Number Of Symbols Research Articles

EEG decoding of finger numeral configurations with machine learning

In this study, we used multivariate decoding methods to study processing differences between canonical (montring and count) and noncanonical finger numeral configurations (FNCs). While previous research investigated these processing differences using behavioral and event-related potentials (ERP) methods, conventional univariate ERP analyses focus on specific time intervals and electrode sites and fail to capture broader scalp distribution and EEG frequency patterns. To address this issue a supervised learning classifier—support vector machines (SVM)—was used to decode ERP scalp distributions and alpha-band power for montring, counting, and noncanonical FNCs (for integers 1 to 4). The SVM was used to test whether the numerical information presented in FNCs can be decoded from the EEG data. Differences in the magnitude and timing of accuracy rates were used to compare the three types of FNCs. Overall, the algorithm was able to predict numerical information presented in FNCs beyond the random chance level accuracy, with higher rates for ERP scalp distributions than alpha-power. Montring had lower peak accuracy compared to counting and noncanonical configurations, likely due to automaticity in processing montring configurations leading to less distinct scalp distributions for the four numerical magnitudes (1 to 4). Paralleling the response time data, the peak decoding accuracy time for montring was earlier for montring (472 ms), compared to counting (577 ms) and noncanonical FNCs (604 ms). The results provide support for montring configurations being processed automatically, somewhat similar to number symbols, and provide additional insights for processing differences across different forms of FNCs. This study also highlights the strengths of decoding methods in EEG/ERP research on numerical cognition.

A Novel Parameter Estimation Method of FHSS Signal with Low SNR

A novel parameter estimation method of frequency hopping spread spectrum (FHSS) signal is proposed. The observed signal is divided into multiple segments and forms an observed matrix, performing FFT on the observed matrix with different segment lengths to obtain the corresponding spectrum matrix. By analyzing the convergence characteristics of the spectrum matrix, the estimation of the symbol period is realized, on this basis, the symbol‐frequency distribution is obtained and its projected spectrum in Frequency‐Amplitude plane is further obtained to select the candidate frequencies. The matrix composed of multiple single frequency signals is constructed according to the candidate frequencies and multiplied with the observed matrix under the segment length of symbol period, then the number of symbols per hopping duration is estimated according to the matrix multiplication result, so as to realize the estimation of the hopping duration, and finally the real hopping frequencies and hopping sequence can be found out from the candidate frequencies. Simulation results are presented to indicate that the proposed method has good estimation performance especially under the condition of low SNR. © 2023 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

Analysis of the metaphorical meanings of symbols in Milan Kundera’s novels

Abstract Milan Kundera is one of the most influential writers in contemporary world literature. In his novels, there are many symbolic metaphors related to numbers, dreams, and animals. Combing through the plots of Kundera’s novels, we can discover that among all the numbers, seven and twenty are used most frequently. These two numbers have rich metaphorical meanings. Besides, there are many other digital metaphors in Kundera’s novels, including 6, 4, etc. Apart from number symbols, Kundera has also inserted various kinds of dream symbols in his artistic creation. For Kundera, dreams are not just an individual’s physical and psychological activities, but also a continuation and supplement of real life. It can be concluded that dream narration is a perfect medium for the author to express his philosophical ideology. In addition, dream symbols also serve as an important medium for Kundera to demonstrate narrative skills and present important themes. In Kundera’s novels, animal symbols are integrated with the plots, revealing the personal traits of the relevant characters, and mirroring their spiritual world at the same time. Besides, Kundera also expressed his ecological ethics through the narration of animals’ death. In conclusion, the metaphorical meanings of different symbols in Kundera’s novels play an active role in highlighting the themes, revealing the inner thoughts of the characters, showing the special features of the characters, and expressing the author’s philosophical thoughts. These symbols help Kundera to break the limitations of time and space, which has become an important part of his polyphonic art. What’s more, Kundera has also tried to expand the original metaphorical meanings of these symbols to create some new poetic meanings.

