1-EDGE FAULT-TOLERANT DESIGNS FOR MESHES

1994 ◽  
Vol 04 (04) ◽  
pp. 385-389 ◽  
Author(s):  
RAY-SHYNG CHOU ◽  
LIH-HSING HSU
Keyword(s):  
Fault Tolerant ◽  
Minimum Number

A graph G* is k-edge fault-tolerant with respect to a graph G, denoted by k- EFT (G), if every graph obtained by removing any k edges from G* contains G. A k- EFT (G) graph is optimal if it contains the minimum number of edges among all k- EFT (G) graphs. Recently, Harary and Hayes have presented a design which is 1-EFT with respect to meshes and conjectured that their design is optimal. We prove their conjecture is false by giving another design which is 1-EFT with respect to meshes.

The Relationship Between Extra Connectivity and t/k-Diagnosability of Regular Networks

2020 ◽  
Vol 20 (01) ◽  
pp. 2050003
Author(s):  
WENJUN LIU
Keyword(s):  
Fault Tolerant ◽  
Cayley Graphs ◽  
General Relationship ◽  
Multiprocessor System ◽  
Diagnostic Model ◽  
Star Network ◽  
Minimum Number ◽  
Two Parameters ◽  
Regular Networks ◽  
The Relationship

The g-extra connectivity of a multiprocessor system modeled by a graph G, denoted by [Formula: see text] (G), is the minimum number of removed vertices such that the network is disconnected and each residual component has no less than g + 1 vertices. The t/k-diagnosis strategy can detect up to t faulty processors which might include at most k misdiagnosed processors. These two parameters are important to measure the fault tolerant ability of a multiprocessor system. The extra connectivity and t/k-diagnosability of many well-known networks have been investigated extensively and independently. However, the general relationship between the extra connectivity and the t/k-diagnosability of general regular networks has not been established. In this paper, we explore the relationship between the k-extra connectivity and t/k-diagnosability for regular networks under the classic PMC diagnostic model. More specifically, we derive the relationship between 1-extra connectivity and pessimistic diagnosability for regular networks. Furthermore, the t/k-diagnosability and pessimistic diagnosability of some networks, including star network, BC networks, Cayley graphs generated by transposition trees etc., are determined.

scholarly journals Fault-Tolerant quantum computation with constant overhead

2014 ◽  
Vol 14 (15&16) ◽  
pp. 1339-1371
Author(s):  
Daniel Gottesman
Keyword(s):  
Fault Tolerant ◽  
Quantum Circuit ◽  
Error Correcting Codes ◽  
Parity Check ◽  
Low Density Parity Check ◽  
The Family ◽  
Minimum Number ◽  
Logical Qubits ◽  
Quantum Error ◽  
Parity Check Codes

What is the minimum number of extra qubits needed to perform a large fault-tolerant quantum circuit? Working in a common model of fault-tolerance, I show that in the asymptotic limit of large circuits, the ratio of physical qubits to logical qubits can be a constant. The construction makes use of quantum low-density parity check codes, and the asymptotic overhead of the protocol is equal to that of the family of quantum error-correcting codes underlying the fault-tolerant protocol.

Hamiltonian graphs with minimum number of edges for fault-tolerant topologies

1992 ◽  
Vol 44 (2) ◽  
pp. 95-99 ◽  
Author(s):  
Krishnendu Mukhopadhyaya ◽  
Bhabani P. Sinha
Keyword(s):  
Fault Tolerant ◽  
Hamiltonian Graphs ◽  
Minimum Number

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.

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