Search results for: clusters

Authors: G. Candel, D. Naccache

Abstract:

t-SNE is an embedding method that the data science community has widely used. It helps two main tasks: to display results by coloring items according to the item class or feature value; and for forensic, giving a first overview of the dataset distribution. Two interesting characteristics of t-SNE are the structure preservation property and the answer to the crowding problem, where all neighbors in high dimensional space cannot be represented correctly in low dimensional space. t-SNE preserves the local neighborhood, and similar items are nicely spaced by adjusting to the local density. These two characteristics produce a meaningful representation, where the cluster area is proportional to its size in number, and relationships between clusters are materialized by closeness on the embedding. This algorithm is non-parametric. The transformation from a high to low dimensional space is described but not learned. Two initializations of the algorithm would lead to two different embedding. In a forensic approach, analysts would like to compare two or more datasets using their embedding. A naive approach would be to embed all datasets together. However, this process is costly as the complexity of t-SNE is quadratic, and would be infeasible for too many datasets. Another approach would be to learn a parametric model over an embedding built with a subset of data. While this approach is highly scalable, points could be mapped at the same exact position, making them indistinguishable. This type of model would be unable to adapt to new outliers nor concept drift. This paper presents a methodology to reuse an embedding to create a new one, where cluster positions are preserved. The optimization process minimizes two costs, one relative to the embedding shape and the second relative to the support embedding’ match. The embedding with the support process can be repeated more than once, with the newly obtained embedding. The successive embedding can be used to study the impact of one variable over the dataset distribution or monitor changes over time. This method has the same complexity as t-SNE per embedding, and memory requirements are only doubled. For a dataset of n elements sorted and split into k subsets, the total embedding complexity would be reduced from O(n2) to O(n2/k), and the memory requirement from n2 to 2(n/k)2 which enables computation on recent laptops. The method showed promising results on a real-world dataset, allowing to observe the birth, evolution and death of clusters. The proposed approach facilitates identifying significant trends and changes, which empowers the monitoring high dimensional datasets’ dynamics.

Keywords: Concept drift, data visualization, dimension reduction, embedding, monitoring, reusability, t-SNE, unsupervised learning.

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Authors: K. D. Mroczek

Abstract:

In the study presented institutional context is discussed in terms of companies’ entry mode choice. In contrary to many previous analyses, instead of using one or two aggregated variables, a set of eleven determinants is used to establish equity and non-equity internationalization friendly conditions. Based on secondary data, 140 countries are analyzed and grouped into clusters revealing similar framework. The range of the economies explored is wide as it covers all regions distinguished by The World Bank. The results can prove a useful alternative for operationalization of institutional variables in further research concerning entry modes or strategic management in international markets.

Keywords: Clustering, entry mode choice, institutional environment, transaction costs.

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Authors: M. Chumburidze, N. Salia, T. Namchevadze

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This work deals with case processing problems in business. The task of strategic credit requirements management of cases portfolio is discussed. The information model of credit requirements in a binary tree diagram is considered. The algorithms to solve issues of prioritizing clusters of cases in business have been investigated. An implementation of priority queues to support case management operations has been presented. The corresponding pseudo codes for the programming application have been constructed. The tools applied in this development are based on binary tree ordering algorithms, optimization theory, and business management methods.

Keywords: Credit network, case portfolio, binary tree, priority queue, stack.

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Authors: Elaine C. Barboza, Antonio J. Machado

Abstract:

This paper discusses micrometeorological aspects of the urban climate in three cities in Western São Paulo State: Presidente Prudente, Assis and Iepê. Particular attention is paid to the method used to estimate the components of the energy balance at the surface. Estimates of convective fluxes showed that the Bowen ratio was an indicator of the local climate and that its magnitude varied between 0.3 and 0.7. Maximum values for the Bowen ratio occurred earlier in Iepê (11:00 am) than in Presidente Prudente (4:00 pm). The results indicate that the Bowen ratio is modulated by the radiation balance at the surface and by different clusters of vegetation.

Keywords: Bowen ratio, medium-sized cities, surface energy balance, urban climate.

