Journal articles: 'Symbolic comparison'

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Masson, Nicolas, Mauro Pesenti, and Valérie Dormal. "Spatial bias in symbolic and non-symbolic numerical comparison in neglect." Neuropsychologia 51, no. 10 (August 2013): 1925–32. http://dx.doi.org/10.1016/j.neuropsychologia.2013.06.004.

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Pollack, Courtney, Eric D. Wilkey, and Gavin R. Price. "Predictors of middle school students’ growth in symbolic number comparison performance." Journal of Numerical Cognition 8, no. 1 (March 31, 2022): 53–72. http://dx.doi.org/10.5964/jnc.8069.

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The ability to efficiently compare number symbols, such as digits, is associated with mathematics competence across the lifespan. Performance on symbolic number comparison tasks differ across age groups; young students who are developing fluency with digits improve on symbolic number comparison, and performance is better in adults than children. However, whether this improvement continues for older students who are fluent with number symbols, and what cognitive factors relate to this improvement, is unknown. This study used a longitudinal sample of U.S. middle school students (n = 394) to examine whether symbolic number comparison performance changes over middle school (i.e., students aged 11-14), whether there are individual differences in students’ rate of change, and potential predictors of that change. Students completed measures of single-digit symbolic number comparison, nonsymbolic number comparison, executive function (EF), and mathematics competence in Grade 5 (M = 11.02 years; SD = 0.32), and double-digit symbolic number comparison in Grades 6-8. Results showed that, on average, students’ symbolic number comparison performance improved from Grades 6-8. Grade 5 Symbolic number comparison performance predicted Grade 8 symbolic number comparison and rate of change over Grades 6-8. Grade 5 nonsymbolic number comparison, EF, and mathematics competence predicted Grade 8 symbolic number comparison performance. Results suggest that numerical magnitude processing, executive functions, and mathematics competence are related to symbolic number processing well into middle school, and that students continue to refine their ability to process number symbols into adolescence.

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Scalise, Nicole R., Emily N. Daubert, and Geetha B. Ramani. "Narrowing the early mathematics gap: A play-based intervention to promote low-income preschoolers’ number skills." Journal of Numerical Cognition 3, no. 3 (January 30, 2018): 559–81. http://dx.doi.org/10.5964/jnc.v3i3.72.

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Preschoolers from low-income households lag behind preschoolers from middle-income households on numerical skills that underlie later mathematics achievement. However, it is unknown whether these gaps exist on parallel measures of symbolic and non-symbolic numerical skills. Experiment 1 indicated preschoolers from low-income backgrounds were less accurate than peers from middle-income backgrounds on a measure of symbolic magnitude comparison, but they performed equivalently on a measure of non-symbolic magnitude comparison. This suggests activities linking non-symbolic and symbolic number representations may be used to support children’s numerical knowledge. Experiment 2 randomly assigned low-income preschoolers (Mean Age = 4.7 years) to play either a numerical magnitude comparison or a numerical matching card game across four 15 min sessions over a 3-week period. The magnitude comparison card game led to significant improvements in participants’ symbolic magnitude comparison skills in an immediate posttest assessment. Following the intervention, low-income participants performed equivalently to an age- and gender-matched sample of middle-income preschoolers in symbolic magnitude comparison. These results suggest a brief intervention that combines non-symbolic and symbolic magnitude representations can support low-income preschoolers’ early numerical knowledge.

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Laino, Luigi. "Man and Future: a Palaeontological and Chronological Foundation of Cassirer's Definition of Man as Animal Symbolicum." ETHICS IN PROGRESS 8, no. 1 (May 1, 2017): 12–40. http://dx.doi.org/10.14746/eip.2017.1.2.

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In the present paper, the author aims at laying the foundations of a symbolics of technical gesture, according to the thesis that symbolic faculty is another face of the technological one, and that they are both in truth two sides of the same coin. Accordingly, the author suggests to rename the whole dimension as “meta-environmentality”. The analysis is carried out on the basis of a specific comparison between Cassirer’s definition of “animal symbolicum” and its scientific consistence in the light of modern palaeontology. “Animal symbolicum” is here compared with Leroi-Gourhan’s homo technologicus, and Cassirer’s ideas on human identity tested starting from paleoanthropological data. The result of the inquiry lead us to recognize the urgency of integrating Cassirer’s argument with the primacy of the technological capacity, but a deep analysis of the characterizing attributes of the latter compels us to uphold the symbolic attitude of the technological dimension. The author then sketches a basic description ofthe guidelines of a symbolic theory of technology (especially §§ 6-7), and tries to show how the basic elements of such an approach were familiar both to Cassirer and Leroi-Gourhan. As a consequence of the whole theory, the author elaborates a chronological analysis of human identity, whose basic result is the determination of the future as main temporal dimension of human acting.

