Diagnosis of neurological diseases is a growing concern and one of the most difficult challenges for modern medicine. According to the World Health Organisation’s recent report, neurological disorders, such as epilepsy, Alzheimer’s disease and stroke to headache, affect up to one billion people worldwide. An estimated 6.8 million people die every year as a result of neurological disorders. Current diagnosis technologies (e.g. magnetic resonance imaging, electroencephalogram) produce huge quantity data (in size and dimension) for detection, monitoring and treatment of neurological diseases. In general, analysis of those medical big data is performed manually by experts to identify and understand the abnormalities. It is really difficult task for a person to accumulate, manage, analyse and assimilate such large volumes of data by visual inspection. As a result, the experts have been demanding computerised diagnosis systems, called “computer-aided diagnosis (CAD)” that can automatically detect the neurological abnormalities using the medical big data. This system improves consistency of diagnosis and increases the success of treatment, save lives and reduce cost and time. Recently, there are some research works performed in the development of the CAD systems for management of medical big data for diagnosis assessment. This paper explores the challenges of medical big data handing and also introduces the concept of the CAD system how it works. This paper also provides a survey of developed CAD methods in the area of neurological diseases diagnosis. This study will help the experts to have some idea and understanding how the CAD system can assist them in this point.

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Medical Big Data: Neurological Diseases Diagnosis Through Medical Data Analysis

The goal of program transformation is to improve efficiency while preserving meaning. One of the best-known transformation techniques is Burstall and Darlington's unfold-fold method. Unfortunately the unfold-fold method itself guarantees neither improvement in efficiency nor total correctness. The correctness problem for unfold-fold is an instance of a strictly more general problem: transformation by locally equivalence-preserving steps does not necessarily preserve (global) equivalence. This article presents a condition for the total correctness of transformations on recursive programs, which, for the first time, deals with higher-order functional languages (both strict and nonstrict) including lazy data structures. The main technical result is an improvement theorem which says that if the local transformation steps are guided by certain optimization concerns (a fairly natural condition for a transformation), then correctness of the transformation follows. The improvement theorem makes essential use of a formalized improvement theory; as a rather pleasing corollary it also guarantees that the transformed program is a formal improvement over the original. The theorem has immediate practical consequences: it is a powerful tool for proving the correctness of existing transformation methods for higher-order functional programs, without having to ignore crucial factors such as memoization or folding, and it yields a simple syntactic method for guiding and constraining the unfold-fold method in the general case so that total correctness (and improvement) is always guaranteed.

Total correctness by local improvement in the transformation of functional programs

This paper discusses the transformation power of Burstall and Darlington's folding/unfolding system, i.e. what kind of programs can be derived from a given one. A necessary condition of derivability is proved. The notion of inherent complexity of recursive functions in introduced. A bound on efficiency gain by folding/unfolding transformations is obtained for all reasonable computation models. The well-known partial correctness and incompleteness of the system are corollaries of the result. Examples of underivability are given, e.g. binary searching cannot be derived from linear searching, merge sorting cannot be derived from insert sorting.

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How powerful are folding/unfolding transformations?

Program transformation is a promising area of software methodology. The Folding/Unfolding method proposed by Burstall/Darlington is a simple and powerful transformation method for applicative programs. The only operations used are folding and unfolding of function definitions and substitution using laws. The major drawback of this method is that only partial correctness of functions is preserved and termination may be lost. That is if functionf1 is transformed tofn, the computation offn on an objectx will reach the same result of the computation off1 onx, provided the computation terminates. But there may be objectsx, on which the computation off1 terminates, butfn does not. This problem has not been solved with satisfaction. The idea of “reductive measure” of functions and “reductive” transformation is put forward here to solve the problem. It has been proved that if functions “complexity” is not increased under some reductive measure in the transformation process, termination will be preserved. The termination problem is thus solved to some extent. The most important thing is that the simplicity of the original method is fully preserved. Because with the help of FP algebraic laws, the new restriction is expressed completely syntatically. Namely, only the direction of using laws (algebraic equations) for substitution is restricted.

Termination preserving problem in the transformation of applicative programs

Equational programming language (EP) is a novel intelligence language This paper describes our EP system based on equational logic Its execution mechanism is pattern matching The paper focuses the discussion on the improvement to bottom-up tree pattern matching The new bottom-up method shows high execution efficiency

Ruzhan Lu

Papers

Termination preserving problem in the transformation of applicative programs

An improved bottom-up method for implementing equational programming language