Refocusing generalised normalisation

When defined with general elimination/application rules, natural deduction and $\lambda$-calculus become closer to sequent calculus. In order to get real isomorphism, normalisation has to be defined in a ``multiary'' variant, in which reduction rules are necessarily non-local (reason: nomalisation, like cut-elimination, acts at the \emph{head} of applicative terms, but natural deduction focuses at the \emph{tail} of such terms). Non-local rules are bad, for instance, for the mechanization of the system. A solution is to extend natural deduction even further to a \emph{unified calculus} based on the unification of cut and general elimination. In the unified calculus, a sequent term behaves like in the sequent calculus, whereas the reduction steps of a natural deduction term are interleaved with explicit steps for bringing heads to focus. A variant of the calculus has the symmetric role of improving sequent calculus in dealing with tail-active permutative conversions

Characterising strongly normalising intuitionistic sequent terms

This paper gives a characterisation, via intersection types, of the strongly normalising terms of an intuitionistic sequent calculus (where LJ easily embeds). The soundness of the typing system is reduced to that of a well known typing system with intersection types for the ordinary lambda-calculus. The completeness of the typing system is obtained from subject expansion at root position. This paper's sequent term calculus integrates smoothly the lambda-terms with generalised application or explicit substitution. Strong normalisability of these terms as sequent terms characterises their typeability in certain "natural'' typing systems with intersection types. The latter are in the natural deduction format, like systems previously studied by Matthes and Lengrand et al., except that they do not contain any extra, exceptional rules for typing generalised applications or substitution

A multistratigraphic approach to pinpoint the Permian-Triassic boundary in continental depositsThe Zechstein–Lower Buntsandstein transition in Germany

© 2017 Elsevier B.V.The Central European Basin is very suitable for high-resolution multistratigraphy of Late Permian to Early Triassic continental deposits. Here the well exposed continuous transition of the lithostratigraphic Zechstein and Buntsandstein Groups of Central Germany was studied for isotope-chemostratigraphy (δ13Corg, δ13Ccarb, δ18Ocarb), major and trace element geochemistry, magnetostratigraphy, palynology, and conchostracan biostratigraphy. The analysed material was obtained from both classical key sections (abandoned Nelben clay pit, Caaschwitz quarries, Thale railway cut, abandoned Heinebach clay pit) and a recent drill core section (Caaschwitz 6/2012) spanning the Permian-Triassic boundary. The Zechstein–Buntsandstein transition of Central Germany consists of a complex sedimentary facies comprising sabkha, playa lake, aeolian, and fluvial deposits of predominantly red-coloured siliciclastics and intercalations of lacustrine oolitic limestones. The new data on δ13Corg range from − 28.7 to − 21.7 ‰ showing multiple excursions. Most prominent negative shifts correlate with intercalations of oolites and grey-coloured clayey siltstones, while higher δ13Corg values correspond to an onset of palaeosol overprint. The δ13Ccarb values range from − 9.7 to − 1.3 ‰ with largest variations recorded in dolomitic nodules from the Zechstein Group. In contrast to sedimentary facies shifts across the Zechstein-Buntsandstein boundary, major element values used as a proxy (CIA, CIA*, CIA-K) for weathering conditions indicate climatic stability. Trace element data used for a geochemical characterization of the Late Permian to Early Triassic transition in Central Germany indicate a decrease in Rb contents at the Zechstein-Buntsandstein boundary. New palynological data obtained from the Caaschwitz quarry section reveal occurrences of Late Permian palynomorphs in the Lower Fulda Formation, while Early Triassic elements were recorded in the upper part of the Upper Fulda Formation. The present study confirms an onset of a normal-polarized magnetozone in the Upper Fulda Formation of the Caaschwitz quarry section supporting an interregional correlation of this crucial stratigraphic interval with the normal magnetic polarity of the basal Early Triassic known from marine sections in other regions. Based on a synthesis of the multistratigraphic data, the Permian-Triassic boundary is proposed to be placed in the lower part of the Upper Fulda Formation, which is biostratigraphically confirmed by the first occurrence date of the Early Triassic Euestheria gutta-Palaeolimnadiopsis vilujensis conchostracan fauna. Rare records of conchostracans reported from the siliciclastic deposits of the lower to middle Zechstein Group may point to its potential for further biostratigraphic subdivision of the Late Permian continental deposits

