Search results for: local polynomial regression

Authors: Y. Harold Robinson, M. Rajaram, Honey Raju

Abstract:

Image segmentation and color identification is an important process used in various emerging fields like intelligent robotics. A method is proposed for the manipulator to grasp and place the color object into correct location. The existing methods such as PSO, has problems like accelerating the convergence speed and converging to a local minimum leading to sub optimal performance. To improve the performance, we are using watershed algorithm and for color identification, we are using EPSO. EPSO method is used to reduce the probability of being stuck in the local minimum. The proposed method offers the particles a more powerful global exploration capability. EPSO methods can determine the particles stuck in the local minimum and can also enhance learning speed as the particle movement will be faster.

Keywords: Color information, EPSO, hue, saturation, value (HSV), image segmentation, particle swarm optimization (PSO). Active Contour, GMM.

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Authors: Amic G. Ho

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Language usage and typography in Hong Kong are unique, as can be seen clearly on the streets of the city. In contrast to many other parts of the world, where there is only one language, in Hong Kong many signs and billboards display two languages: Chinese and English. The language usage on signage, fonts and types used, and the designs in magazines and advertisements all demonstrate the unique features of Hong Kong typographic design, which reflect the multicultural nature of Hong Kong society. This study is the first step in investigating the nature and development of Hong Kong typography. The preliminary research explored how the historical development of Hong Kong is reflected in its unique typography. Following a review of historical development, a quantitative study was designed: Local Hong Kong participants were invited to provide input on what makes the Hong Kong typographic style unique. Their input was collected and analyzed. This provided us with information about the characteristic criteria and features of Hong Kong typography, as recognized by the local people. The most significant typographic designs in Hong Kong were then investigated and the influence of Chinese and other cultures on Hong Kong typography was assessed. The research results provide an indication to local designers on how they can strengthen local design outcomes and promote the values and culture of their mother town.

Keywords: Typography, Hong Kong, historical developments, multiple cultures.

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Authors: R. Nedunchezhian, K. Anbumani

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A big organization may have multiple branches spread across different locations. Processing of data from these branches becomes a huge task when innumerable transactions take place. Also, branches may be reluctant to forward their data for centralized processing but are ready to pass their association rules. Local mining may also generate a large amount of rules. Further, it is not practically possible for all local data sources to be of the same size. A model is proposed for discovering valid rules from different sized data sources where the valid rules are high weighted rules. These rules can be obtained from the high frequency rules generated from each of the data sources. A data source selection procedure is considered in order to efficiently synthesize rules. Support Equalization is another method proposed which focuses on eliminating low frequency rules at the local sites itself thus reducing the rules by a significant amount.

Keywords: Association rules, multiple data stores, synthesizing, valid rules.

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Authors: Hassan E. A. Ibrahim, Mohamed F. Serag

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In this paper, Novel method, Particle Swarm Optimization (PSO) algorithm, based technique is proposed to estimate and analyze the steady state performance of self-excited induction generator (SEIG). In this novel method the tedious job of deriving the complex coefficients of a polynomial equation and solving it, as in previous methods, is not required. By comparing the simulation results obtained by the proposed method with those obtained by the well known mathematical methods, a good agreement between these results is obtained. The comparison validates the effectiveness of the proposed technique.

Keywords: Evolution theory, MATLAB, optimization, PSO, SEIG.

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Authors: Ar. Amitava Sarkar

Abstract:

In the traditional architecture, buildings were designed to achieve human comfort by using locally available building materials and construction technology which were more responsive to their climatic and geographic condition. This paper will try to bring out the wisdom of the local masons and builders, often the inhabitants themselves, about their way of living, and shaping their built environment, indoor and outdoor spaces, as a response to the local climatic conditions, from the findings of a field settlement.

Keywords: Traditional architecture, High altitude, Climatic adaptation, Sustainable construction

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Authors: F. Apaydın

Abstract:

In this empirical research, how marketing managers evaluate their firms- performances and decide to make innovation is examined. They use some standards which are past performance of the firm, target performance of the firm, competitor performance, and average performance of the industry to compare and evaluate the firms- performances. It is hypothesized that marketing managers and owners of the firm compare the firms- current performance with these four standards at the same time to decide when to make innovation relating to any aspects of the firm, either management style or products. Relationship between the comparison of the firm-s performance with these standards and innovation are searched in the same regression model. The results of the regression analysis are discussed and some recommendations are made for future studies and applicants.

