Efficient schemes on solving fractional integro-differential equations

Fractional integro-differential equation (FIDE) emerges in various modelling of physical phenomena. In most cases, finding the exact analytical solution for FIDE is difficult or not possible. Hence, the methods producing highly accurate numerical solution in efficient ways are often sought after. This research has designed some methods to find the approximate solution of FIDE. The analytical expression of Genocchi polynomial operational matrix for left-sided and right-sided Caputo’s derivative and kernel matrix has been derived. Linear independence of Genocchi polynomials has been proved by deriving the expression for Genocchi polynomial Gram determinant. Genocchi polynomial method with collocation has been introduced and applied in solving both linear and system of linear FIDE. The numerical results of solving linear FIDE by Genocchi polynomial are compared with certain existing methods. The analytical expression of Bernoulli polynomial operational matrix of right-sided Caputo’s fractional derivative and the Bernoulli expansion coefficient for a two-variable function is derived. Linear FIDE with mixed left and right-sided Caputo’s derivative is first considered and solved by applying the Bernoulli polynomial with spectral-tau method. Numerical results obtained show that the method proposed achieves very high accuracy. The upper bounds for th

Flattening an object algebra to provide performance

Algebraic transformation and optimization techniques have been the method of choice in relational query execution, but applying them in object-oriented (OO) DBMSs is difficult due to the complexity of OO query languages. This paper demonstrates that the problem can be simplified by mapping an OO data model to the binary relational model implemented by Monet, a state-of-the-art database kernel. We present a generic mapping scheme to flatten data models and study the case of straightforward OO model. We show how flattening enabled us to implement a query algebra, using only a very limited set of simple operations. The required primitives and query execution strategies are discussed, and their performance is evaluated on the 1-GByte TPC-D (Transaction-processing Performance Council's Benchmark D), showing that our divide-and-conquer approach yields excellent result

A Hash Based Frequent Item set Mining using Rehashing

Data mining is the use of automated data analysis techniques to uncover previously undetected relationships among data items. Mining frequent item sets is one of the most important concepts of data mining. Frequent item set mining has been a highly concerned field of data mining for researcher for over two decades. It plays an essential role in many data mining tasks that try to find interesting itemsets from databases, such as association rules, correlations, sequences, classifiers and clusters . In this paper, we propose a new association rule mining algorithm called Rehashing Based Frequent Item set (RBFI) in which hashing technology is used to store the database in vertical data format. To avoid hash collision and secondary clustering problem in hashing, rehashing technique is utilized here. The advantages of this new hashing technique are easy to compute the hash function, fast access of data and efficiency. This algorithm provides facilities to avoid unnecessary scans to the database

i-Eclat: performance enhancement of eclat via incremental approach in frequent itemset mining

One example of the state-of-the-art vertical rule mining technique is called equivalence class transformation (Eclat) algorithm. Neither horizontal nor vertical data format, both are still suffering from the huge memory consumption. In response to the promising results of mining in a higher volume of data from a vertical format, and taking consideration of dynamic transaction of data in a database, the research proposes a performance enhancement of Eclat algorithm that relies on incremental approach called an Incremental-Eclat (i-Eclat) algorithm. Motivated from the fast intersection in Eclat, this algorithm of performance enhancement adopts via my structured query language (MySQL) database management system (DBMS) as its platform. It serves as the association rule mining database engine in testing benchmark frequent itemset mining (FIMI) datasets from online repository. The MySQL DBMS is chosen in order to reduce the preprocessing stages of datasets. The experimental results indicate that the proposed algorithm outperforms the traditional Eclat with 17% both in chess and T10I4D100K, 69% in mushroom, 5% and 8% in pumsb_star and retail datasets. Thus, among five (5) dense and sparse datasets, the average performance of i-Eclat is concluded to be 23% better than Eclat

Multi-relational data mining

An important aspect of data mining algorithms and systems is that they should scale well to large databases. A consequence of this is that most data mining tools are based on machine learning algorithms that work on data in attribute-value format. Experience has proven that such 'single-table' mining algorithms indeed scale well. The downside of this format is, however, that more complex patterns are simply not expressible in this format and, thus, cannot be discovered. One way to enlarge the expressiveness is to generalize, as in ILP, from one-table mining to multiple table mining, i.e., to support mining on full relational databases. The key step in such a generalization is to ensure that the search space does not explode and that efficiency and, thus, scalability are maintained. In this paper we present a framework and an architecture that provide such a generalization. In this framework the semantic information in the database schema, e.g., foreign keys, are exploited to prune the search space and, in the architecture, database primitives are defined to ensure efficiency. Moreover, the framework induces a canonical generalization of algorithms, i.e., if the generalized algorithms are run on a single table database, they give the same results as their single-table counterparts. The framework is illustrated by the Warmr algorithm, which is a multi-relational generalization of the Apriori algorithm

Linear discriminant analysis and principal component analysis to predict coronary artery disease

Coronary artery disease is one of the most prevalent chronic pathologies in the modern world, leading to the deaths of thousands of people, both in the United States and in Europe. This article reports the use of data mining techniques to analyse a population of 10,265 people who were evaluated by the Department of Advanced Biomedical Sciences for myocardial ischaemia. Overall, 22 features are extracted, and linear discriminant analysis is implemented twice through both the Knime analytics platform and R statistical programming language to classify patients as either normal or pathological. The former of these analyses includes only classification, while the latter method includes principal component analysis before classification to create new features. The classification accuracies obtained for these methods were 84.5 and 86.0 per cent, respectively, with a specificity over 97 per cent and a sensitivity between 62 and 66 per cent. This article presents a practical implementation of traditional data mining techniques that can be used to help clinicians in decision-making; moreover, principal component analysis is used as an algorithm for feature reduction

Scalable storage for a DBMS using transparent distribution

Scalable Distributed Data Structures (SDDSs) provide a self-managing and self-organizing data storage of potentially unbounded size. This stands in contrast to common distribution schemas deployed in conventional distributed DBMS. SDDSs, however, have mostly been used in synthetic scenarios to investigate their properties. In this paper we concentrate on the integration of the LH* SDDS into our efficient and extensible DBMS, called Monet. We show that this merge permits processing very large sets of distributed data. In our implementation we extended the relational algebra interpreter in such a way that access to data, whether it is distributed or locally stored, is transparent to the user. The on-the-fly optimization of operations --- heavily used in Monet --- to deploy different strategies and scenarios inside the primary operators associated with an SDDS adds self-adaptiveness to the query system; it dynamically adopts itself to unforeseen situations. We illustrate the performance efficiency by experiments on a network of workstations. The transparent integration of SDDSs opens new perspectives for very large self-managing database systems