A novel conditional diagnosability algorithm under the PMC model

Conditionally t-diagnosable and t-diagnosable are important in system level diagnosis. Therefore,it is valuable to identify whether the system is conditionally t-diagnosable or t-diagnosable and derive the corresponding conditional diagnosability and diagnosability. In the paper,distinguishable measures of pairs of distinct faulty sets with a new perspective on establishing functions are focused.Applying distinguishable function and decision function,it is determined whether a system is conditionally t-diagnosable( or t-diagnosable) or not under the PMC( Preparata,Metze,and Chien)model directly. Based on the decision function,a novel conditional diagnosability algorithm under the PMC model is introduced which can calculate conditional diagnosability rapidly.

Evaluation of fault diagnosability for nonlinear uncertain systems with multiple faults occurring simultaneously

Up to present,the problem of the evaluation of fault diagnosability for nonlinear systems has been investigated by many researchers.However,no attempt has been done to evaluate the diagnosability of multiple faults occurring simultaneously for nonlinear systems.This paper proposes a method based on differential geometry theories to solve this problem.Then the evaluation of fault diagnosability for affine nonlinear systems with multiple faults occurring simultaneously is achieved.To deal with the effect of control laws on the evaluation results of fault diagnosability,a design scheme of the evaluation of fault diagnosability is proposed.Then the influence of uncertainties on the evaluation results of fault diagnosability for affine nonlinear systems with multiple faults occurring simultaneously is analyzed.The numerical simulation results are obtained to show the effectiveness of the proposed evaluation scheme of fault diagnosability.

The 1-Good-neighbor Connectivity and Diagnosability of Locally Twisted Cubes

Diagnosability of a multiprocessor system is one important study topic. In 2012, Peng et al. proposed the g-good-neighbor diagnosability that restrains every fault-free node to contain at least g fault-free neighbors. The locally twisted cube LTQ_n has many good properties. In this paper, we show that the 1-good-neighbor connectivity κ~1(LTQ_n) = 2n-2 and the 1-good-neighbor diagnosability of LTQ_n is 2n-1 under the PMC model for n ≥ 4 and the MM~*model for n ≥ 5.

Conditional Diagnosability of the Locally Twisted Cubes under the PMC Model

In a multiprocessor systems, it is important to local and to replace the faulty processors to maintain systempsilas high reliability. The fault diagnosis, which is the process of identifying fault processors in a multiprocessor system through testing. The conditional diagnosis requires that for each processor u in a system, all the processors that are directly connected to u do not fail at the same time. In this paper, we study the conditional diagnosability of the n-dimensional locally twisted cubes. After showing some properties of the locally twisted cubes, we prove that it under the PMC model is 4n – 7 for n ≥ 5.

The Tightly Super 3-Extra Connectivity and Diagnosability of Locally Twisted Cubes

Diagnosability of a multiprocessor system G is one important measure of the reliability of interconnection networks. In 2016, Zhang et al. proposed the g-extra diagnosability of G, which restrains that every component of G – S has at least (g + 1) vertices. The locally twisted cube LTQn is applied widely. In this paper, we show that LTQn is tightly (4n – 9) super 3-extra connected for n ≥ 6 and the 3-extra diagnosability of LTQn under the PMC model and MM* model is 4n - 6 for n ≥ 5 and n ≥ 7, respectively.

The 2-Extra Diagnosability of Alternating Group Graphs under the PMC Model and MM* Model

Diagnosability of a multiprocessor system is one important study topic. In 2015, Zhang et al. proposed a new measure for fault diagnosis of the system, namely, g-extra diagnosability, which restrains that every fault-free component has at least (g + 1) fault-free nodes. As a favorable topology structure of interconnection networks, the n-dimensional alternating group graph AGn has many good properties. In this paper, we give that the 2-extra diagnosability of AGn is 6n - 17 for n≥ 5 under the PMC model and MM* model.

Some Properties of the g-Good-Neighbor (g-Extra) Diagnosability of a Multiprocessor System

Diagnosability of a multiprocessor system is one important study topic. In 2012, Peng et al. proposed a measure for fault tolerance of the system, which is called the g-good-neighbor diagnosability that restrains every fault-free node containing at least g fault-free neighbors. In 2015, Zhang et al. proposed a measure for fault diagnosis of the system, namely, g-extra diagnosability, which restrains that every fault-free component has at least g+1 fault-free nodes. In this paper, we obtain some properties of the g-good-neighbor (g-extra) diagnosability of the system and give the g-good-neighbor (g-extra) diagnosability of some graphs under the PMC model and MM* model.

