scholarly journals Hat Guessing Numbers of Degenerate Graphs

10.37236/9449 ◽  
2020 ◽  
Vol 27 (3) ◽  
Author(s):  
Xiaoyu He ◽  
Ray Li
Keyword(s):  
Upper Bounds ◽  
General Method

Recently, Farnik asked whether the hat guessing number $\mathrm{HG}(G)$ of a graph $G$ could be bounded as a function of its degeneracy $d$, and Bosek, Dudek, Farnik, Grytczuk and Mazur showed that $\mathrm{HG}(G)\ge 2^d$ is possible. We show that for all $d\ge 1$ there exists a $d$-degenerate graph $G$ for which $\mathrm{HG}(G) \ge 2^{2^{d-1}}$. We also give a new general method for obtaining upper bounds on $\mathrm{HG}(G)$. The question of whether $\mathrm{HG}(G)$ is bounded as a function of $d$ remains open.

scholarly journals Forcing with Δ perfect trees and minimal Δ-degrees

1981 ◽  
Vol 46 (4) ◽  
pp. 803-816 ◽  
Author(s):  
Alexander S. Kechris
Keyword(s):  
Upper Bounds ◽  
Natural Numbers ◽  
Cantor Space ◽  
Standard Notation ◽  
General Method

This paper is a sequel to [3] and it contains, among other things, proofs of the results announced in the last section of that paper.In §1, we use the general method of [3] together with reflection arguments to study the properties of forcing with Δ perfect trees, for certain Spector pointclasses Γ, obtaining as a main result the existence of a continuum of minimal Δ-degrees for such Γ's, under determinacy hypotheses. In particular, using PD, we prove the existence of continuum many minimal Δ½n+1-degrees, for all n.Following an idea of Leo Harrington, we extend these results in §2 to show the existence of minimal strict upper bounds for sequences of Δ-degrees which are not too far apart. As a corollary, it is computed that the length of the natural hierarchy of Δ½n+1-degrees is equal to ω when n ≥ 1. (By results of Sacks and Richter the length of the natural hierarchy of -degrees is known to be equal to the first recursively inaccessible ordinal.)We will follow in this paper standard notation and terminology, as in Moschovakis' book [7]. Letters e, i, j, k, l, m, n vary over the set of natural numbers ω, a, b, c over the Cantor space 2ω and α, β, γ, δ, … over the set of reals ωω. Finally ξ, η, κ, λ always denote ordinals.

A General Method to Determine Asymptotic Capacity Upper Bounds for Wireless Networks

2019 ◽  
Vol 6 (1) ◽  
pp. 2-15
Author(s):  
Canming Jiang ◽  
Yi Shi ◽  
Y. Thomas Hou ◽  
Wenjing Lou ◽  
Sastry Kompella ◽  
...  
Keyword(s):  
Wireless Networks ◽  
Upper Bounds ◽  
General Method

scholarly journals General Upper Bounds on the Runtime of Parallel Evolutionary Algorithms*

2014 ◽  
Vol 22 (3) ◽  
pp. 405-437 ◽  
Author(s):  
Jörg Lässig ◽  
Dirk Sudholt
Keyword(s):  
Evolutionary Algorithms ◽  
Upper Bounds ◽  
Constant Factor ◽  
Structured Populations ◽  
Fitness Level ◽  
Performance Guarantees ◽  
Parallel Evolutionary Algorithms ◽  
Spatially Structured Populations ◽  
Boolean Optimization ◽  
General Method

We present a general method for analyzing the runtime of parallel evolutionary algorithms with spatially structured populations. Based on the fitness-level method, it yields upper bounds on the expected parallel runtime. This allows for a rigorous estimate of the speedup gained by parallelization. Tailored results are given for common migration topologies: ring graphs, torus graphs, hypercubes, and the complete graph. Example applications for pseudo-Boolean optimization show that our method is easy to apply and that it gives powerful results. In our examples the performance guarantees improve with the density of the topology. Surprisingly, even sparse topologies such as ring graphs lead to a significant speedup for many functions while not increasing the total number of function evaluations by more than a constant factor. We also identify which number of processors lead to the best guaranteed speedups, thus giving hints on how to parameterize parallel evolutionary algorithms.

