Chebanov law and Vakar formula in mathematical models of complex systems

Ecological models written in a mathematical language L(M) or model language, with a given style or methodology can be considered as a text. It is possible to apply statistical linguistic laws and the experimental results demonstrate that the behaviour of a mathematical model is the same of any literary text of any natural language. A text has the following characteristics: (a) the variables, its transformed functions and parameters are the lexic units or LUN of ecological models; (b) the syllables are constituted by a LUN, or a chain of them, separated by operating or ordering LUNs; (c) the flow equations are words; and (d) the distribution of words (LUM and CLUN) according to their lengths is based on a Poisson distribution, the Chebanov's law. It is founded on Vakar's formula, that is calculated likewise the linguistic entropy for L(M). We will apply these ideas over practical examples using MARIOLA model. In this paper it will be studied the problem of the lengths of the simple lexic units composed lexic units and words of text models, expressing these lengths in number of the primitive symbols, and syllables. The use of these linguistic laws renders it possible to indicate the degree of information given by an ecological model.

Reducing visual deficits caused by refractive errors in school and preschool children: results of a pilot school program in the Andean region of Apurimac, Peru

Background: Refractive error is defined as the inability of the eye to bring parallel rays of light into focus on the retina, resulting in nearsightedness (myopia), farsightedness (Hyperopia) or astigmatism. Uncorrected refractive error in children is associated with increased morbidity and reduced educational opportunities. Vision screening (VS) is a method for identifying children with visual impairment or eye conditions likely to lead to visual impairment. Objective: To analyze the utility of vision screening conducted by teachers and to contribute to a better estimation of the prevalence of childhood refractive errors in Apurimac, Peru. Design: A pilot vision screening program in preschool (Group I) and elementary school children (Group II) was conducted with the participation of 26 trained teachers. Children whose visual acuity was<6/9 [20/30] (Group I) and≤6/9 (Group II) in one or both eyes, measured with the Snellen Tumbling E chart at 6 m, were referred for a comprehensive eye exam. Specificity and positive predictive value to detect refractive error were calculated against clinical examination. Program assessment with participants was conducted to evaluate outcomes and procedures. Results: A total sample of 364 children aged 3–11 were screened; 45 children were examined at Centro Oftalmológico Monseñor Enrique Pelach (COMEP) Eye Hospital. Prevalence of refractive error was 6.2% (Group I) and 6.9% (Group II); specificity of teacher vision screening was 95.8% and 93.0%, while positive predictive value was 59.1% and 47.8% for each group, respectively. Aspects highlighted to improve the program included extending training, increasing parental involvement, and helping referred children to attend the hospital. Conclusion: Prevalence of refractive error in children is significant in the region. Vision screening performed by trained teachers is a valid intervention for early detection of refractive error, including screening of preschool children. Program sustainability and improvements in education and quality of life resulting from childhood vision screening require further research.

Efficient Mitigation of Data and Control Flow Errors in Microprocessors

The use of microprocessor-based systems is gaining importance in application domains where safety is a must. For this reason, there is a growing concern about the mitigation of SEU and SET effects. This paper presents a new hybrid technique aimed to protect both the data and the control-flow of embedded applications running on microprocessors. On one hand, the approach is based on software redundancy techniques for correcting errors produced in the data. On the other hand, control-flow errors can be detected by reusing the on-chip debug interface, existing in most modern microprocessors. Experimental results show an important increase in the system reliability even superior to two orders of magnitude, in terms of mitigation of both SEUs and SETs. Furthermore, the overheads incurred by our technique can be perfectly assumable in low-cost systems.

Algorithm for Correcting the Keratometric Error in the Estimation of the Corneal Power in Eyes With Previous Myopic Laser Refractive Surgery

Purpose: To calculate theoretically the errors in the estimation of corneal power when using the keratometric index (nk) in eyes that underwent laser refractive surgery for the correction of myopia and to define and validate clinically an algorithm for minimizing such errors. Methods: Differences between corneal power estimation by using the classical nk and by using the Gaussian equation in eyes that underwent laser myopic refractive surgery were simulated and evaluated theoretically. Additionally, an adjusted keratometric index (nkadj) model dependent on r1c was developed for minimizing these differences. The model was validated clinically by retrospectively using the data from 32 myopic eyes [range, −1.00 to −6.00 diopters (D)] that had undergone laser in situ keratomileusis using a solid-state laser platform. The agreement between Gaussian (PGaussc) and adjusted keratometric (Pkadj) corneal powers in such eyes was evaluated. Results: It was found that overestimations of corneal power up to 3.5 D were possible for nk = 1.3375 according to our simulations. The nk value to avoid the keratometric error ranged between 1.2984 and 1.3297. The following nkadj models were obtained: nkadj= −0.0064286r1c + 1.37688 (Gullstrand eye model) and nkadj = −0.0063804r1c + 1.37806 (Le Grand). The mean difference between Pkadj and PGaussc was 0.00 D, with limits of agreement of −0.45 and +0.46 D. This difference correlated significantly with the posterior corneal radius (r = −0.94, P < 0.01). Conclusions: The use of a single nk for estimating the corneal power in eyes that underwent a laser myopic refractive surgery can lead to significant errors. These errors can be minimized by using a variable nk dependent on r1c.