Along with the adoption of 5G, the development of neutral host solutions provides a unique opportunity for mobile networks operators to accommodate the needs of emerging use-cases and in the consolidation of new business models. By exploiting the concept of network slicing, as one key enabler in the transition to 5G, infrastructure and service providers can logically split a shared physical network into multiple isolated and customized networks to flexibly address the specific demands of those tenant slices. Motivated by this reality, the H2020 5GCity project proposed a novel 5G-enabled neutral host framework for three European cities: Barcelona (ESP), Bristol (UK), and Lucca (IT). This article revises the main achievements and contributions of the 5GCity project, focusing on the deployment and validation of the proposed framework. The developed neutral host framework encompasses two main parts: the infrastructure and the software platform. A detailed description of the framework implementation, in terms of functional capabilities and practical implications of city-wide deployments, is provided in this article. This work also presents the performance evaluation of the proposed solution during the implementation of real vertical use cases. Obtained results validate the feasibility of the neutral host model and the proposed framework to be deployed in city-wide 5G infrastructures. In the apogee of a new digital era, communication technologies and businesses evolved towards 11 billion interconnected devices worldwide, triggering a rapid adoption of online and mobile digital services . This reThe 5G architecture combines emerging Radio Access Network (RAN) technologies with advances in Software-Defined Networks (SDN) and Network Function Virtualization (NFV) . Such enEnabled by the introduction of network slicing in 5G , the neuSeveral private and public initiatives are supporting research and innovation projects to deal with challenges for 5G technology realization (5G Public Private Partnership (5G PPP) in Europe  and the In this article, we refer to the term 5G-enabled neutral host framework to define a system capable of dynamically managing and orchestrating a virtualized network infrastructure to allocate 5G services with disparate requirements for multiple relevant stakeholders. The 5G-enabled neutral host framework provides multitenancy to a city-wide deployment by realizing and combining enhancements of 5G enabling technologies required by the neutral host model. This article revises the main achievements and contributions of the 5GCity project, focusing on the deployment and validation of the proposed 5G-enabled neutral host framework in the three aforementioned cities. The developed neutral host framework consists of a software platform for slicing and orchestrating computing and network resources from a 5G-enabled cloud, edge, and radio infrastructure. A detailed description of the framework implementation, in terms of functional capabilities and practical implications in city-wide deployments, is described in this work. In addition, this paper presents the validation of the proposed neutral host framework in city-wide deployments and provides the obtained results of measuring several Key Performance Indicators (KPIs) with real smart-city and media use cases.The remainder of this article is organized as follows. The 5G technology is increasing network convergence, flexibility, and mobile broadband capacity in response to the growth in number and diversity of consumers, industries, and service demands in society ,12. HoweAn increasing need for enhanced and ubiquitous connectivity in urban context coupled with more demanding requirements of radio coverage and bandwidth.The pivotal role within 5G of smart cities, in which municipalities may act as potential 5G neutral host providers.A neutral host framework is a perfect candidate to fully satisfy the 5G requirements for different use cases  concurrently deployed over a shared infrastructure.A neutral and sliceable 5G infrastructure is a promising solution for network infrastructure sharing challenges ,15. FromThe neutral host model has an important business dimension focused on the creation of new Service Level Agreements (SLAs) categories to rule the interactions between the host and content/service providers ,17. A keIndeed, a neutral host framework provides automated or dynamic multi-tenancy by combining a wide range of well-known technical enablers via end-to-end network slicing. While network slicing is not new in the academia and industry community, the 5G technology and the neutral host model are revitalizing the interest from the community by extending it to the next level .The Next Generation Mobile Networks (NGMN)  redefineOverall, end-to-end network slicing in 5G requires an NFV Management and Orchestration (MANO) solution to deploy Virtual Network Functions (VNFs) on cloud/edge resources and a virtualized RAN solution to slice and control the radio resources .A Multi-Access Edge Computing (MEC) network architecture uses edge resources to enable cloud computing capabilities and IT service environments at the edge of the cellular network . As a reThe neutral host model leverages multiple MEC deployments to fully cope with 5G requirements in terms of bandwidth, coverage, and latency. Indeed, distributed edge resources allow neutral host frameworks to deploy end-to-end services across distributed pools of edge resources, enforcing ultra-low latency and high bandwidth, while real-time access to radio network information can be leveraged by applications.A MEC architecture poses some real challenges for the design of end-to-end services, mainly since the resources locally offered can be limited, thus highlighting the need for tightly centralized orchestration, which can dynamically operate the life-cycle of edge computing applications ,24.End-to-end network slicing, over the distributed cloud and edge resources for enhanced computing and processing capabilities, requires extensions or a new NFV MANO framework to support multitier orchestration, covering also different edges . As such, multitier orchestration in network slicing is getting attention from industry and academia .Among well-known NFV MANO solutions only Open Source MANO (OSM) , an ETSIThe Cloud Radio Access Network (C-RAN) concept  defines Targeted for 5G framework and strictly coupled with edge architectures, the virtualized RAN (vRAN) approach empowers the neutral host scenario with the capability of sharing the radio access part, by slicing its resources in multiple tenants, each one operated by a different Mobile Virtual Network Operator (MVNO). Moreover, given the high flexibility of the neutral host framework, different sharing and architecture models  and Multioperator Core Network (MOCN)) can be realized, thus providing a wide range of deployment solutions.For neutral host and 5G deployments, network slicing between Multiradio Access Technologies (Multi-RAT) will be essential. Hence, efforts from industry and academia are focusing on the integration of Long Term Evolution (LTE) and 5G New Radio (5GNR) technologies with various slicing approaches   does with computing resources). A recently proposed SODALITE framework integrates back-haul traffic from Wi-Fi and 4G/5G in dense small cell networks . Then, tSome other relevant 5GPPP projects that also deal with expanding network slicing functionalities are 5G SESAME , 5G ESSEIn addition to the complexity associated with the integration and demonstration of all the technologies mentioned above, implementing a neutral host solution becomes even more challenging when considering real-world city scenarios. In this regard, the infrastructure planning and deployment phases play a fundamental role in achieving the potential added values of the system in operational conditions. While the feasibility of city-driven neutral host deployments was acknowledged from the study of business model perspective in previous works ,44,45, tIn short, the 5G-enabled neutral host framework allows tenants to create and consume slices using a set of virtualized resources over a common infrastructure. The conceived framework, presented in Software Development Kit (SDK) for network functions developers and service providers to combine new and pre-existing functions for new service deployments. Likewise, a 5G Service & Apps Catalogue is also provided to store network services previously created and published. This component is also responsible for the onboarding of functions and services into the NFVO.In the Application layer, a set of tools oriented to facilitate service design and composition is available for service providers, tenants, and any related third party. In particular, the innovative nature of the neutral host framework is further enhanced at the service layer with a Dashboard with a Graphical User Interface (GUI) and a component for Authentication, Authorization, and Accounting (AAA) are placed at the northbound side, to facilitate the interaction between infrastructure owners and tenants and to enforce the required security and billing. Network slices of different tenants are properly separated for security reasons, and the full isolation of information and data is preserved.The Orchestration & Control layer is the logical core of our neutral host framework  composedSlice Manager has a central role in the platform, especially in the provision of the required logic for dynamic creation and management of slices. Each slice is defined as a collection of logical network partitions or chunks, combined with the network services deployed on top of them [Slice Manager performs several automated tasks seamlessly, to:Activate deployed slices by launching required servers , together with the corresponding configuration of radio access chunks.Monitoring component), and DNS deployments.Perform required postinstantiation configurations to deploy VNFs, in terms of enabling external connectivity, registering tasks and alerts for monitoring purposes , such aThe  of them . Apart fResource Placement component is also provided. In essence, this component determines the most suitable VNF-to-compute-chunk mapping by taking into consideration the service requirements and the resources usage.To compute the optimal allocation of VNFs to be deployed over a given slice, a Multitier Orchestrator component [The orchestration capabilities of the presented platform are extended to support NFV/MEC integration following the ETSI MEC specification  by complomponent  is incluSDN-based RAN controllers are placed beneath the aforementioned components to manage the radio components and enforce many of the required actions. To support multiple underlying RAN controllers and