Search results for: entropy function

Authors: Chad Goldsworthy, B. Rajeswari Matam

Abstract:

The use of deep learning for species identification in camera trap images has revolutionised our ability to study, conserve and monitor species in a highly efficient and unobtrusive manner, with state-of-the-art models achieving accuracies surpassing the accuracy of manual human classification. The high imbalance of camera trap datasets, however, results in poor accuracies for minority (rare or endangered) species due to their relative insignificance to the overall model accuracy. This paper investigates the use of Focal Loss, in comparison to the traditional Cross Entropy Loss function, to improve the identification of minority species in the “255 Bird Species” dataset from Kaggle. The results show that, although Focal Loss slightly decreased the accuracy of the majority species, it was able to increase the F1-score by 0.06 and improve the identification of the bottom two, five and ten (minority) species by 37.5%, 15.7% and 10.8%, respectively, as well as resulting in an improved overall accuracy of 2.96%.

Keywords: Convolutional neural networks, data imbalance, deep learning, focal loss, species classification, wildlife conservation.

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Authors: Kyu Chul Lee, Sung Hyun Yoo, Choon Ki Ahn, Myo Taeg Lim

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Recent experimental evidences have shown that because of a fast convergence and a nice accuracy, neural networks training via extended kalman filter (EKF) method is widely applied. However, as to an uncertainty of the system dynamics or modeling error, the performance of the method is unreliable. In order to overcome this problem in this paper, a new finite impulse response (FIR) filter based learning algorithm is proposed to train radial basis function neural networks (RBFN) for nonlinear function approximation. Compared to the EKF training method, the proposed FIR filter training method is more robust to those environmental conditions. Furthermore , the number of centers will be considered since it affects the performance of approximation.

Keywords: Extended kalmin filter (EKF), classification problem, radial basis function networks (RBFN), finite impulse response (FIR)filter.

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Authors: A. Mirzaaghazadeh, H. Motameni, M. Karshenas, H. Nematzadeh

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Learning the gradient of neuron's activity function like the weight of links causes a new specification which is flexibility. In flexible neural networks because of supervising and controlling the operation of neurons, all the burden of the learning is not dedicated to the weight of links, therefore in each period of learning of each neuron, in fact the gradient of their activity function, cooperate in order to achieve the goal of learning thus the number of learning will be decreased considerably. Furthermore, learning neurons parameters immunes them against changing in their inputs and factors which cause such changing. Likewise initial selecting of weights, type of activity function, selecting the initial gradient of activity function and selecting a fixed amount which is multiplied by gradient of error to calculate the weight changes and gradient of activity function, has a direct affect in convergence of network for learning.

Keywords: Back propagation, Flexible, Gradient, Learning, Neural network, Pattern recognition.

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Authors: Sukhwinder Singh Billing, Sushma Gupta, Sukhjit Singh Dhaliwal

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In the present paper, we investigate a differential subordination involving multiplier transformation related to a sector in the open unit disk E = {z : |z| < 1}. As special cases to our main result, certain sufficient conditions for strongly starlike and strongly convex functions are obtained.

Keywords: Analytic function, Multiplier transformation, Strongly starlike function, Strongly convex function.

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Authors: Samira Malekmohammadi Golsefid, Mehdi Ghazanfari, Somayeh Alizadeh

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The goal of this paper is to segment the countries based on the value of export from Iran during 14 years ending at 2005. To measure the dissimilarity among export baskets of different countries, we define Dissimilarity Export Basket (DEB) function and use this distance function in K-means algorithm. The DEB function is defined based on the concepts of the association rules and the value of export group-commodities. In this paper, clustering quality function and clusters intraclass inertia are defined to, respectively, calculate the optimum number of clusters and to compare the functionality of DEB versus Euclidean distance. We have also study the effects of importance weight in DEB function to improve clustering quality. Lastly when segmentation is completed, a designated RFM model is used to analyze the relative profitability of each cluster.

