BC Networks Research Articles

Multi-Functional Repair and Long-Term Preservation of Paper Relics by Nano-MgO with Aminosilaned Bacterial Cellulose.

Paper relics, as carrieres of historical civilization's records and inheritance, could be severely acidic and brittle over time. In this study, the multi-functional dispersion of nanometer magnesium oxide (MgO) carried by 3-aminopropyl triethoxysilane-modified bacterial cellulose (KH550-BC) was applied in the impregnation process to repair aged paper, aiming at solving the key problems of anti-acid and strength recovery in the protection of ancient books. The KH550-BC/MgO treatment demonstrated enhanced functional efficacy in repairing aged paper, attributed to the homogeneous and stable distribution of MgO within the nanofibers of BC networks, with minimal impact on the paper's wettability and color. Furthermore, the treatment facilitated the formation of adequate alkali reserves and hydrogen bonding, resulting in superior anti-aging properties in the treated paper during prolonged preservation. Even after 30 days of hygrothermal aging tests, the paper repaired by KH550-BC/MgO was still in a gently alkaline environment (pH was about 7.56), alongside a 32.18% elevation compared to the untreated paper regarding the tear index. The results of this work indicate that KH550-BC/MgO is an effective reinforcement material for improving the long-term restoration of ancient books.

Link fault tolerance of BC networks and folded hypercubes on h-extra r-component edge-connectivity

Parallel and distributed systems play a significant role in high-performance computing, prompting us to investigate qualitative and quantitative metrics to indicate the fault tolerance and vulnerability of systems. Consider the setup where there are large-scale link malfunctions that disconnect the network and result in various components, each with multiple processors. In this paper, we propose and study the h-extra r-component edge-connectivity of a connected graph G, which is denoted by cλrh(G) and has not been addressed before. Let h and r be two positive integers with r≥2. An edge subset F⊆E(G) is said to be an h-extra r-component edge-cut of G, if any, G−F has at least r components and every component of G−F has at least h vertices. The cardinality of the minimum h-extra r-component edge-cut of G is the h-extra r-component edge-connectivity of G. Let h be a positive integer with the decomposition h=∑i=0t2ki, where ki>ki+1, 0≤i≤t−1. In this paper, we derive a lower bound for the exact value of h-extra 3-component edge-connectivity of BC networks Bn and demonstrate that it is tight for one member of Bn, hypercube Qn, in the interval 1≤h≤2⌊n2⌋−1−1, n≥4. This lower bound is also tight for the exact value of 2c-extra 3-component edge-connectivity of Bn with 0≤c≤n−2, n≥4. Specifically, cλ3h(Qn)=2nh−∑i=0tki2ki+1−∑i=0ti2ki+2−h for 1≤h≤2⌊n2⌋−1−1, n≥4 and cλ32c(Bn)=(2n−2c−1)2c for 0≤c≤n−2, n≥4. Exact value of h-extra 3-component edge-connectivity of n-dimensional folded hypercube FQn, cλ3h(FQn) is 2(n+1)h−∑i=0tki2ki+1−∑i=0ti2ki+2−h for 1≤h≤2⌈n2⌉−1−1, n≥4, and that of 2c-extra 3-component edge-connectivity of FQn, cλ32c(FQn), is (2n−2c+1)2c for 0≤c≤n−2, n≥4.

Fault tolerance of recursive match networks based on g-good-neighbor fault pattern

The rapid informatization and digitalization of the society heavily rely on the extensive use of parallel and distributed, networked computer systems. It is important for large-scale parallel and distributed systems to be able to detect and tolerate faulty vertices in the network. A network's fault status can often be characterized with the network's connectivity and diagnosability. The connectivity/diagnosability can be defined under various conditions. This paper is concerned with the connectivity/diagnosability under the “g-good-neighbor condition”, which can more accurately measure a network's fault status. In this paper, we propose a new class of recursive networks, named recursive match networks (RMNs), which contain the well-known BCube and BC networks. We determine the RMNs' g-good-neighbor connectivity and g-good-neighbor conditional diagnosability under the classic MM* and PMC diagnostic models for g≥0. Since the RMN is a more general network covering the BCube and BC networks, our results can be directly applied to these two networks.

