dataesr/scientific-paragraphs-categorization huggingface dataset:
Equation (  9 ) represents the specific mode's normalized fractional power of the total propagating E-field. The remaining power is either in other guided modes or lost through unguided, radiative modes. During beam propagation, BPM-Matlab can calculate and plot the normalized fractional power in any choice of set of LP modes, independent of fiber used or level of bending present. For example, in Sec. 3. , we will calculate and show the coupling between straight fiber LP modes as a field distribution propagates through a fiber bent in the x and y directions. We can also use the mode solver to study the limitations of the scalar paraxial Helmholtz equation. We calculated the mode field diameter of the fundamental mode of a small strongly guiding waveguide and compared it to the results of simulations in the commercial software Lumerical, which solves for waveguide modes in a fully vectorial, non-paraxial manner.
For light with a wavelength of 1000 nm, the BPM-Matlab estimation of the mode field diameter of an air-clad cylindrical waveguide of refractive index 1. 46 and diameter 400 nm still agreed with that of Lumerical to within 1%, while the same comparison for a waveguide of diameter 300 nm was underestimated by 6%, with the deviation further increasing for decreasing waveguide diameter.
Validation In this section, we present the BPM-Matlab results of simulations with various geometries such as single-mode fibers (SMFs), multimode fibers (MMFs), and multicore fibers (MCFs). These results are validated by comparing them to published experimental, numerical, and theoretical data and results of the commercially available BeamLab toolbox. MMFs are widely studied for their applicability in endoscopic illumination  [14, 46, 47]  and signal collection  [48] [49] [50]. By shaping the light appropriately into the proximal end of a MMF, one can achieve a variety of beam shapes at the distal end, even forming a focal point at a short distance in front of the fiber facet. A larger number of fiber modes provide more degrees of freedom and correspondingly better control of the output field pattern, which increase the complexity and variety of the fiber's beam shaping abilities.
Straight multimode fiber propagation In our first validation model, we simulate launching a Gaussian beam with an arbitrary wavelength λ = 800 nm and beam waist w 0 = 2. 5 µm into a straight 1 mm long MMF of core radius a = 10 µm, n core = 1. 4833, n cl = 1. 4533, and V-number V = 23. 3. Figure  1  shows the normalized intensity profiles at the proximal and distal ends. The input beam is offset by 5 µm along the y-axis and enters the MMF at a 5 • angle to the facet normal in air, corresponding to 3. 37 • inside the fiber due to refraction. For this specific example, executed on a Dell Latitude E6530 laptop PC with an Intel i7-3630QM CPU, BeamLab took 15. 8 minutes and BPM-Matlab took 2. 2 minutes for evaluation with a resolution of ∆x = ∆y = 0. 067 µm and ∆z = 0. 4 µm. The resulting intensity profiles, shown in Fig.
Bent fiber propagation in multi-and single-mode fibers MMFs are sensitive to bending  [15, 41] , which is why most experiments demonstrating beam shaping through MMFs are performed with a fixed fiber. This is not transferable to applied endoscopy, and hence studying the sensitivity of fibers to bending is highly important. It has been shown that some modes are more resilient to bending than others  [45] , which is relevant for practical implementation of MMF beam shaping. Figure  2  shows the simulated mode field intensity profiles of the five lowest order modes of a MMF in a straight and a bent configuration, calculated using BPM-Matlab's mode solver. The fiber has core radius a = 12. 5 µm, cladding refractive index n clad = 1. 52, and NA = 0. 1, where NA = √︂ n 2 core -n 2 clad. The bending radius was set to 1.
24 cm and the wavelength to 1064 nm. The mode profiles of the straight MMF shown in Fig. 2 (a) are consistent with the profiles dictated by analytically calculated profiles based on the well known formulas involving Bessel and modified Bessel functions  [42, 43]. Moreover, the BPM-Matlab results for both bent and straight fibers agree with Ref. [41] , Fig. 4 , demonstrating that bending is modeled correctly. Furthermore, to illustrate that bending loss is correctly estimated in BPM-Matlab, we performed a simulation study of fiber bending loss in a Corning SMF-28 single-mode fiber with core diameter a = 4. 1 µm for two different wavelengths, the results of which are provided in Table  1. For 1320 nm, n clad = 1. 447, NA = 0. 117, and V = 2. 28 while for 1550 nm, n clad = 1. 440, NA = 0. 117, and V = 1.
