Decimal Research Articles

MoTe2-based low energy consumption artificial synapse for neuromorphic behavior and decimal arithmetic

Two-dimensional material-based memristors have shown attractive research prospects as brain-like devices for neuromorphic computing. Among them, transition metal dichalcogenides–based memristors have proved to be one of the most promising competitors. In this work, a two-dimensional memristor based on MoTe2 nanosheets was fabricated and demonstrated. The experimental results illustrate that the two-terminal synaptic based on the Ag/MoTe2/ITO structure exhibits stable bipolar and non-volatile resistive switching characteristics attributed to the controllable formation and rupturing of silver conductive filaments. The device can be successively modulated by a pulse train with a minimum pulse width of 40 ns. More interestingly, the energy consumption of the device to complete one write event is only 74.2 pJ. In addition, biological synaptic behaviors, such as excitatory postsynaptic current gain properties, long-term potentiation (LTP)/long-term depression, spike-timing-dependent- plasticity, short-term plasticity, long-term potentiation (LTP), paired-pulse facilitation, post-tetanic potentiation, and learning-experimental behaviors were mimicked faithfully. Finally, the decimal arithmetic application was introduced to the device, and it is confirmed that addition and multiplication functions can be performed. Therefore, the artificial synapse based on MoTe2 nanosheets not only exhibits the stable non-volatile resistive switching behavior but also facilitates the development of low-energy consumption neuromorphic computing chips based on transition metal dichalcogenides.

Imprint of f(R) gravity in the cosmic magnification

ABSTRACT f(R) gravity is one of the simplest viable modifications to General Relativity: it passes local astrophysical tests, predicts both the early-time cosmic inflation and the late-time cosmic acceleration, and describes dark matter. In this paper, we probe cosmic magnification on large scales in f(R) gravity, using the well-known Hu-Sawicki model as an example. Our results indicate that at redshifts $z \, {\lt }\, 3$, values of the model exponent $n \, {\gt }\, 1$ lead to inconsistent behaviour in the evolution of the scalar perturbations. Moreover, when relativistic effects are taken into account in the large-scale analysis, our results show that as z increases, large-scale changes in the cosmic magnification angular power spectrum owing to integral values of n tend to share a similar pattern, while those of decimal values tend to share another. This feature could be searched for in the experimental data, as a potential ‘smoking gun’ for the given class of gravity models. Furthermore, we found that at $z \, {=}\, 1$ and lower, relativistic effects lead to a suppression of the cosmic magnification on large scales in f(R) gravity, relative to the concordance model; whereas, at $z \, {\gt }\, 1$, relativistic effects lead to a relative boost of the cosmic magnification. In general, relativistic effects enhance the potential of the cosmic magnification as a cosmological probe.

Evaluation of Postoperative Total Ocular Aberrations After Bilateral Implantation of Monofocal IOL with Extended Depth of Focus in Phacoemulsification.

To evaluate postoperative visual performance and total ocular aberration in cataract patients after implantation of the TECNIS Eyhance™ intraocular lens (IOL). Our study is a prospective interventional non-comparative study that was conducted on 34 eyes of 17 patients who underwent phacoemulsification and Eyhance IOL implantation. Postoperative corrected and uncorrected near and far visual acuity and total ocular aberration were assessed 3 months after surgery. Our study included 34 eyes of 17 patients. At the third postoperative month, the mean spherical equivalent (SE) was -0.32 diopters (D) (SD ±0.62), and the mean distance-corrected near visual acuity (DCNVA) was 0.33 (SD ±0.15) and 0.42 (SD ±0.17) decimal notation (DN) monocular and binocular, respectively. The mean near distance with maximum visual acuity was 79.47 cm (SD ±7.70) and 74.76 cm (SD ±7.90) monocular and binocular, respectively. The mean postoperative minimum reading addition (add) was 1.6 D (SD ±0.47). The mean spherical aberration (SA) was 0.13 µm (SD ±0.09). The correlation of amount of spherical aberration with power of minimum reading add at 40 cm was not statistically significant (p=0.324). The TECNIS Eyhance IOL provides good intermediate visual acuity and decreases the power of the reading add needed after phacoemulsification.

