Search results for: sequential pattern mining

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: 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: 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: 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: H. S. Saini, K. Vijayalakshmi, Rishi Sayal

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Network-based education has been growing rapidly in size and quality. Knowledge clustering becomes more important in personalized information retrieval for web-learning. A personalized-Learning service after the learners’ knowledge has been classified with clustering. Through automatic analysis of learners’ behaviors, their partition with similar data level and interests may be discovered so as to produce learners with contents that best match educational needs for collaborative learning. We present a specific mining tool and a recommender engine that we have integrated in the online learning in order to help the teacher to carry out the whole e-learning process. We propose to use sequential pattern mining algorithms to discover the most used path by the students and from this information can recommend links to the new students automatically meanwhile they browse in the course. We have Developed a specific author tool in order to help the teacher to apply all the data mining process. We tend to report on many experiments with real knowledge so as to indicate the quality of using both clustering and sequential pattern mining algorithms together for discovering personalized e-learning systems.

Keywords: e-learning, cluster, personalization, sequence, pattern

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Authors: Zaky Musyarof, Dwi Yono Sutarto, Dwima Rindy Atika, R. B. Fajriya Hakim

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Each country should be responsible for the safety of people, especially responsible for the safety of people living in disaster-prone areas. One of those services is provides evacuation route for them. But all this time, the selection of evacuation route is seem doesn’t well organized, it could be seen that when a disaster happen, there will be many accumulation of people on the steps of evacuation route. That condition is dangerous to people because hampers evacuation process. By some methods in Statistical analysis, author tries to give a suggestion how to prepare evacuation route which is organized and based on people habit. Those methods are association rules, sequential pattern mining, hierarchical cluster analysis and fuzzy logic.

Keywords: association rules, sequential pattern mining, cluster analysis, fuzzy logic, evacuation route

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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: Usman Qamar, Younus Javed

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Frequent pattern mining is the process of finding a pattern (a set of items, subsequences, substructures, etc.) that occurs frequently in a data set. It was proposed in the context of frequent itemsets and association rule mining. Frequent pattern mining is used to find inherent regularities in data. What products were often purchased together? Its applications include basket data analysis, cross-marketing, catalog design, sale campaign analysis, Web log (click stream) analysis, and DNA sequence analysis. However, one of the bottlenecks of frequent itemset mining is that as the data increase the amount of time and resources required to mining the data increases at an exponential rate. In this investigation a new algorithm is proposed which can be uses as a pre-processor for frequent itemset mining. FASTER (FeAture SelecTion using Entropy and Rough sets) is a hybrid pre-processor algorithm which utilizes entropy and rough-sets to carry out record reduction and feature (attribute) selection respectively. FASTER for frequent itemset mining can produce a speed up of 3.1 times when compared to original algorithm while maintaining an accuracy of 71%.

Keywords: rough-sets, classification, feature selection, entropy, outliers, frequent itemset mining

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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: Jaishree Ranganathan, Poonam Rajurkar, Angelina A. Tzacheva, Zbigniew W. Ras

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In today’s world, business often depends on the customer feedback and reviews. Sentiment analysis helps identify and extract information about the sentiment or emotion of the of the topic or document. Attribute selection is a challenging problem, especially with large datasets in actionable pattern mining algorithms. Action Rule Mining is one of the methods to discover actionable patterns from data. Action Rules are rules that help describe specific actions to be made in the form of conditions that help achieve the desired outcome. The rules help to change from any undesirable or negative state to a more desirable or positive state. In this paper, we present a Lexicon based weighted scheme approach to identify emotions from customer feedback data in the area of manufacturing business. Also, we use Rough sets and explore the attribute selection method for large scale datasets. Then we apply Actionable pattern mining to extract possible emotion change recommendations. This kind of recommendations help business analyst to improve their customer service which leads to customer satisfaction and increase sales revenue.

