Search results for: Detour eigenvalue (of a graph)

Authors: Kemal Efe, Gui-Liang Feng

Abstract:

The optimal bisection width of r-dimensional N× · · ·× N grid is known to be Nr-1 when N is even, but when N is odd, only approximate values are available. This paper shows that the exact bisection width of grid is Nr -1 N-1 when N is odd.

Keywords: Grids, Parallel Architectures, Graph Bisection, VLSI Layouts.

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Authors: Edward Aris D. Fajardo, Hamdi Muhyuddin D. Barra

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This study employs the use of the fourth order Numerov scheme to determine the eigenstates and eigenvalues of particles, electrons in particular, in single and double delta function potentials. For the single delta potential, it is found that the eigenstates could only be attained by using specific potential depths. The depth of the delta potential well has a value that varies depending on the delta strength. These depths are used for each well on the double delta function potential and the eigenvalues are determined. There are two bound states found in the computation, one with a symmetric eigenstate and another one which is antisymmetric.

Keywords: Double Delta Potential, Eigenstates, Eigenvalue, Numerov Method, Single Delta Potential

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Authors: A. Meftah, D. Zarga, M. Yahiaoui

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In this paper, we have used an analytical method to analyze the vibratory behavior of plates in materials with gradient of properties, simply supported, proposing a refined non polynomial theory. The number of unknown functions involved in this theory is only four, as compared to five in the case of other higher shear deformation theories. The transverse shearing effects are studied according to the thickness of the plate. The motion equations for the FGM plates are obtained by the Hamilton principle application, the solutions are obtained using the Navier method, and then the fundamental frequencies are found, solving an eigenvalue equation system, the results of this analysis are presented and compared to those available in the literature.

Keywords: FGM plates, Navier method, vibratory behavior.

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Authors: Dia I. Abu-Al-Nadi, M. J. Mismar, T. H. Ismail

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A technique for estimating the direction-of-arrival (DOA) of unknown number of source signals is presented using the eigen-approach. The eigenvector corresponding to the minimum eigenvalue of the autocorrelation matrix yields the minimum output power of the array. Also, the array polynomial with this eigenvector possesses roots on the unit circle. Therefore, the pseudo-spectrum is found by perturbing the phases of the roots one by one and calculating the corresponding array output power. The results indicate that the DOAs and the number of source signals are estimated accurately in the presence of a wide range of input noise levels.

Keywords: Array signal processing, direction-of-arrival, antenna arrays, eigenvalues, eigenvectors.

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Authors: Hui-Chuan Lu

Abstract:

A perfect secret-sharing scheme is a method to distribute a secret among a set of participants in such a way that only qualified subsets of participants can recover the secret and the joint share of participants in any unqualified subset is statistically independent of the secret. The collection of all qualified subsets is called the access structure of the perfect secret-sharing scheme. In a graph-based access structure, each vertex of a graph G represents a participant and each edge of G represents a minimal qualified subset. The average information ratio of a perfect secret-sharing scheme  realizing the access structure based on G is defined as AR = (Pv2V (G) H(v))/(|V (G)|H(s)), where s is the secret and v is the share of v, both are random variables from  and H is the Shannon entropy. The infimum of the average information ratio of all possible perfect secret-sharing schemes realizing a given access structure is called the optimal average information ratio of that access structure. Most known results about the optimal average information ratio give upper bounds or lower bounds on it. In this present structures based on bipartite graphs and determine the exact values of the optimal average information ratio of some infinite classes of them.

Keywords: secret-sharing scheme, average information ratio, star covering, core sequence.

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Authors: Mahdi Nouri

Abstract:

In this paper Algebraic Riccati matrix equation is used for Eigen-decomposition of special structured matrices. This is achieved by similarity transformation and then using algebraic riccati matrix equation to triangulation of matrices. The process is decomposition of matrices into small and specially structured submatrices with low dimensions for fast and easy finding of Eigenpairs. Numerical and structural examples included showing the efficiency of present method.

Keywords: Riccati, matrix equation, eigenvalue problem, symmetric, bisymmetric, persymmetric, decomposition, canonical forms, Graphs theory, adjacency and Laplacian matrices.

