Arithmetic Domain Research Articles

ZNO-Eval: Benchmarking reasoning capabilities of large language models in Ukrainian

As the usage of large language models for problems outside of simple text understanding or generation increases, assessing their abilities and limitations becomes crucial. While significant progress has been made in this area over the last few years, most research has focused on benchmarking English, leaving other languages underexplored. This makes evaluating the reasoning and robustness level of language models in Ukrainian particularly challenging. The purpose of this work is to establish a comprehensive benchmark for the reasoning capabilities evaluation of large language models in the Ukrainian language. This paper presents the ZNO-Eval benchmark based on real exam tasks from Ukraine's standardized educational testing system: the External Independent Evaluation and the National Multi-subject Test. With single- answer options, multiple-choice, matching, and open-ended questions from diverse subjects, including Ukrainian language, mathematics, history, and geography, this dataset paves the way toward a thorough analysis of reasoning capabilities across different domains and complexities. Evaluation of several well-known language models, such as GPT-3.5-Turbo, GPT-4o, GPT-4-Turbo, Mistral Large, Claude 3 Opus, and Gemini-1.5 Pro on this benchmark demonstrated the superiority of GPT-4o in both common knowledge reasoning and intricate language tasks. At the same time, Gemini Pro and GPT-4 Turbo excelled in the arithmetic domain, leading in single-answer and open-ended math problems. While all models were close to max performance in text-only common knowledge tasks like history and geography, there still is a gap for Ukrainian language and math, thus highlighting the importance of developing specialized language benchmarks for more accurate assessments of model capabilities and limitations across different languages and contexts. This research introduced ZNO-Eval, an effective benchmark for evaluating reasoning capabilities, and thoroughly explored the abilities and limitations of modern solutions in the Ukrainian language. Future research should aim to expand the scope of ZNO-Eval to other modalities like images commonly used for exam problem description.

Brain markers of subtraction and multiplication skills in childhood: task-based functional connectivity and individualized structural similarity.

Arithmetic, a high-order cognitive ability, show marked individual difference over development. Despite recent advancements in neuroimaging techniques have enabled the identification of brain markers for individual differences in high-order cognitive abilities, it remains largely unknown about the brain markers for arithmetic. This study used a data-driven connectome-based prediction model to identify brain markers of arithmetic skills from arithmetic-state functional connectivity and individualized structural similarity in 132 children aged 8 to 15years. We found that both subtraction-state functional connectivity and individualized SS successfully predicted subtraction and multiplication skills but multiplication-state functional connectivity failed to predict either skill. Among the four successful prediction models, most predictive connections were located in frontal-parietal, default-mode, and secondary visual networks. Further computational lesion analyses revealed the essential structural role of frontal-parietal network in predicting subtraction and the essential functional roles of secondary visual, language, and ventral multimodal networks in predicting multiplication. Finally, a few shared nodes but largely nonoverlapping functional and structural connections were found to predict subtraction and multiplication skills. Altogether, our findings provide new insights into the brain markers of arithmetic skills in children and highlight the importance of studying different connectivity modalities and different arithmetic domains to advance our understanding of children's arithmetic skills.

Long-term outcome of pediatric head injuries – A five-year follow-up

Objectives: Traumatic brain injury (TBI) disrupts the developing brain in the pediatric population. This study aims to look at the outcomes of moderate and severe TBI over a five-year follow-up to look for the long-term sequelae of head injury in the pediatric population. Materials and Methods: A prospective observational study was conducted after obtaining the permission of the Institutional Ethics Committee with the primary study participants admitted between 2015 and 2017 with follow-up extending up to 2022 in 118 pediatric patients, aged between 1 and 15 years who required admission in the pediatric intensive care unit with moderate and severe TBI. Results: Language impairment was noted in 33.63% (n = 37) patients during early follow-up, and 12 of them continued to have impaired language skills and communication at the end of five years. With regard to school functioning, children had more difficulty in the arithmetic domain (n = 33) compared to language domains (n = 17). While the parents noted improvements in scholastic performances, some degree of difficulty in learning was noted in most of the children, who sustained TBI. Despite these difficulties, 27 out of 41 participants, who gave their higher secondary examinations have gone on to pursue undergraduate courses in colleges. Conclusion: Our study indicates that over the passage of time, children tend to have a reasonable chance at recovery, and with the potential for plasticity, early and aggressive rehabilitative services may enable the child to have a decent quality of life and in selected cases, even an independent life.