Preliminary results obtained by a new intraocular lens based on accommodative technology for the treatment of cataract and presbyopia

AbstractPurpose: The aim of this study was to report the clinical results obtained by a new accommodative intraocular lens (AIOL) in terms of visual acuity, refraction, defocus curve, contrast sensitivity and complications incidence for multiple follow‐up phases.Methods: This is a prospective and experimental study composed by patients interested in an AIOL implantation (Lumina, Akkolens) to improve their visual performance. An exhaustive postoperative follow‐up (1 week, 1 month, 3 months, 6 months, 1 year) was performed including the measurements of visual acuity for multiple distances in decimal notation, subjective refraction, accommodative evaluation by defocus curve, contrast sensitivity and a slit lamp and fundus exploration.Results: The study included 42 eyes of 21 patients (mean age of 61.4 ± 10.9 years; 52% females, 48% males). The mean uncorrected distance visual acuity at week was 0.71 ± 0.28, but it improved to 0.85 ± 0.27 a year after the surgery. Similarly, the mean uncorrected near visual acuity improved for 0.48 ± 0.23 at 1 week to 0.60 ± 0.17 at 1 year. The mean equivalent sphere was −0.39 ± 0.60 diopters and the mean corrected distance visual acuity was 1.04 ± 0.16 at 1 year. For a defocus range comprised between 0.00 and −2.00 diopters the mean visual acuity was better than 0.50. The contrast sensitivity assessment showed values higher than 1.10 log units for all frequencies. Capsule opacification with YAG laser requirement was present in 21% of cases (N = 9). At the end of the follow‐up all minimal complications were resolved.Conclusions: The AIOL Lumina Akkolens provided suitable distance vision and functional near vision improving its performance over time. Contrast sensitivity was good being comparable with a monofocal design, but the Lumina IOL shows better near visual performance as revealed in the defocus curve. Significant persistent complications were not observed. These results will be updated with more patients and will be compared with a control group.

Prospective Teachers’ Diagnostic Thinking on Students’ Understanding of Multi-Digit Multiplication: A Content-Related Analysis on Unpacking of Knowledge Elements

Teachers’ in-depth diagnostic thinking has been shown to be crucial for student-centered teaching as they need to perceive and interpret students’ understanding for well-informed decision-making on adaptive teaching practices. The paper presents a content-related approach to analyzing diagnostic thinking processes with respect to the mathematical knowledge elements that prospective teachers identify as students’ resources and obstacles. Prospective teachers’ challenge is that some relevant knowledge elements first have to be unpacked, because compact concepts (such as the place value concept) or procedures (such as for multi-digit multiplication) comprise several smaller knowledge elements (such as the positional property) that have to be made explicit for students to foster their learning processes adequately. Our study examines what knowledge elements prospective teachers perceive and interpret in a transcript vignettes on multi-digit multiplication (of decimal and natural numbers) and its underlying basic arithmetic concepts (place value understanding and meaning of multiplication) in written diagnostic judgments on students’ resources and obstacles (N = 196). A comparative design within the vignette is used to investigate how far the process of perceiving can be supported by thematic cues. The analysis reveals that those knowledge elements cued in the vignette by being already unpacked and explicitly addressed are perceived and interpreted more often (but with lower correctness) than those that are uncued and therefore have to be unpacked by the prospective teachers themselves. This confirms the need to prepare prospective teachers for unpacking mathematical concepts themselves.