Keywords: Customers segmentation, Customer relationship management, Clustering, Data Mining

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Authors: Mohammed Qasim, Kyoung-Dae Kim

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In this paper, we present the design of the super-ellipsoidal potential function (SEPF), that can be used for autonomous collision avoidance of an unmanned aerial vehicle (UAV) in a 3-dimensional space. In the design of SEPF, we have the full control over the shape and size of the potential function. In particular, we can adjust the length, width, height, and the amount of flattening at the tips of the potential function so that the collision avoidance motion vector generated from the potential function can be adjusted accordingly. Based on the idea of the SEPF, we also propose an approach for the local autonomy of a UAV for its collision avoidance when the UAV is teleoperated by a human operator. In our proposed approach, a teleoperated UAV can not only avoid collision autonomously with other surrounding objects but also track the operator’s control input as closely as possible. As a result, an operator can always be in control of the UAV for his/her high-level guidance and navigation task without worrying too much about the UAVs collision avoidance while it is being teleoperated. The effectiveness of the proposed approach is demonstrated through a human-in-the-loop simulation of quadrotor UAV teleoperation using virtual robot experimentation platform (v-rep) and Matlab programs.

Keywords: Artificial potential function, autonomy, collision avoidance, teleoperation, quadrotor, UAV.

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Authors: Anita S. Gangal, P. K. Kalra, D. S. Chauhan

Abstract:

The backpropagation algorithm in general employs quadratic error function. In fact, most of the problems that involve minimization employ the Quadratic error function. With alternative error functions the performance of the optimization scheme can be improved. The new error functions help in suppressing the ill-effects of the outliers and have shown good performance to noise. In this paper we have tried to evaluate and compare the relative performance of complex valued neural network using different error functions. During first simulation for complex XOR gate it is observed that some error functions like Absolute error, Cauchy error function can replace Quadratic error function. In the second simulation it is observed that for some error functions the performance of the complex valued neural network depends on the architecture of the network whereas with few other error functions convergence speed of the network is independent of architecture of the neural network.

Keywords: Complex backpropagation algorithm, complex errorfunctions, complex valued neural network, split activation function.

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Authors: Hsuan-Chu Li

Abstract:

We demonstrate a way to count the number of Young tableau u of shape λ = (k, k,L, k) with | λ |= lk by expanding Schur function. This result gives an answer to the question that was put out by Jenny Buontempo and Brian Hopkins.

Keywords: Young tableau, Schur function.

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Authors: Hadi Taghvafard

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We present a new quadrature rule based on the spline interpolation along with the error analysis. Moreover, some error estimates for the reminder when the integrand is either a Lipschitzian function, a function of bounded variation or a function whose derivative belongs to Lp are given. We also give some examples to show that, practically, the spline rule is better than the trapezoidal rule.

Keywords: Quadrature, Spline interpolation, Trapezoidal rule, Numericalintegration, Error analysis.

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Authors: Marko A. Rodriguez

Abstract:

There exists an injective, information-preserving function that maps a semantic network (i.e a directed labeled network) to a directed network (i.e. a directed unlabeled network). The edge label in the semantic network is represented as a topological feature of the directed network. Also, there exists an injective function that maps a directed network to an undirected network (i.e. an undirected unlabeled network). The edge directionality in the directed network is represented as a topological feature of the undirected network. Through function composition, there exists an injective function that maps a semantic network to an undirected network. Thus, aside from space constraints, the semantic network construct does not have any modeling functionality that is not possible with either a directed or undirected network representation. Two proofs of this idea will be presented. The first is a proof of the aforementioned function composition concept. The second is a simpler proof involving an undirected binary encoding of a semantic network.

Keywords: general-modeling, multi-relational networks, semantic networks

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Authors: Moataz M. Naguib, Hatem Khater, A. Baith Mohamed

Abstract:

MARS is a shared-key (symmetric) block cipher algorithm supporting 128-bit block size and a variable key size of between 128 and 448 bits. MARS has a several rounds of cryptographic core that is designed to take advantage of the powerful results for improving security/performance tradeoff over existing ciphers. In this work, a new function added to improve the ciphering process it is called, Meta-Morphic function. This function use XOR, Rotating, Inverting and No-Operation logical operations before and after encryption process. The aim of these operations is to improve MARS cipher process and makes a high confusion criterion for the Ciphertext.

Keywords: AES, MARS, Metamorphic, Cryptography, Block Cipher.

