Search results for: extended modular group.

Authors: S. Dehghan, A.M. Rahmani

Abstract:

The group mutual exclusion (GME) problem is an interesting generalization of the mutual exclusion problem. In the group mutual exclusion, multiple processes can enter a critical section simultaneously if they belong to the same group. In the extended group mutual exclusion, each process is a member of multiple groups at the same time. As a result, after the process by selecting a group enter critical section, other processes can select the same group with its belonging group and can enter critical section at the moment, so that it avoids their unnecessary blocking. This paper presents a quorum-based distributed algorithm for the extended group mutual exclusion problem. The message complexity of our algorithm is O(4Q ) in the best case and O(5Q) in the worst case, where Q is a quorum size.

Keywords: Group Mutual Exclusion (GME), Extended GME, Distributed systems.

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Authors: M. Ghorbany

Abstract:

A square matrix over the complex field with non- negative integral trace is called a quasi-permutation matrix. For a finite group G the minimal degree of a faithful representation of G by quasi-permutation matrices over the rationals and the complex numbers are denoted by q(G) and c(G) respectively. Finally r (G) denotes the minimal degree of a faithful rational valued complex character of C. The purpose of this paper is to calculate q(G), c(G) and r(G) for the group S L(2, q) when extended by a certain group of order two.

Keywords: General linear group, Quasi-permutation

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Authors: Rupali Verma, Maitreyee Dutta, Renu Vig

Abstract:

Encryption and decryption in RSA are done by modular exponentiation which is achieved by repeated modular multiplication. Hence efficiency of modular multiplication directly determines the efficiency of RSA cryptosystem. This paper designs a Modified Montgomery Modular Multiplication in which addition of operands is computed by 4:2 compressor. The basic logic operations in addition are partitioned over two iterations such that parallel computations are performed. This reduces the critical path delay of proposed Montgomery design. The proposed design and RSA are implemented on Virtex 2 and Virtex 5 FPGAs. The two factors partitioning and parallelism have improved the frequency and throughput of proposed design.

Keywords: RSA, Montgomery modular multiplication, 4:2 compressor, FPGA.

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Authors: Ivan C. Mustakerov, Daniela I. Borissova

Abstract:

The paper proposes an approach for design of modular systems based on original technique for modeling and formulation of combinatorial optimization problems. The proposed approach is described on the example of personal computer configuration design. It takes into account the existing compatibility restrictions between the modules and can be extended and modified to reflect different functional and users- requirements. The developed design modeling technique is used to formulate single objective nonlinear mixedinteger optimization tasks. The practical applicability of the developed approach is numerically tested on the basis of real modules data. Solutions of the formulated optimization tasks define the optimal configuration of the system that satisfies all compatibility restrictions and user requirements.

Keywords: Constrained discrete combinatorial choice, modular systems design, optimization problem, PC configuration.

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Authors: Achim Kampker, Peter Burggräf, Moritz Krunke, Hanno Voet

Abstract:

As a reaction to current challenges in factory planning, many companies think about introducing factory standards to lower planning times and decrease planning costs. If these factory standards are set-up with a high level of modularity, they are defined as modular factory systems. This paper deals with the main current problems in the application of modular factory systems in practice and presents a solution approach with its basic models. The methodology is based on methods from factory planning but also uses the tools of other disciplines like product development or technology management to deal with the high complexity, which the development of modular factory systems implies. The four basic models that such a methodology has to contain are introduced and pointed out.

Keywords: Factory planning, modular factory systems, factory standards, cost-benefit analysis.

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Authors: Seung-Kyung Kye, Young-Hyo Son, Jin-Woong Choi, Dooyong Cho, Sun-Kyu Park

Abstract:

Recently in the field of bridges that are newly built or repaired, fast construction is required more than ever. For these reasons, precast prefabricated bridge that enables rapid construction is actively discussed and studied today. In South Korea, it is called modular bridge. Cross beam is an integral component of modular bridge. It functions for load distribution, reduction of bending moment, resistance of horizontal strength on lateral upper structure. In this study, the structural characteristics of domestic and foreign cross beam types were compared. Based on this, alternative cross beam connection types suitable for modular bridge were selected. And bulb-T girder specimens were fabricated with each type of connection. The behavior of each specimen was analyzed under static loading, and cross beam connection type which is expected to be best suited to modular bridge proposed.

Keywords: Bulb-T girder, Cross beam, Modular bridge.