Characterization of component diagnosability of regular networks

Multiprocessor systems, which usually take interconnection network (or graph) as underlying topologies, are commonly deployed for big data analysis because of evolution in technologies such as cloud computing, IoT, social network and so on. Reliability evaluation is of significant importance to characterize fault tolerability for the topologies of multiprocessor systems, and system-level diagnosis is a primary strategy to identify the faulty processors in the systems. The g-component connectivity cκg(G) of a graph G is the size of a minimal vertex-set, whose removal will disconnect G to possess at least g components, which reflects the invulnerability of the topology graph. Based on g-component connectivity of graph G, the g-component diagnosability ctg(G) of regular networks has been proposed as a parameter to measure network fault-tolerability. The g-component diagnosability ctg(G) is the maximum t such that the graph G is g-component t-diagnosable. We first propose some general characterizations of the component diagnosability of regular networks under the classic PMC model and MM∗ model based on the component connectivity. And then we present some empirical analysis for some kinds of well-known regular networks, such as BC networks, star graphs, bubble-sort star graphs, alternating group graphs.

A parallel algorithm to construct edge independent spanning trees on the line graphs of conditional bijective connection networks

The line graphs of some well-known graphs, such as the generalized hypercube and the crossed cube, have been adopted for the logic graphs of data center networks (DCNs). Conditional bijective connection networks (conditional BC networks) are a class of networks which have been proved to include hypercubes, crossed cubes, locally twisted cubes and Möbius cubes, etc. Hence, the researches on the line graphs of conditional BC networks can be applied to DCNs. Edge independent spanning trees (EISTs) on a graph have received extensive attention because of their applications in reliable communication, fault-tolerant broadcasting and secure message distribution. Since the line graph of an n-dimensional conditional BC network, denoted as L(XCn), is (2n−2)-regular, whether there exist 2n−2 EISTs on L(XCn) is an open question. In this paper, we first propose a parallel algorithm to construct 2n−2 EISTs rooted at an arbitrary node on L(XCn), where n≥2. Then, we prove the correctness of our algorithm. Finally, we give a simulation result of our algorithm.

Can Blockchain based Supply Chain Create a Stock Market Reaction? Evidence from an Event Study

This study investigates Blockchain based Supply chain (BC-SC) announcements impact on the stock market. Using a sample of 104 announcements between 2016 and 2021, we conduct an international event study to determine the market reaction. We find that an overall positive market reaction of 1.45% to all BC-SC announcements on the announcement day. In addition, we find that the stock market reaction slightly differs when different SC challenges are targeted by the announcing firm. When blockchain is used for traceability purposes, the market response is less positive when compared to other SC challenges like resolving disputes, maintaining cargo integrity and data security. We further find that firms that are part of BC industrial collaborations experience a more positive stock market response, when compared to firms using private or public BC networks. When looking into firm characteristics, we find that innovative firms experience greater positive reaction to BC-SC announcements. Interestingly, we find that smaller firms do not experience a strong positive market response. Leveraging the diverse industries in our sample, we investigated the effect of early adoption of BC-SC with respect to the industry. The late BC-SC adoption in the manufacturing sector only received a significantly positive market reaction. Overall, it seems that the market views many BC initiatives as adding to the competitiveness and long-term profitability of organizations. It also shows that BC, as a multi-stakeholder technology should be evaluated from both a strategic and operational perspective. Other implications and research directions are also identified; especially given the limitations of the study and the relatively early BC-SC supply chain developments.

