Search results for: primal-dual interior point method

Authors: Viriyavudh Sim, WooYoung Jung

Abstract:

Window system in high rise building is occasionally subjected to an excessive wind intensity, particularly during typhoon. The failure of window system did not affect overall safety of structural performance; however, it could endanger the safety of the residents. In this paper, comparison of fragility curves for window system of two residential buildings was studied. The probability of failure for individual window was determined with Monte Carlo Simulation method. Then, lognormal cumulative distribution function was used to represent the fragility. The results showed that windows located on the edge of leeward wall were more susceptible to wind load and the probability of failure for each window panel increased at higher floors.

Keywords: Wind fragility, window system, high rise building.

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Authors: Csaba Tóth, Éva Lakatos, László Pethő, Seoyoung Cho

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The temperature effect on asphalt pavement structure is a crucial factor at the design stage. In this paper, by applying the German guidelines for temperature along the asphalt depth is estimated. The aim is to consider temperature profiles in different seasons in numerical modelling. The model is built with an elastic and isotropic solid element with 19 subdivisions of asphalt layers to reflect the temperature variation. Comparison with the simple three-layer pavement system (asphalt layers, base, and subgrade layers) will be followed to see the difference in result without temperature variation along with the depth. Finally, the fatigue life calculation was checked to prove the validity of the methodology of considering the temperature in the numerical modelling.

Keywords: Temperature profile, flexible pavement modelling, finite element method, temperature modelling.

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Authors: H. Abaali, M. T. Lamchich, M. Raoufi

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There are a variety of reference current identification methods, for the shunt active power filter (SAPF), such as the instantaneous active and reactive power, the instantaneous active and reactive current and the synchronous detection method are evaluated and compared under ideal, non sinusoidal and unbalanced voltage conditions. The SAPF performances, for the investigated identification methods, are tested for a non linear load. The simulation results, using Matlab Power System Blockset Toolbox from a complete structure, are presented and discussed.

Keywords: Shunt active power filter, Current perturbation, Non sinusoidal and unbalanced voltage conditions.

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Authors: Nidal F. Shilbayeh, Belal AbuHaija, Zainab N. Al-Qudsy

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In this paper, we propose a new robust and secure system that is based on the combination between two different transforms Discrete wavelet Transform (DWT) and Contourlet Transform (CT). The combined transforms will compensate the drawback of using each transform separately. The proposed algorithm has been designed, implemented and tested successfully. The experimental results showed that selecting the best sub-band for embedding from both transforms will improve the imperceptibility and robustness of the new combined algorithm. The evaluated imperceptibility of the combined DWT-CT algorithm which gave a PSNR value 88.11 and the combination DWT-CT algorithm improves robustness since it produced better robust against Gaussian noise attack. In addition to that, the implemented system shored a successful extraction method to extract watermark efficiently.

Keywords: DWT, CT, Digital Image Watermarking, Copyright Protection.

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Authors: O. A. Akinfenwa, N.M. Yao, S. N. Jator

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In this paper, a self starting two step continuous block hybrid formulae (CBHF) with four Off-step points is developed using collocation and interpolation procedures. The CBHF is then used to produce multiple numerical integrators which are of uniform order and are assembled into a single block matrix equation. These equations are simultaneously applied to provide the approximate solution for the stiff ordinary differential equations. The order of accuracy and stability of the block method is discussed and its accuracy is established numerically.

Keywords: Collocation and Interpolation, Continuous HybridBlock Formulae, Off-Step Points, Stability, Stiff ODEs.

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Authors: A. A. Shafie, M. H. Ali

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Continuously variable transmission (CVT) is a type of automatic transmission that can change the gear ratio to any arbitrary setting within the limits. The most common type of CVT operates on a pulley system that allows an infinite variability between highest and lowest gears with no discrete steps. However, the current CVT system with hydraulic actuation method suffers from the power loss. It needs continuous force for the pulley to clamp the belt and hold the torque resulting in large amount of energy consumption. This study focused on the development of an electromechanical actuated control CVT to eliminate the problem that faced by the existing CVT. It is conducted with several steps; computing and selecting the appropriate sizing for stroke length, lead screw system and etc. From the visual observation it was found that the CVT system of this research is satisfactory.

Keywords: CVT, Hydraulic Actuator, Discrete shifts, Electromechanical system, Lead screws.

