Search results for: node-disjoint paths

Authors: Mehmet Karaata

Abstract:

Given two distinct vertices (nodes) source s and target t of a graph G = (V, E), the two node-disjoint paths problem is to identify two node-disjoint paths between s ∈ V and t ∈ V . Two paths are node-disjoint if they have no common intermediate vertices. In this paper, we present an algorithm with O(m)-time complexity for finding two node-disjoint paths between s and t in arbitrary graphs where m is the number of edges. The proposed algorithm has a wide range of applications in ensuring reliability and security of sensor, mobile and fixed communication networks.

Keywords: disjoint paths, distributed systems, fault-tolerance, network routing, security

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Authors: Li-Zhi Liao

Abstract:

The central path has played the key role in the interior point method. However, the convergence of the central path may not be true even in some convex programming problems with linear constraints. In this paper, the generalized central paths are introduced for convex programming. One advantage of the generalized central paths is that the paths will always converge to some optimal solutions of the convex programming problem for any initial interior point. Some additional theoretical properties for the generalized central paths will be also reported.

Keywords: central path, convex programming, generalized central path, interior point method

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Authors: C. P. Autry, A. W. Roscoe, Mykhailo Magal

Abstract:

We discuss the theoretical model underlying 2BPA (two-band peer authentication), a practical alternative to conventional authentication of entities and data in IoT. In essence, this involves assembling a virtual map of authentication assets in the network, typically leading to many paths of confirmation between any pair of entities. This map is continuously updated, confirmed, and evaluated. The value of authentication along multiple disjoint paths becomes very clear, and we require analogues of triangulation to extend authentication along extended paths and deliver it along all possible paths. We discover that if an attacker wants to make an honest node falsely believe she has authenticated another, then the length of the authentication paths is of little importance. This is because optimal attack strategies correspond to minimal cuts in the authentication graph and do not contain multiple edges on the same path. The authentication provided by disjoint paths normally is additive (in entropy).

Keywords: authentication, edge computing, industrial IoT, post-quantum resistance

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Authors: Ahmed R. Ismail, Hatem A. El Tawil, Nevin G. Rezk

Abstract:

Historic paths in today's cities are facing the pressure of the urban development due to the rapid urban growth. Every new development is tearing the old urban fabric and the socio-economic character of the historic paths. Furthermore, in some cases historic paths suffer from negligence and decay. Kom El Dekka historic path was one of those deteriorated paths in the city of Alexandria, Egypt, in spite of its high heritage and socio-economic value. Therefore, there was a need to develop urban regeneration strategies as a part of a wider sustainable development vision, to handle the situation and revitalize the path as a livable space in the heart of the city. This study aims to develop a comprehensive assessment methodology to evaluate the different values of the path and to create community-oriented and economic-based analysis methodology for its socio-economic values. These analysis and assessments provide strategies for any regeneration action plan for Kom El Dekka historic path.

Keywords: community-oriented, economic-based, syntactical analysis, urban regeneration

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Authors: Manas Tripathi, Arunabha Mukhopadhyay

Abstract:

In Cloud computing environment, cloud servers, sometimes may crash after receiving huge amount of request and cloud services may stop which can create huge loss to users of that cloud services. This situation is called Denial of Service (DoS) attack. In Distributed Denial of Service (DDoS) attack, an attacker targets multiple network paths by compromising various vulnerable systems (zombies) and floods the victim with huge amount of request through these zombies. There are many solutions to mitigate this challenge but most of the methods allows the attack traffic to arrive at Cloud Service Provider (CSP) and then only takes actions against mitigation. Here in this paper we are rather focusing on preventive mechanism to deal with these attacks. We analyze network topology and find most vulnerable paths beforehand without waiting for the traffic to arrive at CSP. We have used Dijkstra's and Yen’s algorithm. Finally, risk assessment of these paths can be done by multiplying the probabilities of attack for these paths with the potential loss.