Keywords: actionable pattern discovery, attribute selection, business data, data mining, emotion

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Authors: Jaishree Ranganathan, MuthuPriya Shanmugakani Velsamy, Shamika Kulkarni, Angelina Tzacheva

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Emotions play an important role in everyday life. An-alyzing these emotions or feelings from social media platforms like Twitter, Facebook, blogs, and forums based on user comments and reviews plays an important role in various factors. Some of them include brand monitoring, marketing strategies, reputation, and competitor analysis. The opinions or sentiments mined from such data helps understand the current state of the user. It does not directly provide intuitive insights on what actions to be taken to benefit the end user or business. Actionable Pattern Mining method provides suggestions or actionable recommendations on what changes or actions need to be taken in order to benefit the end user. In this paper, we propose automatic classification of emotions in Twitter data using Recurrent Neural Network - Gated Recurrent Unit. We achieve training accuracy of 87.58% and validation accuracy of 86.16%. Also, we extract action rules with respect to the user emotion that helps to provide actionable suggestion.

Keywords: emotion mining, twitter, recurrent neural network, gated recurrent unit, actionable pattern mining

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Authors: Suzan Wedyan

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Data mining is one of the main phases in the Knowledge Discovery Database (KDD) which is responsible of finding hidden and useful knowledge from databases. There are many different tasks for data mining including regression, pattern recognition, clustering, classification, and association rule. In recent years a promising data mining approach called associative classification (AC) has been proposed, AC integrates classification and association rule discovery to build classification models (classifiers). This paper surveys and critically compares several AC algorithms with reference of the different procedures are used in each algorithm, such as rule learning, rule sorting, rule pruning, classifier building, and class allocation for test cases.

Keywords: associative classification, classification, data mining, learning, rule ranking, rule pruning, prediction

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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: Sikander Singh Cheema, Jasmeen Kaur

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In this paper, the concept of data mining is summarized and its one of the important process i.e KDD is summarized. The data mining based on Genetic Algorithm is researched in and ways to achieve the data mining Genetic Algorithm are surveyed. This paper also conducts a formal review on the area of data mining tasks and genetic algorithm in various fields.

Keywords: data mining, KDD, genetic algorithm, descriptive mining, predictive mining

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Authors: Muhammad Usman

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Pattern extraction has been done in past to extract hidden and interesting patterns from large datasets. Recently, advancements are being made in these techniques by providing the ability of multi-level mining, effective dimension reduction, advanced evaluation and visualization support. This paper focuses on reviewing the current techniques in literature on the basis of these parameters. Literature review suggests that most of the techniques which provide multi-level mining and dimension reduction, do not handle mixed-type data during the process. Patterns are not extracted using advanced algorithms for large datasets. Moreover, the evaluation of patterns is not done using advanced measures which are suited for high-dimensional data. Techniques which provide visualization support are unable to handle a large number of rules in a small space. We present a theoretical model to handle these issues. The implementation of the model is beyond the scope of this paper.

Keywords: association rule mining, data mining, data warehouses, visualization of association rules

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Authors: Oshin Anand, Atanu Rakshit

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The vast increment in the e-commerce ventures makes this area a prominent research stream. Besides several quantified parameters, the textual content of reviews is a storehouse of many information that can educate companies and help them earn profit. This study is an attempt in this direction. The article attempts to categorize data based on a computed metric that quantifies the influencing capacity of reviews rendering two categories of high and low influential reviews. Further, each of these document is studied to conclude several product feature categories. Each of these categories along with the computed metric is converted to linguistic identifiers and are used in an association mining model. The article makes a novel attempt to combine feature attraction with quantified metric to categorize review text and finally provide frequent patterns that depict customer preferences. Frequent mentions in a highly influential score depict customer likes or preferred features in the product whereas prominent pattern in low influencing reviews highlights what is not important for customers. This is achieved using a hybrid approach of text mining for feature and term extraction, sentiment analysis, multicriteria decision-making technique and association mining model.

Keywords: association mining, customer preference, frequent pattern, online reviews, text mining

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Authors: Hoda A. Abdel Hafez

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Mining big data represents a big challenge nowadays. Many types of research are concerned with mining massive amounts of data and big data streams. Mining big data faces a lot of challenges including scalability, speed, heterogeneity, accuracy, provenance and privacy. In telecommunication industry, mining big data is like a mining for gold; it represents a big opportunity and maximizing the revenue streams in this industry. This paper discusses the characteristics of big data (volume, variety, velocity and veracity), data mining techniques and tools for handling very large data sets, mining big data in telecommunication and the benefits and opportunities gained from them.