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Authors: Yuan-Kang Shih, Shu-Li Chang, Shin-Shin Kao

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Qk n has been shown as an alternative to the hypercube family. For any even integer k ≥ 4 and any integer n ≥ 2, Qk n is a bipartite graph. In this paper, we will prove that given any pair of vertices, w and b, from different partite sets of Qk n, there exist 2n internally disjoint paths between w and b, denoted by {Pi | 0 ≤ i ≤ 2n-1}, such that 2n-1 i=0 Pi covers all vertices of Qk n. The result is optimal since each vertex of Qk n has exactly 2n neighbors.

Keywords: container, Hamiltonian, k-ary n-cube, m*-connected.

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Authors: Norihan Md Arifin, Norfifah Bachok

Abstract:

The onset of Marangoni convection in a horizontal fluid layer with internal heat generation overlying a solid layer heated from below is studied. The upper free surface of a fluid is nondeformable and the bottom boundary are rigid and no-slip. The resulting eigenvalue problem is solved exactly. The critical values of the Marangoni numbers for the onset of Marangoni convection are calculated and the latter is found to be critically dependent on the internal heating, depth ratio and conductivity ratio. The effects of the thermal conductivity and the thickness of the solid plate on the onset of convective instability with internal heating are studied in detail.

Keywords: Linear stability, Marangoni convection, Internal Heatgeneration.

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Authors: Andrii Shalaginov, Katrin Franke, Xiongwei Huang

Abstract:

One of the leading problems in Cyber Security today is the emergence of targeted attacks conducted by adversaries with access to sophisticated tools. These attacks usually steal senior level employee system privileges, in order to gain unauthorized access to confidential knowledge and valuable intellectual property. Malware used for initial compromise of the systems are sophisticated and may target zero-day vulnerabilities. In this work we utilize common behaviour of malware called ”beacon”, which implies that infected hosts communicate to Command and Control servers at regular intervals that have relatively small time variations. By analysing such beacon activity through passive network monitoring, it is possible to detect potential malware infections. So, we focus on time gaps as indicators of possible C2 activity in targeted enterprise networks. We represent DNS log files as a graph, whose vertices are destination domains and edges are timestamps. Then by using four periodicity detection algorithms for each pair of internal-external communications, we check timestamp sequences to identify the beacon activities. Finally, based on the graph structure, we infer the existence of other infected hosts and malicious domains enrolled in the attack activities.

Keywords: Malware detection, network security, targeted attack.

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Authors: Shih-Yi Chao

Abstract:

The similarity comparison of RNA secondary structures is important in studying the functions of RNAs. In recent years, most existing tools represent the secondary structures by tree-based presentation and calculate the similarity by tree alignment distance. Different to previous approaches, we propose a new method based on maximum clique detection algorithm to extract the maximum common structural elements in compared RNA secondary structures. A new graph-based similarity measurement and maximum common subgraph detection procedures for comparing purely RNA secondary structures is introduced. Given two RNA secondary structures, the proposed algorithm consists of a process to determine the score of the structural similarity, followed by comparing vertices labelling, the labelled edges and the exact degree of each vertex. The proposed algorithm also consists of a process to extract the common structural elements between compared secondary structures based on a proposed maximum clique detection of the problem. This graph-based model also can work with NC-IUB code to perform the pattern-based searching. Therefore, it can be used to identify functional RNA motifs from database or to extract common substructures between complex RNA secondary structures. We have proved the performance of this proposed algorithm by experimental results. It provides a new idea of comparing RNA secondary structures. This tool is helpful to those who are interested in structural bioinformatics.

Keywords: Clique detection, labeled vertices, RNA secondary structures, subgraph, similarity.

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Authors: Kyekyung Kim, Sangseung Kang, Suyoung Chi, Jaehong Kim

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In recent years, IT convergence technology has been developed to get creative solution by combining robotics or sports science technology. Object detection and recognition have mainly applied to sports science field that has processed by recognizing face and by tracking human body. But object detection and recognition using vision sensor is challenge task in real world because of illumination. In this paper, object detection and recognition using vision sensor applied to sports simulator has been introduced. Face recognition has been processed to identify user and to update automatically a person athletic recording. Human body has tracked to offer a most accurate way of riding horse simulator. Combined image processing has been processed to reduce illumination adverse affect because illumination has caused low performance in detection and recognition in real world application filed. Face has recognized using standard face graph and human body has tracked using pose model, which has composed of feature nodes generated diverse face and pose images. Face recognition using Gabor wavelet and pose recognition using pose graph is robust to real application. We have simulated using ETRI database, which has constructed on horse riding simulator.

Keywords: Horse riding simulator, Object detection, Object recognition, User identification, Pose recognition.