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Opfer, John E., Dan Kim, Lisa K. Fazio, Xinlin Zhou, and Robert S. Siegler. "Cognitive mediators of US—China differences in early symbolic arithmetic." PLOS ONE 16, no. 8 (August 25, 2021): e0255283. http://dx.doi.org/10.1371/journal.pone.0255283.

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Chinese children routinely outperform American peers in standardized tests of mathematics knowledge. To examine mediators of this effect, 95 Chinese and US 5-year-olds completed a test of overall symbolic arithmetic, an IQ subtest, and three tests each of symbolic and non-symbolic numerical magnitude knowledge (magnitude comparison, approximate addition, and number-line estimation). Overall Chinese children performed better in symbolic arithmetic than US children, and all measures of IQ and number knowledge predicted overall symbolic arithmetic. Chinese children were more accurate than US peers in symbolic numerical magnitude comparison, symbolic approximate addition, and both symbolic and non-symbolic number-line estimation; Chinese and U.S. children did not differ in IQ and non-symbolic magnitude comparison and approximate addition. A substantial amount of the nationality difference in overall symbolic arithmetic was mediated by performance on the symbolic and number-line tests.

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Finke, Sabrina, Chiara Banfi, H. Harald Freudenthaler, Anna F. Steiner, Stephan E. Vogel, Silke M. Göbel, and Karin Landerl. "Common and distinct predictors of non-symbolic and symbolic ordinal number processing across the early primary school years." PLOS ONE 16, no. 10 (October 21, 2021): e0258847. http://dx.doi.org/10.1371/journal.pone.0258847.

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What are the cognitive mechanisms supporting non-symbolic and symbolic order processing? Preliminary evidence suggests that non-symbolic and symbolic order processing are partly distinct constructs. The precise mechanisms supporting these skills, however, are still unclear. Moreover, predictive patterns may undergo dynamic developmental changes during the first years of formal schooling. This study investigates the contribution of theoretically relevant constructs (non-symbolic and symbolic magnitude comparison, counting and storage and manipulation components of verbal and visuo-spatial working memory) to performance and developmental change in non-symbolic and symbolic numerical order processing. We followed 157 children longitudinally from Grade 1 to 3. In the order judgement tasks, children decided whether or not triplets of dots or digits were arranged in numerically ascending order. Non-symbolic magnitude comparison and visuo-spatial manipulation were significant predictors of initial performance in both non-symbolic and symbolic ordering. In line with our expectations, counting skills contributed additional variance to the prediction of symbolic, but not of non-symbolic ordering. Developmental change in ordering performance from Grade 1 to 2 was predicted by symbolic comparison skills and visuo-spatial manipulation. None of the predictors explained variance in developmental change from Grade 2 to 3. Taken together, the present results provide robust evidence for a general involvement of pair-wise magnitude comparison and visuo-spatial manipulation in numerical ordering, irrespective of the number format. Importantly, counting-based mechanisms appear to be a unique predictor of symbolic ordering. We thus conclude that there is only a partial overlap of the cognitive mechanisms underlying non-symbolic and symbolic order processing.

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Kovács, Zoltán, and Róbert Vajda. "Symbolic Comparison of Geometric Quantities in GeoGebra." Electronic Proceedings in Theoretical Computer Science 354 (February 8, 2022): 13–25. http://dx.doi.org/10.4204/eptcs.354.2.

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Ruiz, Manuel, Fernando López, and Antonio Páez. "Comparison of thematic maps using symbolic entropy." International Journal of Geographical Information Science 26, no. 3 (March 2012): 413–39. http://dx.doi.org/10.1080/13658816.2011.586327.

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Dumais, Susan T., and William P. Jones. "A comparison of symbolic and spatial filing." ACM SIGCHI Bulletin 16, no. 4 (April 1985): 127–30. http://dx.doi.org/10.1145/1165385.317479.

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Chen, Dawn, Hongjing Lu, and Keith J. Holyoak. "The discovery and comparison of symbolic magnitudes." Cognitive Psychology 71 (June 2014): 27–54. http://dx.doi.org/10.1016/j.cogpsych.2014.01.002.

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Gans, Herbert J. "Symbolic ethnicity and symbolic religiosity: Towards a comparison of ethnic and religious acculturation." Ethnic and Racial Studies 17, no. 4 (October 1994): 577–92. http://dx.doi.org/10.1080/01419870.1994.9993841.

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Raizis, Marios-Byron. "Σονέτα στον Ορφέα του R. M. RILKE: ερμηνευτική προσέγγιση." Σύγκριση 11 (January 31, 2017): 122. http://dx.doi.org/10.12681/comparison.10769.

