Classical Connection Research Articles

The Generalized 3-Connectivity of a Family of Regular Networks

The generalized [Formula: see text]-connectivity of a graph [Formula: see text], denoted by [Formula: see text], is the minimum number of internally edge disjoint [Formula: see text]-trees for any [Formula: see text] with [Formula: see text]. The generalized [Formula: see text]-connectivity of a graph is a natural extension of the classical connectivity and can be served as an essential parameter for measuring reliability and fault tolerance of the network. Hierarchical interconnection networks (HIN’s) are very important in applications related to the modern interconnection networks since they posses many desirable properties. In this paper, we firstly introduce a family of regular networks [Formula: see text] that can be obtained from [Formula: see text] by adding a matching, where [Formula: see text] and [Formula: see text] are vertex-disjoint subgraphs and each [Formula: see text] is isomorphic to a given graph [Formula: see text] ([Formula: see text]). Then we determine the generalized 3-connectivity of [Formula: see text]. As applications of the main result, the generalized 3-connectivity of some HIN’s, such as the hierarchical star network [Formula: see text], the hierarchical cubic network [Formula: see text] and the hierarchical folded hypercube [Formula: see text], can be determined immediately.

Structure connectivity and substructure connectivity of Möbius cubes

Abstract The connectivity is an important measurement for the fault-tolerance of networks. To provide more accurate measures for the fault-tolerance of networks than the connectivity, some generalizations of connectivity have been introduced. Substructure connectivity and structure connectivity are two extended concepts of classical connectivity. As a variant of the popular network hypercube, the Möbius cubes is also a famous interconnection network in parallel and distributed systems. In this article, we calculate $H$-substructure connectivity and $H$-structure connectivity of Möbius cubes when $H$ is isomorphic to $P_{m},C_{m}$ and $K_{1,m}$.

High fault-tolerant performance of the divide-and-swap cube network

Two crucial metrics used to evaluate the fault tolerance of interconnection networks are connectivity and diagnosability. By improving the connectivity and diagnosability of the interconnection network, its fault tolerance can be enhanced. In this paper, we focus on determining the g-extra connectivity (0≤g≤10) of the divide-and-swap cube DSCn, as well as its diagnosability based on the pessimistic diagnosis strategy and g-extra precise diagnosis strategy, under the PMC and MM* models. The research analysis suggests that compared with some other connectivity and diagnosability of DSCn, such as classical connectivity, structure connectivity, super connectivity, and classical diagnosability, the extra connectivity/diagnosability and pessimistic diagnosability of DSCn enable it to have a higher fault tolerance. Moreover, we propose two O(Nlog2⁡N) effective diagnosis algorithms of DSCn: the g-extra diagnosis algorithm (EX-DiagnosisDSCn) and the pessimistic diagnosis algorithm (PE-DiagnosisDSCn), where the EX-DiagnosisDSCn algorithm can accurately diagnose the state of all processors in DSCn.

The 4-Set Tree Connectivity of Folded Hypercube

The [Formula: see text]-set tree connectivity, as a natural extension of classical connectivity, is a very important index to evaluate the fault-tolerance of interconnection networks. Let [Formula: see text] be a connected graph and a subset [Formula: see text], an [Formula: see text]-tree of graph [Formula: see text] is a tree [Formula: see text] that contains all the vertices of [Formula: see text] and [Formula: see text]. Two [Formula: see text]-trees [Formula: see text] and [Formula: see text] are internally disjoint if and only if [Formula: see text] and [Formula: see text]. The cardinality of maximum internally disjoint [Formula: see text]-trees is defined as [Formula: see text], and the [Formula: see text]-set tree connectivity is defined by [Formula: see text]. In this paper, we show that the [Formula: see text]-set tree connectivity of folded hypercube when [Formula: see text], that is, [Formula: see text], where [Formula: see text] is folded hypercube for [Formula: see text].

Automated Design of Fault Diagnosis CNN Network for Satellite Attitude Control Systems.