technologies, the Infrastructure Abstraction module is located as an intermediate component between the Slice Manager and the underlying SDN controllers.Additionally, this platform also enables virtual RAN slicing and RAN function virtualization for 5GNR, LTE, and Wi-Fi. To do so, The Infrastructure layer contains the resources in terms of computing, network, and radio components managed by the neutral host. This layer is graphically divided into several Network Functions Virtualization Infrastructure (NFVI) sections and access nodes to identify the distributed compute and radio architecture conceived for municipalities and infrastructure owners acting as 5G neutral host providers. Moreover, this framework is also aligned with 5G performance requirements by providing edge computing capabilities. This will result in real-time access to radio network information, thereby unlocking the potential of advanced future applications.Following the architecture presented in (i)Infrastructure Deployment: the conceived three-tier architecture, including a RAN tier, an edge tier, which can be further extended to be closer to end-users, and a core Data Center (DC) tier, is mapped into physical infrastructure resources consisting of radio components, edge/MEC servers, and DC servers;(ii)Infrastructure Setup Validation: to verify the correct installation and performance of the deployed infrastructure in the three cities, a similar set of validation tests was conducted. The main objective of these tests was to verify performance and better profile configurations in the three pilot environments;(iii)Platform Installation: deployed servers at edge and DC sites in every city provide computing resources to host the different components of the software platform of the neutral host framework. In general, each software module of the platform is installed as a Virtual Machine (VM) in the virtualized computing infrastructure and interconnected to allow the required interaction among them;(iv)Platform Setup Validation: the validation of the deployed platform consisted of a set of functional tests aimed at verifying the correct integration of the various orchestration elements, as well as the execution of lifecycle management operations for infrastructure resources, slices, and network services.The general methodology followed for deploying the proposed neutral host framework consisted of the following sequential phases in every city pilot:Next, we first detail the infrastructure components deployed per testbed. Then, we describe the platform implementation, which is a common factor for the three city pilots.OMEGA-DC at i2CAT Foundation; (ii) the edge computing nodes and on-street RAN deployed in the super square 22@ area (Glòries); (iii) an additional RAN deployed within the city hall (Plaza Sant Miquel), located in the Barrio Gòtico district. This third location added value to the media use cases by providing connectivity in the most central and lively area of the city with the potential to cover major public events. The resulting physical deployment of the neutral host infrastructure interconnecting the three city areas of Barcelona is presented in The neutral host infrastructure deployed in Barcelona comprises three city areas: (i) the core node hosted in OMEGA-DC at i2CAT. This DC hosts two compute servers providing the core NFVI. The fiber infrastructure connects this location to the on-street components deployed in the 22@ area and the city hall using L2/L3 network devices. To add resilience, two end-to-end fiber connections of 10 Gbps were deployed. Each fiber provides end-to-end redundancy in case of interruptions.The core DC in Barcelona infrastructure is deployed in the 22@ area. The primary location is in BeTeVé premises, hosting two edge servers, which act as edge NFVI. The second edge/MEC node is deployed in a street cabinet at the crossing of the Llacuna and Pere IV streets, where an edge server provides the extended edge NFVI. These two edge locations are equipped with dedicated L2/L3 routers (Cisco ASR920) to connect the edge computing nodes with the core DC located at i2CAT. Likewise, as shown in 22@ area and the city hall using a dedicated fiber.The edge/MEC nodes in Barcelona are installed in two locations within the 22@ area is mounted on six lampposts with their own energy supply and 1 Gbps fiber connection. Three of them are equipped with LTE small cells (Accelleran E1010), whereas the other three lampposts are equipped with Wi-Fi nodes (i2CAT custom hardware). The RAN equipment in the city hall consists of two LTE small cells installed next to the Salo de Cent room covering city council meetings and public events. The small cells deployed in Barcelona use Band 42 and follow the TDD config mode 2 on 20 MHz, providing a maximum of 90 Mbps Down-Link (DL) and 10 Mbps Up-Link (UL).The RAN equipment in the MShed Museum. This new location enables a wider experimentation area covering the harbour part on the other side of the Avon river. The overall connectivity and main infrastructure locations of the Bristol pilot deployment are depicted in The neutral host infrastructure deployed in Bristol extends the 5GUK test network  by impleWe-The-Curious (WTC-DC) and MShed Museum (M-DC).The core DC of Bristol infrastructure is deployed at the University of Bristol High-Performance Network Group Data Centre (HPN-DC). More in detail, this DC hosts two compute servers configured as core NFVI, which are interconnected via fiber to the other two pilot locations in We-The-Curious (WTC-DC) and the MShed Museum (M-DC). In both locations, standard rack servers and edge-format servers are installed, which are configured to act as edge NFVI. Both locations are interconnected with the core DC and corresponding RAN devices.In Bristol, the edge/MEC nodes are deployed in two locations: the Millennium Square are used, each one equipped with a dedicated Wi-Fi node (Ruckus T710) to provide coverage to the square and the close surrounding areas, down to the harbourside area. Additionally, the MShed Museum location hosts two small cells (Accelleran E1000 series) and three Wi-Fi nodes (Ruckus T710) at East Roof, Middle Roof, and West Roof, respectively. The location of each node can be corroborated in For the RAN in Bristol, a total of four towers in the The deployment of the neutral host infrastructure in Lucca was conceived to take into account the very specific historical characteristics of the city  and the most appropriate target areas for demonstrations and validations of the use cases planned for Lucca. For this reason, the infrastructure deployment in Lucca has privileged green areas and squares close to the historical wall with pathways, since public events typically occur there. An overview of the physical deployment of the neutral host infrastructure in the Lucca pilot is presented in Villa San Paolino (VSP-DC) hosting three compute servers, one for orchestration and interconnection services (VPN concentrator), whereas the two others act as core NFVI to host the workload from the various use cases. The three servers are interconnected with the edge cabinet and an outdoor CCTV IP camera (required for one of the use cases deployed in this city pilot) via a fiber network. One of the compute servers includes a GPU for video analytic.The core DC in Lucca is deployed in Villa della Cavallerizza is hosted in a street cabinet, which is connected via a fiber link to the core DC in VSP-DC. One compute node is installed in the cabinet, which is used as edge NFVI. In the same cabinet, one L2 switching device interconnects the edge server with the small cell in Sortita San Paolino and the core DC.The edge/MEC node deployed at Villa San Paolino and Sortita San Paolino). In this case, the deployed small cells use Band 38 and are configured to follow the TDD config mode 1 on 15 MHz, providing a maximum of 55 Mbps DL and 13 Mbps UL.In Lucca, the RAN infrastructure is composed of two small cells (Accelleran E1013), which are deployed in two different locations around the city . This cloud platform is currently the most widely deployed open-source cloud infrastructure software in the industry.Additionally, to support the deployment of NSs based on containers, we also installed Fog05  as the eTo orchestrate the lifecycle of NSs within the 5G-enabled slices, we deployed OSM as the NFVO of the platform.Finally, as part of the vRAN capabilities offered by the neutral host framework, we also deployed the dRAX Open Interface RAN Intelligence  solutionBelow, we provide a brief description of the main technologies that enable the deployment of the neutral host platform:The rest of the components that integrate the neutral host platform , slices , and services .Given the importance of ensuring the proper deployment and functionality of the conceived platform, multiple validation tests were executed. In general, tests were designed taking into account the components involved, the defined interactions, as well as the expected results. Therefore, two groups of tests were conducted:The deployment of use cases over the proposed neutral host framework follows a common workflow. In general, tenants access and interact with the framework via the platform Dashboard. The following subsections describe the operations performed by tenants using the platform to deploy different vertical use cases, as described in . For illThe platform administrator acting as neutral host provider creates a dedicated repository and user account for the media vertical tenant. The referred user is granted the role of Designer, which allows tenants to design functions as well as compose them into services.In turn, the media vertical tenant, using the platform SDK, conducts the creation of the required functions and composes an NS for the application.Once the service creation is completed, the resulting function and service descriptors are published into the 5G Apps & Services Catalogue of the platform.At first, users create the virtualized functions and services to be instantiated, through the following steps:Next, a customized and dedicated slice is created. In particular, each slice is conceived as a collection of compute, network and radio chunks, as logical and isolated partitions over the common infrastructure. To perform this step, the media vertical tenant composes an end-to-end slice by selecting the desired compute, network and radio infrastructure resources and specifying the requirements to be allocated into the slice. The slice creation request is then processed by the Slice Manager, which interacts with other platform components  to create the required chunks at each network segment.Following the slice creation, the next step is its activation. Essentially, as the considered