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Authors: Anirudh Sunil Warrier, Saba Al-Rubaye, Dimitrios Panagiotakopoulos, Gokhan Inalhan, Antonios Tsourdos

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The demand for increased data transfer rate and network traffic capacity has given rise to the concept of heterogeneous networks. Heterogeneous networks are wireless networks, consisting of devices using different underlying radio access technologies (RAT). For Unmanned Aerial Vehicles (UAVs) this enhanced data rate and network capacity are even more critical especially in their applications of medicine, delivery missions and military. In an urban heterogeneous network environment, the UAVs must be able switch seamlessly from one base station (BS) to another for maintaining a reliable link. Therefore, seamless handover in such urban environments has become a major challenge. In this paper, a scheme to achieve seamless handover is developed, an algorithm based on Received Signal Strength (RSS) criterion for network selection is used and Entropy Weighted Method (EWM) is implemented for decision making. Seamless handover using EWM decision-making is demonstrated successfully for a UAV moving across fifth generation (5G) and long-term evolution (LTE) networks via a simulation level analysis. Thus, a solution for UAV-5G communication, specifically the mobility challenge in heterogeneous networks is solved and this work could act as step forward in making UAV-5G architecture integration a possibility.

Keywords: Air to ground, A2G, fifth generation, 5G, handover, mobility, unmanned aerial vehicle, UAV, urban environments.

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Authors: Cuneyt Yucelbas, Seral Ozsen, Sule Yucelbas, Gulay Tezel

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Due to the fact that there exist only a small number of complex systems in artificial immune system (AIS) that work out nonlinear problems, nonlinear AIS approaches, among the well-known solution techniques, need to be developed. Gaussian function is usually used as similarity estimation in classification problems and pattern recognition. In this study, diagnosis of breast cancer, the second type of the most widespread cancer in women, was performed with different distance calculation functions that euclidean, gaussian and gaussian-euclidean hybrid function in the clonal selection model of classical AIS on Wisconsin Breast Cancer Dataset (WBCD), which was taken from the University of California, Irvine Machine-Learning Repository. We used 3-fold cross validation method to train and test the dataset. According to the results, the maximum test classification accuracy was reported as 97.35% by using of gaussian-euclidean hybrid function for fold-3. Also, mean of test classification accuracies for all of functions were obtained as 94.78%, 94.45% and 95.31% with use of euclidean, gaussian and gaussian-euclidean, respectively. With these results, gaussian-euclidean hybrid function seems to be a potential distance calculation method, and it may be considered as an alternative distance calculation method for hard nonlinear classification problems.

Keywords: Artificial Immune System, Breast Cancer Diagnosis, Euclidean Function, Gaussian Function.

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Authors: R. Uthayakumar, G. Arockia Prabakar

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In this paper, we introduce R Iterated Function System and employ the Hutchinson Barnsley theory (HB) to construct a fractal set as its unique fixed point by using Reich contractions in a complete b metric space. We discuss about well posedness of fixed point problem for b metric space.

Keywords: Fractals, Iterated Function System, Compact set, Reich Contraction, Well posedness.

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Authors: Hamid Abdi, Abolfazl Salami, Abolfazl Ahmadi

Abstract:

Programmable logic controllers are the main controllers in the today's industries; they are used for several applications in industrial control systems and there are lots of examples exist from the PLC applications in industries especially in big companies and plants such as refineries, power plants, petrochemical companies, steel companies, and food and production companies. In the PLCs there are some functions in the function library in software that can be used in PLC programs as basic program elements. The aim of this project are introducing and implementing a new function block of a neural network to the function library of PLC. This block can be applied for some control applications or nonlinear functions calculations after it has been trained for these applications. The implemented neural network is a Perceptron neural network with three layers, three input nodes and one output node. The block can be used in manual or automatic mode. In this paper the structure of the implemented function block, the parameters and the training method of the network are presented by considering the especial method of PLC programming and its complexities. Finally the application of the new block is compared with a classic simulated block and the results are presented.

Keywords: Programmable Logic Controller, PLC Programming, Neural Networks, Perception Network, Intelligent Control.

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Authors: Sizhong Zhou, Hongxia Liu

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Let G be a graph of order n, and let k  2 and m  0 be two integers. Let h : E(G)  [0, 1] be a function. If e∋x h(e) = k holds for each x  V (G), then we call G[Fh] a fractional k-factor of G with indicator function h where Fh = {e  E(G) : h(e) > 0}. A graph G is called a fractional (k,m)-deleted graph if there exists a fractional k-factor G[Fh] of G with indicator function h such that h(e) = 0 for any e  E(H), where H is any subgraph of G with m edges. In this paper, it is proved that G is a fractional (k,m)-deleted graph if (G)  k + m + m k+1 , n  4k2 + 2k − 6 + (4k 2 +6k−2)m−2 k−1 and max{dG(x), dG(y)}  n 2 for any vertices x and y of G with dG(x, y) = 2. Furthermore, it is shown that the result in this paper is best possible in some sense.

