scholarly journals Perfectly Balanced Partitions of Smoothed Graphs

10.37236/252 ◽  
2009 ◽  
Vol 16 (1) ◽  
Author(s):  
Ido Ben-Eliezer ◽  
Michael Krivelevich
Keyword(s):  
Random Graph ◽  
Direct Consequence ◽  
Base Graph ◽  
Even Order ◽  
Balanced Partition

For a graph $G=(V,E)$ of even order, a partition $(V_1,V_2)$ of the vertices is said to be perfectly balanced if $|V_1|=|V_2|$ and the numbers of edges in the subgraphs induced by $V_1$ and $V_2$ are equal. For a base graph $H$ define a random graph $G(H,p)$ by turning every non-edge of $H$ into an edge and every edge of $H$ into a non-edge independently with probability $p$. We show that for any constant $\epsilon$ there is a constant $\alpha$, such that for any even $n$ and a graph $H$ on $n$ vertices that satisfies $\Delta(H)-\delta(H) \leq \alpha n$, a graph $G$ distributed according to $G(H,p)$, with ${\epsilon\over n} \leq p \leq 1-{\epsilon\over n}$, admits a perfectly balanced partition with probability exponentially close to $1$. As a direct consequence we get that for every $p$, a random graph from $G(n,p)$ admits a perfectly balanced partition with probability tending to $1$.

scholarly journals Small Subgraphs in the Trace of a Random Walk

10.37236/6169 ◽  
2017 ◽  
Vol 24 (1) ◽  
Author(s):  
Michael Krivelevich ◽  
Peleg Michaeli
Keyword(s):  
Random Walk ◽  
Random Graph ◽  
Complete Graph ◽  
Combinatorial Properties ◽  
Base Graph

We consider the combinatorial properties of the trace of a random walk on the complete graph and on the random graph $G(n,p)$. In particular, we study the appearance of a fixed subgraph in the trace. We prove that for a subgraph containing a cycle, the threshold for its appearance in the trace of a random walk of length $m$ is essentially equal to the threshold for its appearance in the random graph drawn from $G(n,m)$. In the case where the base graph is the complete graph, we show that a fixed forest appears in the trace typically much earlier than it appears in $G(n,m)$.

Electron Diffraction Analysis of Microtwin Structures in Regrown (III) Silicon

1982 ◽  
Vol 40 ◽  
pp. 460-461
Author(s):  
P. Ling ◽  
R. Gronsky ◽  
J. Washburn
Keyword(s):  
Electron Diffraction ◽  
Ion Implantation ◽  
Diffraction Analysis ◽  
Diffraction Pattern ◽  
Direct Consequence ◽  
The Other ◽  
Electron Diffraction Analysis ◽  
Defect Microstructures ◽  
Ion Implanted

The defect microstructures of Si arising from ion implantation and subsequent regrowth for a (111) substrate have been found to be dominated by microtwins. Figure 1(a) is a typical diffraction pattern of annealed ion-implanted (111) Si showing two groups of extra diffraction spots; one at positions (m, n integers), the other at adjacent positions between <000> and <220>. The object of the present paper is to show that these extra reflections are a direct consequence of the microtwins in the material.

Audiology Service Models in a Family Physician Practice Setting

2010 ◽  
Vol 6 (1) ◽  
pp. 24-32 ◽  
Author(s):  
Sridhar Krishnamurti
Keyword(s):  
Pediatric Patients ◽  
Practice Patterns ◽  
Healthcare Delivery ◽  
Direct Consequence ◽  
Direct Access ◽  
Practice Setting ◽  
Pediatric Populations ◽  
Family Practice Physicians ◽  
Primary Focus ◽  
Balance Problems

This article illustrates the potential of placing audiology services in a family physician’s practice setting to increase referrals of geriatric and pediatric patients to audiologists. The primary focus of family practice physicians is the diagnosis/intervention of critical systemic disorders (e.g., cardiovascular disease, diabetes, cancer). Hence concurrent hearing/balance disorders are likely to be overshadowed in such patients. If audiologists get referrals from these physicians and have direct access to diagnose and manage concurrent hearing/balance problems in these patients, successful audiology practice patterns will emerge, and there will be increased visibility and profitability of audiological services. As a direct consequence, audiological services will move into the mainstream of healthcare delivery, and the profession of audiology will move further towards its goals of early detection and intervention for hearing and balance problems in geriatric and pediatric populations.

THE EFFECT OF GONADECTOMY ON THE RESPONSE OF THE PITUITARY I. C. S. H.-CONTENT TO STEROID SEX HORMONES

1960 ◽  
Vol XXXV (II) ◽  
pp. 245-252 ◽  
Author(s):  
G. P. van Rees ◽  
F. J. A. Paesi
Keyword(s):  
Sex Hormones ◽  
Sex Steroids ◽  
Low Dose ◽  
Testosterone Propionate ◽  
Preceding Paper ◽  
Direct Consequence ◽  
Two Factors ◽  
Reflex Stimulation ◽  
Steroid Sex Hormones ◽  
Stimulation Of

ABSTRACT In the experiments reported in this paper the hypothesis that the decrease in the pituitary I. C. S. H.-content, which occurs after administration of steroid sex hormones in gonadectomized animals, is counteracted by a reflex stimulation of the hypophysis initiated by the operation has been investigated. If treatment with a low dose of testosterone propionate (100 μg) was started immediately after castration, the resulting decrease in the pituitary I. C. S. H.-content became more marked if the reflex stimulation of the hypophysis had been prevented. If, however, two months were allowed to elapse before the beginning of treatment, the presence or absence of this reflex was no longer of importance for the effect of testosterone propionate on the pituitary I. C. S. H.-content. And yet, in this case too, the decrease in the pituitary I. C. S. H.-content by testosterone propionate was less than in intact animals (see preceding paper). Hence this decrease appears to be counteracted by two factors: one rapidly occurring and short lasting, resulting from a reflex elicited by gonadectomy; the other gradually increasing in potency and possibly a direct consequence of the continued absence of pituitary inhibiting sex steroids.