Keywords: mining big data, big data, machine learning, telecommunication

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Authors: Seema Vaidya

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Mining association rule is a key issue in data mining. In any case, the standard models ignore the distinction among the exchanges, and the weighted association rule mining does not transform on databases with just binary attributes. This paper proposes a novel continuous example and executes a tree (FP-tree) structure, which is an increased prefix-tree structure for securing compacted, discriminating data about examples, and makes a fit FP-tree-based mining system, FP enhanced capacity algorithm is used, for mining the complete game plan of examples by illustration incessant development. Here, this paper handles the motivation behind making remarkable and weighted item sets, i.e. rare weighted item set mining issue. The two novel brightness measures are proposed for figuring the infrequent weighted item set mining issue. Also, the algorithm are handled which perform IWI which is more insignificant IWI mining. Moreover we utilized the rare item set for choice based structure. The general issue of the start of reliable definite rules is troublesome for the grounds that hypothetically no inciting technique with no other person can promise the rightness of influenced theories. In this way, this framework expects the disorder with the uncommon signs. Usage study demonstrates that proposed algorithm upgrades the structure which is successful and versatile for mining both long and short diagnostics rules. Structure upgrades aftereffects of foreseeing rare diseases of patient.

Keywords: association rule, data mining, IWI mining, infrequent item set, frequent pattern growth

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Authors: J. K. Kavitha, D. Manjula, U. Kanimozhi

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Mining frequent and high utility item sets have gained much significance in the recent years. When the data arrives sporadically, incremental and interactive rule mining and utility mining approaches can be adopted to handle user’s dynamic environmental needs and avoid redundancies, using previous data structures, and mining results. The dependence on recommendation systems has exponentially risen since the advent of search engines. This paper proposes a model for building a recommendation system that suggests frequent and high utility item sets over dynamic datasets for a cluster based location prediction strategy to predict user’s trajectories using the Efficient Incremental Rule Mining (EIRM) algorithm and the Fast Update Utility Pattern Tree (FUUP) algorithm. Through comprehensive evaluations by experiments, this scheme has shown to deliver excellent performance.

Keywords: data sets, recommendation system, utility item sets, frequent item sets mining

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Authors: Tanvi P. Patel, Warish D. Patel

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Association rule mining forms the core of data mining and it is termed as one of the well-known methodologies of data mining. Objectives of mining is to find interesting correlations, frequent patterns, associations or casual structures among sets of items in the transaction databases or other data repositories. Hence, association rule mining is imperative to mine patterns and then generate rules from these obtained patterns. For efficient targeted query processing, finding frequent patterns and itemset mining, there is an efficient way to generate an itemset tree structure named Memory Efficient Itemset Tree. Memory efficient IT is efficient for storing itemsets, but takes more time as compare to traditional IT. The proposed strategy generates maximal frequent itemsets from memory efficient itemset tree by using levelwise pruning. For that firstly pre-pruning of items based on minimum support count is carried out followed by itemset tree reconstruction. By having maximal frequent itemsets, less number of patterns are generated as well as tree size is also reduced as compared to MEIT. Therefore, an enhanced approach of memory efficient IT proposed here, helps to optimize main memory overhead as well as reduce processing time.

Keywords: association rule mining, itemset mining, itemset tree, meit, maximal frequent pattern

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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: Yayun Hsu, Henry Horng-Shing Lu

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This paper proposes a data-driven, biology-inspired neural segmentation method of 3D drosophila Brainbow images. We use Bayesian Sequential Partitioning algorithm for probabilistic modeling, which can be used to detect somas and to eliminate cross talk effects. This work attempts to develop an automatic methodology for neuron image segmentation, which nowadays still lacks a complete solution due to the complexity of the image. The proposed method does not need any predetermined, risk-prone thresholds since biological information is inherently included in the image processing procedure. Therefore, it is less sensitive to variations in neuron morphology; meanwhile, its flexibility would be beneficial for tracing the intertwining structure of neurons.

