Search results for: Matrix game
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 1216

Search results for: Matrix game

1186 Markov Game Controller Design Algorithms

Authors: Rajneesh Sharma, M. Gopal

Abstract:

Markov games are a generalization of Markov decision process to a multi-agent setting. Two-player zero-sum Markov game framework offers an effective platform for designing robust controllers. This paper presents two novel controller design algorithms that use ideas from game-theory literature to produce reliable controllers that are able to maintain performance in presence of noise and parameter variations. A more widely used approach for controller design is the H∞ optimal control, which suffers from high computational demand and at times, may be infeasible. Our approach generates an optimal control policy for the agent (controller) via a simple Linear Program enabling the controller to learn about the unknown environment. The controller is facing an unknown environment, and in our formulation this environment corresponds to the behavior rules of the noise modeled as the opponent. Proposed controller architectures attempt to improve controller reliability by a gradual mixing of algorithmic approaches drawn from the game theory literature and the Minimax-Q Markov game solution approach, in a reinforcement-learning framework. We test the proposed algorithms on a simulated Inverted Pendulum Swing-up task and compare its performance against standard Q learning.

Keywords: Reinforcement learning, Markov Decision Process, Matrix Games, Markov Games, Smooth Fictitious play, Controller, Inverted Pendulum.

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1185 The Design and Analysis of Learning Effects for a Game-based Learning System

Authors: Wernhuar Tarng, Weichian Tsai

Abstract:

The major purpose of this study is to use network and multimedia technologies to build a game-based learning system for junior high school students to apply in learning “World Geography" through the “role-playing" game approaches. This study first investigated the motivation and habits of junior high school students to use the Internet and online games, and then designed a game-based learning system according to situated and game-based learning theories. A teaching experiment was conducted to analyze the learning effectiveness of students on the game-based learning system and the major factors affecting their learning. A questionnaire survey was used to understand the students- attitudes towards game-based learning. The results showed that the game-based learning system can enhance students- learning, but the gender of students and their habits in using the Internet have no significant impact on learning. Game experience has a significant impact on students- learning, and the higher the experience value the better the effectiveness of their learning. The results of questionnaire survey also revealed that the system can increase students- motivation and interest in learning "World Geography".

Keywords: Game-based learning, situated learning, role playing, learning effectiveness, learning motivation.

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1184 Investigating Mental Workload of VR Training versus Serious Game Training on Shoot Operation Training

Authors: Ta-Min Hung, Tien-Lung Sun

Abstract:

Thanks to VR technology advanced, there are many researches had used VR technology to develop a training system. Using VR characteristics can simulate many kinds of situations to reach our training-s goal. However, a good training system not only considers real simulation but also considers learner-s learning motivation. So, there are many researches started to conduct game-s features into VR training system. We typically called this is a serious game. It is using game-s features to engage learner-s learning motivation. However, VR or Serious game has another important advantage. That is simulating feature. Using this feature can create any kinds of pressured environments. Because in the real environment may happen any emergent situations. So, increasing the trainees- pressure is more important when they are training. Most pervious researches are investigated serious game-s applications and learning performance. Seldom researches investigated how to increase the learner-s mental workload when they are training. So, in our study, we will introduce a real case study and create two types training environments. Comparing the learner-s mental workload between VR training and serious game.

Keywords: Intrinsic Motivation, Mental Workload, VR Training, Serious Game

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1183 Metaphorical Perceptions of Middle School Students Regarding Computer Games

Authors: Ismail Celik, Ismail Sahin, Fetah Eren

Abstract:

The computer, among the most important inventions of the twentieth century, has become an increasingly important component in our everyday lives. Computer games also have become increasingly popular among people day-by-day, owing to their features based on realistic virtual environments, audio and visual features, and the roles they offer players. In the present study, the metaphors students have for computer games are investigated, as well as an effort to fill the gap in the literature. Students were asked to complete the sentence—‘Computer game is like/similar to….because….’— to determine the middle school students’ metaphorical images of the concept for ‘computer game’. The metaphors created by the students were grouped in six categories, based on the source of the metaphor. These categories were ordered as ‘computer game as a means of entertainment’, ‘computer game as a beneficial means’, ‘computer game as a basic need’, ‘computer game as a source of evil’, ‘computer game as a means of withdrawal’, and ‘computer game as a source of addiction’, according to the number of metaphors they included.

Keywords: Computer game, metaphor, middle school students.

