Virtual Links Research Articles

The computational complexity of classical knot recognition

The classical knot recognition problem is the problem of determining whether the virtual knot represented by a given diagram is classical. We prove that this problem is in NP, and we give an exponential time algorithm for the problem.

The intersection polynomials of a virtual knot II: Connected sums

Although the connected sum of trivial knots is trivial in classical knot theory, there is a nontrivial connected sum of trivial knots in virtual knot theory. In this paper, we give connected sum formulae of the intersection polynomials of virtual knots introduced in the preceding paper [6]. As an application, we show that there are infinitely many connected sums of any pair of virtual knots.

Simplified Self-Coherent FSO Transmission Boosted by Digital Resolution Enhancer

The joint application of free-space optics (FSO) transmission with coherent detection has recently appeared to enable unprecedented optical wireless capacity. Nevertheless, due to the associated cost and power consumption, simplified self-coherent FSO links are currently being explored to optimize the performance vs. complexity tradeoff. In particular, the utilization of low-complexity virtual carrier self-coherent transmission provides an appealing cost-effective alternative for high-capacity FSO links. However, this transmission paradigm is associated with quantization noise problems due to limited digital-to-analog converter (DAC) resolution. Following all the stated requirements, this work presents a simplified virtual carrier-assisted self-coherent FSO link supported by a low-resolution DAC and Nyquist rate phase reconstruction using the DC-Value algorithm. The utilization of such a low-resolution DAC is aided by a digital resolution enhancement (DRE) method. Employing this simplified self-coherent approach, we experimentally demonstrated 100 Gbps FSO transmission over an outdoor 42 m link using a DAC with resolution as low as 3 bits.

SURVEILLANCE AND SECURITY MODELS BASED ON THE ARDUINO UNO INTERFACE

The issue demonstrated in the article covers construction of surveillance and security systems on Arduino UNO platform Technological and Software aspect which are based on Quality Semiconductor Sensor-MQ135; PIR Motion Sensor and use of blocking peculiarities. 
 The project model integration process in both a virtual and physical context is described in detail and analyzed in the paper. The following are specifically used: An Arduino UNO microcontroller board, the Arduino Software IDE (Integrated Development Environment), a local code editor on the PC, and the virtual online platform tinkercad.com. The work is supplemented by pertinent electronic diagrams, schemes, software code, descriptions of fundamental functionalities, links to virtual project simulation, real-world application, and links to video recordings of the experiment in order to demonstrate the project model's smooth operation.

Runtime Adaptation Framework for Fulfilling Availability and Continuity Requirements of Network Services

The Network Function Virtualization (NFV) framework is an enabler for the automation of Network Service (NS) management. In the context of NFV, an NS is realized by interconnecting Virtual Network Functions (VNF) using Virtual Links (VL). Availability and continuity are among the important characteristics of an NS. These characteristics depend on the availability of the VNFs and VLs composing the NS, which are usually selected at NS design time. VNFs and VLs utilize the resources of the underlying infrastructure, and their availability (partially) depends on the availability of these resources. To design an NS to fulfill availability and continuity requirements, the availability required from the resources is constrained at design time. However, the characteristics of these resources may change at runtime due to the dynamicity of NFV infrastructure. Thus, impacting the availability of the VNFs and the VLs, which in turn may impact the availability and continuity of the NS. To fulfill these requirements at runtime despite the changes in the infrastructure, the NS should be adapted. In this paper, we propose a framework for the runtime adaptation of NSs that reacts to changes and adapts the NS configuration so that it can fulfill its availability and continuity requirements during the NS lifetime. We also propose a method to develop machine learning models that are used within the framework to determine the required adjustments at runtime. We implemented the proposed framework, the method for developing the machine learning models, a testbed, and NSs to assess the feasibility and validity of our approach through experiments.

A Single-Phase Seven-Level Triple Boost Inverter for Grid-Connected Transformerless PV Applications

A new seven-level common ground (CG) switched capacitor (SC)-based grid tied transformerless inverter has been introduced in this paper, which has three times boosting capability of input voltage. Thus, this inverter is preferable for low voltage PV applications without any boost conversion stage. To step-up the input PV voltage and facilitate seven steps in output voltage, two SC cells are connected in parallel. A virtual dc link capacitor serves key role for negative half cycle on behalf of H-Bridge and helping in constructing topology with common ground. The common grounding configuration of this inverter helps in bypassing the stray capacitance, which eliminates the leakage current and consequently reduces EMI considerably. Hence, further no requirement of any electro-magnetic interference (EMI) filter for electro-magnetic compatibility (EMC). Additionally, this inverter handles reactive power during the grid's lagging/leading power factor (pf) condition. To regulate active and reactive grid power, a proportional resonant (PR) current controller is designed. The proposed modulation scheme helps in balancing capacitor's voltages at their base values with allowable ripple. A detailed comparison also has been presented with other contemporary seven level inverters. The inverter circuit details, control technique, PWM scheme, thermal modeling, and loss analysis with component design guidelines are described in detail. Experimental results are presented to validate the effectiveness and feasibility of this proposed inverter.