It has been shown that a MCF with a periodic core pattern, such as the traditional hexagonal pattern, gives rise to significant side lobes in the distal field image  [58]. However, the aperiodicity of patterns such as the Fermat's golden spiral core pattern  [58]  and pseudo-random or random patterns  [54]  have all been shown to reduce the side-lobes. Recent theoretical and experimental studies have shown that a conformationally invariant (bending resilient) MCF can be fabricated with twisted cores, thereby providing promising fibers for lensless endoscopes  [59]. The simulated intensity profiles of the focal spot pattern made in free space near the distal end of a 41 cm long MCF demonstrated in Ref. [59]  using BPM-Matlab are presented in Fig. 5  in the presence and absence of fiber bending and fiber twisting.
Although non-twisted and twisted MCFs provide similar focal patterns when kept straight as seen in Fig. 5 (a,b), Fig. 5(c, d ) indicates that the focal pattern formed by a non-twisted MCF is sensitive to bending, whereas the one corresponding to a twisted MCF stays invariant with respect to bending. These results are congruous with the earlier observations stated in Ref. [59] , demonstrating that BPM-Matlab models twisted fibers correctly.
Conclusion We have presented the application of the Douglas-Gunn Alternating Direction Implicit method to the problem of finite-difference beam propagation in a numerical simulation tool called BPM-Matlab. The tool is capable of modeling light propagation in a wide variety of optical fiber geometries with refractive index profiles of arbitrary shape incorporating fiber bending, twisting, and tapering deformations and solve for modes for arbitrary refractive index profiles even in the presence of bending. It is provided for open-source and gratis download at https://gitlab. gbar. dtu. dk/biophotonics/BPM-Matlab. Due to the use of the DG-ADI method, BPM-Matlab provides fast results with optional CUDA acceleration on GPUs. The simulation tool is compared against state-of-the-art simulation software BeamLab and other relevant experimental and theoretical research outcomes to establish the accuracy and versatility of the code-base.
Initial results based on this work can be found in Refs. [60, 61]. The absence of axial symmetry assumptions in BPM-Matlab enables the user to model any arbitrary refractive index geometries. A few carefully selected cases demonstrating the versatility of the code are shown, and other geometries may easily be simulated by straightforward adaptation of the code. BPM-Matlab is beneficial in a wide variety of fields owing to its ability to model arbitrary refractive indices in both the transverse and longitudinal directions. In imaging modalities, BPM-Matlab could be used in designing experiments based on light delivery through optical fibers such as beam shaping and scanning at fiber distal end for lensless endoscopes utilizing confocal point-scanning microscopy or light-sheet microscopy, fiber-based spatially-offset optical coherence tomography (SO-OCT), etc.
Circular dichroism CD measurements were performed using a JASCO Spectropolarimeter equipped with a thermoelectric temperature controller. Spectra of gp41-TM were recorded at 20˚C in 1 nm steps from 190 to 260 nm in a buffer containing PBS supplemented with 1% n-octyl b-D-glucopyranoside. For thermal denaturation experiments, the ellipticity was recorded at 222 nm with 1˚C steps from 20˚to 95˚C with an increment of 80˚C h À1 , and an averaging time of 30 s/step. For data analysis, raw ellipticity values recorded at 222 nm were converted to mean residue ellipticity.
Isothermal titration calorimetry (ITC) The stoichiometry and binding constants of 2H10 binding to gp41 FP-TM was measured by ITC200 (MicroCal Inc). All samples used in the ITC experiments were purified by SEC in a buffer containing 20 mM Tris pH 8. 0, 100 mM NaCl and 1% n-octyl b-D glucopyranoside and used without further concentration. Samples and were equilibrated at 25˚C before the start of the experiment. The ITC measurements were performed at 25˚C by making 20 2 ml injections of 267 mM 2H10 to 0. 2 ml of 19. 5 mM gp41FP-TM. Curve fitting was performed with MicroCal Origin software. Three experiments were performed, with an average stoichiometry N = 1. 1 +/-0. 2. 2H10 binds to gp41FP-TM with a KD of 2. 1 mM ± 0. 9.