Keywords: Innovation, performance evaluation standards

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Authors: Kalsoom Sumra

Abstract:

The increasing concern of public sector reforms brings new challenges to public service ethics in developing countries not only at central level but also at local level. This paper aims to identify perceptions on public service ethics of public officials and examines more generally the understanding of public servants in Pakistan towards public service ethics in local public organizations. The study uses an independently administered structured questionnaire to collect data to know the extent of the recognition of public service ethics in local organizations. A total of 150 completed questionnaires are analyzed received from public servants working at the local level in Pakistan. The analysis explores how traditional, social patterns and cultural ethics can provide us with a rounded picture of the main antecedents, moderators of public service ethics in Pakistan. Moreover, the findings of this study contribute in association of public service ethics which are crucial in ongoing political and administrative culture of Pakistan, the most crucial core for public organizational ethical climate. This study also has numerous implications for local public administration and it highlights the importance of expanding research agenda on public service ethics in developing settings with challenging institutional contexts with imperfect training and operating environments. This study may well be particularly important for practice of public service ethics in developing countries in public administration. To the best of author’s knowledge, this study is the first of its kind to provide an initial step in practical implications to emphasize relevant public service ethics in public administration in developing transparent and accountable organization.

Keywords: Public service ethics, accountability and transparency, public service reforms, public administration, organizational ethical climate.

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Authors: S. Bougrine, S. Ouchraa, B. Ahiod, A. A. El Imrani

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Ant colony optimization is an ant algorithm framework that took inspiration from foraging behavior of ant colonies. Indeed, ACO algorithms use a chemical communication, represented by pheromone trails, to build good solutions. However, ants involve different communication channels to interact. Thus, this paper introduces the acoustic communication between ants while they are foraging. This process allows fine and local exploration of search space and permits optimal solution to be improved.

Keywords: Acoustic Communication, Ant Colony Optimization, Local Search, Traveling Salesman Problem.

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Authors: Salwa Aftab, Sehrish Riaz

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The objective of this study was to check the impact of grade sensitivity on learning motivation and academic performance of students and to remove the degree of difference that exists among students regarding the cause of their learning motivation and also to gain knowledge about this matter since it has not been adequately researched. Data collection was primarily done through the academic sector of Pakistan and was depended upon the responses given by students solely. A sample size of 208 university students was selected. Both paper and online surveys were used to collect data from respondents. The results of the study revealed that grade sensitivity has a positive relationship with the learning motivation of students and their academic performance. These findings were carried out through systematic correlation and regression analysis.

Keywords: Academic performance, correlation, grade sensitivity, learning motivation, regression.

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Authors: Hassnen M. Jafer, Khalid S. Hashim, W. Atherton, Ali W. Alattabi

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This study investigates the effect of two important parameters (length of curing period and percentage of the added binder) on the strength of soil treated with OPC. An intermediate plasticity silty clayey soil with medium organic content was used in this study. This soft soil was treated with different percentages of a commercially available cement type 32.5-N. laboratory experiments were carried out on the soil treated with 0, 1.5, 3, 6, 9, and 12% OPC by the dry weight to determine the effect of OPC on the compaction parameters, consistency limits, and the compressive strength. Unconfined compressive strength (UCS) test was carried out on cement-treated specimens after exposing them to different curing periods (1, 3, 7, 14, 28, and 90 days). The results of UCS test were used to develop a non-linear multi-regression model to find the relationship between the predicted and the measured maximum compressive strength of the treated soil (qu). The results indicated that there was a significant improvement in the index of plasticity (IP) by treating with OPC; IP was decreased from 20.2 to 14.1 by using 12% of OPC; this percentage was enough to increase the UCS of the treated soil up to 1362 kPa after 90 days of curing. With respect to the statistical model of the predicted qu, the results showed that the regression coefficients (R2) was equal to 0.8534 which indicates a good reproducibility for the constructed model.

Keywords: Cement admixtures, soft soil stabilisation, geotechnical parameters, unconfined compressive strength, multi-regression model.