Slice-Based Service Function Chain Embedding for End-to-End Network Slice Deployment

This paper investigates the slice-based service function chain embedding (SBSFCE) problem, which is to embed the service function chains (SFCs) of flows from different slices on a physical network for end-to-end network slice deployment. Compared with regarding slice deployment as complete virtual network embedding (VNE), deploying slices from the perspective of SBSFCE is beneficial for achieving more delicate resource allocation and jointly optimizing virtual network function (VNF) mapping and link mapping without the need for particular virtual topology designs. However, performing effective SBSFCE also faces several key challenges like diversified and differentiated requirements of flows, inter-slice and intra-slice VNF sharing, priority-aware admission control, and VNF placement restrictions, and few existing SBSFCE works have comprehensively considered or solved these challenges. In view of this, we address the SBSFCE problem by jointly considering the above key challenges in this paper. Specifically, we formulate the SBSFCE problem as an integer linear programming (ILP) that aims to maximize flow acceptance ratios and minimize network resource costs. Then, we propose two novel heuristic algorithms, weight-oriented embedding (WOE) and weight-oriented ratio embedding (WORE), to solve the problem. Simulation results demonstrate that our algorithms outperform benchmark algorithms and achieve near-optimal performance.

Disjoint Paths Construction and Fault-Tolerant Routing in BCube of Data Center Networks

BCube is a promising structure of data center network, as it can significantly improve the performance of typical applications. With the expansion of network scale and increasement of complexity, reliability and stability of networks have become more essential. In this paper, we study the fault-tolerant routings in BCube. Firstly, we design a fault-tolerant routing algorithm based on node disjoint multi-paths. The proposed multi-path routing has stronger fault tolerance, since each path has no other common nodes except the source node and the destination node. Secondly, we investigate an effective fault-tolerant routing based on routing capabilities algorithm for BCube. The proposed algorithm has higher fault tolerance and success rate of finding feasible routes, since it does not limit the faults number. Thirdly, we present an adaptive path finding algorithm for establishing virtual links between any two nodes in BCube, which can shorten the diameter of BCube. Extensive simulation results show that the proposed routing scheme outperforms the existing popular algorithms. Compared with the state-of-the-art fault-tolerant routing algorithms, the proposed algorithm has a 21.5% to 25.3% improvement on both throughput and packet arrival rate. Meanwhile, it reduces the average latency of 18.6% and the maximum latency of 23.7% in networks.

Analyzing the Impact of Blackhole Attacks on AODV and DSR Routing Protocols’ Performance in NS-2

Mobile Ad-Hoc Networks (MANETs) are wireless networks characterized by their lack of a fixed infrastructure, allowing nodes to move freely and serve as both routers and hosts. These nodes establish virtual links and utilize routing protocols such as AODV, DSR, and DSDV to establish connections. However, security is a significant concern, with the Blackhole attack posing a notable threat, wherein a malicious node drops packets instead of forwarding them. To investigate the impact of Blackhole nodes and assess the performance of AODV and DSR protocols, the researchers employed the NS-2.35 ns-allinone2.35 version for simulation purposes. The study focused on several metrics, including average throughput, packet delivery ratio, and residual energy. The findings revealed that AODV demonstrated better energy efficiency and packet delivery compared to DSR, but DSR outperformed AODV in terms of throughput. Additionally, environmental factors and data sizes were taken into account during the analysis.

Conjectures about virtual Legendrian knots and links

We formulate conjectures generalizing some known results to the category of virtual Legendrian knots. This includes statements relating virtual Legendrian knots to ordinary Legendrian knots, non-existence of positive virtual Legendrian self isotopies for the class of the fiber of ST⁎M and the conjectural relation of virtual Legendrian isotopies to causality in generalized spacetimes. We prove the conjectures in the case of 2-dimensional M and (2+1)-dimensional spacetimes. We also formulate and prove the version of the Arnold's 4 cusp conjecture for virtual isotopies.