DUAL SENSORY LOSS AND COGNITIVE TEST PERFORMANCE IN OLDER ADULTS IN INDIA

Abstract Dementia is rising in the global population, especially in low- and middle-income countries like India. Hearing and vision loss are risk factors for cognitive decline/dementia, but studies have primarily been in high income countries. This study aims to investigate the association between dual sensory loss and cognitive function with specific domains among the older Indian population. Data was from the 2017-2019 Wave 1 of the population-based Longitudinal Aging Study in India. The analysis sample consists of 27,975 individuals aged 60 years and older in 35 states and union territories. Dual sensory loss was determined by respondents’ self-reported, perceived difficulty regarding hearing and vision function. Linear regression was used to model associations of dual sensory loss with global cognitive performance, summarized as a z-score, and in the domains of memory, orientation, arithmetic, and executive function, adjusted for demographics and health characteristics. Overall, 5.9% had hearing loss, 24.1% had vision loss, and 3.4% had both. In fully adjusted models, hearing loss only, vision loss only, and dual sensory loss were associated with a change of -0.08 (95%CI: -0.1, -0.04), -0.11 (95%CI: -0.12, -0.09), and -0.22 (95%CI: -0.27, -0.18) standard deviations, respectively. Associations were also observed for all domains. Poor hearing and/or vision loss is associated with lower cognitive performance across various cognitive domains in older adults in India. The association was strongest for those with dual sensory loss. Rehabilitative interventions for hearing and vision may be an additional resource in reducing dementia risk in India.

Higher level domain specific skills in mathematics; The relationship between algebra, geometry, executive function skills and mathematics achievement.

Algebra and geometry are important components of mathematics that are often considered gatekeepers for future success. However, most studies that have researched the cognitive skills required for success in mathematics have only considered the domain of arithmetic. We extended models of mathematical skills to consider how executive function skills play both a direct role in secondary-school-level mathematical achievement as well as an indirect role via algebra and geometry, alongside arithmetic. We found that verbal and visuospatial working memory were indirectly associated with mathematical achievement via number fact knowledge, calculation skills, algebra and geometry. Inhibition was also indirectly associated with mathematical achievement via number fact knowledge and calculation skills. These findings highlight that there are multiple mechanisms by which executive function skills may be involved in mathematics outcomes. Therefore, using specific measures of mathematical processes as well as context-rich assessments of mathematical achievement is important to understand these mechanisms.

Counteracting the dynamic degradation of high-dimensional digital chaotic systems via a stochastic jump mechanism

To analyze the periodic distribution and state-mapping structures of high-dimensional digital chaotic systems in fixed-point arithmetic domain. A chaotic cycle-finding algorithm (CCFA) can be designed to precisely calculate the period length of the orbit of digital chaos under different finite calculation accuracy. Furthermore, to test the versatility and effectiveness of our proposed algorithm, the periodic distribution and security of the digital Sprott D system are analyzed in detail. Numerical simulation results show that the chaotic system have potential security risks, such as short period and low sequence complexity. In addition, we put forward a new resistance method based on automatic cycle detection and random jump of chaotic trajectories for the objective of enhancing the dynamical properties of high-dimensional digital chaotic systems. This scheme can construct a new chaotic model with many desirable properties, such as long period, high state-space utilization, low autocorrelation, and good ergodicity.