Embedded connectivity of some BC networks

Embedded connectivity of some BC networks

Relation of Extra Edge Connectivity and Component Edge Connectivity for Regular Networks

Reliability of interconnection networks is important to design multiprocessor systems. The extra edge connectivity and component edge connectivity are two parameters for the reliability evaluation. The [Formula: see text]-extra edge connectivity [Formula: see text] is the cardinality of the minimum extra edge cut [Formula: see text] such that [Formula: see text] is not connected and each component of [Formula: see text] has at least [Formula: see text] vertices. The [Formula: see text]-component edge connectivity [Formula: see text] of a graph [Formula: see text] is the minimum edge number of a set [Formula: see text] such that [Formula: see text] is not connected and [Formula: see text] has at least [Formula: see text] components. In this paper, we find the relation of extra edge connectivity and component edge connectivity for regular networks. As an application, we determine the component edge connectivity of BC networks, [Formula: see text]-ary [Formula: see text]-cubes, enhanced hypercubes.

Theg-Extra Conditional Diagnosability of Graphs in Terms ofg-Extra Connectivity

The [Formula: see text]-extra conditional diagnosability and [Formula: see text]-extra connectivity are two important parameters to measure ability of diagnosing faulty processors and fault tolerance in a multiprocessor system. The [Formula: see text]-extra conditional diagnosability [Formula: see text] of graph [Formula: see text] is defined as the diagnosability of a multiprocessor system under the assumption that every fault-free component contains more than [Formula: see text] vertices. While the [Formula: see text]-extra connectivity [Formula: see text] of graph [Formula: see text] is the minimum number [Formula: see text] for which there is a vertex cut [Formula: see text] with [Formula: see text] such that every component of [Formula: see text] has more than [Formula: see text] vertices. In this paper, we study the [Formula: see text]-extra conditional diagnosability of graph [Formula: see text] in terms of its [Formula: see text]-extra connectivity, and show that [Formula: see text] under the MM* model with some acceptable conditions. As applications, the [Formula: see text]-extra conditional diagnosability is determined for some BC networks such as hypercubes, varietal hypercubes, and [Formula: see text]-ary [Formula: see text]-cubes under the MM* model.

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

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.

A Survey on Wide Diameter of BC Networks

Wide diameter is an important parameter to measure the performance of network parallel communication. The hypercube is one of the most popular interconnection networks. The BC networks consist of the hypercube and most of the hypercube variations. In this paper, we give a survey of the research results on wide diameter of BC networks.

Reliability Analysis of the Bijective Connection Networks for Components

Connectivity is a critical parameter that can measure the reliability of networks. Let Q ⊆ V ( G ) be a vertex set. If G − Q is disconnected and every component of G − Q contains at least k + 1 vertices, then Q is an extra-cut. The number of vertices in the smallest extra-cut is the extraconnectivity κ k ( G ) . Suppose ω ( G ) is the number of components of G and W ⊆ V ( G ) ; if ω ( G − W ) ≥ t , then w is a t-component cut of G. The number of vertices in the least t-component cut is the t-component connectivity c κ t ( G ) of G. The t-component edge connectivity c λ t ( G ) is defined similarly. In this note, we study the BC networks and obtain the t-component (edge) connectivity of bijective connection networks for some t.

Analysis of Hybrid Broadcast/Broadband Networks With Multiple Broadcasting Stations

Hybrid broadcast/broadband network (HBBN) presents a potential solution to mitigate the increasing demand for mobile TV. A proper HBBN deployment alleviates the limitations that each standalone network faces, thereby enhancing the global network coverage and efficiency. In this paper, we propose to address the question of performance improvement expected from such HBBN by means of an analytical framework based on stochastic geometry modeling. To this end, we introduce a generic model of the HBBN where multiple broadcast transmitters and a broadband network are deployed in the same area, jointly offering linear services, one of the mobile TV services. Two different approaches derived from stochastic geometry are applied and compared through the analysis of what is commonly referred to as a Point Hole Process (PHP): Original Poisson Point Process (PPP), and reduced PPP. Both approaches are thoroughly analyzed to give better insights into broadcast/broadband coexistence while taking into account the inter-cell interference of both networks. Exact and simplified expressions for the key performance metrics are derived such as the probability of coverage and ergodic capacity. Those expressions are then used to numerically maximize the spectral and power efficiency of the HBBN regarding the broadcast coverage radius and transmitters' density. The results show that for a wide range of user density, the HBBN introduces gain compared to either BB or BC networks. To the best of the authors' knowledge, this paper presents the first work dealing with the optimization of HBBN based on such a generic model and taking inter-cell and inter-network interference into consideration.