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Authors: Emad Hazbkhah, Abdolreza Zahiri, Hossein Ghorbanizade Kharazi, Afshin Kiani

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Establishing pumping stations is one of the most common ways of providing water from rivers. There are many issues involved in the design and operation of pumping stations most important of which is the problem of sedimentation. One of the significant issues which must be taken into consideration in designing pumping stations is the operation method and technical matters related to it. Safety and convenience of operation is one of the issues that must be always considered by the designer. Some of the major issues in making decisions regarding the type of design for the station are geographical condition, the location of the station and availability of experts in maintenance and operation of the station. Dimensions of the station must allow free movement for checking and operating pumps after installation of pumps and plumbing system.

Keywords: Boneh Basht, Iran, pumping station.

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Authors: Prasannakumar Palaniappan, Dong Ho Shin, Chul Gyu Song

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The photoacoustic images are obtained from a custom developed linear array photoacoustic tomography system. The biological specimens are imitated by conducting phantom tests in order to retrieve a fully functional photoacoustic image. The acquired image undergoes the active region based contour filtering to remove the noise and accurately segment the object area for further processing. The universal back projection method is used as the image reconstruction algorithm. The active contour filtering is analyzed by evaluating the signal to noise ratio and comparing it with the other filtering methods.

Keywords: Contour filtering, linear array, photoacoustic tomography, universal back projection.

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Authors: Yohei Saika

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On the basis of Bayesian inference using the maximizer of the posterior marginal estimate, we carry out phase unwrapping using multiple interferograms via generalized mean-field theory. Numerical calculations for a typical wave-front in remote sensing using the synthetic aperture radar interferometry, phase diagram in hyper-parameter space clarifies that the present method succeeds in phase unwrapping perfectly under the constraint of surface- consistency condition, if the interferograms are not corrupted by any noises. Also, we find that prior is useful for extending a phase in which phase unwrapping under the constraint of the surface-consistency condition. These results are quantitatively confirmed by the Monte Carlo simulation.

Keywords: Bayesian inference, generalized mean-field theory, phase unwrapping, statistical mechanics.

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Authors: Ingrid Majerová, Michaela Horúcková

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The concept of competitiveness is currently very frequently used term. However, the interpretation of its essence is different. In this paper, one of the many concepts of competitiveness will be analyzed and that is macroeconomic competitiveness, which is understood as a process, which is based on the productivity growth through the growth of key macroeconomic indicators such as standards of living and employment, where all of these variables must have a sustainable basis. Given the competition is a relative quantity it must be constantly compared with the development of competitiveness in other economies or regions. And this comparison method is also used in the article that compares the macrocompetitiveness of selected economies of the European Economic Area – the Czech Republic, Poland, Austria, Switzerland and Germany. The aim of the paper is to verify the hypothesis concerning the direct correlation between the size of the economy and its competitiveness.

Keywords: Comparison, Competitiveness, European Economic Area, Global Competitiveness Index, Immeasurable Indicators of Competitiveness, Macro-competitiveness.

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Authors: Yuan J. Lui

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Prospective readers can quickly determine whether a document is relevant to their information need if the significant phrases (or keyphrases) in this document are provided. Although keyphrases are useful, not many documents have keyphrases assigned to them, and manually assigning keyphrases to existing documents is costly. Therefore, there is a need for automatic keyphrase extraction. This paper introduces a new domain independent keyphrase extraction algorithm. The algorithm approaches the problem of keyphrase extraction as a classification task, and uses a combination of statistical and computational linguistics techniques, a new set of attributes, and a new machine learning method to distinguish keyphrases from non-keyphrases. The experiments indicate that this algorithm performs better than other keyphrase extraction tools and that it significantly outperforms Microsoft Word 2000-s AutoSummarize feature. The domain independence of this algorithm has also been confirmed in our experiments.

Keywords: classification, keyphrase extraction, machine learning, summarization

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Authors: M. Abdallah

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Urban development requires deep excavations near buildings and other structures. Deep excavation has become more a necessity for better utilization of space as the population of the world has dramatically increased. In Lebanon, some urban areas are very crowded and lack spaces for new buildings and underground projects, which makes the usage of underground space indispensable. In this paper, a numerical modeling is performed using the finite element method to study the deep excavation-diaphragm wall soil-structure interaction in the case of nonlinear soil behavior. The study is focused on a comparison of the results obtained using different support systems. Furthermore, a parametric study is performed according to the remoteness of the structure.