media vertical use case requires cellular access for the final users to consume the media application via smartphones attached to the slice, the activation step consists of the instantiation of an open-source mobile core server  togetherOnce the function and services descriptors, as well as the slice, are available, the last step is the instantiation of the virtualized service over the given slice. In this step, the application is deployed in the form of VMs or containers. More in detail, the virtualized functions are placed over the compute chunk of the slice and connected to the network chunk, providing end-to-end connectivity with the access chunk of the slice. The successful instantiation of the network services related to the considered media vertical over the neutral host framework are reported by the platform Dashboard and can be also corroborated by checking underlying systems (such as OSM and OpenStack).Additionally, to complement the programmability principles of the proposed framework, a DNS server is automatically deployed by the platform to support the service operation in terms of IP addresses and domain names resolution.In this section, we focus our attention on the performance validation of the proposed neutral host framework. In particular, several slices are created to demonstrate the multi-tenancy as an intrinsic feature of the neutral host model.The conducted experimental trials enable the measurement of relevant KPIs, which reflect the service requirements and contribute to validating the benefits of the proposed framework. The definition and measurement methodology are described next for each one of the considered KPIs.The minimum data rate required to ensure a sufficient quality experience (without considering broadcast services) . In thisThe time required to transfer a given piece of information between two nodes, measured from the moment it is transmitted by the source to the moment it is successfully received at the destination. This metric was evaluated by computing half of the round trip time experienced between a UE and a remote server.In particular, in the scope of the proposed framework, this performance was improved by enabling a more suitable allocation of remote servers closer to the end-user, i.e., at the edge to reduce network latency.The overall time required to deliver an active slice over the neutral host infrastructure. In essence, the SDT refers to the time required for the creation and activation of an end-to-end network slice, including the creation and configuration of all the virtual components that are entailed in the slice. This metric takes into account the execution of two main steps in the neutral host platform workflow: the slice creation and activation see .Slice Creation Time (SCT): refers to the amount of time it takes the Slice Manager to return the results of a submitted slice creation request to an end-user. This operation includes the sequential creation of all the chunks belonging to the slice and the grouping of those chunks. This time is measured from the moment when the creation request of a slice is sent to the Slice Manager, until receiving the confirmation that the slice was created.Slice Activation Time (SAT): refers to the amount of time it takes the Slice Manager to return the results of a submitted slice activation request to an end-user. This operation includes the instantiation of the mobile core and the configuration of the corresponding PLMNID in the RAN nodes included in the slice. This time is measured from the moment that the request is sent to the Slice Manager, until receiving the confirmation that the slice is ready to be used. Such confirmation is provided after receiving the acknowledgement from OpenStack about the mobile core instantiation and from the RAN Controller regarding the radio nodes configuration. Note that still additional seconds might be required to complete both operations as well as to finalize the Day1 configurations on the mobile core (based on cloud-init).Henceforth, in the scope of the proposed framework, the SDT can be computed according to the following equation:To compute this KPI, a custom Python script was developed to automate the slice deployment, time measurement and slice removal by sending the required REST API calls to the platform Slice Manager. This script measures and stores the times involved in each operation in a database, simulating user requests (like the ones done via the Dashboard).Set up of the networking in OpenStack required to connect each VNF included in the NS with the Monitoring component;Computation of the VNFs allocation  according to the algorithm employed by the Resource Placement component;Deployment and configuration of the NS instance through OSM as NFVO.The time required for the provisioning and deployment of an NS over a given slice. This operation includes three main actions, namely:In essence, the SIT is measured from the instant when the instantiation request of an NS is sent to the Slice Manager, until the moment when the service instantiation is completed, i.e., when all the virtual components that are entailed in the service descriptor are active and running. Since in the proposed framework OSM is used as NFVO, the indication of a successful deployment is triggered when the service instance in OSM appears as running  and configured (configuration status).As with the SDT, to compute this KPI, a custom Python script was used to automate the service instantiation over a given slice by sending the required REST API calls to the Slice Manager. For this test, all the required descriptors are available in the platform Catalogue and onboarded to OSM. Likewise, all the required images are already available in OpenStack, therefore only the instantiation time is considered without including the descriptors creation and onboarding processes.The time required to launch an additional instance of a specific VNF contained in a given NS. This operation is requested via the platform Dashboard as a particular case of reaction in the face of an alarm triggering event. Once a reaction request for a given NS is launched, the rule associated with that event for horizontal scaling  is retrieved and the corresponding scaling request is consequently delegated to OSM .In particular, the SST is measured from the instant when the reaction request of an NS is sent to the Slice Manager, until the moment when the new instance is running. As with the SIT, a scaling request is successfully completed upon the appearance of the running indicator as operational status in OSM. The time required by the Monitoring component for anomaly detection and alarm triggering is not contemplated by this metric.As with the previous two metrics, this KPI is measured via a custom Python script that automates the service scaling operation by sending the required REST API calls to the Slice Manager. After completing this action, the script also performs the service and slice removal to leave the system in the original state before repeating the entire sequence . Multiple iterations of this deployment lifecycle are conducted to obtain meaningful results.To demonstrate the benefits of the proposed framework, we deploy three slices over the neutral host infrastructure and measure the required SDT as expressed in Equation . The comIn Although obtained results in most of the cases are very well aligned with the expected KPI outcomes, some differences in performance are observed when comparing the three city testbeds. In particular, higher SDT, SIT, and SST are experienced in the Lucca pilot, which is mainly due to the smaller capabilities of the servers deployed in that city. Nevertheless, observed differences between the three pilots are not significant, and in overall, this analysis demonstrates the good performance, in terms of deployment times, of the proposed neutral host solution to be deployed in city-wide 5G infrastructures.To evaluate the impact of using the proposed framework for service orchestration, we compare the obtained results for SIT and SST considering as baseline the standalone use of OSM to perform the instantiation and scaling operations. Likewise, Summing up, In addition to the previously discussed results in terms of SDT, SIT, and SST, the User Experienced Data Rate and Data Plane Delay measurements are also outlined in this table.Regarding the User Experienced Data Rate, measured values report the cumulative DL throughput achieved by end-users in the considered multitenant scenario with three concurrent active slices, sampled every second during a period of 60 s. As for the Data Plane Delay, values included in Service Creation Times in minutes instead of hours.Overall, the conducted trials and performed evaluations validate the feasibility of the proposed neutral host framework by demonstrating the correct operation and benefits of its technology components. Furthermore, regarding the slicing and orchestration (main research focus of our solution), related results demonstrate that the developed platform performs well, achieving the 5G PPP programmatic KPI for Turning a city into a distributed, multitenant and neutral host model-compliant infrastructure demands a comprehensive framework able to support and integrate end-to-end 5G services upon different network technologies. Towards such a goal, this article provides insights into the design and deployment of a three-tier infrastructure and an orchestration platform that enables municipalities and infrastructure providers to create dynamic end-to-end slices composed of both virtualized cloud/edge and network resources and to lease such slices to third party operators/verticals. The developed solution also provides lifecycle management and orchestration of 5G-based edge services, together with the control of the available underlying city-wide infrastructure. Through the execution of use case trials, the benefits of using the neutral host model for deploying, provisioning, and managing vertical services over a virtualized and shared infrastructure was demonstrated. Moreover, obtained results confirm the feasibility of the proposed framework to be deployed as a neutral host solution in city-wide 5G infrastructures.Our future work will further exploit, in the context of the 5GVictori project, the potential of the 5GUK testbed to develop media vertical demos and experimentation scenarios over common large-scale field trials. In addition, we will work on the evolution of neutral host platform components, such as the Slice Manager and the RAN Controller, to support 5G Non-Standalone (NSA) and SA technologies together with the deployment of slices with distributed mobile core architectures based on the separation of user and control plane functions.


