Solution to the Henckell--Rhodes problem: finite FF-inverse covers do exist

For a finite connected graph $\mathcal{E}$ with set of edges $E$, a finite $E$-generated group $G$ is constructed such that the set of relations $p=1$ satisfied by $G$ (with $p$ a word over $E\cup E^{-1}$) is closed under deletion of generators (i.e.~edges). As a consequence, every element $g\in G$ admits a unique minimal set $\mathrm{C}(g)$ of edges (the \emph{content} of $g$) needed to represent $g$ as a word over $\mathrm{C}(g)\cup\mathrm{C}(g)^{-1}$. The crucial property of the group $G$ is that connectivity in the graph $\mathcal{E}$ is encoded in $G$ in the following sense: if a word $p$ forms a path $u\longrightarrow v$ in $\mathcal{E}$ then there exists a $G$-equivalent word $q$ which also forms a path $u\longrightarrow v$ and uses only edges from their content; in particular, the content of the corresponding group element $[p]_G=[q]_G$ spans a connected subgraph of $\mathcal{E}$ containing the vertices $u$ and $v$. As an application it is shown that every finite inverse monoid admits a finite $F$-inverse cover. This solves a long-standing problem of Henckell and Rhodes.Comment: 46 pages, 14 figures, new result Cor. 2.7 included, several inaccuracies removed, more details include

Strict Forest Reserve Research in the Margin of the Carpathians, the Vár-hegy Case-Study

Sixteen forest reserves are situated in the northern part of Hungary which belongs to the Carpathian region according to EURAC delimitation (Ruffini et al. 2006). These Hungarian forest reserves expand the natural forest remnant/forest reserve net of the Carpathians towards the lower hilly region, representing the deciduous beech and oak forest belts near their lower (xeric) distribution limits. This paper outlines the Hungarian forest reserves belonging to the Carpathian region and the preliminary results of current projects in the Vár-hegy Forest Reserve (Bükk Mts., Hungary) as a case study. The alteration of tree species composition was investigated here based on the reconstruction of forest history in the previous 130 years (management period) and analyses of forest stand inventory. In another project CO2 sequestration changes of these forest stands were modeled since the clear-cutting in the 1880th and carbon stored in the forest ecosystem compartments was estimated. Our results show that the forest reserve stands are presently in a transition state from the managed forest towards a more natural mixed forest with several age-classes

An easily implemented agro-hydrological procedure with dynamic root simulation for water transfer in the crop–soil system: validation and application

Models for water transfer in the crop–soil system are key components of agro-hydrological models for irrigation, fertilizer and pesticide practices. Many of the hydrological models for water transfer in the crop–soil system are either too approximate due to oversimplified algorithms or employ complex numerical schemes. In this paper we developed a simple and sufficiently accurate algorithm which can be easily adopted in agro-hydrological models for the simulation of water dynamics. We used a dual crop coefficient approach proposed by the FAO for estimating potential evaporation and transpiration, and a dynamic model for calculating relative root length distribution on a daily basis. In a small time step of 0.001 d, we implemented algorithms separately for actual evaporation, root water uptake and soil water content redistribution by decoupling these processes. The Richards equation describing soil water movement was solved using an integration strategy over the soil layers instead of complex numerical schemes. This drastically simplified the procedures of modeling soil water and led to much shorter computer codes. The validity of the proposed model was tested against data from field experiments on two contrasting soils cropped with wheat. Good agreement was achieved between measurement and simulation of soil water content in various depths collected at intervals during crop growth. This indicates that the model is satisfactory in simulating water transfer in the crop–soil system, and therefore can reliably be adopted in agro-hydrological models. Finally we demonstrated how the developed model could be used to study the effect of changes in the environment such as lowering the groundwater table caused by the construction of a motorway on crop transpiration

Developing a reliable strategy to infer the effective soil hydraulic properties from field evaporation experiments for agro-hydrological models

The Richards equation has been widely used for simulating soil water movement. However, the take-up of agro-hydrological models using the basic theory of soil water flow for optimizing irrigation, fertilizer and pesticide practices is still low. This is partly due to the difficulties in obtaining accurate values for soil hydraulic properties at a field scale. Here, we use an inverse technique to deduce the effective soil hydraulic properties, based on measuring the changes in the distribution of soil water with depth in a fallow field over a long period, subject to natural rainfall and evaporation using a robust micro Genetic Algorithm. A new optimized function was constructed from the soil water contents at different depths, and the soil water at field capacity. The deduced soil water retention curve was approximately parallel but higher than that derived from published pedo-tranfer functions for a given soil pressure head. The water contents calculated from the deduced soil hydraulic properties were in good agreement with the measured values. The reliability of the deduced soil hydraulic properties was tested in reproducing data measured from an independent experiment on the same soil cropped with leek. The calculation of root water uptake took account for both soil water potential and root density distribution. Results show that the predictions of soil water contents at various depths agree fairly well with the measurements, indicating that the inverse analysis is an effective and reliable approach to estimate soil hydraulic properties, and thus permits the simulation of soil water dynamics in both cropped and fallow soils in the field accurately

Blumenols as shoot markers of root symbiosis with arbuscular mycorrhizal fungi.

