In this paper, we generalize Thomassen’s useful technique to matroids. The GF (q)-representable matroid analogue of a clique is a projective geom- etry over GF (q). A given simple graph G sits inside a clique on V (G) in the same way that a simple GF (q)-representable matroid M with rank r sits inside P G(r − 1, q). In the above technique, edges are added to an “area” of G to form a clique restriction, so that the altered graph has a clique vertex-cut. This can be viewed as adding edges from the clique on V (G) to the graph G to obtain a clique, across which our graph may be broken. In this paper, we show how to add elements from P G(r − 1, q) to a certain “area” of M in order to get a GF (q)-representable matroid with a certain projective geometry restriction, across which our matroid may be broken. The map that we use to break apart a matroid is a tree-decomposition, which was established by Hlin˘en´ y and Whittle in . They developed a matroid analogue of graph tree-width, which we define formally in Section 3.
from ours in two significant ways. For one, Agol’s examples are non-Haken, while we work with knots and their complements, which are necessarily Haken. Furthermore, there is an inequality between the diagrammatic tree-width of a knot and the tree-width of its complement which cannot be reversed. That is, given a knot diagram of tree-width k, there are standard techniques to build a triangulation of its complement of tree-width O(k). For example, one may use the method embedded in SnapPy [8, link_complement.c]; see the discussion of [15, Remark 6.2].
Generally, saddle fitting is subjective and relies on the skills of an individual to assess the suitability of a saddle for both the horse and rider. In an attempt to standardise saddle fitting, the Society of Master Saddlers (SMS) has produced guidelines that qualified saddle fitters follow. Initially, a static saddle fitting assessment is performed featuring several criteria, as described elsewhere . Once each criterion is met, a dynamic ridden assessment is performed, requiring the saddle fitter to observe the horse and rider in all gaits and in both directions. Treewidth is one of the criteria used to determine the correct saddle width (here on, width). Industry guidelines (Society of Master Saddlers) state that the angle of the tree points should correspond to the angle of the horse’s back 5 cm from the caudal edge of the scapula in the static horse. Anecdotally, some saddle fitters (and others), despite industry guidelines, prefer to fit a saddle wider on the assumption that this will allow increased movement of the scapula and of the thoracic spine, both of which are not supported by any scientific evidence. Previously, the agreement between a cohort of Society of Master Saddlers Qualified Saddle Fitters (SMSQSF) when performing a static saddle fitting assessment was reported. Moderate to substantial agreement between saddle fitters was found for eight of the static saddle fitting criteria, that is, (8/10), while only slight (51%, k 0.12) agreement was found for treewidth and tree length .
Figure 17 illustrates a visualization of this speedup information. For tree-widths, 2, 3,4, we show the speedup expected for each pair of values (n,d). Given fixed w,d we expect the speedup to increase as n increases. The empirical evaluation illustrates this trend; for example, at w = 3 and d = 4, we see a five-fold or more speedup starting with input graphs with n ≈ 100. As the plots illustrate, we observe that when the tree-width is 2 or less, as in Figure 17a, adaptive inference is preferable in many cases even for small graphs. With tree-widths 3 and 4, we obtain speedups for dimensions below 10 and 6 respectively. We further observe that for a given width w, we obtain higher speedups as we reduce the dimensionality d and as we increase n, except for small values of n. Disregarding such small graphs, this is consistent with our theoretical bounds. In small graphs (n < 100) we see higher speedups than predicted because our method’s worst-case exponential dependence is often not achieved, a phenomenon we examine in more detail shortly.
Let us remark that some work goes into generalising tools from property testing on graphs to relational databases. For this we could reprove the relevant results in our slightly more general setting (this is not done in this extended abstract for space constraints). A different approach would be to encode relational structures as (coloured) incidence graphs, and apply the known results for graphs. This can be done, because bounded degree, bounded tree-width and hyperfiniteness carry over to incidence graphs. Nevertheless, it involves some technicalities, in particular when simulating testing algorithms on incidence graphs. We plan to take this approach in the journal version.
In this paper we address these two questions of how and when through the lens of worst-case complexity analysis. We identify the domain’s causal graph as an essential struc- ture in the analysis of factored planning, showing that it cap- tures all the sufficient and necessary information about vari- able interactions. In particular, we show that our approach based on causal graphs is strictly more efficient (by up to an exponential factor) than the AE approach. We show that the tree-width of causal graphs plays a key role in the com- plexity of both our approach to factored planning, as well as existing methods for non-factored step-optimal planning. This finding allows us to relate factored and non-factored methods and understand when each is likely to work best.