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Authors: Nazrina Aziz, Dong Q. Wang

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There have been various methods created based on the regression ideas to resolve the problem of data set containing censored observations, i.e. the Buckley-James method, Miller-s method, Cox method, and Koul-Susarla-Van Ryzin estimators. Even though comparison studies show the Buckley-James method performs better than some other methods, it is still rarely used by researchers mainly because of the limited diagnostics analysis developed for the Buckley-James method thus far. Therefore, a diagnostic tool for the Buckley-James method is proposed in this paper. It is called the renovated Cook-s Distance, (RD* i ) and has been developed based on the Cook-s idea. The renovated Cook-s Distance (RD* i ) has advantages (depending on the analyst demand) over (i) the change in the fitted value for a single case, DFIT* i as it measures the influence of case i on all n fitted values Yˆ∗ (not just the fitted value for case i as DFIT* i) (ii) the change in the estimate of the coefficient when the ith case is deleted, DBETA* i since DBETA* i corresponds to the number of variables p so it is usually easier to look at a diagnostic measure such as RD* i since information from p variables can be considered simultaneously. Finally, an example using Stanford Heart Transplant data is provided to illustrate the proposed diagnostic tool.

Keywords: Buckley-James estimators, censored regression, censored data, diagnostic analysis, product-limit estimator, renovated Cook's Distance.

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Authors: R. Ferdous

Abstract:

Power, responsibility sharing, and democratic decision-making are the central ethos to co-management. It is assumed that involving local community in the decision-making process can create a sense of ownership and responsibility of that community and motivate the community towards collective action. But this paper demonstrated that the process to involve local community is not simple and straightforward as it is influenced by structural aspects, power relations among the actors, and social embedded institutions. These factors shape the process in that way who will participate, how they will participate and how the local community maneuvers their agency in the decision-making process. To grasp the complexities that materialize in the process of participation and to understand the inclusionary and exclusionary nature of participation, this paper examines the subjective understanding of different stakeholders concerning participation and furthermore observes the enabling or constraining factors that affect the community to exercise their agency.

Keywords: Participation, social embeddedness, power, structure.

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Authors: Martin Bader

Abstract:

During the last years, the genomes of more and more species have been sequenced, providing data for phylogenetic recon- struction based on genome rearrangement measures. A main task in all phylogenetic reconstruction algorithms is to solve the median of three problem. Although this problem is NP-hard even for the sim- plest distance measures, there are exact algorithms for the breakpoint median and the reversal median that are fast enough for practical use. In this paper, this approach is extended to the transposition median as well as to the weighted reversal and transposition median. Although there is no exact polynomial algorithm known even for the pairwise distances, we will show that it is in most cases possible to solve these problems exactly within reasonable time by using a branch and bound algorithm.

Keywords: Comparative genomics, genome rearrangements, me-dian, reversals, transpositions.

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Authors: Karolina Patora

Abstract:

This article investigates liquidity risk management by banks, which has gained significant importance since the global financial crisis of 2008. The issue is of particular interest for countries like Poland, in which foreign capital plays a dominant role. Such an ownership structure poses certain risks to the local banking sector, which faces an increased probability of the withdrawal of funding or assets’ transfers abroad in case of a crisis. Both these factors can have a detrimental influence on the liquidity position of foreign-owned banks and hence negatively affect the financial stability of the whole banking sector. The aim of this study is to evaluate the impact of a dominating share of foreign investors in the Polish banking sector on the liquidity position of commercial banks. The study hypothesizes that the ownership structure of the Polish banking sector, in which there are banks predominantly controlled by foreign investors, does not pose a threat to the liquidity position of Polish banks. A supplementary research hypothesis is that the liquidity risk profile of foreign-owned banks differs from that of domestic banks. The sample consists of 14 foreign-owned banks and 5 domestic banks owned by local investors, which together constitute approximately 87% of the banking sector’s assets. The data covers the period of 2004–2014. The results of the regression models show no evidence of significant differences in terms of the dynamics of changes of the liquidity buffers between the foreign-owned and domestic banks, although the signs of the coefficients might suggest that the foreign-owned banks were decreasing the holdings of liquid assets at a slower pace over the examined period, compared to the domestic banks. However, no proof of the statistical significance of these findings has been found. The supplementary research hypothesis that the liquidity risk profile of foreign-controlled banks differs from that of domestic banks was rejected.

Keywords: Financial stability, foreign-owned banks, liquidity position, liquidity risk.