Nonsymbolic Numerosity Maps at the Occipitotemporal Cortex Respond to Symbolic Numbers.

Numerosity, the set size of a group of items, helps guide human and animals' behavior and decisions. Numerosity perception is thought to be a precursor of symbolic numerical cognition. Previously, we uncovered neural populations selectively tuned to numerosities organized in a network of topographic maps in human association cortex. Here we investigate whether these numerosity maps are also involved in the processing of symbolic numbers, using 7T fMRI and a number-detection task. We recruited 7 participants (3 females) and found that the numerosity map at the temporal-occipital cortex (NTO) also responds to symbolic numbers. Furthermore, we found that numerosity-tuned neuronal populations at the NTO map in the left hemisphere are tuned to symbolic numbers. These results reveal different functions of the numerosity maps and support a link between numerosity representation and symbolic number processing in the ventral temporal-occipital cortex.SIGNIFICANCE STATEMENT Humans and other animals share an intuitive "number sense" to approximately represent numerosity. However, humans possess a unique ability to process number symbols (e.g., Arabic numbers). It has been argued that the human understanding of symbolic numbers is rooted in our ability to numerosity perception. Here we investigate whether numerosity-tuned neuronal populations organized at a network of topographic maps also respond to symbolic numbers. We find one of the maps at the temporal-occipital cortex is involved in symbolic numerical cognition and the neuronal populations are tuned to numbers. These results provide evidence for a link between nonsymbolic numerosity and symbolic number processing.

Estimating the target DOA, range and velocity using subspace methods in a MIMO OFDM DFRC system

Dual-function Radar communication (DFRC) systems implement Radar detection and communication using the same hardware simultaneously. Significant attention has been paid to a multiple-input multiple-output DFRC system based on orthogonal frequency division multiplexing (OFDM). So far, the directions of arrival of the targets have been well estimated using subspace methods. In this paper, the ranges and/or velocities are estimated using the subspace methods. To this end, the Radar waveform must be based on the data symbols that are replicated over a few sub-carriers and/or during a few OFDM symbols. To avoid data replication, the target ranges and velocities can be estimated based on a least-squares (LS) or total LS method. After giving a few practical considerations, simulation results show that the proposed approaches outperform the existing ones based on the Fourier transform and/or Lasso algorithm. The performance of the proposed approaches is compared with the Cramer–Rao bound. Moreover, we show how the performance of the DFRC system (in terms of the accuracy of the estimated target parameters and data rate) evolves when modifying the system parameters, such as the number of sub-carriers and the number of OFDM symbols.

The symbolic thinking ability of kindergarten students in central Aceh through Montessori games based on gender

<span lang="EN-US">Student’s cognitive abilities can be developed early, including thinking logically and symbolically and problem-solving using various methods. Therefore, this quantitative descriptive research aims to determine the symbolic thinking ability of kindergarten students through Montessori games based on gender. The subjects of this study were 112 kindergarten students from eight schools in the Central Aceh district who were selected by random sampling. Data processing techniques include editing, coding, scoring, and tabulation. The analysis was carried out using a frequency table with guidelines for assessing child development. Data were obtained from tests, observations, and interviews. Based on the analysis, it is known that the symbolic thinking abilities of male and female students are at the level of developing as expected. There are still students at the beginning to develop and undeveloped levels for both male and female students in this ability. There are differences in ability between male and female students, especially in indicators: i) Mentioning numbers 1-10 and ii) Counting and matching numbers with number symbols. While on the indicator of recognizing vowel and consonant symbols, there is no difference in ability between male and female students.</span>

PENINGKATAN KEMAMPUAN MENGENAL KONSEP BILANGAN DENGAN MENGGUNAKAN MEDIA APRON PADA ANAK USIA DINI KELOMPOK B TKIT NUSANTARA BANTEN

