DECOM - Artigos publicados em periódicos

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Toward an efficient data dissemination protocol for vehicular ad-hoc networks.
(2022) Guidoni, Daniel Ludovico; Gottsfritz, Euclydes Nasorri; Meneguette, Rodolfo Ipolito; Silva, Cristiano Maciel da; Rocha Filho, Geraldo Pereira; Souza, Fernanda Sumika Hojo de
Data Dissemination protocols are used for several vehicular applications, varying from warning messages to real-time video delivery. The majority of literature solutions consider the distance from the sender to choose the vehicle to forward the message. Basically, the solutions introduce a delay in the forwarding procedure, which is inversely proportional to the distance from the sender vehicle. In order to improve the forwarding procedure, this work introduces the concept of Road Covered Area to improve the overall data dissemination process and we describe how to calculate the road covered area by a node transmission. We present the D&RCA, the combination of Distance and Road Covered Area strategies to enhance the re-transmission during communication. Instead of considering the distance, we propose a function to combine the distance and road covered area to introduce a small delay before re-transmissions. We compare the proposed protocol with literature solutions considering the metrics of number of collisions, network coverage and communication latency for different density of vehicles in the network. When the network has 700 vehicles/km2 , the data dissemination latency and number of collisions of the proposed D&RCA is, respectively, 1.24 and 1.32 times smaller than the literature solutions. When we increase the density of vehicles, all evaluated solutions present a network coverage above 90%.
A variable neighborhood search-based algorithm with adaptive local search for the vehicle routing problem with time windows and multi-depots aiming for vehicle fleet reduction.
(2023) Bezerra, Sinaide Nunes; Souza, Marcone Jamilson Freitas; Souza, Sérgio Ricardo de
This article addresses the Multi-Depot Vehicle Routing Problem with Time Windows with the minimization of the number of used vehicles, denominated as MDVRPTW*. This problem is a variant of the classical MDVRPTW, which only minimizes the total traveled distance. We developed an algorithm named Smart General Variable Neighborhood Search with Adaptive Local Search (SGVNSALS) to solve this problem, and, for comparison purposes, we also implemented a Smart General Variable Neighborhood Search (SGVNS) and a General Variable Neighborhood Search (GVNS) algorithms. The SGVNSALS algorithm alternates the local search engine between two different strategies. In the first strategy, the Randomized Variable Neighborhood Descent method (RVND) performs the local search, and, when applying this strategy, most successful neighborhoods receive a higher score. In the second strategy, the local search method is applied only in a single neighborhood, chosen by a roulette method. Thus, the application of the first local search strategy serves as a learning method for applying the second strategy. To test these algorithms, we use benchmark instances from MDVRPTW involving up to 960 customers, 12 depots, and 120 vehicles. The results show SGVNSALS performance surpassed both SGVNS and GVNS concerning the number of used vehicles and covered distance. As there are no algorithms in the literature dealing with MDVRPTW*, we compared the results from SGVNSALS with those of the best-known solutions concerning these instances for MDVRPTW, where the objective is only to minimize the total distance covered. The results showed that the proposed algorithm reduced the vehicle fleet by 91.18% of the evaluated instances, and the fleet size achieved an average reduction of up to 23.32%. However, there was an average increase of up to 31.48% in total distance traveled in these instances. Finally, the article evaluated the contribution of each neighborhood to the local search and shaking operations of the algorithm, allowing the identification of the neighborhoods that most contribute to a better exploration of the solution space of the problem.
Collecting large volume data from wireless sensor network by drone.
