Dense Topologies Research Articles

Crystal Chemistry and Structural Complexity of the Uranyl Molybdate Minerals and Synthetic Compounds

This paper reviews not the largest, but at the same time quite an interesting, group of natural and synthetic uranyl molybdate compounds. Nowadays, nine minerals of U and Mo are known, but the crystal structures have only been reported for five of them. Almost an order of magnitude more (69) synthetic compounds are known. A significant discrepancy in the topological types for natural and synthetic phases is shown, which is most likely due to elevated temperatures of laboratory experiments (up to 1000 °C), while natural phases apparently grow at significantly lower temperatures. At the same time, the prevalence of dense topologies (with edge-sharing interpolyhedral linkage) among natural phases can be noted, which is fully consistent with other recently considered mineral groups. Uranyl molybdates demonstrate several similarities with compounds of other U-bearing groups; however, even topological matches do not lead to the appearance of completely isotypic compounds. Structural complexity calculations confirm, in general, crystal chemical observations. Considering the prevalence of dense structures in which coordination polyhedra of uranium and molybdenum are connected through common edges as well as framework architectures, one can expect a less significant influence of interlayer species on the formation of the crystal structure than the main U-bearing complexes. The more structural complexity of the uranyl molybdate units, the more complex of the entire crystal structure is. In addition, there is a tendency for complexity to increase with increasing density of the complex; the simplest structures are vertex-shared, while the complexity increases with the appearance of common edges.

Low-cost and high-performance channel access strategies for Internet of Nano-Things applications

Nanodevices, which are only a few nanometers (nm) in size, are interconnected to form the Internet of Nano-Things (IoNT) that performs complex operations. One of the key challenges is ensuring efficient channel access control for nanodevices, especially when dealing with large network sizes. Medium access control (MAC) protocols serve this purpose, but traditional approaches are not practical due to the inherent constraints of nanodevices. In this paper, we propose two novel MAC protocols for IoNT applications. The first protocol, Slot Assignment-Based (SAB) MAC, is a contention-free method relying on scheduling. In contrast to its counterparts, it enables simultaneous packet transmission through Time Spread On-Off Keying (TS-OOK), effectively minimizing the collision probability and end-to-end delay. The second protocol, Receiver-Initiated and Directed (RID) MAC, adopts a contention-based approach to reduce unnecessary transmissions caused by flooding. It achieves this by limiting the number of active nanodevices within a time interval using directional antennas without incurring scheduling overhead. We evaluated the performance of these protocols through comprehensive simulations, comparing them with counterparts in terms of packet transmission success, energy consumption, end-to-end delay and setup overhead. In dense topologies, SAB-MAC outperforms Transparent (TRN) MAC by approximately twice the packet transmission success reaching up to 95.73%. It accomplishes this with 1000 times lower end-to-end delay and reduced setup overhead than Time Division Multiple Access (TDMA). Conversely, RID-MAC achieves twice the packet transmission success of TRN-MAC and ten times that of unicast-based methods, all with lower end-to-end delay and nearly equivalent energy consumption. Consequently, due to its superior performance SAB-MAC is the optimal choice for communication between nanorouters (NRs). However, RID-MAC is more suitable for communication between nanosensors (NSs), as it incurs no setup overhead.

Search for dark matter produced in association with a dark Higgs boson decaying into W+W− in the one-lepton final state at sqrt{s} = 13 TeV using 139 fb−1 of pp collisions recorded with the ATLAS detector

Several extensions of the Standard Model predict the production of dark matter particles at the LHC. A search for dark matter particles produced in association with a dark Higgs boson decaying into W+W− in the {ell}^{pm}nu q{overline{q}}^{prime }, final states with ℓ = e, μ is presented. This analysis uses 139 fb−1 of pp collisions recorded by the ATLAS detector at a centre-of-mass energy of 13 TeV. The W± → qoverline{q^{prime }} decays are reconstructed from pairs of calorimeter-measured jets or from track-assisted reclustered jets, a technique aimed at resolving the dense topology from a pair of boosted quarks using jets in the calorimeter and tracking information. The observed data are found to agree with Standard Model predictions. Scenarios with dark Higgs boson masses ranging between 140 and 390 GeV are excluded.