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The collection Sonette an Orpheus, by Rainer Maria Rilke (1923), is discussed and interpreted as having two functions. First, it constitutes an elegiac composition honoring the memory of a prematurely deceased young lady, and second -and most important- it obliquely suggests and illustrates his personal poetics. His sonnets A-l, B-5, B-6, B-28 and the last one B-29, are presented in a precise rhyming translation into Greek, and their individual symbolic or structural features (e.g., tree, woods, hearing, ear, melody, rose, anemone etc.) are explained as personal signs signifying beauty, transience, vulnerability, emotion, inspiration, creativity etc. which constitute the main themes and artistic concerns of a mature and almost existential Rilke, intimating how he functions as a poet.

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Kravchenko, N. K. "Panteleimon Kulish’s symbolic imagery in comparison to the cristian and mythological archetypal symbolism (based on the story “granny from the other world”)." Mìžnarodnij fìlologìčnij časopis 1, no. 10 (August 28, 2019): 14–19. http://dx.doi.org/10.31548/philolog2019.01.014.

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Conrad, Benjamin N., Eric D. Wilkey, Darren J. Yeo, and Gavin R. Price. "Network topology of symbolic and nonsymbolic number comparison." Network Neuroscience 4, no. 3 (January 2020): 714–45. http://dx.doi.org/10.1162/netn_a_00144.

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Studies of brain activity during number processing suggest symbolic and nonsymbolic numerical stimuli (e.g., Arabic digits and dot arrays) engage both shared and distinct neural mechanisms. However, the extent to which number format influences large-scale functional network organization is unknown. In this study, using 7 Tesla MRI, we adopted a network neuroscience approach to characterize the whole-brain functional architecture supporting symbolic and nonsymbolic number comparison in 33 adults. Results showed the degree of global modularity was similar for both formats. The symbolic format, however, elicited stronger community membership among auditory regions, whereas for nonsymbolic, stronger membership was observed within and between cingulo-opercular/salience network and basal ganglia communities. The right posterior inferior temporal gyrus, left intraparietal sulcus, and two regions in the right ventromedial occipital cortex demonstrated robust differences between formats in terms of their community membership, supporting prior findings that these areas are differentially engaged based on number format. Furthermore, a unified fronto-parietal/dorsal attention community in the nonsymbolic condition was fractionated into two components in the symbolic condition. Taken together, these results reveal a pattern of overlapping and distinct network architectures for symbolic and nonsymbolic number processing.

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Hyde, Daniel C., Yi Mou, Ilaria Berteletti, Elizabeth S. Spelke, Stanislas Dehaene, and Manuela Piazza. "Testing the role of symbols in preschool numeracy: An experimental computer-based intervention study." PLOS ONE 16, no. 11 (November 15, 2021): e0259775. http://dx.doi.org/10.1371/journal.pone.0259775.

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Numeracy is of critical importance for scholastic success and modern-day living, but the precise mechanisms that drive its development are poorly understood. Here we used novel experimental training methods to begin to investigate the role of symbols in the development of numeracy in preschool-aged children. We assigned pre-school children in the U.S. and Italy (N = 215; Mean age = 49.15 months) to play one of five versions of a computer-based numerical comparison game for two weeks. The different versions of the game were equated on basic features of gameplay and demands but systematically varied in numerical content. Critically, some versions included non-symbolic numerical comparisons only, while others combined non-symbolic numerical comparison with symbolic aids of various types. Before and after training we assessed four components of early numeracy: counting proficiency, non-symbolic numerical comparison, one-to-one correspondence, and arithmetic set transformation. We found that overall children showed improvement in most of these components after completing these short trainings. However, children trained on numerical comparisons with symbolic aids made larger gains on assessments of one-to-one correspondence and arithmetic transformation compared to children whose training involved non-symbolic numerical comparison only. Further exploratory analyses suggested that, although there were no major differences between children trained with verbal symbols (e.g., verbal counting) and non-verbal visuo-spatial symbols (i.e., abacus counting), the gains in one-to-one correspondence may have been driven by abacus training, while the gains in non-verbal arithmetic transformations may have been driven by verbal training. These results provide initial evidence that the introduction of symbols may contribute to the emergence of numeracy by enhancing the capacity for thinking about exact equality and the numerical effects of set transformations. More broadly, this study provides an empirical basis to motivate further focused study of the processes by which children’s mastery of symbols influences children’s developing mastery of numeracy.

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Rubinsten, Orly, Nachshon Korem, Naama Levin, and Tamar Furman. "Frequency-based Dissociation of Symbolic and Nonsymbolic Numerical Processing during Numerical Comparison." Journal of Cognitive Neuroscience 32, no. 5 (May 2020): 762–82. http://dx.doi.org/10.1162/jocn_a_01550.