Knowing the concept of numbers is very important, because it is indirectly related to human daily life. In the introduction of the concept of numbers in group B it is still relatively lacking, which is marked by the lack of children's ability to say numbers in sequence, connecting number symbols with the number of objects. If learning the concept of numbers is given according to the child's abilities, then the child will have more control over the ability to recognize the concept of numbers. In learning to recognize the concept of numbers, it requires media that is attractive to children, one of which is the counting apron media. This study aims to improve the ability to recognize the concept of numbers in early childhood through the media of calculating aprons. This research method is classroom action research which refers to the Kemmis and Mc. Taggart includes four stages, namely (1) planning (2) action (3) observation (4) reflection. This research consists of 1 cycle, with 2 meetings. The data analysis technique used in this research is qualitative and quantitative data analysis. Data collection techniques using observation instruments, interviews, documentation, field notes and discussions. The results of this study stated that there was an increase in children's gross motor skills through traditional games, as evidenced by the average score of children's initial gross motor skills of 63.61% and the first cycle of 79.33%. The research findings that traditional games of cat and mouse can improve gross motor skills of TKIT Nusantara Banten children.

An Efficient Aggregation Method for the Symbolic Representation of Temporal Data

Symbolic representations are a useful tool for the dimension reduction of temporal data, allowing for the efficient storage of and information retrieval from time series. They can also enhance the training of machine learning algorithms on time series data through noise reduction and reduced sensitivity to hyperparameters. The adaptive Brownian bridge-based aggregation (ABBA) method is one such effective and robust symbolic representation, demonstrated to accurately capture important trends and shapes in time series. However, in its current form, the method struggles to process very large time series. Here, we present a new variant of the ABBA method, called fABBA. This variant utilizes a new aggregation approach tailored to the piecewise representation of time series. By replacing the k-means clustering used in ABBA with a sorting-based aggregation technique, and thereby avoiding repeated sum-of-squares error computations, the computational complexity is significantly reduced. In contrast to the original method, the new approach does not require the number of time series symbols to be specified in advance. Through extensive tests, we demonstrate that the new method significantly outperforms ABBA with a considerable reduction in runtime while also outperforming the popular SAX and 1d-SAX representations in terms of reconstruction accuracy. We further demonstrate that fABBA can compress other data types such as images.

Symbolic number ordering strategies and math anxiety

ABSTRACT Math anxiety results in a drop in performance on various math-related tasks, including the symbolic number ordering task in which participants decide whether a triplet of digits is presented in order (e.g. 3-5-7) or not (e.g. 3-7-5). We investigated whether the strategy repertoire and reaction times during a symbolic ordering task were affected by math anxiety. In study 1, participants performed an untimed symbolic number ordering task and indicated the strategy they used on a trial-by-trial basis. The use of the memory retrieval strategy, based on the immediate recognition of the triplet, decreased with high math anxiety, but disappeared when controlling for general anxiety. In the study 2, participants completed a timed version of the number order task. High math-anxious participants used the decomposition strategy (e.g. 5 is larger than 3 and 7 is larger than 5 to decide whether 3-5-7 is in the correct order) more often, and were slower in responding when both memory- and other decomposition strategies were used. Altogether, both studies demonstrate that high-math anxious participants are not only slower to decide whether a number triplet is in the correct order, but also rely more on procedural strategies.

The plural counts: Inconsistent grammatical number hinders numerical development in preschoolers — A cross-linguistic study