(2023) Silva, Rone Ilídio da; Rezende, Josiane da Costa Vieira; Souza, Marcone Jamilson Freitas
Data collection is the most important task in wireless sensor networks (WSN). Each sensor node has to send the sensed data to a special node called sink, which is the user interface. The sensor nodes far from the sink send data to intermediate nodes that forward it by multi-hop data paths. This characteristic leads to higher energy consumption in the sensor nodes close to the sink since they have to relay data from all other sensor nodes. The literature presents several studies that use mobile sinks for data collection to reduce the number of hops in the data paths and distributes the energy consumption, considering that the nodes close to the mobile sink change. However, the majority of these studies consider only the network limitation, such as energy. Furthermore, they also consider sensor nodes sending only one data packet to the mobile sink. This work assumes a quad-copter drone as a mobile sink and sensor nodes having several data packets to send to the sink. We propose two GRASP-based heuristics to define drone tours for data collection. Since this vehicle has limited flight time, the primary metric analyzed here is the overall data collection time. Furthermore, they guarantee that the mobile sink will stay a minimal time inside the radio range of each sensor node to ensure that all of them will have enough time to send all data. The heuristics achieve this guarantee by looking for a subset of locations, among the infinite points inside the monitored area, where the drone will hover for data gathering. Hence, the proposed heuristics have to search for good locations to reduce the data gathering time and define the shortest path to reduce the trip time. Simulated experiments showed that the proposed GRASP-based heuristics outperformed the greed algorithm found as state of the art for this type of scenario, mainly when the volume of data stored in each sensor node is high.
Lexicographic goal programming approach for a short-term mining planning problem.
(2023) Martins, Aldrin Gustavo; Souza, Marcone Jamilson Freitas
This article addresses a short-term mining planning problem. There are four objectives to be minimized: the deviations in grades and ore proportion in particle size ranges of the plant goals, the deviation in the waste mass to achieve the stripping rate, and the number of truck trips between mining fronts and discharges. The problem was solved through the lexicograph- ical goal programming (LGP) method, which generates solutions that can guarantee a more comprehensive analysis of the decision-making process. The LGP method was tested by using several scenarios of a Brazilian mining company. These scenarios differ in the number of excavators and the toler- ances concerning meeting the plants’ ore grades. In the results, the impact on the values of the other objectives is analysed of varying the number of excavators and the tolerances in the plants’ grade targets.
Localização de mamógrafos : um estudo de caso para novos investimentos em Rondônia.
(2023) Paiva, Jéssica Natália Miranda; Rosa, Patrick Moreira; Penna, Puca Huachi Vaz; Monteiro, Janne Cavalcante; Lisboa, Maillene Rodrigues; Souza, Marcone Jamilson Freitas
O acesso a mamografia é diretriz estruturante do cuidado às mulheres no diagnóstico precoce do câncer de mama, devendo estar acessível a 60 km, no máximo, no Brasil. No entanto, essa não é a realidade para parte da população brasileira. Neste trabalho, trata-se o problema de localização de mamógrafos no Sistema Público de Saúde do Estado de Rondônia. O objetivo foi desenvolver dois modelos logísticos de localização baseados no acesso para maximizar a cobertura de exames, minimizar o número de equipamentos a serem adquiridos e a distância do atendimento. Os modelos se diferem pelo atendimento parcial ou total de uma localidade. Foram analisados vários cenários e os resultados mostraram que, com os modelos propostos e a utilização das atuais microrregiões de saúde, as soluções obtidas possibilitam uma distribuição espacial dos mamógrafos mais equilibrada e acessível, com aumento quantitativo e geográfico da cobertura de exames.
Short-term planning of a work shift for open-pit mines : a case study.
(2023) Silva Júnior, Ademar Lopes da; Martins, Aldrin Gustavo; Pantuza Júnior, Guido; Cota, Luciano Perdigão; Souza, Marcone Jamilson Freitas
This work deals with the short-term planning problem of a work shift for open-pit mines. The problem involves ore and waste fronts, shovels, heterogeneous truck fleets, and discharge points. The allocation of trucks is dynamic to allow multiple routes to be assigned to each truck. The problem consists of deciding which fronts must be mined and establishing the number of trucks, their routes, and the amount of material transported by them to each discharge point, satisfying a stripping ratio at the desired level. The objectives are to minimize the deviations from the targets for production, chemical grade, and particle size range of each control parameter at each plant and reduce the number of trucks needed for the process. To solve the problem, we developed a mixed-integer linear goal program- ming model and tested it using real data from an iron ore mine. The results showed that the proposed approach supports decision-makers in the sizing and allocation of truck fleets and in meeting the production and control parameter targets required by the ore processing plants according to the daily scenario, such as low availability of shovels and trucks, flexibility in ore quality, and need for increased production.
A general VNS for the multi‐depot open vehicle routing problem with time windows.
