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Define a sequence of elements from a partially ordered set to be heapable if it can be successively inserted as the leaves of a binary tree, not necessarily complete, such that children nodes are always greater or equal than parent nodes. This is a natural binary analog of the notion of a chain in a poset and an easy extension of a definition for integers due to Byers et al. (2011). A set of elements is called heapable if some permutation of its elements is. We investigate the partitioning of sequences from a poset into a minimal number of heapable subsequences. We give an extension of Fulkerson's proof of Dilworth's theorem to decomposition into heapable subsequences which yields as a byproduct a flow-based algorithm for computing such a minimal decomposition. On the other hand, for sets and sequences of intervals and for trapezoid partial orders we prove that such minimal decompositions can be computed via simple greedy-type algorithms. Second, while the complexity of computing a maximal heapable subsequence of integers is still open, we show that this problem has a polynomial time algorithm for sequences of intervals. The paper concludes with a couple of open problems related to the analog of the Ulam-Hammersley problem for sets and sequences of random intervals. [ABSTRACT FROM AUTHOR]

Scheduling over scenarios is one of the latest approaches in modelling scheduling problems including uncertainty. However, to the best of our knowledge, scenarios have never been applied to the bin packing problem, so here we introduce the bin packing problem with scenarios. In this model, we have a list of items with sizes between 0 and 1, and each item is assigned to one or more scenarios. In reality, the items of only one scenario will occur, but this chosen scenario is unknown at the time of packing, so the algorithms have to examine all scenarios. This means that the items have to be packed into bins such that for any scenario, the total size of the items in this scenario is at most 1 in each bin. The objective of the standard bin packing problem is to minimize the number of bins. Here, we introduce some extensions of the objective function to the scenario based model, and we present our competitive analysis of some online bin packing algorithms adapted to scenarios. [ABSTRACT FROM AUTHOR]

Spatial patterns of ecosystem processes constitute significant sources of uncertainty in greenhouse gas flux estimations partly because the patterns are temporally dynamic. The aim of this study was to describe temporal variability in the spatial patterns of grassland CO2 and N2O flux under varying environmental conditions and to assess effects of the grassland management (grazing and mowing) on flux patterns. We made spatially explicit measurements of variables including soil respiration, aboveground biomass, N2O flux, soil water content, and soil temperature during a 4-year study in the vegetation periods at grazed and mowed grasslands. Sampling was conducted in 80 × 60 m grids of 10 m resolution with 78 sampling points in both study plots. Soil respiration was monitored nine times, and N2O flux was monitored twice during the study period. Altitude, soil organic carbon, and total soil nitrogen were used as background factors at each sampling position, while aboveground biomass, soil water content, and soil temperature were considered as covariates in the spatial analysis. Data were analyzed using variography and kriging. Altitude was autocorrelated over distances of 40–50 m in both plots and influenced spatial patterns of soil organic carbon, total soil nitrogen, and the covariates. Altitude was inversely related to soil water content and aboveground biomass and positively related to soil temperature. Autocorrelation lengths for soil respiration were similar on both plots (about 30 m), whereas autocorrelation lengths of N2O flux differed between plots (39 m in the grazed plot vs. 18 m in the mowed plot). Grazing appeared to increase heterogeneity and linkage of the spatial patterns, whereas mowing had a homogenizing effect. Spatial patterns of soil water content, soil respiration, and aboveground biomass were temporally variable especially in the first 2 years of the experiment, whereas spatial patterns were more persistent (mostly significant correlation at p < 0.05 between location ranks) in the second 2 years, following a wet year. Increased persistence of spatial patterns after a wet year indicated the recovery potential of grasslands following drought and suggested that adequate water supply could have a homogenizing effect on CO2 and N2O fluxes. [ABSTRACT FROM AUTHOR]

Thefree N-heterocyclic carbene IPent (1; IPent =1,3-bis(2,6-bis(1-ethylpropyl)phenyl)imidazol-2-ylidene) was preparedfrom the corresponding imidazolium chloride salt (2).The steric and electronic parameters of 1were determinedby synthesis of the gold(I) chloride complex [Au(IPent)Cl] (3) and the nickel–carbonyl complex [Ni(IPent)(CO)3] (4), respectively. 3and 4were fully characterized by NMR spectroscopy, elementalanalysis, and X-ray diffraction studies on single crystals. [ABSTRACT FROM AUTHOR]