Keywords: Graph, degree condition, fractional k-factor, fractional (k, m)-deleted graph.

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Authors: A. H. Fatah, A. H. Ahmed

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Levenberg-Marquardt method (LM) was proposed to be applied as a non-linear least-square fitting in the analysis of a natural gamma-ray spectrum that was taken by the Hp (Ge) detector. The Gaussian function that composed of three components, main Gaussian, a step background function and tailing function in the lowenergy side, has been suggested to describe each of the y-ray lines mathematically in the spectrum. The whole spectrum has been analyzed by determining the energy and relative intensity for the strong y-ray lines.

Keywords: Gamma-Ray, Spectrum analysis, Non-linear leastsquare fitting.

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Authors: Shun Horikoshi, Tohru Kawabe

Abstract:

This study presents performance analysis results of SMC (Sliding mode control) with changing the chattering functions applied to slip suppression problem of electric vehicles (EVs). In SMC, chattering phenomenon always occurs through high frequency switching of the control inputs. It is undesirable phenomenon and degrade the control performance, since it causes the oscillations of the control inputs. Several studies have been conducted on this problem by introducing some general saturation function. However, study about whether saturation function was really best and the performance analysis when using the other functions, weren’t being done so much. Therefore, in this paper, several candidate functions for SMC are selected and control performance of candidate functions is analyzed. In the analysis, evaluation function based on the trade-off between slip suppression performance and chattering reduction performance is proposed. The analyses are conducted in several numerical simulations of slip suppression problem of EVs. Then, we can see that there is no difference of employed candidate functions in chattering reduction performance. On the other hand, in slip suppression performance, the saturation function is excellent overall. So, we conclude the saturation function is most suitable for slip suppression sliding mode control.

Keywords: Sliding mode control, chattering function, electric vehicle, slip suppression, performance analysis.

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Authors: Mohanad Alhabo, Li Zhang, Naveed Nawaz

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Small cell deployment in 5G networks is a promising technology to enhance the capacity and coverage. However, unplanned deployment may cause high interference levels and high number of unnecessary handovers, which in turn result in an increase in the signalling overhead. To guarantee service continuity, minimize unnecessary handovers and reduce signalling overhead in heterogeneous networks, it is essential to properly model the handover decision problem. In this paper, we model the handover decision problem using Multiple Attribute Decision Making (MADM) method, specifically Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS), and propose a hybrid TOPSIS method to control the handover in heterogeneous network. The proposed method adopts a hybrid weighting policy, which is a combination of entropy and standard deviation. A hybrid weighting control parameter is introduced to balance the impact of the standard deviation and entropy weighting on the network selection process and the overall performance. Our proposed method show better performance, in terms of the number of frequent handovers and the mean user throughput, compared to the existing methods.

Keywords: Handover, HetNets, interference, MADM, small cells, TOPSIS, weight.

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Authors: Ahmed A. A. Radwan, Bahgat A. Abdel Latef, Abdel Mgeid A. Ali, Osman A. Sadek

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This study investigates the use of genetic algorithms in information retrieval. The method is shown to be applicable to three well-known documents collections, where more relevant documents are presented to users in the genetic modification. In this paper we present a new fitness function for approximate information retrieval which is very fast and very flexible, than cosine similarity fitness function.

Keywords: Cosine similarity, Fitness function, Genetic Algorithm, Information Retrieval, Query learning.

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Authors: Chukiat Chaiboonsri, Satawat Wannapan

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This paper used an asymmetric informative concept to apply in the macroeconomic model estimation of the tourism sector in Thailand. The variables used to statistically analyze are Thailand international and domestic tourism revenues, the expenditures of foreign and domestic tourists, service investments by private sectors, service investments by the government of Thailand, Thailand service imports and exports, and net service income transfers. All of data is a time-series index which was observed between 2002 and 2015. Empirically, the tourism multiplier and accelerator were estimated by two statistical approaches. The first was the result of the Generalized Method of Moments model (GMM) based on the assumption which the tourism market in Thailand had perfect information (Symmetrical data). The second was the result of the Maximum Entropy Bootstrapping approach (MEboot) based on the process that attempted to deal with imperfect information and reduced uncertainty in data observations (Asymmetrical data). In addition, the tourism leakages were investigated by a simple model based on the injections and leakages concept. The empirical findings represented the parameters computed from the MEboot approach which is different from the GMM method. However, both of the MEboot estimation and GMM model suggests that Thailand’s tourism sectors are in a period capable of stimulating the economy.

