality enables us to prove as equal terms that are not judgementally equal, which means that the typechecker can’t always obtain equalities by reduction. As far as possible, we would like to solve such proof obligations automatically. In this paper, we show one way to automate these proofs by reflection in the dependently typed programming language Idris. We show how defining reflected terms indexed by the original Idris expression allows us to construct and manipulate proofs. We build a hierarchy of tactics for proving equivalences in semi-groups, monoids, commutative monoids, groups, commutative groups, semi-rings and rings. We also show how each tactic reuses those from simpler structures, thus avoiding duplication of code and proofs.Postprin

Quantifying Robotic Swarm Coverage

In the field of swarm robotics, the design and implementation of spatial density control laws has received much attention, with less emphasis being placed on performance evaluation. This work fills that gap by introducing an error metric that provides a quantitative measure of coverage for use with any control scheme. The proposed error metric is continuously sensitive to changes in the swarm distribution, unlike commonly used discretization methods. We analyze the theoretical and computational properties of the error metric and propose two benchmarks to which error metric values can be compared. The first uses the realizable extrema of the error metric to compute the relative error of an observed swarm distribution. We also show that the error metric extrema can be used to help choose the swarm size and effective radius of each robot required to achieve a desired level of coverage. The second benchmark compares the observed distribution of error metric values to the probability density function of the error metric when robot positions are randomly sampled from the target distribution. We demonstrate the utility of this benchmark in assessing the performance of stochastic control algorithms. We prove that the error metric obeys a central limit theorem, develop a streamlined method for performing computations, and place the standard statistical tests used here on a firm theoretical footing. We provide rigorous theoretical development, computational methodologies, numerical examples, and MATLAB code for both benchmarks.Comment: To appear in Springer series Lecture Notes in Electrical Engineering (LNEE). This book contribution is an extension of our ICINCO 2018 conference paper arXiv:1806.02488. 27 pages, 8 figures, 2 table

Fabrication of super-hydrophobic nickel film on copper substrate with improved corrosion inhibition by electrodeposition process

Inspired by the famous “lotus effect”, we have fabricated the super-hydrophobic surfaces with nickel film on copper substrates using a one-step electrodeposition method. By adjusting processing time, water contact angle of as-prepared surfaces can reach as high as 160.3 ± 1.5° with small rolling angle of 3.0 ± 0.5°, showing excellent super-hydrophobicity. After the deposition of nickel coating, the pristine copper surfaces became much rough with packed cauliflower-/thorn-like clusters. This unique surface texture contributed to trapping large amount of air and forming the air cushion underneath the water droplet, which can prevent the liquids contacting the copper substrate. The examination of surface chemical compositions implied that the deposited super-hydrophobic coating consisted of nickel crystals and nickel myristate. In this research, the formation mechanism of the electrodeposited super-hydrophobicity was extensively explained based on the analyses of surface texture and surface chemistry. Moreover, the corrosion resistance of the as-fabricated super-hydrophobic surface was estimated by the potentiodynamic polarization tests as well as the electrochemical impedance spectroscopy (EIS) measurements. The results demonstrate that the super-hydrophobic nickel coating showed excellent corrosion inhibition in simulated seawater solution. The existence of the super-hydrophobic coating could be regarded as a barrier and thus provide a perfect air-liquid interface that inhibits the penetration of the corrosive ions. This facile and effective method of electrodeposition process offers a promising approach for mass production of super-hydrophobic surfaces on various metals

Explosive Nucleosynthesis: What we learned and what we still do not understand

This review touches on historical aspects, going back to the early days of nuclear astrophysics, initiated by B$^2$FH and Cameron, discusses (i) the required nuclear input from reaction rates and decay properties up to the nuclear equation of state, continues (ii) with the tools to perform nucleosynthesis calculations and (iii) early parametrized nucleosynthesis studies, before (iv) reliable stellar models became available for the late stages of stellar evolution. It passes then through (v) explosive environments from core-collapse supernovae to explosive events in binary systems (including type Ia supernovae and compact binary mergers), and finally (vi) discusses the role of all these nucleosynthesis production sites in the evolution of galaxies. The focus is put on the comparison of early ideas and present, very recent, understanding.Comment: 11 pages, to appear in Springer Proceedings in Physics (Proc. of Intl. Conf. "Nuclei in the Cosmos XV", LNGS Assergi, Italy, June 2018

Vascular plants of mount uyuca

Alrededor de siete millas al oeste de El Zamorano, una alta montaña pico llamado Uyuca eleva abruptamente! y del che colinas circundantes. Bañado en una tapa de nubes casi constante, el vértice de la pico ha desarrollado un extraña y maravillosa flora través de los  siglos. Para un Visitar movimiento hacia arriba en el área de bosque nublado, es como entrar hacia atrás en el tiempo

On the Generalizability of Experimental Results

The age-old question of the generalizability of the results of experiments that are conducted in artificial laboratory settings to more realistic inferential and decision making situations is considered in this paper. Conservatism in probability revision provides an example of a result that 1) has received wide attention, including attention in terms of implications for real-world decision making, on the basis of experiments conducted in artificial settings and 2) is now apparently thought by many to be highly situational and not at all a ubiquitous phenomenon, in which case its implications for real-world decision making are not as extensive as originally claimed. In this paper we consider the questions of generalizations from the laboratory to the real world in some detail, both within the context of the experiments regarding conservatism and within a more general context. In addition, we discuss some of the difficulties inherent in experimentation in realistic settings, suggest possible procedures for avoiding or at least alleviating such difficulties, and make a plea for more realistic experiments

