Improving Newton-Schulz Method for Approximating Matrix Generalized Inverse by Using Schemes with Memory

[EN] Some iterative schemes with memory were designed for approximating the inverse of a nonsingular square complex matrix and the Moore-Penrose inverse of a singular square matrix or an arbitrary m x n complex matrix. A Kurchatov-type scheme and Steffensen's method with memory were developed for estimating these types of inverses, improving, in the second case, the order of convergence of the Newton-Schulz scheme. The convergence and its order were studied in the four cases, and their stability was checked as discrete dynamical systems. With large matrices, some numerical examples are presented to confirm the theoretical results and to compare the results obtained with the proposed methods with those provided by other known ones.Cordero Barbero, A.; Maimo, JG.; Torregrosa Sánchez, JR.; Vassileva, MP. (2023). Improving Newton-Schulz Method for Approximating Matrix Generalized Inverse by Using Schemes with Memory. Mathematics. 11(14). https://doi.org/10.3390/math11143161111

Iterative methods with memory for solving systems of nonlinear equations using a second order approximation

[EN] Iterative methods for solving nonlinear equations are said to have memory when the calculation of the next iterate requires the use of more than one previous iteration. Methods with memory usually have a very stable behavior in the sense of the wideness of the set of convergent initial estimations. With the right choice of parameters, iterative methods without memory can increase their order of convergence significantly, becoming schemes with memory. In this work, starting from a simple method without memory, we increase its order of convergence without adding new functional evaluations by approximating the accelerating parameter with Newton interpolation polynomials of degree one and two. Using this technique in the multidimensional case, we extend the proposed method to systems of nonlinear equations. Numerical tests are presented to verify the theoretical results and a study of the dynamics of the method is applied to different problems to show its stability.This research was supported by PGC2018-095896-B-C22 (MCIU/AEI/FEDER, UE), Generalitat Valenciana PROMETEO/2016/089, and FONDOCYT 2016-2017-212 Republica Dominicana.Cordero Barbero, A.; Maimó, JG.; Torregrosa Sánchez, JR.; Vassileva, MP. (2019). Iterative methods with memory for solving systems of nonlinear equations using a second order approximation. Mathematics. 7(11):1-12. https://doi.org/10.3390/math7111069S112711Soleymani, F., Lotfi, T., Tavakoli, E., & Khaksar Haghani, F. (2015). Several iterative methods with memory using self-accelerators. Applied Mathematics and Computation, 254, 452-458. doi:10.1016/j.amc.2015.01.045Petković, M. S., & Sharma, J. R. (2015). On some efficient derivative-free iterative methods with memory for solving systems of nonlinear equations. Numerical Algorithms, 71(2), 457-474. doi:10.1007/s11075-015-0003-9Narang, M., Bhatia, S., Alshomrani, A. S., & Kanwar, V. (2019). General efficient class of Steffensen type methods with memory for solving systems of nonlinear equations. Journal of Computational and Applied Mathematics, 352, 23-39. doi:10.1016/j.cam.2018.10.048Potra, F. A. (1982). An error analysis for the secant method. Numerische Mathematik, 38(3), 427-445. doi:10.1007/bf01396443Fatou, P. (1919). Sur les équations fonctionnelles. Bulletin de la Société mathématique de France, 2, 161-271. doi:10.24033/bsmf.998Cordero, A., & Torregrosa, J. R. (2007). Variants of Newton’s Method using fifth-order quadrature formulas. Applied Mathematics and Computation, 190(1), 686-698. doi:10.1016/j.amc.2007.01.062Campos, B., Cordero, A., Torregrosa, J. R., & Vindel, P. (2015). A multidimensional dynamical approach to iterative methods with memory. Applied Mathematics and Computation, 271, 701-715. doi:10.1016/j.amc.2015.09.056Chicharro, F. I., Cordero, A., & Torregrosa, J. R. (2013). Drawing Dynamical and Parameters Planes of Iterative Families and Methods. The Scientific World Journal, 2013, 1-11. doi:10.1155/2013/78015

Does gamification work for boys and girls?: An exploratory study with a virtual learning environment