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Authors: Chih-Wei Hsieh, Chau-Yi Chou, Sheng-HsiuKuo, Tsung-Che Tsai, I-Chen Wu

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This paper presents the benchmarking results and performance evaluation of differentclustersbuilt atthe National Center for High-Performance Computingin Taiwan. Performance of processor, memory subsystem andinterconnect is a critical factor in the overall performance of high performance computing platforms. The evaluation compares different system architecture and software platforms. Most supercomputer used HPL to benchmark their system performance, in accordance with the requirement of the TOP500 List. In this paper we consider system memory access factors that affect benchmark performance, such as processor and memory performance.We hope these works will provide useful information for future development and construct cluster system.

Keywords: Performance Evaluation, Benchmarking and High-Performance Computing

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Authors: Fayez Mostafa Alhamoui, Adnan Hadi Mahdi Al- Helali

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The main issue in designing a wireless sensor network (WSN) is the finding of a proper routing protocol that complies with the several requirements of high reliability, short latency, scalability, low power consumption, and many others. This paper proposes a novel routing algorithm that complies with these design requirements. The new routing protocol divides the WSN into several subnetworks and each sub-network is divided into several clusters. This division is designed to reduce the number of radio transmission and hence decreases the power consumption. The network division may be changed dynamically to adapt with the network changes and allows the realization of the design requirements.

Keywords: Wireless sensor networks, routing protocols, ad hoc topology, cluster, sub-network, WSN design requirements.

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Authors: M. Vivodík, Ž. Balážová, Z. Gálová

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The aim of this work was to detect genetic variability among the set of 40 castor genotypes using 8 RAPD markers. Amplification of genomic DNA of 40 genotypes, using RAPD analysis, yielded in 66 fragments, with an average of 8.25 polymorphic fragments per primer. Number of amplified fragments ranged from 3 to 13, with the size of amplicons ranging from 100 to 1200 bp. Values of the polymorphic information content (PIC) value ranged from 0.556 to 0.895 with an average of 0.784 and diversity index (DI) value ranged from 0.621 to 0.896 with an average of 0.798. The dendrogram based on hierarchical cluster analysis using UPGMA algorithm was prepared and analyzed genotypes were grouped into two main clusters and only two genotypes could not be distinguished. Knowledge on the genetic diversity of castor can be used for future breeding programs for increased oil production for industrial uses.

Keywords: Dendrogram, polymorphism, RAPD technique, Ricinus communis L.

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Authors: S.Aranganayagi, K.Thangavel

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Clustering categorical data is more complicated than the numerical clustering because of its special properties. Scalability and memory constraint is the challenging problem in clustering large data set. This paper presents an incremental algorithm to cluster the categorical data. Frequencies of attribute values contribute much in clustering similar categorical objects. In this paper we propose new similarity measures based on the frequencies of attribute values and its cardinalities. The proposed measures and the algorithm are experimented with the data sets from UCI data repository. Results prove that the proposed method generates better clusters than the existing one.

Keywords: Clustering, Categorical, Incremental, Frequency, Domain

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Authors: Soumya Banerjee, Indrajit Mukherjee, P.K. Mahanti

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Scheduling of diversified service requests in distributed computing is a critical design issue. Cloud is a type of parallel and distributed system consisting of a collection of interconnected and virtual computers. It is not only the clusters and grid but also it comprises of next generation data centers. The paper proposes an initial heuristic algorithm to apply modified ant colony optimization approach for the diversified service allocation and scheduling mechanism in cloud paradigm. The proposed optimization method is aimed to minimize the scheduling throughput to service all the diversified requests according to the different resource allocator available under cloud computing environment.

Keywords: Ant Colony, Cloud Computing, Grid, Resource allocator, Service Request.

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Authors: S.Aksoy, Y.Caglar

Abstract:

n-CdO/p-Si heterojunction diode was fabricated using sol-gel spin coating technique which is a low cost and easily scalable method for preparing of semiconductor films. The structural and morphological properties of CdO film were investigated. The X-ray diffraction (XRD) spectra indicated that the film was of polycrystalline nature. The scanning electron microscopy (SEM) images indicate that the surface morphology CdO film consists of the clusters formed with the coming together of the nanoparticles. The electrical characterization of Au/n-CdO/p–Si/Al heterojunction diode was investigated by current-voltage. The ideality factor of the diode was found to be 3.02 for room temperature. The reverse current of the diode strongly increased with illumination intensity of 100 mWcm-2 and the diode gave a maximum open circuit voltage Voc of 0.04 V and short-circuits current Isc of 9.92×10-9 A.

