Search results for: rank deficient least squares problems

Authors: Thomas M. Prinz Wilhelm R. Rossak, Kai Gebhardt

Abstract:

A straightforward and intuitive combination of single simulations into an aggregated master-simulation is not trivial. There are lots of problems, which trigger-specific difficulties during the modeling and execution of such a simulation. In this paper we identify these problems and aim to solve them by mapping the task to the field of multi agent systems. The solution is a new meta-model named AGENTMAP, which is able to mitigate most of the problems and to support intuitive modeling at the same time. This meta-model will be introduced and explained on basis of an example from the e-commerce domain.

Keywords: Multi Agent System, Agent-based Simulation, Distributed Systems, Meta-models.

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Authors: Yi Zhang, Kai Lu, Ying-hui Gao, Mo Wang

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Histogram plays an important statistical role in digital image processing. However, the existing quantum image models are deficient to do this kind of image statistical processing because different gray scales are not distinguishable. In this paper, a novel quantum image representation model is proposed firstly in which the pixels with different gray scales can be distinguished and operated simultaneously. Based on the new model, a fast quantum algorithm of constructing histogram for quantum image is designed. Performance comparison reveals that the new quantum algorithm could achieve an approximately quadratic speedup than the classical counterpart. The proposed quantum model and algorithm have significant meanings for the future researches of quantum image processing.

Keywords: Quantum Image Representation, Quantum Algorithm, Image Histogram.

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Authors: Mohammad Reza Kangavari, Samira Ghandchi, Manak Golpour

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Most of the Question Answering systems composed of three main modules: question processing, document processing and answer processing. Question processing module plays an important role in QA systems. If this module doesn't work properly, it will make problems for other sections. Moreover answer processing module is an emerging topic in Question Answering, where these systems are often required to rank and validate candidate answers. These techniques aiming at finding short and precise answers are often based on the semantic classification. This paper discussed about a new model for question answering which improved two main modules, question processing and answer processing. There are two important components which are the bases of the question processing. First component is question classification that specifies types of question and answer. Second one is reformulation which converts the user's question into an understandable question by QA system in a specific domain. Answer processing module, consists of candidate answer filtering, candidate answer ordering components and also it has a validation section for interacting with user. This module makes it more suitable to find exact answer. In this paper we have described question and answer processing modules with modeling, implementing and evaluating the system. System implemented in two versions. Results show that 'Version No.1' gave correct answer to 70% of questions (30 correct answers to 50 asked questions) and 'version No.2' gave correct answers to 94% of questions (47 correct answers to 50 asked questions).

Keywords: Answer Processing, Classification, QuestionAnswering and Query Reformulation.

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Authors: Pulak Swain, A. K. Ojha

Abstract:

Portfolio optimization is based on dealing with the problems of efficient asset allocation. Risk and Expected return are two conflicting criteria in such problems, where the investor prefers the return to be high and the risk to be low. Using multi-objective approach we can solve those type of problems. However the information which we have for the input parameters are generally ambiguous and the input values can fluctuate around some nominal values. We can not ignore the uncertainty in input values, as they can affect the asset allocation drastically. So we use Robust Optimization approach to the problems where the input parameters comes under box uncertainty. In this paper, we solve the multi criteria robust problem with the help of  E- constraint method.

Keywords: Portfolio optimization, multi-objective optimization, E-constraint method, box uncertainty, robust optimization.

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Authors: Miloje S. Radenkovic, Tamal Bose

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This paper presents the convergence analysis of a prediction based blind equalizer for IIR channels. Predictor parameters are estimated by using the recursive least squares algorithm. It is shown that the prediction error converges almost surely (a.s.) toward a scalar multiple of the unknown input symbol sequence. It is also proved that the convergence rate of the parameter estimation error is of the same order as that in the iterated logarithm law.

Keywords: Adaptive blind equalizer, Recursive leastsquares, Adaptive Filtering, Convergence analysis.

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Authors: Benshi Zhu

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In this paper, multiple positive solutions for semipositone discrete eigenvalue problems are obtained by using a three critical points theorem for nondifferentiable functional.