The role of grammar in numerical development, and particularly the role of grammatical number inflection, has already been well-documented in toddlerhood. It is unclear, however, whether the influence of grammatical language structure further extends to more complex later stages of numerical development. Here, we addressed this question by exploiting differences between Polish, which has a complex grammatical number paradigm, leading to a partially inconsistent mapping between numerical quantities and grammatical number, and German, which has a comparatively easy verbal paradigm: 151 Polish-speaking and 123 German-speaking kindergarten children were tested using a symbolic numerical comparison task. Additionally, counting skills (Give-a-Number and count-list), and mapping between non-symbolic (dot sets) and symbolic representations of numbers, as well as working memory (Corsi blocks and Digit span) were assessed. Based on the Give-a-Number and mapping tasks, the children were divided into subset-knowers, CP-knowers-non-mappers, and CP-knowers-mappers.Linguistic background was related to performance in several ways: Polish-speaking children expectedly progressed to the CP-knowers stage later than German children, despite comparable non-numerical capabilities, and even after this stage was achieved, they fared worse in the numerical comparison task. There were also meaningful differences in spatial-numerical mapping between the Polish and German groups.Our findings are in line with the theory that grammatical number paradigms influence.the development of representations and processing of numbers, not only at the stage of acquiring the meaning of the first number-words but at later stages as well, when dealing with symbolic numbers.

PENINGKATAN KEMAMPUAN BERHITUNG MELALUI PERMAINAN ULAR TANGGA PADA ANAK KELAS B DI TK BUKIT PERMAI 2 DI DESA KAMPILI KABUPATEN GOWA

The main problem in this study is how to improve children's numeracy skills through snakes and ladders games in class B at Bukit Permai 2 Kindergarten in Kampili Village, Gowa Regency. This type of research is classroom action research consisting of implementation planning, observation and reflection. The research subjects were 1 teacher and 17 children in class B at Bukit Permai 2 Kindergarten. The object of this study was the ability to recognize number symbols through a game of snakes and ladders. Data collection techniques used observation and documentation. The instruments used were observation sheets and documentation results. Data analysis used is descriptive quantitative. The results of this study indicate that there is an increase in numeracy skills in class B children at Bukit Permai 2 Kindergarten. The research implementation in cycle I and cycle II showed that children's numeracy skills could be seen from the percentage of observations of children's numeracy abilities in cycle I was 39.7% and the percentage of observations on the ability to recognize children's number symbols in cycle II was 82.8% with very good development criteria. Thus it can be concluded that using the snake and ladder game can improve the ability to recognize number symbols in class B children at Bukit Permai 2 Kindergarten.

Efficient Channel Estimation for RIS-Aided MIMO Communications With Unitary Approximate Message Passing

Reconfigurable intelligent surface (RIS) is very promising for wireless networks to achieve high energy efficiency, extended coverage, improved capacity, massive connectivity, etc. To unleash the full potentials of RIS-aided communications, acquiring accurate channel state information is crucial, which however is very challenging. For RIS-aided multiple-input and multiple-output (MIMO) communications, the existing channel estimation methods have computational complexity growing rapidly with the number of RIS units <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> (e.g., in the order of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N^{2}$ </tex-math></inline-formula> or <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N^{3}$ </tex-math></inline-formula> ) and/or have special requirements on the matrices involved (e.g., the matrices need to be sparse for algorithm convergence to achieve satisfactory performance), which hinder their applications. In this work, instead of using the conventional signal model in the literature, we derive a new signal model obtained through proper vectorization and reduction operations. Then, leveraging the unitary approximate message passing (UAMP), we develop a more efficient channel estimator that has complexity linear with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> and does not have special requirements on the relevant matrices, thanks to the robustness of UAMP. These facilitate the applications of the proposed algorithm to a general RIS-aided MIMO system with a larger <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> . Moreover, extensive numerical results show that the proposed estimator delivers much better performance and/or requires significantly less number of training symbols, thereby leading to notable reductions in both training overhead and latency.