In the "Decrease number of columns if treewidth exceeds <value> characters" checkbox: If enabled, the number of columns displayed register of fields will be decreased if the width of the tree exceedes defined number of characters. This option prevents registers from the displayed fields to be not fit in narrow window, making the perfil unreadable.
For each ring series, linear increment trend (LIT) was computed for cambial age classes 21–40, 41–60, 61–80 and 81–100 years as the slope of the fractional straight line for each class. If on average the incremental curve shows an upward trend in the range of the age class, LIT is > 0, if the trend is downward, LIT is < 0. Cluster analysis was used to group similar ring series according to LIT val- ues for age classes that represent input variables. Hierarchical clustering by Ward’s method and Eu- clidean distances was used for the estimation of the number of clusters. For the final grouping of ring series, K-means clustering for the predefined num- ber of clusters by the method of maximum starting distance between clusters was applied. Software STATISTICA 7.0 (StatSoft, Inc., 2009) was used. Consequently, selected site-related (altitude and soil quality), stand-related (stand density, vertical structure, stand damage) and tree-related param- eters (tree age, crown length, health status) of clus- ters were compared between the clusters.
The weaving length determines the ease with which the vehicle can maneuver through the weaving section and thus determines the capacity of the rotary. The weaving length is decided on the basis of the factors, such as, the width of weaving section, average width of entry, total traffic and proportion of weaving traffic in it. It is desirable to prevent direct traffic cuts and this can be achieved by making the ratio of weaving length to weaving width large enough. A ratio 4:1 is regarded as minimum. The minimum values of weaving lengths as recommended by IRC are given below:
For Mongoloids, inter-pupillary can be used to determine anterior teeth widths. A study was performed by Kini AY., Angadi GS in 2013 to correlate dental measurements i.e. combined mesio-distal width of six maxillary anterior teeth with facial measurements i.e. inner canthal distance, interpupillary distance and intercommissural width . Two standardized digital photographs of the face were generated; one, when the facial muscles were relaxed and the other, when the subject was smiling; thereby, revealing the maxillary anterior teeth up to the canine tip. Inner canthal distance, interpupillary distance, intercommissural distance, distance between the tips of the maxillary canines and distance between the distal surfaces of the canines were measured. On the cast, the distance between tips of maxillary canines and distance between distal surfaces of maxillary canines were noted. Extra oral anthropometric measurements of the interpupillary distances and the intercommissural distances with the help of standardized photographs can help us determine the combined widths of the anterior teeth accurately, thus aiding their selection in the absence of pre-extraction records. A study was conducted by Glynis Anita Miranda, Mariette D’Souza in 2016 to evaluate the reliability of interalar width and intercommissural width as guide in selection of artificial maxillary anterior teeth. Total of 200 samples were selected. The four parameters such as interalar width, intercanine distance, intercommissural width, and distance between distal aspects of canines were measured. The data obtained were statistically analyzed. A correlation was observed between the interalar distance and the intercanine distance and also between the intercommissural distance and the distance between the distal aspects of canines. With the review of literature it is clear that, in the absence of pre-extraction records, there is however, no accurate objective method in order to select the width of maxillary anterior teeth for edentulous patients. Although many methods have been utilized, none of these methods are absolutely reliable for teeth selection. The anatomical -landmark as a guide for selecting maxillary anterior teeth will vary from population to population. Development of a more scientific or objective method of teeth selection would greatly assist dentist in delivering their service for patient care and satisfaction confidently and will also enable lab technician to accurately pick the teeth without seeing the patient on dental chair, computer would also be used to scan and measure cast to give image of patient teeth in the proper size relationship.
To study the morphological variability of Quercus suber 50 leaves were randomly taken at different part of the tree and thirteen vegetative variables (leaf length, leaf width, petioles length, numbers of leaf veins, petioles width, spines numbers, leaf area, length nipples, diameter nipples, weight nipples, height trees, diameter trees) were measured. All morphmetric measurements were taken using a Vernier caliper with digital display. The leaf areas were calculated using Microtech Scanmaker HP SCANJET G2710 scanner and were measured by image analysis logiciel (Optimas V6.0).
proposed that the date of snowmelt, which was estimated from temperature and winter precipitation, has a significant effect on ring width. They stated that the trend toward increasing precipi- tation in winter and a delay in snowmelt might have a significant effect on the radial growth of larch trees in Sibe- ria. The present study revealed similar results for the north- facing slope; however, no significant response to snow cover was identified on the south-facing slope. Thus, the negative effect of snow cover seems to vary and to depend on microscale topography. The present study suggests that changes in spring temperatures and accumulated snow are important in assessing the effect of future changes in cli- mate on radial growth of L. gmelinii in central Siberia. The study also suggests the importance of microscale topogra- phy in assessing the effects of snow accumulation.
