Amalgamation and interpolation in ordered algebras

The first part of this paper provides a comprehensive and self-contained account of the interrelationships between algebraic properties of varieties and properties of their free algebras and equational consequence relations. In particular, proofs are given of known equivalences between the amalgamation property and the Robinson property, the congruence extension property and the extension property, and the flat amalgamation property and the deductive interpolation property, as well as various dependencies between these properties. These relationships are then exploited in the second part of the paper in order to provide new proofs of amalgamation and deductive interpolation for the varieties of lattice-ordered abelian groups and MV-algebras, and to determine important subvarieties of residuated lattices where these properties hold or fail. In particular, a full description is given of all subvarieties of commutative GMV-algebras possessing the amalgamation property.

Precipitation isoscape of high reliefs: interpolation scheme designed and tested for monthly resolved precipitation oxygen isotope records of an Alpine domain

Stable oxygen isotope composition of atmospheric precipitation (δ18Op) was scrutinized from 39 stations distributed over Switzerland and its border zone. Monthly amount-weighted δ18Op values averaged over the 1995–2000 period showed the expected strong linear altitude dependence (−0.15 to −0.22‰ per 100 m) only during the summer season (May–September). Steeper gradients (~ −0.56 to −0.60‰ per 100 m) were observed for winter months over a low elevation belt, while hardly any altitudinal difference was seen for high elevation stations. This dichotomous pattern could be explained by the characteristically shallower vertical atmospheric mixing height during winter season and provides empirical evidence for recently simulated effects of stratified atmospheric flow on orographic precipitation isotopic ratios. This helps explain "anomalous" deflected altitudinal water isotope profiles reported from many other high relief regions. Grids and isotope distribution maps of the monthly δ18Op have been calculated over the study region for 1995–1996. The adopted interpolation method took into account both the variable mixing heights and the seasonal difference in the isotopic lapse rate and combined them with residual kriging. The presented data set allows a point estimation of δ18Op with monthly resolution. According to the test calculations executed on subsets, this biannual data set can be extended back to 1992 with maintained fidelity and, with a reduced station subset, even back to 1983 at the expense of faded reliability of the derived δ18Op estimates, mainly in the eastern part of Switzerland. Before 1983, reliable results can only be expected for the Swiss Plateau since important stations representing eastern and south-western Switzerland were not yet in operation.

Quantitative morphometric analysis of lakes using GIS: rectangularity R , ellipticity E , orientation O , and the rectangularity vs. ellipticity index, REi

Quantitative measures of polygon shapes and orientation are important elements of geospatial analysis. These kinds of measures are particularly valuable in the case of lakes, where shape and orientation patterns can help identifying the geomorphological agents behind lake formation and evolution. However, the lack of built-in tools in commercial geographic information system (GIS) software packages designed for this kind of analysis has meant that many researchers often must rely on tools and workarounds that are not always accurate. Here, an easy-to-use method to measure rectangularity R, ellipticity E, and orientation O is developed. In addition, a new rectangularity vs. ellipticity index, REi, is defined. Following a step-by-step process, it is shown how these measures and index can be easily calculated using a combination of GIS built-in functions. The identification of shapes and estimation of orientations performed by this method is applied to the case study of the geometric and oriented lakes of the Llanos de Moxos, in the Bolivian Amazon, where shape and orientation have been the two most important elements studied to infer possible formation mechanisms. It is shown that, thanks to these new indexes, shape and orientation patterns are unveiled, which would have been hard to identify otherwise.

A global radiosonde and tracked balloon archive on 16 pressure levels (GRASP) back to 1905 – Part 1: Merging and interpolation to 00:00 and 12:00 GMT