We consider the dynamics of a three-species system incorporating the Allee Effect, focussing on its influence on the emergence of extreme events in the system. First we find that under Allee effect the regular periodic dynamics changes to chaotic. Further, we find that the system exhibits unbounded growth in the vegetation population after a critical value of the Allee parameter. The most significant finding is the observation of a critical Allee parameter beyond which the probability of obtaining extreme events becomes non-zero for all three population densities. Though the emergence of extreme events in the predator population is not affected much by the Allee effect, the prey population shows a sharp increase in the probability of obtaining extreme events after a threshold value of the Allee parameter, and the vegetation population also yields extreme events for sufficiently strong Allee effect. Lastly we consider the influence of additive noise on extreme events. First, we find that noise tames the unbounded vegetation growth induced by Allee effect. More interestingly, we demonstrate that stochasticity drastically diminishes the probability of extreme events in all three populations. In fact for sufficiently high noise, we do not observe any more extreme events in the system. This suggests that noise can mitigate extreme events, and has potentially important bearing on the observability of extreme events in naturally occurring systems. So understanding the underlying mechanisms that may trigger extreme events have commanded considerable recent research interest4. An extreme event may be defined as an event where one or more variables of a system, arising in nature or in the laboratory, exhibits very large deviations from the mean value. So the dynamics of the system is characterized by excursions to values that differ significantly from the average. Further, though recurrent, these large deviations are rare vis-a-vis the characteristic time scale of the system, and their occurrences are aperiodic and uncorrelated in time. Without loss of generality, an event is typically labelled ‘extreme’ if a state variable, in the course of its temporal evolution, takes values that are several standard deviations away from the average value, thereby signalling dynamical behaviour beyond normal variability. Such extreme events have been observed in natural systems such as rogue ocean waves5, laboratory systems such as optical systems6, as well as financial phenomena like market crashes7. Interestingly, other definitions of extreme events, more appropriate to the context, have also been employed. Notably, in the specific important problem relating climate change to ecological dynamics, a synthetic definition of extreme events involving both the driver and response system is proposed8. However in this work we will employ the most commonly used marker for extreme events: namely, recurrent and aperiodic deviations larger than a prescribed threshold from the mean value, are considered to be extreme events, with the threshold typically taken to be 3-8 standard deviations from the mean.The emergence of extreme events in the dynamical evolution of systems ranging from weather10, for instance random walk models of transport on networks11. The emergence of extreme events in deterministic dynamical systems, manifested as intermittent large amplitude events, have also been investigated recently. Broadly speaking, the statistical features of deterministic systems is an active research direction that can lead to understanding extreme events that arise in the context of deterministic dynamics13. The search for dynamical systems that yield extreme events, without the drive of external stochastic influences or intrinsic random fluctuations, is a focus of much ongoing research effort from the point of view of basic understanding of complex systems17. Additionally, such probabilistic outcomes in dynamical systems are most relevant in the applied context as well, such as in engineering sciences where this direction of research leads to better assessment of risks18.A central direction in understanding extreme events is to find generic mechanisms that can give rise such large fluctuations. Typical studies of extreme events have involved stochastic models21, and has bearing on the long-term persistence of a population as a consequence of small size. Further we investigate the effect of additive noise in the system, focusing on the role of stochasticity in the emergence of extreme events. In a larger context, this research direction also has bearing on the important general question of the emergence of extremely large events in deterministic dynamical systems, and the effect of noise on their sustained prevalence.In this broad direction, in this work we explore the dynamics of a vegetation-prey-predator system, coupled through interactions of the Lotka-Volterra type. Importantly, our model system also incorporates the biologically significant Allee effect, which is one of the classic phenomena of population ecology. The Allee effect reflects the beneficial effects on the growth of individuals arising from conspecific interactionsOur central findings in this work are as follows: the system under Allee effect yields chaotic dynamics. Further, it leads to unbounded vegetation growth for sufficiently strong Allee effect. Most significantly, Allee effect aids the emergence of extreme events in this three-species chain. Interestingly, we also observe that noise suppresses the unbounded blow-up of vegetation induced by Allee effect. Lastly, sufficiently strong noise also subdues the extreme events in vegetation, prey and predator populations, thus suggesting a significant natural mechanism to mitigate extreme events in population chains.In second section we present results arising in the model of three interacting species, incorporating the Allee effect. In third section we explore the effect of additive noise in the system. We conclude with discussions of the scope of our findings in fourth section.25. Here we will focus on the emergence of extreme events and consider as our test-bed the well-known model for the dynamics of the snowshoe hare and the Canadian lynx populations, based on observed data22. Specifically, the system incorporates a three species vertical food chain, consisting of vegetation (denoted by u), prey (denoted by v) and predator (denoted by w). Additionally, we will incorporate in this model a term to reflect the Allee effect in the growth of the prey. The dynamics of this three species trophic system is described by the following sets of coupled differential equations:k is the average time spent on processing a food item, which is termed the handling time in literature.Complex systems research in general, and theoretical ecology in particular, has seen intense research activity in networks modelling interacting species, often focusing on local and global stability propertiesa, b and c represent the intrinsic growth rates of the three species u, v and w respectively. Further, the model allows the predator population to maintain a equilibrium population The interaction of the predator population with the prey is considered to follow the well-known Lotka-Volterra type interaction, described by the function 26, here we will also explicitly consider the Allee effect. Specifically, the Allee effect is considered in growth of the prey by introducingA(v) describes the mating success at the low population density28. This kind of Allee effect in two and three dimensional population models has drawn much research attention30.Importantly, in contrast to work on similar systems22. We explore the dynamics of the system under varying In this work we consider the parameter values Our main focus is to explore the dynamical consequences of the Allee effect in the population of the prey, in this three-species model system. We will first show that there is a sharp increase in the probability of obtaining unbounded vegetation growth beyond a critical value of the Allee parameter. We will then demonstrate that, interestingly, the system exhibits chaos as the Allee effect becomes more significant. Then we will move on to the central focus of this work, namely the influence of Allee effect on the emergence of extreme events. We will explicitly demonstrate that there is a pronounced increase in the propensity of extreme events under increasing Allee parameter 31. In order to quantify this blow-up, we estimate the probability of unbounded vegetation growth from a large sample of random initial states, followed over a long period of time. We also ascertain that the estimated values are converged with respect to increasing sample size, and thus can be considered to be robust numerically. The results thus obtained, for varying Allee parameter Our first observation is the emergence of explosive runaway growth in vegetation when the Allee effect is too strong, i.e. when the Allee parameter mentclass2pt{minimNext we investigate the temporal evolution of the population densities. Figure entclass1pt{minimaentclass1pt{minimaentclass1pt{minimaOn further increasing entclass1pt{minimaOne of the most interesting observations from the time series presented in the section above is the following: when the magnitude of the Allee parameter entclass1pt{minimaIn order to illustrate this, we mark the time instances at which a population exceeds the In order to understand the phenomena quantitatively, we first estimate the maximum densities of vegetation, prey and predator populations , g and h have the functional forms given in Eq. (Specifically we investigate the dynamics of the three species system  under admentclass2pt{minimFirst we investigate if the boundedness of the system  is affecmentclass2pt{minimFigure mentclass2pt{minimNext we examine how noise influences the extreme events which were observed to emerge in this system in the presence of Allee effect. We first examine the temporal evolution of the population densities and their corresponding phase-space attractors. In Fig. see Fig. b. On furFurther, in order to quantify how noise influences the emergence of extreme events, we again estimate the probability of obtaining extreme events, mentclasspt{minimaIn summary, we explored the dynamics of a three-species trophic system incorporating the Allee Effect in the prey population. Our focus is on the emergence of extreme events in the system. In particular we address the significant question of whether or not Allee effect suppresses or enhances extreme events.Our key observations are as follows: First, under Allee effect the regular periodic dynamics changes to chaotic, as evident from the emergence of chaotic attractors for increasing Allee parameter Lastly we consider the influence of additive noise on extreme events. First, we find that noise tames the unbounded vegetation growth induced by Allee effect. More interestingly, we demonstrate that stochasticity drastically diminishes the probability of extreme events in all three populations. In fact for sufficiently high noise, we do not observe any more extreme events in the system. This indicates that noise can mitigate extreme events, and has potentially important impact on the observability of extreme events in naturally occurring systems.


