Search results for: sequential patterns

Authors: J. Suneetha, Vijayalaxmi

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Sequential Pattern Mining involves applying data mining methods to large data repositories to extract usage patterns. Sequential pattern mining methodologies used to analyze the data and identify patterns. The patterns have been used to implement efficient systems can recommend on previously observed patterns, in making predictions, improve usability of systems, detecting events, and in general help in making strategic product decisions. In this paper, identified performance of approximate sequential pattern mining defines as identifying patterns approximately shared with many sequences. Approximate sequential patterns can effectively summarize and represent the databases by identifying the underlying trends in the data. Conducting an extensive and systematic performance over synthetic and real data. The results demonstrate that ApproxMAP effective and scalable in mining large sequences databases with long patterns.

Keywords: multiple data, performance analysis, sequential pattern, sequence database scalability

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Authors: Safa Adi

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This paper will consider the problem of sequential mining patterns embedded in a database by handling the time constraints as defined in the GSP algorithm (level wise algorithms). We will compare two previous approaches GTC and PSP, that resumes the general principles of GSP. Furthermore this paper will discuss PG-hybrid algorithm, that using PSP and GTC. The results show that PSP and GTC are more efficient than GSP. On the other hand, the GTC algorithm performs better than PSP. The PG-hybrid algorithm use PSP algorithm for the two first passes on the database, and GTC approach for the following scans. Experiments show that the hybrid approach is very efficient for short, frequent sequences.

Keywords: database, GTC algorithm, PSP algorithm, sequential patterns, time constraints

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Authors: Rizka Aisha Rahmi Hariadi, Chao Ou-Yang, Han-Cheng Wang, Rajesri Govindaraju

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As the increasing of medical check-up popularity, there are a huge number of medical check-up data stored in database and have not been useful. These data actually can be very useful for future strategic planning if we mine it correctly. In other side, a lot of patients come with unpredictable coming and also limited available facilities make medical check-up service offered by hospital not maximal. To solve that problem, this study used those medical check-up data to predict patient re-coming. Sequential pattern mining (SPM) and association rules method were chosen because these methods are suitable for predicting patient re-coming using sequential data. First, based on patient personal information the data was grouped into … groups then discriminant analysis was done to check significant of the grouping. Second, for each group some frequent patterns were generated using SPM method. Third, based on frequent patterns of each group, pairs of variable can be extracted using association rules to get general pattern of re-coming patient. Last, discussion and conclusion was done to give some implications of the results.

Keywords: patient re-coming, medical check-up, health examination, data mining, sequential pattern mining, association rules, discriminant analysis

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Authors: Meng-Hui Chen, Chen-Yu Kao, Chia-Yu Hsu, Pei-Chann Chang

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The main idea in this paper is using sequential pattern mining to find the information which is helpful for finding high performance solutions. By combining this information, it is defined as blocks. Using the blocks to generate artificial chromosomes (ACs) could improve the structure of solutions. Estimation of Distribution Algorithms (EDAs) is adapted to solve the combinatorial problems. Nevertheless many of these approaches are advantageous for this application, but only some of them are used to enhance the efficiency of application. Generating ACs uses patterns and EDAs could increase the diversity. According to the experimental result, the algorithm which we proposed has a better performance to solve the permutation flow-shop problems.

Keywords: combinatorial problems, sequential pattern mining, estimationof distribution algorithms, artificial chromosomes

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Authors: Jung–Min Yang

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In this paper, fault recovery for parallel interconnected asynchronous sequential machines is studied. An adversarial input can infiltrate into one of two submachines comprising parallel composition of the considered asynchronous sequential machine, causing an unauthorized state transition. The control objective is to elucidate the condition for the existence of a corrective controller that makes the closed-loop system immune against any occurrence of adversarial inputs. In particular, an efficient existence condition is presented that does not need the complete modeling of the interconnected asynchronous sequential machine.

Keywords: asynchronous sequential machines, parallel composi-tion, corrective control, fault tolerance

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Authors: Yangrae Cho, Jinseok Kim, Yongtae Park

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Mobile app service ecosystem has been abruptly emerged, explosively grown, and dynamically transformed. In contrast with product markets in which product sales directly cause increment in firm’s income, customer’s usage is less visible but more valuable in service market. Especially, the market situation with cutthroat competition in mobile app store makes securing and keeping of users as vital. Although a few service firms try to manage their apps’ usage patterns by fitting on S-curve or applying other forecasting techniques, the time series approaches based on past sequential data are subject to fundamental limitation in the market where customer’s attention is being moved unpredictably and dynamically. We therefore propose a new conceptual approach for detecting usage pattern of mobile app service with Hidden Markov Model (HMM) which is based on the dual stochastic structure and mainly used to clarify unpredictable and dynamic sequential patterns in voice recognition or stock forecasting. Our approach could be practically utilized for app service firms to manage their services’ lifecycles and academically expanded to other markets.

