Virtual Links Research Articles

Model-Based Anticancer Effect of Botulinum Neurotoxin Type A1 on Syngeneic Melanoma Mice

In recent, Botulinum Neurotoxin A1 (BoNT/A1) has been suggested as a potential anticancer agent due to neuronal innervation in tumor cells. Although potential BoNT/A1’s mechanism of action for the tumor suppression has been gradually revealed so far, there were no reports to figure out the exposure-response relationships because of the difficulty of its quantitation in the biological matrix. The main objectives of this study were to measure the anticancer effect of BoNT/A1 using a syngeneic mouse model transplanted with melanoma cells (B16-F10) and developed a kinetic-pharmacodynamic (K-PD) model for quantitative exposure-response evaluation. To overcome the lack of exposure information, the K-PD model was implemented by the virtual pharmacokinetic compartment link to the pharmacodynamic compartment of Simeoni’s tumor growth inhibition model and evaluated using curve-fitting for the tumor growth-time profile after intratumoral injection of BoNT/A1. The final K-PD model was adequately explained for a pattern of tumor growth depending on represented exposure parameters and simulation studies were conducted to determine the optimal dose under various scenarios considering dose strength and frequency. The optimal dose range and regimen of ≥13.8 units kg−1 once a week or once every 3 days was predicted using the final model in B16-F10 syngeneic model and it was demonstrated with an extra in-vivo experiment. In conclusion, the K-PD model of BoNT/A1 was well developed to optimize the dosing regimen for evaluation of anticancer effect and this approach could be expandable to figure out quantitative interpretation of BoNT/A1’s efficacy in various xenograft and/or syngeneic models.

Load-Balancing Method for LEO Satellite Edge-Computing Networks Based on the Maximum Flow of Virtual Links

With the increasing number of satellites in orbit, traditional scheduling methods can no longer satisfy the increasing data demands of users. The timeliness of remote sensing images with large data volumes is poor in the backhaul process through low-earth-orbit (LEO) satellite networks. To address the above problems, we propose an edge-computing load-balancing method for LEO satellite networks based on the maximum flow of virtual links. First, the minimum rectangle composed of computing nodes is determined by the source and destination nodes of the transmission task under the configuration of the 2D-Torus topology of LEO satellite networks. Second, edge computing virtual links are established between computing nodes and users. Third, the Ford-Fulkerson algorithm is used to obtain the maximum flow of the topology with virtual links. Finally, a strategy is generated for computing and transmission resource allocation. The simulation results show that the proposed method can optimize the total capacity of the multi-node information backhaul in the remote sensing scenario of LEO satellite networks. The effectiveness of the proposed algorithm is verified in several special scenarios.

Mapping the VNFs and VLs of a RAN Slice Onto Intelligent PoPs in Beyond 5G Mobile Networks

The mapping of a virtual network service onto a physical network infrastructure is a challenging task due to the joint allocation of virtual resources across nodes and links, the diverse technical requirements of end-users, the coordination between multiple host domains, and others. This issue is exacerbated further by the extension of virtualization to the next-generation radio access network (NG-RAN) architecture and the provisioning of radio access network (RAN) slicing. To that end, this article focuses on the mapping problem of the virtual network functions (VNFs), as well as their internal and external virtual links (VLs), of a RAN slice subnet onto intelligent points of presence (I-PoPs) and transport networks in the NG-RAN architecture. In this context, in contrast to the majority of the state-of-the-art proposals, which frequently fail to achieve performance objectives and neglect resource allocation constraints, this article introduces automation and intelligence at an architectural level to map VNFs and VLs onto their corresponding physical nodes and links, with the goal of achieving superior efficiency in virtual resource utilization while granting the performance of a RAN slice subnet. Benefiting from a top-down approach, the key contributions of this article are: <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(i)</i> to extend the architectural framework of network slicing towards the NG-RAN architecture and provide a comprehensive overview and critical analysis of the components and functionalities of a RAN slice subnet; <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(ii)</i> to integrate the Experiential Network Intelligence (ENI) framework into a joint architecture of the network functions virtualization–management and orchestration (NFV–MANO), Third Generation Partnership Project-network slicing management system (3GPP-NSMS), and I-PoPs in order to render automation and intelligence to the management and orchestration aspects of a RAN slice subnet in the NG-RAN architecture; and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(iii)</i> to propose a learning-assisted architectural solution for mapping the VNFs, as well as their internal and external VLs, of a RAN slice subnet onto the underlying I-PoPs and transport networks.

