scholarly journals Generalizations of the Strong Arnold Property and the Minimum Number of Distinct Eigenvalues of a Graph

10.37236/5725 ◽  
2017 ◽  
Vol 24 (2) ◽  
Author(s):  
Wayne Barrett ◽  
Shaun Fallat ◽  
H. Tracy Hall ◽  
Leslie Hogben ◽  
Jephian C.-H. Lin ◽  
...  
Keyword(s):  
Spectral Property ◽  
Symmetric Matrices ◽  
Minimum Number ◽  
Strong Multiplicity

For a given graph $G$ and an associated class of real symmetric matrices whose diagonal entries are governed by the adjacencies in $G$, the collection of all possible spectra for such matrices is considered. Building on the pioneering work of Colin de Verdière in connection with the Strong Arnold Property, two extensions are devised that target a better understanding of all possible spectra and their associated multiplicities. These new properties are referred to as the Strong Spectral Property and the Strong Multiplicity Property. Finally, these ideas are applied to the minimum number of distinct eigenvalues associated with $G$, denoted by $q(G)$. The graphs for which $q(G)$ is at least the number of vertices of $G$ less one are characterized.

scholarly journals Diagonalizable matrices whose graph is a tree: the minimum number of distinct eigenvalues and the feasibility of eigenvalue assignments

2019 ◽  
Vol 7 (1) ◽  
pp. 316-326
Author(s):  
Carlos M. Saiago
Keyword(s):  
Necessary Conditions ◽  
Symmetric Case ◽  
Recent Analysis ◽  
Symmetric Matrices ◽  
Hermitian Matrices ◽  
Geometric Multiplicity ◽  
The Real ◽  
Multiple Eigenvalues ◽  
Minimum Number

Abstract Considered are combinatorially symmetric matrices, whose graph is a given tree, in view of the fact recent analysis shows that the geometric multiplicity theory for the eigenvalues of such matrices closely parallels that for real symmetric (and complex Hermitian) matrices. In contrast to the real symmetric case, it is shown that (a) the smallest example (13 vertices) of a tree and multiplicity list (3, 3, 3, 1, 1, 1, 1) meeting standard necessary conditions that has no real symmetric realizations does have a diagonalizable realization and for arbitrary prescribed (real and multiple) eigenvalues, and (b) that all trees with diameter < 8 are geometrically di-minimal (i.e., have diagonalizable realizations with as few of distinct eigenvalues as the diameter). This re-raises natural questions about multiplicity lists that proved subtly false in the real symmetric case. What is their status in the geometric multiplicity list case?

Preservers of term ranks and star cover numbers of symmetric matrices

2016 ◽  
Vol 31 ◽  
pp. 549-564 ◽  
Author(s):  
LeRoy Beasley
Keyword(s):  
Linear Operators ◽  
Symmetric Matrices ◽  
Minimum Number ◽  
Term Rank

Let $\S$ denote the set of symmetric matrices over some semiring, $\s$. A line of $A\in\S$ is a row or a column of $A$. A star of $A$ is the submatrix of $A$ consisting of a row and the corresponding column of $A$. The term rank of $A$ is the minimum number of lines that contain all the nonzero entries of $A$. The star cover number is the minimum number of stars that contain all the nonzero entries of $A$. This paper investigates linear operators that preserve sets of symmetric matrices of specified term rank and sets of symmetric matrices of specific star cover numbers. Several equivalences to the condition that $T$ preserves the term rank of any matrix are given along with characterizations of a couple of types of linear operators that preserve certain sets of matrices defined by the star cover number that do not preserve all term ranks.

Information capacity and bandwidth limitations in the SEM

1989 ◽  
Vol 47 ◽  
pp. 84-85
Author(s):  
D. C. Joy ◽  
R. D. Bunn
Keyword(s):  
Signal To Noise Ratio ◽  
Critical Dimension ◽  
Information Capacity ◽  
Acquisition Time ◽  
Signal To Noise ◽  
Sem Image ◽  
Probe Size ◽  
Minimum Number ◽  
Noise Ratio ◽  
Signal Channel

The information available from an SEM image is limited both by the inherent signal to noise ratio that characterizes the image and as a result of the transformations that it may undergo as it is passed through the amplifying circuits of the instrument. In applications such as Critical Dimension Metrology it is necessary to be able to quantify these limitations in order to be able to assess the likely precision of any measurement made with the microscope.The information capacity of an SEM signal, defined as the minimum number of bits needed to encode the output signal, depends on the signal to noise ratio of the image - which in turn depends on the probe size and source brightness and acquisition time per pixel - and on the efficiency of the specimen in producing the signal that is being observed. A detailed analysis of the secondary electron case shows that the information capacity C (bits/pixel) of the SEM signal channel could be written as :