Keywords: CdO, heterojunction semiconductor devices, ideality factor, current-voltage characteristics

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Authors: I. Erins, J. Erina

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The aim of this article is to assess the existing business models used by the banks operating in the CEE countries in the time period from 2006 till 2011. In order to obtain research results, the authors performed qualitative analysis of the scientific literature on bank business models, which have been grouped into clusters that consist of such components as: 1) capital and reserves; 2) assets; 3) deposits, and 4) loans. In their turn, bank business models have been developed based on the types of core activities of the banks, and have been divided into four groups: Wholesale, Investment, Retail and Universal Banks. Descriptive statistics have been used to analyse the models, determining mean, minimal and maximal values of constituent cluster components, as well as standard deviation. The analysis of the data is based on such bank variable indices as Return on Assets (ROA) and Return on Equity (ROE).

Keywords: Banks, Business model, CEE, ROA, ROE.

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Authors: Shuhua Lai, Kairui Chen

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In this paper, we present a fast and efficient mesh coarsening algorithm for 3D triangular meshes. Theis approach can be applied to very complex 3D meshes of arbitrary topology and with millions of vertices. The algorithm is based on the clustering of the input mesh elements, which divides the faces of an input mesh into a given number of clusters for clustering purpose by approximating the Centroidal Voronoi Tessellation of the input mesh. Once a clustering is achieved, it provides us an efficient way to construct uniform tessellations, and therefore leads to good coarsening of polygonal meshes. With proliferation of 3D scanners, this coarsening algorithm is particularly useful for reverse engineering applications of 3D models, which in many cases are dense, non-uniform, irregular and arbitrary topology. Examples demonstrating effectiveness of the new algorithm are also included in the paper.

Keywords: Coarsening, mesh clustering, shape approximation, mesh simplification.

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Authors: George E. Tsekouras, Dimitris Papageorgiou, Sotiris Kotsiantis, Christos Kalloniatis, Panagiotis Pintelas

Abstract:

We develop a three-step fuzzy logic-based algorithm for clustering categorical attributes, and we apply it to analyze cultural data. In the first step the algorithm employs an entropy-based clustering scheme, which initializes the cluster centers. In the second step we apply the fuzzy c-modes algorithm to obtain a fuzzy partition of the data set, and the third step introduces a novel cluster validity index, which decides the final number of clusters.

Keywords: Categorical data, cultural data, fuzzy logic clustering, fuzzy c-modes, cluster validity index.

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Authors: L. Petrovičová, Ž. Balážová, Z. Gálová, M. Wójcik-Jagła, M. Rapacz

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In the present study, RAPD-PCR was used to assess genetic diversity of the rye including landrances and new rye cultivars coming from Central Europe and the Union of Soviet Socialist Republics (SUN). Five arbitrary random primers were used to determine RAPD polymorphism in the set of 38 rye genotypes. These primers amplified altogether 43 different DNA fragments with an average number of 8.6 fragments per genotypes. The number of fragments ranged from 7 (RLZ 8, RLZ 9 and RLZ 10) to 12 (RLZ 6). DI and PIC values of all RAPD markers were higher than 0.8 that generally means high level of polymorphism detected between rye genotypes. The dendrogram based on hierarchical cluster analysis using UPGMA algorithm was prepared. The cultivars were grouped into two main clusters. In this experiment, RAPD proved to be a rapid, reliable and practicable method for revealing of polymorphism in the rye cultivars.

Keywords: Genetic diversity, polymorphism, RAPD markers, Secalecereale L.

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Authors: H. Dujmic, V. Papic, H. Turic

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The article presents a new method for detection of artificial objects and materials from images of the environmental (non-urban) terrain. Our approach uses the hue and saturation (or Cb and Cr) components of the image as the input to the segmentation module that uses the mean shift method. The clusters obtained as the output of this stage have been processed by the decision-making module in order to find the regions of the image with the significant possibility of representing human. Although this method will detect various non-natural objects, it is primarily intended and optimized for detection of humans; i.e. for search and rescue purposes in non-urban terrain where, in normal circumstances, non-natural objects shouldn-t be present. Real world images are used for the evaluation of the method.

Keywords: Landscape surveillance, mean shift algorithm, image segmentation, target detection.

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Authors: Afonso, S. C., Fernandes, P. O., Monte, A. P.