Keywords: cloud computing, DDoS, Dijkstra, Yen’s k-shortest path, network security

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Authors: Tarek Ninouh, Ahmed Rouili

Abstract:

The Roman paths or roads offer a very interesting archaeological material, because they allow us to understand the history of human settlement and are also factors that increase territorial identity. Roman roads are one of the hallmarks of the Roman empire, which extends to North Africa. The objective of this investigation is to attract the attention of researchers to the importance of Roman roads and paths, which are found in Algeria, according to the quality of the materials and techniques used in this period of our history, and to encourage other decision makers to protect and enhance these routes because the current urbanization, intensive agricultural practices, or simply forgotten, decreases the sustainability of this important historical heritage.

Keywords: Roman paths, quality of materials, property, valuation

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Authors: Mei-Fang Wu, Shu-Li Wang, Feng-Tsung Cheng

Abstract:

Highly developed technology and highly competitive global market highlight the important role of competitive advantages and operation performances in sustainable company operation. Activity-Based Costing (ABC) provides accurate operation cost and operation performance information. Rich literature provide relevant research with cases study on Activity-Based Costing application, and yet, there is no research studying on cause relationship between key success factors of applying Activity-Based Costing and its specific outcomes, such as profitability or share market. These relationships provide the ways to handle the key success factors to achieve the specific outcomes for ensuring to promote the competitive advantages and operation performances. The main purposes of this research are exploring the key success paths by Key Success Paths approach which will lead the ways to apply Activity-Base Costing. The Key Success Paths is the innovative method which is exploring the cause relationships and explaining what are the effects of key success factors to specific outcomes of Activity-Based Costing implementation. The cause relationships between key success factors and successful specific outcomes are Key Success Paths (KSPs). KSPs are the guidelines to lead the cost management strategies to achieve the goals of competitive advantages and operation performances. The research findings indicate that good management system design may impact the good outcomes of Activity-Based Costing application and achieve to outstanding competitive advantage, operating performance and profitability as well by KSPs exploration.

Keywords: activity-based costing, key success factors, key success paths approach, key success paths, key failure paths

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Authors: Chae Hoon Park, Jong Kang Park, Jong Tae Kim

Abstract:

Electrical characteristics of capacitive touchscreen need to be accurately analyzed to result in better performance for multi-channel capacitance sensing. In this paper, we extracted the panel resistances and capacitances of the touchscreen by comparing measurement data and model data. By employing a lumped RC model for driver-to-receiver paths in touchscreen, we estimated resistance and capacitance values according to the physical lengths of channel paths which are proportional to the RC model. As a result, we obtained the model having 95.54% accuracy of the measurement data.

Keywords: electrical characteristics of capacitive touchscreen, iterative extraction, lumped RC model, physical lengths of channel paths

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Authors: Mounir Zili

Abstract:

We will introduce a new extension of the Brownian motion, that could serve to get a good model of many natural phenomena. It is a linear combination of a finite number of sub-fractional Brownian motions; that is why we will call it the mixed sub-fractional Brownian motion. We will present some basic properties of this process. Among others, we will check that our process is non-Markovian and that it has non-stationary increments. We will also give the conditions under which it is a semimartingale. Finally, the main features of its sample paths will be specified.

Keywords: mixed Gaussian processes, Sub-fractional Brownian motion, sample paths

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Authors: Mary Ann Cristine R. Olgado

Abstract:

This tracer study aimed to track down the TVL-ICT and EIM graduates of Las Piñas City Technical-Vocational High School as they pursue their career path and incorporated the evidence-based insights from this study as the basis for informed career pathing program and the implementation of placement exams for incoming senior high school students. The researcher utilized a graduate tracer study (GTS) using a descriptive research method employing a quanti-qualitative research design to gather data on the demographic and academic profiles of the respondents, chosen career paths, and the relevance and significance of their senior high school (SHS) track/strand to their chosen career paths. Findings revealed a diverse range of career paths pursued by SHS graduates, with a majority opting for higher education. However, there was a notable mismatch between SHS tracks/strands and higher education programs, highlighting the need for improved career paths and guidance. The study also assessed the relevance of SHS education to graduates' current jobs, with mixed results indicating areas for improvement. Despite challenges, graduates generally perceived their SHS education positively, particularly in providing hands-on experiences and relevant skills. The study concluded by emphasizing the importance of aligning SHS tracks/strands with future career paths by enhancing career pathing and guidance services to better support students in making informed decisions about their careers and incorporating assessments for personal interests and aptitudes could assist students in making more informed decisions about their career paths.