Applying Generalizability Theory to Optimize Analysis of Spontaneous Teacher Talk in Elementary Classrooms

2020 ◽  
Vol 63 (6) ◽  
pp. 1947-1957
Author(s):  
Alexandra Hollo ◽  
Johanna L. Staubitz ◽  
Jason C. Chow
Keyword(s):  
Special Education Teachers ◽  
Generalizability Theory ◽  
Child Outcomes ◽  
Elementary Classrooms ◽  
Teacher Talk ◽  
Group Instruction ◽  
Data Set ◽  
School Year ◽  
Minimum Number ◽  
Representative Samples

Purpose Although sampling teachers' child-directed speech in school settings is needed to understand the influence of linguistic input on child outcomes, empirical guidance for measurement procedures needed to obtain representative samples is lacking. To optimize resources needed to transcribe, code, and analyze classroom samples, this exploratory study assessed the minimum number and duration of samples needed for a reliable analysis of conventional and researcher-developed measures of teacher talk in elementary classrooms. Method This study applied fully crossed, Person (teacher) × Session (samples obtained on 3 separate occasions) generalizability studies to analyze an extant data set of three 10-min language samples provided by 28 general and special education teachers recorded during large-group instruction across the school year. Subsequently, a series of decision studies estimated of the number and duration of sessions needed to obtain the criterion g coefficient ( g > .70). Results The most stable variables were total number of words and mazes, requiring only a single 10-min sample, two 6-min samples, or three 3-min samples to reach criterion. No measured variables related to content or complexity were adequately stable regardless of number and duration of samples. Conclusions Generalizability studies confirmed that a large proportion of variance was attributable to individuals rather than the sampling occasion when analyzing the amount and fluency of spontaneous teacher talk. In general, conventionally reported outcomes were more stable than researcher-developed codes, which suggests some categories of teacher talk are more context dependent than others and thus require more intensive data collection to measure reliably.

RGB Frequency Based Image Steganography

2020 ◽  
pp. 549-553
Author(s):  
Himanshu Kumar ◽  
Nitesh Kumar
Keyword(s):  
Image Steganography ◽  
Minimum Number

In this paper, we introduced a new RGB technique for image steganography. In this technique we introduced the idea of storing a different number of bits per channel (R, G or B) of a pixel based on the frequency of color values of pixel. The higher color frequency retains the maximum number of bits and lower color frequency stores the minimum number of bits.

On Number of Planes of Rearrangeably Nonblocking Optical Banyan Networks with Link Failures

2008 ◽  
Vol 1 (1) ◽  
pp. 43-54
Author(s):  
Basra Sultana ◽  
Mamun-ur-Rashid Khandker
Keyword(s):  
Optical Switching ◽  
Blocking Probability ◽  
Link Failure ◽  
Link Failures ◽  
Small Depth ◽  
Internal Link ◽  
Banyan Network ◽  
Minimum Number ◽  
Switch Design ◽  
Banyan Networks

Vertically stacked optical banyan (VSOB) networks are attractive for serving as optical switching systems due to the desirable properties (such as the small depth and self-routing capability) of banyan network structures. Although banyan-type networks result in severe blocking and crosstalk, both these problems can be minimized by using sufficient number of banyan planes in the VSOB network structure. The number of banyan planes is minimum for rearrangeably nonblocking and maximum for strictly nonblocking structure. Both results are available for VSOB networks when there exist no internal link-failures. Since the issue of link-failure is unavoidable, we intend to find the minimum number of planes required to make a VSOB network nonblocking when some links are broken or failed in the structure. This paper presents the approximate number of planes required to make a VSOB networks rearrangeably nonblocking allowing link-failures. We also show an interesting behavior of the  blocking  probability of a faulty VSOB networks that the blocking probability may not  always  increase monotonously with  the  increase  of  link-failures; blocking probability  decreases  for  certain range of  link-failures, and then increases again. We believe that such fluctuating behavior of blocking probability with the increase of link failure probability deserves special attention in switch design.  Keywords: Banyan networks; Blocking probability; Switching networks; Vertical stacking; Link-failures. © 2009 JSR Publications. ISSN: 2070-0237(Print); 2070-0245 (Online). All rights reserved. DOI: 10.3329/jsr.v1i1.1070

Mathematics of a Sudo-Kurve

2018 ◽  
Vol 5 (10) ◽  
pp. 5-28
Author(s):  
Tanya Khovanova ◽  
Wayne Zhao
Keyword(s):  
Minimum Number ◽  
Distinct Solution ◽  
Equivalent Variant

Abstract We investigate a type of a Sudoku variant called Sudo-Kurve, which allows bent rows and columns, and develop a new, yet equivalent, variant we call a Sudo-Cube. We examine the total number of distinct solution grids for this type with or without symmetry. We study other mathematical aspects of this puzzle along with the minimum number of clues needed and the number of ways to place individual symbols.