Nonlinear effects in the radio front-end can degrade communication quality and system performance. In this paper we present a new design technique for reconfigurable antennas that minimizes the nonlinear distortion and maximizes power efficiency through the minimization of the coupling between the internal switching ports and the external feeding ports. As a nonlinear design and validation instance, we present the nonlinear characterization up to 50 GHz of a PIN diode commonly used as a switch for reconfigurable devices in the microwave band. Nonlinear models are extracted through X-parameter measurements supported by accurate calibration and de-embedding procedures. Nonlinear switch models are validated by S-parameter measurements in the low power signal regime and by harmonic measurements in the large-signal regime and are further used to predict the measured nonlinearities of a reconfigurable antenna. These models have the desired particularity of being integrated straightforwardly in the internal multi-port method formulation, which is used and extended to account for the power induced on the switching elements. A new figure of merit for the design of reconfigurable antennas is introduced—the power margin, that is, the power difference between the fed port and the switching elements, which combined with the nonlinear load models directly translates into nonlinearities and power-efficiency-related metrics. Therefore, beyond traditional antenna aspects such as port match, gain, and beam orientation, switch power criteria are included in the design methodology. Guidelines for the design of reconfigurable antennas and parasitic layers of minimum nonlinearity are provided as well as the inherent trade-offs. A particular antenna design suitable for 5G communications in the 3.5 GHz band is presented according to these guidelines, in which the specific switching states for a set of target performance metrics are obtained via a balancing of the available figures of merit with multi-objective separation criteria, which enables good control of the various design trade-offs. Average Error Vector Magnitude (EVM) and power efficiency improvement of 12 and 6 dB, respectively, are obtained with the application of this design approach. In summary, this paper introduces a new framework for the nonlinear modeling and design of reconfigurable antennas and provides a set of general-purpose tools applicable in cases beyond those used as examples and validation in this work. Additionally, the use of these models and guidelines is presented, demonstrating one of the most appealing advantages of the reconfigurable parasitic layer approach, their low nonlinearity. Wireless communications systems using medium and high transmitter power and advanced modulation techniques must ensure that nonlinearities are below certain safety levels as harmonic components and intermodulation products can degrade system performance and even damage components.In particular, for New Radio (NR), the Fifth Generation of Mobile Communications 5G), very stringent performance requirements in terms of signal quality, unwanted emissions, and intermodulation are specified ,2,3,4. TG, very sAs power handling is higher in the BS, attention is focused on this component for which the values specified in  are takeOn the side of signal quality, the metric of interest is the Error-Vector Magnitude (EVM), defined according to the modulation scheme used—QPSK These metrics and performance requirements imply stringent design goals, but even with a careful engineering some undesired nonlinearities can still persist; therefore, nowadays it is common the use of digital compensation techniques to mitigate the effects of the analog components to achieve conformance to the technical specifications. For these compensation techniques to be effective, a nonlinear model of the analog device to be compensated for is required ,8.Even though antennas are traditionally reckoned as inherently linear devices, the recent evolution of the field has relied on introducing nonlinear loads and components such as integrated switches, varactors, and PIN diodes into or in the surroundings of the (re-)radiating structure. This evolution has raised concerns on how these new kinds of nonlinear devices can impact system performance. Consequently, accurate nonlinear antenna modeling is a need that must be addressed, bearing a twofold advantage, as a component design tool and as input for RF system designers to integrate the antenna into the transceiver chain.The use of PIN diode switches in microwave radio front ends is widespread, and new applications are rapidly emerging, for example in Reconfigurable Antenna (RA) ,10, recoAlthough the initial design and proof of concept of reconfigurable devices can rely on models such as the ideal switch abstraction, linear circuit equivalents, or measured S parameters, the validity and accuracy of these models are rapidly lost as biasing, frequency, and power are changed. Therefore, in stringent applications such as 5G, nonlinear models of the PIN diode should be used to predict system behavior in different operation conditions.Nonlinear models of microwave devices and circuits  can be cThe X parameters  stand ouAlbeit the nonlinear behavior of the PIN diode is widely reported and mostly attributed to its nonlinear resistance characteristic ,24,25, aConsequently, X parameters are proposed in this work to experimentally obtain a behavioral model of a PIN diode commonly used for mmW applications. The extracted diode model is validated through independent S parameters and harmonic distortion measurements.Reconfigurable antennas in general and parasitic layer based reconfigurable antennas  presentiThe extracted nonlinear model of the PIN diode switch is a useful input to gain insight into the nonlinear behavior of reconfigurable antennas using PIN diode switches like the one illustrated in The nonlinear behavior of RAs is scarcely reported in the literature, and design strategies considering nonlinearities are non-existent. Two recent experimentally-oriented works are , where TNotwithstanding the lack of theoretical approaches and the scarcity of experimental works studying nonlinear effects in RA, the case of nonlinearly loaded basic antennas and arrays has been tackled to some extent. With few exceptions that deal with the nonlinear problem entirely within the electromagnetic solution, which proves useful in cases where nonlinearities are inherent to the antenna or propagation medium materials, the most reasonable approach to the analysis of nonlinearly loaded antennas is to split the problem into an electromagnetic (linear) and a circuital (nonlinear) problem. The former is commonly dealt with by Full-Wave Electromagnetic (FWEM) numerical techniques, whereas the latter can be tackled by formulations such as the Harmonic Balance (HB) analysis .Nonlinear antenna analysis can be traced back to the works of , based oA common drawback in these works is that they assume a given simplified model for the nonlinear switching element Therefore, given the nonlinear characteristics of the loads, a suitable modeling technique must be used. Measured X-parameters of the PIN diode are developed in this work as a convenient alternative for stating the characteristics of the nonlinear loads.Likewise, the Internal Multi-Ports Method (IMPM) ,40,41 isThe remainder of this paper is organized as follows—The PIN diode MACOM MA4AGBLP912, operating over the 50 MHz–40 GHz frequency range, was selected for testing. The measurements are performed using a Keysight N5245A PNA-X network analyzer capable of extracting X parameters, connected by means of a Cascade-Microtech 150 µm-pitch Ground-Signal-Ground (GSG) Co-Planar Waveguide (CPW) probe to the test fixture.q, while p.The notation used in X parameters is based on port, harmonic and propagation direction convention, in which In the general X-parameters formulation, outgoing port waves are expressed as a function of the Large Signal Operating Point Stimuli (LSOPS), which is composed of the device DC Stimulus (DCS), and the RF Stimuli, which in turn is composed of the fundamental magnitude A common approximation, valid for most devices, that significantly reduces the computational resources required for measurement, is to consider that the fundamental is the only large RF signal entering the DUT, hence, the only one that can drive it into a nonlinear behavior, while the injected/reflected signals at the remaining ports and harmonics combinations are considered small-signal components. Accordingly, the reference LSOPS is solely defined by S, and T respectively, whose interpretation is as follows: the p and harmonic m for a system perfectly matched at the output port and perfectly matched at each harmonic at all ports. The q at harmonic n to the outgoing wave at port p and harmonic m.Then, with the aid of linearization and harmonic superposition assumptions, dropping the dependence on  related  through:The X-parameters model states that the set of outgoing port waves  result from a linear mapping of the set of incoming port waves , but in contrast to S-parameters, not only signal ratios are combined, but additionally this modeling considers the contributions depending on the amplitude of the RF Stimulus (RFS) and the relative phases of the remaining incoming signals (harmonics and intermodulation products) with respect to this reference stimulus.The test-fixture used is supported on an Alumina substrate  calibration is first performed, followed by input power calibration and harmonics phase reference calibration as is required for the measurement of X parameters . The dioeven mode accounting for dispersion, obtained with the aid of accurate 2.5D electromagnetic simulation using Keysight Momentum, is used for that purpose.As the SOLT calibration reference plane is defined on the GSG probe-CPW line contact, a de-embedding procedure is applied to remove the contribution of the CPW line from the measured diode S parameters and retrieve the actual diode reflection coefficient. A model for the CPW-Considering the diode mounting and that the X-parameters measurement system used in this work requires the calibration and registering of both ports, some comments on the validity of the measurements are deemed convenient.Although in the case of S parameters, it is clear that two- and one-port S-parameter measurements would yield the same reflection coefficient, this may not be evident in the case of X-parameters, as in general, the nonlinear functions involved depend on the incoming signals from all the ports/harmonics combinations. However, as in the test fixture used for diode characterization both ports are physically uncoupled, the waves injected at port 2 do not affect the measurement at port 1, hence, inter-port wave dependence vanishes. This is expressed by the reduced one port X-parametersExtensive measurements of S- and X-parameters of diode MA4AGBLP912 were performed in the 1–50 GHz range, using different biasing levels. Note that in the case of the PIN diode, the biasing current Measurements of One-port X-parameter measurements were carried out at different biasing levels To ease the comparison of X parameters for the different diode biasing levels, slices of Valuable information about the nonlinearity of the DUT can be extracted from the variation with RFS power of the large signal response Another common approach to estimate the nonlinearity of the DUT is by defining the nonlinear transition as the input power resulting in the 1dB CP of the reflected fundamental wave; this value can be extracted directly from On the other hand, the variation with input power of the set of functions The X parameters convergence to the S parameters in the small-signal regime is verified for both the “ON” and “OFF” states. Direct S-parameter measurements are compared to X-parameter reduced to S parameters using circuit simulation in Keysight ADS. Results are reported in A further validation was performed contrasting The extracted diode model based on the X-parameters measurements, once validated, becomes a fundamental input to assess the possible nonlinear behavior of reconfigurable antennas and parasitic layers from an analytical viewpoint, and ultimately, a valuable piece of information to be further used as a design tool in the case of minimum nonlinearities reconfigurable antennas and parasitic layers.To illustrate the use of the X-parameters in a particular case, the antenna reported in  and reprNotwithstanding that this antenna has 6 diverse modes of operation allowing for beam-steering and bandwidth reconfigurability, given the antenna symmetries and the expected small contribution to nonlinearity of the switches on the upper PL, only modes As mentioned in the introduction, a common approach for the analysis of nonlinearly loaded antennas is to split the problem into an electromagnetic (linear) and a circuital network (nonlinear) problem. The first one can be dealt by numerical techniques such as MoM, Finite Elements Method (FEM), Finite-Differences Time-Domain (FDTD), whereas the second one can be tackled by nonlinear formulations like the Harmonic Balance (HB).The internal multi-port method, illustrated in Afterwards, two relevant metrics to assess the nonlinearity of the antenna are determined by means of an HB simulation in which the input power is swept from −10 to 30 dBm. One step further, the Error Vector Magnitude can also be derived with the aid of the X-parameters nonlinear model. The EVM is a communications performance metric  that gaiThe EVM is related to transmitter imperfections  such as In general, the EVM is defined asAlthough it is valid only in “Data-aided receivers” , the SigUsing a base-band signal model and reasoning similar to that in , the EVMThe approximated EVM is calculated using the results of the HB simulation of the PL-based RA under test, and assuming a moderately high noise floor of The advanced design of parasitic layers, and reconfigurable antennas in