Keywords: Deep excavation, ground anchors, interaction, struts.

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Authors: R. Ahmad, S. Abdul-Kareem

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It is a challenge to provide a wide range of queries to database query systems for small mobile devices, such as the PDAs and cell phones. Currently, due to the physical and resource limitations of these devices, most reported database querying systems developed for them are only offering a small set of pre-determined queries for users to possibly pose. The above can be resolved by allowing free-form queries to be entered on the devices. Hence, a query language that does not restrict the combination of query terms entered by users is proposed. This paper presents the free-form query language and the method used in translating free-form queries to their equivalent SQL statements.

Keywords: Cell phone, database query language, free-formqueries, unplanned queries.

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Authors: JunSeok Hwang, Mohsen Gerami

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Knowledge is the foundation for growth and development. Investment in knowledge improves new method for originate knowledge society and knowledge economy. Investment in knowledge embraces expenditure on education and R&D and software. Measuring of investment in knowledge is characteristically complicated. We examine the influence of investment in knowledge in multifactor productivity growth and numbers of patent. We analyze the annual growth of investment in knowledge and we estimate portion of each country intended for produce total investment in knowledge on the whole OECD. We determine the relative efficiency of average patent numbers with average investment in knowledge and we compare GDP growth rates and growth of knowledge investment. The main purpose in this paper is to study to evaluate different aspect, influence and output of investment in knowledge in OECD countries.

Keywords: Knowledge, GDP, Multifactor productivity, Investment, efficiency.

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Authors: Yasser R. Tawfic, Mohamed A. Eid

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Foundation differential settlement and supported structure tilting are an occasionally occurred engineering problem. This may be caused by overloading, changes in ground soil properties or unsupported nearby excavations. Engineering thinking points directly toward the logic solution for such problem by uplifting the settled side. This can be achieved with deep foundation elements such as micro-piles and macro-piles™, jacked piers, and helical piers, jet grouted mortar columns, compaction grout columns, cement grouting or with chemical grouting, or traditional pit underpinning with concrete and mortar. Although, some of these techniques offer economic, fast and low noise solutions, many of them are quite the contrary. For tilted structures, with the limited inclination, it may be much easier to cause a balancing settlement on the less-settlement side which shall be done carefully in a proper rate. This principal has been applied in Leaning Tower of Pisa stabilization with soil extraction from the ground surface. In this research, the authors attempt to introduce a new solution with a different point of view. So, the micro-tunneling technique is presented in here as an intended ground deformation cause. In general, micro-tunneling is expected to induce limited ground deformations. Thus, the researchers propose to apply the technique to form small size ground unsupported holes to produce the target deformations. This shall be done in four phases: 1. Application of one or more micro-tunnels, regarding the existing differential settlement value, under the raised side of the tilted structure. 2. For each individual tunnel, the lining shall be pulled out from both sides (from jacking and receiving shafts) in the slow rate. 3. If required, according to calculations and site records, an additional surface load can be applied on the raised foundation side. 4. Finally, a strengthening soil grouting shall be applied for stabilization after adjustment. A finite element based numerical model is presented to simulate the proposed construction phases for different tunneling positions and tunnels group. For each case, the surface settlements are calculated and induced plasticity points are checked. These results show the impact of the suggested procedure on the tilted structure and its feasibility. Comparing results also show the importance of the position selection and tunnels group gradual effect. Thus, a new engineering solution is presented to one of the structural and geotechnical engineering challenges.

Keywords: Differential settlement, micro-tunnel, soil-structure interaction, tilted structures.

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Authors: Orkide Donma, Mustafa M. Donma

