dataesr/scientific-paragraphs-categorization huggingface dataset:
Intuitively, a property is monitorable if every prefix can be extended by a finite continuation that gives a definite verdict. We adapt the definition to robust monitoring and show that neither does LTL monitorability imply rLTL monitorability, nor vice versa. Notwithstanding the above, empirical data suggests that rLTL monitoring indeed provides more information than LTL monitoring: This paper presents an algorithm synthesizing monitors for rLTL specifications. An implementation thereof allows us to validate the approach by replicating the experiments of Bauer et al. [12]. As performance metric, we use LTL and rLTL monitorability. They showed that 44% of their formulas are not LTL-monitorable whereas we show all of them to be rLTL-monitorable. This indicates that rLTL monitoring is an improvement over LTL monitoring in terms of monitorability and complements the theoretical results with a practical validation.
The resulting verdict is quinary: satisfying/violating, presumably satisfying/violating, or inconclusive. This approach is similar in nature to our work as it assesses the degree of satisfaction or violation of a given prefix. However, the motivation and niche of both approaches differs: Bartocci et al. 's approach computes -intuitively speaking -the amount of work that is required to satisfy or violate a specification, which allows for estimating the likelihood of satisfaction. Our approach, however, focusses on measuring to what an extend a specification was satisfied or violated. Apart from that, monitoring tools collecting statistics  [1, 4, 26]  become increasingly popular: Snort  [48]  is a commercial tool for rule-based network monitoring and computing efficient statistics, Beep Beep 3  [29]  is a tool based on a query language allowing for powerful aggregation functions and statistical measures.
[13] , which is based on a survey by Dwyer on frequently used software specification patterns  [20]. This benchmark suite consists of 97 LTL formulas and covers a wide range of patterns, including safety, scoping, precedence, and response patterns. For our rLTL monitor construction, we interpreted each LTL formula in the benchmark suite as an rLTL formula (by treating every operator as a robust operator). We compared rLTL-mon to Bauer et al. 's implementation of their LTL monitoring approach, which the authors named LTL 3 tools. This tool uses LTL2BA  [28]  to translate LTL formulas into Büchi automata and AT&T's fsmlib as a means to manipulate finite-state machines. Since LTL2BA's and Owl's input format for LTL formulas do not match exactly, we have translated all benchmarks into a suitable format using a python script.
B Experimental Results The evaluation is based on the original benchmark suite of Bauer et al. [13] , which is in turn based on a survey by Dwyer on frequently used software specification patterns  [20]. This benchmark suite consists of 97 LTL formulas and covers a wide range of patterns, including safety, scoping, precedence, and response patterns. For our rLTL monitor construction, we interpreted each LTL formula in the benchmark suite as an rLTL formula (by treating every operator as a robust operator). We compared rLTL-mon to Bauer et al. 's implementation of their LTL monitoring approach, which the authors named LTL 3 tools. All experiments were conducted on an Intel Core i5-6600 @ 3. 3 GHz in a virtual machine with 4 GB of RAM running Ubuntu 18. 04 LTS. As no monitor construction took longer than 600 s, we did not impose any time limit.
Acknowledgements The authors would like to thank  Li Bingchen  for discovering the formula mentioned in Footnote 11. The work of  Maximilian Schwenger  was supported by the  European Research Council (ERC)  Grant  OSARES  (No. 683300 ) and the  German Research Foundation (DFG)  as part of the  Collaborative Research Center "Center for Perspicuous Computing"  ( TRR 248 ,  389792660 ). The work of  Paulo Tabuada  was partially supported by the  NSF  project  1645824. The work of  Alexander Weinert  was supported by the  Saarbrücken Graduate School of Computer Science. The work of  Martin Zimmermann  was supported by the  Engineering and Physical Sciences Research Council (EPSRC)  project  EP/S032207/1.