general, heavily relies on optimization techniques to find an adequate set of switching states to achieve a target set of figures of merit. These figures of merit are usually specified in terms of fundamental antenna parameters for example, port parameters, such as match and coupling, and pattern features such as direction of maximum, gain and polarization.Although nothing prevents the inclusion of system-related performance metrics impacted by the antenna, such as coverage, throughput, BER or EVM, or any other parameter of interest in particular applications, the use of basic antenna properties is often the most efficient option, as the computational cost of calculating these derived quantities make them impractical when evaluating beyond a few thousands of switch states. This complexity is exacerbated if structural variations of the basic radiator are to be considered in a co-optimization process as for example in .Therefore, the use of basic antenna parameters and system-level performance estimators directly derived through simple calculations may be used whenever possible to predict the better performing configuration when comparing among several different alternatives.Choose an optimal trade-off starting point for the antenna geometry.Determine the optimum switch configurations using the performance metrics vector defined in terms of fundamental antenna parameters derived from small-signal formulations.Based on nonlinear load models, accurately calculate the nonlinearities and system-related parameters for the optimum configurations.As the main interest of this work is the design of reconfigurable antennas and parasitic layers with minimum nonlinearities and impact on related system-level metrics such as EVM, a partitioning of the design process into three stages is proposed aiming to reduce the computation time and achieving controllable results. The stages of the design methodology are:A high level flowchart diagram illustrating the main elements of the proposed design methodology is presented in n-dimensional decision space, mapped through a cost function f to a lower k-dimensionality objective space, in which a comparison of elements x in the original space is performed through metrics y defined in the destination space. In the case of RA design, diverse antenna parameters compose the comparison metrics, hence, a multiobjective optimization problem is implicit.A general optimization problem is defined as a search in an f be a surjective projection of Common RA design approaches mix multiple parameters to obtain a single performance indicator to facilitate decision, however, if the cost function is defined in a way such that Adding dimensions to the objective space allows the creation of Pareto fronts, representing the best objective combination, enabling the visualization of trade-offs and exploring the interrelation between objectives. Furthermore, adding new decision axes to the objective space creates new separation criteria for configurations with very similar performance on the other axes.In this work, a new power-related metric is defined in addition to the port parameters and far-field related metrics allowing to account for antenna port match, isolation, beam pointing, gain, power efficiency and nonlinearity.The Internal Multi-Ports Method (IMPM) is an efficient way to characterize the behavior of a reconfigurable device for a set of switch states, requiring only one FWEM simulation at setup. After setup, formulations yielding results equivalent to circuital simulations allow to determine the effects of the terminating loads on the fundamental antenna parameters. A simple extension to the IMPM is added to account for the power delivered to the fed ports and to the switches, becoming a useful indicator of power efficiency and possible excitation of nonlinearities. Expressions to calculate loaded port parameters, radiated field and port power are briefly summarized.The setup FWEM simulation is performed to obtain the reference network scattering parameters From the defining relation of the total S-matrix Noting that only input ports have a source signal From the expressions above, we can compute all the unknown wave amplitudes from the known input amplitudes Now, the aggregated radiated field for a particular excitation and load condition can be calculated as follows from both A number of quantities of interest can now be obtained from these wave amplitudes:Under a pure tone excitation, and considering that the antenna building materials and surrounding environment have a linear behavior for all operating circumstances, the only source of nonlinear distortion are the internal port loads and their frequency conversion characteristics.Although the presented formulation relates only one input frequency to the same output frequency, it can be extended to account for harmonics induced by the nonlinear loads by properly adapting the vectors and matrices involved in the calculations. In particular, if In this case, On the other hand, given the non-linearity of the terminating loads (switches), From this expression, the convenience of the X-parameter formulation for the loads modelling results evident as it embeds the required frequency conversion as a function of the input power.As an additional remark, it must be noted that when input power is low enough, the cross-frequency components are negligible and consequently the As mentioned earlier, for the optimization stage the interest is on efficiently comparing several thousands of configurations; therefore, a valid indicator of the nonlinear performance of a given switch configuration is adopted instead of solving the nonlinear extended system. For this purpose, the power margin Reducing the (2)Reducing the From the expressions obtained above, it can be observed that the nonlinear perturbation comes from the waves reflected by the loads, given by the term h’ over one basic antenna and its effects on the reconfigurability of parameters like port matching, radiated field, and nonlinearities, the parasitic-layer-based reconfigurable-antenna illustrated in To examine the effects of the PL height ‘h’ is performed on this reference antenna, aiming to determine a feasible trade-off region which can be used as design guideline, even for other PL pixellations and number of switches, as well as other antenna configurations. Therefore, the interest is in average or expected behavior rather than in particular switch states behavior. Aggregated port match bandwidth, maximum steering angle, and average power margin are used as metrics of comparison.A parametric variation of ‘h from the basic antenna, with size and switches numbering as illustrated in The PL based RA is composed of a basic 2-ports aperture-coupled microstrip patch radiator matched at h. Results for port 2 are almost identical and are omitted.The parametric sweep is performed using the frequency-domain solver of CST studio, for The first that can be observed in h. Although high power margins ∼9 dB can be achieved for some configurations with very narrow separations, average margins in excess of 6 dB are achieved for separations beyond On the other hand, h is shown in Variation of directivity with h to get an exact description of the angular distribution of pattern maximum. From this depiction a trend was observed, and is that the maximum deviation tends to cluster at Finally, the angular variation of the pattern maximum with the PL height over the basic antenna, allows to determine the feasibility of finding patterns with maximum radiation pointing towards specific directions Finally, aiming to capture the overall reconfigurability potential of the PL-based-RA, and as a general purpose design guideline, the average metrics encountered are expressed by means of a tradeoffs surface as illustrated in The set of plots of It is foreseen that a large portion of the initial deployments of the 5G-NR will be concentrated on the Freuency Range 1 (FR1) (sub-6 GHz portion of the spectrum) , and speh as there is not a straightforward way to reuse simulation results for other h values. Accordingly, the presented guidelines for determining the optimum h are intended to greatly reduce the design time.The most computationally expensive part of the design process is the initial FWEM simulation to get the ‘unloaded’ antenna parameters, this simulation must be performed for any candidate value of After the fundamental design trade-offs of the reconfigurable parasitic layer are established, an optimum region for the separation between the basic antenna and the PL can be determined based on the compromise that must be made between bandwidth, linearity, and beam-steering. For instance, for 5G applications covering the n78 band at 3.5 GHz, a good starting point should be However, beyond appropriate region for PL placement, particular indications on how to determine the switch states to achieve the optimum compromise of the objectives are not yet given. The optimum switch states determination is demonstrated by means of a particular design example.In this case, the same topology used to determine the basic trade-offs is employed with some variations, first the basic antenna is modified to resonate at a lower frequency aiming to have a lower cutoff frequency and a richer number of well-matched configurations at the central frequency of The switch state determination is posed as a multidimensional optimization problem, in which a 3D cost function considering S-parameters, beam pointing and switches power, is defined and explored using Pareto fronts to obtain antenna realizations with an optimum objective compromise. The cost function vector is defined as:After each individual is assigned a cost vector, weak Pareto optimality criterion is used to retain only the better performing configurations for each of the desired modes of operation. The process is illustrated for the Depending on the reachable cost vector for a particular target mode of operation, and whether a small mismatch, miss-pointing, or higher power going to the switches is tolerable, the designer can evaluate a subset of the configurations on the non-dominated set and determine, based on features like for instance pattern shape, impedance bandwidth, or nonlinear metrics, the configurations that better suits the application.The procedure illustrated in Once the better performing configurations are found, these are validated by simulation with CST Design Studio, finding an almost exact match. Similarly, the port parameters calculated using the measured S- and X-parameters models of the loads are verified to be in a very good agreement.The final configuration of the antenna have a satisfactory performance characterized by an aggregated bandwidth of On the other hand, the power margin for the optimum configurations are  dB, demonstrating a mean value of Likewise, Finally, the IP3 and further EVM nonlinear metrics of the antenna optimum configurations are calculated using the diode nonlinear diode models extracted by X-parameters measurements. Results for EVM are illustrated in This result confirms the suitability of this parasitic-layer-based reconfigurable-antenna design for 5G NR mobile broadband systems, and at the same time shows the benefits of the new design approach considering the switches power to minimize the nonlinear distortion.Even though, to the best of the authors’ knowledge, this is the first effort to minimize the nonlinear distortion of a reconfigurable antenna, and the design technique has implications beyond the particular results presented as example, a comparison with similar works reported in the literature, in terms of basic antenna parameters, size, and nonlinearities when available, is presented in A method for the nonlinear characterization of a mmW PIN diode has been proposed. It is based on X-parameters measurements obtained using a test set composed of a nonlinear network analyzer, a one-port on-wafer probe station and a CPW test fixture.The proposed method has been applied to characterize a commercial PIN diode commonly used in reconfigurable antenna applications spanning a frequency range from 1 to 48 GHz.The measured X parameters have been validated by good agreement obtained between the harmonic rejection derived from X parameters to independent harmonic measurements, as well as from measurements in the small signal regime, where nonlinear X-parameters converge to measured S parameters.The X parameters model is used to assess the possible nonlinearities on a reconfigurable antenna, showing consistency with experimental results.Guidelines for the design of Reconfigurable Antennas in general and particular application to Parasitic Layers have been presented accounting for a new performance metric related to the power efficiency and possible emergence of nonlinearities.Optimum tradeoffs for the separation of the basic antenna and a reconfigurable parasitic layer to attaining particular objectives related to port match, nonlinearity, and beam-steering have been discussed.A complete methodology for the design of minimum nonlinearity reconfigurable antennas has been presented, accounting also for port match and beam-steering.The methodology is based on (i) Determining the optimal PL distance to the basic antenna. (ii) Determine the optimum switch configurations. (iii) Based on nonlinear load models, accurately calculate the nonlinearities and system-related parameters only for the optimum configurations.A design example of a parasitic-layer-based reconfigurable-antenna suitable for 5G NR communications in the 3.5 GHz band, from the port match, beam-steering and nonlinear distortion is presented.The particular antenna design is a suitable alternative for 5G-NR EMB usage scenarios in the 3.5 GHz band, bearing 2 ports with a 11% bandwidth, 9 beams pointing in With the application of this new design methodology an improvement of 12 and 6 dB of the EVM and power efficiency, respectively, were obtained when compared with conventional reconfigurable antenna design strategies.


