On the Edge Distribution of a Graph

2001 ◽  
Vol 10 (6) ◽  
pp. 543-555 ◽  
Author(s):  
V. NIKIFOROV
Keyword(s):  
Positive Constant ◽  
Local Density ◽  
Free Graph ◽  
Least Eigenvalue ◽  
Edge Distribution ◽  
Graph Function

We investigate a graph function which is related to the local density, the maximal cut and the least eigenvalue of a graph. In particular it enables us to prove the following assertions.Let p [ges ] 3 be an integer, c ∈ (0, 1/2) and G be a Kp-free graph on n vertices with e [les ] cn2 edges. There exists a positive constant α = α (c, p) such that:(a) some [lfloor ]n/2[rfloor ]-subset of V (G) induces at most (c-4 − α) n2 edges (this answers a question of Paul Erdős);(b) G can be made bipartite by the omission of at most (c-2 − α) n2 edges.

scholarly journals Toughness of $K_{a,t}$-Minor-free Graphs

10.37236/635 ◽  
2011 ◽  
Vol 18 (1) ◽  
Author(s):  
Guantao Chen ◽  
Yoshimi Egawa ◽  
Ken-ichi Kawarabayashi ◽  
Bojan Mohar ◽  
Katsuhiro Ota
Keyword(s):  
Planar Graph ◽  
Positive Constant ◽  
Complete Graph ◽  
Planar Graphs ◽  
Spanning Tree ◽  
Maximum Degree ◽  
Free Graph ◽  
Minor Free Graphs ◽  
Vertex Sets ◽  
Connected Planar Graph

The toughness of a non-complete graph $G$ is the minimum value of $\frac{|S|}{\omega(G-S)}$ among all separating vertex sets $S\subset V(G)$, where $\omega(G-S)\ge 2$ is the number of components of $G-S$. It is well-known that every $3$-connected planar graph has toughness greater than $1/2$. Related to this property, every $3$-connected planar graph has many good substructures, such as a spanning tree with maximum degree three, a $2$-walk, etc. Realizing that 3-connected planar graphs are essentially the same as 3-connected $K_{3,3}$-minor-free graphs, we consider a generalization to $a$-connected $K_{a,t}$-minor-free graphs, where $3\le a\le t$. We prove that there exists a positive constant $h(a,t)$ such that every $a$-connected $K_{a,t}$-minor-free graph $G$ has toughness at least $h(a,t)$. For the case where $a=3$ and $t$ is odd, we obtain the best possible value for $h(3,t)$. As a corollary it is proved that every such graph of order $n$ contains a cycle of length $\Omega(\log_{h(a,t)} n)$.

scholarly journals Induced Trees in Triangle-Free Graphs

10.37236/765 ◽  
2008 ◽  
Vol 15 (1) ◽  
Author(s):  
Jiří Matoušek ◽  
Robert Šámal
Keyword(s):  
Positive Constant ◽  
Upper Bound ◽  
Free Graph

We prove that every connected triangle-free graph on $n$ vertices contains an induced tree on $\exp(c\sqrt{\log n}\,)$ vertices, where $c$ is a positive constant. The best known upper bound is $(2+o(1))\sqrt n$. This partially answers questions of Erdős, Saks, and Sós and of Pultr.

Ab initio band theory approach to electron energy loss near edge structures

1988 ◽  
Vol 46 ◽  
pp. 506-507
Author(s):  
Xudong Weng ◽  
O.F. Sankey ◽  
Peter Rez
Keyword(s):  
Ab Initio ◽  
Local Density ◽  
Interpolation Method ◽  
Atomic Orbital ◽  
Plane Waves ◽  
Large Set ◽  
Theory Approach ◽  
Band Theory ◽  
Atomic Orbitals ◽  
Pseudopotential Calculations

Single electron band structure techniques have been applied successfully to the interpretation of the near edge structures of metals and other materials. Among various band theories, the linear combination of atomic orbital (LCAO) method is especially simple and interpretable. The commonly used empirical LCAO method is mainly an interpolation method, where the energies and wave functions of atomic orbitals are adjusted in order to fit experimental or more accurately determined electron states. To achieve better accuracy, the size of calculation has to be expanded, for example, to include excited states and more-distant-neighboring atoms. This tends to sacrifice the simplicity and interpretability of the method.In this paper. we adopt an ab initio scheme which incorporates the conceptual advantage of the LCAO method with the accuracy of ab initio pseudopotential calculations. The so called pscudo-atomic-orbitals (PAO's), computed from a free atom within the local-density approximation and the pseudopotential approximation, are used as the basis of expansion, replacing the usually very large set of plane waves in the conventional pseudopotential method. These PAO's however, do not consist of a rigorously complete set of orthonormal states.

