Search results for: networks without scaling

Authors: Amir Reza Saffari Azar Alamdari

Abstract:

In this paper, a model of self-organizing spiking neural networks is introduced and applied to mobile robot environment representation and path planning problem. A network of spike-response-model neurons with a recurrent architecture is used to create robot-s internal representation from surrounding environment. The overall activity of network simulates a self-organizing system with unsupervised learning. A modified A* algorithm is used to find the best path using this internal representation between starting and goal points. This method can be used with good performance for both known and unknown environments.

Keywords: Mobile Robot, Path Planning, Self-organization, Spiking Neural Networks.

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Authors: Bharadwaj Kadiyala, Sunitha V

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Most routing protocols (DSR, AODV etc.) that have been designed for wireless adhoc networks incorporate the broadcasting operation in their route discovery scheme. Probabilistic broadcasting techniques have been developed to optimize the broadcast operation which is otherwise very expensive in terms of the redundancy and the traffic it generates. In this paper we have explored percolation theory to gain a different perspective on probabilistic broadcasting schemes which have been actively researched in the recent years. This theory has helped us estimate the value of broadcast probability in a wireless adhoc network as a function of the size of the network. We also show that, operating at those optimal values of broadcast probability there is at least 25-30% reduction in packet regeneration during successful broadcasting.

Keywords: Crossover length, Percolation, Probabilistic broadcast, Wireless adhoc networks

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Authors: Marina Velikova, Hennie Daniels, Ad Feelders

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In many data mining applications, it is a priori known that the target function should satisfy certain constraints imposed by, for example, economic theory or a human-decision maker. In this paper we consider partially monotone prediction problems, where the target variable depends monotonically on some of the input variables but not on all. We propose a novel method to construct prediction models, where monotone dependences with respect to some of the input variables are preserved by virtue of construction. Our method belongs to the class of mixture models. The basic idea is to convolute monotone neural networks with weight (kernel) functions to make predictions. By using simulation and real case studies, we demonstrate the application of our method. To obtain sound assessment for the performance of our approach, we use standard neural networks with weight decay and partially monotone linear models as benchmark methods for comparison. The results show that our approach outperforms partially monotone linear models in terms of accuracy. Furthermore, the incorporation of partial monotonicity constraints not only leads to models that are in accordance with the decision maker's expertise, but also reduces considerably the model variance in comparison to standard neural networks with weight decay.

Keywords: mixture models, monotone neural networks, partially monotone models, partially monotone problems.

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Authors: Heejin Lee, Yeonjoo Kim, Kyungrak Sohn

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We present a white LED-based optical wireless communication systems for indoor ubiquitous sensor networks. Each sensor node could access to the server through the PLC (Power Line Communication)-Ethernet interface. The proposed system offers a full-duplex wireless link by using different wavelengths to reduce the inter-symbol interference between uplink and downlink. Through the 1-to-n optical wireless sensor network and PLC modem, the mobile terminals send a temperature data to server. The data transmission speed and distance are 115.2kbps and about 60cm, respectively.

Keywords: Visible light communications, LED lighting, powerline communications, ubiquitous sensor networks, full-duplex links

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Authors: Yongzhi Liao

Abstract:

By using the theory of exponential dichotomy and Banach fixed point theorem, this paper is concerned with the problem of the existence and uniqueness of positive almost periodic solution in a delayed Lotka-Volterra recurrent neural networks with harvesting terms. To a certain extent, our work in this paper corrects some result in recent years. Finally, an example is given to illustrate the feasibility and effectiveness of the main result.

Keywords: positive almost periodic solution, Lotka-Volterra, neural networks, Banach fixed point theorem, harvesting

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Authors: Dai Miyamoto

Abstract:

This paper examines the factors, which determine R&D outsourcing behaviour at Japanese firms, from the viewpoints of transaction cost and strategic management, since the latter half of the 1990s. This study uses empirical analysis, which involves the application of large-sample data. The principal findings of this paper are listed below. Firms that belong to a wider corporate group are more active in executing R&D outsourcing activities. Diversification strategies such as the expansion of product and sales markets have a positive effect on the R&D outsourcing behaviour of firms. Moreover, while quantitative R&D resources have positive influences on R&D outsourcing, qualitative indices have no effect. These facts suggest that R&D outsourcing behaviour of Japanese firms are consistent with the two perspectives of transaction cost and strategic management. Specifically, a conventional corporate group network plays an important role in R&D outsourcing behaviour. Firms that execute R&D outsourcing leverage 'old' networks to construct 'new' networks and use both networks properly.

