Maximum size of a planar graph with given degree and diameter

2008 ◽  
Vol 31 ◽  
pp. 157-159
Author(s):  
S.A. Tishchenko
Keyword(s):  
Planar Graph ◽  
Maximum Size

On the Maximum Degree of a Random Planar Graph

2008 ◽  
Vol 17 (4) ◽  
pp. 591-601 ◽  
Author(s):  
COLIN McDIARMID ◽  
BRUCE REED
Keyword(s):  
Planar Graph ◽  
Random Graph ◽  
Planar Graphs ◽  
Maximum Degree ◽  
High Probability ◽  
Maximum Size ◽  
Maximum Increase ◽  
Number Of Components

Let the random graphRnbe drawn uniformly at random from the set of all simple planar graphs onnlabelled vertices. We see that with high probability the maximum degree ofRnis Θ(lnn). We consider also the maximum size of a face and the maximum increase in the number of components on deleting a vertex. These results extend to graphs embeddable on any fixed surface.

Computational Micrograph Registration with Sieve Processes

1996 ◽  
Vol 54 ◽  
pp. 440-441
Author(s):  
P.J. Phillips ◽  
J. Huang ◽  
S. M. Dunn
Keyword(s):  
Planar Graph ◽  
Efficient Algorithm ◽  
Spatial Organization ◽  
Spatial Arrangement ◽  
Stereo Image ◽  
Image Model ◽  
Geometric Invariants ◽  
Point Set

In this paper we present an efficient algorithm for automatically finding the correspondence between pairs of stereo micrographs, the key step in forming a stereo image. The computation burden in this problem is solving for the optimal mapping and transformation between the two micrographs. In this paper, we present a sieve algorithm for efficiently estimating the transformation and correspondence.In a sieve algorithm, a sequence of stages gradually reduce the number of transformations and correspondences that need to be examined, i.e., the analogy of sieving through the set of mappings with gradually finer meshes until the answer is found. The set of sieves is derived from an image model, here a planar graph that encodes the spatial organization of the features. In the sieve algorithm, the graph represents the spatial arrangement of objects in the image. The algorithm for finding the correspondence restricts its attention to the graph, with the correspondence being found by a combination of graph matchings, point set matching and geometric invariants.

Continuous Quantitative Monitoring of Mural, Platelet-Dependent, Thrombus Kinetics in the Crushed Rat Femoral Vein

1991 ◽  
Vol 65 (04) ◽  
pp. 425-431 ◽  
Author(s):  
F Stockmans ◽  
H Deckmyn ◽  
J Gruwez ◽  
J Vermylen ◽  
R Acland
Keyword(s):  
Thrombus Formation ◽  
Femoral Vein ◽  
Maximum Size ◽  
Digital Analysis ◽  
Video Recordings ◽  
Quantitative Monitoring ◽  
Set Up ◽  
Kinetics Of ◽  
Quantitative Nature

SummaryA new in vivo method to study the size and dynamics of a growing mural thrombus was set up in the rat femoral vein. The method uses a standardized crush injury to induce a thrombus, and a newly developed transilluminator combined with digital analysis of video recordings. Thrombi in this model formed rapidly, reaching a maximum size 391 ± 35 sec following injury, after which they degraded with a half-life of 197 ± 31 sec. Histological examination indicated that the thrombi consisted mainly of platelets. The quantitative nature of the transillumination technique was demonstrated by simultaneous measurement of the incorporation of 111In labeled platelets into the thrombus. Thrombus formation, studied at 30 min interval in both femoral veins, showed satisfactory reproducibility overall and within a given animalWith this method we were able to induce a thrombus using a clinically relevant injury and to monitor continuously and reproducibly the kinetics of thrombus formation in a vessel of clinically and surgically relevant size

Persistence of giants: population dynamics of the limpet Scutellastra laticostata on rocky shores in Western Australia