Case study: Facebook's data center traffic We investigate Facebook's data center traffic data  [33] [34] [35] , using their database and Hadoop clusters at the pod level. Their data set covers a sample of traffic traces over 24 h. Fig. 2  shows boxplots for 100 samples taken uniformly spaced over the course of the day, for interval sizes of 1, 10, and 100 s. For each of these samples, we take all the traffic at the pod level and investigate what level of average degree can cover how much of the total traffic. As can be seen and as expected, the average degree goes up over longer interval sizes, very slightly from 7 to 8 for the database cluster, and from 10 to 18 for the hadoop cluster. On the other hand, with longer interval sizes, the amount of traffic covered by small average degrees increases: from a median of ≈ 65% to ≈ 68% for the database cluster, and even from ≈ 59% to ≈ 76% for the hadoop cluster.
While the following average degree sizes remain relatively stable in their traffic coverage for the database cluster, the trend continues for the hadoop cluster: for example, for an average demand degree of 2, from ≈ 88% to ≈ 98%. In terms of hardware feasibility, we consider both free-space optics architectures similar to ProjecToR  [10]  and emerging optical circuit switches. First, ProjecToR proposes to use 16 lasers and receivers for 128 nodes in their simulations. For our spare network designs with maximum degree ∆ max = 3∆ avg + 8, we can hence utilize an average demand degree of 2, due to 3 • 2 + 6 = 14 < 16, covering a median of between ≈ 84% to ≈ 98% of the traffic, but at least about 80%. Second, e. g. , already Alistarh et al. [36]  demonstrate the feasibility of efficient optical switches in the order of 1000 ports, i.
ground components in plant and ecosystem studies has been consistently called for in recent decades, but methodology is disparate and sometimes inappropriate. This handbook, based on the collective effort of a large team of experts, will improve trait comparisons across studies and integration of information across databases by providing standardised methods and controlled vocabularies. It is meant to be used not only as starting point by students and scientists who desire working on below-ground ecosystems, but also by experts for consolidating and broadening their views on multiple aspects of root ecology. Beyond the classical compilation of measurement protocols, we have synthesised recommendations from the literature to provide key background knowledge useful for: (1) defining below-ground plant entities and giving keys for their meaningful dissection, classification and naming beyond the classical fine-root vs coarse-root approach; (2) considering the specificity of root research to produce sound laboratory and field data; (3) describing typical, but overlooked steps for studying roots (e.
Acknowledging this variation implies both establishing guidelines for a minimal characterisation and contextualisation of plant measurements (see section VI. Experimentation and sampling in laboratory and field) and improving our understanding of general patterns of below-ground trait variation across environmental gradients and temporal cycles  (Freschet et al. , 2021). A third challenge is linked to the high number of technical and practical choices associated with both laboratory and field studies (see section VI. Experimentation and sampling in laboratory and field) that have important consequences for the value and interpretation made of trait measurements (e. g. Poorter et al. , 2012a Poorter et al. , , 2016)). Designing sound experiments requires for instance anticipating the methodological bias induced by inadequate experimental features or sampling location, finding the right balance between exhaustively sampling and cleaning of roots and minimising root damages and labour, or even using appropriate methods for storing roots over short to long periods of time (see section VII.
After the initial development of a range of specialised (e. g. CLO-PLA;  Klimešová & de Bello, 2009)  and generalist (e. g. TRY;  Kattge et al. , 2011)  databases including below-ground plant organs, the most significant effort in this direction has been done by the community working in below-ground functional ecology, who recently collated root trait data from across the globe into the Fine-Root Ecology Database (FRED). FRED includes observations from more than 2000 plant species encompassing more than 300 types of root traits, along with metadata (i. e. information about data, necessary to interpret these data, see  Michener et al. , 1997) , are now freely available for download at http://roots. ornl. gov in FRED v. 2. 0  (McCormack et al. , 2018). Furthermore, each new version of FRED is submitted to the TRY database  (Kattge et al.