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Authors: Hui-Chuan Lu

Abstract:

In a perfect secret-sharing scheme, a dealer distributes a secret among a set of participants in such a way that only qualified subsets of participants can recover the secret and the joint share of the participants in any unqualified subset is statistically independent of the secret. The access structure of the scheme refers to the collection of all qualified subsets. In a graph-based access structures, each vertex of a graph G represents a participant and each edge of G represents a minimal qualified subset. The average information ratio of a perfect secret-sharing scheme realizing a given access structure is the ratio of the average length of the shares given to the participants to the length of the secret. The infimum of the average information ratio of all possible perfect secret-sharing schemes realizing an access structure is called the optimal average information ratio of that access structure. We study the optimal average information ratio of the access structures based on bipartite graphs. Based on some previous results, we give a bound on the optimal average information ratio for all bipartite graphs of girth at least six. This bound is the best possible for some classes of bipartite graphs using our approach.

Keywords: Secret-sharing scheme, average information ratio, star covering, deduction, core cluster.

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Authors: Alessandro Cincotti, Timothee Bossart

Abstract:

Col is a classic combinatorial game played on graphs and to solve a general instance is a PSPACE-complete problem. However, winning strategies can be found for some specific graph instances. In this paper, the solution of Col on complete k-ary trees is presented.

Keywords: Combinatorial game, Complete k-ary tree, Mapcoloring game.

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Authors: Olus N. Boratav, Zheming Zheng, Chunfeng Zhou

Abstract:

The stability of Newtonian and Non-Newtonian extending films under local or global heating or cooling conditions are considered. The thickness-averaged mass, momentum and energy equations with convective and radiative heat transfer are derived, both for Newtonian and non-Newtonian fluids (Maxwell, PTT and Giesekus models considered). The stability of the system is explored using either eigenvalue analysis or transient simulations. The results showed that the influence of heating and cooling on stability strongly depends on the magnitude of the Peclet number. Examples of stabilization or destabilization of heating or cooling are shown for Pe<< 1, and Pe = O(1) cases, for Newtonian and non-Newtonian flows.

Keywords: Extended films, stability, eigen-analysis for stability, transient response, polymer instability, Non-Newtonian fluids.

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Authors: M. H. Kargarnovin, A. Mamandi

Abstract:

This paper presents investigation effects of a sharp edged gust on aeroelastic behavior and time-domain response of a typical section model using Jones approximate aerodynamics for pure plunging motion. Flutter analysis has been done by using p and p-k methods developed for presented finite-state aerodynamic model for a typical section model (airfoil). Introduction of gust analysis as a linear set of ordinary differential equations in a simplified procedure has been carried out by using transformation into an eigenvalue problem.

Keywords: Aeroelastic response, jones approximation, pure plunging motion, sharp edged gust.

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Authors: Manisha Dubey, Pankaj Gupta

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This paper presents a systematic approach for the design of power system stabilizer using genetic algorithm and investigates the robustness of the GA based PSS. The proposed approach employs GA search for optimal setting of PSS parameters. The performance of the proposed GPSS under small and large disturbances, loading conditions and system parameters is tested. The eigenvalue analysis and nonlinear simulation results show the effectiveness of the GPSS to damp out the system oscillations. It is found tat the dynamic performance with the GPSS shows improved results, over conventionally tuned PSS over a wide range of operating conditions.

Keywords: Genetic Algorithm, Genetic power system stabilizer, Power system stabilizer, Small signal stability

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Authors: Hidetoshi Nonaka

Abstract:

This paper presents an interactive modeling system of polyhedra using the isomorphic graphs. Especially, Conway polyhedron notation is implemented. The notation can be observed as interactive animation.

Keywords: Conway polyhedron notation, Polyhedral graph, Visualization.

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Authors: Patrick Cummings, Laura Cassani, Deirdre Kelliher

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In this paper we present findings from a research effort to apply a hybrid collaborative-context approach for a system focused on Marine Corps civil affairs data collection, aggregation, and analysis called the Marine Civil Information Management System (MARCIMS). The goal of this effort is to provide operators with information to make sense of the interconnectedness of entities and relationships in their area of operation and discover existing data to support civil military operations. Our approach to build a recommendation engine was designed to overcome several technical challenges, including 1) ensuring models were robust to the relatively small amount of data collected by the Marine Corps civil affairs community; 2) finding methods to recommend novel data for which there are no interactions captured; and 3) overcoming confirmation bias by ensuring content was recommended that was relevant for the mission despite being obscure or less well known. We solve this by implementing a combination of collective matrix factorization (CMF) and graph-based random walks to provide recommendations to civil military operations users. We also present a method to resolve the challenge of computation complexity inherent from highly connected nodes through a precomputed process.