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1182 Optimal Transmission Network Usage and Loss Allocation Using Matrices Methodology and Cooperative Game Theory

Authors: Baseem Khan, Ganga Agnihotri

Abstract:

Restructuring of Electricity supply industry introduced many issues such as transmission pricing, transmission loss allocation and congestion management. Many methodologies and algorithms were proposed for addressing these issues. In this paper a power flow tracing based method is proposed which involves Matrices methodology for the transmission usage and loss allocation for generators and demands. This method provides loss allocation in a direct way because all the computation is previously done for usage allocation. The proposed method is simple and easy to implement in a large power system. Further it is less computational because it requires matrix inversion only a single time. After usage and loss allocation cooperative game theory is applied to results for finding efficient economic signals. Nucleolus and Shapely value approach is used for optimal allocation of results. Results are shown for the IEEE 6 bus system and IEEE 14 bus system.

Keywords: Modified Kirchhoff Matrix, Power flow tracing, Transmission Pricing, Transmission Loss Allocation.

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1181 A Multi-Agent Simulation of Serious Games to Predict Their Impact on E-Learning Processes

Authors: Ibtissem Daoudi, Raoudha Chebil, Wided Lejouad Chaari

Abstract:

Serious games constitute actually a recent and attractive way supposed to replace the classical boring courses. However, the choice of the adapted serious game to a specific learning environment remains a challenging task that makes teachers unwilling to adopt this concept. To fill this gap, we present, in this paper, a multi-agent-based simulator allowing to predict the impact of a serious game integration in a learning environment given several game and players characteristics. As results, the presented tool gives intensities of several emotional aspects characterizing learners reactions to the serious game adoption. The presented simulator is tested to predict the effect of basing a coding course on the serious game ”CodeCombat”. The obtained results are compared with feedbacks of using the same serious game in a real learning process.

Keywords: Emotion, learning process, multi-agent simulation, serious games.

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1180 Game based Learning to Enhance Cognitive and Physical Capabilities of Elderly People: Concepts and Requirements

Authors: Aurelie Aurilla Bechina Arntzen

Abstract:

The last decade has seen an early majority of people The last decade, the role of the of the information communication technologies has increased in improving the social and business life of people. Today, it is recognized that game could contribute to enhance virtual rehabilitation by better engaging patients. Our research study aims to develop a game based system enhancing cognitive and physical capabilities of elderly people. To this end, the project aims to develop a low cost hand held system based on existing game such as Wii, PSP, or Xbox. This paper discusses the concepts and requirements for developing such game for elderly people. Based on the requirement elicitation, we intend to develop a prototype related to sport and dance activities.

Keywords: Elderly people, Game based learning system, Health systems, rehabilitation

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1179 The Study of Game Interface Improvement due to the Game Operation Dilemma of Player in the Side-Scrolling Shooting Game

Authors: Shih-Chieh Liao, Cheng-Yan Shuai

Abstract:

The feature of a side-scrolling shooting game is facing the surrounding enemy and barraging in an entire screen. The player will be in trouble when they are trying to do complicated operations because of the physical and system limitations of the joystick in the games. This study designed the prototype of a type of arcade stick by focus group and assessed by the expert. We selected the most representative joystick prototype and built the control system for the joystick. We conducted two experimental tests using time and bullet consumption as objective indicators, aiming to demonstrate its efficiency in the game. Finally, the prototype of L-1 solves the dilemma of scroll shooting games when the player uses the arcade stick and improves the function of the arcade stick.

Keywords: Joystick, user interface, side-scrolling shooting game, improved user experience.

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1178 Performance Evaluation of an Online Text-Based Strategy Game

Authors: Nazleeni S. Haron, Mohd K. Zaime , Izzatdin A. Aziz, Mohd H. Hasan

Abstract:

Text-based game is supposed to be a low resource consumption application that delivers good performances when compared to graphical-intensive type of games. But, nowadays, some of the online text-based games are not offering performances that are acceptable to the users. Therefore, an online text-based game called Star_Quest has been developed in order to analyze its behavior under different performance measurements. Performance metrics such as throughput, scalability, response time and page loading time are captured to yield the performance of the game. The techniques in performing the load testing are also disclosed to exhibit the viability of our work. The comparative assessment between the results obtained and the accepted level of performances are conducted as to determine the performance level of the game. The study reveals that the developed game managed to meet all the performance objectives set forth.