Meningkatkan Kemampuan Mengenal Angka Anak PAUD Nasyithatun Nisa Desa Teluk Kiambang melalui Puzzel Angka

The ability to recognize numbers is the ability to recognize the concept of numbers and number symbols that become the basis for mastering mathematical concepts. The facts reveal that the ability of most children to recognize numbers is still weak and tends not to develop optimally. It is seen that children do not know numbers correctly. This study aims to find out the ability of group B students of PAUD Nasyithatun Nisa Teluk Kiambang in recognizing numbers before and after using puzzles number. This belonged to the Class Action Research (CAR), with 12 subjects. Data was collected through tests, observations, and field notes; and analyzed descriptively. The findings stated that children’s ability to recognize numbers were at 36.66% (pre-cycle), 58.32% (cycle I), and 86.66% (cycle II). Thus, these confirm that the media of puzzles number can improve children’s ability to recognize numbers. In addition, the enthusiasm of the children increases and the learning atmosphere is more fun.

MEDIA PEMBELAJARAN PENGENALAN LAMBANG BILANGAN PADA ANAK USIA 4-6 TAHUN: KAJIAN LITERATUR

This study aims to determine the learning media for the introduction of number symbols for Early Childhood Education. The data in this study were obtained through a literature study research method. The researcher collects and analyzes all the data in the study from various existing sources to obtain information relevant to the problem to be solved through a systematic technique using the keywords symbol number and early childhood education. The data or information comes from books, theses, theses, journals and research articles from official websites that have been indexed and accredited. Early Childhood Education basically has to pay attention to aspects of development in children, especially cognitive development to recognize number symbols. The introduction of number symbols emphasizes the understanding of number symbols that must be understood by children. Children aged 4-6 years are in the pre-operational stage, the stage where children begin to recognize symbols or symbols, so teachers need interesting learning media as a tool to introduce number plates to children so that children can easily understand the material and learning will become more meaningful. The results of the study show a variety of learning media developed to help introduce number symbols to children aged 4-6 years

Early neural markers for individual difference in mathematical achievement determined from rational number processing

The neural markers for individual differences in mathematical achievement have been studied extensively using magnetic resonance imaging; however, high temporal resolution electrophysiological evidence for individual differences in mathematical achievement require further elucidation. This study evaluated the event-related potential (ERP) when 48 college students with high or low mathematical achievement (HA vs. LA) matched non-symbolic and symbolic rational numbers. Behavioral results indicated that HA students had better performance in the discretized non-symbolic matching, although the two groups showed similar performances in the continuous matching. ERP data revealed that even before non-symbolic stimulus presentation, HA students had greater Bereitschaftspotential (BP) amplitudes over posterior central electrodes. After the presentation of non-symbolic numbers, HA students had larger N1 amplitudes at 160 ms post-stimulus, over left-lateralized parieto-occipital electrodes. After the presentation of symbolic numbers, HA students displayed more profound P1 amplitudes at 100 ms post-stimulus, over left parietal electrodes. Furthermore, larger BP and N1 amplitudes were associated with the shorter reaction times, and larger P1 amplitudes corresponded to lower error rates. The BP effect could indicate preparation processing, and early left-lateralized N1 and P1 effects could reflect the non-symbolic and symbolic number processing along the dorsal neural pathways. These results suggest that the left-lateralized P1 and N1 components elicited by matching non-symbolic and symbolic rational numbers can be considered as neurocognitive markers for individual differences in mathematical achievement.

Meningkatkan Kemampuan Memahami Konsep Bilangan 1-10 Dengan Kartu Angka Melalui Metode Demonstrasi Pada Anak Didik Kelompok B TK Bakti Mulia Tlepokkulon

This research was conducted on the grounds that group B students at Bakti Mulia Kindergarten Tlepokkulon had low cognitive abilities. The purpose of this study was to describe the effect of using number card media in improving students' cognitive abilities. This research uses classroom action research which is carried out in three cycles and each cycle through planning, implementing actions, observing, and reflecting. The subjects of this study were group B students of Bakti Mulia Kindergarten, Tlepokkulon Village, Grabag District, Purworejo Regency, which collected 15 children. The object of the research is to increase children's cognitive abilities in understanding the concept of numbers with number symbols using number cards as media. The results showed an increase in children's cognitive abilities through the connection of a collection of objects 1-10 with number cards through the demonstration method, namely students who developed according to expectations which previously reached 2 children (13%), in the cycle to 4 children (27%), cycle 2 became 7 children (46%) and cycle 3 became 13 children (86%).