Keywords: Thailand tourism, maximum entropy bootstrapping approach, macroeconomic model, asymmetric information.

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Authors: Nurcan Tuncbag, Turkan Haliloglu, Ozlem Keskin

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Understanding the cell's large-scale organization is an interesting task in computational biology. Thus, protein-protein interactions can reveal important organization and function of the cell. Here, we investigated the correspondence between protein interactions and function for the yeast. We obtained the correlations among the set of proteins. Then these correlations are clustered using both the hierarchical and biclustering methods. The detailed analyses of proteins in each cluster were carried out by making use of their functional annotations. As a result, we found that some functional classes appear together in almost all biclusters. On the other hand, in hierarchical clustering, the dominancy of one functional class is observed. In the light of the clustering data, we have verified some interactions which were not identified as core interactions in DIP and also, we have characterized some functionally unknown proteins according to the interaction data and functional correlation. In brief, from interaction data to function, some correlated results are noticed about the relationship between interaction and function which might give clues about the organization of the proteins, also to predict new interactions and to characterize functions of unknown proteins.

Keywords: Pair-wise protein interactions, DIP database, functional correlations, biclustering.

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Authors: N.E.Galich

Abstract:

We develop new nonlinear methods of immunofluorescence analysis for a sensitive technology of respiratory burst reaction of DNA fluorescence due to oxidative activity in the peripheral blood neutrophils. Histograms in flow cytometry experiments represent a fluorescence flashes frequency as functions of fluorescence intensity. We used the Shannon-Weaver index for definition of neutrophils- biodiversity and Hurst index for definition of fractal-s correlations in immunofluorescence for different donors, as the basic quantitative criteria for medical diagnostics of health status. We analyze frequencies of flashes, information, Shannon entropies and their fractals in immunofluorescence networks due to reduction of histogram range. We found the number of simplest universal correlations for biodiversity, information and Hurst index in diagnostics and classification of pathologies for wide spectra of diseases. In addition is determined the clear criterion of a common immunity and human health status in a form of yes/no answers type. These answers based on peculiarities of information in immunofluorescence networks and biodiversity of neutrophils. Experimental data analysis has shown the existence of homeostasis for information entropy in oxidative activity of DNA in neutrophil nuclei for all donors.

Keywords: blood and cells fluorescence in diagnostics ofdiseases, cytometric histograms, entropy and information in fractalnetworks of oxidative activity of DNA, long-range chromosomalcorrelations in living cells.

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Authors: Komeil Jahanifar, Zahra Abedi, Yaghob Zeraatkish

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This research was conducted for the first time at the southeastern coasts of the Caspian Sea in order to evaluate the performance of osteichthyes cooperatives through production (catch) function. Using one of the indirect valuation methods in this research, contributory factors in catch were identified and were inserted into the function as independent variables. In order to carry out this research, the performance of 25 Osteichthyes catching cooperatives in the utilization year of 2009 which were involved in fishing in Miankale wildlife refuge region. The contributory factors in catch were divided into groups of economic, ecological and biological factors. In the mentioned function, catch rate of the cooperative were inserted into as the dependant variable and fourteen partial variables in terms of nine general variables as independent variables. Finally, after function estimation, seven variables were rendered significant at 99 percent reliably level. The results of the function estimation indicated that human resource (fisherman quantity) had the greatest positive effect on catch rate with an influence coefficient of 1.7 while weather conditions had the greatest negative effect on the catch rate of cooperatives with an influence coefficient of -2.07. Moreover, factors like member's share, experience and fisherman training and fishing effort played the main roles in the catch rate of cooperative with influence coefficients of 0.81, 0.5 and 0.21, respectively.

Keywords: Production Function, Coefficient, Variable, Osteichthyes, Caspian Sea

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Authors: Ruhugül Özge Ocak, Banu Öztürk Kurtaslan

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Botanical gardens are very significant organizations which protect the environment against the increasing environmental problems, provide environmental education for people, offer recreation possibilities, etc. This article describes botanical gardens and their functions. The most important function of botanical garden is to provide environmental education for people and improve environmental awareness. Considering this function, some botanical gardens were examined and opinions were suggested about the subject.