2020 ◽  
Vol 646 ◽  
pp. 79-92
Author(s):  
RE Scheibling ◽  
R Black
Keyword(s):  
Population Dynamics ◽  
Western Australia ◽  
Size Structure ◽  
Survival Rates ◽  
Maximum Size ◽  
High Rate ◽  
Adult Survival ◽  
Rocky Shores ◽  
Adult Size ◽  
Decadal Time Scale

Population dynamics and life history traits of the ‘giant’ limpet Scutellastra laticostata on intertidal limestone platforms at Rottnest Island, Western Australia, were recorded by interannual (January/February) monitoring of limpet density and size structure, and relocation of marked individuals, at 3 locations over periods of 13-16 yr between 1993 and 2020. Limpet densities ranged from 4 to 9 ind. m-2 on wave-swept seaward margins of platforms at 2 locations and on a rocky notch at the landward margin of the platform at a third. Juvenile recruits (25-55 mm shell length) were present each year, usually at low densities (<1 m-2), but localized pulses of recruitment occurred in some years. Annual survival rates of marked limpets varied among sites and cohorts, ranging from 0.42 yr-1 at the notch to 0.79 and 0.87 yr-1 on the platforms. A mass mortality of limpets on the platforms occurred in 2003, likely mediated by thermal stress during daytime low tides, coincident with high air temperatures and calm seas. Juveniles grew rapidly to adult size within 2 yr. Asymptotic size (L∞, von Bertalanffy growth model) ranged from 89 to 97 mm, and maximum size from 100 to 113 mm, on platforms. Growth rate and maximum size were lower on the notch. Our empirical observations and simulation models suggest that these populations are relatively stable on a decadal time scale. The frequency and magnitude of recruitment pulses and high rate of adult survival provide considerable inertia, enabling persistence of these populations in the face of sporadic climatic extremes.

scholarly journals A Thomassen-type method for planar graph recoloring

2021 ◽  
Vol 95 ◽  
pp. 103319
Author(s):  
Zdeněk Dvořák ◽  
Carl Feghali
Keyword(s):  
Planar Graph ◽  
Type Method

scholarly journals ON THE HEIGHT AND RELATIONAL COMPLEXITY OF A FINITE PERMUTATION GROUP

2021 ◽  
pp. 1-40
Author(s):  
NICK GILL ◽  
BIANCA LODÀ ◽  
PABLO SPIGA
Keyword(s):  
Permutation Group ◽  
Model Theory ◽  
Independent Set ◽  
Maximum Size ◽  
Proper Subset ◽  
Permutation Groups ◽  
Finite Permutation Group ◽  
Pointwise Stabilizer ◽  
Relational Complexity

Abstract Let G be a permutation group on a set $\Omega $ of size t. We say that $\Lambda \subseteq \Omega $ is an independent set if its pointwise stabilizer is not equal to the pointwise stabilizer of any proper subset of $\Lambda $ . We define the height of G to be the maximum size of an independent set, and we denote this quantity $\textrm{H}(G)$ . In this paper, we study $\textrm{H}(G)$ for the case when G is primitive. Our main result asserts that either $\textrm{H}(G)< 9\log t$ or else G is in a particular well-studied family (the primitive large–base groups). An immediate corollary of this result is a characterization of primitive permutation groups with large relational complexity, the latter quantity being a statistic introduced by Cherlin in his study of the model theory of permutation groups. We also study $\textrm{I}(G)$ , the maximum length of an irredundant base of G, in which case we prove that if G is primitive, then either $\textrm{I}(G)<7\log t$ or else, again, G is in a particular family (which includes the primitive large–base groups as well as some others).

scholarly journals Optimizing the Properties of La0.8Sr0.2CrO3 Thin Films through Post-Annealing for High-Temperature Sensing