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Authors: E. Farjami, La. Mohammadzadeh Afshar, Li. Mohammadzade Afshar, A. Taran

Abstract:

Nowadays, flexibility introduced as a modern technology in furniture systems especially in interior planning design. According to results, the most important impact of these systems can be seen on open plan design that makes workspaces comfortable and increases the productivity of employees besides making good relationship between them. Briefly, there are some factors along with new systems in furniture design help create inappropriate space to make working better and easier while it has modular planning organization. It brings about some approaches to have a successful space for open offices with modular design and flexible furniture systems. These approaches have been investigated in open and close offices at Eastern Mediterranean University (EMU) in Famagusta, Cyprus, using information extracted from questionnaires.

Keywords: Flexibility, Flexible Furniture, Modular design, Open offices, Modular furniture systems.

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Authors: Kyung-Suk Choi, Hyung-Joon Kim

Abstract:

Modular structural systems are constructed using a method that they are assembled with prefabricated unit modular frames on-site. This provides a benefit that can significantly reduce building construction time. The structural design is usually carried out under the assumption that their load-carrying mechanism is similar to that of traditional steel moment-resisting systems. However, both systems are different in terms of beam-column connection details which may strongly influence the lateral structural behavior. Specially, the presence of access holes in a beam-column joint of a unit modular frame could cause undesirable failure during strong earthquakes. Therefore, this study carried out finite element analyses (FEMs) of unit modular frames to investigate the cyclic behavior of beam-column joints with the access holes. Analysis results show that the unit modular frames present stable cyclic response with large deformation capacities and their joints are classified into semi-rigid connections even if there are access holes.

Keywords: Unit modular frame, steel moment connection, nonlinear analytical model, moment-rotation relation, access holes.

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Authors: Jongho Park, Jinwoong Choi, Sungnam Hong, Seung-Kyung Kye, Sun-Kyu Park

Abstract:

Recently, to cope with the rapidly changing construction trend with aging infrastructures, modular bridge technology has been studied actively. Modular bridge is easily constructed by assembling standardized precast structure members in the field. It will be possible to construct rapidly and reduce construction cost efficiently. However, the shape of the transverse connection of T-type girder newly developed between the segmented modules is not verified. Therefore, the verification of the connection shape is needed. In this study, shape of the modular T-girder bridge transverse connection was analyzed by finite element model that was verified in study which was verified model of transverse connection using Abaqus. Connection angle was chosen as the parameter. The result of analyses showed that optimal value of angle is 130 degree.

Keywords: Modular bridge, optimal transverse shape, parameter, FEM.

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Authors: Ahmad M. Abdel Fattah, Ayman M. Bahaa El-Din, Hossam M.A. Fahmy

Abstract:

Modular multiplication is the basic operation in most public key cryptosystems, such as RSA, DSA, ECC, and DH key exchange. Unfortunately, very large operands (in order of 1024 or 2048 bits) must be used to provide sufficient security strength. The use of such big numbers dramatically slows down the whole cipher system, especially when running on embedded processors. So far, customized hardware accelerators - developed on FPGAs or ASICs - were the best choice for accelerating modular multiplication in embedded environments. On the other hand, many algorithms have been developed to speed up such operations. Examples are the Montgomery modular multiplication and the interleaved modular multiplication algorithms. Combining both customized hardware with an efficient algorithm is expected to provide a much faster cipher system. This paper introduces an enhanced architecture for computing the modular multiplication of two large numbers X and Y modulo a given modulus M. The proposed design is compared with three previous architectures depending on carry save adders and look up tables. Look up tables should be loaded with a set of pre-computed values. Our proposed architecture uses the same carry save addition, but replaces both look up tables and pre-computations with an enhanced version of sign detection techniques. The proposed architecture supports higher frequencies than other architectures. It also has a better overall absolute time for a single operation.

Keywords: Montgomery multiplication, modular multiplication, efficient architecture, FPGA, RSA

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Authors: Dario Ramirez de Leon, Oscar Chavez Bosquez, Julian J. Francisco Leon

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Since the conception of JML, many tools, applications and implementations have been done. In this context, the users or developers who want to use JML seem surounded by many of these tools, applications and so on. Looking for a common infrastructure and an independent language to provide a bridge between these tools and JML, we developed an approach to embedded contracts in XML for Java: XJML. This approach offer us the ability to separate preconditions, posconditions and class invariants using JML and XML, so we made a front-end which can process Runtime Assertion Checking, Extended Static Checking and Full Static Program Verification. Besides, the capabilities for this front-end can be extended and easily implemented thanks to XML. We believe that XJML is an easy way to start the building of a Graphic User Interface delivering in this way a friendly and IDE independency to developers community wich want to work with JML.