Despite the dominance of unsupervised and self-supervised anomaly detection methods in the current satellite fault diagnosis domain, supervised anomaly detection offers a superior alternative for high-sensitivity detection and lightweight deployment requirements specific to subsystems or components, such as attitude control systems (ACSs). This article addresses the issues of over-design and insufficient accuracy in the CNN network design for satellite ACS fault diagnosis by introducing the modified particle swarm optimization-advanced convolution blocks-based CNN (MPSO-ACBCNN) method. First, we present the ACBCNN, a lightweight, flexible-layer CNN architecture. This architecture leverages advanced convolution blocks (ACBs), which incorporate numerous efficient design elements to enhance feature extraction capabilities within power spectral density (PSD) graphs of various fault samples, and employs classical dense connection methods to prevent the issue of gradient vanishing. Second, we devise the MPSO-ACBCNN algorithm to optimize the ACBCNN fault diagnosis architecture for specified ACS using MPSO. In MPSO-ACBCNN, several optimizations to the canonical PSO are implemented, including the fitness design that balances the tradeoff between total parameter quantity and the training effectiveness, and methods to ensure feasible solutions, etc. Finally, numerical experimental results demonstrate the effectiveness and superiority of MPSO-ACBCNN in fault diagnosis for ACS.

Eigenvector Centrality Mapping Reveals Volatility of Functional Brain Dynamics in Anti-NMDA Receptor Encephalitis

BackgroundAnti-NMDA receptor encephalitis (NMDARE) causes long-lasting cognitive deficits associated with altered functional connectivity. Eigenvector centrality (EC) mapping represents a powerful new method for data-driven voxelwise and time-resolved estimation of network importance—beyond changes in classical static functional connectivity. MethodsTo assess changes in functional brain network organization, we applied EC mapping in 73 patients with NMDARE and 73 matched healthy control participants. Areas with significant group differences were further investigated using 1) spatial clustering analyses, 2) time series correlation to assess synchronicity between the hippocampus and cortical brain regions, and 3) correlation with cognitive and clinical parameters. ResultsDynamic, time-resolved EC showed significantly higher variability in 13 cortical areas (familywise error p < .05) in patients with NMDARE compared with healthy control participants. Areas with dynamic EC group differences were spatially organized in centrality clusters resembling resting-state networks. Importantly, variability of dynamic EC in the frontotemporal cluster was associated with impaired verbal episodic memory in patients (r = −0.25, p = .037). EC synchronicity between the hippocampus and the medial prefrontal cortex was reduced in patients compared with healthy control participants (familywise error p < .05, tmax = 3.76) and associated with verbal episodic memory in patients (r = 0.28, p = .019). Static EC analyses showed group differences in only one brain region (left intracalcarine cortex). ConclusionsWidespread changes in network dynamics and reduced hippocampal-medial prefrontal synchronicity were associated with verbal episodic memory deficits and may thus represent a functional neural correlate of cognitive dysfunction in NMDARE. Importantly, dynamic EC detected substantially more network alterations than traditional static approaches, highlighting the potential of this method to explain long-term deficits in NMDARE.

Религиозная лексика в современном русском и польском языках в переводоведческом, лексикографическом и лингвокультурологическом освещении

During the first quarter of the 21st century, Polish and Russian linguistics have been experiencing an intensification of research into the languages of various Christian denominations. In Poland, it is usually the language of the Polish Catholic Church, traditionally associated with the Polish language; in Russia, it is the language of the Russian Orthodox Church, speaking of which, Church Slavonic and Russian are usually meant. Due to the ongoing geopolitical processes, wellknown classical parallels or connections such as “Polish – Catholic”, “Russian – Orthodox” and directions of this kind of research are undergoing changes. In the Polish Orthodox Church, whose ministers and parishioners until recently used mainly Church Slavonic and Polish, today they increasingly turn to Russian, Belarusian, Ukrainian and other Slavic languages in their daily lives. Therefore, against the background of the predominance of Catholicism and the Polish language, problems arise with the correct interpretation and correct understanding of basic religious names by representatives of various Christian denominations speaking related Slavic languages. As a result, there are studies of parallels and connections such as “Polish, Russian, Ukrainian – Orthodox”, and questions arise, the answers to which can be tried to find in lexicography.