Keywords: Discrete eigenvalue problems, positive solutions, semipositone, three critical points theorem

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Authors: Nhon Van Do

Abstract:

In the artificial intelligence field, knowledge representation and reasoning are important areas for intelligent systems, especially knowledge base systems and expert systems. Knowledge representation Methods has an important role in designing the systems. There have been many models for knowledge such as semantic networks, conceptual graphs, and neural networks. These models are useful tools to design intelligent systems. However, they are not suitable to represent knowledge in the domains of reality applications. In this paper, new models for knowledge representation called computational networks will be presented. They have been used in designing some knowledge base systems in education for solving problems such as the system that supports studying knowledge and solving analytic geometry problems, the program for studying and solving problems in Plane Geometry, the program for solving problems about alternating current in physics.

Keywords: Artificial intelligence, artificial intelligence and education, knowledge engineering, knowledge representation.

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Authors: Songyi Kim, Kwangwoo Lee, Seungjoo Kim, Dongho Won

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RFID (Radio Frequency IDentification) system has been widely used in our life, such as transport systems, passports, automotive, animal tracking, human implants, library, and so on. However, the RFID authentication protocols between RF (Radio Frequency) tags and the RF readers have been bring about various privacy problems that anonymity of the tags, tracking, eavesdropping, and so on. Many researchers have proposed the solution of the problems. However, they still have the problem, such as location privacy, mutual authentication. In this paper, we show the problems of the previous protocols, and then we propose a more secure and efficient RFID authentication protocol.

Keywords: RFID, mutual authentication, serverless, anonymity.

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Authors: Nhon Do

Abstract:

Ontology is a terminology which is used in artificial intelligence with different meanings. Ontology researching has an important role in computer science and practical applications, especially distributed knowledge systems. In this paper we present an ontology which is called Computational Object Knowledge Base Ontology. It has been used in designing some knowledge base systems for solving problems such as the system that supports studying knowledge and solving analytic geometry problems, the program for studying and solving problems in Plane Geometry, the knowledge system in linear algebra.

Keywords: Artificial intelligence, knowledge representation, knowledge base system, ontology.

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Authors: Viet-Hung Nguyen, Luh-Maan Chang

Abstract:

Design should be viewed concurrently by three ways as transformation, flow and value generation. An innovative approach to solve design – related problems is described as the integrated product - process design. As a foundation for a formal framework consisting of organizing principles and techniques, Work Structuring has been developed to guide efforts in the integration that enhances the development of operation and process design in alignment with product design. Vietnam construction projects are facing many delays, and cost overruns caused mostly by design related problems. A better design management that integrates product and process design could resolve these problems. A questionnaire survey and in – depth interviews were used to investigate the feasibility of applying Work Structuring to construction projects in Vietnam. The purpose of this paper is to present the research results and to illustrate the possible problems and potential solutions when Work Structuring is implemented to construction projects in Vietnam.

Keywords: integrated product – process design, Work Structuring, construction projects, Vietnam

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Authors: M. Fakharian, M. I. Khodakarami

Abstract:

In this paper, a new trend for improvement in semianalytical method based on scale boundaries in order to solve the 2D elastodynamic problems is provided. In this regard, only the boundaries of the problem domain discretization are by specific subparametric elements. Mapping functions are uses as a class of higherorder Lagrange polynomials, special shape functions, Gauss-Lobatto- Legendre numerical integration, and the integral form of the weighted residual method, the matrix is diagonal coefficients in the equations of elastodynamic issues. Differences between study conducted and prior research in this paper is in geometry production procedure of the interpolation function and integration of the different is selected. Validity and accuracy of the present method are fully demonstrated through two benchmark problems which are successfully modeled using a few numbers of DOFs. The numerical results agree very well with the analytical solutions and the results from other numerical methods.

Keywords: 2D Elastodynamic Problems, Lagrange Polynomials, G-L-Lquadrature, Decoupled SBFEM.

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Authors: Meng-Hui Chen, Pei-Chann Chang, Wei-Hsiu Huang

Abstract:

Artificial Immune System is adopted as a Heuristic Algorithm to solve the combinatorial problems for decades. Nevertheless, many of these applications took advantage of the benefit for applications but seldom proposed approaches for enhancing the efficiency. In this paper, we continue the previous research to develop a Self-evolving Artificial Immune System II via coordinating the T and B cell in Immune System and built a block-based artificial chromosome for speeding up the computation time and better performance for different complexities of problems. Through the design of Plasma cell and clonal selection which are relative the function of the Immune Response. The Immune Response will help the AIS have the global and local searching ability and preventing trapped in local optima. From the experimental result, the significant performance validates the SEAIS II is effective when solving the permutation flows-hop problems.