Many observed time series of the global radiosonde or PILOT networks exist as fragments distributed over different archives. Identifying and merging these fragments can enhance their value for studies on the three-dimensional spatial structure of climate change. The Comprehensive Historical Upper-Air Network (CHUAN version 1.7), which was substantially extended in 2013, and the Integrated Global Radiosonde Archive (IGRA) are the most important collections of upper-air measurements taken before 1958. CHUAN (tracked) balloon data start in 1900, with higher numbers from the late 1920s onward, whereas IGRA data start in 1937. However, a substantial fraction of those measurements have not been taken at synoptic times (preferably 00:00 or 12:00 GMT) and on altitude levels instead of standard pressure levels. To make them comparable with more recent data, the records have been brought to synoptic times and standard pressure levels using state-of-the-art interpolation techniques, employing geopotential information from the National Oceanic and Atmospheric Administration (NOAA) 20th Century Reanalysis (NOAA 20CR). From 1958 onward the European Re-Analysis archives (ERA-40 and ERA-Interim) available at the European Centre for Medium-Range Weather Forecasts (ECMWF) are the main data sources. These are easier to use, but pilot data still have to be interpolated to standard pressure levels. Fractions of the same records distributed over different archives have been merged, if necessary, taking care that the data remain traceable back to their original sources. If possible, station IDs assigned by the World Meteorological Organization (WMO) have been allocated to the station records. For some records which have never been identified by a WMO ID, a local ID above 100 000 has been assigned. The merged data set contains 37 wind records longer than 70 years and 139 temperature records longer than 60 years. It can be seen as a useful basis for further data processing steps, most notably homogenization and gridding, after which it should be a valuable resource for climatological studies. Homogeneity adjustments for wind using the NOAA-20CR as a reference are described in Ramella Pralungo and Haimberger (2014). Reliable homogeneity adjustments for temperature beyond 1958 using a surface-data-only reanalysis such as NOAA-20CR as a reference have yet to be created. All the archives and metadata files are available in ASCII and netCDF format in the PANGAEA archive

Interpolation of hard and soft dilepton rates

Strict next-to-leading order (NLO) results for the dilepton production rate from a QCD plasma at temperatures above a few hundred MeV suffer from a breakdown of the loop expansion in the regime of soft invariant masses M 2 ≪ (πT)2. In this regime an LPM resummation is needed for obtaining the correct leading-order result. We show how to construct an interpolation between the hard NLO and the leading-order LPM expression, which is theoretically consistent in both regimes and free from double counting. The final numerical results are presented in a tabulated form, suitable for insertion into hydrodynamical codes.

GIS-Karte des Südsudans gewinnt Kartografie-Preis

Eine vom Centre for Develpment and Environment (CDE) der Universität Bern gestaltete Karte der südsudanesischen Region East Equatoria hat den „New Mapmaker Award 2009“ gewonnen. Der Preis wird gemeinsam von der britischen Kartografiegesellschaft und der amerikanischen National Geographic Society vergeben. Die im Rahmen eines Capacity-Development- Programms für Geoinformationsmanagement entworfene Karte wurde vollumfänglich in ArcMap aufgebaut, ohne Einsatz von Graphiksoftware.

Modal interpolation via nested sequents

The main method of proving the Craig Interpolation Property (CIP) constructively uses cut-free sequent proof systems. Until now, however, no such method has been known for proving the CIP using more general sequent-like proof formalisms, such as hypersequents, nested sequents, and labelled sequents. In this paper, we start closing this gap by presenting an algorithm for proving the CIP for modal logics by induction on a nested-sequent derivation. This algorithm is applied to all the logics of the so-called modal cube.

GIS layers on Human-Elephant conflicts in Laikipia District

GIS layers on Human-Elephant conflicts in Laikipia District: aerial counts, wildlife distribution, land-use, Human-Elephant conflicts hotspots and temporal patterns, and conflict deterrence activities

An automated method for mapping physical soil and water conservation structures on cultivated land using GIS and remote sensing techniques

An efficient and reliable automated model that can map physical Soil and Water Conservation (SWC) structures on cultivated land was developed using very high spatial resolution imagery obtained from Google Earth and ArcGIS, ERDAS IMAGINE, and SDC Morphology Toolbox for MATLAB and statistical techniques. The model was developed using the following procedures: (1) a high-pass spatial filter algorithm was applied to detect linear features, (2) morphological processing was used to remove unwanted linear features, (3) the raster format was vectorized, (4) the vectorized linear features were split per hectare (ha) and each line was then classified according to its compass direction, and (5) the sum of all vector lengths per class of direction per ha was calculated. Finally, the direction class with the greatest length was selected from each ha to predict the physical SWC structures. The model was calibrated and validated on the Ethiopian Highlands. The model correctly mapped 80% of the existing structures. The developed model was then tested at different sites with different topography. The results show that the developed model is feasible for automated mapping of physical SWC structures. Therefore, the model is useful for predicting and mapping physical SWC structures areas across diverse areas.