Bio-layer interferometry binding analysis Binding measurements between antibodies (10E8 IgG, LN01 IgG, and 2H10) were carried out on an Octet Red instrument (ForteBio). For the determination of the binding between antibodies and gp41FP-TM, 10E8 IgG or LN01 IgG or 2H10 were labeled with biotin (EZ-Link NHS-PEG4-Biotin) and bound to Streptavidin (SA) biosensors (ForteBio). The biosensors loaded with the antibodies were equilibrated in the kinetic buffer (20 mM Tris pH 8. 0, 100 mM NaCl and 1% n-octyl b-D glucopyranoside) for 200-500 s prior to measuring association with different concentrations of gp41FP-TM for 100-200 s at 25˚C. Data were analyzed using the ForteBio analysis software version 11. 1. 0. 25 (Forte-Bio). For 10E8, the kinetic parameters were calculated using a global fit 1:1 model and 2:1 model.
Crystallization, data collection, and structure determination For crystallization, 1 mg of gp41FP-TM was mixed with 1. 5 mg of 2H10. The complex was purified by SEC on a Superdex 200 column in a buffer containing 100 mM NaCl, 20 mM Tris pH 8,0 and 1% n-octyl b-D-glucopyranoside and concentrated to 7-10 mg/ml. Crystal screening was performed at the EMBL High-Throughput Crystallization Laboratory (HTX lab, Grenoble) in 96-well sitting drop vapor diffusion plates (Greiner). Following manual refinement of crystallization conditions, crystals of gp41FP-TM in complex with 2H10 were grown by mixing 1 ml of protein with 1 ml of reservoir buffer containing 0. 1 M sodium citrate pH 6. 0, 0. 2 M ammonium sulfate, 20% polyethylene glycol 2000 and 0. 1 M NaCl at 20˚C (293 K) in hanging drop vapor diffusion plates.
Before data collection, crystals were flash frozen at 100K in reservoir solution supplemented with 1% n-octyl b-D-glucopyranoside and 25% ethylene glycol for cryo-protection. Data were collected on the ESRF beamline ID30b at a wavelength of 0. 9730 A ˚. Data were processed with the program XDS  (Kabsch, 2010). The data from two crystals were merged with Aimless  (Evans and Murshudov, 2013). The data set displayed strong anisotropy in its diffraction limits and was submitted to the STARANISO Web server  (Tickle et al. , 2018). The merged STARANISO protocol produced a best-resolution limit of 3. 28 A ˚and a worst-resolution limit of 4. 74 A ˚at a cutoff level of 1. 2 for the local I mean / s(I mean ) (note that STARANISO does not employ ellipsoidal truncations coincident with the crystal axes).
The gp41FP-TM-2H10 crystals belong to space group C 2 2 2 1 and the structure was solved by molecular replacement using the program Phaser  (McCoy et al. , 2007)  and pdb entries 1env and 4b50. The model was rebuilt using COOT  (Emsley et al. , 2010)  and refined using Phenix  (Adams et al. , 2010). Data up to 3. 28 A ˚were initially used for model building but were finally truncated to 3. 8 A ˚. Statistics for data reduction and structure refinement are presented in Table  1. One copy of gp41FP-TM in complex with 2H10 are present in the asymmetric unit. Numbering of the nanobody 2H10 was performed according to Kabat. The gp41FP-TM-2H10 complex was refined to 3. 8 A ˚data with an R/Rfree of 26. 6/30. 8%. 99. 6% of the residues are within the most favored and allowed regions of a Ramachandran plot  (Evans and Murshudov, 2013).
Molecular dynamics (MD) simulation Molecular assays Starting from the crystal structure determined herein, we built two molecular assays. The first is based on the crystal structure of gp41FP-TMin complex with 2H10. The disordered FP and TM residues were modeled as helices. The second assay is based on a symmetric gp41 model which was generated from protomer B by applying a three-fold symmetry operation. Missing FP residues 512-517 and TM residues 701-709 were modeled as helices (Figure  4 -figure supplement 1B), and TM residues were modeled based on Env gp41 TM structures (pdb entry 6SNE and 6B3U). All residues were taken in their standard protonation state. The first assay included a fully hydrated membrane composed of 190 cholesterol, 40 1-palmitoyl-2-oleoyl-glycero-3-phosphocholine (POPC), 88 1-palmitoyl-2-oleoyl-sn-glycero-3-phospho-ethanolamine (POPE), 36 1-palmitoyl-2-oleoyl-sn-glycero-3-phospho-L-serine (POPS) and 56 N-stearoyl sphingomyelin, present in the HIV-1 lipid envelope  (Bru ¨gger et al.