Quantifying Moss Response to Metal Contaminant Exposure Using Laser-Induced Fluorescence

Tracing sources of contamination, including potentially toxic elements (PTEs), has historically been achieved through sampling and analysis of soil or biota, which are labor-intensive, costly, and destructive methods. Thus, availability of a non-destructive in situ remote sensing method for monitoring metals deposited in biota is of great interest. Laser-induced fluorescence (LIF) is an emerging spectroscopic and imaging technique that documents changes in molecular energy level in plants as a biological response to metal contamination. For a proof-of-concept study and preliminary experiment, moss was selected for experimentation due to its long history of use in tracing atmospheric deposition of PTEs. Consecutive treatments of copper chloride (CuCl2) were administered to three moss samples, simulating wet deposition every 48 h over 10 days until reaching cumulative Cu concentrations of 2.690 to 8.075 μmol/cm2. While these Cu amounts are above environmentally relevant concentrations, they allowed the best conditions for testing and fine tuning of the imaging and data processing protocols presented in this paper. Moss fluorescence was induced using both 532 nm green and 355 nm UV lasers. A CMOS camera captured images of the LIF response, and red–green–blue (RGB) decimal code values were extracted for each pixel in the images, and pixel densities of color channels from treated and untreated moss samples were compared. Results show a shift towards lower color decimal codes corresponding to increased Cu concentration. We developed and contrasted multiple quantitative analyses of color distributions and demonstrated that LIF shows great promise for remote sensing of Cu accumulation in moss at μmol/cm2 levels. Though currently, the method would be limited to highly toxic sites, it illustrates the possibility and provides a framework for development of higher-sensitivity methods to detect nmol/cm2 that are viable for urban contamination level monitoring.

Quantifying the Theory Vs. Programming Disparity using Spectral Bipartivity Analysis and Principal Component Analysis

Some students in the Computer Science and related majors excel very well in programming-related assignments, but not equally well in the theoretical assignments (that are not programming-based) and vice-versa. We refer to this as the "Theory vs. Programming Disparity (TPD)". In this paper, we propose a spectral bipartivity analysis-based approach to quantify the TPD metric for any student in a course based on the percentage scores (considered as decimal values in the range of 0 to 1) of the student in the course assignments (that involves both theoretical and programming-based assignments). We also propose a principal component analysis (PCA)-based approach to quantify the TPD metric for the entire class based on the percentage scores (in a scale of 0 to 100) of the students in the theoretical and programming assignments. The spectral analysis approach partitions the set of theoretical and programming assignments to two disjoint sets whose constituents are closer to each other within each set and relatively more different from each across the two sets. The TPD metric for a student is computed on the basis of the Euclidean distance between the tuples representing the actual numbers of theoretical and programming assignments vis-a-vis the number of theoretical and programming assignments in each of the two disjoint sets. The PCA-based analysis identifies the dominating principal components within the sets of theoretical and programming assignments and computes the TPD metric for the entire class as a weighted average of the correlation coefficients between the dominating principal components representing these two sets.

Profiles in understanding the density of rational numbers among primary and secondary school students

The present cross-sectional study investigated 953 fifth to tenth grade students’ understanding of the dense structure of rational numbers. After an inductive analysis, coding the answers based on three types of items on density, a TwoStep Cluster Analysis revealed different intermediate profiles in the understanding of density along grades. The analysis highlighted qualitatively different ways of thinking: i) the idea of consecutiveness, ii) the idea of a finite number of numbers, and iii) the idea that between fractions, there are only fractions, and between decimals, there are only decimals. Furthermore, our profiles showed differences regarding rational number representation since students first recognised the dense nature of decimal numbers and then of fractions. Learners, however, were still found to have a natural number-based idea of the rational number structure by the end of secondary school, especially when they had to write a number between two pseudo-consecutive rational numbers.

Decimal reduction value (D) from fraction negative experiments via maximum likelihood estimation: An enabling spreadsheet and its implications on methodology and current standards

AbstractResistance of biological indicators for sterilization in pharma and food applications is often determined via fraction negative experiments. The ISO 11138 standards prescribe the Holcomb–Spearman–Karber procedure (HSKP) for calculating D value using these methods. However, HSKP imposes limitations on experimental designs. While ISO 11138 requires inactivation kinetics to not significantly deviate from first order, the HSKP does not provide a step to check such departure, or its extent. Maximum likelihood estimation (MLE) is an alternative approach for D value determination from fraction negative experiments. Compared to HSKP, it allows researchers to tailor the experimental design to practical needs, potentially reducing overall sample size in the process. This work presents a development of a 2004 published worksheet for MLE calculation, providing tighter confidence intervals and an improved way for Improbability calculation. Ways to exploit the design flexibility of MLE approach are presented, including simulated experiments and examples on how to optimize experimental design according to various situational needs, also in cases where expected D values are of the order of one or a few seconds as is commonly encountered in the sterilization of aseptic fillers for food. Detection of deviation from first‐order kinetics using the enhanced Improbability methods is discussed; one of the examples provided by ISO 11138‐1 for D value determination by HSKP contains data that deviate significantly from first order.