The 1-Good-Neighbor Conditional Diagnosability of Some Regular Graphs

The g-good-neighbor conditional diagnosability is the maximum number of faulty vertices a network can guarantee to identify, under the condition that every fault-free vertex has at least g fault-free neighbors. In this paper, we study the 1-good-neighbor conditional diagnosabilities of some general k-regular k-connected graphs G under the PMC model and the MM* model. The main result [Formula: see text] under some conditions is obtained, where l is the maximum number of common neighbors between any two adjacent vertices in G. Moreover, the following results are derived: [Formula: see text] for the hierarchical star networks, [Formula: see text] for the BC networks, [Formula: see text] for the alternating group graphs [Formula: see text].

Equal relation between the extra connectivity and pessimistic diagnosability for some regular graphs

Extra connectivity and the pessimistic diagnosis are two crucial subjects for a multiprocessor system's ability to tolerate and diagnose faulty processor. The pessimistic diagnosis strategy is a classic strategy based on the PMC model in which isolates all faulty vertices within a set containing at most one fault-free vertex. In this paper, the result that the pessimistic diagnosability tp(G) equals the extra connectivity κ1(G) of a regular graph G under some conditions are shown. Furthermore, the following new results are gotten: the pessimistic diagnosability tp(Sn2)=4n−9 for split-star networks Sn2; tp(Γn)=2n−4 for Cayley graphs generated by transposition trees Γn; tp(Γn(Δ))=4n−11 for Cayley graph generated by the 2-tree Γn(Δ); tp(BPn)=2n−2 for the burnt pancake networks BPn. As corollaries, the known results about the extra connectivity and the pessimistic diagnosability of many famous networks including the alternating group graphs, the alternating group networks, BC networks, the k-ary n-cube networks etc. are obtained directly.

The pessimistic diagnosability of three kinds of graphs

A system is t/t-diagnosable if, provided the number of faulty processors is bounded by t, all faulty processors can be isolated within a set of size at most t with at most one fault-free processor mistaken as a faulty one. The pessimistic diagnosability of a system G, denoted by tp(G), is the maximal number of faulty processors so that the system G is t/t-diagnosable. The pessimistic diagnosability of alternating group graphs AGn (Tsai, 2015); BC networks (Fan, 2005; Tsai, 2013); the k-ary n-cube networks Qnk, (Wang et al., 2012); regular graphs including the alternating group networks ANn (Hao et al., 2016) etc. But most of these results are about networks G with cn(G)≤2 (where cn(G) is the maximum number of common neighbors for any two distinct vertices). In this paper, we study the pessimistic diagnosability of three kinds of graphs which are (n,k)-arrangement graphs An,k, (n,k)-star graphs Sn,k and balanced hypercubes BHn, where cn(An,k)=cn(Sn,k)=n−k−1 and cn(BHn)=2n. We proved that tp(An,k)=(2k−1)(n−k)−1 for n≥k+2 and k≥3, tp(Sn,k)=n+k−3 for n≥k+2 and k≥3, and tp(BHn)=2n for n≥2. As corollaries, the pessimistic diagnosability of the known results about AGn and ANn is obtained directly.

The pessimistic diagnosability of bubble-sort star graphs and augmented k-ary n-cubes

ABSTRACTA system is t/t-diagnosable if, provided the number of faulty processors is bounded by t, all faulty processors can be isolated within a set of size at most t with at most one fault-free processor mistaken as a faulty one. The pessimistic diagnosability of a system G, denoted by , is the maximal number of faulty processors so that the system G is t/t-diagnosable. The known results about for alternating group graphs [Inform. Process. Lett. (2015), pp. 151–154]; BC networks [IEEE Trans. Comput. (2005), pp. 176–184]; the k-ary n-cube networks [IEEE Trans. Comput. (1991), pp. 232–237], [Int. J. Comput. Math. (2012), pp. 1–10] etc. have property that . In this paper, we study the pessimistic diagnosability of two kinds of graphs with , those are: bubble-sort star graphs and augmented k-ary n-cubes , and prove that for , for , and for and.