A Discussion on Ultrahigh Efficiency and Ultrahigh Power Density DC–DC Converter Technologies

This paper discusses the challenges in achieving ultra-high efficiency, defined here as higher than 99% efficiency, as well as high power density of more than 2kW/in <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> for DC-DC converters. For simplicity, our discussion focuses on 48V to 12V converters aimed primarily at data center applications, but the concepts discussed are broadly applicable to DC-DC conversion at a wide range of voltage levels. This paper will present a review of the fundamental sources of losses in DC-DC converters and how to minimize them, as well as a more in-depth look at some of the most efficient and dense topologies presented in literature thus far. Based on this analysis and review the key concepts that enable DC-DC converters to achieve higher than 99% efficiency at a power density of more than 2kW/in <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> will be summarized which include: easily paralleled “modular” designs to reduce conduction loss, multi-level structures that reduce individual component voltage stresses, utilizing lower switching frequencies to reduce switching and quiescent losses, operating with full duty ratio to ensure maximum utilization of the power components, and utilizing novel circuit topologies that nearly eliminate bulky, lossy magnetic components when compared with conventional topologies.

Parallel Load Balancing on constrained client-server topologies

We study parallel Load Balancing protocols for the client-server distributed model defined as follows. There is a set C of n clients and a set S of n servers where each client has (at most) a constant number d⩾1 of requests that must be assigned to some server. The client set and the server one are connected to each other via a fixed bipartite graph: the requests of client v can only be sent to the servers in its neighborhood N(v). The goal is to assign every client request so as to minimize the maximum load of the servers.In this setting, efficient parallel protocols are available only for dense topologies. In particular, a simple protocol, named raes, has been recently introduced by Becchetti et al. [1] for regular dense bipartite graphs. They show that this symmetric, non-adaptive protocol achieves constant maximum load with parallel completion time O(log⁡n) and overall work O(n), w.h.p.Motivated by proximity constraints arising in some client-server systems, we analyze raes over almost-regular bipartite graphs where nodes may have neighborhoods of small size. In detail, we prove that, w.h.p., the raes protocol keeps the same performances as above (in terms of maximum load, completion time, and work complexity, respectively) on any almost-regular bipartite graph with degree Ω(log2⁡n).Our analysis significantly departs from that in [1] since it requires to cope with non-trivial stochastic-dependence issues on the random choices of the algorithmic process which are due to the worst-case, sparse topology of the underlying graph.

Policy-rich interdomain routing with local coordination

The Internet has evolved from a hierarchical and multi-tiered interconnection network to a meshed network, where autonomous systems (ASes) are interconnected with a dense topology and more and more potential paths can be used to reach a destination. However, routing policies are the key to enable these potential paths and to allow the selection of these paths. While the Gao–Rexford guidelines provide routing policies that derive a safe routing system, those potential paths are not enabled by the Gao–Rexford guidelines. A survey on deployed routing policies has shown that a significant portion of networks or ASes do not follow the Gao–Rexford guidelines completely. In this paper, we propose to broaden routing policies that enable the availability of diverse paths and provide flexibility in selecting these paths. We systematically bring out more and more flexible routing policies to implement various routing requirements. More specifically, we propose FlexibleRC, PeerBoost and hierarchical sibling routing policies and derive sufficient conditions for guaranteeing the routing system derived by these routing policies to be safe. The sufficient conditions can be verified through coordination among neighboring ASes. Thus, local coordination guarantees the routing system to be safe.

