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

Cooperation between expert knowledge and data mining discovered knowledge: Lessons learned

Expert systems are built from knowledge traditionally elicited from the human expert. It is precisely knowledge elicitation from the expert that is the bottleneck in expert system construction. On the other hand, a data mining system, which automatically extracts knowledge, needs expert guidance on the successive decisions to be made in each of the system phases. In this context, expert knowledge and data mining discovered knowledge can cooperate, maximizing their individual capabilities: data mining discovered knowledge can be used as a complementary source of knowledge for the expert system, whereas expert knowledge can be used to guide the data mining process. This article summarizes different examples of systems where there is cooperation between expert knowledge and data mining discovered knowledge and reports our experience of such cooperation gathered from a medical diagnosis project called Intelligent Interpretation of Isokinetics Data, which we developed. From that experience, a series of lessons were learned throughout project development. Some of these lessons are generally applicable and others pertain exclusively to certain project types

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