Abstract:

Modern times call organizations to have an active role in the social arena, through Corporate Social Responsibility (CSR). The objective of this research was to test the hypothesis that there is a positive relation between social performance and economic performance, and if there is a positive correlation between social performance and financial-economic performance. To test these theories a measure of social performance, based on the Green Book of Commission of the European Community, was used in a group of nineteen Portuguese top companies, listed on the PSI 20 index, through a period of five years, since 2005 to 2009. A clusters analysis was applied to group companies by their social performance and to compare and correlate their economic performance. Results indicate that companies that had a better social performance are not the ones who had a better economic performance, and suggest that the middle path might provide a good relation CSR-Economic performance, as a basis to a sustainable development.

Keywords: Corporate Social Responsibility, Economic Performance, Win-Win relationship

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Authors: Z. Zainuddin, W. K. Lye

Abstract:

In this paper, a clustering algorithm named KHarmonic means (KHM) was employed in the training of Radial Basis Function Networks (RBFNs). KHM organized the data in clusters and determined the centres of the basis function. The popular clustering algorithms, namely K-means (KM) and Fuzzy c-means (FCM), are highly dependent on the initial identification of elements that represent the cluster well. In KHM, the problem can be avoided. This leads to improvement in the classification performance when compared to other clustering algorithms. A comparison of the classification accuracy was performed between KM, FCM and KHM. The classification performance is based on the benchmark data sets: Iris Plant, Diabetes and Breast Cancer. RBFN training with the KHM algorithm shows better accuracy in classification problem.

Keywords: Neural networks, Radial basis functions, Clusteringmethod, K-harmonic means.

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Authors: Tudor Barbu

Abstract:

An automatic moment-based texture segmentation approach is proposed in this paper. First, we describe the related work in this computer vision domain. Our texture feature extraction, the first part of the texture recognition process, produces a set of moment-based feature vectors. For each image pixel, a texture feature vector is computed as a sequence of area moments. Then, an automatic pixel classification approach is proposed. The feature vectors are clustered using an unsupervised classification algorithm, the optimal number of clusters being determined using a measure based on validation indexes. From the resulted pixel classes one determines easily the desired texture regions of the image.

Keywords: Image segmentation, moment-based texture analysis, automatic classification, validity indexes.

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Authors: Tadeusz Pieczonka, Jan Kazior

Abstract:

The influence of SiC powder addition on densification of Al-SiC compacts during sintering in different atmospheres was investigated. It was performed in a dilatometer in flowing nitrogen, nitrogen/hydrogen (95/5 by volume) and argon. Fine, F500 grade of SiC powder was used. Mixtures containing 10 and 30 vol.% of SiC reinforcement were prepared in a Turbula mixer. Green compacts of about 82% of theoretical density were made of each mixture. For comparison, compacts made of pure aluminum powder were also investigated. It was shown that nitrogen is the best sintering atmosphere because only in this atmosphere did shrinkage take place. Its amount is lowered by ceramic powder addition, i.e. the more SiC the less densification occurs. Additionally, the formation of clusters, enhanced in compacts containing 30 vol.% SiC, is also responsible for limiting the shrinkage. Microstructural examinations of sintered composites revealed that sintering of compacts occurs in the presence of the liquid phase exclusively in nitrogen.

Keywords: Al-SiC composites, densification, sintering atmosphere.

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Authors: Surat Srinoy, Werasak Kurutach, Witcha Chimphlee, Siriporn Chimphlee

Abstract:

One main drawback of intrusion detection system is the inability of detecting new attacks which do not have known signatures. In this paper we discuss an intrusion detection method that proposes independent component analysis (ICA) based feature selection heuristics and using rough fuzzy for clustering data. ICA is to separate these independent components (ICs) from the monitored variables. Rough set has to decrease the amount of data and get rid of redundancy and Fuzzy methods allow objects to belong to several clusters simultaneously, with different degrees of membership. Our approach allows us to recognize not only known attacks but also to detect activity that may be the result of a new, unknown attack. The experimental results on Knowledge Discovery and Data Mining- (KDDCup 1999) dataset.

Keywords: Network security, intrusion detection, rough set, ICA, anomaly detection, independent component analysis, rough fuzzy .