Visualization of clinical teaching citations using social network analysis

BackgroundAnalyzing the previous research literature in the field of clinical teaching has potential to show the trend and future direction of this field. This study aimed to visualize the co-authorship networks and scientific map of research outputs of clinical teaching and medical education by Social Network Analysis (SNA).MethodsWe Identified 1229 publications on clinical teaching through a systematic search strategy in the Scopus (Elsevier), Web of Science (Clarivate Analytics) and Medline (NCBI/NLM) through PubMed from the year 1980 to 2018.The Ravar PreMap, Netdraw, UCINet and VOSviewer software were used for data visualization and analysis.ResultsBased on the findings of study the network of clinical teaching was weak in term of cohesion and the density in the co-authorship networks of authors (clustering coefficient (CC): 0.749, density: 0.0238) and collaboration of countries (CC: 0.655, density: 0.176). In regard to centrality measures; the most influential authors in the co-authorship network was Rosenbaum ME, from the USA (0.048). More, the USA, the UK, Canada, Australia and the Netherlands have central role in collaboration countries network and has the vertex co-authorship with other that participated in publishing articles in clinical teaching. Analysis of background and affiliation of authors showed that co-authorship between clinical researchers in medicine filed is weak. Nineteen subject clusters were identified in the clinical teaching research network, seven of which were related to the expected competencies of clinical teaching and three related to clinical teaching skills.ConclusionsIn order to improve the cohesion of the authorship network of clinical teaching, it is essential to improve research collaboration and co-authorship between new researchers and those who have better closeness or geodisk path with others, especially those with the clinical background. To reach to a dense and powerful topology in the knowledge network of this field encouraging policies to be made for international and national collaboration between clinicians and clinical teaching specialists. In addition, humanitarian and clinical reasoning need to be considered in clinical teaching as of new direction in the field from thematic aspects.

Search for Dark Matter Produced in Association with a Dark Higgs Boson Decaying into W^{±}W^{∓} or ZZ in Fully Hadronic Final States from sqrt[s]=13 TeV pp Collisions Recorded with the ATLAS Detector.

Several extensions of the Standard Model predict the production of dark matter particles at the LHC. An uncharted signature of dark matter particles produced in association with VV=W^{±}W^{∓} or ZZ pairs from a decay of a dark Higgs boson s is searched for using 139 fb^{-1} of pp collisions recorded by the ATLAS detector at a center-of-mass energy of 13TeV. The s→V(qq[over ¯])V(qq[over ¯]) decays are reconstructed with a novel technique aimed at resolving the dense topology from boosted VV pairs using jets in the calorimeter and tracking information. Dark Higgs scenarios with m_{s}>160 GeV are excluded.

Innovative Techniques for Attack Detection in Wireless Ad-Hoc Networks

As a result of the inherent weaknesses of the wireless medium, ad hoc networks are susceptible to a broad variety of threats and assaults. As a direct consequence of this, intrusion detection, as well as security, privacy, and authentication in ad-hoc networks, have developed into a primary focus of the current study. This body of research aims to identify the dangers posed by a variety of assaults that are often seen in wireless ad-hoc networks and provide strategies to counteract those dangers. The Black hole assault, Wormhole attack, Selective Forwarding attack, Sybil attack, and Denial-of-Service attack are the specific topics covered in this proposed work. In this paper, we describe a trust-based safe routing protocol with the goal of mitigating the interference of black hole nodes while routing in mobile ad-hoc networks. The overall performance of the network is negatively impacted when there are black hole nodes in the route that routing takes. As a result, we have developed a routing protocol that reduces the likelihood that packets would be lost because of black hole nodes. This routing system has been subjected to experimental testing to guarantee that the most secure path will be selected for the delivery of packets between a source and a destination. The invasion of wormholes into wireless networks results in the segmentation of the network as well as a disorder in the routing. As a result, we provide an effective approach for locating wormholes by using ordinal multi-dimensional scaling and round-trip duration in wireless ad hoc networks with either sparse or dense topologies. Wormholes that are linked by both short-route and long-path wormhole linkages may be found using the approach that was given. To guarantee that this ad hoc network does not include any wormholes that go unnoticed, this method is subjected to experimental testing. To fight against selective forwarding attacks in wireless ad-hoc networks, we have developed three different techniques. The first method is an incentive-based algorithm that makes use of a reward-punishment system to drive cooperation among three nodes for forwarding messages in crowded ad-hoc networks. A unique adversarial model has been developed by our team, and inside it, three distinct types of nodes and the activities they participate in are specified. We have demonstrated that the proposed method that is based on incentives prevents nodes from adopting individualistic behaviour, which ensures cooperation in the process of packet forwarding. In the second algorithm, a game theoretic model is proposed that uses non-cooperative game theory to ensure that intermediate nodes in resource-constrained ad-hoc networks faithfully forward packets.