Keywords: mobile app service, usage pattern, Hidden Markov Model, pattern detection

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Authors: Weisi Guo

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It is well established that there may be running correlations in sequential exam marks due to students sitting in the order of course registration patterns. As such, a random and non-sequential sampling of exam marks is a standard recommended practice. Here, the paper examines a large number of exam data stretching several years across different modules to see the degree to which it is true. Using the real mark distribution as a generative process, it was found that random simulated data had no more sequential randomness than the real data. That is to say, the running correlations that one often observes are statistically identical to chance. Digging deeper, it was found that some high running correlations have students that indeed share a common course history and make similar mistakes. However, at the statistical scale of a module question, the combined effect is statistically similar to the random shuffling of papers. As such, there may not be the need to take random samples for marks, but it still remains good practice to mark papers in a random sequence to reduce the repetitive marking bias and errors.

Keywords: data analysis, empirical study, exams, marking

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Authors: Mohammed M. Siddeq, Mohammed H. Rasheed, Omar M. Salih, Marcos A. Rodrigues

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This research proposes a data encoding and decoding method based on the Matrix Minimization algorithm. This algorithm is applied to high-frequency coefficients for compression/encoding. The algorithm starts by converting every three coefficients to a single value; this is accomplished based on three different keys. The decoding/decompression uses a search method called QSS (Quick Sequential Search) Decoding Algorithm presented in this research based on the sequential search to recover the exact coefficients. In the next step, the decoded data are saved in an auxiliary array. The basic idea behind the auxiliary array is to save all possible decoded coefficients; this is because another algorithm, such as conventional sequential search, could retrieve encoded/compressed data independently from the proposed algorithm. The experimental results showed that our proposed decoding algorithm retrieves original data faster than conventional sequential search algorithms.

Keywords: matrix minimization algorithm, decoding sequential search algorithm, image compression, DCT, DWT

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Authors: B. Manikandan, A. Vijayaprabhu

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The conservative reversible gates are used to designed reversible sequential circuits. The sequential circuits are flip-flops and latches. The conservative logic gates are Feynman, Toffoli, and Fredkin. The design of two vectors testable sequential circuits based on conservative logic gates. All sequential circuit based on conservative logic gates can be tested for classical unidirectional stuck-at faults using only two test vectors. The two test vectors are all 1s, and all 0s. The designs of two vectors testable latches, master-slave flip-flops and double edge triggered (DET) flip-flops are presented. We also showed the application of the proposed approach toward 100% fault coverage for single missing/additional cell defect in the quantum- dot cellular automata (QCA) layout of the Fredkin gate. The conservative logic gates are in terms of complexity, speed, and area.

Keywords: DET, QCA, reversible logic gates, POS, SOP, latches, flip flops

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Authors: Khadidja Belbachir, Hafida Belbachir

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subsequently the expansion of the physical supports storage and the needs ceaseless to accumulate several data, the sequential algorithms of associations’ rules research proved to be ineffective. Thus the introduction of the new parallel versions is imperative. We propose in this paper, a parallel version of a sequential algorithm “Partition”. This last is fundamentally different from the other sequential algorithms, because it scans the data base only twice to generate the significant association rules. By consequence, the parallel approach does not require much communication between the sites. The proposed approach was implemented for an experimental study. The obtained results, shows a great reduction in execution time compared to the sequential version and Count Distributed algorithm.

Keywords: association rules, distributed data mining, partition, parallel algorithms

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Authors: Rezky Rifaini, Raden Bagus Fajriya Hakim

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This research was conducted at the Bolo primary health Care in Bima Regency. The purpose of the research is to find out the association pattern that is formed of medical record database from Bolo Primary health care’s patient. The data used is secondary data from medical records database PHC. Sequential pattern mining technique is the method that used to analysis. Transaction data generated from Patient_ID, Check_Date and diagnosis. Sequential Pattern Discovery Algorithms Using Equivalent Classes (SPADE) is one of the algorithm in sequential pattern mining, this algorithm find frequent sequences of data transaction, using vertical database and sequence join process. Results of the SPADE algorithm is frequent sequences that then used to form a rule. It technique is used to find the association pattern between items combination. Based on association rules sequential analysis with SPADE algorithm for minimum support 0,03 and minimum confidence 0,75 is gotten 3 association sequential pattern based on the sequence of patient_ID, check_Date and diagnosis data in the Bolo PHC.