High-through-put (HTP) screening for functional arbuscular mycorrhizal fungi (AMF)-associations is challenging because roots must be excavated and colonization evaluated by transcript analysis or microscopy. Here we show that specific leaf-metabolites provide broadly applicable accurate proxies of these associations, suitable for HTP-screens. With a combination of untargeted and targeted metabolomics, we show that shoot accumulations of hydroxy- and carboxyblumenol C-glucosides mirror root AMF-colonization in Nicotiana attenuata plants. Genetic/pharmacologic manipulations indicate that these AMF-indicative foliar blumenols are synthesized and transported from roots to shoots. These blumenol-derived foliar markers, found in many di- and monocotyledonous crop and model plants (Solanum lycopersicum, Solanum tuberosum, Hordeum vulgare, Triticum aestivum, Medicago truncatula and Brachypodium distachyon), are not restricted to particular plant-AMF interactions, and are shown to be applicable for field-based QTL mapping of AMF-related genes

Electronic structure and nesting-driven enhancement of the RKKY interaction at the magnetic ordering propagation vector in Gd2PdSi3 and Tb2PdSi3

We present first-time measurements of the Fermi surface and low-energy electronic structure of intermetallic compounds Gd2PdSi3 and Tb2PdSi3 by means of angle-resolved photoelectron spectroscopy (ARPES). Both materials possess a flower-like Fermi surface consisting of an electron barrel at the G point surrounded by spindle-shaped electron pockets originating from the same band. The band bottom of both features lies at 0.5 eV below the Fermi level. From the experimentally measured band structure, we estimate the momentum-dependent RKKY coupling strength and demonstrate that it is peaked at the 1/2 GK wave vector. Comparison with neutron diffraction data from the same crystals shows perfect agreement of this vector with the propagation vector of the low-temperature in-plane magnetic order, thereby demonstrating the decisive role of the Fermi surface geometry in explaining the complex magnetically ordered ground state of ternary rare earth silicides.Comment: 4 pages, 4 figure

Modelling the probability of microhabitat formation on trees using cross-sectional data

The rate of TreM formation per unit diameter growth was modelled as a function of tree diameter at breast height (DBH), and the model was calibrated considering cross-sectional observations TreMs on trees of different sizes. The model predicted realistic TreM formation rates at the tree and stand levels in forests dominated by Abies alba and Fagus sylvatica. This approach opens new perspectives to the analysis of forest biodiversity conservation strategies

Terrestrial laser scanning for plot-scale forest measurement

Plot-scale measurements have been the foundation for forest surveys and reporting for over 200 years. Through recent integration with airborne and satellite remote sensing, manual measurements of vegetation structure at the plot scale are now the basis for landscape, continental and international mapping of our forest resources. The use of terrestrial laser scanning (TLS) for plot-scale measurement was first demonstrated over a decade ago, with the intimation that these instruments could replace manual measurement methods. This has not yet been the case, despite the unparalleled structural information that TLS can capture. For TLS to reach its full potential, these instruments cannot be viewed as a logical progression of existing plot-based measurement. TLS must be viewed as a disruptive technology that requires a rethink of vegetation surveys and their application across a wide range of disciplines. We review the development of TLS as a plotscale measurement tool, including the evolution of both instrument hardware and key data processing methodologies. We highlight two broad data modelling approaches of gap probability and geometrical modelling and the basic theory that underpins these. Finally, we discuss the future prospects for increasing the utilisation of TLS for plot-scale forest assessment and forest monitoring

Species-specific, pan-European diameter increment models based on data of 2.3 million trees

ResearchBackground: Over the last decades, many forest simulators have been developed for the forests of individual European countries. The underlying growth models are usually based on national datasets of varying size, obtained from National Forest Inventories or from long-term research plots. Many of these models include country- and location-specific predictors, such as site quality indices that may aggregate climate, soil properties and topography effects. Consequently, it is not sensible to compare such models among countries, and it is often impossible to apply models outside the region or country they were developed for. However, there is a clear need for more generically applicable but still locally accurate and climate sensitive simulators at the European scale, which requires the development of models that are applicable across the European continent. The purpose of this study is to develop tree diameter increment models that are applicable at the European scale, but still locally accurate. We compiled and used a dataset of diameter increment observations of over 2.3 million trees from 10 National Forest Inventories in Europe and a set of 99 potential explanatory variables covering forest structure, weather, climate, soil and nutrient deposition. Results: Diameter increment models are presented for 20 species/species groups. Selection of explanatory variables was done using a combination of forward and backward selection methods. The explained variance ranged from 10% to 53% depending on the species. Variables related to forest structure (basal area of the stand and relative size of the tree) contributed most to the explained variance, but environmental variables were important to account for spatial patterns. The type of environmental variables included differed greatly among species. Conclusions: The presented diameter increment models are the first of their kind that are applicable at the European scale. This is an important step towards the development of a new generation of forest development simulators that can be applied at the European scale, but that are sensitive to variations in growing conditions and applicable to a wider range of management systems than before. This allows European scale but detailed analyses concerning topics like CO2 sequestration, wood mobilisation, long term impact of management, etcinfo:eu-repo/semantics/publishedVersio