High-Throughput Blood- and Lymph-Capillaries with Open-Ended Pores Which Allow the Transport of Drugs and Cells.

High-throughput screening of drug diffusion and cell transports from the blood-/lymph-capillary (BC/LC) networks to the peripheral cells in 3D engineered tissues using a microplate would make a powerful tool for in vitro pharmacokinetic assessments. Here, perfusable BC/LC networks embedded in 3D-tissues inside a 24-microplate using a cell-coating technology are reported which allows location control of cell layers. Arrangement of an endothelial cell layer at the top, middle, and bottom of dermal fibroblast tissues provides an interconnected BC/LC networks possessing open pores on both surfaces. When fluorescently labeled dextran, microparticles, and red blood cells are applied to the top surfaces, diffusion and penetration through the networks are observed depending on the size of the substances. Moreover, BC networks mimick a series of in vivo processes of cancer metastasis, extravasation, growth, and growth suppression with drug treatment. The perfusable networks existing in 3D-tissues show great potential for in vitro pharmacokinetic studies.

Dimensional-Permutation-Based Independent Spanning Trees in Bijective Connection Networks

In recent years, there are many new findings on independent spanning trees (ISTs for short) in hypercubes, crossed cubes, locally twisted cubes, and Mobius cubes, which all belong to a more general network category called bijective connection networks (BC networks). However, little progress has been made for ISTs in general BC networks. In this paper, we first propose the definitions of conditional BC networks and V -dimensional-permutation. We then give a linear parallel algorithm of ISTs rooted at an arbitrary vertex in conditional BC networks, which include hypercubes, crossed cubes, locally twisted cubes, and Mobius cubes, based on the ascending circular dimensional-permutation, where the ISTs are all isomorphic to the binomial-like tree. In addition, we show that there exists an efficient algorithm to construct a spanning tree rooted at an arbitrary vertex in any BC network X <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sub> , and all V-dimensional-permutations can be used to construct spanning trees isomorphic to the n-level binomial tree and rooted at an arbitrary vertex in X <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sub> .

Reliability Evaluation of BC Networks in Terms of the Extra Vertex- and Edge-Connectivity

Reliability evaluation of interconnection network is important to the design and maintenance of multiprocessor systems. The extra connectivity and the extra edge-connectivity are two important parameters for the reliability evaluation of interconnection networks. The <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">${\mbi {n}}$</tex> </formula> -dimensional bijective connection network (in brief, BC network) includes several well known network models, such as, hypercubes, Möbius cubes, crossed cubes, and twisted cubes. In this paper, we explore the extra connectivity and the extra edge-connectivity of BC networks, and discuss the structure of BC networks with many faults. We obtain a sharp lower bound of <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">${{g}}$</tex> </formula> -extra edge-connectivity of an <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">${\mbi {n}}$</tex> </formula> -dimensional BC network for <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">${{n}} \geq 4$</tex> </formula> and <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$1 \leq { {g}} \leq {2^{[{{{n}} \over 2}]}}$</tex> </formula> . We also obtain a sharp lower bound of <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">${ {g}}$</tex> </formula> -extra connectivity of an <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">${{n}}$</tex> </formula> -dimensional BC network for <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">${{n}} \geq 4$</tex> </formula> and <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$1 \leq { {g}} \leq 2{ {n}}$</tex> </formula> which improves the result in [“Reliability evaluation of BC networks,” IEEE Trans. Computers, DOI: 10.1109/tc.2012.106.] for <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$1 \leq { {g}} \leq { {n}} - 3$</tex> </formula> . Furthermore, we give a remark about exploring the <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">${ {g}}$</tex> </formula> -extra edge-connectivity of BC networks for the more general <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">${\mbi {g}}$</tex> </formula> , and we also characterize the structure of BC networks with many faulty nodes or links. As an application, we obtain several results on the <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">${\mbi {g}}$</tex> </formula> -extra (edge-) connectivity and the structure of faulty networks on hypercubes, Möbius cubes, crossed cubes, and twisted cubes.