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Authors: Ngono Mindzeng Terencia

Abstract:

Community based tourism, as a sustainable tourism approach, has been adopted as a tool for development among local communities in third world countries with income generation as the main driver. However, an analysis of community based tourism and development brings to light another driving force which is paramount to development strategies in the difficult conditions of third world countries: this driving force is “place revitalization”. This paper seeks to assess the relevance of “place revitalization” to the enhancement of development within the challenging context of developing countries. The research provides a community based tourism model to development in third world countries through a three step process based on awareness, mentoring and empowerment at the local level. It also tries to examine how effectively this model can address the development problems faced by the local communities of third world countries. The case study for this research is the Bamiléké region of Cameroon, the breeding ground of community based tourism initiatives and a region facing the difficulties of third world countries that are great impediments to community based tourism.

Keywords: Awareness, empowerment, local communities, mentoring, place revitalization, third world countries.

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Authors: Mario Gonzalez, David Dominguez, Francisco B. Rodriguez

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An attractor neural network on the small-world topology is studied. A learning pattern is presented to the network, then a stimulus carrying local information is applied to the neurons and the retrieval of block-like structure is investigated. A synaptic noise decreases the memory capability. The change of stability from local to global attractors is shown to depend on the long-range character of the network connectivity.

Keywords: Hebbian learning, image recognition, small world, spatial information.

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Authors: Yoshimoto Kurihara, Tad Gonsalves

Abstract:

Currently, in the field of object posture estimation, there is research on estimating the position and angle of an object by storing a 3D model of the object to be estimated in advance in a computer and matching it with the model. However, in this research, we have succeeded in creating a module that is much simpler, smaller in scale, and faster in operation. Our 6D pose estimation model consists of two different networks – a classification network and a regression network. From a single RGB image, the trained model estimates the class of the object in the image, the coordinates of the object, and its rotation angle in 3D space. In addition, we compared the estimation accuracy of each camera position, i.e., the angle from which the object was captured. The highest accuracy was recorded when the camera position was 75°, the accuracy of the classification was about 87.3%, and that of regression was about 98.9%.

Keywords: AlexNet, Deep learning, image recognition, 6D posture estimation.

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Authors: Seda Yavuz, Anıl Çelebi, Aysun Taşyapı Çelebi, Oğuzhan Urhan

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Nowadays, demand for using real-time video transmission capable devices is ever-increasing. So, high resolution videos have made efficient video compression techniques an essential component for capturing and transmitting video data. Motion estimation has a critical role in encoding raw video. Hence, various motion estimation methods are introduced to efficiently compress the video. Low bit‑depth representation based motion estimation methods facilitate computation of matching criteria and thus, provide small hardware footprint. In this paper, a hardware implementation of a two-bit transformation based low-complexity motion estimation method using local binary pattern approach is proposed. Image frames are represented in two-bit depth instead of full-depth by making use of the local binary pattern as a binarization approach and the binarization part of the hardware architecture is explained in detail. Experimental results demonstrate the difference between the proposed hardware architecture and the architectures of well-known low-complexity motion estimation methods in terms of important aspects such as resource utilization, energy and power consumption.

Keywords: Binarization, hardware architecture, local binary pattern, motion estimation, two-bit transform.

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Authors: Eva Kotlánová

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After recession that began in 2007 in the United States and subsequently spilled over the Europe we could expect recovery of economic growth. According to the last estimation of economic progress of European countries, this recovery is not strong enough. Among others, it will depend on economic policy, where and in which way, the economic indicators will proceed. Economic theories postulate that the economic subjects prefer stably, continual economic policy without repeated and strong fluctuations. This policy is perceived as support of economic growth. Mostly in crises period, when the government must cope with consequences of recession, the economic policy becomes unpredictable for many subjects and economic policy uncertainty grows, which have negative influence on economic growth. The aim of this paper is to use panel regression to prove or disprove this hypothesis on the example of five largest European economies in the period 2008–2012.

Keywords: Economic Crises in Europe, Economic Policy, Uncertainty, Panel Analysis Regression.

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Authors: Koushlendra Kumar Singh, Manish Kumar Bajpai, Rajesh K. Pandey

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The edges of low contrast images are not clearly distinguishable to human eye. It is difficult to find the edges and boundaries in it. The present work encompasses a new approach for low contrast images. The Chebyshev polynomial based fractional order filter has been used for filtering operation on an image. The preprocessing has been performed by this filter on the input image. Laplacian of Gaussian method has been applied on preprocessed image for edge detection. The algorithm has been tested on two test images.