Keywords: Botanical garden, environment, environmental education, recreation.

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Authors: Ali Dorostkar

Abstract:

In this paper, a basic schematic of fractional dimensional optimization problem is presented. As will be shown, a method is performed based on a relation between roots and tangent lines of function in fractional dimensions for an arbitrary initial point. It is shown that for each polynomial function with order N at least N tangent lines must be existed in fractional dimensions of 0 < α < N+1 which pass exactly through the all roots of the proposed function. Geometrical analysis of tangent lines in fractional dimensions is also presented to clarify more intuitively the proposed method. Results show that with an appropriate selection of fractional dimensions, we can directly find the roots. Method is presented for giving a different direction of optimization problems by the use of fractional dimensions.

Keywords: Tangent line, fractional dimension, root, optimization problem.

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Authors: N. Tuncbag, T. Haliloglu, O. Keskin

Abstract:

Understanding the cell's large-scale organization is an interesting task in computational biology. Thus, protein-protein interactions can reveal important organization and function of the cell. Here, we investigated the correspondence between protein interactions and function for the yeast. We obtained the correlations among the set of proteins. Then these correlations are clustered using both the hierarchical and biclustering methods. The detailed analyses of proteins in each cluster were carried out by making use of their functional annotations. As a result, we found that some functional classes appear together in almost all biclusters. On the other hand, in hierarchical clustering, the dominancy of one functional class is observed. In brief, from interaction data to function, some correlated results are noticed about the relationship between interaction and function which might give clues about the organization of the proteins.

Keywords: Pair-wise protein interactions, DIP database, functional correlations, biclustering.

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Authors: Subariah Ibrahim, Mohd Aizaini Maarof

Abstract:

A generalization of the concepts of Feistel Networks (FN), known as Extended Feistel Network (EFN) is examined. EFN splits the input blocks into n > 2 sub-blocks. Like conventional FN, EFN consists of a series of rounds whereby at least one sub-block is subjected to an F function. The function plays a key role in the diffusion process due to its completeness property. It is also important to note that in EFN the F-function is the most computationally expensive operation in a round. The aim of this paper is to determine a suitable type of EFN for a scalable cipher. This is done by analyzing the threshold number of rounds for different types of EFN to achieve the completeness property as well as the number of F-function required in the network. The work focuses on EFN-Type I, Type II and Type III only. In the analysis it is found that EFN-Type II and Type III diffuses at the same rate and both are faster than Type-I EFN. Since EFN-Type-II uses less F functions as compared to EFN-Type III, therefore Type II is the most suitable EFN for use in a scalable cipher.

Keywords: Cryptography, Extended Feistel Network, Diffusion Analysis.

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Authors: Y. Long, L. Liu, K. V. Branin

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One challenge faced by procurement decision-maker during the acquisition process is how to compare similar products from different suppliers and allocate orders among different products or services. This work focuses on allocating orders among multiple suppliers considering rebate. The objective function is to minimize the total acquisition cost including purchasing cost and rebate benefit. Rebate benefit is complex and difficult to estimate at the ordering step. Rebate rules vary for different suppliers and usually change over time. In this work, we developed a system to collect the rebate policies, standardized the rebate policies and developed two-stage optimization models for ordering allocation. Rebate policy with multi-tiers is considered in modeling. The discontinuous cost function of rebate benefit is formulated for different scenarios. A piecewise linear function is used to approximate the discontinuous cost function of rebate benefit. And a Mixed Integer Programing (MIP) model is built for order allocation problem with multi-tier rebate. A case study is presented and it shows that our optimization model can reduce the total acquisition cost by considering rebate rules.

Keywords: Discontinuous cost function, mixed integer programming, optimization, procurement, rebate.

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Authors: Rassoul Abdelaziz

Abstract:

We develop a new estimator of the renewal function for heavy-tailed claims amounts. Our approach is based on the peak over threshold method for estimating the tail of the distribution with a generalized Pareto distribution. The asymptotic normality of an appropriately centered and normalized estimator is established, and its performance illustrated in a simulation study.

Keywords: Renewal function, peak-over-threshold, POT method, extremes value, generalized pareto distribution, heavy-tailed distribution.

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