Keywords: Model checking, verification and validation, JML, XML, java, runtime assertion checking, extended static checking, full static program verification.

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Authors: Khaled Elbehiery, Hussam Elbehiery

Abstract:

Smart cities are a framework of technologies along with sustainable infrastructure to provide their citizens an improved quality of life, safer environment, affordability, and more, which in turn helps with the society's economic growth. The proposed research will focus on the primary building block of the smart city; the infrastructure of the house itself. The traditional method of building houses has been, for a long time, nothing but a costly manufacturing process, and consequently, buying a house becomes not an option for everyone anymore. The smart cities' Modular Houses are not using traditional building construction materials; the design reduces the common lengthy construction times and associated high costs. The Modular Houses are technological homes, low-cost and customizable based on a family's requirements. In addition, the Modular Houses are environmentally friendly and healthy enough to assist with the pandemic situation.

Keywords: Smart cities, modular houses, single-unit property, multi-unit property, mobility features, chain-supply, livable environment, carbon footprint.

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Authors: C. Copilusi, C. Ploscaru

Abstract:

This paper addresses attention to a research regarding the design of a knee orthosis in a modular form used on children walking rehabilitation. This research is focused on the human lower limb kinematic analysis which will be used as input data on virtual simulations and prototype validation. From this analysis, important data will be obtained and used as input for virtual simulations of the knee modular orthosis. Thus, a knee orthosis concept was obtained and validated through virtual simulations by using MSC Adams software. Based on the obtained results, the modular orthosis prototype will be manufactured and presented in this article.

Keywords: Human lower limb, children orthoses, kinematic analysis, knee orthosis.

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Authors: Uday Hameed Farhan, Majid Tolouei-Rad, Simona O'Brien

Abstract:

Modular fixtures (MFs) are very important tools in manufacturing processes in terms of reduction the cost and the production time. This paper introduces an automated approach for assembling MFs elements by employing SolidWorks as a powerful 3D CAD software. Visual Basic (VB) programming language was applied integrating with SolidWorks API (Application programming interface) functions. This integration allowed creating plug-in file and generating new menus in the SolidWorks environment. The menus allow the user to select, insert, and assemble MFs elements.

Keywords: Assembly automation, modular fixtures, SolidWorks, Visual Basic.

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Authors: Hazem M. El-Bakry

Abstract:

In this paper a new fast simplification method is presented. Such method realizes Karnough map with large number of variables. In order to accelerate the operation of the proposed method, a new approach for fast detection of group of ones is presented. Such approach implemented in the frequency domain. The search operation relies on performing cross correlation in the frequency domain rather than time one. It is proved mathematically and practically that the number of computation steps required for the presented method is less than that needed by conventional cross correlation. Simulation results using MATLAB confirm the theoretical computations. Furthermore, a powerful solution for realization of complex functions is given. The simplified functions are implemented by using a new desigen for neural networks. Neural networks are used because they are fault tolerance and as a result they can recognize signals even with noise or distortion. This is very useful for logic functions used in data and computer communications. Moreover, the implemented functions are realized with minimum amount of components. This is done by using modular neural nets (MNNs) that divide the input space into several homogenous regions. Such approach is applied to implement XOR function, 16 logic functions on one bit level, and 2-bit digital multiplier. Compared to previous non- modular designs, a clear reduction in the order of computations and hardware requirements is achieved.

Keywords: Boolean Functions, Simplification, KarnoughMap, Implementation of Logic Functions, Modular NeuralNetworks.

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Authors: Hazem M. El-Bakry

Abstract:

In this paper a new fast simplification method is presented. Such method realizes Karnough map with large number of variables. In order to accelerate the operation of the proposed method, a new approach for fast detection of group of ones is presented. Such approach implemented in the frequency domain. The search operation relies on performing cross correlation in the frequency domain rather than time one. It is proved mathematically and practically that the number of computation steps required for the presented method is less than that needed by conventional cross correlation. Simulation results using MATLAB confirm the theoretical computations. Furthermore, a powerful solution for realization of complex functions is given. The simplified functions are implemented by using a new desigen for neural networks. Neural networks are used because they are fault tolerance and as a result they can recognize signals even with noise or distortion. This is very useful for logic functions used in data and computer communications. Moreover, the implemented functions are realized with minimum amount of components. This is done by using modular neural nets (MNNs) that divide the input space into several homogenous regions. Such approach is applied to implement XOR function, 16 logic functions on one bit level, and 2-bit digital multiplier. Compared to previous non- modular designs, a clear reduction in the order of computations and hardware requirements is achieved.