The GRW of M. azedarach was on average 7.44 mm, with an average range between trees from 6.53 to 8.64 mm (Table 4). Site and tree-to-tree within a site were not a source of variations of GRW, explaining only 0.28 and 1.58% of the total variation, respectively (Table 5). The radial variation of GRW was highly (P \ 0.001) significant and contributed the highest (52.58%) of the total variation. Mean GRW near the pith was large and decreased rapidly with cambial age up to 5 and 6 years before being less or more stable to the bark. However, there were some fluc- tuations and spikes in some trees (Fig. 2).
Department of Horticulture, Institute of Agricultural Science, University of Calcutta, West Bengal, India, during the year 2011-2013. The genotypes (G) are selected from various walnut growing areas of Ladakh viz. G 1 from Skara (34° 9.907´ N and 77° 33.437´ E), G 2 from Nurla (34° 17.968´ N and 76° 59.473´ E), G 3 from Temisgam (34° 19.242´ N and 76° 59.260´ E) and G 4 from Dhomkhar (34° 24.179´ N and 76° 45.995´ E) with an altitude of 3360, 3005, 3231 and 3045 meters above sea level respectively. The maximum and minimum temperature recorded at the time of investigation was 32 °C and 10 °C respectively with an average relative humidity of 63% and 15 mm rainfall. A sample size of 15 sun dried nuts was collected from each bearing trees for kernel and nut characters. The genotypes were characterized for various characters following Biodiversity International Walnut Descriptor (1994). The characters selected for characterization were tree vigour, growth habit, branching, leaf length (cm), leaf width (cm), number of leaflets, leaflet shape, leaflet margin, leaf colour, rachis colour, shoot pubescence, shoot colour, leaf and rachis pubescence, nut shape, nut diameter (mm), nut length (mm), shell texture, shell colour, shell seal, shell strength, shell integrity, shell thickness (mm), inshell nut weight (g), kernel weight (g), kernel percentage (%), kernel flavor, kernel fill, kernel plumpness, ease of removal of kernel halves and kernel colour. Analysis was done by one-way ANOVA technique. Duncan’s test at 5% was also followed by comparing genotypic means if significant. All analysis was done following SPSS. 17.0 software.
Daniel et al.  reported that mesio-distal width of all maxillary six anteriors is equal to bizygomatic width / 3.3. John H. Lee  reported that combined mesio-distal width of maxillary Central Incisor to be equal to width of Philtrum. Bell. R.A  studied photographs of dental casts, x-rays of Central Incisors and photographs of face and he did not support Williams method . Mavroskoufis et al.  studied the nasal width and incisive papilla as guide of selection of maxillary anterior teeth. Vuttiparum et al.  studied the relationship between width of the maxillary Central Incisors and the philtrum and found a direct correlation between the width of the Central Incisor and philtrum. Al wazzan  reported intercanthal distance can be used as the preliminary method of determining width of maxillary anterior teeth in edentulous patients. Abdullah  reported intercanthal distances and geometric progression as a predictor of maxillary Central Incisor width .
The forested landscape of north-eastern Uttar Pradesh includes 366 species under 83 families. Data for five morphometric traits viz., plant height, leaf length, leaf width, flower size and fruit size, were observed for 193 woody (tree, shrub and liana) species belonging to 56 families within understorey of sal forest. Plant heights (m) were measured with the help of clinometer as the maximum height for each species during field survey. At least 10 separate individuals of a species were used for measurement of height. For leaf trait measurement 20 leaves were taken from 10 non-damaged and mature individuals of a species. We measured leaf length (cm) and leaf width (cm) with simple measuring scale. Leaf length was the maximum length of frond excluding petiole. Leaf width was measured as the maximum diameter of the imaginary circle that can be fitted anywhere in the leaf (Westoby 1998, Cornelissen et al., 2003). For flower size (cm) we measured fully opened, intact flowers with simple scale as the measure of the length of the corolla or perianth followed by Osunkoya (1996). Flower size was grouped into three categories: small (< 2 cm), medium (2-5 cm) and large (> 5 cm). For this trait we measured 3 flowers from each inflorescence of 10 different individuals of each species. Fruit size expanse was measured by multiplying its maximum length and width, accommodating the bias caused by long and linear fruits (Carpenter et al., 2003). The data were analyzed using each species as an independent observation. The G-test for goodness of fit was
Red blood cell distribution width (RDW) is widely used laboratory parameter for anemia . However, recent stud- ies have reported that RDW can be used laboratory param- eter for inflammatory diseases and cancers, such as atherosclerosis, inflammatory bowel diseases, breast cancer and lung cancer [10–13]. Platelet distribution width (PDW) is a measure of variation in platelet size and a direct flow cytometric measurement of platelet cell volume. PDW has been evaluated as a marker of platelet morphology and ac- tivation [14, 15]. Recent studies also showed the association of PDW with CBC and CRP which indicated the wide rela- tion between platelets and inflammation .