Flux-pinning-related defect structures in melt-processed YBa2Cu3O7-x

1993 ◽  
Vol 51 ◽  
pp. 936-937
Author(s):  
Z. L. Wang ◽  
R. Kontra ◽  
A. Goyal ◽  
D. M. Kroeger ◽  
L.F. Allard
Keyword(s):  
Volume Fraction ◽  
Local Density ◽  
Stacking Faults ◽  
Image Resolution ◽  
Defect Structures ◽  
Atomic Structures ◽  
Transmission Electron ◽  
Point Image ◽  
Related Defect ◽  
Point To Point

Previous studies of Y2BaCuO5/YBa2Cu3O7-δ(Y211/Y123) interfaces in melt-processed and quench-melt-growth processed YBa2Cu3O7-δ using high resolution transmission electron microscopy (HRTEM) and energy dispersive X-ray spectroscopy (EDS) have revealed a high local density of stacking faults in Y123, near the Y211/Y123 interfaces. Calculations made using simple energy considerations suggested that these stacking faults may act as effective flux-pinners and may explain the observations of increased Jc with increasing volume fraction of Y211. The present paper is intended to determine the atomic structures of the observed defects. HRTEM imaging was performed using a Philips CM30 (300 kV) TEM with a point-to-point image resolution of 2.3 Å. Nano-probe EDS analysis was performed using a Philips EM400 TEM/STEM (100 kV) equipped with a field emission gun (FEG), which generated an electron probe of less than 20 Å in diameter.Stacking faults produced by excess single Cu-O layers: Figure 1 shows a HRTEM image of a Y123 film viewed along [100] (or [010]).

Lane mark identification method based on edge distribution function

2010 ◽  
Vol 30 (4) ◽  
pp. 974-976 ◽  
Author(s):  
Xu-qin YAN ◽  
Xiao-bing WU ◽  
Xiao-bo CHE ◽  
Yun ZHANG ◽  
Zhi-xue WANG
Keyword(s):  
Distribution Function ◽  
Identification Method ◽  
Edge Distribution

scholarly journals The local density of optical states of a metasurface

2016 ◽  
Vol 6 (1) ◽  
Author(s):  
Per Lunnemann ◽  
A. Femius Koenderink
Keyword(s):  
Local Density

scholarly journals The Struggle of Ash—Insights from Long-Term Survey in Latvia

Forests ◽  
2021 ◽  
Vol 12 (3) ◽  
pp. 340
Author(s):  
Ilze Matisone ◽  
Roberts Matisons ◽  
Āris Jansons
Keyword(s):  
Local Density ◽  
Additive Model ◽  
Tree Height ◽  
Natural Resistance ◽  
Critical Conditions ◽  
Tree Level ◽  
Future Potential ◽  
Genetic And Environmental Factors ◽  
Long Term Survey

The dieback of common ash (Fraxinus excelsior L.) has dramatically decreased the abundance of the species in Europe; however, tolerance of trees varies regionally. The tolerance of trees is considered to be a result of synergy of genetic and environmental factors, suggesting an uneven future potential of populations. This also implies that wide extrapolations would be biased and local information is needed. Survival of ash during 2005–2020, as well as stand- and tree-level variables affecting them was assessed based on four surveys of 15 permanent sampling plots from an eastern Baltic region (Latvia) using an additive model. Although at the beginning of dieback a relatively low mortality rate was observed, it increased during the 2015–2020 period, which was caused by dying of the most tolerant trees, though single trees have survived. In the studied stands, ash has been gradually replaced by other local tree species, though some recruitment of ash was locally observed, implying formation of mixed broadleaved stands with slight ash admixture. The survival of trees was related to tree height and position within a stand (relative height and local density), though the relationships were nonlinear, indicating presence of critical conditions. Regarding temporal changes, survival rapidly dropped during the first 16 years, stabilizing at a relatively low level. Although low recruitment of ash still implies plummeting economic importance of the species, the observed responses of survival, as well as the recruitment, imply potential to locally improve the survival of ash via management (tending), hopefully providing time for natural resistance to develop.

scholarly journals Do galactic bars depend on environment?: an information theoretic analysis of Galaxy Zoo 2

2020 ◽  
Vol 501 (1) ◽  
pp. 994-1001
Author(s):  
Suman Sarkar ◽  
Biswajit Pandey ◽  
Snehasish Bhattacharjee
Keyword(s):  
Spatial Distribution ◽  
Mutual Information ◽  
Local Density ◽  
Statistical Significance ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Host Galaxy ◽  
Data Sets ◽  
Data Set ◽  
Information Theoretic

ABSTRACT We use an information theoretic framework to analyse data from the Galaxy Zoo 2 project and study if there are any statistically significant correlations between the presence of bars in spiral galaxies and their environment. We measure the mutual information between the barredness of galaxies and their environments in a volume limited sample (Mr ≤ −21) and compare it with the same in data sets where (i) the bar/unbar classifications are randomized and (ii) the spatial distribution of galaxies are shuffled on different length scales. We assess the statistical significance of the differences in the mutual information using a t-test and find that both randomization of morphological classifications and shuffling of spatial distribution do not alter the mutual information in a statistically significant way. The non-zero mutual information between the barredness and environment arises due to the finite and discrete nature of the data set that can be entirely explained by mock Poisson distributions. We also separately compare the cumulative distribution functions of the barred and unbarred galaxies as a function of their local density. Using a Kolmogorov–Smirnov test, we find that the null hypothesis cannot be rejected even at $75{{\ \rm per\ cent}}$ confidence level. Our analysis indicates that environments do not play a significant role in the formation of a bar, which is largely determined by the internal processes of the host galaxy.

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