Keywords: Chebyshev polynomials, Fractional order differentiator, Laplacian of Gaussian (LoG) method, Low contrast image.

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Authors: Blaise Fyama, Elie Museng, Grace Mukoma

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In this article we present a java implementation of video telephony using the SIP protocol (Session Initiation Protocol). After a functional analysis of the SIP protocol, we relied on the work of Italian researchers of University of Parma-Italy to acquire adequate libraries for the development of our own communication tool. In order to optimize the code and improve the prototype, we used, in an incremental approach, test techniques based on a static analysis based on the evaluation of the complexity of the software with the application of metrics and the number cyclomatic of Mccabe. The objective is to promote the emergence of local start-ups producing IP video in a well understood local context. We have arrived at the creation of a video telephony tool whose code is optimized.

Keywords: Static analysis, coding, complexity, mccabe metrics, Sip, uml.

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Authors: Aiyeloja A.A, Ogunjinmi A.A

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The recurring decimal of rural and urban poverty in Nigeria, resulting from lack of sustainable livelihood activities by the people due to non-diversification of the economy, necessitated this study. One hundred snail farmers were randomly selected in Akure North and Akure South Local Government areas of Ondo State, Southwest Nigeria where snail farming is widely practised. Data collection was through questionnaires administration and onsite observation of farms. Data obtained were subjected to descriptive statistics, Student-s t-test and regression analysis. Cost benefit ratio (CBR) and rate of return on investment (RORI) were calculated in order to determine the poverty alleviation potentials of snail farming in the study areas. Although snail farming was profitable and viable, it was below poverty line. With time and more knowledge in its farming activities, and with more people taking to snail production, its poverty alleviation and reduction potentials will increase.

Keywords: Alleviation, farming, Nigeria, potential, poverty, snail.

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Authors: W. Y. Wan Fairos, W. H. Wan Azaki, L. Mohamad Alias, Y. Bee Wah

Abstract:

Dengue fever has become a major concern for health authorities all over the world particularly in the tropical countries. These countries, in particular are experiencing the most worrying outbreak of dengue fever (DF) and dengue haemorrhagic fever (DHF). The DF and DHF epidemics, thus, have become the main causes of hospital admissions and deaths in Malaysia. This paper, therefore, attempts to examine the environmental factors that may influence the recent dengue outbreak. The aim of this study is twofold, firstly is to establish a statistical model to describe the relationship between the number of dengue cases and a range of explanatory variables and secondly, to identify the lag operator for explanatory variables which affect the dengue incidence the most. The explanatory variables involved include the level of cloud cover, percentage of relative humidity, amount of rainfall, maximum temperature, minimum temperature and wind speed. The Poisson and Negative Binomial regression analyses were used in this study. The results of the analyses on the 915 observations (daily data taken from July 2006 to Dec 2008), reveal that the climatic factors comprising of daily temperature and wind speed were found to significantly influence the incidence of dengue fever after 2 and 3 weeks of their occurrences. The effect of humidity, on the other hand, appears to be significant only after 2 weeks.

Keywords: Dengue Fever, Dengue Hemorrhagic Fever, Negative Binomial Regression model, Poisson Regression model.

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Authors: Francesca Affortunato, Edgardo Bucciarelli, Mariateresa Ciommi, Gianfranco Giulioni

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The paper represents a reflection on how to select proper indicators to assess the progress of regional contexts towards a knowledge-based society. Taking the first research methodologies elaborated at an international level (World Bank, OECD, etc.) as a reference point, this work intends to identify a set of indicators of the knowledge economy suitable to adequately understand in which manner and to which extent the territorial development dynamics are correlated with the knowledge-base of the considered local society. After a critical survey of the variables utilized within other approaches adopted by international or national organizations, this paper seeks to elaborate a framework of variables, named Regional Knowledge Economy Indicators (ReKEI), necessary to describe the knowledge-based relations of subnational socio-economic contexts. The realization of this framework has a double purpose: an analytical one consisting in highlighting the regional differences in the governance of knowledge based processes, and an operative one consisting in providing some reference parameters for contributing to increasing the effectiveness of those economic policies aiming at enlarging the knowledge bases of local societies.