One of the vital challenges for cancer diseases is efficient biomarkers monitoring formation and development are limited. Omics data integration plays a crucial role in the mining of biomarkers in the human condition. As the link between omics study on biomarkers discovery and cancer diseases is deepened, defining the principal technologies applied in the field is a must not only for the current period but also for the future. We utilize topic modeling to extract topics (or themes) as a probabilistic distribution of latent topics from the dataset. To predict the future trend of related cases, we utilize the Prophet neural network to perform a prediction correction model for existing topics. A total of 2,318 pieces of literature (from 2006 to 2020) were retrieved from MEDLINE with the query on “omics” and “cancer.” Our study found 20 topics covering current research types. The topic extraction results indicate that, with the rapid development of omics data integration research, multi-omics analysis (Topic 11) and genomics of colorectal cancer (Topic 10) have more studies reported last 15 years. From the topic prediction view, research findings in multi-omics data processing and novel biomarker discovery for cancer prediction  will be heavily focused in the future. From the topic visuallization and evolution trends, metabolomics of breast cancer (Topic 9), pharmacogenomics (Topic 15), genome-guided therapy regimens (Topic 16), and microRNAs target genes (Topic 17) could have more rapidly developed in the study of cancer treatment effect and recurrence prediction. Genomics, proteomics, metabolomics, transcriptomics, and other -omics studies involve comprehensive investigations , as a statistical technique, is available to capture and explain potential relationships between the high-frequently-used terms in recent scientific products with high precision through a layered aggregation system of words Hence, compared with traditional bibliometric research paper, this article is characterized by natural language processing of many title texts and predictive analysis based on time series. From this perspective, we summarize the scientific terms presented on MEDLINE over the past 15 years. Research topics are extracted, and then theme intensity is calculated based on the time segment of the month. From the perspective of topic modeling and the predictive correction algorithm optimization, our study provides specific methods for scientific researchers in the cell development field. It furnishes more followers with intuitive understanding and disciplinary analysis in the study of omics data integration to biomarkers.This study evaluates the “Omics data integration” in “Cancers” to explore the research topic's evolution. The research framework contains seven steps, which are mainly embodied in two stages. The first phase is data preprocessing and topic extractions , the number of circles represents the number of topics, and its size means the corpus belonging to the topic. The quadrants of circle distribution represent the clustering situation. The distance between circles represents the semantic distance between topics. The farther space is, the higher the discrimination between topics is.e time slice, in the document set, the number of documents is Ne, and the intensity of topic X, TX means the number of articles attributed to topic X:Topic intensity is a statistical attribute of topic, indicating the degree of concern of the topic. In our research, we employed the number of documents distributed to each topic to calculate intensity. The intensity index of each topic constitutes a series of time. Define in In our study, we use the time series model, the Prophet neural network, to predict the topic trend. Compared with the classical ARIMA model and LSTM model, the Prophet model can better predict the growth trend. It does not require extensive sample data for text training, so it is easier to achieve convergence than the LSTM method. Since the minimum unit for the journal publication cycle in the data sample is monthly. When predicting the size trend of each topic, we take it monthly, ignoring the influence of cycle factors and holiday factors.R2_score represents the deviation between the observed value and the real value, ranging from 0 to 1. This is used to evaluate the quality of the trend predictions. The case that R2_score is closer to 1 means the fitting effect is ideal. Besides, we compare Prophet-Liner and Prophet-Logistic results to examine whether the topic trend is linear or not. Intuitively, the Prophet-Liner result represents the direct prediction on linear trend, while the other is the direct prediction on logistic trend.The ECharts ThemeRriver diagrams are used in the series to represent changes in events or topics over time. The different colored river branches in the theme river encode various topics. The width of the river branch encodes the value in the original dataset. In Column 3 in From the overall development trend of the subject, the research achievements of omics analysis in cancer research increase year by year. Column 5 in Machine learning is an intelligent scientific tool to improve concrete algorithms in experiential learning  is a common and lethal disease with a high therapeutic need. In a range of protein, DNA, and RNA-based biomarkers under investigation for CRC, long non-coding RNAs (lncRNA) plasmacytoma variant translocation have been evaluated as a diagnostic, prognostic, and therapeutic biomarker in colorectal cancer  are short, non-coding RNA that negatively regulates gene expression and are differentially expressed in human cancers  (Gwak et al., To sum up, the recent development of omics and biomarker discovery technology in the past two decades has brought a burst inflection point in the above fields. The above eight topics will keep a rapid development in the future. Even though the remaining topics trends show decreases, it does not mean the related research are getting less. In The scientific panorama involved in studying the omics data integration toward the mining of biomarkers in cancers is described in the 20 extracted topics. Among the 2,318 sample studies, the core element from the current scientific discussion is the multi-omics analysis. For each topic, the Prophet model can better adapt to the evolution trend. In addition, all of the research topics are in line with the Liner trend, indicating a development stage for omics analysis in cancer studies. The research methodology proposed in this study is hoped to promote a different approach to conceptualizing and treating omics data integration study based on existing methods.From the perspective of the distance between topics and the evolution of distribution, the innovative technologies of biomarker discovery represented by genomics, metabolomics, and proteomics are the actual contents of integrating omics data in cancer research. Genomics has done extensive research on cancer cells and cancer patients in different treatment stages. With the continuous development and update of international genome-related databases, traditional machine learning algorithms and deep neural networks are essential for data integration and disease prediction. In the future, innovative algorithms will be explored for biomarker discovery technology in different stages of different types of cancer diseases. There will be more research performing clustering optimizations in the development of multi-omics data integration.Metabolomics has made many achievements in the research of genitourinary tumors, lung cancer, and breast cancer, mainly reflected in the study of metabolic phenotype biomarkers in the metabolic pathway. It is also used in the research of cancer treatment and prognosis prediction. Vertically omics data integration among proteomics, genomics, and metabolomics is becoming more common in the study of cancers. To obtain biological information through omics technology and to discover the molecular mechanism related to cancers are the primary purpose of proteomics research. To detect new marker molecules and to improve the clinical treatment effect, the development of a multi-omics data platform and schema database together with the exploration of a multi-omics feature expression algorithm will have more practical significance.In omics research toward the mining of biomarkers in cancers, our study summarizes the existing evolution and predicts the future trends of researches. Specifically, the adopted topic model describes and forecasts the change of time segments, which helps track the research development. Additionally, as our results go beyond the original thinking of theory and framework, this study also helps scholars and readers to understand the hot spots and future opportunities regarding omics data integration in cancer studies.It is noted that there also exist some limitations. On the one hand, although we described the hot research issues and predicted the frontier research issues, there is still a shortage in natural language processing. Due to the variety of text language rules in different stages and different cancer diseases, the same substance can be expounded in several ways. In the process of document-level natural language processing, the expression differences of specific terms cannot be avoided. On the other hand, this paper's conclusion does not involve finding out the research deficiencies, technical challenges, and other omics research problems toward the mining of phenotype-specific biomarkers. Expert systems development and optimizing algorithms will be performed in the next study to provide a more comprehensive analysis of the research problems.The original contributions presented in the study are included in the article/supplementary material, further inquiries can be directed to the corresponding author.LN wrote the manuscript. HH contributed to the modification of the manuscript. All authors contributed to the article and approved the submitted version.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