Keywords: Boolean functions, simplification, Karnough map, implementation of logic functions, modular neural networks.

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Authors: Pucheng Zhou, Bingrong Hong

Abstract:

How to coordinate the behaviors of the agents through learning is a challenging problem within multi-agent domains. Because of its complexity, recent work has focused on how coordinated strategies can be learned. Here we are interested in using reinforcement learning techniques to learn the coordinated actions of a group of agents, without requiring explicit communication among them. However, traditional reinforcement learning methods are based on the assumption that the environment can be modeled as Markov Decision Process, which usually cannot be satisfied when multiple agents coexist in the same environment. Moreover, to effectively coordinate each agent-s behavior so as to achieve the goal, it-s necessary to augment the state of each agent with the information about other existing agents. Whereas, as the number of agents in a multiagent environment increases, the state space of each agent grows exponentially, which will cause the combinational explosion problem. Profit sharing is one of the reinforcement learning methods that allow agents to learn effective behaviors from their experiences even within non-Markovian environments. In this paper, to remedy the drawback of the original profit sharing approach that needs much memory to store each state-action pair during the learning process, we firstly address a kind of on-line rational profit sharing algorithm. Then, we integrate the advantages of modular learning architecture with on-line rational profit sharing algorithm, and propose a new modular reinforcement learning model. The effectiveness of the technique is demonstrated using the pursuit problem.

Keywords: Multi-agent learning; reinforcement learning; rationalprofit sharing; modular architecture.

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Authors: Pei-yih Ting, Dream-Ming Huang, Xiao-Wei Huang

Abstract:

Frequently a group of people jointly decide and authorize a specific person as a representative in some business/poitical occasions, e.g., the board of a company authorizes the chief executive officer to close a multi-billion acquisition deal. In this paper, an integrated proxy multi-signature scheme that allows anonymously vetoable delegation is proposed. This protocol integrates mechanisms of private veto, distributed proxy key generation, secure transmission of proxy key, and existentially unforgeable proxy multi-signature scheme. First, a provably secure Guillou-Quisquater proxy signature scheme is presented, then the “zero-sharing" protocol is extended over a composite modulus multiplicative group, and finally the above two are combined to realize the GQ proxy multi-signature with anonymously vetoable delegation. As a proxy signature scheme, this protocol protects both the original signers and the proxy signer. The modular design allows simplified implementation with less communication overheads and better computation performance than a general secure multi-party protocol.

Keywords: GQ proxy signature, proxy multi-signature, zero-sharing protocol, secure multi-party protocol, private veto protocol

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Authors: Ahmet Tekcan, Arzu Özkoç

Abstract:

Let D = 1 be a positive non-square integer and let δ = √D or 1+√D 2 be a real quadratic irrational with trace t =δ + δ and norm n = δδ. Let γ = P+δ Q be a quadratic irrational for positive integers P and Q. Given a quadratic irrational γ, there exist a quadratic ideal Iγ = [Q, δ + P] and an indefinite quadratic form Fγ(x, y) = Q(x−γy)(x−γy) of discriminant Δ = t 2−4n. In the first section, we give some preliminaries form binary quadratic forms, quadratic irrationals and quadratic ideals. In the second section, we obtain some results on γ, Iγ and Fγ for some specific values of Q and P.

Keywords: Quadratic irrationals, quadratic ideals, indefinite quadratic forms, extended modular group.

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Authors: AHM Shamsuzzoha, Tauno Kekäle, Petri Helo

Abstract:

Product customization is an essential requirement for manufacturing firms to achieve higher customers- satisfaction and fulfill business target. In order to achieve these objectives, firms need to handle both external varieties such as customer preference, government regulations, cultural considerations etc and internal varieties such as functional requirements of product, production efficiency, quality etc. Both of the varieties need to be accumulated and integrated together for the purpose of producing customized product. These varieties are presented and discussed in this paper along with the perspectives of modular product design and development process. Other development strategies such as modularity, component commonality, product family design and product platform are presented with a view to achieve product variety quickly and economically. A case example both for the concept of modular design and platform based product development process is also presented with the help of design structure matrix (DSM) tool. This paper is concluded with several managerial implications and future research direction.