(2023) Bezerra, Sinaide Nunes; Souza, Sergio Ricardo de; Souza, Marcone Jamilson Freitas
This paper presents an algorithm based on the variable neighborhood search (VNS) metaheuristic, called smart general VNS (SGVNS), to solve the multi-depot open vehicle routing problem with time windows (MDOVRPTW). For the problem, two single-objective approaches are proposed for cost assessment: one for reducing the total distance covered and the other for reducing the total number of vehicles used and, after, the total distance covered. SGVNS involves the perturbation and local search phases. In the perturbation phase, gradual changes are carried out in the neighborhoods to expand the diversifcation of solutions and escape from local optima. The random combination of specifc neighborhood structures is used in the local search to refne the solution generated in the previous phase. As no instances are known in the literature for MDOVRPTW, the computational tests are executed in two groups of classic MDVRPTW instances, involving up to 960 customers, 12 depots, and 120 vehicles. The present study made it possible to investigate cost improvements through the use of the MDOVRPTW model when compared to the MDVRPTW. There was a reduction in the distance covered in all instances evalu- ated. The total distance covered decreased by 12.07% in one of the reference groups and 10.43% in the other. For the frst group, the feet reduction occurred in 75% of the instances. In the second group, there was a reduction in all instances. It corre- sponds to −10.42% and −24.13% of the total vehicles used in each group, respec- tively. The SGVNS algorithm proved efective for the two problems for which it was applied, either in reducing the total traveled distance or in reducing the feet.
ILS-based algorithms for the profit maximizing uncapacitated hub network design problem with multiple allocation.
(2023) Oliveira, Fabricio Alves; Sá, Elisangela Martins de; Souza, Sergio Ricardo de; Souza, Marcone Jamilson Freitas
This study addresses a hub network design problem to maximize net profit. This problem considers an incomplete hub network with multiple allocation that does not impose capacity constraints, does not allow direct connections between non-hub nodes, and accepts the demand to be partially met, being satisfied only when profitable. To tackle this problem, which is NP-hard, we propose two heuristic algorithms based on the Iterated Local Search (ILS) metaheuristic, a standard ILS algorithm, and an Enhanced ILS algorithm, which increases the perturbation level only after a few unsuccessful attempts at improvement. Both algorithms use Random Variable Neighborhood Descent in the local search. Computational experiments were performed using benchmark instances for hub location problems, and statistical analyzes of the algorithms were presented. Numerical results confirm that both algorithms yield good-quality solutions with an acceptable runtime. In particular, the proposed algorithms obtain the optimal solution for most instances with up to 150 nodes, which have known optimal solutions. Furthermore, the proposed algorithms were able to handle instances with up to 500 nodes.
Product sequencing and blending of raw materials to feed arc furnaces : a decision support system for a mining-metallurgical industry.
(2022) Bacharel, Rafael de Freitas; Souza, Marcone Jamilson Freitas; Cota, Luciano Perdigão
A large amount of data available today and the complex situations present in the industry make decision support systems increasingly necessary. This work deals with a problem of a mining-metallurgical industry in which the production of products used to feed arc furnaces must be sequenced in work shifts. There is a due date and a quality specification for each product. These products are generated from raw materials available in a set of silos and must satisfy the required quality specifications. The aim is to minimize the total production time and the total tardiness. To solve it, we developed a decision support system that applies a matheuristic algorithm to do the product schedule and determine the amount of raw material to produce each product. In the proposed algorithm, the products generated in each work shift are chosen through a dispatch heuristic rule based on the shortest production time. In turn, the amount of raw material to be used is calculated by solving a goal linear programming formulation of a blending problem. We generate instances that simulate real cases to evaluate the developed algorithm. The results show a good performance of the proposed algorithm, validating its use as a tool to support decision-making.
Vulnerability analysis in complex networks under a flood risk reduction point of view.
(2023) Santos, Leonardo Bacelar Lima; Soares, Giovanni Guarnieri; Garg, Tanishq; Jorge, Aurelienne Aparecida Souza; Londe, Luciana de Resende; Reani, Regina Tortorella; Bacelar, Roberta Baldo; Oliveira, Carlos Eduardo S. de; Freitas, Vander Luis de Souza; Sokolov, Igor Mikhailovich
The measurement and mapping of transportation network vulnerability to natural hazards constitute subjects of global interest for a sustainable development agenda and as means of adaptation to climate change. During a flood, some elements of a transportation network can be affected, causing the loss of lives. Furthermore, impacts include damage to vehicles, streets/roads, and other logistics services - sometimes with severe economic consequences. The Network Science approach may offer a valuable perspective considering one type of vulnerability related to network-type critical infrastructures: the topological vulnerability. The topological vulnerability index associated with an element is defined as reducing the network’s average efficiency due to removing the set of edges related to that element. In this paper, we present the results of a systematic literature overview and a case study applying the topological vulnerability index for the highways in Santa Catarina (Brazil). We produce a map considering that index and areas susceptible to urban floods and landslides. Risk knowledge, combining hazard and vulnerability, is the first pillar of an Early Warning System and represents an important tool for stakeholders of the transportation sector in a disaster risk reduction agenda.