Keywords: Corporate Group Networks, R&D Outsourcing, Strategic Management Perspective, Transaction Cost Perspective.

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Authors: Amandeep Singh Dhaliwal

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Networking solutions, particularly wireless local area networks have revolutionized the technological advancement. Wireless Local Area Networks (WLANs) have gained a lot of popularity as they provide location-independent network access between computing devices. There are a number of access methods used in Wireless Networks among which DCF and PCF are the fundamental access methods. This paper emphasizes on the impact of DCF and PCF access mechanisms on the performance of the IEEE 802.11a, 802.11b and 802.11g standards. On the basis of various parameters viz. throughput, delay, load etc performance is evaluated between these three standards using above mentioned access mechanisms. Analysis revealed a superior throughput performance with low delays for 802.11g standard as compared to 802.11 a/b standard using both DCF and PCF access methods.

Keywords: DCF, IEEE, PCF, WLAN.

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Authors: Rade M. Ciric

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The paper shows the development and implementation of the syllabus of the subject 'Distribution and Industrial Networks', attended by the vocational specialist Year 4 students of the Electric Power Engineering study programme at the Higher Education Technical School of Vocational Studies in Novi Sad. The aim of the subject is to equip students with the knowledge necessary for planning, exploitation and management of distributive and industrial electric power networks in an open electricity market environment. The results of the evaluation of educational outcomes on the subject are presented and discussed.

Keywords: Engineering education, power distribution network, syllabus implementation, outcome evaluation.

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Authors: Y. Harold Robinson, E. Golden Julie

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Dynamic Routing in Wireless Sensor Networks (WSNs) has played a significant task in research for the recent years. Energy consumption and data delivery in time are the major parameters with the usage of sensor nodes that are significant criteria for these networks. The location of sensor nodes must not be prearranged. Clustering in WSN is a key methodology which is used to enlarge the life-time of a sensor network. It consists of numerous real-time applications. The features of WSNs are minimized the consumption of energy. Soft computing techniques can be included to accomplish improved performance. This paper surveys the modern trends in routing enclose fuzzy logic and Neuro-fuzzy logic based on the clustering techniques and implements a comparative study of the numerous related methodologies.

Keywords: Wireless sensor networks, clustering, fuzzy logic, neuro-fuzzy logic, energy efficiency.

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Authors: A. Derardja

Abstract:

The present work is motivated by the idea that the layer deformation in anisotropic elasticity can be estimated from the theory of interfacial dislocations. In effect, this work which is an extension of a previous approach given by one of the authors determines the anisotropic displacement fields and the critical thickness due to a complex biperiodic network of MDs lying just below the free surface in view of the arrangement of dislocations. The elastic fields of such arrangements observed along interfaces play a crucial part in the improvement of the physical properties of epitaxial systems. New results are proposed in anisotropic elasticity for hexagonal networks of MDs which contain intrinsic and extrinsic stacking faults. We developed, using a previous approach based on the relative interfacial displacement and a Fourier series formulation of the displacement fields, the expressions of elastic fields when there is a possible dissociation of MDs. The numerical investigations in the case of the observed system Si/(111)Si with low twist angles show clearly the effect of the anisotropy and thickness when the misfit networks are dissociated.

Keywords: Angular misfit, dislocation networks, plane interfaces, stacking faults.

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Authors: Feng-Sheng Wang, Wu-Hsiung Wu, Kai-Cheng Hsu