Keywords: Customization modular design, platform development, product variety.

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Authors: Manpreet Singh, V. P. Agrawal, Gurmanjot Singh Bhatti

Abstract:

From the last decades, there is a significant technological advancement in the field of robotics, and a number of modular self-reconfigurable robots were introduced that can help in space exploration, bucket to stuff, search, and rescue operation during earthquake, etc. As there are numbers of self-reconfigurable robots, choosing the optimum one is always a concern for robot user since there is an increase in available features, facilities, complexity, etc. The objective of this research work is to present a multiple attribute decision making based methodology for coding, evaluation, comparison ranking and selection of modular self-reconfigurable robots using a technique for order preferences by similarity to ideal solution approach. However, 86 attributes that affect the structure and performance are identified. A database for modular self-reconfigurable robot on the basis of different pertinent attribute is generated. This database is very useful for the user, for selecting a robot that suits their operational needs. Two visual methods namely linear graph and spider chart are proposed for ranking of modular self-reconfigurable robots. Using five robots (Atron, Smores, Polybot, M-Tran 3, Superbot), an example is illustrated, and raking of the robots is successfully done, which shows that Smores is the best robot for the operational need illustrated, and this methodology is found to be very effective and simple to use.

Keywords: Self-reconfigurable robots, MADM, TOPSIS, morphogenesis, scalability.

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Authors: Sang-Yoon Lee, Jung-Mi Lee, Hyeong-Yeol Kim, Jae-Joon Song

Abstract:

In this study, a longitudinal joint connection was proposed for the short-span slab-type modular bridges with rapid construction. The slab-type modular bridge consists of a number of precast slab modules and has the joint connection between the modules in the longitudinal direction of the bridge. A finite element based parameter analysis was conducted to design the shape and the dimensions of the longitudinal joint connection. Numbers of shear keys within the joint, height and depth of the shear key, tooth angle, and the spacing were considered as the design parameters. Using the local cracking load at the corner of the shear key and the cross-sectional area of the joint, an efficiency factor was proposed to evaluate the effectiveness of the longitudinal joint connection. The dimensions of shear key were determined by comparing the cracking loads and the efficiency factors obtained from the finite element analysis.

Keywords: precast, slab bridge, modular bridge, shear key

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Authors: Majid Tolouei-Rad, Anurag Dhull

Abstract:

This paper describes various stages of design and prototyping of a modular robot for use in various industrial applications. The major goal of current research has been to design and make different robotic joints at low cost capable of being assembled together in any given order for achieving various robot configurations. Five different types of joins were designed and manufactured where extensive research has been carried out on the design of each joint in order to achieve optimal strength, size, modularity, and price. This paper presents various stages of research and development undertaken to engineer these joints that include material selection, manufacturing, and strength analysis. The outcome of this research addresses the birth of a new generation of modular industrial robots with a wider range of applications and greater efficiency.

Keywords: Actuator, control system, configuration, robot.

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Authors: O. Kurtulus, C. Yavuz

Abstract:

The end of the line controls of the finished products in the automotive industry is important. The control that has been conducted with the manual methods for the sliding doors tracks is not sufficient and faulty products cannot be identified. As a result, the customer has the faulty products. In the scope of this study, the design criteria of the PLC integrated modular end of line control unit has been examined, designed and manufactured to make the control of the 10 different track profile to 2 different vehicles with an objective to minimize the salvage costs by obtaining more sensitive, certain and accurate measurement results. In the study that started with literature and patent review, the design inputs have been specified, the technical concept has been developed, computer supported mechanic design, control system and automation design, design review and design improvement have been made. Laser analog sensors at high sensitivity, probes and modular blocks have been used in the unit. The measurement has been conducted in the system and it is observed that measurement results are more sensitive than the previous methods that we use.

Keywords: Control unit design, end of line, modular design, sliding door system.

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Authors: Ivan C. Mustakerov, Daniela I. Borissova

Abstract:

In recent years, new product development became more and more competitive and globalized, and the designing phase is critical for the product success. The concept of modularity can provide the necessary foundation for organizations to design products that can respond rapidly to market needs. The paper describes data structures and algorithms of intelligent Web-based system for modular design taking into account modules compatibility relationship and given design requirements. The system intelligence is realized by developed algorithms for choice of modules reflecting all system restrictions and requirements. The proposed data structure and algorithms are illustrated by case study of personal computer configuration. The applicability of the proposed approach is tested through a prototype of Web-based system.