SIGAPP ACM Special Interest Group on Applied ComputingThe development and use of Virtual Learning Environments (VLE) has increased considerably over the past decades. Following that trend, many research findings have shown the benefits of using VLE during the learning process. Nevertheless, there are important problems that hinder their use requiring further investigation. Among them, one of the main problems is the inappropriate use of these systems by students. The boredom, lack of interest, monotony, lack of motivation, among other factors, ultimately causes students to behave inappropriately and lead them to a lower performance. In this context, the proposed study investigates whether it is possible to reduce undesirable behaviors and increase performance of students through the use of game mechanics (i.e. gamification). We develop a VLE, E-Game, that can turn on/off several game mechanics, such as points, badges, levels and so on. A case study was conducted with two groups of students to investigate their behavior during their interaction with E-Game with and without gamification. The results indicate that the gamification implemented by E-Game contributed to improve student performance in the case of boys. Yet, improvement was not observed in the case of girls. Furthermore, it was not possible to conclude whether the use of gamification helps to prevent inappropriate student behavior, and therefore, further studies and experiments are needed

Early anti-VEGF treatment in CRVO assures better prognosis

Introduction: Central retinal vein occlusion (CRVO) is the second most common cause of visual impairment due to retinal vascular disease in developed countries. The prevalence of CRVO is ranging from 0.1 to 0.5%. Risk factors are numerous, and fluctuations of IOP and thrombophilic conditions are considered to be the most important. Recently, extremely high levels of intraocular vascular endothelial growth factor (VEGF) were demonstrated in CRVO, leading to increased vascular permeability and leakage. Our objective is to present our approach in the management of treatment-naïve patients with CRVO. Methods: All consecutive patients with CRVO referred to our tertiary eye hospital for a period of 2 years were evaluated. Inclusion criteria: retinal and optic disk edema, dilatation and turtuosity of all retinal veins, widespread deep and superficial hemorrhages, cotton wool spots. We performed comprehensive eye exam, detailed medical history, specialized imaging methods, glaucoma evaluation, (AS-OCT, gonioscopy, IOP control), as well as hematological investigation in all patients. Treatment included intravitreal anti-VEGF application with personalized regimen. Glaucoma patients were treated with medications, laser and trabeculectomy (TE). We analyzed several variables: the period between the CRVO diagnosis and the start of anti-VEGF treatment, number of injections, changes in central macular thickness (CMT) and in visual acuity (VA). Results: Our pool of patients consisted of 38 persons, mean age 66.4 (29 -86). In 21 (56%) the CRVO is ischemic type, in 16 (42%) patients we diagnosed initial glaucoma damage (in 15 patients exfoliation syndrome was present). An interesting observation was the high number of patients - 13 (35%) with narrow, closed or occludable anterior chamber angle, diagnosed soon after the first CRVO symptoms. This finding was associated with history of accidental transient vision blurring and pain. In patients with start of treatment at the very beginning of macular edema we achieved immediate and excellent response after the first anti-VEGF application, and fast disappearance of exudations and hemorrhages. Hematologic studies demonstrated different types of hereditary thrombophilia in 7 patients. Conclusions: Our clinical experience demonstrate that best results in CRVO treatment could be obtained at early diagnosis, close follow up and early start of anti-VEGF treatment before pronounced macular edema occurs. Detailed evaluation of anterior chamber angle configuration and glaucoma management are mandatory for successful outcome in patients with initial CRVO symptoms

Providing awareness, explanation and control of personalized filtering in a social networking site

Social networking sites (SNSs) have applied personalized filtering to deal with overwhelmingly irrelevant social data. However, due to the focus of accuracy, the personalized filtering often leads to “the filter bubble” problem where the users can only receive information that matches their pre-stated preferences but fail to be exposed to new topics. Moreover, these SNSs are black boxes, providing no transparency for the user about how the filtering mechanism decides what is to be shown in the activity stream. As a result, the user’s usage experience and trust in the system can decline. This paper presents an interactive method to visualize the personalized filtering in SNSs. The proposed visualization helps to create awareness, explanation, and control of personalized filtering to alleviate the “filter bubble” problem and increase the users’ trust in the system. Three user evaluations are presented. The results show that users have a good understanding about the filter bubble visualization, and the visualization can increase users’ awareness of the filter bubble, understandability of the filtering mechanism and to a feeling of control over the data stream they are seeing. The intuitiveness of the design is overall good, but a context sensitive help is also preferred. Moreover, the visualization can provide users with better usage experience and increase users’ trust in the system