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Recent evidence suggests that during numerical calculation, symbolic and nonsymbolic processing are functionally distinct operations. Nevertheless, both roughly recruit the same brain areas (spatially overlapping networks in the parietal cortex) and happen at the same time (roughly 250 msec poststimulus onset). We tested the hypothesis that symbolic and nonsymbolic processing are segregated by means of functionally relevant networks in different frequency ranges: high gamma (above 50 Hz) for symbolic processing and lower beta (12–17 Hz) for nonsymbolic processing. EEG signals were quantified as participants compared either symbolic numbers or nonsymbolic quantities. Larger EEG gamma-band power was observed for more difficult symbolic comparisons (ratio of 0.8 between the two numbers) than for easier comparisons (ratio of 0.2) over frontocentral regions. Similarly, beta-band power was larger for more difficult nonsymbolic comparisons than for easier ones over parietal areas. These results confirm the existence of a functional dissociation in EEG oscillatory dynamics during numerical processing that is compatible with the notion of distinct linguistic processing of symbolic numbers and approximation of nonsymbolic numerical information.

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Hochster, Melvin, and Craig Huneke. "Comparison of symbolic and ordinary powers of ideals." Inventiones Mathematicae 147, no. 2 (February 1, 2002): 349–69. http://dx.doi.org/10.1007/s002220100176.

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Shavlik, Jude W., Raymond J. Mooney, and Geoffrey G. Towell. "Symbolic and neural learning algorithms: An experimental comparison." Machine Learning 6, no. 2 (March 1991): 111–43. http://dx.doi.org/10.1007/bf00114160.

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Cañizares, Danilka Castro, Vivian Reigosa Crespo, and Eduardo González Alemañy. "Symbolic and Non-Symbolic Number Magnitude Processing in Children with Developmental Dyscalculia." Spanish journal of psychology 15, no. 3 (November 2012): 952–66. http://dx.doi.org/10.5209/rev_sjop.2012.v15.n3.39387.

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The aim of this study was to evaluate if children with Developmental Dyscalculia (DD) exhibit a general deficit in magnitude representations or a specific deficit in the connection of symbolic representations with the corresponding analogous magnitudes. DD was diagnosed using a timed arithmetic task. The experimental magnitude comparison tasks were presented in non-symbolic and symbolic formats. DD and typically developing (TD) children showed similar numerical distance and size congruity effects. However, DD children performed significantly slower in the symbolic task. These results are consistent with the access deficit hypothesis, according to which DD children's deficits are caused by difficulties accessing magnitude information from numerical symbols rather than in processing numerosities per se.

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Berka, Petr, and Ivan Bruha. "Empirical Comparison of Various Discretization Procedures." International Journal of Pattern Recognition and Artificial Intelligence 12, no. 07 (November 1998): 1017–32. http://dx.doi.org/10.1142/s0218001498000567.

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The genuine symbolic machine learning (ML) algorithms are capable of processing symbolic, categorial data only. However, real-world problems, e.g. in medicine or finance, involve both symbolic and numerical attributes. Therefore, there is an important issue of ML to discretize (categorize) numerical attributes. There exist quite a few discretization procedures in the ML field. This paper describes two newer algorithms for categorization (discretization) of numerical attributes. The first one is implemented in the KEX (Knowledge EXplorer) as its preprocessing procedure. Its idea is to discretize the numerical attributes in such a way that the resulting categorization corresponds to KEX knowledge acquisition algorithm. Since the categorization for KEX is done "off-line" before using the KEX machine learning algorithm, it can be used as a preprocessing step for other machine learning algorithms, too. The other discretization procedure is implemented in CN4, a large extension of the well-known CN2 machine learning algorithm. The range of numerical attributes is divided into intervals that may form a complex generated by the algorithm as a part of the class description. Experimental results show a comparison of performance of KEX and CN4 on some well-known ML databases. To make the comparison more exhibitory, we also used the discretization procedure of the MLC++ library. Other ML algorithms such as ID3 and C4.5 were run under our experiments, too. Then, the results are compared and discussed.

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Starling-Alves, Isabella, Annelise Júlio-Costa, Ricardo José de Moura, and Vitor Geraldi Haase. "Nonsymbolic and Symbolic Numerical Magnitude Processing in the Brazilian Children with Mathematics Difficulties." Dementia & Neuropsychologia 15, no. 4 (December 2021): 524–32. http://dx.doi.org/10.1590/1980-57642021dn15-040013.