Keywords: Artificial Immune System, Clonal Selection, Immune Response, Permutation Flow-shop Scheduling Problems

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Authors: Theddeus T. Akano, Omotayo A. Fakinlede

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The modelling of physical phenomena, such as the earth’s free oscillations, the vibration of strings, the interaction of atomic particles, or the steady state flow in a bar give rise to Sturm- Liouville (SL) eigenvalue problems. The boundary applications of some systems like the convection-diffusion equation, electromagnetic and heat transfer problems requires the combination of Dirichlet and Neumann boundary conditions. Hence, the incorporation of Robin boundary condition in the analyses of Sturm-Liouville problem. This paper deals with the computation of the eigenvalues and eigenfunction of generalized Sturm-Liouville problems with Robin boundary condition using the finite element method. Numerical solution of classical Sturm–Liouville problem is presented. The results show an agreement with the exact solution. High results precision is achieved with higher number of elements.

Keywords: Sturm-Liouville problem, Robin boundary condition, finite element method, eigenvalue problems.

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Authors: Amit Kumar, Anila Gupta, Amarpreet Kaur

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In this paper, a new method is proposed to find the fuzzy optimal solution of fuzzy assignment problems by representing all the parameters as triangular fuzzy numbers. The advantages of the pro-posed method are also discussed. To illustrate the proposed method a fuzzy assignment problem is solved by using the proposed method and the obtained results are discussed. The proposed method is easy to understand and to apply for finding the fuzzy optimal solution of fuzzy assignment problems occurring in real life situations.

Keywords: Fuzzy assignment problem, Ranking function, Triangular fuzzy numbers.

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Authors: I. Grigoraviciute-Puroniene, K. Tsuru, E. Garskaite, Z. Stankeviciute, A. Beganskiene, K. Ishikawa, A. Kareiva

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Tricalcium phosphate (β-Ca₃(PO₄)₂, β-TCP) powders were synthesized using wet polymeric precipitation method for the first time to our best knowledge. The results of X-ray diffraction analysis showed the formation of almost single a Ca-deficient hydroxyapatite (CDHA) phase of a poor crystallinity already at room temperature. With continuously increasing the calcination temperature up to 800 °C, the crystalline β-TCP was obtained as the main phase. It was demonstrated that infrared spectroscopy is very effective method to characterize the formation of β-TCP. The SEM results showed that β-TCP solids were homogeneous having a small particle size distribution. The β-TCP powders consisted of spherical particles varying in size from 100 to 300 nm. Fabricated β-TCP specimens were placed to the bones of the rats and maintained for 1-2 months.

Keywords: β-TCP, bone regeneration, wet chemical processing, polymeric precipitation.

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Authors: Zayed Freah Zeadat

Abstract:

The wellbeing of urban dwellers is strongly associated with the quality and quantity of green infrastructure. Nevertheless, urban green infrastructure is still lagging in many Arab cities, and Jordan is no exception. The capital city of Jordan, Amman, is becoming more urban dense with limited green spaces. The unplanned urban growth in Amman has caused several environmental problems such as urban heat islands, air pollution and lack of green spaces. This study aims to investigate the most suitable drivers to leverage the implementation of urban green infrastructure in Jordan through qualitative and quantitative analysis. The qualitative research includes an extensive literature review to discuss the most common drivers used internationally to promote urban green infrastructure implementation in the literature. The quantitative study employs a questionnaire survey to rank the suitability of each driver. Consultants, contractors and policymakers were invited to fill the research questionnaire according to their judgments and opinions. Relative Importance Index has been used to calculate the weighted average of all drivers and the Kruskal-Wallis test to check the degree of agreement among groups. This study finds that research participants agreed that indirect financial incentives (i.e., tax reductions, reduction in stormwater utility fee, reduction of interest rate, density bonus etc.) are the most effective incentive policy whilst granting sustainability certificate policy is the least effective driver to ensure widespread of UGI is elements in Jordan.