Turaev hyperbolicity of classical and virtual knots

By work of W. Thurston, knots and links in the 3-sphere are known to either be torus links, or to contain an essential torus in their complement, or to be hyperbolic, in which case a unique hyperbolic volume can be calculated for their complement. We employ a construction of Turaev to associate a family of hyperbolic 3-manifolds of finite volume to any classical or virtual link, even if non-hyperbolic. These are in turn used to define the Turaev volume of a link, which is the minimal volume among all the hyperbolic 3-manifolds associated via this Turaev construction. In the case of a classical link, we can also define the classical Turaev volume, which is the minimal volume among all the hyperbolic 3-manifolds associated via this Turaev construction for the classical projections only. We then investigate these new invariants.

Recurrent Generalization of F-Polynomials for Virtual Knots and Links

F-polynomials for virtual knots were defined by Kaur, Prabhakar and Vesnin in 2018 using flat virtual knot invariants. These polynomials naturally generalize Kauffman’s affine index polynomial and use smoothing in the classical crossing of a virtual knot diagram. In this paper, we introduce weight functions for ordered orientable virtual and flat virtual links. A flat virtual link is an equivalence class of virtual links with respect to a local symmetry changing a type of classical crossing in a diagram. By considering three types of smoothing in classical crossings of a virtual link diagram and suitable weight functions, there is provided a recurrent construction for new invariants. It is demonstrated by explicit examples that newly defined polynomial invariants are stronger than F-polynomials.

Virtual optical network embedding of time-varying traffic in elastic optical networks

Network virtualization can enhance the flexibility of Internet infrastructure resources and the scalability of the substrate elastic optical networks (EONs) through the coexistence of multiple virtual optical networks supporting different services. Traditional virtual optical network embedding mostly assumed fixed embedding, that is, once a virtual optical network (VON) is embedded, the network resources allocated to it are almost unchanged during its lifetime. However, the actual traffic demand on a VON usually changes over time. To address the problems of high bandwidth blocking probability and low spectrum utilization caused by the mismatch between the resources allocated and the required resources during the virtual optical network embedding of the time-varying traffic in the elastic optical networks (EONs), we propose a virtual optical network embedding algorithm of the time-varying traffic (TVT-VONE). Firstly, in the node embedding stage, a node weight value measurement is designed based on the attributes of virtual nodes and physical nodes. Secondly, in the virtual optical link embedding stage, a measurement formula for path spectrum resource richness is designed to decrease link embedding failure due to insufficient spectrum resources on the path. Finally, in order to adapt to the characteristics of dynamic changes in bandwidth requirements of time-varying traffic, we design a resource-aware virtual network reconfiguration strategy when the spectrum resources of traffic required do not match the resources allocated to the changed traffic. Simulation results show that the proposed algorithm can effectively reduce the bandwidth blocking probability of VON requests and improve spectrum utilization of EONs.

Virtually symmetric representations and marked Gauss diagrams

In this paper, we define the notion of a virtually symmetric representation of representations of virtual braid groups and prove that many known representations are equivalent to virtually symmetric. Using one such representation, we define the notion of virtual link groups which is an extension of virtual link groups defined by Kauffman. Moreover, we introduce the concept of marked Gauss diagrams as a generalisation of Gauss diagrams and their interpretation in terms of knot-like diagrams. We extend the definition of virtual link groups to marked Gauss diagrams and define their peripheral structure. We define Cm-groups and prove that every group presented by a 1-irreducible C1-presentation of deficiency 1 or 2 can be realised as the group of a marked Gauss diagram.

A Virtual Clinic for DDH Pavlik Harness Monitoring.