Aims: The relative importance of species within an ecosystem shows spatio‐temporal variability related to both the terrain features and numerous rapidly changing factors. Accordingly, functional and species patterns may show some level of persistence, or, due to various disturbances, fluctuations. Communities with high species richness were found to maintain a higher degree of stability than species‐poor or perturbed vegetations; however, diversity and its stability may be spatio‐temporally variable. Based on these considerations, our aim was to assess the responses of a sandy pasture, both species‐wise and at the community level, to the relatively invariant habitat, and to the more rapidly changing environmental conditions. Location: Hungary. Methods: We surveyed the vegetation in an area of about 1 ha by means of high‐resolution spatio‐temporal sampling: we recorded the surface aerial cover (%) of the plant species during 15 campaigns covering spring, summer and autumn aspects for seven years (2013–2019) in 80 × 60 m grids. The biological activity of the ecosystem (above‐ground biomass, soil respiration) was also followed up together with the environmental limiting factors. Results: During the study period, which was characterized by significant warming, the grassland showed a balanced physiological performance with year‐to‐year variability. Fluctuating differentiation of the plant species with different environmental optima along with the terrain attributes was assumed to be responsible for this balanced physiological performance. Although community‐level diversity remained stable, some species favoring cooler, wetter positions disappeared. Conclusions: Terrain features of the study area within 1.5 m or less elevation differences created considerably heterogeneous conditions for a high number (114) of plant species with different ecological needs to co‐occur. The stability of the diversity was found to show terrain relatedness, that is spatial as well as temporal patterns compared to the null model of spatio‐temporal independence, and the ecosystem functions followed these patterns. [ABSTRACT FROM AUTHOR]

A series of studies were conducted to probe the stabilityand reactivity of a very sterically encumbered N-heterocyclic carbene.The X-ray structure of the NHC IPr* (IPr* = 1,3-bis(2,6-bis(diphenylmethyl)-4-methylphenyl)imidazol-2-ylidene)was determined. IPr* was used as an organocatalyst in transesterificationreactions. Steric and electronic parameters characterizing IPr* weredetermined via the synthesis of a nickel-carbonyl complex, [Ni(CO)3(IPr*)]. A related complex, [(Cp*)Ru(IPr*)Cl] (Cp* = η5-C5Me5), was prepared and characterizedby X-ray crystallography, and its catalytic performance in the racemizationof chiral alcohols is reported. The catalytic performance of the NHCand of its transition metal derivatives permit establishing the standingof this uniquely bulky member among the NHC family. [ABSTRACT FROM AUTHOR]

Abstract: Novel 2-(1-ferrocenyl-methylidene)-malonic acid derivatives are obtained upon reacting ethyl diazoacetate, carbon monoxide and ferrocenylimines in the presence of Co2(CO)8 as catalyst under mild conditions. Presumably, the reaction involves three steps taking place in a domino fashion, (i) carbonylation of ethyl diazoacetate leading to a ketene derivative, (ii) [2+2] cycloaddition of the ketene with the ferrocenylimine present in the reaction mixture resulting in the formation of a β-lactam and (iii) N(1)-C(4) cleavage of the β-lactam ring. In most cases, 2-(1-ferrocenyl-methylidene)-malonic acid derivatives are obtained as a separable mixture of E- and Z-isomers in ratios depending on the structure of the imine component. [Copyright &y& Elsevier]

Production, dry matter (including reproductive) allocation, photosynthesis, transpiration, water use efficiency and carbon and nitrogen responses of a Hungarian sweet pepper (Capsicum annum L.) to growth under continuous elevated CO2 concentrations are reported. Plants were grown in open top chambers under a temperate-continental climate in Hungary from plantation at ambient (350 µmol mol-1) and elevated (700 µmol mol-1) CO2 concentrations. The CO2 assimilation responses of the green pepper plants grown in high CO2 from plantation until final harvest reflected down-regulation of their photosynthesis. The integrated and combined effect of the increased net CO2 assimilation rate and the unchanged rate of transpiration resulted in higher WUE at elevated CO2 concentrations in the high CO2 plants than in the control ones grown at ambientCO2. However, the improved water use efficiency in the high CO2 plants was not followed by an acclimation in C-translocation and C-allocation to the reproductive organs in the required degree. This was reflected in a slightly increased overall plant production and higher reproductive allocation, but was not accompanied by an increased fresh or dry berry mass production. The acclimation discussed may be of advantage for plant growth in a high CO2 environment with restricted water availability. We did not find worthy statistical difference between the yield mass of the control and elevated CO2, although the dry matter production parameters of the high CO2 plants had statistically not significantly higher values. [ABSTRACT FROM PUBLISHER]

The ability to access physiologically driven signals, such as surface temperature, photochemical reflectance index (PRI), and sun-induced chlorophyll fluorescence (SIF), through remote sensing (RS) are exciting developments for vegetation studies. Accessing this ecophysiological information requires considering processes operating at scales from the top-of-the-canopy to the photosystems, adding complexity compared to reflectance index-based approaches. To investigate the maturity and knowledge of the growing RS community in this area, COST Action CA17134 SENSECO organized a Spatial Scaling Challenge (SSC). Challenge participants were asked to retrieve four key ecophysiological variables for a field each of maize and wheat from a simulated field campaign: leaf area index (LAI), leaf chlorophyll content (Cab), maximum carboxylation rate (Vcmax,25), and non-photochemical quenching (NPQ). The simulated campaign data included hyperspectral optical, thermal and SIF imagery, together with ground sampling of the four variables. Non-parametric methods that combined multiple spectral domains and field measurements were used most often, thereby indirectly performing the top-of-the-canopy to photosystem scaling. LAI and Cab were reliably retrieved in most cases, whereas Vcmax,25 and NPQ were less accurately estimated and demanded information ancillary to RS imagery. The factors considered least by participants were the biophysical and physiological canopy vertical profiles, the spatial mismatch between RS sensors, the temporal mismatch between field sampling and RS acquisition, and measurement uncertainty. Furthermore, few participants developed NPQ maps into stress maps or provided a deeper analysis of their parameter retrievals. The SSC shows that, despite advances in statistical and physically based models, the vegetation RS community should improve how field and RS data are integrated and scaled in space and time. We expect this work will guide newcomers and support robust advances in this research field. [ABSTRACT FROM AUTHOR]