Molecular dynamics All simulations were performed using the NAMD 2. 14 program  (Phillips et al. , 2005). Proteins, cholesterol, lipids and ions were described using the CHARMM force field  (Best et al. , 2012; Klauda et al. , 2010; MacKerell et al. , 1998)  and the TIP3P model  (Jorgensen et al. , 1983)  was used for water. MD trajectories were generated in the isobaric-isothermal ensemble at a temperature of 300 K and a pressure of 1 atm. Pressure and temperature were kept constant using the Langevin thermostat and the Langevin piston method  (Feller et al. , 1995) , respectively. Long-range electrostatic interactions were evaluated by the particle-mesh Ewald (PME) algorithm  (Darden et al. , 1993). Hydrogen mass repartitioning  (Hopkins et al. , 2015)  was employed for all simulations, allowing for using a time step of 4 fs.
Acknowledgements WW acknowledges support from the  Institut Universitaire de France (IUF) , from the  European Union 's  Horizon 2020 research and innovation program  under grant agreement No. 681137 ,  H2020  EAVI and the platforms of the Grenoble Instruct-ERIC center (IBS and ISBG;  UMS 3518 CNRS-CEA-UGA-EMBL ) within the  Grenoble Partnership for Structural Biology  (PSB). Platform access was supported by  FRISBI  ( ANR-10-INBS-05-02 ) and GRAL, a project of the  University Grenoble Alpes graduate school (Ecoles Universitaires de Recherche) CBH-EUR-GS  ( ANR-17-EURE-0003 ). IBS is part of the  CEA DRF Interdisciplinary Research Institute of Grenoble (IRIG). JLN acknowledges funding from  Spanish MCIU  ( RTI2018-095624-B-C21 ;  MCIU/AEI/FEDER, UE)  and  Basque Government  ( IT1196-19 ). We thank  Miriam Hock  and  Serafima Guseva  for previous contributions to the project,  Davide Corti  for providing bnAb LN01, the  ESRF-EMBL Joint Structural Biology Group  for access and support at the  ESRF beam lines ,  J Marquez  (EMBL) from the  HTX crystallization facility  and  C Mas  and  J-B Reiser  for assistance on ISBG platforms.
The CESC, which is composed by a SC physical network function (PNF) attached to an execution platform (i. e. micro-server) can "run" several appropriately defined Virtual Network Functions (VNFs) that correlate to the small cell functionality or to specific servicelevel functions. These can comprise radio specific operations, appearing as advanced scheduling algorithms, as well as network functions appearing in a virtualised form. Furthermore, data sets and metric collection for analysis and optimisation purposes, can also be incorporated. For our case, the existing 5G architectures act as a "solid reference point" combining the current 3GPP framework for network management in RAN sharing scenarios  [43]  and the ETSI NFV framework  [44]  for managing virtualised network functions. The CESC offers virtualised computing, storage and radio resources and the CESC cluster is considered as a cloud.
To that end, 5G ESSENCE envisages to virtualize and to partition SC capacity while, at the same time, it aims to support enhanced edge cloud services by enriching the network infrastructure with an edge cloud. In particular, the 5G ESSENCE framework combines the MEC and NFV concepts with SC virtualisation in 5G networks  [56]  and enhances them for supporting multi-tenancy and for increasing the network capacity and the available computational resources at the edge  [38]. At the network's edge, each CESC is able to host one or more service VNFs, directly applying to the users of a specific operator. Similarly, VNFs can be instantiated inside the Main DC (Data Centre) and be parts of a Service Function Chaining (SFC) procedure. The Light DC can be used to implement different functional splits of the SCs as well as to support the mobile edge applications of the end-users.
The linking between the SC Physical Network Functions (PNFs) and the SC VNFs can be performed through the network Functional Application Platform Interface (nFAPI). The second tier proposed by the corresponding architecture (i. e. , the Main DC), can accommodate more computation-intensive tasks and processes that have to be centralised with the intention of realising a broader view of the underlying infrastructure. This involves the cSD-RAN (centralised Software-Defined Radio Access Network) controller which is delivered as a dedicated VNF running in the Main DC and makes control plane decisions for all the radio elements in the geographical area of the CESC cluster, including the centralised Radio Resource Management (cRRM) over the entire CESC cluster, also in a multi-RAT environment. As the geographic area of the cell cluster is at the edge of the 5G network, both main and light DCs can be logically grouped together to form an edge DC.