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Association between insulin resistance (IR) and hematological parameters has long been a matter of interest. Within this context, body mass index (BMI), red blood cells, white blood cells and platelets were involved in this discussion. Parameters related to platelets associated with IR may be useful indicators for the identification of IR. Platelet indices such as mean platelet volume (MPV), platelet distribution width (PDW) and plateletcrit (PCT) are being questioned for their possible association with IR. The aim of this study was to investigate the association between platelet (PLT) count as well as PLT indices and the surrogate indices used to determine IR in morbid obese (MO) children. A total of 167 children participated in the study. Three groups were constituted. The number of cases was 34, 97 and 36 children in the normal BMI, MO and metabolic syndrome (MetS) groups, respectively. Sex- and age-dependent BMI-based percentile tables prepared by World Health Organization were used for the definition of morbid obesity. MetS criteria were determined. BMI values, homeostatic model assessment for IR (HOMA-IR), alanine transaminase-to-aspartate transaminase ratio (ALT/AST) and diagnostic obesity notation model assessment laboratory (DONMA-lab) index values were computed. PLT count and indices were analyzed using automated hematology analyzer. Data were collected for statistical analysis using SPSS for Windows. Arithmetic mean and standard deviation were calculated. Mean values of PLT-related parameters in both control and study groups were compared by one-way ANOVA followed by Tukey post hoc tests to determine whether a significant difference exists among the groups. The correlation analyses between PLT as well as IR indices were performed. Statistically significant difference was accepted as p-value < 0.05. Increased values were detected for PLT (p < 0.01) and PCT (p > 0.05) in MO group compared to those observed in children with N-BMI. Significant increases for PLT (p < 0.01) and PCT (p < 0.05) were observed in MetS group in comparison with the values obtained in children with N-BMI (p < 0.01). Significantly lower MPV and PDW values were obtained in MO group compared to the control group (p < 0.01). HOMA-IR (p < 0.05), DONMA-lab index (p < 0.001) and ALT/AST (p < 0.001) values in MO and MetS groups were significantly increased compared to the N-BMI group. On the other hand, DONMA-lab index values also differed between MO and MetS groups (p < 0.001). In the MO group, PLT was negatively correlated with MPV and PDW values. These correlations were not observed in the N-BMI group. None of the IR indices exhibited a correlation with PLT and PLT indices in the N-BMI group. HOMA-IR showed significant correlations both with PLT and PCT in the MO group. All of the three IR indices were well-correlated with each other in all groups. These findings point out the missing link between IR and PLT activation. In conclusion, PLT and PCT may be related to IR in addition to their identities as hemostasis markers during morbid obesity. Our findings have suggested that DONMA-lab index appears as the best surrogate marker for IR due to its discriminative feature between morbid obesity and MetS.

Keywords: Children, insulin resistance, metabolic syndrome, plateletcrit, platelet indices.

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Authors: Leo Galambos, Jan Lansky, Katsiaryna Chernik

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EGOTHOR is a search engine that indexes the Web and allows us to search the Web documents. Its hit list contains URL and title of the hits, and also some snippet which tries to shortly show a match. The snippet can be almost always assembled by an algorithm that has a full knowledge of the original document (mostly HTML page). It implies that the search engine is required to store the full text of the documents as a part of the index. Such a requirement leads us to pick up an appropriate compression algorithm which would reduce the space demand. One of the solutions could be to use common compression methods, for instance gzip or bzip2, but it might be preferable if we develop a new method which would take advantage of the document structure, or rather, the textual character of the documents. There already exist a special compression text algorithms and methods for a compression of XML documents. The aim of this paper is an integration of the two approaches to achieve an optimal level of the compression ratio

Keywords: Compression, search engine, HTML, XML.

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Authors: Vesna Bosilj Vuksic, Mirjana Pejic Bach

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Business process management (BPM) has become widely accepted within business community as a means for improving business performance. However, it is of the highest importance to incorporate BPM as part of the curriculum at the university level education in order to achieve the appropriate acceptance of the method. Goal of the paper is to determine the current state of education in business process management (BPM) at the Croatian universities and abroad. It investigates the applied forms of instruction and teaching methods and gives several proposals for BPM courses improvement. Since majority of undergraduate and postgraduate students have limited understanding of business processes and lack of any practical experience, there is a need for introducing new teaching approaches. Therefore, we offer some suggestions for further improvement, among which the introduction of simulation games environment in BPM education is strongly recommended.

Keywords: business process management, simulation games, education

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Authors: Aqeel S. Jaber, Abu Zaharin Ahmad, Ahmed N. Abdalla

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The artificial intelligent controller in power system plays as most important rule for many applications such as system operation and its control specially Load Frequency Controller (LFC). The main objective of LFC is to keep the frequency and tie-line power close to their decidable bounds in case of disturbance. In this paper, parallel fuzzy PI adaptive with conventional PD technique for Load Frequency Control system was proposed. PSO optimization method used to optimize both of scale fuzzy PI and tuning of PD. Two equal interconnected power system areas were used as a test system. Simulation results show the effectiveness of the proposed controller compared with different PID and classical fuzzy PI controllers in terms of speed response and damping frequency.