, 2011)  to facilitate above-ground and below-ground linkages. The FRED database was begun to answer important questions on the variation of root traits within and among species, across environmental gradients, and with regard to other root and whole-plant traits  (Iversen et al. , 2017). However, FRED also provides an important framework for understanding the diversity of root traits that are measured by the broader community of root and rhizosphere ecologists, the methodology most commonly used, and where the largest gaps in observations lie (i. e. physiological root traits, plants in tropical ecosystems, plant communities underlain by organic soils). Importantly, FRED also provides a house for new observations; this handbook will help to guide measurements in a way that the resulting data can easily find a home in FRED (data can be contributed at https://roots.
ornl. gov/upload). Ultimately, the more observations that are measured on a range of well described root entities, using the same methodology, the better our understanding of the important processes occurring below ground. To be shared and reused in a relevant way using publicly available databases, supplementary information should be given in addition to the primary data at stake (Fig. 6 ). First, the variables retained (here those describing the different root traits) should be formalised in a relevant semantic framework (see section II. Semantics) including variables' entity and quality. Second, the protocols used for data collectionthe main topic of this handbookmust be recorded, enabling end users to establish links between data collected in the same way. Third, measurement standards (i.
Forum Community resources New Phytologist species sampled, type of ecosystem, plant growth conditions, relevant environmental factors, etc. ) must be given, to enable the assessment of the sources of variations driving the changes in the variables concerned. For example, while FRED collects relevant metadata, only 60% of observations in FRED 1. 0 were georeferenced in their original publication, making it difficult to assess root trait variation across biomes and also develop linkages among databases  (Iversen et al. , 2017). The relevant community should therefore work towards an agreement on a minimum set of metadata, preferably chosen from existing frameworks such as the Ecological Metadata Language (EML;  Michener et al. , 1997). Regarding below-ground plant traits, it is critical to consider that the resolution of current worldwide databases of soil properties is unlikely to capture the large heterogeneity in soil properties occurring at much smaller scale, stressing further the need to adequately characterise soil conditions for plant growth.
A rule of thumb is that equilibration has occurred once fine-root productivity and mortality are roughly equal. Minirhizotron cameras can be purchased commercially, and are used to acquire images, either from the upper surface of the tube or from a nearly 360°view of the tube. These images are then used to trace individual root length and diameter over time, to estimate rates of root birth, growth and death. Several software options are available to assist in processing minirhizotron images including ROOTFLY 2. 0. 2 (Clemson University, Clemson, SC; https://sourcef orge. net/projects/rootfly/), RootSnap! (CID Bioscience), and rhizoTrak (Halle University, https://github. com/prbio-hub/ rhizoTrak; https://www. biorxiv. org/content/10. 1101/547604v1). These may also be used to keep a record of changes in various qualities of individual roots such are root colour or root order.
Ability to grow clonally Ability to grow clonally is the potential of a plant to produce physically independent rooting units (ramets) from one genetic individual (genet)  (Aarssen, 2008) (Categories: clonal, nonclonal). As this trait is not strongly conserved at the plant species level, data from databases (e. g. CLO-PLA database;  Klimešová et al. , 2017)  should be treated with caution and direct measurements on plants are recommended. The clonal multiplication may be attained by different organs located above or below ground. Here, we refer only to clonal growth organs that not only lead to clonal growth but also enable sharing resources among rooting units and therefore affect resource acquisition. Consequently, we do not consider here the production of dispersible above-ground clonal propagules (e.
Recent modelling studies have suggested that not only the average but especially the within-root system variation in RGA might be of importance for nitrate uptake  (Dathe et al. , 2016). RGA is easily determined by placing the root system or root crown on a board with drawn angles  (Trachsel et al. , 2011). Alternatively, they can be determined using image analysis software, after taking a picture using a tripod or any type of fixed structure setting the camera lens parallel to the root plane  (York et al. , 2018). Software developed for root crown evaluation are DIRT and REST  (Colombi et al. , 2015; Das et al. , 2015)  whereas SmartRoot is an example of a software that can be used on 2D paper pouch images  (Lobet et al. , 2011). More recent options include the RhizoVision Crown hardware platform, which combines a back light, a monochrome camera, and a clip-andreplace system for high-throughput and reproducible imaging of root crowns  (Seethepalli et al.
