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

CRIS-IR 2006

The recognition of entities and their relationships in document collections is an important step towards the discovery of latent knowledge as well as to support knowledge management applications. The challenge lies on how to extract and correlate entities, aiming to answer key knowledge management questions, such as; who works with whom, on which projects, with which customers and on what research areas. The present work proposes a knowledge mining approach supported by information retrieval and text mining tasks in which its core is based on the correlation of textual elements through the LRD (Latent Relation Discovery) method. Our experiments show that LRD outperform better than other correlation methods. Also, we present an application in order to demonstrate the approach over knowledge management scenarios.Fundação para a Ciência e a Tecnologia (FCT) Denmark's Electronic Research Librar

Data mining in soft computing framework: a survey

The present article provides a survey of the available literature on data mining using soft computing. A categorization has been provided based on the different soft computing tools and their hybridizations used, the data mining function implemented, and the preference criterion selected by the model. The utility of the different soft computing methodologies is highlighted. Generally fuzzy sets are suitable for handling the issues related to understandability of patterns, incomplete/noisy data, mixed media information and human interaction, and can provide approximate solutions faster. Neural networks are nonparametric, robust, and exhibit good learning and generalization capabilities in data-rich environments. Genetic algorithms provide efficient search algorithms to select a model, from mixed media data, based on some preference criterion/objective function. Rough sets are suitable for handling different types of uncertainty in data. Some challenges to data mining and the application of soft computing methodologies are indicated. An extensive bibliography is also included

A comprehensive study on disease risk predictions in machine learning

Over recent years, multiple disease risk prediction models have been developed. These models use various patient characteristics to estimate the probability of outcomes over a certain period of time and hold the potential to improve decision making and individualize care. Discovering hidden patterns and interactions from medical databases with growing evaluation of the disease prediction model has become crucial. It needs many trials in traditional clinical findings that could complicate disease prediction. Comprehensive survey on different strategies used to predict disease is conferred in this paper. Applying these techniques to healthcare data, has improvement of risk prediction models to find out the patients who would get benefit from disease management programs to reduce hospital readmission and healthcare cost, but the results of these endeavours have been shifted

Data mining in manufacturing: a review based on the kind of knowledge

In modern manufacturing environments, vast amounts of data are collected in database management systems and data warehouses from all involved areas, including product and process design, assembly, materials planning, quality control, scheduling, maintenance, fault detection etc. Data mining has emerged as an important tool for knowledge acquisition from the manufacturing databases. This paper reviews the literature dealing with knowledge discovery and data mining applications in the broad domain of manufacturing with a special emphasis on the type of functions to be performed on the data. The major data mining functions to be performed include characterization and description, association, classification, prediction, clustering and evolution analysis. The papers reviewed have therefore been categorized in these five categories. It has been shown that there is a rapid growth in the application of data mining in the context of manufacturing processes and enterprises in the last 3 years. This review reveals the progressive applications and existing gaps identified in the context of data mining in manufacturing. A novel text mining approach has also been used on the abstracts and keywords of 150 papers to identify the research gaps and find the linkages between knowledge area, knowledge type and the applied data mining tools and techniques