Keywords: Load frequency control, PSO, fuzzy control.

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Authors: I. Nassiri, B. Goliaei, M. Tavassoli

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The ability to distinguish missense nucleotide substitutions that contribute to harmful effect from those that do not is a difficult problem usually accomplished through functional in vivo analyses. In this study, instead current biochemical methods, the effects of missense mutations upon protein structure and function were assayed by means of computational methods and information from the databases. For this order, the effects of new missense mutations in exon 5 of PTEN gene upon protein structure and function were examined. The gene coding for PTEN was identified and localized on chromosome region 10q23.3 as the tumor suppressor gene. The utilization of these methods were shown that c.319G>A and c.341T>G missense mutations that were recognized in patients with breast cancer and Cowden disease, could be pathogenic. This method could be use for analysis of missense mutation in others genes.

Keywords: Bioinformatics, missense mutations, PTEN tumorsuppressor gene.

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Authors: Andrey V. Timofeev, Dmitry V. Egorov, Viktor M. Denisov

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This paper presents development results of usage of C-OTDR monitoring systems for rail traffic management. The COTDR method is based on vibrosensitive properties of optical fibers. Analysis of Rayleigh backscattering radiation parameters changes which take place due to microscopic seismoacoustic impacts on the optical fiber allows to determine seismoacoustic emission source positions and to identify their types. This approach proved successful for rail traffic management (moving block system, weigh- in-motion system etc.).

Keywords: C-OTDR systems, moving block-sections, rail traffic management, Rayleigh backscattering, weigh-in-motion.

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Authors: Faisal Alshuwaier, Ali Areshey

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Text mining techniques are generally applied for classifying the text, finding fuzzy relations and structures in data sets. This research provides plenty text mining capabilities. One common application is text classification and event extraction, which encompass deducing specific knowledge concerning incidents referred to in texts. The main contribution of this paper is the clarification of a concept graph generation mechanism, which is based on a text classification and optimal fuzzy relationship extraction. Furthermore, the work presented in this paper explains the application of fuzzy relationship extraction and branch and bound (BB) method to simplify the texts.

Keywords: Extraction, Max-Prod, Fuzzy Relations, Text Mining, Memberships, Classification.

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Authors: Mehran Yazdi, Mehdi Seyfi, Amirhossein Rafati, Meghdad Asadi

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Detection and tracking of the lip contour is an important issue in speechreading. While there are solutions for lip tracking once a good contour initialization in the first frame is available, the problem of finding such a good initialization is not yet solved automatically, but done manually. We have developed a new tracking solution for lip contour detection using only few landmarks (15 to 25) and applying the well known Active Shape Models (ASM). The proposed method is a new LMS-like adaptive scheme based on an Auto regressive (AR) model that has been fit on the landmark variations in successive video frames. Moreover, we propose an extra motion compensation model to address more general cases in lip tracking. Computer simulations demonstrate a fair match between the true and the estimated spatial pixels. Significant improvements related to the well known LMS approach has been obtained via a defined Frobenius norm index.

Keywords: Lip contour, Tracking, LMS-Like

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Authors: MohammadReza HeidariNezhad, Zuriati Ahmad Zukarnain, Nur Izura Udzir, Mohamed Othman

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In this paper, we propose APO, a new packet scheduling scheme with Quality of Service (QoS) support for hybrid of real and non-real time services in HSDPA networks. The APO scheduling algorithm is based on the effective channel anticipation model. In contrast to the traditional schemes, the proposed method is implemented based on a cyclic non-work-conserving discipline. Simulation results indicated that proposed scheme has good capability to maximize the channel usage efficiency in compared to another exist scheduling methods. Simulation results demonstrate the effectiveness of the proposed algorithm.

Keywords: Scheduling Algorithm, Quality of Service, HSDPA.