Principal Component Analysis of Oxford Cognitive Screen in Patients With Stroke.

Cognitive deficits occur in most patients with stroke and are the important predictors of adverse long-term outcome. Early identification is fundamental to plan the most appropriate care, including rehabilitation and discharge decisions. The Oxford Cognitive Screen (OCS) is a simple, valid, and reliable tool for the assessment of cognitive deficits in patients with stroke. It contains 10 subtests, providing 14 scores referring to 5 theoretically derived cognitive domains: attention, language, number, praxis, and memory. However, an empirical verification of the domain composition of the OCS subtests in stroke data is still lacking in the literature. A principal component analysis (PCA) was performed on 1,973 patients with stroke who were enrolled in OCS studies in the UK and in Italy. A number of six main components were identified relating to the domains of language and arithmetic, memory, visuomotor ability, orientation, spatial exploration, and executive functions. Bootstrapped split-half reliability analysis on patients and comparison between patients and 498 healthy participants, as that between patients with left and right hemisphere damage, confirmed the results obtained by the principal component analysis. A clarification about the contribution of each score to the theoretical original domains and to the components identified by the PCA is provided with the aim to foster the usability of OCS for both clinicians and researchers.

The Graph Structure of the Generalized Discrete Arnold's Cat Map

Chaotic dynamics is an important source for generating pseudorandom binary sequences (PRBS). Much efforts have been devoted to obtaining period distribution of the generalized discrete Arnold&#x0027;s Cat map in various domains using all kinds of theoretical methods, including Hensel&#x0027;s lifting approach. Diagonalizing the transform matrix of the map, this article gives the explicit formulation of any iteration of the generalized Cat map. Then, its real graph (cycle) structure in any binary arithmetic domain is disclosed. The subtle rules on how the cycles (itself and its distribution) change with the arithmetic precision <inline-formula><tex-math notation="LaTeX">$e$</tex-math><alternatives><mml:math><mml:mi>e</mml:mi></mml:math><inline-graphic xlink:href="li-ieq1-3051387.gif"/></alternatives></inline-formula> are elaborately investigated and proved. The regular and beautiful patterns of Cat map demonstrated in a computer adopting fixed-point arithmetics are rigorously proved and experimentally verified. The results can serve as a benchmark for studying the dynamics of the variants of the Cat map in any domain. In addition, the used methodology can be used to evaluate randomness of PRBS generated by iterating any other maps.

Modelling for Clinical and Psysiological Evaluation of Diabetes and Glucose Homeostasis

There is a long history of arithmetic simulations in the domain of gluconeogenesis. There are various reasons why frameworks are used. Paradigms have been employed to calculate physiologically relevant parameters from intermediate experimental evidence, to offer a clear quantitative description of pathophysiology processes, and to identify clinical relevance indicators from basic empirical procedures. The creation and application of frameworks in this field has expanded in response to the rising social effect of type 2 diabetes that entails a disruption of the glycemic homeostasis system. The frameworks' emphasis has ranged from depictions of entire body functions to lymphocytes (form “in Vivo” to “in Vitro”) study, following the methodologies of physiologic and medicinal exploration. Framework-based techniques to connecting in vivo and in vitro research, and also multi-resolution systems that combine the two domains, have been presented. The arithmetic and psychological domains have had varying levels of effectiveness and influence.

Relationships between cognitive pattern recognition and specific mathematical domains in mathematics education

ABSTRACT The understanding of the relationships between pattern recognition and mathematical abilities is important for students in their learning of mathematics and mathematics teachers in the design of their teaching pedagogies. This study examines the connections between pattern recognition and mathematical abilities of students from four Singapore private schools (52.7% male and 47.3% female) in arithmetic, algebra and geometry. Two validated instruments are used to measure the cognitive skills. At the end of the study, it is found that the students have moderate mastery levels of pattern recognition and mathematical ability. The study also discovers that most of the correlations between pattern recognition and mathematical abilities in the domains of arithmetic, algebra, and geometry are statistically significant. This lent support to not only the results from recent studies but also indicates that the long-standing relationships between these two cognitive abilities remain valid.