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The optimization of biological systems, which is a branch of metabolic engineering, has generated a lot of industrial and academic interest for a long time. In the last decade, metabolic engineering approaches based on mathematical optimizations have been used extensively for the analysis and manipulation of metabolic networks. In practical optimization of metabolic reaction networks, designers have to manage the nature of uncertainty resulting from qualitative characters of metabolic reactions, e.g., the possibility of enzyme effects. A deterministic approach does not give an adequate representation for metabolic reaction networks with uncertain characters. Fuzzy optimization formulations can be applied to cope with this problem. A fuzzy multi-objective optimization problem can be introduced for finding the optimal engineering interventions on metabolic network systems considering the resilience phenomenon and cell viability constraints. The accuracy of optimization results depends heavily on the development of essential kinetic models of metabolic networks. Kinetic models can quantitatively capture the experimentally observed regulation data of metabolic systems and are often used to find the optimal manipulation of external inputs. To address the issues of optimizing the regulatory structure of metabolic networks, it is necessary to consider qualitative effects, e.g., the resilience phenomena and cell viability constraints. Combining the qualitative and quantitative descriptions for metabolic networks makes it possible to design a viable strain and accurately predict the maximum possible flux rates of desired products. Considering the resilience phenomena in metabolic networks can improve the predictions of gene intervention and maximum synthesis rates in metabolic engineering. Two case studies will present in the conference to illustrate the phenomena.

Keywords: Fuzzy multi-objective optimization problem, kinetic model, metabolic engineering.

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Authors: Mohsen Hayati, Yazdan Shirvany

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In this paper, the application of neural networks to study the design of short-term load forecasting (STLF) Systems for Illam state located in west of Iran was explored. One important architecture of neural networks named Multi-Layer Perceptron (MLP) to model STLF systems was used. Our study based on MLP was trained and tested using three years (2004-2006) data. The results show that MLP network has the minimum forecasting error and can be considered as a good method to model the STLF systems.

Keywords: Artificial neural networks, Forecasting, Multi-layer perceptron.

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Authors: Samee Ullah Khan, C. Ardil

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In this paper, a mathematical model for data object replication in ad hoc networks is formulated. The derived model is general, flexible and adaptable to cater for various applications in ad hoc networks. We propose a game theoretical technique in which players (mobile hosts) continuously compete in a non-cooperative environment to improve data accessibility by replicating data objects. The technique incorporates the access frequency from mobile hosts to each data object, the status of the network connectivity, and communication costs. The proposed technique is extensively evaluated against four well-known ad hoc network replica allocation methods. The experimental results reveal that the proposed approach outperforms the four techniques in both the execution time and solution quality

Keywords: Data replication, auctions, static allocation.

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Authors: Gülfem I. Alptekin, S. Emre Alptekin

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The next generation wireless systems, especially the cognitive radio networks aim at utilizing network resources more efficiently. They share a wide range of available spectrum in an opportunistic manner. In this paper, we propose a quality management model for short-term sub-lease of unutilized spectrum bands to different service providers. We built our model on competitive secondary market architecture. To establish the necessary conditions for convergent behavior, we utilize techniques from game theory. Our proposed model is based on potential game approach that is suitable for systems with dynamic decision making. The Nash equilibrium point tells the spectrum holders the ideal price values where profit is maximized at the highest level of customer satisfaction. Our numerical results show that the price decisions of the network providers depend on the price and QoS of their own bands as well as the prices and QoS levels of their opponents- bands.

Keywords: cognitive radio networks, game theory, nextgeneration wireless networks, spectrum management.

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Authors: Masatora Daito, Hisashi Kojima

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In this research, the authors analyze network stability using agent-based simulation. Firstly, the authors focus on analyzing large networks (eight agents) by connecting different two stable small social networks (A small stable network is consisted on four agents.). Secondly, the authors analyze the network (eight agents) shape which is added one agent to a stable network (seven agents). Thirdly, the authors analyze interpersonal comparison of utility. The “star-network "was not found on the result of interaction among stable two small networks. On the other hand, “decentralized network" was formed from several combination. In case of added one agent to a stable network (seven agents), if the value of “c"(maintenance cost of per a link) was larger, the number of patterns of stable network was also larger. In this case, the authors identified the characteristics of a large stable network. The authors discovered the cases of decreasing personal utility under condition increasing total utility.

Keywords: Social Network, Symmetric Situation, Network Stability, Agent-Based Modeling.

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Authors: Rachelle Bosua, Nina Evans

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The resource-based view of the firm regards knowledge as one of the most important organizational assets and a key strategic resource that contributes unique value to organizations. The acquisition, absorption and internalization of external knowledge are central to an organization-s innovative capabilities. This ability to evaluate, acquire and integrate new knowledge from its environment is referred to as a firm-s absorptive capacity (AC). This research in progress paper explores the link between interorganizational Social Networks (SNs) and a firm-s Absorptive Capacity (AC). Based on an in-depth literature survey of both concepts, four propositions are proposed that explain the link between AC and SNs. These propositions suggest that SNs are key to a firm-s AC. A qualitative research method is proposed to test the set of propositions in the next stage of this research.