Comprehensive screening of low nitrogen tolerant maize based on multiple traits at the seedling stage.

BackgroundPlants tolerant to low nitrogen are a quantitative trait affected by many factors, and the different parameters were used for stress-tolerant plant screening in different investigations. But there is no agreement on the use of these indicators. Therefore, a method that can integrate different parameters to evaluate stress tolerance is urgently needed.MethodsSix maize genotypes were subject to low nitrogen stress for twenty days. Then seventeen traits of the six maize genotypes related to nitrogen were investigated. Nitrogen tolerance coefficient (NTC) was calculated as low nitrogen traits to high nitrogen traits. Then principal component analysis was conducted based on the NTC. Based on fuzzy mathematics theory, a D value (decimal comprehensive evaluation value) was introduced to evaluate maize tolerant to low nitrogen.ResultsThree maize (SY998, GEMS42-I and GEMS42-II) with the higher D value have better growth and higher nitrogen accumulation under low nitrogen conditions. In contrast, Ji846 with the lowest D value has the lowest nitrogen accumulation and biomass in response to nitrogen limitation. These results indicated that the D value could help to screen low nitrogen tolerant maize, given that the D value was positively correlated with low nitrogen tolerance in maize seedlings.ConclusionsThe present study introduced the D value to evaluate stress tolerance. The higher the D value, the greater tolerance of maize to low nitrogen stress. This method may reduce the complexity of the investigated traits and enhance the accuracy of stress-tolerant evaluation. In addition, this method not only can screen potentially tolerant germplasm for low-nitrogen tolerance quickly, but also can comprise the correlated traits as many as possible to avoid the one-sidedness of a single parameter.

Deep learning to infer visual acuity from optical coherence tomography in diabetic macular edema.

PurposeDiabetic macular edema (DME) is one of the leading causes of visual impairment in diabetic retinopathy (DR). Physicians rely on optical coherence tomography (OCT) and baseline visual acuity (VA) to tailor therapeutic regimen. However, best-corrected visual acuity (BCVA) from chart-based examinations may not wholly reflect DME status. Chart-based examinations are subjected findings dependent on the patient’s recognition functions and are often confounded by concurrent corneal, lens, retinal, optic nerve, or extraocular disorders. The ability to infer VA from objective optical coherence tomography (OCT) images provides the predicted VA from objective macular structures directly and a better understanding of diabetic macular health. Deviations from chart-based and artificial intelligence (AI) image-based VA will prompt physicians to assess other ocular abnormalities affecting the patients VA and whether pursuing anti-VEGF treatment will likely yield increment in VA.Materials and methodsWe enrolled a retrospective cohort of 251 DME patients from Big Data Center (BDC) of Taipei Veteran General Hospital (TVGH) from February 2011 and August 2019. A total of 3,920 OCT images, labeled as “visually impaired” or “adequate” according to baseline VA, were grouped into training (2,826), validation (779), and testing cohort (315). We applied confusion matrix and receiver operating characteristic (ROC) curve to evaluate the performance.ResultsWe developed an OCT-based convolutional neuronal network (CNN) model that could classify two VA classes by the threshold of 0.50 (decimal notation) with an accuracy of 75.9%, a sensitivity of 78.9%, and an area under the ROC curve of 80.1% on the testing cohort.ConclusionThis study demonstrated the feasibility of inferring VA from routine objective retinal images.Translational relevanceServes as a pilot study to encourage further use of deep learning in deriving functional outcomes and secondary surrogate endpoints for retinal diseases.

Toward a unified theory of rational number arithmetic.