Measurement of the B+ and B-0 lifetimes and search for CP(T) violation using reconstructed secondary vertices

The lifetimes of the B+ and B-0 mesons, and their ratio, have been measured in the OPAL experiment using 2.4 million hadronic Z(0) decays recorded at LEP. Z(0) --> b (b) over bar decays were tagged using displaced secondary vertices and high momentum electrons and muons. The lifetimes were then measured using well-reconstructed charged and neutral secondary vertices selected in this tagged data sample. The results aretau(B+) = 1.643 +/- 0.037 +/- 0.025 pstau(Bo) = 1.523 +/- 0.057 +/- 0.053 pstau(B+)/tau(Bo) = 1.079 +/- 0.064 +/- 0.041,where in each case the first error is statistical and the second systematic.A larger data sample of 3.1 million hadronic Z(o) decays has been used to search for CP and CPT violating effects by comparison of inclusive b and (b) over bar hadron decays, No evidence fur such effects is seen. The CP violation parameter Re(epsilon(B)) is measured to be Re(epsilon(B)) = 0.001 +/- 0.014 +/- 0.003and the fractional difference between b and (b) over bar hadron lifetimes is measured to(Delta tau/tau)(b) = tau(b hadron) - tau((b) over bar hadron)/tau(average) = -0.001 +/- 0.012 +/- 0.008

A Measurement of Rb using a Double Tagging Method

The fraction of Z to bbbar events in hadronic Z decays has been measured by the OPAL experiment using the data collected at LEP between 1992 and 1995. The Z to bbbar decays were tagged using displaced secondary vertices, and high momentum electrons and muons. Systematic uncertainties were reduced by measuring the b-tagging efficiency using a double tagging technique. Efficiency correlations between opposite hemispheres of an event are small, and are well understood through comparisons between real and simulated data samples. A value of Rb = 0.2178 +- 0.0011 +- 0.0013 was obtained, where the first error is statistical and the second systematic. The uncertainty on Rc, the fraction of Z to ccbar events in hadronic Z decays, is not included in the errors. The dependence on Rc is Delta(Rb)/Rb = -0.056*Delta(Rc)/Rc where Delta(Rc) is the deviation of Rc from the value 0.172 predicted by the Standard Model. The result for Rb agrees with the value of 0.2155 +- 0.0003 predicted by the Standard Model.Comment: 42 pages, LaTeX, 14 eps figures included, submitted to European Physical Journal

The Impact of Global Warming and Anoxia on Marine Benthic Community Dynamics: an Example from the Toarcian (Early Jurassic)

The Pliensbachian-Toarcian (Early Jurassic) fossil record is an archive of natural data of benthic community response to global warming and marine long-term hypoxia and anoxia. In the early Toarcian mean temperatures increased by the same order of magnitude as that predicted for the near future; laminated, organic-rich, black shales were deposited in many shallow water epicontinental basins; and a biotic crisis occurred in the marine realm, with the extinction of approximately 5% of families and 26% of genera. High-resolution quantitative abundance data of benthic invertebrates were collected from the Cleveland Basin (North Yorkshire, UK), and analysed with multivariate statistical methods to detect how the fauna responded to environmental changes during the early Toarcian. Twelve biofacies were identified. Their changes through time closely resemble the pattern of faunal degradation and recovery observed in modern habitats affected by anoxia. All four successional stages of community structure recorded in modern studies are recognised in the fossil data (i.e. Stage III: climax; II: transitional; I: pioneer; 0: highly disturbed). Two main faunal turnover events occurred: (i) at the onset of anoxia, with the extinction of most benthic species and the survival of a few adapted to thrive in low-oxygen conditions (Stages I to 0) and (ii) in the recovery, when newly evolved species colonized the re-oxygenated soft sediments and the path of recovery did not retrace of pattern of ecological degradation (Stages I to II). The ordination of samples coupled with sedimentological and palaeotemperature proxy data indicate that the onset of anoxia and the extinction horizon coincide with both a rise in temperature and sea level. Our study of how faunal associations co-vary with long and short term sea level and temperature changes has implications for predicting the long-term effects of “dead zones” in modern oceans

Organism-sediment interactions govern post-hypoxia recovery of ecosystem functioning

Hypoxia represents one of the major causes of biodiversity and ecosystem functioning loss for coastal waters. Since eutrophication-induced hypoxic events are becoming increasingly frequent and intense, understanding the response of ecosystems to hypoxia is of primary importance to understand and predict the stability of ecosystem functioning. Such ecological stability may greatly depend on the recovery patterns of communities and the return time of the system properties associated to these patterns. Here, we have examined how the reassembly of a benthic community contributed to the recovery of ecosystem functioning following experimentally-induced hypoxia in a tidal flat. We demonstrate that organism-sediment interactions that depend on organism size and relate to mobility traits and sediment reworking capacities are generally more important than recovering species richness to set the return time of the measured sediment processes and properties. Specifically, increasing macrofauna bioturbation potential during community reassembly significantly contributed to the recovery of sediment processes and properties such as denitrification, bedload sediment transport, primary production and deep pore water ammonium concentration. Such bioturbation potential was due to the replacement of the small-sized organisms that recolonised at early stages by large-sized bioturbating organisms, which had a disproportionately stronger influence on sediment. This study suggests that the complete recovery of organism-sediment interactions is a necessary condition for ecosystem functioning recovery, and that such process requires long periods after disturbance due to the slow growth of juveniles into adult stages involved in these interactions. Consequently, repeated episodes of disturbance at intervals smaller than the time needed for the system to fully recover organism-sediment interactions may greatly impair the resilience of ecosystem functioning.