Completeness and Decidability of Converse PDL in the Constructive Type Theory of Coq

International audienceThe completeness proofs for Propositional Dynamic Logic (PDL) in the literature are non-constructive and usually presented in an informal manner. We obtain a formal and constructive completeness proof for Converse PDL by recasting a completeness proof by Kozen and Parikh into our constructive setting. We base our proof on a Pratt-style decision method for satisfiability constructing finite models for satisfiable formulas and pruning refutations for unsatisfiable formulas. Completeness of Segerberg's axiomatization of PDL is then obtained by translating pruning refutations to derivations in the Hilbert system. We first treat PDL without converse and then extend the proofs to Converse PDL. All results are formalized in Coq/Ssreflect

The mitotic spindle mediates inheritance of the Golgi ribbon structure

The mammalian Golgi ribbon disassembles during mitosis and reforms in both daughter cells after division. Mitotic Golgi membranes concentrate around the spindle poles, suggesting that the spindle may control Golgi partitioning. To test this, cells were induced to divide asymmetrically with the entire spindle segregated into only one daughter cell. A ribbon reforms in the nucleated karyoplasts, whereas the Golgi stacks in the cytoplasts are scattered. However, the scattered Golgi stacks are polarized and transport cargo. Microinjection of Golgi extract together with tubulin or incorporation of spindle materials rescues Golgi ribbon formation. Therefore, the factors required for postmitotic Golgi ribbon assembly are transferred by the spindle, but the constituents of functional stacks are partitioned independently, suggesting that Golgi inheritance is regulated by two distinct mechanisms

Stainless steel made to rust: a robust water-splitting catalyst with benchmark characteristics

The oxygen evolution reaction (OER) is known as the efficiency-limiting step for the electrochemical cleavage of water mainly due to the large overpotentials commonly used materials on the anode side cause. Since Ni–Fe oxides reduce overpotentials occurring in the OER dramatically they are regarded as anode materials of choice for the electrocatalytically driven water-splitting reaction. We herewith show that a straightforward surface modification carried out with AISI 304, a general purpose austenitic stainless steel, very likely, based upon a dissolution mechanism, to result in the formation of an ultra-thin layer consisting of Ni, Fe oxide with a purity >99%. The Ni enriched thin layer firmly attached to the steel substrate is responsible for the unusual highly efficient anodic conversion of water into oxygen as demonstrated by the low overpotential of 212 mV at 12 mA cm−2 current density in 1 M KOH, 269.2 mV at 10 mA cm−2 current density in 0.1 M KOH respectively. The Ni, Fe-oxide layer formed on the steel creates a stable outer sphere, and the surface oxidized steel samples proved to be inert against longer operating times (>150 ks) in alkaline medium. In addition Faradaic efficiency measurements performed through chronopotentiometry revealed a charge to oxygen conversion close to 100%, thus underpinning the conclusion that no “inner oxidation” based on further oxidation of the metal matrix below the oxide layer occurs. These key figures achieved with an almost unrivalled-inexpensive and unrivalled-accessible material, are among the best ever presented activity characteristics for the anodic water-splitting reaction at pH 13

Temperature and stable isotope variationsin different water masses from the Alboran Sea (western Mediterranean) between 250 150 ka

Mg/Ca, Sr/Ca, and stable isotope measurements have been performed on tests from the planktonic foraminifers Globigerinoides ruber (white), Globigerina bulloides, and Neogloboquadrina pachyderma (right coiling) in samples from Ocean Drilling Program site 977A in the Alboran Sea (Western Mediterranean). The evolution of different water masses between 250 and 150 ka is described. Warm substages were characterized by strong seasonality and thermal stratification of the water column. By contrast, less pronounced seasonality and basin stratification seem to prevail during cold substages. Several periods of stratification due to the low salinity of the upper water mass occurred during the formation of organic-rich layers and also during a possible Heinrich-like event at 220 ka. The three foraminifer species studied show a common and large shell Sr/Ca variability in short timescales, suggesting changes in the global ocean Sr/Ca ratio as one of the main causes of variations in shell composition

Position of the Polar Front along the western Iberian margin during key cold episodes of the last 45 ka