Connectivity Maintenance through Unlabeled Spanning Tree Matching

A key function of mobile networks is the ability to dynamically reshape itself to any desired geometry. Lacking absolute position awareness, agents often rely on distance-limited inter-agent spatial measurements to maintain state awareness. Methods of formation control must therefore ensure a minimal level of persistent pairwise measurement feedback throughout transition, giving rise to the classic connectivity maintenance problem. To address this problem, we propose a method of structure-preserving assignment, matching agents to desired positions such that persistent global connectivity is naturally and automatically satisfied under smooth transition. Compared to other approaches, this complementary technique reduces reliance on aggressive or costly mid-flight formation control protocols. The technique is shown to scale and even improve with network size.

Star structure fault tolerance of Bicube networks

Processor and communication link failures are inevitable in a large multiprocessor system, and so the fault tolerance of its underlying interconnection network has become a key scientific issue. Connectivity is an important parameter to characterize network fault tolerance, and there are many novel variants of classical connectivity to measure the fault tolerance of interconnection networks. However, these new strategies only consider a single faulty vertex. Structure connectivity and substructure connectivity make up for this deficiency, which underline the fault situation with certain specific structures. H-structure-connectivity κ ( G ; H ) (resp. H-substructure-connectivity κ s ( G ; H ) ) of G is the minimum cardinality of H-structure-cuts (resp. H-substructure-cuts). For the n-dimensional Bicube network B Q n , we establish the structure and substructure connectivity of Bicube networks, i.e. κ ( B Q n ; K 1 , 1 ) = κ s ( B Q n ; K 1 , 1 ) = n for odd n ≥ 5 ; κ ( B Q n ; K 1 , 1 ) = κ s ( B Q n ; K 1 , 1 ) = n − 1 for even n ≥ 4 and κ ( B Q n ; K 1 , r ) = κ s ( B Q n ; K 1 , r ) = ⌈ n 2 ⌉ for n ≥ 6 and 2 ≤ r ≤ n − 1 .

The regular edge connectivity of regular networks

Classical connectivity is a vital metric to assess the reliability of interconnection networks, while it has defects in the defective assumption that all neighbours of one node may fail concurrently. To overcome this deficiency, many new generalizations of traditional connectivity, such as g-component (edge) connectivity, restricted (edge) connectivity, g-extra (edge) connectivity and so on, have been suggested. For any positive integer a, the a-regular edge connectivity of a connected graph G is the minimum cardinality of an edge cut, whose deletion disconnects G so that each component is a a-regular graph. In this work, we investigate the a-regular edge connectivity of some regular networks, which provides a novel idea for further exploring the reliability of networks. Finally, simulations are carried out to compare the a-regular connectivity with other types of connectivity in some regular networks. The comparison results imply that the a-regular edge connectivity has its superiority.

Impact of sample size and regression of tissue-specific signals on effective connectivity within the core default mode network.

Interactions within brain networks are inherently directional, which are inaccessible to classical functional connectivity estimates from resting-state functional magnetic resonance imaging (fMRI) but can be detected using spectral dynamic causal modeling (DCM). The sample size and unavoidable presence of nuisance signals during fMRI measurement are the two important factors influencing the stability of group estimates of connectivity parameters. However, most recent studies exploring effective connectivity (EC) have been conducted with small sample sizes and minimally pre-processed datasets. We explore the impact of these two factors by analyzing clean resting-state fMRI data from 330 unrelated subjects from the Human Connectome Project database. We demonstrate that both the stability of the model selection procedures and the inference of connectivity parameters are highly dependent on the sample size. The minimum sample size required for stable DCM is approximately 50, which may explain the variability of the DCM results reported so far. We reveal a stable pattern of EC within the core default mode network computed for large sample sizes and demonstrate that the use of subject-specific thresholded whole-brain masks for tissue-specific signals regression enhances the detection of weak connections.

A Novel Two-Factor Authentication Scheme for Increased Security in Accessing the Moodle E-Learning Platform

Moodle is a platform designed for universal learning to support pedagogical interactions and educational activities. The information technology (IT) administrator uses standard authentication methods for students logging into the Moodle platform. The need for two-factor authentication has grown as institutions, governments, and individuals realize that passwords are not secure enough to protect user accounts in their current technical format. The classic connection methods have vulnerabilities, and account passwords are easy to crack. Analyzing these aspects, the goal is to create a new safe and reliable alternative to the traditional authentication methods in e-learning platforms. The proposed solution introduces a new authentication factor using digital certificates stored on physical devices or the cloud to address the evolving authentication and security challenges effectively. The absence of this authentication within the Moodle ecosystem has imparted a sense of urgency for its implementation. With the innovative authentication scheme, the users have gained confidence, are satisfied with the new solution, and have not reported security breaches. The result is increased security, data protection, and better account management.