Keywords: career pathing, EIM, graduate tracer study, ICT, placement exam, TVL

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Authors: Mounir Zili

Abstract:

We will introduce a new extension of the Brownian motion, that could serve to get a good model of many natural phenomena. It is a linear combination of a finite number of sub-fractional Brownian motions; that is why we will call it the mixed sub-fractional Brownian motion. We will present some basic properties of this process. Among others, we will check that our process is non-markovian and that it has non-stationary increments. We will also give the conditions under which it is a semi-martingale. Finally, the main features of its sample paths will be specified.

Keywords: fractal dimensions, mixed gaussian processes, sample paths, sub-fractional brownian motion

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Authors: Jehnming Lin

Abstract:

In the laser cleavage of glass, the laser is mostly adopted as a heat source to generate a thermal stress state on the substrates. The crack propagation of the soda-lime glass in the laser thermal cleavage with the straight-turning paths was investigated in this study experimentally and numerically. The crack propagation was visualized by a high speed camera with the off-line examination on the micro-crack propagation. The temperature and stress distributions induced by the laser heat source were calculated by ANSYS software based on the finite element method (FEM). With the cutting paths in various turning directions, the experimental and numerical results were in comparison and verified. The fracture modes due to the normal and shear stresses were verified at the turning point of the laser cleavage path. It shows a significant variation of the stress profiles along the straight-turning paths and causes a change on the fracture modes.

Keywords: laser cleavage, glass, fracture, stress analysis

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Authors: Mehmet Hakan Karaata, Ali Hamdan, Omer Yusuf Adam Mohamed

Abstract:

Consider a distributed system that delivers messages from a process to another. Such a system is often required to deliver each message to its destination regardless of whether or not the system components experience arbitrary forms of faults. In addition, each message received by the destination must be a message sent by a system process. In this paper, we first identify the necessary and sufficient conditions to detect some restricted form of Byzantine faults referred to as modifying Byzantine faults. An observable form of a Byzantine fault whose effect is limited to the modification of a message metadata or content, timing and omission faults, and message replay is referred to as a modifying Byzantine fault. We then present a distributed protocol to detect modifying Byzantine faults using optimal number of messages over node-disjoint paths.

Keywords: Byzantine faults, distributed systems, fault detection, network pro- tocols, node-disjoint paths

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Authors: Dongqin Cheng

Abstract:

The n-dimensional balanced hypercube BHn (n ≥ 1) has been proved to be a bipartite graph. Let P be a set of edges whose induced subgraph consists of pairwise vertex-disjoint paths. For any two vertices u, v from different partite sets of V (BHn). In this paper, we prove that if |P| ≤ 2n − 2 and the subgraph induced by P has neither u nor v as internal vertices, or both of u and v as end-vertices, then BHn contains a Hamiltonian path joining u and v passing through P. As a corollary, if |P| ≤ 2n−1, then the BHn contains a Hamiltonian cycle passing through P.

Keywords: interconnection network, balanced hypercube, Hamiltonian cycle, prescribed edges

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Authors: J. S. Kim, N. P. Hong

Abstract:

In this paper, a CMOS vector modulator designed for wireless backhaul system based on 802.11ac is presented. A poly phase filter and sign select switches yield two orthogonal signal paths. Two variable gain amplifiers with strongly reduced phase shift of only ±5 ° are used to weight these paths. It has a phase control range of 360 ° and a gain range of -10 dB to 10 dB. The current drawn from a 1.2 V supply amounts 20.4 mA. Using a 0.13 mm technology, the chip die area amounts 1.47x0.75 mm².