Double-Agent Reinforced vNFC Deployment in EONs for Cloud-Edge Computing

With an effective service provisioning strategy that relies on Network Function Virtualization (NFV), cloud-edge computing can enhance the Quality of Service (QoS) in Elastic Optical Networks (EONs). NFV emerges as a promising technology to provide flexible services by orchestrating different virtual Network Function Chains (vNFCs). However, the vNFC deployment process is complex and involves two stages, i.e., allocating diverse Virtual Network Functions (VNFs) onto different physical nodes and routing suitable paths for Virtual Links (VLs). How to coordinate the above two stages to deploy vNFCs efficiently in EONs for cloud-edge computing is extremely important. Previous vNFC deployment algorithms are heuristic policies that disregard heterogeneous characteristics in cloud-edge computing. Recently, single-agent Deep Reinforcement Learning (DRL) can provide adaptive allocation schemes by perceptual learning from the environment. Whereas, its performance is not as good as expected since it makes the process of VFNs deployment and VLs deployment independent. Therefore, we propose a Double-Agent Reinforced vNFC Deployment algorithm (DARD) to integrate the VNFs and VLs deployment stages by two cooperative DRL agents. Additionally, we formulate the vNFC deployment problem as a Mixed Integer Linear Programming (MILP) model to achieve optimal solutions. The performance of DARD is evaluated in both static and dynamic scenarios. Simulation results show that DARD can achieve approaching performance with the MILP model. Moreover, it performs better than the other five state-of-art algorithms.

Cost-effective network capacity upgrade by heterogeneous wavelength division multiplexing density with bandwidth-variable virtual direct links

A cost-effective and fast network capacity upgrade with what we believe to be novel bandwidth-variable virtual direct links (BV-VDLs) is proposed. BV-VDLs are designed to pass through the physical links expected to be heavily congested and realize very dense path accommodation. We adopt cut-set analysis to identify the links likely to be heavily congested; however, high computation loads will be incurred in finding all the cut-sets, and justifying these loads is essential. Thus a simple-path-search based graph splitting method is proposed that substantially shortens the calculation time. This strategy allows us to efficiently upgrade network capacity while keeping existing facilities unchanged and can be installed in networks in operation. The proposal is also valid for enhancing the capacity of new networks. The capacity enhancement can reach 13%–33% even in dynamic path operation scenarios on the real topologies of pan-European, North American, and Japanese networks.

Representations of Flat Virtual Braids by Automorphisms of Free Group

Representations of braid group Bn on n≥2 strands by automorphisms of a free group of rank n go back to Artin. In 1991, Kauffman introduced a theory of virtual braids, virtual knots, and links. The virtual braid group VBn on n≥2 strands is an extension of the classical braid group Bn by the symmetric group Sn. In this paper, we consider flat virtual braid groups FVBn on n≥2 strands and construct a family of representations of FVBn by automorphisms of free groups of rank 2n. It has been established that these representations do not preserve the forbidden relations between classical and virtual generators. We investigated some algebraic properties of the constructed representations. In particular, we established conditions of faithfulness in case n=2 and proved that the kernel contains a free group of rank two for n≥3.

The H(n)-move is an unknotting operation for virtual and welded links

An unknotting operation is a local move such that any knot diagram can be transformed into a diagram of the trivial knot by a finite sequence of these operations plus some Reidemeister moves. It is known that for all [Formula: see text] the [Formula: see text]-move is an unknotting operation for classical knots and links. In this paper, we extend the classical unknotting operation [Formula: see text]-move to virtual knots and links. Virtualization and forbidden move are well-known unknotting operations for virtual knots and links. We also show that virtualization and forbidden move can be realized by a finite sequence of generalized Reidemeister moves and [Formula: see text]-moves.

On the swap move of letters in words and the forbidden moves in virtual diagrams

In the theory of topology of words, the move to swap two adjacent letters in words is a simple operator that makes an [Formula: see text]-homotopy class of a nanoword into the [Formula: see text]-homotopy class of the empty word. In this paper, we study the relation between the swap move of letters and the forbidden moves of virtual diagrams, that is, local moves of virtual diagrams which unknot any virtual knot.