Keywords: Online text-based games, performance evaluation

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1177 Inverse Matrix in the Theory of Dynamic Systems

Authors: R. Masarova, M. Juhas, B. Juhasova, Z. Sutova

Abstract:

In dynamic system theory a mathematical model is often used to describe their properties. In order to find a transfer matrix of a dynamic system we need to calculate an inverse matrix. The paper contains the fusion of the classical theory and the procedures used in the theory of automated control for calculating the inverse matrix. The final part of the paper models the given problem by the Matlab.

Keywords: Dynamic system, transfer matrix, inverse matrix, modeling.

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1176 The Design and Development of Driving Game as an Evaluation Instrument for Driving License Test

Authors: Abdul Hadi Abdul Razak, Mohd Hairy Manap

Abstract:

The focus of this paper is to highlight the design and development of an educational game prototype as an evaluation instrument for the Malaysia driving license static test. This educational game brings gaming technology into the conventional objective static test to make it more effective, real and interesting. From the feeling of realistic, the future driver can learn something, memorized and use it in the real life. The current online objective static test only make the user memorized the answer without knowing and understand the true purpose of the question. Therefore, in real life, they will not behave as expected due to behavior and moral lacking. This prototype has been developed inform of multiple-choice questions integrated with 3D gaming environment to make it simulate the real environment and scenarios. Based on the testing conducted, the respondent agrees with the use of this game prototype it can increase understanding and promote obligation towards traffic rules.

Keywords: Educational game, evaluation instrument, game, game prototype.

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1175 Numerical Treatment of Matrix Differential Models Using Matrix Splines

Authors: Kholod M. Abualnaja

Abstract:

This paper consider the solution of the matrix differential models using quadratic, cubic, quartic, and quintic splines. Also using the Taylor’s and Picard’s matrix methods, one illustrative example is included.

Keywords: Matrix Splines, Cubic Splines, Quartic Splines.

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1174 Handover for Dense Small Cells Heterogeneous Networks: A Power-Efficient Game Theoretical Approach

Authors: Mohanad Alhabo, Li Zhang, Naveed Nawaz

Abstract:

In this paper, a non-cooperative game method is formulated where all players compete to transmit at higher power. Every base station represents a player in the game. The game is solved by obtaining the Nash equilibrium (NE) where the game converges to optimality. The proposed method, named Power Efficient Handover Game Theoretic (PEHO-GT) approach, aims to control the handover in dense small cell networks. Players optimize their payoff by adjusting the transmission power to improve the performance in terms of throughput, handover, power consumption and load balancing. To select the desired transmission power for a player, the payoff function considers the gain of increasing the transmission power. Then, the cell selection takes place by deploying Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS). A game theoretical method is implemented for heterogeneous networks to validate the improvement obtained. Results reveal that the proposed method gives a throughput improvement while reducing the power consumption and minimizing the frequent handover.

Keywords: Energy efficiency, game theory, handover, HetNets, small cells.

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1173 Protein Quality of Game Meat Hunted in Latvia

Authors: Vita Strazdina, Aleksandrs Jemeljanovs, Vita Sterna

Abstract:

Not all proteins have the same nutritional value, since protein quality strongly depends on its amino acid composition and digestibility. The meat of game animals could be a high protein source because of its well-balanced essential amino acids composition. Investigations about biochemical composition of game meat such as wild boar (Sus scrofa scrofa), roe deer (Capreolus capreolus) and beaver (Castor fiber) are not very much. Therefore, the aim of the investigation was evaluate protein composition of game meat hunted in Latvia. The biochemical analysis, evaluation of connective tissue and essential amino acids in meat samples were done, the amino acids score were calculate. Results of analysis showed that protein content 20.88-22.05% of all types of meat samples is not different statistically. The content of connective tissue from 1.3% in roe deer till 1.5% in beaver meat allowed classified game animal as high quality meat. The sum of essential amino acids in game meat samples were determined 7.05–8.26g100g-1. Roe deer meat has highest protein content and lowest content of connective tissues among game meat hunted in Latvia. Concluded that amino acid score for limiting amino acids phenylalanine and tyrosine is high and shows high biological value of game meat.

Keywords: Dietic product, game meat, amino acids, scores.