Novosti u sprječavanju, dijagnostici i liječenju infektivnih bolesti

Rizični čimbenici za dugoročni mortalitet od bakterijemija koje je uzrokovao Staphylococcus aureus Infekcija virusom Zika u trudnica u Rio de Janeiru – preliminarni izvještaj Fekalni mikrobiom pri pojavi juvenilnog idiopatskog artritisa Treće međunarodne konsenzusne definicije sepse i septičkog šoka (Sepsis-3) Dijagnostička i prognostička korist prokalcitonina u pacijenata koji dolaze u hitne ambulante sa simtomom dispnej

Disparity Changes in 370 Ma Devonian Fossils: The Signature of Ecological Dynamics?

Early periods in Earth's history have seen a progressive increase in complexity of the ecosystems, but also dramatic crises decimating the biosphere. Such patterns are usually considered as large-scale changes among supra-specific groups, including morphological novelties, radiation, and extinctions. Nevertheless, in the same time, each species evolved by the way of micro-evolutionary processes, extended over millions of years into the evolution of lineages. How these two evolutionary scales interacted is a challenging issue because this requires bridging a gap between scales of observation and processes. The present study aims at transferring a typical macro-evolutionary approach, namely disparity analysis, to the study of fine-scale evolutionary variations in order to decipher what processes actually drove the dynamics of diversity at a micro-evolutionary level. The Late Frasnian to Late Famennian period was selected because it is punctuated by two major macro-evolutionary crises, as well as a progressive diversification of marine ecosystem. Disparity was estimated through this period on conodonts, tooth-like fossil remains of small eel-like predators that were part of the nektonic fauna. The study was focused on the emblematic genus of the period, Palmatolepis. Strikingly, both crises affected an already impoverished Palmatolepis disparity, increasing risks of random extinction. The major disparity signal rather emerged as a cycle of increase and decrease in disparity during the inter-crises period. The diversification shortly followed the first crisis and might correspond to an opportunistic occupation of empty ecological niche. The subsequent oriented shrinking in the morphospace occupation suggests that the ecological space available to Palmatolepis decreased through time, due to a combination of factors: deteriorating climate, expansion of competitors and predators. Disparity changes of Palmatolepis thus reflect changes in the structure of the ecological space itself, which was prone to evolve during this ancient period where modern ecosystems were progressively shaped

Evidence for preindustrial variations in the marine surface water carbonate system from coralline sponges

Coralline sponge skeletons are excellent tools for reconstructing the carbon isotope history ofdissolved inorganic carbon (DIC) in tropical surface waters. Carbon isotope records from corallinesponges clearly reflect the industrial12C increase in atmospheric CO2with a precision that permitsquantitative interpretations. We find from a set of d13C records of four Caribbean sponge specimensthat the isotopic response of surface water DIC to the changing isotopic composition of atmosphericCO2varied dynamically during the last century, depending on the rate of atmospheric change. Three ofour sponges provide 600 year long d13C records. For the first time, we can reconstruct surface waterd13CDICfor the full history of the industrial CO2release as well as the preceding preindustrial periodback to the beginning of the Little Ice Age. This provides a well-founded estimate of theanthropogenically uninfluenced, preindustrial background level of surface water13C/12C ratios. Ourrecords show small but systematic variations that appear to be linked to the climate fluctuations of theLittle Ice Age

A formalized proof of strong normalization for guarded recursive types

We consider a simplified version of Nakano’s guarded fixed-point types in a representation by infinite type expressions, defined coinductively. Smallstep reduction is parametrized by a natural number “depth” that expresses under how many guards we may step during evaluation. We prove that reduction is strongly normalizing for any depth. The proof involves a typed inductive notion of strong normalization and a Kripke model of types in two dimensions: depth and typing context. Our results have been formalized in Agda and serve as a case study of reasoning about a language with coinductive type expressions