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ABSTRACT It is still debated if the main deficit in mathematical difficulties (MD) is nonsymbolic or symbolic numerical magnitude processing. Objectives: In the present study, our main goal was to investigate nonsymbolic and symbolic numerical magnitude processing in MD and the relationship between these abilities and arithmetic. Methods: The Brazilian school-age children with MD completed a nonsymbolic and a symbolic numerical magnitude comparison task and an arithmetic task. We compared their performance with a group of children with typical achievement (TA) and investigated the association between numerical magnitude processing and arithmetic with a series of regression analyses. Results: Results indicated that children with MD had low performance in the nonsymbolic numerical magnitude comparison task. Performance in both nonsymbolic and symbolic numerical magnitude comparison tasks predicted arithmetic abilities in children with TA, but not in children with MD. Conclusions: These results indicate that children with MD have difficulties in nonsymbolic numerical magnitude processing, and do not engage basic numerical magnitude representations to solve arithmetic.

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Mitteramskogler, Johann J., and Franz Winkler. "Symbolic solutions of algebraic ODEs: a comparison of methods." Publicationes Mathematicae Debrecen 100, no. 1-2 (January 1, 2022): 143–66. http://dx.doi.org/10.5486/pmd.2022.9100.

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Mussolin, Christophe, Anne De Volder, Cécile Grandin, Xavier Schlögel, Marie-Cécile Nassogne, and Marie-Pascale Noël. "Neural Correlates of Symbolic Number Comparison in Developmental Dyscalculia." Journal of Cognitive Neuroscience 22, no. 5 (May 2010): 860–74. http://dx.doi.org/10.1162/jocn.2009.21237.

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Developmental dyscalculia (DD) is a deficit in number processing and arithmetic that affects 3–6% of schoolchildren. The goal of the present study was to analyze cerebral bases of DD related to symbolic number processing. Children with DD aged 9–11 years and matched children with no learning disability history were investigated using fMRI. The two groups of children were controlled for general cognitive factors, such as working memory, reading abilities, or IQ. Brain activations were measured during a number comparison task on pairs of Arabic numerals and a color comparison task on pairs of nonnumerical symbols. In each task, pairs of stimuli that were close or far on the relevant dimension were constituted. Brain activation in bilateral intraparietal sulcus (IPS) was modulated by numerical distance in controls but not in children with DD. Moreover, although the right IPS responded to numerical distance only, the left IPS was influenced by both numerical and color distances in control children. Our findings suggest that dyscalculia is associated with impairment in areas involved in number magnitude processing and, to a lesser extent, in areas dedicated to domain-general magnitude processing.

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NOBRE, C., E. MARTINELI, A. BRAGA, A. de CARVALHO, S. REZENDE, J. L. BRAGA, and T. LUDERMIR. "Knowledge Extraction: A Comparison Between Symbolic and Connectionist Methods." International Journal of Neural Systems 09, no. 03 (June 1999): 257–64. http://dx.doi.org/10.1142/s0129065799000265.

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The use of a linguistic representation for expressing knowledge acquired by learning systems is an important issue as regards to user understanding. Under this assumption, and to make sure that these systems will be welcome and used, several techniques have been developed by the artificial intelligence community, under both the symbolic and the connectionist approaches. This work discusses and investigates three knowledge extraction techniques based on these approaches. The first two techniques, the C4.5 [12] and CN2 [6] symbolic learning algorithms, extract knowledge directly from the data set. The last technique, the TREPAN algorithm [10] extracts knowledge from a previously trained neural network. The CN2 algorithm induces if … then rules from a given data set. The C4.5 algorithm extracts decision trees, although it can also extract ordered rules, from the data set. Decision trees are also the knowledge representation used by the TREPAN algorithm.

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Dehaene, Stanislas, Emmanuel Dupoux, and Jacques Mehler. "Is numerical comparison digital? Analogical and symbolic effects in two-digit number comparison." Journal of Experimental Psychology: Human Perception and Performance 16, no. 3 (1990): 626–41. http://dx.doi.org/10.1037/0096-1523.16.3.626.

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Miller, Diana L. "Symbolic Capital and Gender: Evidence from Two Cultural Fields." Cultural Sociology 8, no. 4 (July 16, 2014): 462–82. http://dx.doi.org/10.1177/1749975514539800.

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This article builds a gendered understanding of Bourdieu’s concept of symbolic capital. Through a comparison of two cultural fields – the heavy metal scene and the contemporary folk scene in Toronto, Canada – I show that field structure impacts the extent to which gendered dispositions (which we can understand as masculine capital and feminine capital) are exchangeable for symbolic capital, or reputation. Using semi-structured interviews, discourse analysis, and participant observation, I highlight two features of the fields that shape the extent to which masculine and feminine capital produce symbolic capital: the degree to which symbolic capital is institutionalized, and the level of symbolic boundary-drawing in the field. The heavy metal field’s low institutionalization of symbolic capital and high symbolic boundaries heighten the salience of gender as a basis of symbolic capital, while the folk field’s high institutionalization of symbolic capital and low symbolic boundary-drawing reduce the extent to which gender matters.