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1172 Serious Game for Autism Children: Review of Literature

Authors: Helmi Adly Mohd Noor, Faaizah Shahbodin, Naim Che Pee

Abstract:

Autism Spectrum Disorder (ASD) is a pervasive developmental disorder which affects individuals with varying degrees of impairment. Currently, there has been ample research done in serious game for autism children. Although serious games are traditionally associated with software developments, developing them in the autism field involves studying the associated technology and paying attention to aspects related to interaction with the game. Serious Games for autism cover matters related to education, therapy for communication, psychomotor treatment and social behavior enhancement. In this paper, a systematic review sets out the lines of development and research currently being conducted into serious games which pursue some form of benefit in the field of autism. This paper includes a literature review of relevant serious game developments since in year 2007 and examines new trends.

Keywords: Serious Game, Autism, Education, Therapy

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1171 The Relationship of Eigenvalues between Backward MPSD and Jacobi Iterative Matrices

Authors: Zhuan-de Wang, Hou-biao Li, Zhong-xi Gao

Abstract:

In this paper, the backward MPSD (Modified Preconditioned Simultaneous Displacement) iterative matrix is firstly proposed. The relationship of eigenvalues between the backward MPSD iterative matrix and backward Jacobi iterative matrix for block p-cyclic case is obtained, which improves and refines the results in the corresponding references.

Keywords: Backward MPSD iterative matrix, Jacobi iterative matrix, eigenvalue, p-cyclic matrix.

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1170 On Positive Definite Solutions of Quaternionic Matrix Equations

Authors: Minghui Wang

Abstract:

The real representation of the quaternionic matrix is definited and studied. The relations between the positive (semi)define quaternionic matrix and its real representation matrix are presented. By means of the real representation, the relation between the positive (semi)definite solutions of quaternionic matrix equations and those of corresponding real matrix equations is established.

Keywords: Matrix equation, Quaternionic matrix, Real representation, positive (semi)definite solutions.

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1169 Connectivity Estimation from the Inverse Coherence Matrix in a Complex Chaotic Oscillator Network

Authors: Won Sup Kim, Xue-Mei Cui, Seung Kee Han

Abstract:

We present on the method of inverse coherence matrix for the estimation of network connectivity from multivariate time series of a complex system. In a model system of coupled chaotic oscillators, it is shown that the inverse coherence matrix defined as the inverse of cross coherence matrix is proportional to the network connectivity. Therefore the inverse coherence matrix could be used for the distinction between the directly connected links from indirectly connected links in a complex network. We compare the result of network estimation using the method of the inverse coherence matrix with the results obtained from the coherence matrix and the partial coherence matrix.

Keywords: Chaotic oscillator, complex network, inverse coherence matrix, network estimation.

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1168 Developing a Customizable Serious Game and Its Applicability in the Classroom

Authors: Anita Kéri

Abstract:

Recent developments in the field of education have led to a renewed interest in teaching methodologies and practices. Gamification is fast becoming a key instrument in the education of new generations and besides other methods, serious games have become the center of attention. Ready-built serious games are available for most higher education institutions to buy and implement. However, monetary restraints and the unalterable nature of the games might deter most higher education institutions from the application of these serious games. Therefore, there is a continuously growing need for a customizable serious game that has been developed based on a concrete need analysis and experts’ opinion. There has been little evidence so far of serious games that have been created based on relevant and current need analysis from higher education institution teachers, professional practitioners and students themselves. Therefore, the aim of this current paper is to analyze the needs of higher education institution educators with special emphasis on their needs, the applicability of serious games in their classrooms, and exploring options for the development of a customizable serious game framework. The paper undertakes to analyze workshop discussions on implementing serious games in education and propose a customizable serious game framework applicable in the education of the new generation. Research results show that the most important feature of a serious game is its customizability. The fact that practitioners are able to manage different scenarios and upload their own content to a game seems to be a key to the increasingly widespread application of serious games in the classroom.

Keywords: Education, gamification, game-based learning, serious games.

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1167 Porul: Option Generation and Selection and Scoring Algorithms for a Tamil Flash Card Game

Authors: Anitha Narasimhan, Aarthy Anandan, Madhan Karky, C. N. Subalalitha

Abstract:

Games can be the excellent tools for teaching a language. There are few e-learning games in Indian languages like word scrabble, cross word, quiz games etc., which were developed mainly for educational purposes. This paper proposes a Tamil word game called, “Porul”, which focuses on education as well as on players’ thinking and decision-making skills. Porul is a multiple choice based quiz game, in which the players attempt to answer questions correctly from the given multiple options that are generated using a unique algorithm called the Option Selection algorithm which explores the semantics of the question in various dimensions namely, synonym, rhyme and Universal Networking Language semantic category. This kind of semantic exploration of the question not only increases the complexity of the game but also makes it more interesting. The paper also proposes a Scoring Algorithm which allots a score based on the popularity score of the question word. The proposed game has been tested using 20,000 Tamil words.