The Virtualised Infrastructure Manager (VIM) is responsible for controlling and optimising the operation of the NFV Infrastructure (NFVI), which includes the computing, storage and network resources of the Edge DC. The Orchestration module includes the Service Orchestrator (SO) and the Resource Orchestrator (RO) as part of Open Source MANO (MANagement and Orchestration)  [57] , in charge of configuring in one go, both the compute resources and the network resources, and the Virtual Infrastructure Manager (VIM) in combination with OpenStack [58], taking care of the computing resources, and OpenDaylight [59], taking care of flows, connections and communication between VNFs (and maybe other resources).
As of the localisation and messaging service, the proposed solution, called as FeedSync (FS), is based upon an innovative publish subscribe modular solution that operates on top of the 5G ESSENCE leveraging the flexibility of 5G architecture. FeedSync is a web server application for content distribution; it is deployed on a classical server and interacts with a database system management for storing data. The whole system is delimited by the corresponding server and the database, where the former delivers a suitable interface for interacting with client applications (web and mobile device applications) in diverse settings. FeedSync can be simultaneously deployed on various servers and the content can be distributed. The corresponding synchronisation function is realised through the data base system, while an offline mode is also offered by the client-side database.
When a connection link is lost, each connected device can have a client database management and can continue storing new content within, until the server is back online, and the synchronisation is activated again. In addition to classical chat services, FeedSync ensures a set of features including, among others: Blue Force Tracking (BFT) information; geo-located multi-part content; direct communications between terminals; capability to share content; management service, and; geo-content management. From a standardisation perspective, this solution ensures compatibility with current and future standards, by operating as an application on top of the 5G ESSENCE architecture. Moreover, being completely relying on software allows easy virtualisation and deployment of this framework leveraging the SDN and VNF paradigms.
Each network slice is composed of an allocated data rate over a coverage area (which is mapped by the cSD-RAN Controller to a portion of CESC radio resources) and an allocated of cloud resources (which is mapped to processing power/storage capabilities in the Edge DC). For the service of PS organisations, normal operations require a certain amount of access capacity and communications features (e. g. , group communications capabilities) supported in the area of the CESC cluster. This requirement can be mapped to a number of radio KPIs in the CESCs and the deployment of Group Communication service instances at the edge for multimedia and MC Application Servers (ASs) for voice with enhanced responsiveness. In addition to the QoS guarantees for each tenant, the deployment owner has to assure the required levels of isolation in the provisioning of the network slices.
OSM is delivering an open source Management and Orchestration (MANO) stack aligned with ETSI NFV Information Models. As an operator-led community, OSM is offering a production-quality open source MANO stack that meets the requirements of commercial NFV networks. Juju has adopted a domain neutral model and does not encode policy. It can therefore be described as a generic VNF Manager (VNFM) and not a VNF Orchestrator. Juju is useful across many domains and is being adopted in big data, cloud infrastructure, Platform as-a-Service (PaaS) and other scale-out scenarios. OpenStack is the only virtual infrastructure manager in OPNFV. The role of the virtual infrastructure manager is to configure the compute, hypervisor and infrastructure network domains. When there is no SDN controller, it can also configure the underlying physical networks.
g. LightDC with small cell) as well extending a slice with new heterogeneous resources (e. g. LightDC with small cell + LightDC with WiFi). However, the real set of functionalities supporting slicing, largely depend on the selected SD-RAN controller platform. The actual use case is implemented by using 5G-EmPOWER and open-source SDRs (i. e. : OAI, srsLTE) available for the integration of research results. The use case utilises the 5G-EmPOWER Controller  [65, 66]  which is responsible for the management of the heterogeneous RANs. The 5G-EmPOWER Controller supports multiple virtual networks -or tenants-on top of the same physical infrastructure (here a tenant is conceived as a virtual network with its own set of end-points). Network applications (Network Apps) run on top of the Runtime in their own slice of resources and exploit its programming primitives through either a REST API or a native Python API.
The MCPTT-enabled architecture (and correspondingly also the FS solution) involves the following elements: MCPTT clients (devices of first responders and personnel at the central station) and server (providing connection to clients and control-plane operations), media distribution unit (for media transmission on the data-plane), media mixer and the MCPTT user database (for profiling, authentication and authorization (AA) and security). In detail, there are more options for the virtualisation of the MCPTT service architecture. The basic option is with all the functional blocks of the service packed in a single VNF. This configuration simplifies the connection between blocks, but provides little flexibility for scaling possibilities. While, the ultimate step of separation corresponds to the separation of also the data and control planes of the MCPTT service, bringing the data plane and needed control plane elements to the edge to reduce the transmission latencies.