The Bounds of Generalized 4-Connectivity of Folded Divide-and-Swap Cubes

Connectivity along with its extensions are important metrices to estimate the fault-tolerance of interconnection networks. The classic connectivity [Formula: see text] of a graph [Formula: see text] is the minimum cardinality of a vertex set [Formula: see text] such that [Formula: see text] is connected or a single vertex. For any subset [Formula: see text] with [Formula: see text], a tree [Formula: see text] in [Formula: see text] is called an [Formula: see text]-tree if [Formula: see text]. Furthermore, any two [Formula: see text]-tree [Formula: see text] and [Formula: see text] are internally disjoint if [Formula: see text] and [Formula: see text]. We denote by [Formula: see text] the maximum number of pairwise internally disjoint [Formula: see text]-trees in [Formula: see text]. For an integer [Formula: see text], the generalized [Formula: see text]-connectivity of a graph [Formula: see text] is defined as [Formula: see text] and [Formula: see text]. For the [Formula: see text]-dimensional folded divide-and-swap cubes, [Formula: see text], we show the upper bound and the lower bound of [Formula: see text], that is [Formula: see text], where [Formula: see text] and [Formula: see text] in this paper.

Entangled Photon Anti-Correlations Are Evident from Classical Electromagnetism

For any experiment with two entangled photons, some joint measurement outcomes can have zero probability for a precise choice of basis. These perfect anti-correlations would seem to be a purely quantum phenomenon. It is, therefore, surprising that these very anti-correlations are also evident when the input to the same experiment is analyzed via classical electromagnetic theory. Demonstrating this quantum–classical connection for arbitrary two-photon states and analyzing why it is successful motivates alternative perspectives concerning entanglement, the path integral, and other topics in quantum foundations.

THE GENESIS OF ISLAMIC SCIENCE: THE CONTRIBUTION OF CLASSICAL INDIAN SCIENCE REVISITED

The main purpose of this article is to highlight the historical fact that classical Indian civilisation played a significant role in the early civilisational growth of Islam during the three centuries under study, particularly in the field of philosophical-scientific knowledge. The Indian role is now acknowledged to be far more extensive than what many people thought and realised. Quite clearly, the Indian contribution helped pave the way for Islam’s grand knowledge synthesis or its golden age in the tenth and eleventh centuries. Unfortunately, in the Western-centric narrative of the history of science, the role of classical Indian science in the early development of Islamic civilisation was downplayed, with disproportionate prominence given to the role of Greek science. As a result, many Easterners today – Hindus and Muslims included – are unaware of the real extent of the classical Indian role in question. A significant facet of this early civilisational growth of Islam was knowledge transfer from the advanced cultures of the time, of which India was a good example. Rather interestingly, this knowledge transfer appeared to be widely known to the Muslims of the time. According to Joseph Mazur, “by the tenth century, there were numerous Arabic texts on the Indian numerals.” Another notable facet is knowledge organisation, which Muslims consciously pursued in the light of the distinct worldview of the new religion and civilisation. I will now explain what I mean exactly by the term knowledge transfer and the term knowledge organisation that I am using in this article. I will also explain the classical Indian connection to the knowledge activities that were going on in the young Islamic civilisation.

Extra-cardiac and complex Fontan baffle fenestration using radio frequency current via surgical electrocautery