Keywords: sustainable development, urban green infrastructure, relative importance index, urban Jordan

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Authors: Mahnaz Hosseinzadeh, Aliyeh Kazemi

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In this paper, a method is proposed for solving Fuzzy Multi-Objective Linear Programming problems (FMOLPP) with fuzzy right hand side and fuzzy decision variables. To illustrate the proposed method, it is applied to the problem of selecting suppliers for an automotive parts producer company in Iran in order to find the number of optimal orders allocated to each supplier considering the conflicting objectives. Finally, the obtained results are discussed.

Keywords: Fuzzy multi-objective linear programming problems, triangular fuzzy numbers, fuzzy ranking, supplier selection problem.

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Authors: Takeshi Takeda

Abstract:

An experiment utilizing the ROSA/LSTF (rig of safety assessment/large-scale test facility) simulated a 1.9% vessel upper head small-break loss-of-coolant accident with an accident management (AM) measure under the total failure of high-pressure injection system of emergency core cooling system in a pressurized water reactor. Steam generator (SG) secondary-side depressurization on the AM measure was started by fully opening relief valves in both SGs when the maximum core exit temperature rose to 623 K. A large increase took place in the cladding surface temperature of simulated fuel rods on account of a late and slow response of core exit thermocouples during core boil-off. The author analyzed the LSTF test by reference to the matrix of an integral effect test for the validation of a thermal-hydraulic system code. Problems remained in predicting the primary coolant distribution and the core exit temperature with the RELAP5/MOD3.3 code. The uncertainty analysis results of the RELAP5 code confirmed that the sample size with respect to the order statistics influences the value of peak cladding temperature with a 95% probability at a 95% confidence level, and the Spearman’s rank correlation coefficient.

Keywords: LSTF, LOCA, uncertainty analysis, RELAP5.

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Authors: M. Duran Toksarı, B. Uçarkuş

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In this paper, we propose two algorithms to optimally solve makespan and total completion time scheduling problems with learning effect and job dependent delivery times in a single machine environment. The delivery time is the extra time to eliminate adverse effect between the main processing and delivery to the customer. In this paper, we introduce the job dependent delivery times for some single machine scheduling problems with position dependent learning effect, which are makespan are total completion. The results with respect to two algorithms proposed for solving of the each problem are compared with LINGO solutions for 50-jobs, 100-jobs and 150- jobs problems. The proposed algorithms can find the same results in shorter time.

Keywords: Delivery times, learning effect, makespan, scheduling, total completion time.

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Authors: Aizzat Mohd. Nasurdin, Noor Hazlina Ahmad, Cheng Ling Tan

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This study aims to examine the role of career advancement and job security as predictors of employee commitment to their organization. Data was collected from 580 frontline employees attached to two departments of 29 luxury hotels in Peninsular Malaysia. Statistical results using Partial Least Squares technique provided support for the proposed hypotheses. In view of the findings, theoretical and practical implications are discussed.

Keywords: Organizational commitment, career advancement, job security, frontline employees, luxury hotels, Malaysia.

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Authors: Wei Zhang, Jing Dong

Abstract:

This paper introduced the status quo of laws and regulations of sustainable construction in China and investigated the existing problems of current laws and regulations through person-interviews in Beijing, Shanghai, Chongqing and Shenzhen in China. The problems include incomplete legal system, lack of guidance of higher-level laws, backward in some laws and regulations, unclear legal liability and poor law enforcement. Aimed at these problems, this paper also put forward some improvement approaches, such as filling the legal gap, revising laws and regulations, establishing incentive system and keeping pace with level of development.

Keywords: Improvement, laws and regulations, status quo, sustainable construction

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Authors: Mohsen Zand, Ahmadreza Naghsh Nilchi, S. Amirhassan Monadjemi

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Optical character recognition of cursive scripts presents a number of challenging problems in both segmentation and recognition processes in different languages, including Persian. In order to overcome these problems, we use a newly developed Persian word segmentation method and a recognition-based segmentation technique to overcome its segmentation problems. This method is robust as well as flexible. It also increases the system-s tolerances to font variations. The implementation results of this method on a comprehensive database show a high degree of accuracy which meets the requirements for commercial use. Extended with a suitable pre and post-processing, the method offers a simple and fast framework to develop a full OCR system.

Keywords: OCR, Persian, Recognition, Segmentation.