To characterize the closed-mouth temporomandibular joint (TMJ) disc-condyle relationship in a population of individuals who sought hospital services for temporomandibular disorders (TMD).  Two hundred and twenty-four TMJ magnetic resonance images (MRIs) of 112 patients were assessed in all spatial planes to classify disc position with respect to the condyle in a closed-mouth position.  Disc displacement (DD) was present in 62.1% and superior disc position in 29.9% of the patients. Position could not be determined in 8% of the cases. Among DD, pure anteriorized position was the most common condition (34.4%), with different combined translational and rotational displacements in all the other joints (27.7%).  There is a wide biological variability in disc position in closed mouth among patients seeking for TMD advice. Getting deeper into the correlation with clinical symptoms is recommended to refine the potential relevance of any diagnostic and management strategies based on the imaging evaluation of TMJ disc position. Temporomandibular disorders (TMDs) are a group of musculoskeletal pathologies involving the temporomandibular joint, the jaw muscles, and related structures . The etiThe TMJ is a bilateral, complex, and critical load-bearing joint. The articular disc acts as a stress absorber, and its positional relationship with the TMJ condyle has been much studied. In particular, several investigations described the positional changes on the sagittal plane with respect to the purported reference position . In paraFor the evaluation of TMJ soft tissues, magnetic resonance imaging (MRI) is the reference technique –15. SuchDisc-condyle relationships other than the so-called superior position  have historically been considered abnormal. A disc displacement (DD) may be due to factors intrinsic to the TMJ itself  or to external factors  . On the Within these premises, this study aims to characterize the closed-mouth disc-condyle relation in all spatial planes  and all possible positions in a nonselected population of individuals who sought hospital services for TMD.This is an observational study of the MRIs of 112 patients  attending the Treviso Hospital, Italy, between January and May 2019. Patients asked for advice because of TMD signs and symptoms. In this study, the MRIs of patients that satisfied any diagnostic criteria for temporomandibular disorders (DC/TMD) for joint disorders and that reported the signs/symptoms for more than three months were included [All MRIs were collected in the same center and by the same radiologist with expertise in TMJ imaging interpretation, using a MAGNETOM Avanto-Fit 1.5 T scanner . The subjects were positioned in the supine position, with the sagittal plane perpendicular to the horizontal plane and the Frankfurt plane parallel to the scanner gantry. Oblique parasagittal slices were obtained and corrected by the horizontal angulation of the condyle in a closed-mouth position. A 2 mm slice thickness in sequential sagittal, coronal, and frontal T1-weighted images was obtained in the closed-mouth position, with a 140 mm field of view and spin-echo multisection images . A single observer assessed the images in order to classify the disc position in closed mouth according to the classification of Tasaki et al. .Superior disc position: the posterior band of the disc is superior to the condyle, or the central thin zone of the disc is located between the anterior prominence of the condyle and the posterior aspect of the articular eminence  (acement) .Partial anterior disc displacement in the lateral part of the joint: the disc is anteriorly displaced in the lateral part of the joint and is in a superior position in the medial part of the joint with no sideways component of displacement . The characterization of the sample by sex, age, and orofacial pain score according to the visual analogue scale (VAS) is presented in The disc position could not be determined in 8% of the joints, and a posterior disc displacement was not found in any of the TMJ.This investigation described the TMJ disc position in a population of patients seeking for TMD advice. The diagnostic characterization of the sample demonstrates the variability found when open classification systems like DC/TMD are used, which allow the inclusion of a patient in multiple categories. Furthermore, it demonstrates the heterogeneity of clinical conditions that translate into pain in the orofacial area lasting more than 3 months and are often simply categorized as TMDs, in line with literature using similar methodology . Care muThe purpose of this study was to provide a standpoint for future comparisons based on a patient sample of individuals that may be representative of a TMJ disorder population. MRI is considered the reference imaging technique for TMJ conditions since it allows the simultaneous evaluation of the morphology and position of the articular disc and bone structures of the TMJ, in addition to evaluating the functional relationships between the condyle, articular disc, mandibular fossa, and articular eminence. A multisection analysis of MRI images allows distinguishing the normal disc position from disc displacement and can improve the possibility to distinguish between various stages of intra-articular derangement of TMJ. For optimal imaging of the TMJ, small bilateral surface coils with a small field of view were used to achieve a higher signal-to-noise ratio and simultaneous bilateral acquisition. The closed-mouth coronal and frontal T1 sequences were used to evaluate the overall anatomy, disc position, and intra-articular arrangement. Only the closed-mouth position was considered in our study since it is in this position that the condyle/disc relationship is categorized by the Tasaki et al. classification . The opeTo the best of our knowledge, this investigation is one of the first to depict the full spectrum of disc locations with respect to the condyle, thus adding information to the literature studies describing the disc-condyle relation only on the sagittal or coronal planes. Based on that, the findings may offer some interesting points for discussion.As a general remark, findings are in accordance with the literature, showing a high frequency of disc displacement in TMD populations, which is generally higher than in healthy individuals. Tasaki et al. evaluated 600 MR images of 243 TMD patients and 57 volunteers and found disc displacements of different stages in the sagittal plane in 80% of the patients as compared with 30% of the volunteers. A successive study by Larheim and Westesson (2001) also showed a higher frequency of complete anterior and anterolateral disc displacements in patients with TMD than in healthy controls .This study confirmed that the frequency of MRI-depicted disc displacement is high among TMD patients. The so-called physiological superior disc position was found in 29.9% of joints, an undetermined position was shown in 8%, whilst a displacement of a different type and direction was depicted in all the other joints. Amongst those, an anterior position is the most frequent condition (34.4%). These values are in agreement with the study of Emshoff et al. (2002), who reported 64.9% of disc displacements in patients with TMJ pain, of which 34.9% were anterior displacements . PosteriWhilst these findings are supportive of disc-condyle incoordination in the majority of TMD patients, it should nonetheless be noted that even individuals with a “normal”  disc position might require TMD advice. In particular, a little more than one out of four joints did not have an abnormal disc position. The diagnostic variability of our sample also reinforces this need for further studies and understanding of diagnosis and treatment decision trees. This reflects the need for adequate clinical exploration and for an imaging prescription as a complement to clarify certain clinical conditions. This also suggests that a careful evaluation of the correlation between imaging and clinical studies is recommended before assuming that evaluation of disc position is a fundamental factor to explain the clinical picture. Early findings on symptom-free populations showing the presence of disc displacement may support this cautionary statement .Altogether, these findings are open to several considerations.First, the fact that an anterior displacement is the most frequent condition can be related with the anatomical peculiarity of the disc. Its biconcave shape, with a thinner posterior than anterior band, may predispose to a natural tendency to “slide” anteriorly. Besides, the anterior and collateral ligaments may tend to “trap” the disc to a more anterior position. The different elastic characteristics of the ligaments, associated with the nonsymmetrical and nonlinear loads over the TMJ between the medial and lateral sides of the joint, could explain why the third most frequent disc position was the partial anterolateral displacement . A partiSecond, a wide biological variability in the disc-condyle relationship exists in the different planes. Based on that, it is recommended that future work seeks to assess the correlation between specific disc displacements and clinical signs and symptoms, given the noisy annoyance represented by click sounds . The worThird, the possible association between disc displacement and some condylar shapes might be considered for future investigations. Some studies found a higher prevalence of anterior disc displacement in convex and rounded condyles, as well as in angled condyles . AnotherFourth, the fact that some patients did not present any imaging abnormalities suggests that images could not be used as a stand-alone diagnostic finding. In 23% of the study joints, the disc-condyle relationship was physiological, as interpreted based on current diagnostic guidelines, and can be taken as an example of the possible usefulness of MRI to exclude intra-articular disorders . A diagnThere is a relevant frequency and variability of combined positional and rotational MRI displacements of the TMJ disc among patients seeking TMD advice. Based on MRIs, about 30% of joints have a physiological disc-condyle relationship. Based on these findings, it is hardly arguable that MRI disc position may have a clear-cut correlation with clinical signs and symptoms. Thus, while it is recommendable that symptom management strategies are not orientated by the position of the disc or by imaging signs, there is surely a need to understand how much of the biological variability of the disc-condyle relationship is actually part of a natural course of joint wear and ageing and how much of it is the result of joint overload.