Realistic Mathematics Education Principles for Designing a Learning Sequence on Number Patterns

The number pattern is one of mathematics topics taught for junior high school students that relate between arithmetic and algebra domain. This topic bridges arithmetical and algebraic thinking. Therefore, the learning for this topic should be designed meaningfully. This research aims to design a learning sequence on the number patterns using principles of Realistic Mathematics Education (RME). To do this, we used design research method, particularly the preliminary design phase, with the following three steps. First, literature study was conducted to collect student difficulties in the learning of number patterns, relevant studies, and the theory of RME. Second, we observed Indonesian mathematics textbooks addressing the number patterns to see a learning sequence for this topic. Finally, we designed a learning sequence for the number patterns using the RME principles, particularly the reality principle, level principle, and intertwinement principle. The result of this research includes the learning sequence for the number patterns according to the RME principles, which consists of three activities: relationship between patterns and numbers; exploration of numbers; and generalization of number patterns. We conclude that the three principles of RME are fruitful for designing a meaningful learning sequence for the topic of number patterns.

Developmental changes in size effects for simple tie and non-tie addition problems in 6- to 12-year-old children and adults

In the domain of cognitive arithmetic, the size effect corresponds to an increase in solution times as a function of the size of the operands involved in the problems. In this study, we tracked the evolution of size effects associated with tie and non-tie addition problems across development. We scrutinized the progression of solution times for very small problems involving operands from 2 to 4, larger problems, and 1-problems (problems involving 1 as one of the operands) in children from Grade 1 to Grade 5 and adults. For the first time, we document the presence of a size effect for tie problems with a sum up to 8 in Grade 1 children. In contrast, from Grade 3 until adulthood, this size effect could not be evidenced. Crucially, for non-tie problems, whereas a general size effect is observed when contrasting small one-digit additions with large additions, we show that, from Grade 1 until adulthood, a continuous size effect as a function of the sum of the problems is not observed. In fact, for all age groups, medium problems with sums of 8, 9, and 10 do not present a size effect at all. Given that the problem size effect is sometimes referred to as one of the most robust and reliable effects in the numerical cognition literature, our results necessarily challenge its theoretical interpretation.

Interpretation and Implications of Lognormal Linear Regression Used for Bacterial Enumeration.

Bacterial enumeration data are typically log transformed to realize a more normal distribution and stabilize the variance. Unfortunately, statistical results from log transformed data are often misinterpreted as data within the arithmetic domain. To explore the implication of slope and intercept from an unweighted linear regression and compare it to the results of the regression of log transformed data. Mathematical formulae inferencing explained using real dataset. For y=Ax+B+ε, where y is the recovery (CFU/g) and x is the target concentration (CFU/g) with error ε homogeneous across x. When B=0, slope A estimates percent recovery R. In the regression of log transformed data, logy=αlogx+β+εz (equivalent to equation y=Axα·ω), it is the intercept β=logyx=logA that estimates the percent recovery in logarithm when slope α=1, which means that R doesn't vary over x. Error term ω is multiplicative to x, while εz or log(ω) is additive to log(x). Whether the data should be transformed or not is not a choice, but a decision based on the distribution of the data. Significant difference was not found between the five models (the linear regression of log transformed data, three generalized linear models and a nonlinear model) regarding their predicted percent recovery when applied to our data. An acceptable regression model should result in approximately the best normal distribution of residuals. Statistical procedures making use of log transformed data should be studied separately and documented as such, not collectively reported and interpreted with results studied in arithmetic domain. The way to interpret statistical results developed from arithmetic domain does not apply to that of the log transformed data.