Pavlik harness (PH) treatment is successful in treating over 90% of newborns with developmental dysplasia of the hip (DDH). There is a need for close supervision, frequent adjustments, size changes, and monitoring of complications. This paper aims to provide a safe criterion for remote follow-up of DDH patients treated in a PH to reduce the risk of COVID-19 (coronavirus disease 2019) exposure to patients, parents, and health practitioners. All infants with stable hips (Graf I, IIa/b/c/d, treated III/IV) with consenting parents after appropriate counseling were enrolled in a virtual clinic. Clinics were conducted using the NHS "Attend anywhere" virtual link service by an extended scope practitioner-specialist physiotherapist and a clinical nurse specialist. The virtual clinic group was compared with a matched cohort of patients from 2018/2019. A total of 141 patients were referred to the neonatal hip clinic; 45 patients were eligible for harness treatment and 20 patients were selected for virtual clinics. In total, there were 35 virtual clinic appointments. Each of the patients had an average of 1.7 virtual appointments ranging from 1 to 3 (26.3% of total number of clinics). Age at presentation of the treated group was 7±4.2 weeks and control group 5.7±5.5 weeks (P=0.59). PH duration of the study group was 9±2.6 weeks and the control group, 7.8±2.5 weeks (P=0.12). There were no missed complications at the follow-up face-to-face appointment. Patients saved an average of 76 km total travel distance. This study demonstrates adequate evidence that children requiring routine follow-up appointments involving PH adjustment, skincare, and identification of clinical anomalies, can be treated and followed up safely using virtual clinics. Clinical triage of suitable patients for virtual clinic provision must always be made by experienced clinicians. Children presenting with Graf IIa, IIb, IIc, IId, as well as those with stable and improving Graf III at initial diagnoses, had successful treatment with virtual clinic follow-up appointments in this study. Level IV.

Cognitive Control-Loop for Elastic Optical Networks with Space-Division Multiplexing

This paper introduces a new solution to improve network performance by decreasing spectrum fragmentation, crosstalk interference, blocking of virtual networks, cost, and link load imbalance. These problems degrade the performance of Elastic Optical Networks with Space-Division Multiplexing. The proposed solution, called Cognitive control loop (CO-OP), is capable of identifying a set of problems and creating plans to mitigate these problems. The CO-OP comprises four functions that employ learning algorithms to identify problems and plan a series of actions to reduce or eliminate them. The results show that the CO-OP can effectively decrease up to 30% the blocking of requests and up to 50% the crosstalk occurrence compared to existing algorithms.

Error Uncertainty Analysis in Planar Closed-Loop Structure with Joint Clearances

For planar closed-loop structures with clearances, the angular and positional error uncertainties are studied. By using the vector translation method and geometric method, the boundaries of the errors are analyzed. The joint clearance is considered as being distributed uniformly in a circle area. A virtual link projection method is proposed to deal with the clearance affected length error probability density function (PDF) for open-loop links. The error relationship between open loop and closed loop is established. The open-loop length PDF and the closed-loop angular error PDF both approach being Gaussian distribution if there are many clearances. The angular propagation error of multi-loop structures is also investigated by using convolution. The positional errors of single and multiple loops are both discussed as joint distribution functions. Monte Carlo simulations are conducted to verify the proposed methods.

Joint Virtual Network Topology Design and Embedding for Cybertwin-Enabled 6G Core Networks

To efficiently allocate heterogeneous resources for customized services, in this article, we propose a network virtualization (NV)-based network architecture in cybertwin-enabled 6G core networks. In particular, we investigate how to optimize the virtual network (VN) topology (which consists of several virtual nodes and a set of intermediate virtual links) and determine the resultant VN embedding in a joint way over a cybertwin-enabled substrate network. To this end, we formulate an optimization problem whose objective is to minimize the embedding cost, while ensuring that the end-to-end (E2E) packet delay requirements are satisfied. The queueing network theory is utilized to evaluate each service’s E2E packet delay, which is a function of the resources assigned to the virtual nodes and virtual links for the embedded VN. We reveal that the problem under consideration is formally a mixed-integer nonlinear program (MINLP) and propose an improved brute-force search algorithm to find its optimal solutions. To enhance the algorithm’s scalability and reduce the computational complexity, we further propose an adaptively weighted heuristic algorithm to obtain near-optimal solutions to the problem for large-scale networks. Simulations are conducted to show that the proposed algorithms can effectively improve network performance compared to other benchmark algorithms.