Keywords: Recommendation engine, collaborative filtering, context based recommendation, graph analysis, coverage, civil affairs operations, Marine Corps.

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Authors: Nor Fadzillah Mohd Mokhtar, Norihan Md Arifin, Roslinda Nazar, Fudziah Ismail, MohamedSuleiman

Abstract:

The stability analysis of Marangoni convection in porous media with a deformable upper free surface is investigated. The linear stability theory and the normal mode analysis are applied and the resulting eigenvalue problem is solved exactly. The Darcy law and the Brinkman model are used to describe the flow in the porous medium heated from below. The effect of the Crispation number, Bond number and the Biot number are analyzed for the stability of the system. It is found that a decrease in the Crispation number and an increase in the Bond number delay the onset of convection in porous media. In addition, the system becomes more stable when the Biot number is increases and the Daeff number is decreases.

Keywords: Deformable, Marangoni, Porous, Stability.

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Authors: Chia-Feng Lu, Yuh-Jen Wang, Shin Teng, Yu-Te Wu, Sui-Hing Yan

Abstract:

Brain functional networks based on resting-state EEG data were compared between patients with mild Alzheimer’s disease (mAD) and matched patients with amnestic subtype of mild cognitive impairment (aMCI). We integrated the time–frequency cross mutual information (TFCMI) method to estimate the EEG functional connectivity between cortical regions and the network analysis based on graph theory to further investigate the alterations of functional networks in mAD compared with aMCI group. We aimed at investigating the changes of network integrity, local clustering, information processing efficiency, and fault tolerance in mAD brain networks for different frequency bands based on several topological properties, including degree, strength, clustering coefficient, shortest path length, and efficiency. Results showed that the disruptions of network integrity and reductions of network efficiency in mAD characterized by lower degree, decreased clustering coefficient, higher shortest path length, and reduced global and local efficiencies in the delta, theta, beta2, and gamma bands were evident. The significant changes in network organization can be used in assisting discrimination of mAD from aMCI in clinical.

Keywords: EEG, functional connectivity, graph theory, TFCMI.

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Authors: Zhipeng Chen, Peng Zhang, Qingyun Liu, Li Guo

Abstract:

With the Internet becoming the dominant channel for business and life, many IPs are increasingly masked using web proxies for illegal purposes such as propagating malware, impersonate phishing pages to steal sensitive data or redirect victims to other malicious targets. Moreover, as Internet traffic continues to grow in size and complexity, it has become an increasingly challenging task to detect the proxy service due to their dynamic update and high anonymity. In this paper, we present an approach based on behavioral graph analysis to study the behavior similarity of web proxy users. Specifically, we use bipartite graphs to model host communications from network traffic and build one-mode projections of bipartite graphs for discovering social-behavior similarity of web proxy users. Based on the similarity matrices of end-users from the derived one-mode projection graphs, we apply a simple yet effective spectral clustering algorithm to discover the inherent web proxy users behavior clusters. The web proxy URL may vary from time to time. Still, the inherent interest would not. So, based on the intuition, by dint of our private tools implemented by WebDriver, we examine whether the top URLs visited by the web proxy users are web proxies. Our experiment results based on real datasets show that the behavior clusters not only reduce the number of URLs analysis but also provide an effective way to detect the web proxies, especially for the unknown web proxies.

Keywords: Bipartite graph, clustering, one-mode projection, web proxy detection.

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Authors: Mansour Nikkhah-Bahrami, Masih Loghmani, Mostafa Pooyanfar

Abstract:

In this paper, an analytical approach for free vibration analysis of rectangular and circular membranes is presented. The method is based on wave approach. From wave standpoint vibration propagate, reflect and transmit in a structure. Firstly, the propagation and reflection matrices for rectangular and circular membranes are derived. Then, these matrices are combined to provide a concise and systematic approach to free vibration analysis of membranes. Subsequently, the eigenvalue problem for free vibration of membrane is formulated and the equation of membrane natural frequencies is constructed. Finally, the effectiveness of the approach is shown by comparison of the results with existing classical solution.

Keywords: Rectangular and circular membranes, propagation matrix, reflection matrix, vibration analysis.