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Colomé, Àngels. "Representation of numerical magnitude in math-anxious individuals." Quarterly Journal of Experimental Psychology 72, no. 3 (January 23, 2018): 424–35. http://dx.doi.org/10.1177/1747021817752094.

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Larger distance effects in high math-anxious individuals (HMA) performing comparison tasks have previously been interpreted as indicating less precise magnitude representation in this population. A recent study by Dietrich, Huber, Moeller, and Klein limited the effects of math anxiety to symbolic comparison, in which they found larger distance effects for HMA, despite equivalent size effects. However, the question of whether distance effects in symbolic comparison reflect the properties of the magnitude representation or decisional processes is currently under debate. This study was designed to further explore the relation between math anxiety and magnitude representation through three different tasks. HMA and low math-anxious individuals (LMA) performed a non-symbolic comparison, in which no group differences were found. Furthermore, we did not replicate previous findings in an Arabic digit comparison, in which HMA individuals showed equivalent distance effects to their LMA peers. Lastly, there were no group differences in a counting Stroop task. Altogether, an explanation of math anxiety differences in terms of less precise magnitude representation is not supported.

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Cañizares, Danilka Castro, Nancy Estévez Pérez, and Otmara Pérez Marrero. "Typical Development of Quantity Comparison in School-Aged Children." Spanish journal of psychology 14, no. 1 (May 2011): 50–61. http://dx.doi.org/10.5209/rev_sjop.2011.v14.n1.4.

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Although basic numerical skills have been widely studied in the last years, very few studies have undertaken a developmental approach. The present study evaluated the development of the magnitude comparison basic numerical ability, in children from first, third and sixth grades by means of the subject's response time in numerical tasks presented in symbolic and non-symbolic formats. The results showed a significant decrease on quantities processing speed as age increases, which suggests numerical skills tend to become automatic with instruction. The differences found, concerning the general achievement pattern in each school year, might express the maturational specificities of the numerical representation system through development.

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Janssen, Mike, Thomas Kamp, and Jason Vander Woude. "Comparing powers of edge ideals." Journal of Algebra and Its Applications 18, no. 10 (August 6, 2019): 1950184. http://dx.doi.org/10.1142/s0219498819501846.

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Given a nontrivial homogeneous ideal [Formula: see text], a problem of great recent interest has been the comparison of the [Formula: see text]th ordinary power of [Formula: see text] and the [Formula: see text]th symbolic power [Formula: see text]. This comparison has been undertaken directly via an exploration of which exponents [Formula: see text] and [Formula: see text] guarantee the subset containment [Formula: see text] and asymptotically via a computation of the resurgence [Formula: see text], a number for which any [Formula: see text] guarantees [Formula: see text]. Recently, a third quantity, the symbolic defect, was introduced; as [Formula: see text], the symbolic defect is the minimal number of generators required to add to [Formula: see text] in order to get [Formula: see text]. We consider these various means of comparison when [Formula: see text] is the edge ideal of certain graphs by describing an ideal [Formula: see text] for which [Formula: see text]. When [Formula: see text] is the edge ideal of an odd cycle, our description of the structure of [Formula: see text] yields solutions to both the direct and asymptotic containment questions, as well as a partial computation of the sequence of symbolic defects.

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BLOEM, RODERICK, ALESSANDRO CIMATTI, INGO PILL, and MARCO ROVERI. "SYMBOLIC IMPLEMENTATION OF ALTERNATING AUTOMATA." International Journal of Foundations of Computer Science 18, no. 04 (August 2007): 727–43. http://dx.doi.org/10.1142/s0129054107004942.

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This paper addresses the challenges of symbolic model checking and language emptiness checking where the specification is given as an alternating Büchi automaton. We introduce a novel version of Miyano and Hayashi's construction that allows us to directly convert an alternating automaton to a polynomially-sized symbolic structure. We thus avoid building an exponentially-sized explicit representation of the corresponding nondeterministic automaton. For one-weak automata, Gastin and Oddoux' construction produces smaller automata than Miyano and Hayashi's construction. We present a (symbolic) hybrid approach that combines the benefits of both: while retaining full generality, it uses the cheaper construction for those parts of the automaton that are one-weak. We performed a thorough experimental comparison of the explicit and symbolic approaches and several variants of Miyano and Hayashi's construction, using both BDD-based and SAT-based model checking techniques. The symbolic approaches clearly outperform the explicit one.