Keywords: Porul game, Tamil word game, option selection, flash card, scoring, algorithm.

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1166 Solving Linear Matrix Equations by Matrix Decompositions

Authors: Yongxin Yuan, Kezheng Zuo

Abstract:

In this paper, a system of linear matrix equations is considered. A new necessary and sufficient condition for the consistency of the equations is derived by means of the generalized singular-value decomposition, and the explicit representation of the general solution is provided.

Keywords: Matrix equation, Generalized inverse, Generalized singular-value decomposition.

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1165 Enhancement of Capacity in a MC-CDMA based Cognitive Radio Network Using Non-Cooperative Game Model

Authors: Kalyani J. Kulkarni, Bharat S. Chaudhari

Abstract:

This paper addresses the issue of resource allocation in the emerging cognitive technology. Focusing the Quality of Service (QoS) of Primary Users (PU), a novel method is proposed for the resource allocation of Secondary Users (SU). In this paper, we propose the unique Utility Function in the game theoretic model of Cognitive Radio which can be maximized to increase the capacity of the Cognitive Radio Network (CRN) and to minimize the interference scenario. Utility function is formulated to cater the need of PUs by observing Signal to Noise ratio. Existence of Nash Equilibrium for the postulated game is established.

Keywords: Cognitive Networks, Game Theory, Nash Equilibrium, Resource Allocation.

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1164 Control Signal from EOG Analysis and Its Application

Authors: Myoung Ro Kim, Gilwon Yoon

Abstract:

A game using electro-oculography (EOG) as control signal was introduced in this study. Various EOG signals are generated by eye movements. Even though EOG is a quite complex type of signal, distinct and separable EOG signals could be classified from horizontal and vertical, left and right eye movements. Proper signal processing was incorporated since EOG signal has very small amplitude in the order of micro volts and contains noises influenced by external conditions. Locations of the electrodes were set to be above and below as well as left and right positions of the eyes. Four control signals of up, down, left and right were generated. A microcontroller processed signals in order to simulate a DDR game. A LCD display showed arrows falling down with four different head directions. This game may be used as eye exercise for visual concentration and acuity. Our proposed EOG control signal can be utilized in many other applications of human machine interfaces such as wheelchair, computer keyboard and home automation.

Keywords: DDR game, EOG, eye movement.

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1163 A Discriminatory Rewarding Mechanism for Sybil Detection with Applications to Tor

Authors: Asim Kumar Pal, Debabrata Nath, Sumit Chakraborty

Abstract:

This paper presents an economic game for sybil detection in a distributed computing environment. Cost parameters reflecting impacts of different sybil attacks are introduced in the sybil detection game. The optimal strategies for this game in which both sybil and non-sybil identities are expected to participate are devised. A cost sharing economic mechanism called Discriminatory Rewarding Mechanism for Sybil Detection is proposed based on this game. A detective accepts a security deposit from each active agent, negotiates with the agents and offers rewards to the sybils if the latter disclose their identity. The basic objective of the detective is to determine the optimum reward amount for each sybil which will encourage the maximum possible number of sybils to reveal themselves. Maintaining privacy is an important issue for the mechanism since the participants involved in the negotiation are generally reluctant to share their private information. The mechanism has been applied to Tor by introducing a reputation scoring function.

Keywords: Game theory, Incentive mechanism, Reputation, Sybil Attack

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1162 The Convergence Results between Backward USSOR and Jacobi Iterative Matrices

Authors: Zuan-De Wang, Hou-biao Li, Zhong-xi Gao

Abstract:

In this paper, the backward Ussor iterative matrix is proposed. The relationship of convergence between the backward Ussor iterative matrix and Jacobi iterative matrix is obtained, which makes the results in the corresponding references be improved and refined.Moreover,numerical examples also illustrate the effectiveness of these conclusions.