To explain children's difficulties learning fraction arithmetic, Braithwaite et al. (2017) proposed FARRA, a theory of fraction arithmetic implemented as a computational model. The present study tested predictions of the theory in a new domain, decimal arithmetic, and investigated children's use of conceptual knowledge in that domain. Sixth and eighth grade children (N = 92) solved decimal arithmetic problems while thinking aloud and afterward explained solutions to decimal arithmetic problems. Consistent with the hypothesis that FARRA's theoretical assumptions would generalize to decimal arithmetic, results supported 3 predictions derived from the model: (a) accuracies on different types of problems paralleled the frequencies with which the problem types appeared in textbooks; (b) most errors involved overgeneralization of strategies that would be correct for problems with different operations or types of number; and (c) individual children displayed patterns of strategy use predicted by FARRA. We also hypothesized that during routine calculation, overt reliance on conceptual knowledge is most likely among children who lack confidence in their procedural knowledge. Consistent with this hypothesis, (d) many children displayed conceptual knowledge when explaining solutions but not while solving problems; (e) during problem-solving, children who more often overtly used conceptual knowledge also displayed doubt more often; and (f) problem solving accuracy was positively associated with displaying conceptual knowledge while explaining, but not with displaying conceptual knowledge while solving problems. We discuss implications of the results for rational number instruction and for the creation of a unified theory of rational number arithmetic. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

Multi-view clustering with orthogonal mapping and binary graph

The multi-view clustering problem has attracted considerable attention over recent years for the remarkable clustering performance due to exploiting complementary information from multiple views. Most existing related research work processes data in the decimal real value space that is not the most compatible space for computers. Binary code learning, also known as hashing technology, is well-known for fast Hamming distance computation, less storage requirement and accurate calculation results. The Hamming space is most enjoyed by computers because of binary/hash codes. Several studies combine multi-view clustering with binary code learning for improving clustering performance. However, there is much redundant information contained in the learned binary codes, which negatively affects the clustering performance, but these studies ignore eliminating redundant information for learning compact codes. In addition, they don’t give a unified (one-step) clustering framework with binary graph structure, which doesn’t lead to the optimal clustering result due to the information loss during the two-step process. In this paper, to cope with the two issues, we propose an orthogonal mapping binary graph method (OMBG) for the multi-view clustering problem, which makes the mapping matrix of every view orthogonalize for eliminating redundant information and embeds a binary graph structure into the unified binary multi-view clustering framework for extracting local geometric structure information of binary codes and achieving the optimal clustering result. Furthermore, we design an effective optimization algorithm based on alternating direction minimization to solve the model of OMBG. Extensive experiments performed on four frequently-used benchmark multi-view datasets illustrate the superiority of OMBG which is compared with some state-of-the-art clustering baselines.

Texture classification with modified rotation invariant local binary pattern and gradient boosting