Approximately Lossless Model Compression-Based Multilayer Virtual Network Embedding for Edge–Cloud Collaborative Services

Edge-cloud collaboration integrated with network virtualization is indispensable for diversified edge services. Meanwhile, the multilayer elastic optical network (ML-EON) is a promising underlying network for virtual network requests (VNRs) customized for edge-cloud collaborative services. However, the joint allocation of computing resources and high-dimensional ML-EON resources in virtual network embedding (VNE) will pose great computational complexity for online service deployment. In this paper, we propose an approximately lossless model compression mechanism to ease the computing burden of the VNE over ML-EON for edge-cloud collaborative services. An integer quadratic constraint programming (IQCP) model is established for the problem. Model compression based on Virtual Link Mapping Cost Estimation (VLMCE) is investigated to shield the variables and constraints related to ML-EON. In particular, the resource metric and topology metric are introduced into VLMCE to cope with resource contentions among virtual links in the same VNR and improve estimation accuracy. The model solving relies on Hopfield neural network (HNN) is further studied, where optimizing the compressed model is losslessly converted to minimizing the energy function of HNN. The experimental results reveal that the proposed mechanism guarantees an approximately lossless algorithm performance and a high time efficiency compared with the original IQCP model. The performances of VNR cost and blocking ratio are also promoted compared with the benchmarks.

Explore deep reinforcement learning for efficient task processing based on federated optimization in big data

In recent years, along with the extensive application of consumer electronics, the task execution with cloud computing for big data has become one of the research focuses. Nevertheless, the traditional theories and algorithms are still employed by existing research work to explore the feasible solutions, which takes a beating from low generalization performance, system load imbalance, more response delay, etc. To solve the matter, a task execution method called DROP (Deep Reinforcement network aided Optimization method aiming at task Processing) has been put forward, which is capable of completing task request allocation through virtual network embedding. The prominence of this method is explained by its effect in reducing load balancing degree, minimizing bandwidth resource overhead, and preserving electric energy as well as meeting customer demands. It makes use of Deep Deterministic Policy Gradient (DDPG) instead of depending on tons of iterations for better path selection schemes in previous methods, through continuous environment interaction and trial-and-error evaluation to get better strategy selection for virtual link embedding. To realize the virtual node embedding in the federated optimization based system architecture, the intentional deep feature learning network is applied. Compared with the cutting edge approaches, the performance benefits of DROP can be verified by the experimental results in terms of bringing down the extra cost on resources and energy of the substrate network during the task execution for big data.

5G in healthcare: Matching game-empowered intelligent medical network slicing

Improving the healthcare system is imperative for increasing efficiency and reducing costs. The rapid adoption of Internet of Medical Things (IoMT) has facilitated a broad range of healthcare applications and services, from real-time and critical care monitoring to telemedicine. These services typically have highly distinct quality of service (QoS) requirement for communication networks and thus cannot be served with a uniform network. In such a context, network slicing technologies in 5G can be employed to create virtually independent and customized communication networks for these use cases to meet their QoS requirement. In this wok, we model network slicing for healthcare services as a virtual network embedding (VNE) problem and propose a two-sided matching theory-based virtual network embedding (MT-VNE) solution. In MT-VNE, four novel preference indexes are devised to construct differential preference lists. The deferred acceptance and modified shortest path-based algorithms are utilized to perform the virtual node and link mapping, respectively. Extensive simulations demonstrate that MT-VNE outperforms other baselines in terms of accepting more healthcare services and effectively utilizing physical network resources. Moreover, MT-VNE also significantly reduces service embedding time.

Impact of Technology-Evoked Mental Imagery on Brand Personality and Brand Association for Beauty Brands among Women in India

The increased dependence of customers on smart technology for convenience has motivated marketers to turn to new-age technologies for the representation of products and promotion of brands. This study analyses the influence of mental imagery generated by augmented reality on brand personality and brand association for skincare/cosmetics products among women in India. The cross-sectional study collected data through the mall intercept method. The significance of this study is the usage of real brands and gathering real experiences towards mental imagery evoked using virtual try-on links. The originality of the brands and the experience of the respondents could create a realistic relationship between the constructs under study and avoid the researcher’s bias. Path analysis was performed to analyse the statistics and the data fit with the proposed model through IBM AMOS 22.0 software. The findings showcase that elaboration dimension of mental imagery has a significant relationship with brand personality and brand association. However, the quality dimension of mental imagery did not have a significant relationship with brand personality and brand association. The findings contribute to the existing literature on branding and information processing and provide significant insights for marketers when adopting augmented reality to create brand-evoked mental imagery among customers.

Virtual multicrossings and petal diagrams for virtual knots and links

Multicrossings, which have previously been defined for classical knots and links, are extended to virtual knots and links. In particular, petal diagrams are shown to exist for all virtual knots.