This paper documents the migration of the Polar Front (PF) over the Iberian margin during some of the cold climatic extremes of the last 45 ka. It is based on a compilation of robust and coherent paleohydrological proxies obtained from eleven cores distributed between 36 and 42°N. Planktonic δ18O (Globigerina bulloides), ice-rafted detritus concentrations, and the relative abundance of the polar foraminifera Neogloboquadrina pachyderma sinistral were used to track the PF position. These three data sets, compared from core to core, show a consistent evolution of the sea surface paleohydrology along the Iberian margin over the last 45 ka. We focused on five time slices representative of cold periods under distinct paleoenvironmental forcings: the 8.2 ka event and the Younger Dryas (two recent cold events occurring within high values of summer insolation), Heinrich events 1 and 4 (reflecting major episodes of massive iceberg discharges into the North Atlantic), and the Last Glacial Maximum (typifying the highest ice volume accumulated in the Northern Hemisphere). For each event, we generated schematic maps mirroring past sea surface hydrological conditions. The maps revealed that the Polar Front presence along the Iberian margin was restricted to Heinrich events. The sea surface conditions during the Last Glacial Maximum were close to those at present day, except for the northern sites which briefly experienced subarctic conditions

Variability of the western Mediterranean Sea surface temperature during the last 25,000 years and its connection with the Northern Hemisphere climatic changes

Sea surface temperature (SST) profiles over the last 25 kyr derived from alkenone measurements are studied in four cores from a W-E latitudinal transect encompassing the Gulf of Cadiz (Atlantic Ocean), the Alboran Sea, and the southern Tyrrhenian Sea (western Mediterranean). The results document the sensitivity of the Mediterranean region to the short climatic changes of the North Atlantic Ocean, particularly those involving the latitudinal position of the polar front. The amplitude of the SST oscillations increases toward the Tyrrhenian Sea, indicating an amplification effect of the Atlantic signal by the climatic regime of the Mediterranean region. All studied cores show a shorter cooling phase (700 years) for the Younger Dryas (YD) than that observed in the North Atlantic region (1200 years). This time diachroneity is related to an intra-YD climatic change documented in the European continent. Minor oscillations in the southward displacement of the North Atlantic polar front may also have driven this early warming in the studied area. During the Holocene a regional diachroneity propagating west to east is observed for the SST maxima, 11.5-10.2 kyr B.P. in the Gulf of Cadiz, 10-9 kyr B.P. in the Alboran Sea, and 8.9-8.4 kyr B.P. in the Thyrrenian Sea. A general cooling trend from these SST maxima to present day is observed during this stage, which is marked by short cooling oscillations with a periodicity of 730±40 years and its harmonics

Inter- versus intramodal integration in sensorimotor synchronization: a combined behavioral and magnetoencephalographic study

Although the temporal occurrence of the pacing signal is predictable in sensorimotor synchronization tasks, normal subjects perform on-the-beat-tapping to an isochronous auditory metronome with an anticipatory error. This error originates from an intermodal task, that is, subjects have to bring information from the auditory and tactile modality to coincide. The aim of the present study was to illuminate whether the synchronization error is a finding specific to an intermodal timing task and whether the underlying cortical mechanisms are modality-specific or supramodal. We collected behavioral data and cortical evoked responses by magneto-encephalography (MEG) during performance of cross- and unimodal tapping-tasks. As expected, subjects showed negative asynchrony in performing an auditorily paced tapping task. However, no asynchrony emerged during tactile pacing, neither during pacing at the opposite finger nor at the toe. Analysis of cortical signals resulted in a three dipole model best explaining tap-contingent activity in all three conditions. The temporal behavior of the sources was similar between the conditions and, thus, modality independent. The localization of the two earlier activated sources was modality-independent as well whereas location of the third source varied with modality. In the auditory pacing condition it was localized in contralateral primary somatosensory cortex, during tactile pacing it was localized in contralateral posterior parietal cortex. In previous studies with auditory pacing the functional role of this third source was contradictory: A special temporal coupling pattern argued for involvement of the source in evaluating the temporal distance between tap and click whereas subsequent data gave no evidence for such an interpretation. Present data shed new light on this question by demonstrating differences between modalities in the localization of the third source with similar temporal behavior