Since texture is prominent low level feature of an image, most of the image processing and computer vision applications rely on this feature for efficient extraction, retrieval, visualization and classification of the images. Hence, the texture analysis method mainly concentrates on efficient feature extraction and representation of the image. The images captured and analyzed in many of the applications are not in same (or) similar scale, orientation and illumination and also texture has regular, stochastic, periodic, homogeneous (or) inhomogeneous and directional in nature. To address these issues, recent texture analysis method focused on efficient and invariant feature extraction and representation with reduced dimension. Hence this paper proposes a invariant texture descriptor, Locality preserving Rotation Invariant Modified Directional Local Binary Pattern (LRIMDLBP) based on LBP. The classical LBP descriptor is widely used in most of the texture analysis applications due to its simplicity and robustness to illumination changes. However, it does not efficiently capture the discriminative texture information because it uses sign information and ignores the magnitude value of the neighborhood and also suffers from high dimensionality. Hence to improve the performance of LBP, many variants are proposed. Though most of these LBP variants are either geometrical or direction invariant, fails to address the spatial locality and contrast invariance. To address these issues, the proposed LRIMDLBP incorporates spatial locality, contrast and direction information for rotation invariant texture descriptor with reduced dimension. The proposed LRIMDLBP consists of 5 phases: (i) Reference point identification, (ii) Magnitude calculation, (iii) Binary Label computation based on threshold, (iv) Pattern identification in dominant direction and (v) LRIMDLBP code computation. The locality and rotation invariance is achieved by identifying and using reference point in a local neighborhood. The reference point is a dominant pixel whose magnitude is large in the neighborhood excluding center pixel. The spatial locality and rotation invariance is achieved by preserving the weights of LBP dynamically based on the reference point. The proposed method also preserves the direction information of the texture by comparing the magnitude of the pixel in the four dominant directions such as horizontal, vertical, diagonal and anti-diagonal directions. Finally the proposed invariant LRIMDLBP descriptor computes histogram based on decimal pattern value. The proposed LRIMDLBP descriptor results in texture feature with reduced dimension when compared to other LBP variants. The performance of the proposed descriptor is evaluated with large and well known four bench mark texture datasets namely (i) CUReT, (ii) Outex, (iii) KTS-TIPS and (iv) UIUC against three classifiers such as (i). K-Nearest Neighbor (K-NN), (ii). Support Vector Machine (SVM) with Radial Basis Function (RBF) and (iii). Gradient Boosting Classifier (GBC). The intensive experimental result shows that the ensemble based GBC yields superior classification accuracy of 99.38%, 99.43%, 98.67% and 98.82% for the datasets CUReT, Outex, KTH-TIPS and UIUC respectively when compared with other two classifiers and also improves the generalization ability. The proposed LRIMDLBP descriptor achieves approximately 15% more classification accuracy when compared with traditional LBP and also produces 1% to 2.5% more classification accuracy compared with other state of the art LBP variants.

A tale of two selection biases: The independent effects of relative age and biological maturity on player selection in the Football Association of Ireland's national talent pathway

This study investigated the associations between biological maturation status (classified using the Khamis–Roche method for the percentage of predicted adult height at the time of observation) and relative age (expressed as a decimal value relative to the difference between birth date and competition cut-off date) and the extent to which their relative selection biases existed across competitive age groups in an analysis of players within the Football Association of Ireland's (FAI) national talent pathway. The players assessed were either from the U13 FAI National Academy ( n = 125), the Ireland U15 national team ( n = 18), or the Ireland U16 national team ( n = 16). A moderate to very large selection bias in favour of early maturing players was observed across all age groups, increasing in magnitude with successive age groups ( p < 0.05). A total of 46–72% of players selected into the national talent pathway were early maturing; 0% of U15 and U16 players were late maturing. A relative age effect existed across all competitive cohorts ( p < 0.05), although not increasing with chronological age and smaller in magnitude than maturation biases. A small positive correlation between relative age and absolute maturity status at U13 was observed, and an inverse correlation between relative age and relative maturity status at U15 ( p < 0.01) was observed. There were no other significant correlations between relative or absolute maturity status and relative age. We encourage Football Associations to critically reflect upon their criteria for national talent squad selection; the current system diminishes the chances of selection for late maturing players.

The Impact of Gender in Learning With Games

There is an established gender gap in middle school math education, where female students report higher anxiety and lower engagement, which negatively impact their performance and even long-term career choices. This work investigates the role of digital learning games in addressing this issue by studying Decimal Point, a math game that teaches decimal numbers and operations to 5th and 6th graders. Through data from four published studies of Decimal Point, involving 624 students in total, the authors identified a consistent gender difference that was replicated across all studies – male students tended to do better at pretest, while female students tended to learn more from the game. In addition, female students were more careful in answering self-explanation questions, which significantly mediated the relationship between gender and learning gains in two out of four studies. These findings show that learning games can be an effective tool for bridging the gender gap in middle school math education, which in turn contributes to the development of more personalized and inclusive learning platforms.