, 2020) , while the RhizoVision Explorer software computes angles for all skeleton pixels in the 'Whole root' mode with average orientation and the frequencies of shallow, medium and steep angles provided. The generic image analysis ImageJ program (http://rsbweb. nih. gov/ij/) also contains a tool for measuring angles. Angles in 3D carved images can be determined using RootReader3D  (Clark et al. , 2011). d. Future research directions As RGA is an important component of root foraging strategies and influences the degree of root growth towards neighbouring plants, RGA measurements may be a promising tool for studying root interactions within and across species. Within pots, the use of magnetic resonance imaging and X-ray microtomography technologies have shown great potential for studying the coarser part of RSA  (Metzner et al.
e. excluding the root segment after the last branching). Including the distal bare zone is a frequent error (as discussed by  Dubrovsky & Forde, 2012). If sampling prohibits collecting the whole root, for example when using root cores, a shorter section (2-5 cm) can also be used. This can be done directly on excavated roots or on images (for obtaining scanned images see section XII. 2. Specific root length). Care needs be taken not to forget the broken roots that normally leave traces of their existence on the parent root, at least in the rather young parts. The root length is typically measured using a ruler or an image analysis software such as ImageJ software, using the 'segmented line' tool. The variations in the branching density trait, when estimated by counting laterals on root parts, are potentially sensitive to the length of the root parts on which they are performed.
The porous basal root with a root tissue density (dry mass per fresh root volume; RTD) of 0. 08 g cm -3 takes up 53% of the sample volume, while the less porous lateral roots with a RTD of 0. 125 g cm -3 take up 47% of the volume, resulting in an average RTD of 0. 10 g cm Once the image is acquired, a range of image analysis software can be used, including the recently released free and open-source RhizoVision Explorer  (Seethepalli & York, 2020 ; fast and reliable even with large size images, can be downloaded at https://doi. org/ 10. 5281/zenodo. 3747697), the free and open-source IJ_Rhizo plugin for ImageJ  (Kimura & Yamasaki, 2003; Pierret et al. , 2013 , can be downloaded at https://www. quantitative-plant. org/softwa re/IJ_Rhizo), or the commonly used commercial WinRhizo  (Regent Instruments, 2000).
RHIZOVISION EXPLORER and WINRHIZO are standalone software with full user interfaces built for the Windows operating system, while IJ_Rhizo is a macro for the cross-platform IMAGEJ software. The accuracy of any digital image analysis strongly depends on the quality of the initial image  (Ortiz-Ribbing et al. , 2003). Digital analyses are sensitive to resolution of the image and to thresholding setting, and care has to be taken with proper settings  (Bouma et al. , 2000; Zobel, 2008; Delory et al. , 2017; Rose & Lobet, 2019). Photographic images are not recommended because shadows are difficult to avoid and distort the analysis  (Ortiz-Ribbing et al. , 2003). The fist step of analysis with all these software is to determine the root from its background, which can be done by simple greyscale thresholding if root images are acquired using the back light described above, assuming the roots are dark and the background is white.
All these software include filtering options that can delete small particles such as sand before trait measurements. Measuring length is generally accomplished using skeletonisation that determines the central pixels of the roots, and then determining the length of the skeleton. Image analysis programs acquire localised root diameters by measuring it from the image at each skeletal pixel, multiplying pixel size by the smallest number of pixels on a line perpendicular to the root axis  (Bouma et al. , 2000). Diagonal pixels are accounted for by using the square root of 2 (√2) during length measurements. All these software packages further provide an average diameter per image. For WinRhizo, average diameter is based on the total.