Keywords: CMOS, phase shifter, backhaul, 802.11ac

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Authors: Pallavi Bhogaram, Xiaolong Wu, Min He, Onyedikachi Okenwa

Abstract:

A transportation network is a realization of a spatial network, describing a structure which permits either vehicular movement or flow of some commodity. Examples include road networks, railways, air routes, pipelines, and many more. The transportation network plays a vital role in maintaining the vigor of the nation’s economy. Hence, ensuring the network stays resilient all the time, especially in the face of challenges such as heavy traffic loads and large scale natural disasters, is of utmost importance. In this paper, we used the Neo4j application to develop the graph. Neo4j is the world's leading open-source, NoSQL, a native graph database that implements an ACID-compliant transactional backend to applications. The Southern California network model is developed using the Neo4j application and obtained the most critical and optimal nodes and paths in the network using centrality algorithms. The edge betweenness centrality algorithm calculates the critical or optimal paths using Yen's k-shortest paths algorithm, and the node betweenness centrality algorithm calculates the amount of influence a node has over the network. The preliminary study results confirm that the Neo4j application can be a suitable tool to study the important nodes and the critical paths for the major congested metropolitan area.

Keywords: critical path, transportation network, connectivity reliability, network model, Neo4j application, edge betweenness centrality index

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Authors: Robert Gold

Abstract:

Control flow graphs are a well-known representation of the sequential control flow structure of programs with a multitude of applications. Not only single functions but also sets of functions or complete programs can be modelled by control flow graphs. In this case the size of the graphs can grow considerably and thus makes it difficult for software engineers to analyse the control flow. Graph reductions are helpful in this situation. In this paper we define reductions to subsets of nodes. Since executions of programs are represented by paths through the control flow graphs, paths should be preserved. Furthermore, the composition of reductions makes a stepwise analysis approach possible.

Keywords: control flow graph, graph reduction, software engineering, software applications

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Authors: M. F. Wu, F. T. Cheng, C. S. Wu, M. C. Tan

Abstract:

It is a critical time to upgrade technology and increase value added with manufacturing skills developing and management strategies that will highly satisfy the customers need in the precision machinery global market. In recent years, the supply side, each precision machinery manufacturers in each country are facing the pressures of price reducing from the demand side voices that pushes the high-end precision machinery manufacturers adopts low-cost and high-quality strategy to retrieve the market. Because of the trend of the global market, the manufacturers must take price reducing strategies and upgrade technology of low-end machinery for differentiations to consolidate the market. By using six key success factors (KSFs), customer perceived value, customer satisfaction, customer service, product design, product effectiveness and machine structure quality are causal conditions to explore the impact of competitive advantage of the enterprise, such as overall profitability and product pricing power. This research uses key success paths (KSPs) approach and f/s QCA software to explore various combinations of causal relationships, so as to fully understand the performance level of KSFs and business objectives in order to achieve competitive advantage. In this study, the combination of a causal relationships, are called Key Success Paths (KSPs). The key success paths guide the enterprise to achieve the specific outcomes of business. The findings of this study indicate that there are thirteen KSPs to achieve the overall profitability, sixteen KSPs to achieve the product pricing power and seventeen KSPs to achieve both overall profitability and pricing power of the enterprise. The KSPs provide the directions of resources integration and allocation, improve utilization efficiency of limited resources to realize the continuous vision of the enterprise.

Keywords: precision machinery industry, key success factors (KSFs), key success paths (KSPs), overall profitability, product pricing power, competitive advantages

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Authors: Eirini Busack

Abstract:

Since the outbreak of the Covid-19 pandemic and the sudden transfer to online teaching, teachers have struggled to reconstruct their teaching and learning materials to adapt them to the new reality of online teaching and learning. Consequently, the pupils’ learning was disrupted during this orientation phase. Due to the above situation, teachers from all fields concluded that it is vital that their pupils should be able to continue their learning even without the teacher being physically present. Various websites and applications have been in use since then in hope that pupils will still enjoy a qualitative education; unfortunately, this was often not the case. To address this issue, it was therefore decided to focus the research on the development of digital learning paths. The fundamentals of these learning paths include the implementation of scenario-based learning (digital storytelling), the integration of media-didactic theory to make it pedagogically appropriate for learners, alongside instructional design knowledge and the drive to promote autonomous learners. This particular research is being conducted within the frame of the research project “Sustainable integration of subject didactic digital teaching-learning concepts” (InDiKo, 2020-2023), which is currently conducted at the University of Education Karlsruhe and investigates how pre-service teachers can acquire the necessary interdisciplinary and subject-specific media-didactic competencies to provide their future learners with digitally enhanced learning opportunities, and how these competencies can be developed continuously and sustainably. As English is one of the subjects involved in this project, the English Department prepared a seminar for the pre-service secondary teachers: “Media-didactic competence development: Developing learning paths & Digital Storytelling for English grammar teaching.” During this seminar, the pre-service teachers plan and design a Moodle-based differentiated lesson sequence on an English grammar topic that is to be tested by secondary school pupils. The focus of the present research is to assess the secondary school pupils’ expectations from an English grammar-focused digital learning path created by pre-service English teachers. The nine digital learning paths that are to be distributed to 25 pupils were produced over the winter and the current summer semester as the artifact of the seminar. Finally, the data to be quantitatively analysed and interpreted derive from the online questionnaires that the secondary school pupils fill in so as to reveal their expectations on what they perceive as a stimulating and thus effective grammar-focused digital learning path.

Keywords: digital storytelling, learning paths, media-didactics, autonomous learning

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Authors: Muna Tabuni

Abstract:

The paper contains an investigation on the special properties of the zeros of the analytic representations of finite quantum systems. These zeros and their paths completely define the finite quantum system. The present paper studies the construction of the analytic representation from its zeros. The analytic functions of finite quantum systems are introduced. The zeros of the analytic theta functions and their paths have been studied. The analytic function f(z) have exactly d zeros. The analytic function has been constructed from its zeros.

Keywords: construction, analytic, representation, zeros

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Authors: Katherine Carl Payne, Moshe Dror

Abstract:

The problem of minimum cost routing has been extensively explored in a variety of contexts. While there is a prevalence of routing applications based on least distance, time, and related attributes, exertion-based routing has remained relatively unexplored. In particular, the network structures traditionally used to construct minimum cost paths are not suited to representing exertion or finding paths of least exertion based on road gradient. In this paper, we introduce a topographical network or “topograph” that enables minimum cost routing based on the exertion metric on each arc in a given road network as it is related to changes in road gradient. We describe an algorithm for topograph construction and present the implementation of the topograph on a road network of the state of California with ~22 million nodes.

Keywords: topograph, RPE, routing, GIS

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Authors: Emilia-Gheorghina Negru

Abstract:

As an EU goal, gender diversity in early year’s education aims and promotes equality of chances and respect for gender peculiarities of the pupils which are involved in formal educational activities. Early year’s education, as the first step to the Curriculum, prints to teachers the need to identify the role of the gender dimension on this stage, depending on the age level of preschool children through effective, complex, innovative and analytical awareness of gender diversity teaching and management strategies. Through gender educational work we, as teachers, will examine the effectiveness of the PATHS (Promoting Alternative Thinking Strategies) curriculum the gender development of school-aged children. PATHS and a school-based preventive intervention model are necessary to be designed to improve children's ability to discuss and understand equality and gender concepts. Our teachers must create an intervention model and provide PATHS lessons during the school year. Results of the intervention will be effective for both low- and high-risk children in improving their range of math’s skills for girls and vocabulary, fluency and emotional part for boys in discussing gender experiences, their efficacy beliefs regarding the management of equality in gender area, and their developmental understanding of some aspects of gender.