Soil respiration of grasslands is spatio-temporally variable reflecting the changing biological activities of the soil. In our study we analysed how the long-term soil respiration activities of dry grasslands would perform in terms of resistance and resilience. We also investigated how terrain features are responsible for response stability. We conducted a 7-year-long spatial study in a Hungarian dry grassland, measuring soil respiration (Rs), soil temperature (Ts) and soil water content (SWC) along 15 measuring campaigns in 80 × 60 m grids and soil organic carbon content in 6 of the occasions. Two proxy variables were introduced to grasp the overall Rs activity, as well as its temporal stability: average rankRs, the temporal average Rs rank of a measuring position from the campaigns revealed the persistent spatial pattern of Rs, while rangeRs, the range of ranks of the positions from the campaigns described the amplitude of the Rs response in time, referring to the response stability in terms of resistance or resilience. We formulated a hypothetic concept of a two-state equilibrium to describe the performance of the long-term Rs activity: Rs activity with smaller rangeRs, that is both the lower elevation positions with larger rankRs ("state I") and the higher elevation positions with smaller rankRs ("state II") correspond to an equilibrium state with several terrain attributes being responsible for the equilibrium responses. Majority of the measuring positions was belonging to none of these equilibrium states. These positions showed higher rangeRs for medium rankRs, suggesting resilience (not resistance) as a major strategy for this ecosystem. [ABSTRACT FROM AUTHOR]

Grasslands, such as other managed fields, release large quantities of greenhouse gases (GHG). Fluxes of GHG are highly variable spatio-temporally, which hampers the quantification of the yearly sum. Although actual spatial patterns of ecosystem functions (EF) are determined by the actual spatial distribution and intensity of background or driving variables, a potential "optimal" or persistent state can also be detected on the basis of long-term climatic, surface relief and soil conditions. Changing climate could alter these instant and long-term patterns through the modification of the drivers. Field studies and spatial analysis can help to reveal such temporal dynamics of spatial patterns and to understand the shifts in EF.We used two ways of spatial analysis to study grassland EF. One way was the geostatistical analysis of low-resolution field-scale manual measurements on 10 × 10 m grids. Geostatistical data processing revealed that topographic differences, however small they might be, had primary importance in the generation of spatial patterns of both the soil nutrients and the microclimate due to the variability of the available soil moisture and fine shading effects of crests and depressions, both the patterns of the above-ground biomass, soil respiration, and nitrous oxide flux. We found that spatial patterns and spatial correlations between variable pairs were dynamically changing characteristics. A further controlling factor was the management of the grasslands, creating different levels of homogeneity/heterogeneity.The other way in spatial analysis can be the use of a high-resolution data. We used a 0.2 × 0.2 m resolution digital elevation model (DEM) in the geostatistical analysis for external drift kriging. In many cases kriging with DEM gave us better result than ordinary kriging with the variable itself. However, a more important use of DEM could be the calculation of different topographic attributes (e.g., slope, aspect, topographic position index, surface rugosity), because these data can reveal more about the neighboring effects within a landscape. We hypothesized that not just DEM, but the calculation of different indices along a spatial series can help to have a more detailed insight into the effects of topography on the spatial patterns of e.g. erosion, soil nutrient horizontal heterogeneity, and also on the EF. [ABSTRACT FROM AUTHOR]

Diel variability of soil respiration could be driven by several factors, but temperature and carbon allocation have the most significant effect on that. However, these two factors covariate on multiple time scales, therefore it is not easy to disentangle their effect.We measured CO2 efflux in undisturbed, root-excluded and root- and mycorrhizal fungi excluded plots and analyzed the diel variability and the responses to GPP in different phenological stages. We used sine wave models to describe the characteristics of diel variability and to estimate the temperature and GPP driven part of total soil respiration.Rhizospheric respiration peaked 8-12 hours after GPP peak, while mycorrhizal fungi respiration had a longer time lag of 13-20 hours. Results of isotopic measurements also showed similar pattern. Drought affected respiration rates as well as carbon allocation pattern; both the amount and the speed of carbon allocated to mycorrhizal fungi were reduced under drought.Based on these results we assume that the commonly used Q10 values does not always reflect the temperature response of soil CO2 efflux, but the propagated effect of the temperature and belowground carbon allocation and those share in soil respiration vary with phenological stages. [ABSTRACT FROM AUTHOR]