Scanning-tunneling spectroscopy on conjugated polymer films

2003 ◽  
Vol 771 ◽  
Author(s):  
M. Kemerink ◽  
S.F. Alvarado ◽  
P.M. Koenraad ◽  
R.A.J. Janssen ◽  
H.W.M. Salemink ◽  
...  
Keyword(s):  
Polymer Films ◽  
Conjugated Polymer ◽  
Three Dimensional ◽  
Field Enhancement ◽  
Direct Consequence ◽  
Scanning Tunneling Spectroscopy ◽  
Tunneling Spectroscopy ◽  
Band Alignment ◽  
Scanning Tunneling ◽  
Order Of Magnitude

AbstractScanning-tunneling spectroscopy experiments have been performed on conjugated polymer films and have been compared to a three-dimensional numerical model for charge injection and transport. It is found that field enhancement near the tip apex leads to significant changes in the injected current, which can amount to more than an order of magnitude, and can even change the polarity of the dominant charge carrier. As a direct consequence, the single-particle band gap and band alignment of the organic material can be directly obtained from tip height-voltage (z-V) curves, provided that the tip has a sufficiently sharp apex.

Q-optimal experimental designs and close to them experimental designs for polynomial regression on the interval

2020 ◽  
Vol 86 (5) ◽  
pp. 65-72
Author(s):  
Yu. D. Grigoriev
Keyword(s):  
Optimal Design ◽  
Polynomial Regression ◽  
Direct Consequence ◽  
Experimental Designs ◽  
Optimal Designs ◽  
Software Systems ◽  
General Character ◽  
Support Points ◽  
Optimal Weights ◽  
Universal Expression

The problem of constructing Q-optimal experimental designs for polynomial regression on the interval [–1, 1] is considered. It is shown that well-known Malyutov – Fedorov designs using D-optimal designs (so-called Legendre spectrum) are other than Q-optimal designs. This statement is a direct consequence of Shabados remark which disproved the Erdős hypothesis that the spectrum (support points) of saturated D-optimal designs for polynomial regression on a segment appeared to be support points of saturated Q-optimal designs. We present a saturated exact Q-optimal design for polynomial regression with s = 3 which proves the Shabados notion and then extend this statement to approximate designs. It is shown that when s = 3, 4 the Malyutov – Fedorov theorem on approximate Q-optimal design is also incorrect, though it still stands for s = 1, 2. The Malyutov – Fedorov designs with Legendre spectrum are considered from the standpoint of their proximity to Q-optimal designs. Case studies revealed that they are close enough for small degrees s of polynomial regression. A universal expression for Q-optimal distribution of the weights pi for support points xi for an arbitrary spectrum is derived. The expression is used to tabulate the distribution of weights for Malyutov – Fedorov designs at s = 3, ..., 6. The general character of the obtained expression is noted for Q-optimal weights with A-optimal weight distribution (Pukelsheim distribution) for the same problem statement. In conclusion a brief recommendation on the numerical construction of Q-optimal designs is given. It is noted that in this case in addition to conventional numerical methods some software systems of symbolic computations using methods of resultants and elimination theory can be successfully applied. The examples of Q-optimal designs considered in the paper are constructed using precisely these methods.

Contemporary Developments Relating to the Inviolability of Mission Premises

2017 ◽  
Author(s):  
Juan E Falconi Puig
Keyword(s):  
Human Rights ◽  
United Kingdom ◽  
Urban Planning ◽  
National Security ◽  
Direct Consequence ◽  
Access To Justice ◽  
Controversial Issues ◽  
The United Kingdom ◽  
Domestic Legislation

This chapter addresses some of the controversial issues relating to the inviolability of mission premises. The Yvonne Fletcher incident of 1984 led to debates about the need to upgrade or reform the VCDR in that regard; and the United Kingdom, as a direct consequence of the incident, adopted the ‘Diplomatic and Consular Premises Act 1987’ to be able to adopt unilateral measures to remove premises immunity where threats to national security, to public integrity and/or the need of urban planning exist. Domestic legislation of this kind, however, also provides ground for conflicts with the VCDR. This chapter explores conflicts between property immunity and issues such as access to justice, human rights, and terrorism and examines ways of overcoming such difficulties through mechanisms which safeguard diplomatic privileges and immunity to allow the pursuit of diplomatic functions.

Random graphs

2018 ◽  
Author(s):  
Mark Newman
Keyword(s):  
Random Graph ◽  
Random Graphs ◽  
Large Scale ◽  
Random Network ◽  
Graph Model ◽  
Clustering Coefficient ◽  
Giant Component ◽  
Random Graph Model ◽  
Definition Of ◽  
Average Size

An introduction to the mathematics of the Poisson random graph, the simplest model of a random network. The chapter starts with a definition of the model, followed by derivations of basic properties like the mean degree, degree distribution, and clustering coefficient. This is followed with a detailed derivation of the large-scale structural properties of random graphs, including the position of the phase transition at which a giant component appears, the size of the giant component, the average size of the small components, and the expected diameter of the network. The chapter ends with a discussion of some of the shortcomings of the random graph model.

Sign in / Sign up

Export Citation Format

Share Document