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Authors: Z. Feng, V. Viswanathan, D. Navarro, I. O'Connor

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This paper presents a new high speed simulation methodology to solve the long simulation time problem of CMOS image sensor matrix. Generally, for integrating the pixel matrix in SOC and simulating the system performance, designers try to model the pixel in various modeling languages such as VHDL-AMS, SystemC or Matlab. We introduce a new alternative method based on spice model in cadence design platform to achieve accuracy and reduce simulation time. The simulation results indicate that the pixel output voltage maximum error is at 0.7812% and time consumption reduces from 2.2 days to 13 minutes achieving about 240X speed-up for the 256x256 pixel matrix.

Keywords: CMOS image sensor, high speed simulation, image sensor matrix simulation.

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Authors: Kuriko Iwai, Michihiro Kita

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This study aims to clarify constructions which enable to improve socio-cultural values of environments and also to obtain new knowledge on selecting development plans. CVM is adopted as a method of evaluation. As a case of the research, university campus (CP; the following) is selected on account of its various environments, institutions and many users. Investigations were conducted from 4 points of view, total value and utility value of whole CP environments, values of each environment existing in CP or development plan assumed in CP. Furthermore, respondents- attributes were also investigated. In consequence, the following is obtained. 1) Almost all of total value of CP is composed of utility value of direct use. 2) Each of environment and development plans whose value is the highest is clarified. 3) Moreover, development plan to improve environmental value the most is specified.

Keywords: CVM, Development Plans, University Campus, Improvement of Environments Value.

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Authors: Jason Zalev, Reza Sedaghat

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This paper describes a complex energy signal model that is isomorphic with digital human fingerprint images. By using signal models, the problem of fingerprint matching is transformed into the signal processing problem of finding a correlation between two complex signals that differ by phase-rotation and time-scaling. A technique for minutiae matching that is independent of image translation, rotation and linear-scaling, and is resistant to missing minutiae is proposed. The method was tested using random data points. The results show that for matching prints the scaling and rotation angles are closely estimated and a stronger match will have a higher correlation.

Keywords: Affine Invariant, Fingerprint Recognition, Matching, Minutiae.

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Authors: Encarnación Álvarez, Rosa M. García-Fernández, Juan F. Muñoz, Francisco J. Blanco-Encomienda

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The problem of estimating a proportion has important applications in the field of economics, and in general, in many areas such as social sciences. A common application in economics is the estimation of the headcount index. In this paper, we define the general headcount index as a proportion. Furthermore, we introduce a new quantitative method for estimating the headcount index. In particular, we suggest to use the logistic regression estimator for the problem of estimating the headcount index. Assuming a real data set, results derived from Monte Carlo simulation studies indicate that the logistic regression estimator can be more accurate than the traditional estimator of the headcount index.

Keywords: Poverty line, poor, risk of poverty, sample, Monte Carlo simulations.

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Authors: Seok Hong Min, Tae Kwon Ha

Abstract:

Phase equilibria of AZ91D Mg alloys for nonflammable use, containing Ca and Y, were carried out by using FactSage® and FTLite database, which revealed that solid solution treatment could be performed at temperatures from 400 to 450oC. Solid solution treatment of AZ91D Mg alloy without Ca and Y was successfully conducted at 420oC and supersaturated microstructure with all beta phase resolved into matrix was obtained. In the case of AZ91D Mg alloy with some Ca and Y; however, a little amount of intermetallic particles were observed after solid solution treatment. After solid solution treatment, each alloy was annealed at temperatures of 180 and 200oC for time intervals from 1 min to 48 hrs and hardness of each condition was measured by micro-Vickers method. Peak aging conditions were deduced as at the temperature of 200oC for 10 hrs.

Keywords: Mg alloy, AZ91D, nonflammable alloy, phase equilibrium, peak aging.

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Authors: Daesung Moon, Woo-Yong Choi, Kiyoung Moon

Abstract:

Fuzzy fingerprint vault is a recently developed cryptographic construct based on the polynomial reconstruction problem to secure critical data with the fingerprint data. However, the previous researches are not applicable to the fingerprint having a few minutiae since they use a fixed degree of the polynomial without considering the number of fingerprint minutiae. To solve this problem, we use an adaptive degree of the polynomial considering the number of minutiae extracted from each user. Also, we apply multiple polynomials to avoid the possible degradation of the security of a simple solution(i.e., using a low-degree polynomial). Based on the experimental results, our method can make the possible attack difficult 2192 times more than using a low-degree polynomial as well as verify the users having a few minutiae.

Keywords: Fuzzy vault, fingerprint recognition multiple polynomials.

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