Thermohaline instability in the North Atlantic during meltwater events: Stable isotope and ice-rafted detritus records from Core SO75-26KL, Portuguese Margin

A benthic isotope record has been measured for core SO75-26KL from the upper Portuguese margin (1099 m water depth) to monitor the response of thermohaline overturn in the North Atlantic during Heinrich events. Evaluating benthic δ18O in TS diagrams in conjunction with equilibrium δc fractionation implies that advection of Mediterranean outflow water (MOW) to the upper Portuguese margin was significantly reduced during the last glacial (< 15% compared to 30% today). The benthic isotope record along core SO75-26KL therefore primarily monitors variability of glacial North Atlantic conveyor circulation. The 14C-accelerator mass spectrometry ages of 13.54±.07 and 20.46±.12 ka for two ice-rafted detritus (IRD) layers in the upper core section and an interpolated age of 36.1 ka for a third IRD layer deeper in the core are in the range of published 14C ages for Heinrich events H1, H2, and H4. Marked depletion of benthic δ13C by 0.7-1.1‰ during the Heinrich events suggests reduced thermohaline overturn in the North Atlantic during these events. Close similarity between meltwater patterns (inferred from planktonic δ18O) at Site 609 and ventilation patterns (inferred from benthic δ13C) in core SO75-26KL implies coupling between thermohaline overturn and surface forcing, as is also suggested by ocean circulation models. Benthic δ13C starts to decrease 1.5-2.5 kyr before Heinrich events Hl and H4, fully increased values are reached 1.5-3 kyr after the events, indicating a successive slowdown of thermohaline circulation well before the events and resumption of the conveyor's full strength well after the events. Benthic δ13C changes in the course of the Heinrich events show subtle maxima and minima suggesting oscillatory behavior of thermohaline circulation, a distinct feature of thermohaline instability in numerical models. Inferrred gradual spin-up of thermohaline circulation after Hl and H4 is in contrast to abrupt wanning in the North Atlantic region that is indicated by sudden increases in Greenland ice core δ18O and in marine faunal records from the northern North Atlantic. From this we infer that thermohaline circulation can explain only in part the rapid climatic oscillations seen in glacial sections of the Greenland ice core record

LSST: from Science Drivers to Reference Design and Anticipated Data Products

(Abridged) We describe here the most ambitious survey currently planned in the optical, the Large Synoptic Survey Telescope (LSST). A vast array of science will be enabled by a single wide-deep-fast sky survey, and LSST will have unique survey capability in the faint time domain. The LSST design is driven by four main science themes: probing dark energy and dark matter, taking an inventory of the Solar System, exploring the transient optical sky, and mapping the Milky Way. LSST will be a wide-field ground-based system sited at Cerro Pach\'{o}n in northern Chile. The telescope will have an 8.4 m (6.5 m effective) primary mirror, a 9.6 deg$^2$ field of view, and a 3.2 Gigapixel camera. The standard observing sequence will consist of pairs of 15-second exposures in a given field, with two such visits in each pointing in a given night. With these repeats, the LSST system is capable of imaging about 10,000 square degrees of sky in a single filter in three nights. The typical 5$\sigma$ point-source depth in a single visit in $r$ will be $\sim 24.5$ (AB). The project is in the construction phase and will begin regular survey operations by 2022. The survey area will be contained within 30,000 deg$^2$ with $\delta<+34.5^\circ$, and will be imaged multiple times in six bands, $ugrizy$, covering the wavelength range 320--1050 nm. About 90\% of the observing time will be devoted to a deep-wide-fast survey mode which will uniformly observe a 18,000 deg$^2$ region about 800 times (summed over all six bands) during the anticipated 10 years of operations, and yield a coadded map to $r\sim27.5$. The remaining 10\% of the observing time will be allocated to projects such as a Very Deep and Fast time domain survey. The goal is to make LSST data products, including a relational database of about 32 trillion observations of 40 billion objects, available to the public and scientists around the world.Comment: 57 pages, 32 color figures, version with high-resolution figures available from https://www.lsst.org/overvie