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Tavakoli, Hamdollah Manzari. "The relationship between accuracy of numerical magnitude comparisons and children’s arithmetic ability: A study in Iranian primary school children." Europe’s Journal of Psychology 12, no. 4 (November 18, 2016): 567–83. http://dx.doi.org/10.5964/ejop.v12i4.1175.

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The relationship between children’s accuracy during numerical magnitude comparisons and arithmetic ability has been investigated by many researchers. Contradictory results have been reported from these studies due to the use of many different tasks and indices to determine the accuracy of numerical magnitude comparisons. In the light of this inconsistency among measurement techniques, the present study aimed to investigate this relationship among Iranian second grade children (n = 113) using a pre-established test (known as the Numeracy Screener) to measure numerical magnitude comparison accuracy. The results revealed that both the symbolic and non-symbolic items of the Numeracy Screener significantly correlated with arithmetic ability. However, after controlling for the effect of working memory, processing speed, and long-term memory, only performance on symbolic items accounted for the unique variances in children’s arithmetic ability. Furthermore, while working memory uniquely contributed to arithmetic ability in one-and two-digit arithmetic problem solving, processing speed uniquely explained only the variance in single-digit arithmetic skills and long-term memory did not contribute to any significant additional variance for one-digit or two-digit arithmetic problem solving.

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Thanigaivelan, Balavelan, Tara Julia Hamilton, and Adam Postula. "A comparison of interval methods in symbolic circuit analysis applications." ANZIAM Journal 52 (January 16, 2012): 1084. http://dx.doi.org/10.21914/anziamj.v52i0.3981.

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Petrusic, William M., Elena Gallitto, and Craig Leth-Steensen. "Short-term memory for the comparative instructions in symbolic comparison." Canadian Journal of Experimental Psychology/Revue canadienne de psychologie expérimentale 68, no. 4 (2014): 242–49. http://dx.doi.org/10.1037/cep0000040.

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Wilkinson, Krista M., and William J. McIlvane. "Blank Comparison Analysis of Emergent Symbolic Mapping by Young Children." Journal of Experimental Child Psychology 67, no. 2 (November 1997): 115–30. http://dx.doi.org/10.1006/jecp.1997.2402.

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Nepop-Aidachych, L. "SYMBOLISM OF FLOWERS IN POLISH LANGUAGE AND CULTURE." Comparative studies of Slavic languages and literatures. In memory of Academician Leonid Bulakhovsky, no. 36 (2020): 48–61. http://dx.doi.org/10.17721/2075-437x.2020.36.05.

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The author explores the symbolism of flowers in the Polish language and culture. On the basis of the articles of the Dictionary of Folk Stereotypes and Symbols („Słownik stereotypów i symboli ludowych”) (Flowers Volume („Kwiaty”)), it is determined which symbolic meaning saregiven to the flower in general and to certain types of flowers, in whichgenres of folklor et hes evalues arerealized, what be camethe basis for the formation of suchmeanings. For the reconstruction of symbolic meanings boththe Polish linguistic information and the information outside the linguistic field are used, which testify to the functioning of the corresponding conceptin Polish culture. Based on the comparison of the linguistic images of the individual flowers and the flowerin generalitisre vealedt hatt hev astmajority of linguistic image softhe flowers have both common withthe general concept and differen tsymbolic meanings, som ehave only specific one sandothers do not have thematall. Ways and technique sof analysis of the symbolism of flowers in Polish language and culture are offered.

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Pinto Doria, Isabel, Ana Sousa Ferreira, Otília Dias, Helena Bacelar-Nicolau, and Georges Le Calvé. "Comparison of Multivariate Analysis Methodologies in a Palliative Care Setting." Biometrical Letters 49, no. 1 (June 1, 2012): 67–79. http://dx.doi.org/10.2478/bile-2013-0005.

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Summary This study is focused on measuring the quality and the satisfaction with the palliative care provided to oncology patients in domicile. The SERVQUAL methodology adapted for the Portuguese context was used to evaluate the quality of palliative care and patient satisfaction. The Portuguese SERVQUAL questionnaire is composed of five perception scales and two questionnaires, one about the patient and another about the caregiver. The data analysis presented is the analysis of the answers to the five perception scales, composed of partial ordered variables, evaluating different aspects of quality and satisfaction.The data was analysed comparing metric and symbolic approaches, using Principal Component Analysis Methods and Agglomerative Hierarchical Cluster Analysis Models. The results suggest that a symbolic approach provides a more comprehensive analysis for this kind of data.

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Cimatti, A., and M. Roveri. "Conformant Planning via Symbolic Model Checking." Journal of Artificial Intelligence Research 13 (December 1, 2000): 305–38. http://dx.doi.org/10.1613/jair.774.