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Authors: Michael P. Herring, Lavrent Khachatryan, Barry Dellinger

Abstract:

Low Temperature Matrix Isolation - Electron Paramagnetic Resonance (LTMI-EPR) Spectroscopy was utilized to identify the species of iron oxide nanoparticles generated during the oxidative pyrolysis of 1-methylnaphthalene (1-MN). The otherwise gas-phase reactions of 1--MN were impacted by a polypropylenimine tetra-hexacontaamine dendrimer complexed with iron (III) nitrate nonahydrate diluted in air under atmospheric conditions. The EPR fine structure of Fe (III)2O3 nanoparticles clusters, characterized by gfactors of 2.00, 2.28, 3.76 and 4.37 were detected on a cold finger maintained at 77 K after accumulation over a multitude of experiments. Additionally, a high valence Fe (IV) paramagnetic intermediate and superoxide anion-radicals, O2•- adsorbed on nanoparticle surfaces in the form of Fe (IV) --- O2•- were detected from the quenching area of Zone 1 in the gas-phase.

Keywords: Cryogenic trapping, EPFRs, dendrimer, Fe2O3 doped silica, soot.

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Authors: Ei Phyo Wai, Nay Min Tun

Abstract:

Computation of facility location problem for every location in the country is not easy simultaneously. Solving the problem is described by using cluster computing. A technique is to design parallel algorithm by using local search with single swap method in order to solve that problem on clusters. Parallel implementation is done by the use of portable parallel programming, Message Passing Interface (MPI), on Microsoft Windows Compute Cluster. In this paper, it presents the algorithm that used local search with single swap method and implementation of the system of a facility to be opened by using MPI on cluster. If large datasets are considered, the process of calculating a reasonable cost for a facility becomes time consuming. The result shows parallel computation of facility location problem on cluster speedups and scales well as problem size increases.

Keywords: cluster, cost, demand, facility location

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Authors: Anod H. Alhazmi, Hanaa A. Yamani

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The lack of digital transformation professionals could prevent Saudi Arabia’s universities from providing digital services. The task of understanding what digital skills are needed within an organization, measuring the existing skills, and developing or attracting talents is a complex task. This paper provides a comprehensive analysis of the digital transformation skills needed in the organizations who seek digital transformation and identifies the skills and competencies framework DigSC built on Skills Framework for the Informational Age (SFIA) framework that is adopted by the Ministry of Communications and Information Technology (MCIT) in Saudi Arabia. The framework adopted identifies the main digital transformation skills clusters, categories and levels of responsibilities for each job description to fill the gap between this requirement and the digital skills supplied by the Umm Alqura University (UQU).

Keywords: Competencies, digital transformation, framework, skills, Umm Alqura University.

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Authors: Neelima Gupta, Seema Aggarwal

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Most of the biclustering/projected clustering algorithms are based either on the Euclidean distance or correlation coefficient which capture only linear relationships. However, in many applications, like gene expression data and word-document data, non linear relationships may exist between the objects. Mutual Information between two variables provides a more general criterion to investigate dependencies amongst variables. In this paper, we improve upon our previous algorithm that uses mutual information for biclustering in terms of computation time and also the type of clusters identified. The algorithm is able to find biclusters with mixed relationships and is faster than the previous one. To the best of our knowledge, none of the other existing algorithms for biclustering have used mutual information as a similarity measure. We present the experimental results on synthetic data as well as on the yeast expression data. Biclusters on the yeast data were found to be biologically and statistically significant using GO Tool Box and FuncAssociate.

Keywords: Biclustering, mutual information.

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Authors: Chiara Verbano, Maria Crema, Karen Venturini

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The company-s ability to draw on a range of external sources to meet their needs for innovation, has been termed 'open innovation' (OI). Very few empirical analyses have been conducted on Small and Medium Enterprises (SMEs) to the extent that they describe and understand the characteristics and implications of this new paradigm. The study's objective is to identify and characterize different modes of OI, (considering innovation process phases and the variety and breadth of the collaboration), determinants, barriers and motivations in SMEs. Therefore a survey was carried out among Italian manufacturing firms and a database of 105 companies was obtained. With regard to data elaboration, a factorial and cluster analysis has been conducted and three different OI modes have emerged: selective low open, unselective open upstream, and mid- partners integrated open. The different behaviours of the three clusters in terms of determinants factors, performance, firm-s technology intensity, barriers and motivations have been analyzed and discussed.

Keywords: Open innovation, R&D management, SMEs.