Keywords: diagnosis, primary health care, medical record, data mining, sequential pattern mining, SPADE algorithm

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Authors: Yingxu Wang

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This work presents basic research on the recursive structures and dual sequential patterns of primes for the formal proof of the Twin-Prime Conjecture (TPC). A rigorous methodology of Twin-Prime Decomposition (TPD) is developed in MATLAB to inductively verify potential twins in the dual sequences of primes. The key finding of this basic study confirms that the dual sequences of twin primes are not only symmetric but also infinitive in the unique base 6 cycle, except a limited subset of potential pairs is eliminated by the lack of dual primality. Both theory and experiments have formally proven that the infinity of twin primes stated in TPC holds in the P x P space.

Keywords: number theory, primes, twin-prime conjecture, dual primes (P x P), twin prime decomposition, formal proof, algorithm

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Authors: R. Ruslee, H. Gollee

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Functional electrical stimulation (FES) is a commonly used technique in rehabilitation and often associated with rapid muscle fatigue which becomes the limiting factor in its applications. The objective of this study is to investigate the effects on the onset of fatigue of conventional synchronous stimulation, as well as asynchronous stimulation that mimic voluntary muscle activation targeting different motor units which are activated sequentially or randomly via multiple pairs of stimulation electrodes. We investigate three different approaches with various electrode configurations, as well as different patterns of stimulation applied to the gastrocnemius muscle: Conventional Synchronous Stimulation (CSS), Asynchronous Sequential Stimulation (ASS) and Asynchronous Random Stimulation (ARS). Stimulation was applied repeatedly for 300 ms followed by 700 ms of no-stimulation with 40 Hz effective frequency for all protocols. Ten able-bodied volunteers (28±3 years old) participated in this study. As fatigue indicators, we focused on the analysis of Normalized Fatigue Index (NFI), Fatigue Time Interval (FTI) and pre-post Twitch-Tetanus Ratio (ΔTTR). The results demonstrated that ASS and ARS give higher NFI and longer FTI confirming less fatigue for asynchronous stimulation. In addition, ASS and ARS resulted in higher ΔTTR than conventional CSS. In this study, we proposed a randomly distributed stimulation method for the application of FES and investigated its suitability for reducing muscle fatigue compared to previously applied methods. The results validated that asynchronous stimulation reduces fatigue, and indicates that random stimulation may improve fatigue resistance in some conditions.

Keywords: asynchronous stimulation, electrode configuration, functional electrical stimulation (FES), muscle fatigue, pattern stimulation, random stimulation, sequential stimulation, synchronous stimulation

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Authors: Myung Ho Lee, Hee Seung Lim, Young Jae Maeng, Chang Hoon Lee

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This study presents an automatic sequential extraction device for Pu and Am isotopes in radioactive waste samples from the nuclear power plant with anion exchange resin and TRU resin. After radionuclides were leached from the radioactive waste samples with concentrated HCl and HNO₃, the sample was allowed to evaporate to dryness after filtering the leaching solution with 0.45 micron filter. The Pu isotopes were separated in HNO₃ medium with anion exchange resin. For leaching solution passed through the anion exchange column, the Am isotopes were sequentially separated with TRU resin. Automatic sequential extraction device built-in software information of separation for Pu and Am isotopes was developed. The purified Pu and Am isotopes were measured by alpha spectrometer, respectively, after the micro-precipitation of neodymium. The data of Pu and Am isotopes in radioactive waste with an automatic sequential extraction device developed in this study were validated with the ICP-MS system.

Keywords: automatic sequential extraction device, Pu isotopes, Am isotopes, alpha spectrometer, radioactive waste samples, ICP-MS system

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Authors: Mohamed Rahal, Djaouida Guetta

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In this paper, the one-dimensional unconstrained global optimization problem of continuous functions satifying a Hölder condition is considered. We extend the algorithm of sequential covering SCA for Lipschitz functions to a large class of Hölder functions. The convergence of the method is studied and the algorithm can be applied to systems of nonlinear equations. Finally, some numerical examples are presented and illustrate the efficiency of the present approach.

