scholarly journals Bounds on minimum number of anchors for iterative localization and its connections to bootstrap percolation

2012 ◽  
Author(s):  
Rahul Vaze ◽  
Piyush Gupta
Keyword(s):  
Bootstrap Percolation ◽  
Minimum Number

scholarly journals Saturation in the Hypercube and Bootstrap Percolation

2016 ◽  
Vol 26 (1) ◽  
pp. 78-98 ◽  
Author(s):  
NATASHA MORRISON ◽  
JONATHAN A. NOEL ◽  
ALEX SCOTT
Keyword(s):  
Bootstrap Percolation ◽  
Spanning Subgraph ◽  
Minimum Number

LetQddenote the hypercube of dimensiond. Givend⩾m, a spanning subgraphGofQdis said to be (Qd,Qm)-saturated if it does not containQmas a subgraph but adding any edge ofE(Qd)\E(G) creates a copy ofQminG. Answering a question of Johnson and Pinto [27], we show that for every fixedm⩾ 2 the minimum number of edges in a (Qd,Qm)-saturated graph is Θ(2d).We also study weak saturation, which is a form of bootstrap percolation. A spanning subgraph ofQdis said to beweakly(Qd,Qm)-saturated if the edges ofE(Qd)\E(G) can be added toGone at a time so that each added edge creates a new copy ofQm. Answering another question of Johnson and Pinto [27], we determine the minimum number of edges in a weakly (Qd,Qm)-saturated graph for alld⩾m⩾ 1. More generally, we determine the minimum number of edges in a subgraph of thed-dimensional gridPkdwhich is weakly saturated with respect to ‘axis aligned’ copies of a smaller gridPrm. We also study weak saturation of cycles in the grid.

scholarly journals On the Size of $(K_t,\mathcal{T}_k)$-Co-Critical Graphs

10.37236/8857 ◽  
2021 ◽  
Vol 28 (1) ◽  
Author(s):  
Zi-Xia Song ◽  
Jingmei Zhang
Keyword(s):  
Graph Theory ◽  
Complete Graph ◽  
Minimum Degree ◽  
Bootstrap Percolation ◽  
Critical Graphs ◽  
Critical Graph ◽  
The Family ◽  
Saturated Graphs ◽  
Minimum Number ◽  
Monochromatic Copy

Given an integer $r\geqslant 1$ and graphs $G, H_1, \ldots, H_r$, we write $G \rightarrow ({H}_1, \ldots, {H}_r)$ if every $r$-coloring of the edges of $G$ contains a monochromatic copy of $H_i$ in color $i$ for some $i\in\{1, \ldots, r\}$. A non-complete graph $G$ is $(H_1, \ldots, H_r)$-co-critical if $G \nrightarrow ({H}_1, \ldots, {H}_r)$, but $G+e\rightarrow ({H}_1, \ldots, {H}_r)$ for every edge $e$ in $\overline{G}$. In this paper, motivated by Hanson and Toft's conjecture [Edge-colored saturated graphs, J Graph Theory 11(1987), 191–196], we study the minimum number of edges over all $(K_t, \mathcal{T}_k)$-co-critical graphs on $n$ vertices, where $\mathcal{T}_k$ denotes the family of all trees on $k$ vertices. Following Day [Saturated graphs of prescribed minimum degree, Combin. Probab. Comput. 26 (2017), 201–207], we apply graph bootstrap percolation on a not necessarily $K_t$-saturated graph to prove that for all $t\geqslant4 $ and $k\geqslant\max\{6, t\}$, there exists a constant $c(t, k)$ such that, for all $n \ge (t-1)(k-1)+1$, if $G$ is a $(K_t, \mathcal{T}_k)$-co-critical graph on $n$ vertices, then $$ e(G)\geqslant \left(\frac{4t-9}{2}+\frac{1}{2}\left\lceil \frac{k}{2} \right\rceil\right)n-c(t, k).$$ Furthermore, this linear bound is asymptotically best possible when $t\in\{4,5\}$ and $k\geqslant6$. The method we develop in this paper may shed some light on attacking Hanson and Toft's conjecture.

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.

Transport through bootstrap percolation clusters

1991 ◽  
Vol 1 (5) ◽  
pp. 685-692 ◽  
Author(s):  
Muhammad Sahimi ◽  
Tane S. Ray
Keyword(s):  
Bootstrap Percolation ◽  
Percolation Clusters

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

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