Keywords: Backward USSOR iterative matrix, Jacobi iterative matrix, convergence, spectral radius

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1161 Design of a Computer Vision Based Exercise Video Game for Senior Citizens

Authors: June Tay, Ivy Chia

Abstract:

There are numerous changes, both mental and physical, taking place when people age. We need to understand the different aspects required for healthy living, including meeting nutritional needs, regular physical activities to keep agility, sufficient rest and sleep to have physical and mental well-being, social engagement to avoid the risk of social isolation and depression, and access to healthcare to detect and manage chronic conditions. Promoting physical activities for an ageing population is necessary as many may have enjoyed sedentary lifestyles for some time. In our study, we evaluate the considerations when designing a computer vision video game for the elderly. We need to design some low-impact activities, such as stretching and gentle movements, because some elderly individuals may have joint pains or mobility issues. The exercise game should consist of simple movements that are easy to follow and remember. It should be fun and enjoyable so that they can be motivated to do some exercise. Social engagement can keep the elderly motivated and competitive, and they are more willing to engage in game exercises. Elderly citizens can compare their game scores and try to improve them. We propose a computer vision-based video game for the elderly that will capture and track the movement of the elderly hand pushing a ball on the screen into a circle. It can be easily set up using a PC laptop with a webcam. Our video game adhered to the design framework we employed, and it encompassed ease of use, a simple graphical interface, easy-to-play game exercise, and fun gameplay.

Keywords: Computer vision, video games, gerontology technology, caregiving.

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1160 An Algorithm of Ordered Schur Factorization For Real Nonsymmetric Matrix

Authors: Lokendra K. Balyan

Abstract:

In this paper, we present an algorithm for computing a Schur factorization of a real nonsymmetric matrix with ordered diagonal blocks such that upper left blocks contains the largest magnitude eigenvalues. Especially in case of multiple eigenvalues, when matrix is non diagonalizable, we construct an invariant subspaces with few additional tricks which are heuristic and numerical results shows the stability and accuracy of the algorithm.

Keywords: Schur Factorization, Eigenvalues of nonsymmetric matrix, Orthoganal matrix.

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1159 Tree Sign Patterns of Small Order that Allow an Eventually Positive Matrix

Authors: Ber-Lin Yu, Jie Cui, Hong Cheng, Zhengfeng Yu

Abstract:

A sign pattern is a matrix whose entries belong to the set {+,−, 0}. An n-by-n sign pattern A is said to allow an eventually positive matrix if there exist some real matrices A with the same sign pattern as A and a positive integer k0 such that Ak > 0 for all k ≥ k0. It is well known that identifying and classifying the n-by-n sign patterns that allow an eventually positive matrix are posed as two open problems. In this article, the tree sign patterns of small order that allow an eventually positive matrix are classified completely.

Keywords: Eventually positive matrix, sign pattern, tree.

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1158 Numerical Simulation of Effect of Various Rib Configurations on Enhancing Heat Transfer of Matrix Cooling Channel

Authors: Seok Min Choi, Minho Bang, Seuong Yun Kim, Hyungmin Lee, Won-Gu Joo, Hyung Hee Cho

Abstract:

The matrix cooling channel was used for gas turbine blade cooling passage. The matrix cooling structure is useful for the structure stability however the cooling performance of internal cooling channel was not enough for cooling. Therefore, we designed the rib configurations in the matrix cooling channel to enhance the cooling performance. The numerical simulation was conducted to analyze cooling performance of rib configured matrix cooling channel. Three different rib configurations were used which are vertical rib, angled rib and c-type rib. Three configurations were adopted in two positions of matrix cooling channel which is one fourth and three fourth of channel. The result shows that downstream rib has much higher cooling performance than upstream rib. Furthermore, the angled rib in the channel has much higher cooling performance than vertical rib. This is because; the angled rib improves the swirl effect of matrix cooling channel more effectively. The friction factor was increased with the installation of rib. However, the thermal performance was increased with the installation of rib in the matrix cooling channel.

Keywords: Matrix cooling, rib, heat transfer, gas turbine.

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1157 Bounds on the Second Stage Spectral Radius of Graphs

Authors: S.K.Ayyaswamy, S.Balachandran, K.Kannan

Abstract:

Let G be a graph of order n. The second stage adjacency matrix of G is the symmetric n × n matrix for which the ijth entry is 1 if the vertices vi and vj are of distance two; otherwise 0. The sum of the absolute values of this second stage adjacency matrix is called the second stage energy of G. In this paper we investigate a few properties and determine some upper bounds for the largest eigenvalue.

Keywords: Second stage spectral radius, Irreducible matrix, Derived graph

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