Keywords: gender, gender differences, gender equality, gender role, gender stereotypes

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Authors: Min Wang, Sergey Utev

Abstract:

The lessons from the 2007-09 global financial crisis have driven scientific research, which considers the design of new methodologies and financial models in the global market. The quantum mechanics approach was introduced in the unpredictable stock market modeling. One famous quantum tool is Feynman path integral method, which was used to model insurance risk by Tamturk and Utev and adapted to formalize the path-dependent option pricing by Hao and Utev. The research is based on the path-dependent calculation method, which is motivated by the Feynman path integral method. The path calculation can be studied in two ways, one way is to label, and the other is computational. Labeling is a part of the representation of objects, and generating functions can provide many different ways of representing share price paths. In this paper, the recent works on graphical theoretical construction of individual share price path via matroid is presented. Firstly, a study is done on the knowledge of matroid, relationship between lattice path matroid and Tutte polynomials and ways to connect points in the lattice path matroid and Tutte polynomials is suggested. Secondly, It is found that a general binary tree can be validly constructed from a connected lattice path matroid rather than general lattice path matroid. Lastly, it is suggested that there is a way to represent share price paths via a general binary tree, and an algorithm is developed to construct share price paths from general binary trees. A relationship is also provided between lattice integer points and Tutte polynomials of a transversal matroid. Use this way of connection together with the algorithm, a share price path can be constructed from a given connected lattice path matroid.

Keywords: combinatorial construction, graphical representation, matroid, path calculation, share price, Tutte polynomial

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Authors: Tuğçe Yücel

Abstract:

A Wireless Sensor Network(WSN) is a collection of sensor nodes which are deployed randomly in an area for surveillance. Efficient utilization of limited battery energy of sensors for increased network lifetime as well as data security are major design objectives for WSN. Moreover secure transmission of data sensed to a base station for further processing. Producing multiple copies of data packets and sending them on different paths is one of the strategies for this purpose, which leads to redundant energy consumption and hence reduced network lifetime. In this work we develop a restricted multi-copy multipath strategy where data move through ‘frequently’ or ‘heavily’ used sensors is copied by the sensor incident to such central nodes and sent on node-disjoint paths. We develop a mixed integer programing(MIP) model and heuristic approach present some preleminary test results.

Keywords: MIP, sensor, telecommunications, WSN

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Authors: Akshit Singhal, Xuan Wang, Zhijun Wang, Hao Che, Hong Jiang

Abstract:

Multiple Path Transmission Control Protocols (MPTCPs) allow flows to explore path diversity to improve the throughput, reliability and network resource utilization. However, the existing solutions may discourage users to adopt the solutions in the face of multipath scenario where different paths are charged based on different pricing structures, e.g., WiFi vs cellular connections, widely available for mobile phones. In this paper, we propose a Hybrid MPTCP (H-MPTCP) with a built-in mechanism to incentivize users to use multiple paths with different pricing structures. In the meantime, H-MPTCP preserves the nice properties enjoyed by the state-of-the-art MPTCP solutions. Extensive real Linux implementation results verify that H-MPTCP can indeed achieve the design objectives.

Keywords: network, TCP, WiFi, cellular, congestion control

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Authors: Fujio Takata

Abstract:

When governments levy taxes on labor income on the basis of a balanced budget rule, two steady states in an economy exist, of which one can cause two movement patterns, namely, indeterminacy paths and a saddle path. However, in this paper, we assume an economy with divisible labor, in which labor adjustment is made by an intensive margin. We demonstrate that there indeed exist the two paths in the economy and that there exists a critical condition dividing them. This is proved by establishing the relationship between a finite elasticity of labor with regard to real wages and the share of capital in output. Consequently, we deduce the existence of an upper limit in the share of capital in output for indeterminacy to occur. The largest possible value of that share is less than 0.5698.

Keywords: balanced budget rule, divisible labor, labor income taxation, two movement patterns

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Authors: Mehmet Hakan Karaata, Ali Hamdan, Omer Yusuf Adam Mohamed

Abstract:

Consider a distributed system that delivers messages from a process to another. Such a system is often required to deliver each message to its destination regardless of whether or not the system components experience arbitrary forms of faults. In addition, each message received by the destination must be a message sent by a system process. In this paper, we first identify the necessary and sufficient conditions to detect some restricted form of Byzantine faults referred to as modifying Byzantine faults. An observable form of a Byzantine fault whose effect is limited to the modification of a message metadata or content, timing and omission faults, and message replay is referred to as a modifying Byzantine fault. We then present a distributed protocol to detect modifying Byzantine faults using optimal number of messages over node-disjoint paths.