Optimization Algorithms for Graph Laplacian Estimation via ADMM and MM

In this paper, we study the graph Laplacian estimation problem under a given connectivity topology. We aim at enriching the unified graph learning framework proposed by Egilmez et al. and improve the optimality performance of the combinatorial graph Laplacian (CGL) case. We apply the well-known alternating direction method of multipliers (ADMM) and majorization–minimization (MM) algorithmic frameworks and propose two algorithms, namely, GLE-ADMM and GLE-MM, for graph Laplacian estimation. Both algorithms can achieve an optimality gap as low as $10^{-4}$ , around three orders of magnitude more accurate than the benchmark. In addition, we find that GLE-ADMM is more computationally efficient in a dense topology (e.g., an almost complete graph), while GLE-MM is more suitable for sparse graphs (e.g., trees). Furthermore, we consider exploiting the leading eigenvectors of the sample covariance matrix as a nominal eigensubspace and propose a third algorithm, named GLENE, which is also based on ADMM. Numerical experiments show that the inclusion of a nominal eigensubspace significantly improves the estimation of the graph Laplacian, which is more evident when the sample size is smaller than or comparable to the problem dimension.

Joint User Association and Power Allocation for Millimeter-Wave Ultra-Dense Networks

To meet the demand of various high-speed data rate services as well as serving an exponential increment of mobile devices, millimeter-Wave (mmWave) communication in ultra-dense networks (UDNs) has been considered as a promising technology for future wireless communication systems. By deploying multiple small-cell base stations (SBSs), the dense topology combining high frequency mmWave is expected to grow not only the users (UEs) throughput but also the energy efficiency (EE) of the whole networks. Exploiting the benefits from mmWave and UDNs, in this paper, we introduce a new approach for jointly optimizing SBS-UE association and power allocation to maximize the system EE while guaranteeing the quality of service (QoS) constraints for each UE. Specifically, the throughput fairness among UEs is also taken into account by formulating UE throughput maxmin problem. Unfortunately, such SBS-UE association problem poses a new challenge since it reflects as a complex mixed-integer non-convex problem. On the other hand, the power allocation problem is in nonconvexity structure, which is impossible to handle with the association problem concurrently. Tackling those issues, an alternating descent method is proposed to separate the primal optimization problem into two subproblems and handle one-by-one at each iteration. In particular, the SBS-UE association problem is reformulated using the penalty approach. Then, successive convex programming is developed to convert non-convex problem into the simple convex quadratic functions at each iteration. Numerical results are provided to demonstrate the convergence and low-complexity of our proposed schemes, where the increment of the objective function is guaranteed at each iteration.

Cooperative Beamforming With Predictive Relay Selection for Urban mmWave Communications

While millimeter wave (mmWave) communications promise high data rates, their sensitivity to blockage and severe signal attenuation presents challenges in their deployment in urban settings. To overcome these effects, we consider a distributed cooperative beamforming system, which relies on static relays deployed in clusters with similar channel characteristics, and where, at every time instance, only one relay from each cluster is selected to participate in beamforming to the destination. To meet the quality-of-service guarantees of the network, a key prerequisite for beamforming is relay selection. However, as the channels change with time, relay selection becomes a resource demanding task. Indeed, estimation of channel state information for all candidate relays, essential for relay selection, is a process that takes up bandwidth, wastes power and introduces latency and interference in the network. We instead propose a unique, predictive scheme for resource efficient relay selection, which exploits the special propagation patterns of the mmWave medium, and can be executed distributively across clusters, and in parallel to optimal beamforming-based communication. The proposed predictive scheme efficiently exploits spatiotemporal channel correlations with current and past networkwide Received Signal Strength (RSS), the latter being invariant to relay cluster size, measured sequentially during the operation of the system. Our numerical results confirm that our proposed relay selection strategy outperforms any randomized selection policy that does not exploit channel correlations, whereas, at the same time, it performs very close to an ideal scheme that uses complete, cluster size dependent RSS, and offers significant savings in terms of channel estimation overhead, providing substantially better network utilization, especially in dense topologies, typical in mmWave networks.