Forum Community resources New Phytologist projected area divided by the total root length in the image, which may be inaccurate when heterogeneous diameter classes are present. RhizoVision Explorer and IJ_Rhizo both report an average diameter using the diameters of all skeleton pixels, which is more accurate. However, both IJ_Rhizo and WinRhizo use the average diameter and total length measured to calculate total volume, which has been shown to lead to severe underestimation of root volume when heterogeneous root diameters are present  (Delory et al. , 2017; Rose & Lobet, 2019). If these software are used to calculate total root volume, it has to be done separately for each diameter class and summed to achieve greater accuracy (see section XII. 3. Root tissue density and root dry matter content).
If high threshold values are needed to detect most or all of the finest roots in a sample (see section XII. 2. Specific root length) and these threshold values are high enough to overestimate root diameter, samples may benefit from staining (see below). For images with poorer contrast or heterogenous lighting, methods such as adaptive or local thresholding may be used in software such as IMAGEJ, before using the thresholded image with whichever root image analysis software. Newer machine learning methods for segmenting roots from complex backgrounds such as soil are becoming available. Alternatively, operators need to find a balance between detecting a reasonably accurate proportion of total root length while not substantially overestimating root diameters. In such cases, the automatic thresholding mode might be preferable, particularly for new operators.
Aerenchyma contributes to volume but have no mass, and the proportion of air space in wetland plant roots can be up to 50%  (Visser et al. , 2000). c. Measurement procedure Root dry mass and volume need to be measured to calculate RTD. Root volume (V) can be calculated based on root diameter (see section XII. 1. Mean root diameter and mode of diameter distribution). Assuming a cylindrical cross-section of the roots, the volume of each diameter class can be calculated as: V = Π r 2 l. where r is the radius of the diameter class, and l is the total length of that diameter class. The volume of the root system is the sum of the volumes of all diameter classes. While this information is provided by most image analysis software, at the date of writing this manuscript, current and previous versions of WinRhizo and IJRhizo still provide an erroneous value of root volume.
Using the mean diameter of the whole root system to calculate its volume leads to an error, which can be considerable  (Ryser, 2006; Rose, 2017). The calculation must be done separately for each diameter class, because the relationship between root volume and root diameter is not linear. Fortunately, most programs also provide this information, which then can be used to calculate a correct root volume. The recently released free and open-source RhizoVision Explorer does not have this bias, as described under section XII. 1. Mean root diameter and mode of diameter distribution  (Seethepalli & York, 2020 ; https://zenodo. org/rec ord/3747698#. Xz0wqn7gpM8). Alternatively, root volume can be measured directly using displacement of liquid  (Curran et al. , 1996) , root buoyancy  (Curran et al.
, 2011; 2013). a. Sampling recommendations See section VI. Experimentation and sampling in laboratory and field. b. Storage and processing See section XIII. 1. Microtechnique method for the analysis of root anatomy. Once anatomical crosssections are produced, they can be stored indefinitely and measured at any time. c. Measurement procedure Root cross-sections should be observed under a light microscope at ×10, ×20 or ×40 objective magnification. Measurements can be made with assistance from an open-source image processing software such as IMAGEJ (https:// imagej. nih. gov/ij/), as well as several commercial software packages (included with the software to make digital images, for example AxioVision or ZEN (Carl Zeiss Microscopy, Jena, Germany), ROXAS (WSL, Birmensdorf, Switzerland)). Calibration is necessary before measurements.
Using microscopy software, calibration is made automatically based on defined image scale. Using other software, for example IMAGEJ, it is necessary to calibrate the image scale and to specify the unit of measurement. After the analysis of cross-sections by the software, they should be screened to ensure that the software was able to capture measurements correctly. Importantly, cortical thicknesses are highly dependent on the longitudinal distance from the root tip. Therefore, it is important to obtain measurements from crosssections obtained from similar distances from the root tip or half way through the root segment in higher root orders when comparing roots between different species or even within a species, especially when examining root response to adverse environments. Measurements should be obtained from root sections at least in two crossing directions to the highest level of precision (1 μm).