Keywords: Byzantine faults, distributed systems, fault detection, network protocols, node-disjoint paths

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Authors: Mohamed O. Babana

Abstract:

In wireless channel multipath is the propagation phenomena where the transmitted signal arrive at the receiver side with many of paths, the signal at these paths arrive with different time delay the results is random signal fading due to intersymbols interference(ISI). This paper deals with identification of orthogonal frequency division multiplexing (OFDM) technology, and how it is used to overcome intersymbol interference due to multipath. Also investigates the effect of Additive White Gaussian Noise Channel (AWGN) on OFDM using multi-level modulation of Phase Shift Keying (PSK), computer simulation to calculate the bit error rate (BER) under AWGN channel is applied. A comparison study is carried out to obtain the Bit Error Rate performance for OFDM to identify the best multi-level modulation of PSK.

Keywords: intersymbol interference(ISI), bit error rate(BER), modulation, multiplexing, simulation

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Authors: Hassam Hassan Elborombaly

Abstract:

The pollution generated from transportation modes, congestion and traffic heritage has led to the deterioration of historic buildings and the urban heritage in historic cities. Accordingly, this paper attempts to diagnose the transport and traffic problems in historic cities. In general and in Heritage Cities, and to investigate methods for conserving the urban heritage from negative effects of traffic congestion and of the traditional red modes of transportation. It also attempts to explore possible areas for intervention to mitigate transportation and traffic problems in the light of the principles of the sustainable transportation framework. It aims to draw conclusion and propose recommendation that would increase the efficiency and effectiveness of transportation plans in historic Cairo and consequently achieve sustainable transportation. Problems In historic cities public paths compose an irregular network enclosing large residential plots (defined as super blocks quarters or hettas). The blocks represent the basic morphology units in historic Cities. Each super block incorporates several uses (i.e. residential, non-residential, service uses and others). Local paths reach the interior of the super blocks in an organized inter core, which deals mainly with residential functions mixed with handicraft activities and is composed of several local path units; (b) the other core, which is bound by the public paths and contains a combination of residential, commercial and social activities. Objectives: 1- To provide amenity convenience and comfort for visitors and people who live and work in the area. Pedestrianizing, accessibility and safety are to be reinforced while respecting the organic urban pattern. 2- To enhance street life, vitality and activity, in order to attract people and increase economic prosperity. Research Contents • Relation between residential areas and transportation in the inner core • Analytical studies for historic areas in heritage cities • Sustainable transportation planning in heritage cities • Dynamic and flexible methodology for achieving sustainable transportation network for the Heritage Cities • Result and Recommendation

Keywords: irregular network, public paths, sustainable transportation, urban heritage

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Authors: M. M. M. Jaradat

Abstract:

For a given graph G, the set Ԑ of all subsets of E(G) forms an |E(G)| dimensional vector space over Z2 with vector addition X⊕Y = (X\Y ) [ (Y \X) and scalar multiplication 1.X = X and 0.X = Ø for all X, Yϵ Ԑ. The cycle space, C(G), of a graph G is the vector subspace of (E; ⊕; .) spanned by the cycles of G. Traditionally there have been two notions of minimality among bases of C(G). First, a basis B of G is called a d-fold if each edge of G occurs in at most d cycles of the basis B. The basis number, b(G), of G is the least non-negative integer d such that C(G) has a d-fold basis; a required basis of C(G) is a basis for which each edge of G belongs to at most b(G) elements of B. Second, a basis B is called a minimum cycle basis (MCB) if its total length Σ BϵB |B| is minimum among all bases of C(G). The lexicographic product GρH has the vertex set V (GρH) = V (G) x V (H) and the edge set E(GρH) = {(u1, v1)(u2, v2)|u1 = u2 and v1 v2 ϵ E(H); or u1u2 ϵ E(G) and there is α ϵ Aut(H) such that α (v1) = v2}. In this work, a construction of a minimum cycle basis for the wreath product of wheels with paths is presented. Also, the length of the longest cycle of a minimum cycle basis is determined. Moreover, the basis number for the wreath product of the same is investigated.

Keywords: cycle space, minimum cycle basis, basis number, wreath product

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