A Multicast Technique for Fixed and Mobile Optical Wireless Backhaul in 5G Networks

The data demand for 5G networks is expected to be much higher than current throughput requirements. To meet this demand, a dense topology of interlinked small cells is needed. Laying new copper and fiber in such a dense network would be cost prohibitive. There is, therefore, an urgent need for high capacity wireless point-to-multipoint backhaul solutions. In this paper, we provide a compendium of solutions for ultrahigh data rate physical-layer broadcast and multicast using free space optics in 5G backhaul networks. We show that the problem of optimal multicast in mobile scenarios with highly directional optical links is a time-dependent prize collecting traveling salesman problem which is NP-hard. In formulating our problem, we develop a novel prize assignment strategy that guarantees the selection of mutually non-disjoint multicast sets. Due to the problem being NP-hard, we provide several potential heuristics for multicast in fixed and mobile scenarios, and present a comprehensive performance evaluation of the developed schemes.

Enhanced capital-asset pricing model for the reconstruction of bipartite financial networks.

Reconstructing patterns of interconnections from partial information is one of the most important issues in the statistical physics of complex networks. A paramount example is provided by financial networks. In fact, the spreading and amplification of financial distress in capital markets are strongly affected by the interconnections among financial institutions. Yet, while the aggregate balance sheets of institutions are publicly disclosed, information on single positions is mostly confidential and, as such, unavailable. Standard approaches to reconstruct the network of financial interconnection produce unrealistically dense topologies, leading to a biased estimation of systemic risk. Moreover, reconstruction techniques are generally designed for monopartite networks of bilateral exposures between financial institutions, thus failing in reproducing bipartite networks of security holdings (e.g., investment portfolios). Here we propose a reconstruction method based on constrained entropy maximization, tailored for bipartite financial networks. Such a procedure enhances the traditional capital-asset pricing model (CAPM) and allows us to reproduce the correct topology of the network. We test this enhanced CAPM (ECAPM) method on a dataset, collected by the European Central Bank, of detailed security holdings of European institutional sectors over a period of six years (2009-2015). Our approach outperforms the traditional CAPM and the recently proposed maximum-entropy CAPM both in reproducing the network topology and in estimating systemic risk due to fire sales spillovers. In general, ECAPM can be applied to the whole class of weighted bipartite networks described by the fitness model.

The Impact of a Sparse Migration Topology on the Runtime of Island Models in Dynamic Optimization

Island models denote a distributed system of evolutionary algorithms which operate independently, but occasionally share their solutions with each other along the so-called migration topology. We investigate the impact of the migration topology by introducing a simplified island model with behavior similar to lambda islands optimizing the so-called Maze fitness function (Kötzing and Molter in Proceedings of parallel problem solving from nature (PPSN XII), Springer, Berlin, pp 113–122, 2012). Previous work has shown that when a complete migration topology is used, migration must not occur too frequently, nor too soon before the optimum changes, to track the optimum of the Maze function. We show that using a sparse migration topology alleviates these restrictions. More specifically, we prove that there exist choices of model parameters for which using a unidirectional ring of logarithmic diameter as the migration topology allows the model to track the oscillating optimum through nMaze-like phases with high probability, while using any graph of diameter less than cln n for some sufficiently small constant c>0 results in the island model losing track of the optimum with overwhelming probability. Experimentally, we show that very frequent migration on a ring topology is not an effective diversity mechanism, while a lower migration rate allows the ring topology to track the optimum for a wider range of oscillation patterns. When migration occurs only rarely, we prove that dense migration topologies of small diameter may be advantageous. Combined, our results show that the sparse migration topology is able to track the optimum through a wider range of oscillation patterns, and cope with a wider range of migration frequencies.

Topology optimization of multiphase architected materials for energy dissipation

In this article, we study the computational design of multiphase architected materials comprising a stiff phase, a dissipative phase, and void space, with enhanced vibration damping characteristics under wave propagation. We develop a topology optimization framework that maximizes a figure of merit comprising of effective stiffness, density and effective damping. We also propose novel material interpolation strategies to avoid the blending of different phases at any given point in the design domain. This is achieved by carefully defining different penalization schemes for different components of the merit function. The effective stiffness of the periodic multiphase material is calculated using homogenization theory and the Bloch–Floquet theorem is used to obtain its damping capacity, allowing for the investigation of the effect of wave directionality, material microarchitecture and intrinsic material properties on the wave attenuation characteristics. It is shown that the proposed topology optimization framework allows for systematic tailoring of microstructure of the multiphase materials for wide ranges of frequencies and densities and results in the identification of optimized multiphase cellular designs with void space that are superior to fully dense topologies.