A General Method for Spectrometer Design in the Scoff Approximation

1976 ◽  
Vol 34 ◽  
pp. 538-539
Author(s):  
J. R. Fields
Keyword(s):  
Electron Microscope ◽  
Transmission Electron Microscope ◽  
Energy Analysis ◽  
Incident Beam ◽  
Scanning Transmission Electron Microscope ◽  
Chemical Identification ◽  
Scanning Transmission Electron ◽  
Transmission Electron ◽  
Scanning Transmission ◽  
General Method

The energy analysis of electrons scattered by a specimen in a scanning transmission electron microscope can improve contrast as well as aid in chemical identification. In so far as energy analysis is useful, one would like to be able to design a spectrometer which is tailored to his particular needs. In our own case, we require a spectrometer which will accept a parallel incident beam and which will focus the electrons in both the median and perpendicular planes. In addition, since we intend to follow the spectrometer by a detector array rather than a single energy selecting slit, we need as great a dispersion as possible. Therefore, we would like to follow our spectrometer by a magnifying lens. Consequently, the line along which electrons of varying energy are dispersed must be normal to the direction of the central ray at the spectrometer exit.

Phase behavior of cationic and anionic surfactants at low concentrations

1992 ◽  
Vol 50 (1) ◽  
pp. 694-695
Author(s):  
E. Naranjo
Keyword(s):  
Phase Behavior ◽  
Structural Characterization ◽  
Dynamic Systems ◽  
Anionic Surfactants ◽  
Intermolecular Forces ◽  
Stable Form ◽  
Surfactant Mixtures ◽  
Low Concentrations ◽  
Cationic And Anionic Surfactants ◽  
General Method

Equilibrium vesicles, those which are the stable form of aggregation and form spontaneously on mixing surfactant with water, have never been demonstrated in single component bilayers and only rarely in lipid or surfactant mixtures. Designing a simple and general method for producing spontaneous and stable vesicles depends on a better understanding of the thermodynamics of aggregation, the interplay of intermolecular forces in surfactants, and an efficient way of doing structural characterization in dynamic systems.

Caricaturing as a general method to improve poor face recognition: Evidence from low-resolution images, other-race faces, and older adults.

2019 ◽  
Vol 25 (2) ◽  
pp. 256-279 ◽  
Author(s):  
Amy Dawel ◽  
Tsz Ying Wong ◽  
Jodie McMorrow ◽  
Callin Ivanovici ◽  
Xuming He ◽  
...  
Keyword(s):  
Older Adults ◽  
Face Recognition ◽  
Low Resolution ◽  
General Method ◽  
Low Resolution Images

Morphosemantic Analysis and Translation of Medical Compound Terms

1991 ◽  
Vol 30 (01) ◽  
pp. 30-35 ◽  
Author(s):  
P. Dujols ◽  
P. Aubas ◽  
C. Baylon ◽  
F. Grémy
Keyword(s):  
Medical Terms ◽  
General Method

This paper describes an automatic procedure for morphosemantic analysis and translation of compound medical terms. This analysis is of interest for the automatic indexation of medical discharge reports and summaries. Since words with the suffix -osis may have many different semantic interpretations, such -osis forms are taken as examples for a general method that avoids the difficulties in interpreting medical terms as reported in other studies.

Extension of the Spatial PDI Model to Three Dimensions

1997 ◽  
Vol 84 (1) ◽  
pp. 176-178
Author(s):  
Frank O'Brien
Keyword(s):  
Population Density ◽  
Dimensional Space ◽  
Finite Lattice ◽  
Three Dimensional ◽  
Upper Bounds ◽  
Three Dimensions ◽  
Lower And Upper Bounds ◽  
Density Index ◽  
Three Dimensional Space

The author's population density index ( PDI) model is extended to three-dimensional distributions. A derived formula is presented that allows for the calculation of the lower and upper bounds of density in three-dimensional space for any finite lattice.

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