Nanomaterials ◽  
2021 ◽  
Vol 11 (7) ◽  
pp. 1802
Author(s):  
Dan Liu ◽  
Peng Shi ◽  
Yantao Liu ◽  
Yijun Zhang ◽  
Bian Tian ◽  
...  
Keyword(s):  
Thin Film ◽  
Thin Films ◽  
Annealing Temperature ◽  
Rf Sputtering ◽  
Maximum Size ◽  
Cross Sectional ◽  
Post Annealing ◽  
Maximum Conductivity ◽  
Different Temperatures ◽  
Post Annealing Temperature

La0.8Sr0.2CrO3 (0.2LSCO) thin films were prepared via the RF sputtering method to fabricate thin-film thermocouples (TFTCs), and post-annealing processes were employed to optimize their properties to sense high temperatures. The XRD patterns of the 0.2LSCO thin films showed a pure phase, and their crystallinities increased with the post-annealing temperature from 800 °C to 1000 °C, while some impurity phases of Cr2O3 and SrCr2O7 were observed above 1000 °C. The surface images indicated that the grain size increased first and then decreased, and the maximum size was 0.71 μm at 1100 °C. The cross-sectional images showed that the thickness of the 0.2LSCO thin films decreased significantly above 1000 °C, which was mainly due to the evaporation of Sr2+ and Cr3+. At the same time, the maximum conductivity was achieved for the film annealed at 1000 °C, which was 6.25 × 10−2 S/cm. When the thin films post-annealed at different temperatures were coupled with Pt reference electrodes to form TFTCs, the trend of output voltage to first increase and then decrease was observed, and the maximum average Seebeck coefficient of 167.8 µV/°C was obtained for the 0.2LSCO thin film post-annealed at 1100 °C. Through post-annealing optimization, the best post-annealing temperature was 1000 °C, which made the 0.2LSCO thin film more stable to monitor the temperatures of turbine engines for a long period of time.

Is the Real Prevalence of Pancreatic Neuroendocrine Tumors Underestimated? A Retrospective Study on a Large Series of Pancreatic Specimens

2019 ◽  
Vol 109 (2) ◽  
pp. 165-170 ◽  
Author(s):  
Stefano Partelli ◽  
Fabio Giannone ◽  
Marco Schiavo Lena ◽  
Francesca Muffatti ◽  
Valentina Andreasi ◽  
...  
Keyword(s):  
Neuroendocrine Tumors ◽  
Smoking Habit ◽  
Maximum Size ◽  
Histological Diagnosis ◽  
Main Diagnosis ◽  
Pancreatic Neuroendocrine Tumors ◽  
Intraductal Papillary Mucinous Neoplasms ◽  
Mucinous Neoplasms ◽  
Median Diameter ◽  
Made In

Background/Aims: The annual incidence of pancreatic neuroendocrine tumors (PanNET) has been estimated to be around 0.8/100,000 inhabitants. The aim of this study was to determine the frequency of incidental histological diagnosis of PanNET in pancreatic specimen evaluation for a purpose other other than PanNET diagnosis. Methods: One thousand seventy-four histopathological examinations of pancreatic specimens performed in 3 centers in Italy were retrospectively reviewed. All cases with a main pathological diagnosis of PanNET were excluded. Results: An incidental associated diagnosis of PanNET was made in 41 specimens (4%). Among those 41 cases, 29 (71%) had a largest diameter <5 mm (microadenoma), whereas the other 12 (29%) had a maximum size ≥5 mm (median diameter of the whole series = 3 mm, range 1–15). The association with a main diagnosis of intraductal papillary mucinous neoplasms (IPMN) was significantly higher for patients who had an incidental PanNET (p = 0.048). There was no association between incidental diagnosis of PanNET and age, gender, BMI, smoking habit, diabetes, and type of operation. Conclusions: The frequency of incidental histological diagnosis of PanNET is considerably high, suggesting that their real prevalence is probably underestimated. The present study suggests a possible correlation between the incidental occurrence of PanNET and IPMN.

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