Flood risk map from hydrological and mobility data : a case study in São Paulo-Brazil.
(2022) Tomás, Lívia Rodrigues; Soares, Giovanni Guarnieri; Jorge‬, ‪Aurelienne Aparecida Souza; Mendes, Jeferson Feitosa; Freitas, Vander Luis de Souza; Santos, Leonardo Bacelar Lima
Cities increasingly face flood risk primarily due to exten-sive changes of the natural land cover to built-up areas with impervious surfaces. In urban areas, flood impacts come mainly from road interruption. This article proposes an urban flood risk map from hydrological and mobility data, considering the megacity of São Paulo, Brazil, as a case study. We estimate the flood susceptibility through the Height Above the Nearest Drainage algorithm; and the potential impact through the exposure and vulnerability components. We aggregate all variables into a regular grid and then classify the cells of each component into three classes: Moderate, High, and Very High. All components, except the flood susceptibility, have few cells in the Very High class. The flood susceptibility component reflects the presence of watercourses, and it has a strong influence on the location of those cells classified as Very High.
Exact and heuristic approaches to truck–drone delivery problems.
(2023) Freitas, Júlia Cária de; Penna, Puca Huachi Vaz; Toffolo, Túlio Ângelo Machado
Collaborative delivery employing drones in last-mile delivery has been an extensively studied topic in recent years. In this paper, it is studied Truck–Drone Delivery Problems (TDDPs) in which a traditional delivery truck is gathered with a drone to cut delivery times and costs. The vehicles work together in a hybrid operation involving one drone launching from a larger vehicle that operates as a mobile depot and a recharging platform. The drone launches from the truck with a single package to deliver to a customer. Each drone must return to the truck to recharge batteries, pick up another package, and launch again to a new customer location. This work proposes a novel Mixed Integer Programming (MIP) formulation and a heuristic approach to address the problem. The proposed MIP formulation yields better linear relaxation bounds than previously proposed formulations for all instances, and was capable of optimally solving several unsolved instances from the literature. A hybrid heuristic based on the General Variable Neighborhood Search metaheuristic combining Tabu Search concepts is employed to obtain high-quality solutions for large-size instances. The efficiency of the algorithm was evaluated on 1415 benchmark instances from the literature, and over 80% of the best known solutions were improved.
Exponential-size neighborhoods for the pickup-and-delivery traveling salesman problem.
(2022) Pacheco, Toni Tiago da Silva; Pinto, Rafael Martinelli; Subramanian, Anand; Toffolo, Túlio Ângelo Machado; Vidal, Thibaut Victor Gaston
Neighborhood search is a cornerstone of state-of-the-art traveling salesman and vehicle routing metaheuristics. While neighborhood exploration procedures are well developed for problems with individual services, their counterparts for one-to-one pickup-and-delivery problems have been more scarcely studied. A direct extension of classic neighborhoods is often inefficient or complex due to the necessity of jointly considering service pairs. To circumvent these issues, we introduce major improvements to existing neighborhood searches for the pickup-and-delivery traveling salesman problem and new large neighborhoods. We show that the classical Relocate-Pair neighborhood can be fully explored in O(n 2 ) instead of O(n 3 ) time. We adapt the 4-Opt and Balas-Simonetti neighborhoods to consider precedence constraints. Moreover, we introduce an exponential-size neighborhood called 2k-Opt, which includes all solutions generated by multiple nested 2-Opts and can be searched in O(n 2 ) time using dynamic programming. We conduct extensive computational experiments, highlighting the significant contribution of these new neighborhoods and speedup strategies within two classical metaheuristics. Notably, our approach permits to repeatedly solve small pickup-and-delivery problem instances to optimality or near-optimality within milliseconds, and therefore it represents a valuable tool for time-critical applications such as meal delivery or mobility on demand.