STIMULASI KEMAMPUAN BERPIKIR SIMBOLIK MENGGUNAKAN AKTIVITAS PLAYDOUGH PADA KELOMPOK B RA ASHABUL KAHFI KOTA PAREPARE

The purpose of this study was to stimulate symbolic thinking skills using playdough activities in group B RA Ashabul Kahfi, Parepare City. The method used in this research is descriptive qualitative method. Data collection is done by interviews, observation and documentation. Playdought activities can stimulate the ability to think symbolically in group B which includes the ability to say the symbols for numbers 1-10, use the symbols for numbers to count, match numbers with symbols for numbers, recognize various kinds of symbols for vowels and consonants and represent various objects in the form of pictures or writing. Based on the research activities carried out, it was found that there was an increase in children's symbolic thinking skills by using playdough activities.

RETRACTED: A Perception Study for Unit Charts in the Context of Large-Magnitude Data Representation

Unit charts are a common type of chart for visualizing scientific data. A unit chart is a chart used to communicate quantities of things by making the number of symbols on the chart proportional to the number of items represented. An accurate perception of the order of magnitude is essential to evaluating whether a unit chart can effectively convey information. Previous studies have primarily focused on perceptual properties at small order-of-magnitude scales or the efficacy of pictographs in unit charts. However, few researchers have explored the perceptual effectiveness of unit charts when representing large orders of magnitude. In this study, we performed a series of sampling measurements to investigate the visual–perceptual characteristics of unit charts when representing asymmetric interactions such as large-scale numbers. The results showed that under the restriction of the current conventional display medium, unit charts still offer a significant advantage over bar charts in a single-scale visual overview. However, this comes at the cost of a longer response time. Although this study constitutes basic research, accumulating evidence about how people reason about magnitudes beyond human perception is critical to the field of information science. This study may contribute to understanding how viewers perceive unit charts and the factors that influence graphical perception. This article provides some specific guidelines for designing unit charts that may be useful to visualization designers.

Manuscript Analysis of Children's Language Skills and Number Concepts through Technology in the Digital Era

Language is one of the elements behind the development of aspects of development that occur in early childhood, as well as a tool or means to communicate with other people and the environment. To develop and stimulate children’s language development, they can carry out activities such as listening, speaking, reading, and writing, as well as saying and counting number symbols with digital-era devices. This study aims to describe language skills and recognize the concept of numbers in early childhood through technology. This research method is a literature study or review with a qualitative approach that collects data or is based on scientific writing, combining research with existing literature to solve problems. Collecting library data includes reading, storing, and managing research and concluding research materials. The research results show that developing language skills and recognizing numbers in early childhood requires activities such as listening, speaking, reading and writing, calling and counting number symbols through technology.

Cortical representations of numbers and nonsymbolic quantities expand and segregate in children from 5 to 8 years of age.

Number symbols, such as Arabic numerals, are cultural inventions that have transformed human mathematical skills. Although their acquisition is at the core of early elementary education in children, it remains unknown how the neural representations of numerals emerge during that period. It is also unclear whether these relate to an ontogenetically earlier sense of approximate quantity. Here, we used multivariate fMRI adaptation coupled with within- and between-format machine learning to probe the cortical representations of Arabic numerals and approximate nonsymbolic quantity in 89 children either at the beginning (age 5) or four years into formal education (age 8). Although the cortical representations of both numerals and nonsymbolic quantities expanded from age 5 to age 8, these representations also segregated with learning and development. Specifically, a format-independent neural representation of quantity was found in the right parietal cortex, but only for 5-year-olds. These results are consistent with the so-called symbolic estrangement hypothesis, which argues that the relation between symbolic and nonsymbolic quantity weakens with exposure to formal mathematics in children.