Logarithmic transformation and peak-discharge power-law analysis

AbstractThe peak-discharge and drainage area power-law relation has been widely used in regional flood frequency analysis for more than a century. The coefficients and can be obtained by nonlinear or log-log linear regression. To illustrate the deficiencies of applying log-transformation in peak-discharge power-law analyses, we studied 52 peak-discharge events observed in the Iowa River Basin in the United States from 2002 to 2013. The results show that: (1) the estimated scaling exponents by the two methods are remarkably different; (2) for more than 80% of the cases, the power-law relationships obtained by log-log linear regression produce larger prediction errors of peak discharge in the arithmetic scale than that predicted by nonlinear regression; and (3) logarithmic transformation often fails to stabilize residuals in the arithmetic domain, it assigns higher weight to data points representing smaller peak discharges and drainage areas, and it alters the visual appearance of the scatter in the data. The notable discrepancies in the scaling parameters estimated by the two methods and the undesirable consequences of logarithmic transformation raise caution. When conducting peak-discharge scaling analysis, especially for prediction purposes, applying nonlinear regression on the arithmetic scale to estimate the scaling parameters is a better alternative.

Julian Huxley and the quantification of relative growth

In 1932, Julian Huxley introduced biologists around the world to a simple method for fitting two-parameter power equations, $$ Y\, = \,b \times \, X^{k} $$, to bivariate observations that follow a curvilinear path on the arithmetic (= linear) scale. The method entails fitting a straight line to logarithmic transformations of the data and then (at least implicitly) back-transforming the resulting equation to the arithmetic domain. This general approach continues to be in wide use by students of biological allometry despite its several limitations and shortcomings. For example, Huxley’s allometric method requires that the bivariate data of interest follow the path of a straight line in log domain (i.e., that the data be loglinear). However, many datasets that are otherwise suitable for allometric analysis do not meet the requirement for loglinearity and consequently are beyond the scope of Huxley’s method. Such data can usually be examined in the untransformed state by nonlinear regression, and the regression approach enables investigators to fit models with different functional form and random error. Moreover, by combining nonlinear regression with a categorical variable, investigators can compare sets of observations that follow curvilinear paths on the arithmetic scale. The regression protocol is illustrated by re-examining data for relative growth by the internal hinge ligament in a bivalve mollusk and by the elongated snout in garfish (Actinopterygii). The methodology promoted by Huxley has played a major role in development of the field of biological allometry, but the procedure has been superseded by nonlinear regression.

Altered association between executive functions and reading and math fluency tasks in children with reading difficulties compared with typical readers.

Fluent reading in children relies on executive functions (EF). Recent research suggests that EF skills also affect arithmetic abilities. Children with reading difficulties (RD) experience deficits in EF. It is still unknown to what extent these EF deficits are the basis for both reading and arithmetic skills in children with RD compared with typical readers. To define the role of EF in reading and arithmetic in children with RD and typical readers, EF measures and reading and arithmetic fluency and non-fluency measures were assessed in 8 to 12-year-old children with RD and age-matched typical readers. Comparison and correlation analyses were performed within and between the two groups. Children with RD scored lower on reading and arithmetic fluency and non-fluency tasks compared with typical readers. For both groups, fluency measures were lower than non-fluency measures. Strong correlations were found within the entire study population between fluency measures and EF, as well as between non-fluency measures and EF compared with mixed correlations observed for the groups separately. Fluency was related to subcomponents of EF expressed in both reading and arithmetic domains for the two groups. The role of each domain and comparison with non-fluency results for each group are discussed.