We developed a 260-year (1751 to 2010) tree-ring chronol- ogy of Scots pine (Pinus sylvestris L. var. mongolica Litv.) from four sample sites in the central Daxing’an Mountains, northeast China. Radial growth of Scots pine was mainly limited by water availability (R = 0.62, p < 0.01). A 260- year dry–wet change history was reconstructed, and the re- construction equation explained 38.2 % of the PDSI vari- ance for the period of 1911–2010. Four dry and wet peri- ods were found in the past 260 years, respectively. The ex- treme dry years in our reconstruction series are consistent with the local historical document records. Our reconstruc- tion series revealed the dry–wet changes in the Daxing’an Mountains and also was the representative of the dry–wet changes in the west-central Mongolian Plateau, especially at the decadal scale. Droughts during the 1920s–1930s in the Daxing’an Mountains were more severe than in surround- ing areas. In addition, the reconstruction series showed that the Daxing’an Mountains have been getting warm and wet since the late 1970s. This is not in line with the situation in the Mongolian Plateau, especially in the transition zones. Our reconstruction also suggests that the MADA by Cook et al. (2010) may not be accurate in the Daxing’an Moun- tains likely due to the insufficient spatiotemporal distribution of the tree-ring data in this area. Overall, drought variability in the central Daxing’an Mountains and its relationship with the surrounding areas might be driven by climate oscillations of the Pacific and Atlantic oceans (e.g., ENSO, PDO, AMO, NAO and SNAO). These large-scale climate oscillations af- fect the Asian monsoon and then lead to dry and wet changes in the Daxing’an Mountains.
whose eruption is counted as the largest historically docu- mented eruption of the modern (instrumental) era (Briffa et al., 1998), is recorded in our tree ring series as the fourth summer with the lowest sunshine values in the reconstruc- tion period. After Tambora, eruptions of Raung and Ijen, also from Indonesia, took place in the year 1817 (Mastin and Wit- ter, 2000). Our reconstruction describes the period of 1813– 1821, with exception of 1817, as summers with a low num- ber of sunshine hours. This decade is also counted as prob- ably the coolest in the last 500 yr (Cole-Dai et al., 2009). We can consider that one massive eruption has influence on more growth periods, like Taal volcanic eruption from Philip- pines in the 1911 (Mastin and Witter, 2000), which seems to have affected tree growth in BiH in the following 4 yr (1912– 1915). We observed the same results in the years after Kraka- toa eruption in 1883 (Rampino and Self, 1982). Closer to BiH an eruption of volcano Vesuvius (Italy) happened in May, 1771 and lasted for a whole month (Scandone et al., 2008). Its influence is not recorded in the same year, but the follow- ing summer had low value of sunshine hours (Table 4). Influ- ence of longer volcanic eruptions on tree-growth is seen in the long Vesuvius eruption, starting in July, 1895 and lasting till September, 1899, being active for more than 1500 days (Scandone et al., 2008). Vesuvius is located southwest from BiH, but as there is in the beginning of the growing season a north–northeasterly flow over the eastern Mediterranean area (Kostopoulou and Jones, 2007), volcanic dust was trans- ported towards the Dinaric mountains. This explains why we identified following years 1897–1900 and 1902 as less-sunny (1 SD) and 1899 as year with extremely low amount of sun- shine (Table 4). With volcanic eruptions, we connected all summers with sunshine values below 2 SD; Vesuvius in 1899 (Scandone et al., 2008), Etna (Italy) in 1843 (Bonaccorso et al., 2004), unknown in 1810 and Tambora in 1815 (Cole-Dai et al., 2009), Awu (Indonesia) in 1712 (Clor et al., 2005) and Taal in 1966 (Mastin and Witter, 2000). The results of this research open many new fields of potential future investiga- tions. But for a more detailed examination of the discovered BiH extreme summer sunshine events and their connection to volcanic eruptions, further inquiries with applications of data on sulphur loadings, power of eruption and its length should be addressed. Further, special investigation on avail- able documentary archives with an emphasis on the whole region of the western Balkans is needed. Especially for those events which may be limited to the BiH area only and are not confirmed by documentary sources from outside the BiH.