22 papers · ranked by Valyu relevance
S. C. Shen, Peijun Shen, Danhao Zhu
This paper presents RevOrder, a novel technique aimed at improving arithmetic operations in large language models (LLMs) by reversing the output digits in addition, subtraction, and n-digit by 1-digit (nD by 1D) multiplication tasks. Our method significantly reduces the Count of Sequential Intermediate Digits (CSID) to…
Dawei Liu, Xin Tan, Huifen Yan, Wei Li + 1 more
Skillful utilization of mental arithmetic can significantly improve students’ mathematical computation ability. However, it was observed that primary school students often resort to reiterating the process of written arithmetic in their minds during mental arithmetic, which is not conducive to their numerical ability…
Yongwen Zhu
Based on the nine-palace diagram, we establish the systematical geometric theory of arithmetic, which can realize the arithmetical addition, subtraction, multiplication, division and other operations thoroughly in the mind. In this paper, we give a brief introduction to this theory, including the rotation invariance…
Shufang Chen, Dawei Liu, Huifen Yan, Yong Ma
Introduction Arithmetic calculation is a fundamental skill for mathematical learning and daily life. However, elementary school students often make errors in practice. Methods Grounded in the schema theory and the memory retrieval theory of mental arithmetic, this study employs a controlled experiment to investigate…
Fredrik Johansson
—Arb is a C library for arbitrary-precision interval arithmetic using the midpoint-radius representation, also known as ball arithmetic. It supports real and complex numbers, polynomials, power series, matrices, and evaluation of many special functions. The core number types are designed for versatility and speed in a…
Elisabeth Goettfried, Laura Zamarian, Jerrell Cassady
The investigation of eye movements has been shown to provide valuable insights into a variety of cognitive processes. A limited number of recent studies have adopted eye-tracking to investigate the processes underlying simple and complex arithmetic. Here, we review and discuss these studies. We identify two lines of…
Pedro Pinheiro-Chagas, Dror Dotan, Manuela Piazza, Stanislas Dehaene
We introduce a novel method capable of dissecting the succession of processing stages underlying mental arithmetic, thus revealing how two numbers are transformed into a third. We asked adults to point to the result of single-digit additions and subtractions on a number line, while their finger trajectory was…
Renato J. Cintra, H. M. de Oliveira
Arithmetic complexity has a main role in the performance of algorithms for spectrum evaluation. Arithmetic transform theory offers a method for computing trigonometrical transforms with minimal number of multiplications. In this paper, the proposed algorithms for the arithmetic Fourier transform are surveyed. A new…
Shri Prakash Dwivedi
—Multiplication is one of the most important operation in computer arithmetic. Many integer operations such as squaring, division and computing reciprocal require same order of time as multiplication whereas some other operations such as computing GCD and residue operation require at most a factor of log n time more…
Jiwei Si, Hongxia Li, Yan Sun, Yanli Xu + 1 more
The present study used the choice/no-choice method to investigate the effect of math anxiety on the strategy used in computational estimation and mental arithmetic tasks and to examine age-related differences in this regard. Fifty-seven fourth graders, 56 sixth graders, and 60 adults were randomly selected to…
Alexandre Zénon, Samuel Salvaggio, Michael Andres
The assumption that the brain relies on Bayesian inference has been successful in accounting for many behavioural and neurophysiological observations, but to date, dependence on such mechanism has not been assessed in the context of arithmetic. Bayesian inference implies the representation of uncertainty and reliance…
Tomoya Nakai, Jérôme Prado
The ability to learn simple arithmetic is often thought to rely on the associative nature of human memory, where repeated exposure to arithmetic problems strengthens the relations between operands and outcomes. This view is reminiscent of learning in large language artificial neural networks (ANNs), where training…
Serena Dattola, Lilla Bonanno, Augusto Ielo, Angelica Quercia + 4 more
'Angelo Quartarone' 'Fabio La Foresta' 'Dante Mantini' 'Larbi Boubchir'] The neural underpinnings of mental calculation, the fundamentals of arithmetic representations and processes, and the development of arithmetic abilities have been explored by researchers over the years. In the present work, we report a study that…
Manqi Zhou, Shiyan Ji, Yalun Zhang, Huijuan Shen + 9 more
Mastering basic arithmetic lays the foundation for lifelong mathematical achievement, yet how the neural mechanisms underlying addition and subtraction calculations develop during childhood remain unclear. This study investigated the developmental trajectories of addition and subtraction calculations in school-aged…
Pedro Pinheiro-Chagas, Clara Sava-Segal, Serdar Akkol, Amy Daitch + 1 more
Previous neuroimaging studies have offered unique insights about the spatial organization of activations and deactivations across the brain, however these were not powered to explore the exact timing of events at the subsecond scale combined with precise anatomical source information at the level of individual brains.…
Gerrit Sommerauer, Karl-Heinz Grass, Roland H. Grabner, Stephan E. Vogel
Behavioral and neuroimaging studies have recently demonstrated that symbolic numerical order processing (i.e., deciding whether numbers are in an increasing/decreasing sequence or not) may engages different cognitive mechanisms and brain regions compared to symbolic numerical magnitude processing (e.g., deciding which…
Zhihao Lan, WanZhen Liang
The variational quantum eigensolver (VQE) algorithm can simulate the chemical systems such as molecules in the noisy intermediate-scale quantum devices and shows promising applications in quantum chemistry simulations. The accuracy and computational cost of the VQE simulations are determined by the underlying Ansätze.…
Linnea Karlsson Wirebring, Carola Wiklund-Hörnqvist, Sara Stillesjö, Carina Granberg + 4 more
Many learning opportunities of mathematical reasoning in school encourage passive imitative learning procedures (algorithmic reasoning, AR) instead of engaging in more active constructive reasoning processes (e.g., creative mathematical reasoning, CMR). In the present study, we employed a within-subject mathematical…
Authors not listed
While the method of manual inspection reliably produces correct results at the introductory level, it can often appear untidy and unintuitive and lacks teachable depth. This paper presents a novel alternative approach designed to achieve the same outcomes as manual inspection but with enhanced clarity. It serves as…
Galina Sinkevich
The idea of the principle of nested intervals or the concept of convergent sequences which is equivalent to this idea dates back to the ancient world. Archimedes calculated the unknown in excess and deficiency, approximating with two sets of values: ambient and nested values. G. Buridan came up with a concept of a…
Yingqi Tian, Zhaoxuan Xie, Zhen Luo, Haibo Ma
Using the mixed precision strategy to optimize quantum chemistry codes has been proved promising in saving computational cost and maintaining chemical accuracy. Here, an efficient mixed-precision density matrix renormalization group (DMRG) scheme, containing a two-level mixed-precision hierarchy, is developed and…
MARCO TODISCO
Determining the distribution of multiple chemical species at equilibrium for a given system is a common problem that must be routinely addressed by scholars. While simple systems consisting of a few species and reactions can be solved manually, most of these problems require the definition and solution of higher-order…