THEORY ON THE DIAGNOSABILITY OF THE FAULT CLASSIFICATION APPROACH

This paper describes, by means of a Voronoi hypersphere, the nearest neighbor relations of all the feature submatrices in the fault classification space and analyses the deviation disturbance angles between fault feature submatrices and a k-dimension unitary matrix of the measured voltage change matrix. With the above two concepts, this paper discusses the diagnos-ability in the fault classification approach. The paper also classifies and defines the fault diagnosis problems. Finally, the paper derives the corresponding necessary and sufficient conditions for correct location of faults.

A Proof for g-Good-Neighbor Diagnosability of Exchanged Hypercubes

The diagnosability of a multiprocessor system or an interconnection network is an important research topic. The system and an interconnection network have an underlying topology, which is usually presented by a graph. In this paper, we show proof for the g-good-neighbor diagnosability of the exchanged hypercube EH (s,t) under the PMC model and MM* model.

The Non-inclusion Diagnosability of Hypercubes Under the PMC Model

Diagnosability of a multiprocessor system is an important measure of the reliability of interconnection networks.System-level diagnosis is a primary strategy to identify the faulty processors in a multiprocessor system.Based on a sound assumption proposed by Zhu et al.recently,we proposed a new diagnosability named non-inclusion diagnosability and showed that the non-inclusion diagnosability t_(N)(Q_(n))of the hypercube under the PMC model is 2n-2.That is,assume that if two vertex sets F_(1) and F_(2) are both consistent with a syndrome and F_(1)C F_(2),then F_(2) is not the faulty set which we are looking for;the faulty set F is 1-step diagnosable if|F|≤2n-2 in Q_(n) under the PMC model.

g-Good-neighbor conditional diagnosability of star graph networks under PMC model and MM＊ model

Diagnosability of a multiprocessor system is an important study topic. S. L. Peng, C. K. Lin, J. J. M. Tan, and L. H. Hsu [Appl. Math. Comput., 2012, 218（21）： 10406-10412] proposed a new measure for fault diagnosis of the system, which is called the 9-good-neighbor conditional diagnosability that restrains every fault-free node containing at least 9 fault-free neighbors. As a famous topological structure of intereonnection networks, the n-dimensional star graph Sn has many good properties. In this paper, we establish the 9_good-neighbor conditional diagnosability of Sn under the PMC model and MM＊ model.

The g-Good-Neighbor Conditional Diagnosability of Locally Twisted Cubes

In the work of Peng et al.(Appl Math Comput 218(21):10406–10412,2012),a new measure was proposed for fault diagnosis of systems:namely g-goodneighbor conditional diagnosability,which requires that any fault-free vertex has at least g fault-free neighbors in the system.In this paper,we establish the g-goodneighbor conditional diagnosability of locally twisted cubes under the PMC model and the MM∗model.

Diagnosability of the Incomplete Star Graphs

The growing size of the multiprocessor systems increases their vulnerability to component failures. It is crucial to local and to replace the fault processors to maintain system’s high reliability. The fault diagnosis is the process of identifying faulty processors in a system through testing. This paper establishes the diagnosabilities of the incomplete star graph Sn (n≥4) with missing links under the PMC model and its variant, the BGM model, and shows that the diagnosabilities of incomplete star graph Sn under these two diagnostic models can be determined by the minimum degree of its topology structure. This method can also be applied to the other existing multiprocessor systems.

Intermittent Fault Diagnosability of Interconnection Networks

An interconnection network＇s diagnosability is an important metric for measuring its self-diagnostic capability. Permanent fault and intermittent fault are two different fault models that exist in an interconnection network. In this paper, we focus on the problem pertaining to the diagnosability of interconnection networks in an intermittent fault situation. First, we study a class of interconnection networks called crisp three-cycle networks, in which the Chin-number （the number of common vertices each pair of vertices share） is no more than one. Necessary and sufficient conditions are derived for the diagnosability of crisp three-cycle networks under the PMC （Preparata, Metze, and Chien） model. A simple check can show that many well-known intereonnection networks are crisp three-cycle networks. Second, we prove that an intereonnection network S is a ti-fault diagnosable system without repair if and only if its minimum in-degree is greater than ti under the BGM （Barsi, Grandoni, and Masetrini） model. Finally, we extend the necessary and sufficient conditions to determine whether an interconnection network S is ti-fault diagnosable without repair under the MM （Maeng and Malek） model from the permanent fault situation to the intermittent fault situation.