Keywords: Knowledge, Innovation, Absorptive Capacity, Social Networks

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Authors: Ashanie Guanathillake, Kithsiri Samarasinghe

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Wireless Sensor Networks consist of inexpensive, low power sensor nodes deployed to monitor the environment and collect data. Gathering information in an energy efficient manner is a critical aspect to prolong the network lifetime. Clustering  algorithms have an advantage of enhancing the network lifetime. Current clustering algorithms usually focus on global re-clustering and local re-clustering separately. This paper, proposed a combination of those two reclustering methods to reduce the energy consumption of the network. Furthermore, the proposed algorithm can apply to homogeneous as well as heterogeneous wireless sensor networks. In addition, the cluster head rotation happens, only when its energy drops below a dynamic threshold value computed by the algorithm. The simulation result shows that the proposed algorithm prolong the network lifetime compared to existing algorithms.

Keywords: Energy efficient, Global re-clustering, Local re-clustering, Wireless sensor networks.

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Authors: Gurjinder Kaur, Yogesh Chaba, V. K. Jain

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The aim of this paper is to explore the security issues that significantly affect the performance of Mobile Adhoc Networks (MANET)and limit the services provided to their intended users. The MANETs are more vulnerable to Distributed Denial of Service attacks (DDoS) because of their properties like shared medium, dynamic topologies etc. A DDoS attack is a coordinated attempt made by malicious users to flood the victim network with the large amount of data such that the resources of the victim network are exhausted resulting in the deterioration of the network performance. This paper highlights the effects of different types of DDoS attacks in MANETs and categorizes them according to their behavior.

Keywords: Distributed Denial, Mobile Adhoc Networks

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Authors: Anne-Lena Kampen, Øivind Kure

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Machine learning (ML) can be implemented in Wireless Sensor Networks (WSNs) as a central solution or distributed solution where the ML is embedded in the nodes. Embedding improves privacy and may reduce prediction delay. In addition, the number of transmissions is reduced. However, quality factors such as prediction accuracy, fault detection efficiency and coordinated control of the overall system suffer. Here, we discuss and highlight the trade-offs that should be considered when choosing between embedding and centralized ML, especially for multihop networks. In addition, we present estimations that demonstrate the energy trade-offs between embedded and centralized ML. Although the total network energy consumption is lower with central prediction, it makes the network more prone for partitioning due to the high forwarding load on the one-hop nodes. Moreover, the continuous improvements in the number of operations per joule for embedded devices will move the energy balance toward embedded prediction.

Keywords: Central ML, embedded machine learning, energy consumption, local ML, Wireless Sensor Networks, WSN.

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Authors: Kettawa Boonprakarn, Jedsarid Sangkaphan, Bejapornd Deekhuntod, Nuntharat Suriyo

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This study aimed to investigate the existence of field corn networks on the Thailand-Burma border under the patron-client contract farming system. The data of this qualitative study were collected through in-depth interviews with nine key informants.

The results of the study revealed that the existence of the field corn networks was associated with the relationship where farmers had to share their crops with protectors in the areas under the influence of the KNU (Karen National Union) and the DKBA (Democratic Karen Buddhist Army) or Burmese soldiers. A Mae Liang, the person who starts a network has a connection with a Thaokae, Luk Rai Hua Chai or the head of a group of farmers, and farmers. They are under the patron-client system with trust and loyalty that enable the head of the group and the farmers in the Burma border side to remain under the same Mae Liang even though the business has been passed down to later generations.

Keywords: Existence, field-corn networks, patron-client system, contract farming.

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Authors: Pilar Rey-del-Castillo, Jesús Cardeñosa

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There are many situations where input feature vectors are incomplete and methods to tackle the problem have been studied for a long time. A commonly used procedure is to replace each missing value with an imputation. This paper presents a method to perform categorical missing data imputation from numerical and categorical variables. The imputations are based on Simpson-s fuzzy min-max neural networks where the input variables for learning and classification are just numerical. The proposed method extends the input to categorical variables by introducing new fuzzy sets, a new operation and a new architecture. The procedure is tested and compared with others using opinion poll data.

Keywords: Classifier, imputation techniques, fuzzy systems, fuzzy min-max neural networks.