Keywords: global optimization, Hölder functions, sequential covering method, systems of nonlinear equations

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Authors: Jung–Min Yang

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Solvability of the model matching problem for input/output switched asynchronous sequential machines is discussed in this paper. The control objective is to determine the existence condition and design algorithm for a corrective controller that can match the stable-state behavior of the closed-loop system to that of a reference model. Switching operations and correction procedures are incorporated using output feedback so that the controlled switched machine can show the desired input/output behavior. A matrix expression is presented to address reachability of switched asynchronous sequential machines with output equivalence with respect to a model. The presented reachability condition for the controller design is validated in a simple example.

Keywords: asynchronous sequential machines, corrective control, model matching, input/output control

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Authors: Mahdy ‎Esmailian, Mahdi ‎Doostparast, Ahmad ‎Parsian

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‎In this article‎, ‎sequential order statistics (SOS) censoring type II samples coming from the generalized Pareto distribution are considered‎. ‎Maximum likelihood (ML) estimators of the unknown parameters are derived on the basis of the available multiple SOS data‎. ‎Necessary conditions for existence and uniqueness of the derived ML estimates are given‎. Due to complexity in the proposed likelihood function‎, ‎a useful re-parametrization is suggested‎. ‎For illustrative purposes‎, ‎a Monte Carlo simulation study is conducted and an illustrative example is analysed‎.

Keywords: bayesian estimation‎, generalized pareto distribution‎, ‎maximum likelihood estimation‎, sequential order statistics

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Authors: Ebtehal Aljedaani, Maha Aljohani

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Privacy and security patterns are both important for developing software that protects users' data and privacy. Privacy patterns are designed to address common privacy problems, such as unauthorized data collection and disclosure. Security patterns are designed to protect software from attack and ensure reliability and trustworthiness. Using privacy and security patterns, software engineers can implement security and privacy by design principles, which means that security and privacy are considered throughout the software development process. These patterns are available to translate "security & privacy-by-design" into practical advice for software engineering. Previous research on privacy and security patterns has typically focused on one category of patterns at a time. This paper aims to bridge this gap by merging the two categories and identifying their similarities and differences. To do this, the authors conducted a systematic literature review of 25 research papers on privacy and security patterns. The papers were analysed based on the category of the pattern, the classification of the pattern, and the security requirements that the pattern addresses. This paper presents the results of a comprehensive review of privacy and security design patterns. The review is intended to help future IT designers understand the relationship between the two types of patterns and how to use them to design secure and privacy-preserving software. The paper provides a clear classification of privacy and security design patterns, along with examples of each type. The authors found that there is only one widely accepted classification of privacy design patterns, while there are several competing classifications of security design patterns. Three types of security design patterns were found to be the most commonly used.

Keywords: design patterns, security, privacy, classification of patterns, security patterns, privacy patterns

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Authors: Seong Woo Kwak, Jung-Min Yang

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A strategy of fault diagnosis and tolerance for asynchronous sequential machines is discussed in this paper. With no synchronizing clock, it is difficult to diagnose an occurrence of permanent or stuck-in faults in the operation of asynchronous machines. In this paper, we present a fault detector comprised of a timer and a set of static functions to determine the occurrence of faults. In order to realize immediate fault tolerance, corrective control theory is applied to designing a dynamic feedback controller. Existence conditions for an appropriate controller and its construction algorithm are presented in terms of reachability of the machine and the feature of fault occurrences.

Keywords: asynchronous sequential machines, corrective control, fault diagnosis and tolerance, fault detector

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Authors: Andrey V. Timofeev, Dmitry V. Egorov

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The practical efficient approach is suggested for estimation of the seismoacoustic sources energy in C-OTDR monitoring systems. This approach represents the sequential plan for confidence estimation both the seismoacoustic sources energy, as well the absorption coefficient of the soil. The sequential plan delivers the non-asymptotic guaranteed accuracy of obtained estimates in the form of non-asymptotic confidence regions with prescribed sizes. These confidence regions are valid for a finite sample size when the distributions of the observations are unknown. Thus, suggested estimates are non-asymptotic and nonparametric, and also these estimates guarantee the prescribed estimation accuracy in the form of the prior prescribed size of confidence regions, and prescribed confidence coefficient value.

Keywords: nonparametric estimation, sequential confidence estimation, multichannel monitoring systems, C-OTDR-system, non-lineary regression

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Authors: Jung-Min Yang

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Fault diagnosis of composite asynchronous sequential machines with parallel composition is addressed in this paper. An adversarial input can infiltrate one of two submachines comprising the composite asynchronous machine, causing an unauthorized state transition. The objective is to characterize the condition under which the controller can diagnose any fault occurrence. Two control configurations, state feedback and output feedback, are considered in this paper. In the case of output feedback, the exact estimation of the state is impossible since the current state is inaccessible and the output feedback is given as the form of burst. A simple example is provided to demonstrate the proposed methodology.