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Authors: Bohuslava Juhasova, Martin Juhas, Renata Masarova, Zuzana Sutova

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The article deals with the tool in Matlab GUI form that is designed to analyse a mechatronic system sensitivity and tolerance. In the analysed mechatronic system, a torque is transferred from the drive to the load through a coupling containing flexible elements. Different methods of control system design are used. The classic form of the feedback control is proposed using Naslin method, modulus optimum criterion and inverse dynamics method. The cascade form of the control is proposed based on combination of modulus optimum criterion and symmetric optimum criterion. The sensitivity is analysed on the basis of absolute and relative sensitivity of system function to the change of chosen parameter value of the mechatronic system, as well as the control subsystem. The tolerance is analysed in the form of determining the range of allowed relative changes of selected system parameters in the field of system stability. The tool allows to analyse an influence of torsion stiffness, torsion damping, inertia moments of the motor and the load and controller(s) parameters. The sensitivity and tolerance are monitored in terms of the impact of parameter change on the response in the form of system step response and system frequency-response logarithmic characteristics. The Symbolic Math Toolbox for expression of the final shape of analysed system functions was used. The sensitivity and tolerance are graphically represented as 2D graph of sensitivity or tolerance of the system function and 3D/2D static/interactive graph of step/frequency response.

Keywords: Mechatronic systems, Matlab GUI, sensitivity, tolerance.

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Authors: Feng-Yi Huang, Yuan-Jye Tseng

Abstract:

In the traditional concept of product life cycle management, the activities of design, manufacturing, and assembly are performed in a sequential way. The drawback is that the considerations in design may contradict the considerations in manufacturing and assembly. The different designs of components can lead to different assembly sequences. Therefore, in some cases, a good design may result in a high cost in the downstream assembly activities. In this research, an integrated design evaluation and assembly sequence planning model is presented. Given a product requirement, there may be several design alternative cases to design the components for the same product. If a different design case is selected, the assembly sequence for constructing the product can be different. In this paper, first, the designed components are represented by using graph based models. The graph based models are transformed to assembly precedence constraints and assembly costs. A particle swarm optimization (PSO) approach is presented by encoding a particle using a position matrix defined by the design cases and the assembly sequences. The PSO algorithm simultaneously performs design evaluation and assembly sequence planning with an objective of minimizing the total assembly costs. As a result, the design cases and the assembly sequences can both be optimized. The main contribution lies in the new concept of integrated design evaluation and assembly sequence planning model and the new PSO solution method. The test results show that the presented method is feasible and efficient for solving the integrated design evaluation and assembly planning problem. In this paper, an example product is tested and illustrated.

Keywords: assembly sequence planning, design evaluation, design for assembly, particle swarm optimization

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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: Transportation network, critical path, connectivity reliability, network model, Neo4J application, optimal path, critical path, edge betweenness centrality index, node betweenness centrality index, Yen’s k-shortest paths.

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Authors: Sunitha S. L., V. Udayashankara

Abstract:

Hearing impairment is the number one chronic disability affecting many people in the world. Background noise is particularly damaging to speech intelligibility for people with hearing loss especially for sensorineural loss patients. Several investigations on speech intelligibility have demonstrated sensorineural loss patients need 5-15 dB higher SNR than the normal hearing subjects. This paper describes Discrete Hartley Transform Power Normalized Least Mean Square algorithm (DHT-LMS) to improve the SNR and to reduce the convergence rate of the Least Means Square (LMS) for sensorineural loss patients. The DHT transforms n real numbers to n real numbers, and has the convenient property of being its own inverse. It can be effectively used for noise cancellation with less convergence time. The simulated result shows the superior characteristics by improving the SNR at least 9 dB for input SNR with zero dB and faster convergence rate (eigenvalue ratio 12) compare to time domain method and DFT-LMS.

Keywords: Hearing Impairment, DHT-LMS, Convergence rate, SNR improvement.

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Authors: Sangjun Park, Sangbae Jeong, Moonsung Han, Minsoo hahn

Abstract:

In this paper, a target signal detection method using multiple signal classification (MUSIC) algorithm is proposed. The MUSIC algorithm is a subspace-based direction of arrival (DOA) estimation method. The algorithm detects the DOAs of multiple sources using the inverse of the eigenvalue-weighted eigen spectra. To apply the algorithm to target signal detection for GSC-based beamforming, we utilize its spectral response for the target DOA in noisy conditions. For evaluation of the algorithm, the performance of the proposed target signal detection method is compared with that of the normalized cross-correlation (NCC), the fixed beamforming, and the power ratio method. Experimental results show that the proposed algorithm significantly outperforms the conventional ones in receiver operating characteristics(ROC) curves.