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Authors: Yaseein S. Hussein, Victor P. Gil Jiménez, Abdulmajeed Al-Jumaily

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Due to the rapid advancement of technology, there is an increasing demand for wireless connections that are both fast and reliable, with minimal latency. New wireless communication standards are developed every decade, and 2030 is expected to see the introduction of 6G. The primary objectives of 6G network and terminal designs are focused on sustainability and environmental friendliness. The International Telecommunication Union-Recommendation division (ITU-R) has established the minimum requirements for 6G, with peak and user data rates of 1 Tbps and 10-100 Gbps, respectively. In this context, Light Fidelity (Li-Fi) technology is the most promising candidate to meet these requirements. This article will explore the various advantages, features, and potential applications of Li-Fi technology, and compare it with 5G networking, to showcase its potential impact among other emerging technologies that aim to enable 6G networks.

Keywords: 6G Networks, artificial intelligence, AI, Li-Fi technology, terahertz communication, visible light communication.

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Authors: Ozlem Faydasicok, Sabri Arik

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This paper derives some new sufficient conditions for the stability of a class of neutral-type neural networks with discrete time delays by employing a suitable Lyapunov functional. The obtained conditions can be easily verified as they can be expressed in terms of the network parameters only. It is shown that the results presented in this paper for neutral-type delayed neural networks establish a new set of stability criteria, and therefore can be considered as the alternative results to the previously published literature results. A numerical example is also given to demonstrate the applicability of our proposed stability criterion.

Keywords: Stability Analysis, Neutral-Type Neural Networks, Time Delay Systems, Lyapunov Functionals.

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Authors: Eugen Pop, Mihai Barbos, Razvan Lupu

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The client server systems using mobile communications networks for data transmission became very attractive for many economic agents, in the purpose of promoting and offering electronic services to their clients. E-services are suitable for business developing and financial benefits increasing. The products or services can be efficiently delivered to a large number of clients, using mobile Internet access technologies. The clients can have access to e-services, anywhere and anytime, with the support of 3G, GPRS, WLAN, etc., channels bandwidth, data services and protocols. Based on the mobile communications networks evolution and development, a convergence of technological and financial interests of mobile operators, software developers, mobile terminals producers and e-content providers is established. These will lead to a high level of integration of IT&C resources and will facilitate the value added services delivery through the mobile communications networks. In this paper it is presented a client server system, for e-services access, with Smartphones and PDA-s mobile software applications, installed on Symbian and Windows Mobile operating systems.

Keywords: Client server system, e-services access, mobile communications, PDA, Smartphone.

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Authors: J. K. Shrestha, A. Benta, R. B. Lopes, N. Lopes

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This paper presents a multi-objective model for addressing two main objectives in designing rural roads networks: minimization of user operation costs and maximization of population covered. As limited budgets often exist, a reasonable trade-off must be obtained in order to account for both cost and social benefits in this type of networks. For a real-world rural road network, the model is solved, where all non-dominated solutions were obtained. Afterwards, an analysis is made on the (possibly) most interesting solutions (the ones providing better trade-offs). This analysis, coupled with the knowledge of the real world scenario (typically provided by decision makers) provides a suitable method for the evaluation of road networks in rural areas of developing countries.

Keywords: Multi-objective, user operation cost, population covered, rural road network.

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Authors: Changzhao Li, Juan Zhang

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In this paper, we investigate a class of fuzzy Cohen- Grossberg neural networks with time delays and impulsive effects. By virtue of stochastic analysis, Halanay inequality for stochastic differential equations, we find sufficient conditions for the global exponential square-mean synchronization of the FCGNNs under noise perturbation. In particular, the traditional assumption on the differentiability of the time-varying delays is no longer needed. Finally, a numerical example is given to show the effectiveness of the results in this paper.

Keywords: Fuzzy Cohen-Grossberg neural networks (FCGNNs), complete synchronization, time delays, impulsive, noise perturbation.