PREPARASI DEINOCOCCUS RADIODURANS DAN KHAMIR DALAM MATERIAL KECAP L-DRYING SEBAGAI BAHAN UJI PROFISIENSI

2016 ◽  
Vol 13 (1) ◽  
pp. 93
Author(s):  
Titin Yulinery ◽  
Ratih M.Dewi
Keyword(s):  
Saccharomyces Cerevisiae ◽  
Deinococcus Radiodurans ◽  
Test Preparation ◽  
Quality Parameters ◽  
Soy Sauce ◽  
Yeast Saccharomyces Cerevisiae ◽  
Microbiological Test ◽  
Bacterial Contaminants ◽  
Minimum Number ◽  
Important Quality

Tes kemampuan adalah salah satu kegiatan penting dalam pengendalian mutu dan jaminan kualitas mikrobiologi laboratorium untuk mengukur kompetensi analis dan analisis uji profisiensi membutuhkan persiapan Model mikroorganisme adalah kualitas standar dan validitas. Mikrobiologi uji kualitas produk kedelai utama diarahkan pada kehadiran Saccharomyces cerevisiae ragi (S. cerevisiae), S. Bailli, S. rouxii dankontaminan bakteri seperti Bacillus dan Deinococcus. Jenis ragi dan bakteri yang terlibat dalam proses dan dapat menjadi salah satu parameter kualitas penting dalam persiapan yang dihasilkan. Jumlah dan viabilitas bakteri dan ragi menjadi parameter utama dalam proses persiapan bahan uji. Jumlah tersebut adalah jumlah minimum yang berlaku dapat dianalisis. Jumlah ini harus dibawah 10 CFU diperlukan untuk menunjukkan tingkat hygienitas proses dan tingkat minimal kontaminasi. Viabilitas bakteri dan bahan tes ragi persiapan untuk tes kemahiran kecap yang diawetkan dengan L-pengeringan adalah teknik Deinococcus radiodurans (D. radiodurans) 16 tahun, 58 tahun S. cerevisiae, dan S. roxii 13 tahun. kata kunci: Viabilitas, Deinococcus, khamir, L-pengeringan, Proficiency AbstractProficiency test is one of the important activities in quality control and quality assurance microbiology laboratory for measuring the competence of analysts and analysis Proficiency test requires a model microorganism preparations are standardized quality and validity. Microbiological test of the quality of the main soy products aimed at thepresence of yeast Saccharomyces cerevisiae (S. cerevisiae), S. bailli, S. rouxii and bacterial contaminants such as Bacillus and Deinococcus. Types of yeasts and bacteria involved in the process and can be one of the important quality parameters in the preparation produced. The number and viability of bacteria and yeasts become themain parameters in the process of test preparation materials. The amount in question is the minimum number that is valid can be analyzed. This amount must be below 10 CFU required to indicate the level of hygienitas process and the minimum level of contamination. Viability of bacteria and yeast test preparation materials for proficiencytest of soy sauce that preserved by L-drying technique is Deinococcus radiodurans ( D. radiodurans ) 16 years, 58 years S. cerevisiae, and S. roxii 13 years. key words : Viability, Deinococcus, Khamir, L-drying, Proficiency

Path Planning of Mobile Robot Using Improved Artificial Bee Colony Algorithm

2020 ◽  
Vol 38 (9A) ◽  
pp. 1384-1395
Author(s):  
Rakaa T. Kamil ◽  
Mohamed J. Mohamed ◽  
Bashra K. Oleiwi
Keyword(s):  
Mobile Robot ◽  
Comparative Research ◽  
Artificial Bee Colony Algorithm ◽  
Artificial Bee Colony ◽  
Dynamic Control ◽  
Computational Time ◽  
Bee Colony ◽  
Shortest Distance ◽  
Minimum Number ◽  
Cubic Polynomial

A modified version of the artificial Bee Colony Algorithm (ABC) was suggested namely Adaptive Dimension Limit- Artificial Bee Colony Algorithm (ADL-ABC). To determine the optimum global path for mobile robot that satisfies the chosen criteria for shortest distance and collision–free with circular shaped static obstacles on robot environment. The cubic polynomial connects the start point to the end point through three via points used, so the generated paths are smooth and achievable by the robot. Two case studies (or scenarios) are presented in this task and comparative research (or study) is adopted between two algorithm’s results in order to evaluate the performance of the suggested algorithm. The results of the simulation showed that modified parameter (dynamic control limit) is avoiding static number of limit which excludes unnecessary Iteration, so it can find solution with minimum number of iterations and less computational time. From tables of result if there is an equal distance along the path such as in case A (14.490, 14.459) unit, there will be a reduction in time approximately to halve at percentage 5%.

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