Keywords: asynchronous sequential machines, parallel composition, fault diagnosis, corrective control

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Authors: Jung-Min Yang

Abstract:

A method of tolerating input faults for input/state asynchronous sequential machines is proposed. A corrective controller is placed in front of the considered asynchronous machine to realize model matching with a reference model. The value of the external input transmitted to the closed-loop system may change by fault. We address the existence condition for the controller that can counteract adverse effects of any input fault while maintaining the objective of model matching. A design procedure for constructing the controller is outlined. The proposed reachability condition for the controller design is validated in an illustrative example.

Keywords: asynchronous sequential machines, corrective control, fault tolerance, input faults, model matching

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Authors: Samson Henry Dogo, Allan Clark, Elena Kulinskaya

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The objective in meta-analysis is to combine results from several independent studies in order to create generalization and provide evidence based for decision making. But recent studies show that the magnitude of effect size estimates reported in many areas of research finding changed with year publication and this can impair the results and conclusions of meta-analysis. A number of sequential methods have been proposed for monitoring the effect size estimates in meta-analysis. However they are based on statistical theory applicable to fixed effect model (FEM). For random-effects model (REM), the analysis incorporates the heterogeneity variance, tau-squared and its estimation create complications. In this paper proposed the use of Gombay and Serbian (2005) truncated CUSUM-type test with asymptotically valid critical values for sequential monitoring of REM. Simulation results show that the test does not control the Type I error well, and is not recommended. Further work required to derive an appropriate test in this important area of application.

Keywords: meta-analysis, random-effects model, sequential test, temporal changes in effect sizes

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Authors: Shaojian Li

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The traditional Chinese patterns, as an integral part of Chinese culture, possess unique values in history, culture, and art. However, with the passage of time and societal changes, many of these traditional patterns are at risk of being lost, damaged, or forgotten. To undertake the digital preservation and protection of these traditional patterns, this paper will collect and organize images of traditional Chinese patterns. It will provide exhaustive and comprehensive semantic annotations, creating a resource library of traditional Chinese pattern images. This will support the digital preservation and application of traditional Chinese patterns.

Keywords: digitization of cultural heritage, traditional Chinese patterns, digital humanities, database construction

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Authors: Asmat Nawaz, Ali Koray Erdinc, Burak Gultekin, Muhammad Tayyib, Ceylan Zafer, Kaiying Wang, M. Nadeem Akram

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In this study, a sequential deposition process is used for the fabrication of PEDOT: PSS based inverted planar perovskite solar cell. A small amount of additive deionized water (DI-H₂O) was added into PbI₂ + Dimethyl formamide (DMF) precursor solution in order to increase the solubility of PbI₂ in DMF, and finally to manipulate the surface morphology of the perovskite films. A morphology transition from needle like structure to hexagonal plates, and then needle-like again has been observed as the DI-H2O was added continuously (0.0 wt% to 3.0wt%). The latter one leads to full surface coverage of the perovskite, which is essential for high performance solar cell.

Keywords: charge carrier diffusion lengths, Methylamonium lead iodide, precursor composition, perovskite solar cell, sequential deposition

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Authors: Jung-Min Yang

Abstract:

Corrective control enables us to change the stable state behavior of an asynchronous sequential machine without modifying inner logic of the machine. This paper addresses corrective control for asynchronous machines with switching capability. The considered asynchronous machine consists of a set of different submachines and switches to each machine according to a constant switching sequence. The control goal is to design a corrective controller such that the closed-loop system can match the behavior of a reference model. The reachability of the switched asynchronous machine is described by a logic calculation of the reachability of submachines. The design procedure of the proposed corrective controller is outlined, and the applicability of the proposed scheme is validated in an example.