Penerapan Normalisasi Data Dalam Mengelompokkan Data Mahasiswa Dengan Menggunakan Metode K-Means Untuk Menentukan Prioritas Bantuan Uang Kuliah Tunggal

At Budi Darma University there are obstacles in providing UKT rocks where it is profitable and less targeted for students who get it. This happened because those who deserved this assistance were students who had difficulty in costs, therefore we needed a way by grouping student data based on their social level. In determining the students who deserve to get the rock, they can use the data of students who are undergoing their studies at Budi Darma University. By digging up information based on student data. So that the data can be used first, the data normalization is carried out in order to obtain more accurate data. Where student data can be grouped correctly, data normalization must be carried out. One of the normalization methods that are often used in normalizing data is the decimal scaling method which is a data transformation method with normalization to equalize the range of values ​​on each attribute with a certain scale by moving the decimal value from data in the desired direction After the data is normalized, the next process is to explore student data information by applying data mining. The application of data mining is carried out to obtain information in the form of student data groups that are used as a priority in obtaining UKT assistance. The method used in classifying student data is using the K-Means algorithm. The manual testing method is that there are 3 clusters where the number of clusters 0 cluster 1 and cluster 3 is the same as testing data mining applications, namely rapidminer so that those who deserve to be prioritized get tuition assistance based on the sample, namely cluster / grouping 0 which consists of 22 people. This study aims to see the effect of applying data normalization in the K-Means method to classify student data which is used as a recommendation in the selection of UKT assistance.

Zero and nothing in medieval Arabic arithmetic†

Whether explaining calculations with decimal or sexagesimal notation, arithmetic books composed in Arabic beginning in the ninth century CE consistently describe the zero (ṣifr) as a sign indicating an empty place where there is no number. And yet we find that some arithmeticians explicitly performed operations on this zero. To understand how the zero was conceived and manipulated in medieval Arabic texts we first address the way that numbers themselves were conceived and how ‘nothing’ entered into arithmetical problem-solving. From there we examine arithmetic books for their treatment of zero. We find that there is no inconsistency in operating on what is literally nothing, and thus there was no motive for arithmeticians to regard zero as a number.

Late-onset glaucoma following congenital cataract surgery: Occurrence, visual acuity and risk factors: A 37-year longitudinal follow-up.

The aim of this study was to determine the prevalence of late-onset glaucoma after surgery for congenital cataract in a cohort with long-term follow-up and to evaluate visual development following the diagnosis of postoperative glaucoma in comparison with no glaucoma development. All children born between 1980 and 1997 in the western counties of Sweden who had undergone congenital cataract surgery were included (patients n=77, eyes n=122). Cataract was considered congenital if there was no proof of clear lens at birth. Medical records were reviewed with regard to onset of glaucoma, age at surgery, surgical technique, coexisting eye anomalies and changes in visual acuity. Glaucoma was considered late onset if occurring after 1year following surgery. Total glaucoma prevalence was 14.8%, including late (10.7%) and early onset (4.1%), with a mean follow-up of 23.2 ± 6.6 years. Microphthalmos was a significant risk factor for developing glaucoma (RR 7.75, p < 0.001). Bilaterally treated eyes had a mean visual acuity of 0.43 ± 0.33 (decimal value) at the last follow-up. With glaucoma, mean visual acuity was 0.19 ± 0.17 (decimal value). Treated eyes of patients with unilateral cataract surgery had a lower visual acuity. Life-long follow-up of all patients who have undergone surgery for congenital cataract in childhood is recommended. Annual check-ups of adults, including measurements of IOP and visual acuity, are recommended for patients with microphthalmos and/or who had surgery <3months of age.

Conocimiento de futuros profesores chilenos de matemática sobre los números decimales

Mathematics teachers' knowledge of the different numerical sets is essential for their appropriate teaching. We analysed and evaluated the knowledge of a group of 25 prospective mathematics teachers at a Chilean university about decimal numbers. Participants were given two tasks, adapted from previous research (Konic, 2011), to describe the strategies they use in relation to the concept and properties of decimal numbers. The study used some elements of the Didactic-Mathematical Knowledge Model proposed by Godino and cols. As results of the content analysis of the answers, the participants show a limited knowledge of common and specialised contents, and different semiotic conflicts are identified, such as the application of the idea of successor or the identification of the decimal number as a number expressed by writing with commas.