Keywords: Knowledge economy, knowledge society, information society, regional innovation system, territorial competitiveness, local development.

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Authors: Shujun Fu, Qiuqi Ruan, Wenqia Wang, Yu Li

Abstract:

Utilizing echoic intension and distribution from different organs and local details of human body, ultrasonic image can catch important medical pathological changes, which unfortunately may be affected by ultrasonic speckle noise. A feature preserving ultrasonic image denoising and edge enhancement scheme is put forth, which includes two terms: anisotropic diffusion and edge enhancement, controlled by the optimum smoothing time. In this scheme, the anisotropic diffusion is governed by the local coordinate transformation and the first and the second order normal derivatives of the image, while the edge enhancement is done by the hyperbolic tangent function. Experiments on real ultrasonic images indicate effective preservation of edges, local details and ultrasonic echoic bright strips on denoising by our scheme.

Keywords: anisotropic diffusion, coordinate transformationdirectional derivatives, edge enhancement, hyperbolic tangentfunction, image denoising.

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Authors: Atilla Akpinar, Basri Celik, Suleyman Ciftci

Abstract:

In this paper, we carry over some of the results which are valid on a certain class of Moufang-Klingenberg planes M(A) coordinatized by an local alternative ring A := A(ε) = A+Aε of dual numbers to finite projective Klingenberg plane M(A) obtained by taking local ring Zq (where prime power q = pk) instead of A. So, we show that the collineation group of M(A) acts transitively on 4-gons, and that any 6-figure corresponds to only one inversible m ∈ A.

Keywords: finite Klingenberg plane, projective collineation, 4-transitivity, 6-figures.

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Authors: Michiharu Maeda, Shinya Tsuda

Abstract:

This paper presents an algorithm of particle swarm optimization with reduction for global optimization problems. Particle swarm optimization is an algorithm which refers to the collective motion such as birds or fishes, and a multi-point search algorithm which finds a best solution using multiple particles. Particle swarm optimization is so flexible that it can adapt to a number of optimization problems. When an objective function has a lot of local minimums complicatedly, the particle may fall into a local minimum. For avoiding the local minimum, a number of particles are initially prepared and their positions are updated by particle swarm optimization. Particles sequentially reduce to reach a predetermined number of them grounded in evaluation value and particle swarm optimization continues until the termination condition is met. In order to show the effectiveness of the proposed algorithm, we examine the minimum by using test functions compared to existing algorithms. Furthermore the influence of best value on the initial number of particles for our algorithm is discussed.

Keywords: Particle swarm optimization, Global optimization, Metaheuristics, Reduction.

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Authors: Pavel K. Lopatin, Artyom S. Yegorov

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An exact algorithm for a n-link manipulator movement amidst arbitrary unknown static obstacles is presented. The algorithm guarantees the reaching of a target configuration of the manipulator in a finite number of steps. The algorithm is reduced to a finite number of calls of a subroutine for planning a trajectory in the presence of known forbidden states. The polynomial approximation algorithm which is used as the subroutine is presented. The results of the exact algorithm implementation for the control of a seven link (7 degrees of freedom, 7DOF) manipulator are given.

Keywords: Manipulator, trajectory planning, unknown obstacles

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Authors: Atilla Akpinar, Basri Celik

Abstract:

In this paper we are interested in Moufang-Klingenberg planesM(A) defined over a local alternative ring A of dual numbers. We show that a collineation of M(A) preserve cross-ratio. Also, we obtain some results about harmonic points.

Keywords: Moufang-Klingenberg planes, local alternative ring, projective collineation, cross-ratio, harmonic points.

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Authors: Roger L Goodwin

Abstract:

This paper presents a rank correlation curve. The traditional correlation coefficient is valid for both continuous variables and for integer variables using rank statistics. Since the correlation coefficient has already been established in rank statistics by Spearman, such a calculation can be extended to the correlation curve. This paper presents two survey questions. The survey collected non-continuous variables. We will show weak to moderate correlation. Obviously, one question has a negative effect on the other. A review of the qualitative literature can answer which question and why. The rank correlation curve shows which collection of responses has a positive slope and which collection of responses has a negative slope. Such information is unavailable from the flat, ”first-glance” correlation statistics.

Keywords: Bayesian estimation, regression model, rank statistics, correlation, correlation curve.

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