Diagrammatic strong coupling expansion of a U(1) lattice model in the Fourier basis

The transfer-matrix of the U(1) lattice gauge theory is investigated in the field Fourier space, the basis of which consists of the quantized currents on lattice links. Based on a lattice version of the current conservation, the transfer-matrix elements are shown to be nonzero only between current states that differ in circulating currents inside plaquettes. In the strong coupling limit, a series expansion is developed for the elements of the transfer matrix, to which a diagrammatic representation based on the occurrence of virtual link and loop currents can be associated. With $g$ as the coupling, the weight of each virtual current in the expansion is $1/{g}^{2}$, by which at any given order the relevant diagrams are determined. Either by interpretation or through their role in fixing the relevant terms, the diagrams are reminiscent of the Feynman ones of the perturbative small coupling expansions.

Modelling the Admission Ratio in NFV-Based Converged Optical-Wireless 5G Networks

Network Function Virtualization (NFV)-based 5G networks deliver specific services to a end-users through the creation of Service Function Chains (SFCs), which are composed of a number of Virtualized Network Functions (VNFs) interconnected via a set of virtual links (vLinks). VNFs consume computational resources of the network's servers, while vLinks utilize the communicational resources of the network. The efficient utilization of network resources remains a challenge in NFV-based networks. To this end, in this paper, we propose an analytical framework for the Admission Ratio (AR) calculation in NFV-based converged optical-wireless 5G networks. The proposed methodology employs a network slicing architecture in which different network slices form end-to-end logically isolated networks and each slice delivers a specific service type to the users through its SFC(s). In the proposed analysis, we not only take into account the occupancy distribution in both the network's computational and communicational domains (servers and fiber links), but we also consider the SFC establishment AR by taking into account different sub-service-classes belonging to different slices. The accuracy of the model is evaluated through the comparison of analytical and simulation results and was found satisfactory. Furthermore, the proposed model is employed for the determination of the optimal (minimum) capacity for all SFCs elements (VNFs and vLinks), in a way that users belonging to a specific slice experience a predefined value of AR as minimum. Additionally, our calculations deploy recursive formulas, which have a low computational complexity, as opposed to time-consuming simulations, without requiring the application of complex optimization algorithms.

Parity, virtual closure and minimality of knotoids

In this paper, we study parity in planar and spherical knotoids in relation to virtual knots. We introduce a planar version of the parity bracket polynomial for planar knotoids. We show that the virtual closure map (a map from the set of knotoids in [Formula: see text] to the set of virtual knots of genus at most one) is not surjective, by utilizing the surface bracket polynomial of virtual knots. We give specific examples of virtual knots that are not in the image of the virtual closure map. Turaev conjectured that minimal diagrams of knot-type knotoids have zero height. We prove this conjecture by using the results of Nikonov and Manturov induced by parities of virtual knots.

An unknotting invariant for welded knots

We study a local twist move on welded knots that is an analog of the virtualization move on virtual knots. Since this move is an unknotting operation we define an invariant, unknotting twist number, for welded knots. We relate the unknotting twist number with warping degree and welded unknotting number, and establish a lower bound on the twist number using Alexander quandle coloring. We also study the Gordian distance between welded knots by twist move and define the corresponding Gordian complex.