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Authors: V. K. Bansal

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Geographic Information System (GIS) is a computerbased tool used extensively to solve various engineering problems related to spatial data. In spite of growing popularity of GIS, its complete potential to construction industry has not been realized. In this paper, the summary of up-to-date work on spatial applications of GIS technologies in construction industry is presented. GIS technologies have the potential to solve space related problems of construction industry involving complex visualization, integration of information, route planning, E-commerce, cost estimation, etc. GISbased methodology to handle time and space issues of construction projects scheduling is developed and discussed in this paper.

Keywords: Construction, GIS in construction, Scheduling, Project Management.

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Authors: Baoguang Tian, Nan Chen

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A new relative efficiency in linear model in reference is instructed into the linear weighted regression, and its upper and lower bound are proposed. In the linear weighted regression model, for the best linear unbiased estimation of mean matrix respect to the least-squares estimation, two new relative efficiencies are given, and their upper and lower bounds are also studied.

Keywords: Linear weighted regression, Relative efficiency, Mean matrix, Trace.

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Authors: T. Qasim, M. Obeidat, S. Al-Sharairi

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The objective of this study is to investigate the effect of the excessive use of smartphones. Smartphones have enormous effects on the human body in that some musculoskeletal disorders (MSDs) and health problems might evolve. These days, there is a wide use of the smartphones among all age groups of society, thus, the focus on smartphone effects on human behavior and health, especially on the young and elderly people, becomes a crucial issue. This study was conducted in Jordan on smartphone users for different genders and ages, by conducting a survey to collect data related to the symptoms and MSDs that are resulted from the excessive use of smartphones. A total of 357 responses were used in the analysis. The main related symptoms were numbness, fingers pain, and pain in arm, all linked to age and gender for comparative reasons. A statistical analysis was performed to find the effects of extensive usage of a smartphone for long periods of time on the human body. Results show that the significant variables were the vision problems and the time spent when using the smartphone that cause vision problems. Other variables including age of user and ear problems due to the use of the headsets were found to be a border line significant.

Keywords: Smartphone, age group, musculoskeletal disorders (MSDs), health problems.

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Authors: Yongzhong Wu, Ping Ji

Abstract:

This paper proposes a genetic algorithm based on a new replacement strategy to solve the quadratic assignment problems, which are NP-hard. The new replacement strategy aims to improve the performance of the genetic algorithm through well balancing the convergence of the searching process and the diversity of the population. In order to test the performance of the algorithm, the instances in QAPLIB, a quadratic assignment problem library, are tried and the results are compared with those reported in the literature. The performance of the genetic algorithm is promising. The significance is that this genetic algorithm is generic. It does not rely on problem-specific genetic operators, and may be easily applied to various types of combinatorial problems.

Keywords: Quadratic assignment problem, Genetic algorithm, Replacement strategy, QAPLIB.

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Authors: Maciej Norberciak

Abstract:

Timetabling problems are often hard and timeconsuming to solve. Most of the methods of solving them concern only one problem instance or class. This paper describes a universal method for solving large, highly constrained timetabling problems from different domains. The solution is based on evolutionary algorithm-s framework and operates on two levels – first-level evolutionary algorithm tries to find a solution basing on given set of operating parameters, second-level algorithm is used to establish those parameters. Tabu search is employed to speed up the solution finding process on first level. The method has been used to solve three different timetabling problems with promising results.

Keywords: Evolutionary algorithms, tabu search, timetabling.

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Authors: Horia Păunescu

Abstract:

Purpose: The study aimed to assess the depressant or antidepressant effects of several Nonsteroidal Anti-Inflammatory Drugs (NSAIDs) in mice: the selective cyclooxygenase-2 (COX-2) inhibitor meloxicam, and the non-selective COX-1 and COX-2 inhibitors lornoxicam, sodium metamizole, and ketorolac. The current literature data regarding such effects of these agents are scarce. Materials and methods: The study was carried out on NMRI mice weighing 20-35 g, kept in a standard laboratory environment. The study was approved by the Ethics Committee of the University of Medicine and Pharmacy „Carol Davila”, Bucharest. The study agents were injected intraperitoneally, 10 mL/kg body weight (bw) 1 hour before the assessment of the locomotor activity by cage testing (n=10 mice/ group) and 2 hours before the forced swimming tests (n=15). The study agents were dissolved in normal saline (meloxicam, sodium metamizole), ethanol 11.8% v/v in normal saline (ketorolac), or water (lornoxicam), respectively. Negative and positive control agents were also given (amitryptilline in the forced swimming test). The cage floor used in the locomotor activity assessment was divided into 20 equal 10 cm squares. The forced swimming test involved partial immersion of the mice in cylinders (15/9cm height/diameter) filled with water (10 cm depth at 28C), where they were left for 6 minutes. The cage endpoint used in the locomotor activity assessment was the number of treaded squares. Four endpoints were used in the forced swimming test (immobility latency for the entire 6 minutes, and immobility, swimming, and climbing scores for the final 4 minutes of the swimming session), recorded by an observer that was „blinded” to the experimental design. The statistical analysis used the Levene test for variance homogeneity, ANOVA and post-hoc analysis as appropriate, Tukey or Tamhane tests. Results: No statistically significant increase or decrease in the number of treaded squares was seen in the locomotor activity assessment of any mice group. In the forced swimming test, amitryptilline showed an antidepressant effect in each experiment, at the 10 mg/kg bw dosage. Sodium metamizole was depressant at 100 mg/kg bw (increased the immobility score, p=0.049, Tamhane test), but not in lower dosages as well (25 and 50 mg/kg bw). Ketorolac showed an antidepressant effect at the intermediate dosage of 5 mg/kg bw, but not so in the dosages of 2.5 and 10 mg/kg bw, respectively (increased the swimming score, p=0.012, Tamhane test). Meloxicam and lornoxicam did not alter the forced swimming endpoints at any dosage level. Discussion: 1) Certain NSAIDs caused changes in the forced swimming patterns without interfering with locomotion. 2) Sodium metamizole showed a depressant effect, whereas ketorolac proved antidepressant. Conclusion: NSAID-induced mood changes are not class effects of these agents and apparently are independent of the type of inhibited cyclooxygenase (COX-1 or COX-2). Disclosure: This paper was co-financed from the European Social Fund, through the Sectorial Operational Programme Human Resources Development 2007-2013, project number POSDRU /159 /1.5 /S /138907 "Excellence in scientific interdisciplinary research, doctoral and postdoctoral, in the economic, social and medical fields -EXCELIS", coordinator The Bucharest University of Economic Studies.

Keywords: Antidepressant, depressant, forced swim, NSAIDs.

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Authors: Shazia Javed, Noor Atinah Ahmad

Abstract:

In this paper an efficient incomplete factorization preconditioner is proposed for the Least Mean Squares (LMS) adaptive filter. The proposed preconditioner is approximated from a priori knowledge of the factors of input correlation matrix with an incomplete strategy, motivated by the sparsity patter of the upper triangular factor in the QRD-RLS algorithm. The convergence properties of IPLMS algorithm are comparable with those of transform domain LMS(TDLMS) algorithm. Simulation results show efficiency and robustness of the proposed algorithm with reduced computational complexity.

Keywords: Autocorrelation matrix, Cholesky's factor, eigenvalue spread, Markov input.

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Authors: Nastaran Hajiheydari, Mohammad Soltani Delgosha

Abstract:

Vendor (supplier) selection is a group decision-making (GDM) process, in which, based on some predetermined criteria, the experts’ preferences are provided in order to rank and choose the most desirable suppliers. In the real business environment, our attitudes or our choices would be made in an uncertain and indecisive situation could not be expressed in a crisp framework. Intuitionistic fuzzy sets (IFSs) could handle such situations in the best way. VIKOR method was developed to solve multi-criteria decision-making (MCDM) problems. This method, which is used to determine the compromised feasible solution with respect to the conflicting criteria, introduces a multi-criteria ranking index based on the particular measure of 'closeness' to the 'ideal solution'. Until now, there has been a little investigation of VIKOR with IFS, therefore we extended the intuitionistic fuzzy (IF) VIKOR to solve vendor selection problem under IF GDM environment. The present study intends to develop an IF VIKOR method in a GDM situation. Therefore, a model is presented to calculate the criterion weights based on entropy measure. Then, the interval-valued intuitionistic fuzzy weighted geometric (IFWG) operator utilized to obtain the total decision matrix. In the next stage, an approach based on the positive idle intuitionistic fuzzy number (PIIFN) and negative idle intuitionistic fuzzy number (NIIFN) was developed. Finally, the application of the proposed method to solve a vendor selection problem illustrated.

Keywords: Group decision making, intuitionistic fuzzy entropy measure, intuitionistic fuzzy set, vendor selection VIKOR.

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