Choice between helping vs not helping: level of mastery in the task

Studies carried out to identify conditions that promote altruism have suggested that factors such as situational consequences and the introduction of verbal components in a task probabilize the individuals' choice to work under shared contingencies. However, it has been found that the presence of these variables is not enough to guarantee that individuals help. It has been considered that the behavioral capacity to perform effectively in a task (i.e. domain level) is a dispositional variable that can facilitate or impede the choice of individuals to work under shared contingencies. Based on this, the objective of this work consisted of evaluating the effects of different levels of domain in an arithmetic task (high and low) on the choice of helping / not helping a partner to perform arithmetic operations. The task was to perform different types of arithmetic operations (addition, subtraction, multiplication and division) to obtain points. Once they accumulated 20 points, participants were presented with the option to choose between helping a partner to solve operations or continue with their task. The results show that participants with high arithmetic domain chose to help their partner more frequently than the participants with low arithmetic domain (40% vs. 23%, respectively). The importance of the task domain level as a dispositional factor in the choice between helping or not helping is discussed.

Relative Growth by the Elongated Jaws of Gars: A Perspective on Polyphasic Loglinear Allometry.

Nonlinear regression was used to fit power functions with different forms for random error to data for length of the upper jaw versus length of the rest of body in two species of gars. Growth by the jaws of these species was reported earlier to conform to a pattern of polyphasic loglinear allometry indicative of relatively rapid growth by the jaw in small individuals (allometric exponent greater than 1) and relatively slow growth by the jaw in larger ones (allometric exponent less than 1). The new analyses revealed, however, that the pattern of relative growth by jaws of these fishes does not change with body size: the jaws grow more slowly than the rest of the body throughout life. The flaw in earlier investigations was the unrealistic assumption that data comprising a single sample in log domain form two (or more) statistically distinct distributions when expressed in arithmetic domain. The paradigm used in the current study provides a simple way to fit and compare different power functions, with different forms for random error, directly to raw data and thereby obviates the use of logarithmic transformations in allometric research.

Quantifying the curvilinear metabolic scaling in mammals.

A perplexing problem confronting students of metabolic allometry concerns the convex curvature that seemingly occurs in log-log plots of basal metabolic rate (BMR) vs. body mass in mammals. This putative curvilinearity has typically been interpreted in the context of a simple power function, Y=a*Xb, on the arithmetic scale, with the allometric exponent, b, supposedly increasing steadily as a dependent function of body size. The relationship can be quantified in arithmetic domain by exponentiating a quadratic equation fitted to logarithmic transformations of the original data, but the resulting model is not in the form of a power function and it is unlikely to describe accurately the pattern in the original distribution. I therefore re-examined a dataset for 636 species of mammal and discovered that the relationship between BMR and body mass is well-described by a power function with an explicit, non-zero intercept and lognormal, heteroscedastic error. The model has an invariant allometric exponent of 0.75, so the appearance in prior investigations of a steadily increasing exponent probably was an aberration resulting from undue reliance on logarithmic transformations to estimate statistical models in arithmetic domain. Theoretical constructs relating BMR to body mass in mammals may need to be modified to accommodate a positive intercept in the statistical model, but they do not need to be revised, or rejected, at present time on grounds that the allometric exponent varies with body size. New data from planned experiments will be needed to confirm any hypothesis based on data currently available.

Autonomous mobile drilling mechanism with metamorphic function

According to the application requirements of aircraft automatic assembly and the principle of metamorphic mechanism,a double eccentric source metamorphic mechanism was presented. On the basis,a autonomous mobile drilling mechanism with metamorphic function was designed,and the switching of changing freedom between the two functional stages of walking and posture alignment drilling. The calculation method of inverse kinematics was provided,which could calculate the driven displacement of legs during the posture alignment process which changed from initial to desired normal direction by pitching and side roll. This could be used to the online control. The offset domain of inverse arithmetic of each leg in working conditions were plotted by Matlab,and the dimensional designing of double eccentric source metamorphic mechanism was achieved. The virtual prototype model was established,and the kinematics simulation was carried out by using examples. The results confirmed that the kinematics calculation method and the double eccentric source metamorphic mechanism were applicable for the mechanism. The prototype of mechanism was developed,and the posture alignment accuracy of the system was tested. The result shows that the mechanism can meet the drilling requirements of the aircraft automatic assembly.