Keywords: brainbow, 3D imaging, image segmentation, neuron morphology, biological data mining, non-parametric learning

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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: Charles Amoatey

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The issue of risk in the mining industry is a global phenomenon and the Ghanaian mining industry is not exempted. The main purpose of this study is to identify the critical risk factors affecting the mining industry. The study takes an integrated view of the mining industry by examining the contribution of various risk factors to mining project failure in Ghana. A questionnaire survey was conducted to solicit the critical risk factors from key mining practitioners. About 80 respondents from 11 mining firms participated in the survey. The study identified 22 risk factors contributing to mining project failure in Ghana. The five most critical risk factors based on both probability of occurrence and impact were: (1) unstable commodity prices, (2) inflation/exchange rate, (3) land degradation, (4) high cost of living and (5) government bureaucracy for obtaining licenses. Furthermore, the study found that risk assessment in the mining sector has a direct link with mining project sustainability. Mitigation measures for addressing the identified risk factors were discussed. The key findings emphasize the need for a comprehensive risk management culture in the entire mining industry.

Keywords: risk, assessment, mining, Ghana

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Authors: G. Surendra Babu

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We all know the importance of mineral wealth, which has been buried inside the layers of the earth for decades. These are the natural energy sources that are used in our day to day life like fuel, electricity, construction, etc. but the process of extraction causes damage to the nature that can’t be returned back and which are left over after completion of mining we can see these are barren from decades these remain unused degraded land. Most of them are covered with vegetation before the start during mining which damages the native vegetation of the region and disturbs the watershed boundary of the regions and it also disturbs the biodiversity of the reign. The major motto of the study is to understand the various issues that are found and to understand various methods of reclamations process that are suitable for revegetating and also variously practiced which are carried out in the different case studies and government guidelines procedure of lease licenses which includes the environmental clearances and also to study the vegetation pattern according to the major issues identified. And finally suggesting the new guidelines with respect to the old guidelines which helps in the revegetation of the mine-sites which helps in establishing of its own sustainable ecosystem in future.

Keywords: reclamation, open-pit mining, revegetation, reclamation methods

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Authors: Tosin Ige

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Ethics must be a condition of the world, like logic. (Ludwig Wittgenstein, 1889-1951). As important as data mining is, it possess a significant threat to ethics, privacy, and legality, since data mining makes it difficult for an individual or consumer (in the case of a company) to control the accessibility and usage of his data. This research focuses on Current issues and the latest research and development on Privacy preserving data mining methods as at year 2022. It also discusses some advances in those techniques while at the same time highlighting and providing a new technique as a solution to an existing technique of privacy preserving data mining methods. This paper also bridges the wide gap between Data mining and the Web Application Programing Interface (web API), where research is urgently needed for an added layer of security in data mining while at the same time introducing a seamless and more efficient way of data mining.

Keywords: data, privacy, data mining, association rule, privacy preserving, mining technique

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Authors: Bharat P. Modi, Jayesh M. Patel

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Mobile Internet is acting as a major source of data. As the number of web pages continues to grow the Mobile web provides the data miners with just the right ingredients for extracting information. In order to cater to this growing need, a special term called Mobile Web mining was coined. Mobile Web mining makes use of data mining techniques and deciphers potentially useful information from web data. Web Usage mining deals with understanding the behavior of users by making use of Mobile Web Access Logs that are generated on the server while the user is accessing the website. A Web access log comprises of various entries like the name of the user, his IP address, a number of bytes transferred time-stamp etc. A variety of Log Analyzer tools exists which help in analyzing various things like users navigational pattern, the part of the website the users are mostly interested in etc. The present paper makes use of such log analyzer tool called Mobile Web Log Expert for ascertaining the behavior of users who access an astrology website. It also provides a comparative study between a few log analyzer tools available.

Keywords: mobile web access logs, web usage mining, web server, log analyzer

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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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