Fontan baffle punctures and creation of Fontan fenestration for cardiac catheterisation procedures remain challenging especially due to the heavy calcification of prosthetic material and complex anatomy. We sought to evaluate our experience using radiofrequency current via surgical electrocautery needle for Fontan baffle puncture to facilitate diagnostic, electrophysiology, and interventional procedures. A retrospective chart review of all Fontan patients (pts) who underwent Fontan baffle puncture using radiofrequency energy via surgical electrocautery from three centres were performed from January 2011 to July 2021. A total of 19 pts underwent 22 successful Fontan baffle puncture. The median age and weight were 17 (3-36 years) and 55 (14-88) kg, respectively. The procedural indications for Fontan fenestration creation included: diagnostic study (n = 1), atrial septostomy and stenting (n = 1), electrophysiology study and ablation procedures (n = 8), Fontan baffle stenting for Fontan failure including protein-losing enteropathy (n = 7), and occlusion of veno-venous collaterals (n = 2) for cyanosis. The type of Fontan baffles included: extra-cardiac conduits (n = 12), lateral tunnel (n = 5), classic atrio-pulmonary connection (n = 1), and intra-cardiac baffle (n = 1). A Fontan baffle puncture was initially attempted using traditional method in 6 pts and Baylis radiofrequency trans-septal system in 2 pts unsuccessfully. In all pts, Fontan baffle puncture using radiofrequency energy via electrocautery needle was successful. The radiofrequency energy utilised was (10-50 W) and required 1-5 attempts for 2-5 seconds. There were no vascular or neurological complications. Radiofrequency current delivery using surgical electrocautery facilitates Fontan baffle puncture in patients with complex and calcified Fontan baffles for diagnostic, interventional, and electrophysiology procedures.

Adjacency-like conditions and induced ideal graphs

In this paper we examine some natural ideal conditions and show how graphs can be defined that give a visualization of these conditions. We examine the interplay between the multiplicative ideal theory and the graph theoretic structure of the associated graph. Behavior of these graphs under standard ring extensions are studied, and in conjunction with the theory, some classical results and connections are made.

Digital transformation in the world city networks’ advanced producer services complex: A technology space analysis

The Advanced Producer Services (APS) sector, long considered to be the vanguard of the knowledge economy and world-city formation, is undergoing a digital transformation. Digital transformation entails an increased engagement with digital technologies in the operation, product offerings and strategies of APS firms, with potentially transformative implications. Such digitization processes are well-established in the morphing of finance into FinTech, with the other APS sub-sectors now allegedly catching-up as evidenced by the arrival of LegalTech, AccountTech, RegTech, PropTech, and AdTech. Moreover, the digital transformation could imply that Information and Communications Technologies (ICT) services are again becoming central to the APS complex after two decades of being largely omitted from world city research. Adopting an evolutionary economic geography perspective, we introduce a new approach that utilizes near real-time data sources to compare local technology spaces with the global picture of digital transformation in world cities. Building a dataset containing information from 40,754 APS start-ups and scale-ups derived from Dealroom.co, this paper explores the geographically uneven digital transformation of the APS sector across European and North American world cities. This allows gauging the extent of digital transformation within APS sectors for each selected city, develop new understandings of the division of labour between world cities, and highlight where sector coalescence between APS sectors is occurring and is more likely to occur. In the process we develop new technological indicators of world-cityness that can be used alongside the classic world city connectivity indicators.

Universal 1-loop divergences for integrable sigma models

We present a simple, new method for the 1-loop renormalization of integrable σ-models. By treating equations of motion and Bianchi identities on an equal footing, we derive ‘universal’ formulae for the 1-loop on-shell divergences, generalizing case-by-case computations in the literature. Given a choice of poles for the classical Lax connection, the divergences take a theory-independent form in terms of the Lax currents (the residues of the poles), assuming a ‘completeness’ condition on the zero-curvature equations. We compute these divergences for a large class of theories with simple poles in the Lax connection. We also show that ℤT coset models of ‘pure-spinor’ type and their recently constructed η- and λ-deformations are 1-loop renormalizable, and 1-loop scale-invariant when the Killing form vanishes.

Component connectivity of augmented cubes

Classical connectivity is a vital metric to explore fault tolerance and reliability of network-based multiprocessor systems. The component connectivity is a more advanced metric to assess the fault tolerance of network structures beyond connectivity and has gained great progress. For a non-complete graph G=(V(G),E(G)), a subset T⊆V(G) is called an r-component cut of G, if G−T is disconnected and has at least r components (r≥2). The r-component connectivity of G, denoted by cκr(G), is the cardinality of the minimum r-component cut. The component connectivities of some networks for small r have been determined, while some progresses for large r only focus on the networks which take hypercube as their modules. In this paper, we determine the (r+1)-component connectivity of augmented cubes cκr+1(AQn)=2nr−4r−(r2)+3, for n≥13, 6≤r≤⌊n−12⌋, and particularly cκr+1(AQn)=2nr−4r−(r2)+2 for n≥5, r∈{4,5}.