Cooperative resynchronization to improve the reliability of colocated IEEE 802.15.4 -TSCH networks in dense deployments

With the large adoption of small and smart objects, the interest of researchers to define new protocols to meet Internet of Things (IoT) requirements is growing. In particular, the Industrial Internet of Things (IIoT) aims to provide high reliability and upper bounded end-to-end latency while interconnecting a large collection of sensors and actuators. The TimeSlotted Channel Hopping (TSCH) mode of IEEE 802.15.4 exploits a slow channel hopping approach to combat efficiently external interference (e.g. Wi-Fi, Bluetooth). We envision in the future very dense deployments and we investigate here the mutual influence among different colocated TSCH networks. We first study analytically with a simple model the performance of several TSCH networks, able or not to be synchronized with each other. We emphasize the multiplication of collisions, exacerbated by clock drifts when no cooperation is achieved. We also highlight experimentally that a mutual synchronization improves very significantly the reliability. We propose here a mechanism to re-synchronize distributively the border routers of different TSCH networks. Our thorough experimental evaluation illustrates the relevance of our approach, able to guarantee high-reliability, even in very dense topologies.

Collaborative Topology Control for Many-to-One Communications in Wireless Sensor Networks

Topology control is relevant in wireless sensor network because of two reasons, namely minimal sensor coverage and power constraints. The former condition is typically satisfied by high-density deployment, whereas the latter mainly concerns with the control protocol design that is adaptable. Controlling communication topology is at the center of the efforts to optimize network performance while improving energy conservation. A dense topology often results in high interference and lower spatial reuse thus reduced capacity, while sparse topology is susceptible to network partitioning and sub-optimal path selection from the routing layer. Topology control has been extensively studied in both flat and hierarchical network by mean of power adjustment and clustering, respectively. Despite a common goal of making the topology less complex both techniques differ in their approach. While the focus of clustering is to form a connected backbone which consists of a minimum subset of nodes, i.e., dominating set, power adjustment focuses on minimizing energy consumption. Combining both approaches remains a relatively lesser explored area. We proposed a hybrid framework called collaborative topology control protocol, which combines dominating set-based clustering and transmission power adjustment. The protocol operates in two stages. During the first stage, a parameterized minimum virtual connected dominating set algorithm is executed to obtain clusters of various desirable properties. In the second stage, each cluster-head executes a distributed power adjustment algorithm. The simulation results show that the proposed topology control framework is capable of versatile performance in terms of transmission range/energy cost, the number of neighbors, edges, and hop distance. Moreover, the topology construction process uses the locally available information only with minimal communication overhead.

On the Stability of a Full-Duplex Aloha Network

This letter offers the first characterization of the stability for full-duplex (FD) large size networks. Through stochastic geometry tools, key performance metrics such as delay and maximum stable arrival rate are derived for the nonsaturated system and compared with a half-duplex counterpart, also accounting for imperfect self-interference cancellation. This analysis better identifies that the FD advantage is prominent for sparse networks, whereas in dense topologies, residual self-interference may hinder achievable gains.

Implementation and Analysis of Density based Location Aware Routing in Intermittently Connected MANETs

Mobile Ad-Hoc Networks (MANETS)[7] are an emerging technology that allows establishing instant communication infrastructures for civilian and military applications. An Intermittently Connected Mobile Ad hoc Networks (ICMANET)[4] operates in environments where the nodes do not form a completely connected network. Existing geographical routing protocol like location-aware routing for delay-tolerant networks (LAROD)[1,3] enhanced with a location service has shown to work well in IC-MANET. But the challenge here is to design a routing protocol to handle intermittently connectivity and dense/sparse topologies and also the performance of this geographical routing protocol degrades with varying network node densities such as sparse and dense topologies. For sparse systems, distribution of location information will probably be very slow. For dense systems, the transfer of location data may start to consume too much bandwidth locally at the dense areas. In this work, we propose a density based geographical routing algorithm called density based location-aware routing for delay tolerant networks (DLAROD). D-LAROD calculates the density of the network based on location of the neighboring nodes information that counter for every route update that is performed at the time of route discovery process. The D-LAROD scheme is compared with the existing LAROD protocol[1] and is shown to have a competitive edge, both in terms of delivery ratio and overhead.