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Authors: Sunil Gupta, Harsh Kumar Verma, AL Sangal

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Wireless sensor networks can be used to measure and monitor many challenging problems and typically involve in monitoring, tracking and controlling areas such as battlefield monitoring, object tracking, habitat monitoring and home sentry systems. However, wireless sensor networks pose unique security challenges including forgery of sensor data, eavesdropping, denial of service attacks, and the physical compromise of sensor nodes. Node in a sensor networks may be vanished due to power exhaustion or malicious attacks. To expand the life span of the sensor network, a new node deployment is needed. In military scenarios, intruder may directly organize malicious nodes or manipulate existing nodes to set up malicious new nodes through many kinds of attacks. To avoid malicious nodes from joining the sensor network, a security is required in the design of sensor network protocols. In this paper, we proposed a security framework to provide a complete security solution against the known attacks in wireless sensor networks. Our framework accomplishes node authentication for new nodes with recognition of a malicious node. When deployed as a framework, a high degree of security is reachable compared with the conventional sensor network security solutions. A proposed framework can protect against most of the notorious attacks in sensor networks, and attain better computation and communication performance. This is different from conventional authentication methods based on the node identity. It includes identity of nodes and the node security time stamp into the authentication procedure. Hence security protocols not only see the identity of each node but also distinguish between new nodes and old nodes.

Keywords: Authentication, Key management, Wireless Sensornetwork, Elliptic curve cryptography (ECC).

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Authors: C. Gallottini, W. Di Mari, A. Amaddeo, K. Barbaro, A. Dolci, G. Dolci, L. Gallottini, G. Barraco, S. Eramo

Abstract:

A group of 10 dogs (group A) with Periodontal Disease in the third stage, were subjected to regenerative therapy of periodontal tissues, by use of nano hydroxy apatite (NHA). These animals induced by general anesthesia, where treated by ultrasonic scaling, root planning, and at the end by a mucogingival flap in which it was applied NHA. The flap was closed and sutured with simple steps. Another group of 10 dogs (group B), control group, was treated only by scaling and root planning. No patient was subjected to antibiotic therapy. After three months, a check was made by inspection of the oral cavity, radiography and bone biopsy at the alveolar level. Group A showed a total restitutio ad integrum of the periodontal structures, and in group B still mild gingivitis in 70% of cases and 30% of the state remains unchanged. Numerous experimental studies both in animals and humans have documented that the grafts of porous hydroxyapatite are rapidly invaded by fibrovascular tissue which is subsequently converted into mature lamellar bone tissue by activating osteoblast. Since we acted on the removal of necrotic cementum and rehabilitating the root tissue by polishing without intervention in the ligament but only on anatomical functional interface of cement-blasts, we can connect the positive evolution of the clinical-only component of the cement that could represent this perspective, the only reason that Periodontal Disease become a Cement Disease, while all other clinical elements as nothing more than a clinical pathological accompanying.

Keywords: Nanoidroxiaphatite, Parodontal Disease, Rigenerative Therapy.

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Authors: Tahar Ezzedine, Mohamed Miladi, Ridha Bouallegue

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Because nodes are usually battery-powered, the energy presents a very scarce resource in wireless sensor networks. For this reason, the design of medium access control had to take energy efficiency as one of its hottest concerns. Accordingly, in order to improve the energy performance of MAC schemes in wireless sensor networks, several ways can be followed. In fact, some researchers try to limit idle listening while others focus on mitigating overhearing (i.e. a node can hear a packet which is destined to another node) or reducing the number of the used control packets. We, in this paper, propose a new hybrid MAC protocol termed ELE-MAC (i.e. Energy Latency Efficient MAC). The ELE-MAC major design goals are energy and latency efficiencies. It adopts less control packets than SMAC in order to preserve energy. We carried out ns- 2 simulations to evaluate the performance of the proposed protocol. Thus, our simulation-s results prove the ELE-MAC energy efficiency. Additionally, our solution performs statistically the same or better latency characteristic compared to adaptive SMAC.

Keywords: Control packet, energy efficiency, medium access control, wireless sensor networks.

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Authors: Miaomiao Yang, Shouming Zhong

Abstract:

This paper studies the problem of exponential stability analysis for uncertain neural networks with discrete and distributed time-varying delays. Together with a suitable augmented Lyapunov Krasovskii function, zero equalities, reciprocally convex approach and a novel sufficient condition to guarantee the exponential stability of the considered system. The several exponential stability criterion proposed in this paper is simpler and effective. Finally,numerical examples are provided to demonstrate the feasibility and effectiveness of our results.

Keywords: Exponential stability, Uncertain Neural networks, LMI approach, Lyapunov-Krasovskii function, Time-varying.

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