Keywords: Data structures, algorithms, intelligent web-based system, modular design.

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Authors: Indradip Banerjee, Souvik Bhattacharyya, Gautam Sanyal

Abstract:

In this paper, an approach is presented to investigate the performance of Pixel Factor Mapping (PFM) and Extended PMM (Pixel Mapping Method) through the qualitative and quantitative approach. These methods are tested against a number of well-known image similarity metrics and statistical distribution techniques. The PFM has been performed in spatial domain as well as frequency domain and the Extended PMM has also been performed in spatial domain through large set of images available in the internet.

Keywords: Qualitative, quantitative, PFM, EXTENDED PMM.

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Authors: Deepthi P.P., P.S. Sathidevi

Abstract:

Proposal for a secure stream cipher based on Linear Feedback Shift Registers (LFSR) is presented here. In this method, shift register structure used for polynomial modular division is combined with LFSR keystream generator to yield a new keystream generator with much higher periodicity. Security is brought into this structure by using the Boolean function to combine state bits of the LFSR keystream generator and taking the output through the Boolean function. This introduces non-linearity and security into the structure in a way similar to the Non-linear filter generator. The security and throughput of the suggested stream cipher is found to be much greater than the known LFSR based structures for the same key length.

Keywords: Linear Feedback Shift Register, Stream Cipher, Filter generator, Keystream generator, Modular division circuit

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Authors: Poramate Manoonpong, Frank Pasemann, Florentin Wörgötter

Abstract:

This paper describes reactive neural control used to generate phototaxis and obstacle avoidance behavior of walking machines. It utilizes discrete-time neurodynamics and consists of two main neural modules: neural preprocessing and modular neural control. The neural preprocessing network acts as a sensory fusion unit. It filters sensory noise and shapes sensory data to drive the corresponding reactive behavior. On the other hand, modular neural control based on a central pattern generator is applied for locomotion of walking machines. It coordinates leg movements and can generate omnidirectional walking. As a result, through a sensorimotor loop this reactive neural controller enables the machines to explore a dynamic environment by avoiding obstacles, turn toward a light source, and then stop near to it.

Keywords: Recurrent neural networks, Walking robots, Modular neural control, Phototaxis, Obstacle avoidance behavior.

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Authors: V. Narasimha Raghavan, T. Peer Meera Labbai, N. Bhalaji, Suvitha Kesavan

Abstract:

In this paper, a new approach based on the extent of friendship between the nodes is proposed which makes the nodes to co-operate in an ad hoc environment. The extended DSR protocol is tested under different scenarios by varying the number of malicious nodes and node moving speed. It is also tested varying the number of nodes in simulation used. The result indicates the achieved throughput by extended DSR is greater than the standard DSR and indicates the percentage of malicious drops over total drops are less in the case of extended DSR than the standard DSR.

Keywords: Mobile Adhoc Networks, DSR, Grudger protocol, Nodes.

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Authors: Wiem Daoud Ben Amor, Luis Martínez López, Jr., Hela Moalla Frikha

Abstract:

Most of the multi-criteria group decision making (MCGDM) problems dealing with qualitative criteria require consideration of the large background of expert information. It is common that experts have different degrees of knowledge for giving their alternative assessments according to criteria. So, it seems logical that they use different evaluation scales to express their judgment, i.e., multi granular linguistic scales. In this context, we propose the extension of the classical additive ratio assessment (ARAS) method to the case of a hierarchical linguistics term for managing multi granular linguistic scales in uncertain context where uncertainty is modeled by means in linguistic information. The proposed approach is called the extended hierarchical linguistics-ARAS method (ELH-ARAS). Within the ELH-ARAS approach, the decision maker (DMs) can diagnose the results (the ranking of the alternatives) in a decomposed style i.e., not only at one level of the hierarchy but also at the intermediate ones. Also, the developed approach allows a feedback transformation i.e., the collective final results of all experts are able to be transformed at any level of the extended linguistic hierarchy that each expert has previously used. Therefore, the ELH-ARAS technique makes it easier for decision-makers to understand the results. Finally, an MCGDM case study is given to illustrate the proposed approach.

Keywords: Additive ratio assessment, extended hierarchical linguistic, multi-criteria group decision making problems, multi granular linguistic contexts.

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