Hybrid project-based learning course approach from face-to-face and remote experiences.
(2022) Silva, Saul Emanuel Delabrida
The Covid-19 pandemic challenged students and educators who quickly migrated face-to-face courses to a remote context. Given this challenge, this paper documents the experience of a Project-Based Learning course originally proposed to a face-to-face and adjusted to the remote context. It is a wearable computing course centralizing on mixed reality technologies and user studies evaluation. The adopted methodology is student-centered based on PjBL practices, emphasizing the Human-Computer interaction subject was applied six times, three times face-to-face, and three times remotely between 2019 and 2021. This paper describes the educator's experiences, learnings, and directions for the arrangement of other PjBL courses.
Combining embeddings and fuzzy time series for high-dimensional time series forecasting in internet of energy applications.
(2023) Bitencourt, Hugo Vinicius; Souza, Luiz Augusto Facury de; Santos, Matheus Cascalho dos; Silva, Rodrigo da Costa; Silva, Petrônio Cândido de Lima e; Guimarães, Frederico Gadelha
High-dimensional time series increasingly arise in the Internet of Energy (IoE), given the use of multi-sensor environments and the two way communication between energy consumers and the smart grid. Therefore, methods that are capable of computing high-dimensional time series are of great value in smart building and IoE applications. Fuzzy Time Series (FTS) models stand out as data-driven non-parametric models of easy implementation and high accuracy. Unfortunately, the existing FTS models can be unfeasible if all variables were used to train the model. We present a new methodology named Embedding Fuzzy Time Series (EFTS), by applying a combination of data embedding transformation and FTS methods. The EFTS is an explainable and data-driven approach, which is flexible and adaptable for many smart building and IoE applications. The experimental results with three public datasets show that our methodology outperforms several machine learning based forecasting methods (LSTM, GRU, TCN, RNN, MLP and GBM), and demonstrates the accuracy and parsimony of the EFTS in comparison to the baseline methods and the results previously published in the literature, showing an enhancement greater than 80%. Therefore, EFTS has a great value in high-dimensional time series forecasting in IoE applications.
Randomized high order fuzzy cognitive maps as reservoir computing models : a first introduction and applications.
(2022) Orang, Omid; Silva, Petrônio Cândido de Lima e; Silva, Rodrigo César Pedrosa; Guimarães, Frederico Gadelha
Fuzzy Cognitive Maps (FCMs) have emerged as an interpretable signed weighted digraph method consisting of nodes (concepts) and weights which represent the dependencies among the concepts. Although FCMs have attained considerable achievements in various time series prediction applications, designing an FCM model with time-efficient training method is still an open challenge. Thus, this paper introduces a novel univariate time series forecasting technique, which is composed of a group of randomized high order FCM models labeled R-HFCM. The novelty of the proposed R-HFCM model is relevant to merging the concepts of FCM and Echo State Network (ESN) as an efficient and particular family of Reservoir Computing (RC) models, where the least squares algorithm is applied to train the model. From another perspective, the structure of R-HFCM consists of the input layer, reservoir layer, and output layer in which only the output layer is trainable while the weights of each sub-reservoir components are selected randomly and kept constant during the training process. As case studies, in this paper we consider solar energy forecasting with public data for Brazilian solar stations, hourly electric load of the power supply company of the city of Johor in Malaysia, solar energy dataset from United States National Renewable Energy Laboratory (NREL), electric load data from the Global Energy Forecasting Competition 2012 (GEFCom 2012), and PJM hourly energy consumption data. The experiments also include the effect of the map size, activation function, the number of order and the size of the reservoir on the accuracy of R-HFCM method. The obtained results confirm the outperformance of the proposed R-HFCM model in comparison to the other methods. This study provides evidence that FCM can be a new way to implement a reservoir of dynamics in time series modeling. The Python code of the model is publicly available for research replication.
Scheduling the Brazilian OR conference.