Keywords: switched asynchronous sequential machines, corrective control, state feedback, switching sequences

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Authors: Sriparna Bandopadhyay

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It is known that irreducible sign patterns in general may not allow diagonalizability and in particular irreducible sign patterns with minimum rank greater than or equal to 4. It is also known that every irreducible sign pattern matrix with minimum rank of 2 allow diagonalizability with rank of 2 and the maximum rank of the sign pattern. In general sign patterns with minimum rank of 3 may not allow diagonalizability if the condition of irreducibility is dropped, but the problem of whether every irreducible sign pattern with minimum rank of 3 allows diagonalizability remains open. In this paper it is shown that irreducible sign patterns with minimum rank of 3 under certain conditions on the underlying graph allow diagonalizability. An alternate proof of the results that every sign pattern matrix with minimum rank of 2 and no zero lines allow diagonalizability with rank of 2 and also that every full sign pattern allows diagonalizability with all permissible ranks of the sign pattern is given. Some open problems regarding composite cycles in an irreducible symmetric sign pattern that support of a rank principal certificate are also answered.

Keywords: irreducible sign patterns, minimum rank, symmetric sign patterns, rank -principal certificate, allowing diagonalizability

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Authors: Mai Anh Pham Ho

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Scarf products today is a symbol of fashion to decorate, to make our life more beautiful and bring new features to our living space. It also shows the cultural identity by using the traditional patterns that make easily to introduce the image of Vietnam to other nations all over the world. Therefore, the purpose of this research is to classify Vietnamese traditional patterns according to the era and dynasties. Vietnamese traditional patterns through the dynasties of Vietnamese history are done and classified by five groups of patterns including the geometric patterns, the natural patterns, the animal patterns, the floral patterns, and the character patterns in the Prehistoric times, the Bronze and Iron age, the Chinese domination, the Ngo-Dinh-TienLe-Ly-Tran-Ho dynasty, and the LeSo-Mac-LeTrinh-TaySon-Nguyen dynasty. Besides, there are some special kinds of Vietnamese traditional patterns like buffalo, lotus, bronze-drum, Phuc Loc Tho character, and so on. Extensive research was conducted for modernizing scarf collection applied Vietnamese traditional patterns which the fashion trend is used on creating works. The concept, target, image map, lifestyle map, motif, colours, arrangement and completion of patterns on scarf were set up. The scarf collection is designed and developed by the Adobe Illustrator program with three colour ways for each scarf. Upon completion of the research, digital printing technology is chosen for using on scarf collection which Vietnamese traditional patterns were researched deeply and widely with the purpose of establishment the basic background for Vietnamese culture in order to identify Vietnamese national personality as well as establish and preserve the cultural heritage.

Keywords: scarf collection, Vietnamese traditional patterns, printing methods, fabric design

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Authors: Rabbia Tariq, Hannan Sajjad, Mehreen Sirshar

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Design patterns are widely used to make the process of development easier as they greatly help the developers to develop the software. Different design patterns have been introduced till now but the behavior of same design pattern may differ in different domains that can lead to the wrong selection of the design pattern. The paper aims to discover the design patterns that suits best with respect to their domain thereby helping the developers to choose an effective design pattern. It presents the comprehensive analysis of design patterns based on different methodologies that include simulation, case study and comparison of various algorithms. Due to the difference of the domain the methodology used in one domain may be inapplicable to the other domain. The paper draws a conclusion based on strength and limitation of each design pattern in their respective domain.

Keywords: design patterns, evaluation, quality assurance, software domains

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Authors: Yen-Luan Chen

Abstract:

Maintenance has a great impact on the capacity of production and on the quality of the products, and therefore, it deserves continuous improvement. Maintenance procedure done before a failure is called preventive maintenance (PM). Sequential PM, which specifies that a system should be maintained at a sequence of intervals with unequal lengths, is one of the commonly used PM policies. This article proposes a generalized sequential PM policy for a system subject to shocks with imperfect maintenance and random working time. The shocks arrive according to a non-homogeneous Poisson process (NHPP) with varied intensity function in each maintenance interval. As a shock occurs, the system suffers two types of failures with number-dependent probabilities: type-I (minor) failure, which is rectified by a minimal repair, and type-II (catastrophic) failure, which is removed by a corrective maintenance (CM). The imperfect maintenance is carried out to improve the system failure characteristic due to the altered shock process. The sequential preventive maintenance-last (PML) policy is defined as that the system is maintained before any CM occurs at a planned time Ti or at the completion of a working time in the i-th maintenance interval, whichever occurs last. At the N-th maintenance, the system is replaced rather than maintained. This article first takes up the sequential PML policy with random working time and imperfect maintenance in reliability engineering. The optimal preventive maintenance schedule that minimizes the mean cost rate of a replacement cycle is derived analytically and determined in terms of its existence and uniqueness. The proposed models provide a general framework for analyzing the maintenance policies in reliability theory.

Keywords: optimization, preventive maintenance, random working time, minimal repair, replacement, reliability

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