Towards distortion-free imaging of the eye

The high power of the eye and optical components used to image it result in “static” distortion, remaining constant across acquired retinal images. In addition, raster-based systems sample points or lines of the image over time, suffering from “dynamic” distortion due to the constant motion of the eye. We recently described an algorithm which corrects for the latter problem but is entirely blind to the former. Here, we describe a new procedure termed “DIOS” (Dewarp Image by Oblique Shift) to remove static distortion of arbitrary type. Much like the dynamic correction method, it relies on locating the same tissue in multiple frames acquired as the eye moves through different gaze positions. Here, the resultant maps of pixel displacement are used to form a sparse system of simultaneous linear equations whose solution gives the common warp seen by all frames. We show that the method successfully handles torsional movement of the eye. We also show that the output of the previously described dynamic correction procedure may be used as input for this new procedure, recovering an image of the tissue that is, in principle, a faithful replica free of any type of distortion. The method could be extended beyond ocular imaging, to any kind of imaging system in which the image can move or be made to move across the detector.

Some Fixed Point Results in b-Metric Spaces and b-Metric-Like Spaces with New Contractive Mappings

The aim of our paper is to present a new class of functions and to define some new contractive mappings in b-metric spaces. We establish some fixed point results for these new contractive mappings in b-metric spaces. Furthermore, we extend our main result in the framework of b-metric-like spaces. Some consequences of main results are also deduced. We present some examples to illustrate and support our results. We provide an application to solve simultaneous linear equations. In addition, we present some open problems.

Evaluation on effectiveness of learning linear algebra using gamification

This study evaluate effectiveness of learning Linear Algebra using gamification strategy. In this study, gamification with storytelling strategy is used as teaching tools to attract student to learn Linear Algebra. This study using Polytechnic Malaysia syllabus with focus group of Diploma students for semester three (Mechanical Engineering) and semester four (Electrical Engineering) for two topics; Matrix and Numerical Method. They are five methods of calculation simultaneous linear equations which is ‘Inverse’, ‘Cramer's Rule’, ‘Gauss Elimination’, ‘Lower Upper Doolittle’ and ‘Lower Upper Crout’. They are three main phases to develop this gamification; Pedagogy Phase, Design Phase and Evaluation Phase. Mixed methods approach combining quantitative (survey) and qualitative (Electroencephalogram) is used to evaluate students learning process using Linear Algebra gamification application. The findings of the five items surveyed showed that the acceptance of the prototype of the Linear Algebra Gamification Application was very encouraging from a total of 104 students. This is because all 38 questions for the five items earn a median of four and this indicates the majority of students choose “Agree” and “Strongly Agree”. The findings also show the percent “Agree” and “Strongly Agree” for all questions having a high percentage of between 61.5 and 94.2. This shows more than half satisfied and likes to use the Linear Algebra Gamification Application prototype. With the development of the Linear Algebra Gamification Application prototype, it is hoped that the use of learning based can be extended to a variety of subjects as well as topics to make the learning process more interesting and fun as well as helping to motivate students to learn

Random Number Generator Untuk Bobot Metode Conjugate Gradient Neural Network

This research develops the theory of NN (neural network) by using CG (conjugate gradient) to speed up the process of convergence on a network of NN. CG algorithm is an iterative algorithm to solve simultaneous linear equations on a large scale and it is used to optimize the process of the network on backpropagation. In the process, a Neural netwok doing random weighting on the weight of v and w and this weight will have an effect on the speed of convergence of an algorithm for NN by the method of CG. Furthermore, generating the random numbers to take a sample as a generator in this research of neural network by using uniform distribution (0,1) methods. Therefore, the aims of this research are to improve the convergence on NN weighting using numbers which are generated randomly by the generator and the will be corrected with the CG method.Keywords: neural network, backpropagation, weighting, conjugate gradient

Algebra

This chapter is concerned with a single textbook written by Dodgson in 1867—An Elementary Treatise on Determinants. His book concerned the study of determinants, an algebraic construct that had come to the fore during the 19th century, and presented a new method, called the method of condensation, for evaluating them; this method was due to Dodgson and was the subject of his only refereed journal paper. The book also applied his results to the solution of simultaneous linear equations, and included the proof of a theorem describing when a system of linear equations is consistent. The book’s impact and influence are discussed in the concluding section of this chapter.

Ancient Chinese Mathematics

The chapter studies nine long-known extant Chinese mathematical texts, and three recently excavated texts, all composed prior to the beginning of the Sui 隋 dynasty (581–618 ce). Most of these were compiled for use as school texts. They include problems on fractions, on proportions and extraction of square and cube roots, on simultaneous linear equations and computations of areas and volumes. Among the more advanced techniques deployed in these texts are computing the area of a circle, that is, obtaining certain approximate values of π; computing the volume of a pyramid; and computing the volume of a sphere.