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Authors: Mounira Taileb, Sami Touati

Abstract:

In Content-Based Image Retrieval systems it is important to use an efficient indexing technique in order to perform and accelerate the search in huge databases. The used indexing technique should also support the high dimensions of image features. In this paper we present the hierarchical index NOHIS-tree (Non Overlapping Hierarchical Index Structure) when we scale up to very large databases. We also present a study of the influence of clustering on search time. The performance test results show that NOHIS-tree performs better than SR-tree. Tests also show that NOHIS-tree keeps its performances in high dimensional spaces. We include the performance test that try to determine the number of clusters in NOHIS-tree to have the best search time.

Keywords: High-dimensional indexing, k-nearest neighborssearch.

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Authors: H. Aoudia, Y. Touati, E. H. Teguig, A. Ali Cherif

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Conceiving and developing routing protocols for wireless sensor networks requires considerations on constraints such as network lifetime and energy consumption. In this paper, we propose a hybrid hierarchical routing protocol named HHRP combining both clustering mechanism and multipath optimization taking into account residual energy and RSSI measures. HHRP consists of classifying dynamically nodes into clusters where coordinators nodes with extra privileges are able to manipulate messages, aggregate data and ensure transmission between nodes according to TDMA and CDMA schedules. The reconfiguration of the network is carried out dynamically based on a threshold value which is associated with the number of nodes belonging to the smallest cluster. To show the effectiveness of the proposed approach HHRP, a comparative study with LEACH protocol is illustrated in simulations.

Keywords: Routing protocols, energy optimization, clustering.

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Authors: V. Rednic, N. Aldea, P. Marginean, D. Macovei, C. M. Teodorescu, E. Dorolti, F. Matei

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The supported Pd catalysts were analyzed by X-ray diffraction and X-ray absorption spectroscopy in order to determine their global and local structure. The average particle size of the supported Pd catalysts was determined by X-ray diffraction method. One of the main purposes of the present contribution is to focus on understanding the specific role of the Pd particle size determined by X-ray diffraction and that of the support oxide. Based on X-ray absorption fine structure spectroscopy analysis we consider that the whole local structure of the investigated samples are distorted concerning the atomic number but the distances between atoms are almost the same as for standard Pd sample. Due to the strong modifications of the Pd cluster local structure, the metal-support interface may influence the electronic properties of metal clusters and thus their reactivity for absorption of the reactant molecules.

Keywords: metal-support interaction, supported metal catalysts, synchrotron radiation, X-ray absorption spectroscopy, X-raydiffraction

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Authors: Ryszard Matysiak, Grzegorz Kamieniarz

Abstract:

The deterministic quantum transfer-matrix (QTM) technique and its mathematical background are presented. This important tool in computational physics can be applied to a class of the real physical low-dimensional magnetic systems described by the Heisenberg hamiltonian which includes the macroscopic molecularbased spin chains, small size magnetic clusters embedded in some supramolecules and other interesting compounds. Using QTM, the spin degrees of freedom are accurately taken into account, yielding the thermodynamical functions at finite temperatures. In order to test the application for the susceptibility calculations to run in the parallel environment, the speed-up and efficiency of parallelization are analyzed on our platform SGI Origin 3800 with p = 128 processor units. Using Message Parallel Interface (MPI) system libraries we find the efficiency of the code of 94% for p = 128 that makes our application highly scalable.

Keywords: Deterministic simulations, low-dimensional magnets, modeling of complex systems, parallelization.

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Authors: Robert Prucek, Aleš Panáček, Jan Filip, Libor Kvítek, Radek Zbořil

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The preparation of Cu nanoparticles (NPs) through the reduction of copper ions by sodium borohydride in the presence of sodium polyacrylate with a molecular weight of 1200 is reported. Cu NPs were synthesized at a concentration of copper salt equal to 2.5, 5, and 10 mM, and at a molar ratio of copper ions and monomeric unit of polyacrylate equal to 1:2. The as-prepared Cu NPs have diameters of about 2.5–3 nm for copper concentrations of 2.5 and 5 mM, and 6 nm for copper concentration of 10 mM. Depending on the copper salt concentration and concentration of additionally added polyacrylate to Cu particle dispersion, primarily formed NPs grow through the process of aggregation and/or coalescence into clusters and/or particles with a diameter between 20–100 nm. The amount of additionally added sodium polyacrylate influences the stability of Cu particles against air oxidation. The catalytic efficiency of the prepared Cu particles for the reduction of 4-nitrophenol is discussed.

Keywords: Copper, nanoparticles, sodium polyacrylate, catalyst, 4-nitrophenol.

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