Advancements and challenges in neuroimaging for the diagnosis of intracranial aneurysms:Addressing false positive diagnoses and emerging techniques

Despite advancements in neuroimaging,false positive diagnoses of intracranial aneurysms remain a significant concern.This article examines the causes,prevalence,and implications of such false-positive diagnoses.We discuss how conditions like arterial occlusion with vascular stump formation and infundibular widening can mimic aneurysms,particularly in the anterior circulation.The article compares various imaging modalities,including computer tomography angiogram,magnetic resonance imaging/angiography,and digital subtraction angiogram,highlighting their strengths and limitations.We emphasize the im-portance of accurate differentiation to avoid unnecessary surgical interventions.The potential of emerging technologies,such as high-resolution vessel wall ima-ging and deep neural networks for automated detection,is explored as promising avenues for improving diagnostic accuracy.This manuscript underscores the need for continued research and clinical vigilance in the diagnosis of intracranial aneurysms.

DIAGNOSABILITY OF CAYLEY GRAPH NETWORKS GENERATED BY TRANSPOSITION TREES UNDER THE COMPARISON DIAGNOSIS MODEL

Diagnosability of a multiprocessor system is one important study topic.Cayley graph network Cay（Tn,Sn） generated by transposition trees Tnis one of the attractive underlying topologies for the multiprocessor system.In this paper,it is proved that diagnosability of Cay（Tn,Sn） is n-1 under the comparison diagnosis model for n ≥ 4.

Diagnosability of a class of discrete event systems based on observations

The diagnosability of discrete event systems has been a topic of interest to many researchers. The diagnosability conditions for various systems have evolved based on a regularity condition that is imposed on faulty traces with respect to their observable continuations. Improving upon this weak but necessary condition, a new model of diagnosability that is based on sensor outputs, which are called observatio ns, upon a command in put is proposed in this paper. Necessary and sufficient con ditions are derived for the proposed diagnosability model. The search performance of the proposed diagnosability condition is of linear complexity in terms of the power set of the system events and observations, compared to the exponential complexity of the search with the existing diag nosability regularity condition. Moreover, a system that is not diag no sable according to the existi ng diag nosability condition may be diagnosable in the proposed diagnosability model, which includes observations.

TOPOLOGICAL CONDITIONS FOR FAULT DIAGNOSABILITY AT SUBNETWORK-LEVEL

The fault analysis of analog circuits at subnetwork-level is confronted with two essentialcore problems: (ⅰ) Is it necessary that all the torn nodes are accessible? (ⅱ) Are there any topological conditions of subnetwork which guarantee the fault at subnetwork-level to bediagnosed correctly? This paper answers the two problems in two theorems. The conditions are necessary and almost sufficient, and if all the torn nodes are accessible, the required topological conditions can be almost satisfied automatically. This is a special situation of our research on the distribution of the accessible nodes.

THE CONDITIONAL DIAGNOSABILITY OF SHUFFLE-CUBES

In the application of multiple-processor systems some processors or links in a system maynot function properly,thus the fault diagnosis is one of the most important issues in the analysisand maintenance of those systems.For the practical fault diagnosis systems,the probability that allneighboring processors of a processor are faulty simultaneously is very small.Thus,the conditionaldiagnosability,which is a new metric for evaluating such systems,assumes that every fault set doesnot contain all neighbors of any processor in the system.In this paper,the authors show that then-dimensional shuffle-cube has the conditional diagnosability of 4n-15 for n = 2 (mod 4) and n ≥ 10.

The Non-Inclusive Diagnosability of Regular Graphs

Fault diagnosis is an important area of study with regard to the design and maintenance of multiprocessor systems.A new measure for fault diagnosis of systems,namely,non-inclusive diagnosability(denoted by MM^(*)),was proposed by Ding et al.In this paper,we establish the non-inclusive diagnosability of a class of regular graphs under the PMC model and the MM^(*)model.As applications,the non-inclusive diagnosabilities of hypercubes,hierarchical hypercubes,folded hypercubes,star graphs,bubble-sort graphs,pancake graphs and dual cubes are determined under the PMC model and the[Math Processing Error]model.