Inclusion of Narrow Flow Paths between Buildings in Coarser Grids for Urban Flood Modeling: Virtual Surface Links

Urban flood modeling benefits from new remote sensing technologies, which provide high-resolution data and allow the consideration of small-scale urban key features. Since high-resolution data often result in large simulation runtimes, coarsening of the 2D grid via resampling techniques can be used to achieve a good balance between accuracy and computation time. However, the representation of urban features and topographical properties degrades, since small-scale features are blurred. Therefore, narrow flow paths between buildings are often not considered, building’s sizes are overestimated, and their arrangement in the grid changes. Thus, flow paths change and waterways are blocked, leading to incorrect inundations around buildings. This paper develops a method to improve the simulation results of coarser grids by adding virtual surface links (VSL) between buildings. The VSL mimic the flow paths of a high-resolution model in the areas of interest. The approach is developed for dual-drainage 1D/2D models. The approach shows a visible improvement at the localized level where the VSL are applied, in terms of under/overestimating flooding and a moderate overall improvement of the simulation results. Relatively to the model resolution of 2 m, the computational time, by applying this method, is reduced by 93.6% when using a 5 m grid and by 99% when using a 10 m grid. For a small test case, where the local effects are investigated, the error in the maximum water volume, relative to a grid size of 2 m, is reduced from 69.63% to 5.03% by using a 5 m grid and from 152.75% to 22.92% for a 10 m grid.

Connected sum of virtual knots and F-polynomials

It is known that connected sum of two virtual knots is not uniquely determined and depends on knot diagrams and choosing the points to be connected. But different connected sums of the same virtual knots cannot be distinguished by Kauffman’s affine index polynomial. For any pair of virtual knots [Formula: see text] and [Formula: see text] with [Formula: see text]-dwrithe [Formula: see text] we construct an infinite family of different connected sums of [Formula: see text] and [Formula: see text] which can be distinguished by [Formula: see text]-polynomials.

Analysis of AFDX Network Delay Based on NS2

AFDX network simulation is of great significance for evaluating and determining whether AFDX can meet the real-time requirements of avionics networks. Compared with theoretical analysis methods such as network calculus, network simulation can better understand the true behavior of the AFDX network. In this paper, we build an AFDX network simulator based on NS2, where AFDX switches, end systems and virtual links are properly modeled. Using this simulator, the end-to-end delay of an AFDX network under different scheduling strategies is studied. Some key performance measures of the system are also analyzed.

Comparison of D-Vine and R-Vine Techniques for Virtual Network Embedding Problem

In Network virtualization, Virtual Network Embedding(VNE) is the process of mapping virtual nodes and links of a virtual network request(VNR) on a substrate network to fulfill the demands of the request. Embedding virtual network requests helps in achieving network virtualization efficiently. This paper presents Vineyard, a set of VN embedding algorithms namely D-Vine and R-Vine, to introduce a finer correlation between the node mapping and link mapping phases. Deterministic Virtual Network Embedding(D-Vine) algorithm is used to embed virtual nodes on to substrate network based on the capacity constraint when it is not satisfied the system takes the Randomised Virtual Network Embedding(R-Vine) algorithm to map the nodes based on location constraint. Subsequently, after the nodes are embedded the link mapping phase is done based on the distance constraint. A window-based virtual embedding algorithm(W-Vine) is also introduced to evaluate the effect of lookahead in Virtual Network Embedding. After the mapping of multiple virtual network requests, analysis is done to compare the node and CPU utilization in both the algorithms and the variations are conserved.

A Dynamic Adjustment Method of Service Function Chain Resource Configuration

In the network function virtualization environment, dynamic changes in network traffic will lead to the dynamic changes of service function chain resource demand, which entails timely dynamic adjustment of service function chain resource configuration. At present, most researches solve this problem through virtual network function migration and link rerouting, and there exist some problems such as long service interruption time, excessive network operation cost and high penalty. This paper proposes a dynamic adjustment method of service function chain resource configuration for the dynamic changes of network traffic. First, a dynamic adjustment request of service function chain is generated according to the prediction of network traffic. Second, a dynamic adjustment strategy of service function chain resource configuration is determined according to substrate network resources. Finally, the resource configuration of a service function chain is pre-adjusted according to the dynamic adjustment strategy. Virtual network functions combination and virtual machine reusing are fully considered in this process. The experimental results show that this method can reduce the influence of service function chain resource configuration dynamic adjustment on quality of service, reduce network operation cost and improve the revenue of service providers.