(2022) Correia, Rubens; Subramanian, Anand; Bulhões, Teobaldo; Penna, Puca Huachi Vaz
In this paper, we propose an efficient matheuristic approach for solving the problem of scheduling the Brazilian OR conference. The event has traditionally around 300 presentations across a period of 3 to 4 days, and building a schedule for the technical sessions is an ardu- ous task. The developed algorithm integrates the concepts of iterated local search and simulated annealing with two mathematical programming-based procedures. The idea is to group the presentations via a clustering procedure, and handle the side constraints in a subproblem via an integer programming formulation. A set partitioning procedure is applied at the end of the algorithm to find the optimal combination of clusters found during the search. We first assess the performance of the method by comparing our results with those attained by other algorithms from the literature on two existing sets of artificial instances derived from two other conferences. Next, we executed our approach on real-life instances derived from different SBPO editions, and compared the solutions with the manual solutions, when available, or with upper bounds (we solve a maximisation problem) found by an exact algorithm from the literature. The results obtained show that the matheuristic is capable of achieving high quality solutions both on the artificial and real-life instances.
The vessel swap-body routing problem.
(2022) Santos, Vinícius Gandra Martins; Çalıka, Hatice; Toffolo, Túlio Ângelo Machado; Carvalho, Marco Antonio Moreira de; Berghe, Greet Vanden
This paper introduces the Vessel Swap-Body Routing problem (VSBR), a generalization of the pickup and delivery problem with time windows, which considers freight distribution between ports located throughout an inland waterway network. Subject to time windows and precedence constraints, each customer request is associated with a number of containers and must be served via a single body. Bodies are capacitated components that cannot move independently and must therefore be towed by a vessel. Bodies can be transferred between vessels at customer locations or transfer points in order to reduce overall costs. Vessels and bodies can end their routes at any location, meaning they do not need to return to a depot. Moreover, every vessel-body combination is permitted, which greatly expands the size of the solution search space. Although body transfers constitute a fundamental component of this realworld problem, the flexibility such transfers engender poses a huge logistical challenge to the human planners tasked with efficiently scheduling vessel routes. In this paper we model the VSBR as an optimization problem and introduce complementary approaches for solving it. We propose a mixed integer programming formulation and a heuristic approach with tailored neighborhoods for body transfers. To help stimulate further research, a set of instances is introduced based on real-world data and benchmarks are made publicly available.
Systematic literature review on parallel trajectory-based metaheuristics.
(2022) Almeida, André Luís Barroso de; Lima, Joubert de Castro; Carvalho, Marco Antonio Moreira de
In the past 35 years, parallel computing has drawn increasing interest from the academic community, especially in solving complex optimization problems that require large amounts of computational power. The use of parallel (multi-core and distributed) architectures is a natural and effective alternative to speeding up search methods, such as metaheuristics, and to enhancing the quality of the solutions. This survey focuses particularly on studies that adopt high-performance computing techniques to design, implement, and experiment trajectory-based metaheuristics, which pose a great challenge to high-performance computing and represent a large gap in the operations research literature. We outline the contributions from 1987 to the present, and the result is a complete overview of the current state-of-the-art with respect to multi-core and distributed trajectory-based metaheuristics. Basic notions of high-performance computing are introduced, and different taxonomies for multi-core and distributed architectures and metaheuristics are reviewed. A comprehensive list of 127 publications is summarized and classified according to taxonomies and application types. Furthermore, past and future trends are indicated, and open research gaps are identified.
Domain adaptation for unconstrained ear recognition with convolutional neural networks.
(2022) Ramos Cooper, Solange; Cámara Chávez, Guillermo
Automatic recognition using ear images is an active area of interest within the biometrics community. Human ears are a stable and reliable source of information since they are not affected by facial expressions, do not suffer extreme change over time, are less prone to injuries, and are fully visible in mask-wearing scenarios. In addition, ear images can be passively captured from a distance, making it convenient when implementing surveillance and security applications. At the same time, deep learning-based methods have proven to be powerful techniques for unconstrained recognition. However, to truly benefit from deep learning techniques, it is necessary to count on a large-size variable set of samples to train and test networks. In this work, we built a new dataset using the VGGFace dataset, fine-tuned pre-train deep models, analyzed their sensitivity to different covariates in data, and explored the score-level fusion technique to improve overall recognition performance. Open-set and close-set experiments were performed using the proposed dataset and the challenging UERC dataset. Results show a significant improvement of around 9% when using a pre-trained face model over a general image recognition model; in addition, we achieve 4% better performance when fusing scores from both models.

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