Keywords: Beamforming, direction of arrival, multiple signal classification, target signal detection.

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Authors: Pa Pa Lin

Abstract:

This research work is concerned with the eigenvalue problem for the integral operators which are obtained by linearization of a nonlocal evolution equation. The purpose of section II.A is to describe the nature of the problem and the objective of the project. The problem is related to the “stable solution" of the evolution equation which is the so-called “instanton" that describe the interface between two stable phases. The analysis of the instanton and its asymptotic behavior are described in section II.C by imposing the Green function and making use of a probability kernel. As a result , a classical Theorem which is important for an instanton is proved. Section III devoted to a study of the integral operators related to interface dynamics which concern the analysis of the Cauchy problem for the evolution equation with initial data close to different phases and different regions of space.

Keywords: Evolution, Green function, instanton, integral operators.

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Authors: Ali Essam El Shazly

Abstract:

The social logic of 'Sequina' slum area in Alexandria details the integral measure of space syntax at the room-level of twenty-building samples. The essence of spatial structure integrates the central 'visitor' domain with the 'living' frontage of the 'children' zone against the segregated privacy of the opposite 'parent' depth. Meanwhile, the multifunctioning of shallow rooms optimizes the integral 'visitor' structure through graph and visibility dimensions in contrast to the 'inhabitant' structure of graph-tails out of sight. Common theme of the layout integrity increases in compensation to the decrease of room visibility. Despite the 'pheno-type' of collective integration, the individual layouts observe 'geno-type' structure of spatial diversity per room adjoins. In this regard, the layout integrity alternates the cross-correlation of the 'kitchen & living' rooms with the 'inhabitant & visitor' domains of 'motherhood' dynamic structure. Moreover, the added 'grandparent' restructures the integral measure to become the deepest space, but opens to the 'living' of 'household' integrity. Some isomorphic layouts change the integral structure just through the 'balcony' extension of access, visual or ignored 'ringiness' of space syntax. However, the most integrated or segregated layouts invert the 'geno-type' into a shallow 'inhabitant' centrality versus the remote 'visitor' structure. Overview of the multivariate social logic of spatial integrity could never clarify without the micro-data analysis.

Keywords: Alexandria, Sequina slum, spatial integration, space syntax.

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Authors: Michel Soto Chalhoub

Abstract:

Building code-related literature provides recommendations on normalizing approaches to the calculation of the dynamic properties of structures. Most building codes make a distinction among types of structural systems, construction material, and configuration through a numerical coefficient in the expression for the fundamental period. The period is then used in normalized response spectra to compute base shear. The typical parameter used in simplified code formulas for the fundamental period is overall building height raised to a power determined from analytical and experimental results. However, reinforced concrete buildings which constitute the majority of built space in less developed countries pose additional challenges to the ones built with homogeneous material such as steel, or with concrete under stricter quality control. In the present paper, the particularities of reinforced concrete buildings are explored and related to current methods of equivalent static analysis. A comparative study is presented between the Uniform Building Code, commonly used for buildings within and outside the USA, and data from the Middle East used to model 151 reinforced concrete buildings of varying number of bays, number of floors, overall building height, and individual story height. The fundamental period was calculated using eigenvalue matrix computation. The results were also used in a separate regression analysis where the computed period serves as dependent variable, while five building properties serve as independent variables. The statistical analysis shed light on important parameters that simplified code formulas need to account for including individual story height, overall building height, floor plan, number of bays, and concrete properties. Such inclusions are important for reinforced concrete buildings of special conditions due to the level of concrete damage, aging, or materials quality control during construction. Overall results of the present analysis show that simplified code formulas for fundamental period and base shear may be applied but they require revisions to account for multiple parameters. The conclusion above is confirmed by the analytical model where fundamental periods were computed using numerical techniques and eigenvalue solutions. This recommendation is particularly relevant to code upgrades in less developed countries where it is customary to adopt, and mildly adapt international codes. We also note the necessity of further research using empirical data from buildings in Lebanon that were subjected to severe damage due to impulse loading or accelerated aging. However, we excluded this study from the present paper and left it for future research as it has its own peculiarities and requires a different type of analysis.

Keywords: Seismic behavior, reinforced concrete, simplified code formulas, equivalent static analysis, base shear, response spectra.

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