Semilocal Convergence of the Extension of Chun's Method

[EN] In this work, we use the technique of recurrence relations to prove the semilocal convergence in Banach spaces of the multidimensional extension of Chun's iterative method. This is an iterative method of fourth order, that can be transferred to the multivariable case by using the divided difference operator. We obtain the domain of existence and uniqueness by taking a suitable starting point and imposing a Lipschitz condition to the first Frechet derivative in the whole domain. Moreover, we apply the theoretical results obtained to a nonlinear integral equation of Hammerstein type, showing the applicability of our results.This research was supported by PGC2018-095896-B-C22 (MCIU/AEI/FEDER, UE) and FONDOCYT 027-2018 Republica Dominicana.Cordero Barbero, A.; Maimó, JG.; Martínez Molada, E.; Torregrosa Sánchez, JR.; Vassileva, MP. (2021). Semilocal Convergence of the Extension of Chun's Method. Axioms. 10(3):1-11. https://doi.org/10.3390/axioms10030161S11110

User-centred design of flexible hypermedia for a mobile guide: Reflections on the hyperaudio experience

A user-centred design approach involves end-users from the very beginning. Considering users at the early stages compels designers to think in terms of utility and usability and helps develop the system on what is actually needed. This paper discusses the case of HyperAudio, a context-sensitive adaptive and mobile guide to museums developed in the late 90s. User requirements were collected via a survey to understand visitors’ profiles and visit styles in Natural Science museums. The knowledge acquired supported the specification of system requirements, helping defining user model, data structure and adaptive behaviour of the system. User requirements guided the design decisions on what could be implemented by using simple adaptable triggers and what instead needed more sophisticated adaptive techniques, a fundamental choice when all the computation must be done on a PDA. Graphical and interactive environments for developing and testing complex adaptive systems are discussed as a further step towards an iterative design that considers the user interaction a central point. The paper discusses how such an environment allows designers and developers to experiment with different system’s behaviours and to widely test it under realistic conditions by simulation of the actual context evolving over time. The understanding gained in HyperAudio is then considered in the perspective of the developments that followed that first experience: our findings seem still valid despite the passed time

Toll-like receptor and IL-12 signaling control susceptibility to contact hypersensitivity.

Allergic contact hypersensitivity (CHS) is a T cell-mediated inflammatory skin disease. Interleukin (IL)-12 is considered to be important in the generation of the allergen-specific T cell response. Loss of IL-12 function in IL-12Rbeta2-deficient mice, however, did not ameliorate the allergic immune response, suggesting alternate IL-12-independent pathways in the induction of CHS. Because exposure to contact allergens always takes place in the presence of microbial skin flora, we investigated the potential role of Toll-like receptors (TLRs) in the induction of CHS. Using mice deficient in TLR4, the receptor for bacterial lipopolysaccharide (LPS), IL-12 receptor (R) beta2, or both, we show that the concomitant absence of TLR4 and IL-12Rbeta2, but not the absence of TLR4 or IL-12Rbeta2 alone, prevented DC-mediated sensitization, generation of effector T cells, and the subsequent CHS response to 2,4,6-trinitro-1-chlorobenzene (TNCB), oxazolone, and fluorescein isothiocyanate. Introduction of the TLR4 transgene into the TLR4/IL-12Rbeta2 mutant restored the CHS inducibility, showing a requirement for TLR4 in IL-12-independent CHS induction. Furthermore, the concomitant absence of TLR2 and TLR4 prevented the induction of CHS to TNCB in IL-12-competent mice. Finally, CHS was inducible in germ-free wild-type and IL-12Rbeta2-deficient mice, but not in germ-free TLR4/IL-12Rbeta2 double deficient mice, suggesting that the necessary TLR activation may proceed via endogenous ligands