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We tackle the problem of planning in nondeterministic domains, by presenting a new approach to conformant planning. Conformant planning is the problem of finding a sequence of actions that is guaranteed to achieve the goal despite the nondeterminism of the domain. Our approach is based on the representation of the planning domain as a finite state automaton. We use Symbolic Model Checking techniques, in particular Binary Decision Diagrams, to compactly represent and efficiently search the automaton. In this paper we make the following contributions. First, we present a general planning algorithm for conformant planning, which applies to fully nondeterministic domains, with uncertainty in the initial condition and in action effects. The algorithm is based on a breadth-first, backward search, and returns conformant plans of minimal length, if a solution to the planning problem exists, otherwise it terminates concluding that the problem admits no conformant solution. Second, we provide a symbolic representation of the search space based on Binary Decision Diagrams (BDDs), which is the basis for search techniques derived from symbolic model checking. The symbolic representation makes it possible to analyze potentially large sets of states and transitions in a single computation step, thus providing for an efficient implementation. Third, we present CMBP (Conformant Model Based Planner), an efficient implementation of the data structures and algorithm described above, directly based on BDD manipulations, which allows for a compact representation of the search layers and an efficient implementation of the search steps. Finally, we present an experimental comparison of our approach with the state-of-the-art conformant planners CGP, QBFPLAN and GPT. Our analysis includes all the planning problems from the distribution packages of these systems, plus other problems defined to stress a number of specific factors. Our approach appears to be the most effective: CMBP is strictly more expressive than QBFPLAN and CGP and, in all the problems where a comparison is possible, CMBP outperforms its competitors, sometimes by orders of magnitude.

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Shokouhifar, Mohammad, and Ali Jalali. "Simplified Symbolic Gain, CMRR and PSRR Analysis of Analog Amplifiers Using Simulated Annealing." Journal of Circuits, Systems and Computers 25, no. 07 (April 22, 2016): 1650082. http://dx.doi.org/10.1142/s0218126616500821.

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Modeling common-mode rejection ratio (CMRR) and power-supply rejection ratio (PSRR) is of utmost importance during the design of analog integrated circuits. Unfortunately, symbolic analysis suffers from the exponential growing of the complexity of expressions with the circuit size, symbolic simplification techniques should be utilized for the analysis of practical circuits. In this paper, we propose a methodology for the automatic simplified symbolic analysis of gain, CMRR and PSRR in analog amplifiers. We introduce a multi-objective simulated annealing for the simplification of derived symbolic expressions. The fitness function is to minimize the number of symbolic terms while satisfying the optimization constraints. In contrast to the classical criteria which simplify different polynomials separately, the main objective of the proposed criterion is to consider the correlation between different polynomials, during the simplification procedure. The method has been successfully coded in MATLAB and simulated over two analog amplifiers. Comparison of the numerical results extracted from the simplified symbolic expressions with HSPICE demonstrates the efficiency of the proposed methodology.

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Schaeben, Helmut. "Non-Parametric Comparison of Crystallographic Orientation Distributions." Materials Science Forum 1016 (January 2021): 1258–63. http://dx.doi.org/10.4028/www.scientific.net/msf.1016.1258.

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Revisiting a spiral design for X-ray pole figure measurementsand a symbolic definition of a cumulative crystallographic orientation distributiona one-dimensional deterministic approximately uniform sequential design is appliedto evaluate and cumulate a given orientation density function resulting in a properly definedcumulative crystallographic orientation distribution.It provides a complementary means to compare distributionsin terms of graphs and the Kolomogorov-Smirnov distance.

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Fias, Wim, Jan Lammertyn, Bert Reynvoet, Patrick Dupont, and Guy A. Orban. "Parietal Representation of Symbolic and Nonsymbolic Magnitude." Journal of Cognitive Neuroscience 15, no. 1 (January 1, 2003): 47–56. http://dx.doi.org/10.1162/089892903321107819.

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The close behavioral parallels between the processing of quantitative information conveyed by symbolic and non-symbolic stimuli led to the hypothesis that there exists a common cerebral representation of quantity (Dehaene, Dehaene-Lambertz, & Cohen, 1998). The neural basis underlying the encoding of number magnitude has been localized to regions in and around the intraparietal sulcus (IPS) by brain-imaging studies. However, it has never been demonstrated that these same regions are also involved in the quantitative processing of nonsymbolic stimuli. Using functional brain imaging, we explicitly tested the hypothesis of a common substrate. Angles, lines, and two-digit numbers were presented pairwise, one to the left and one to the right of the fixation point. In the three comparison tasks, participants (n = 18) pressed the key on the side of the largest quantity. In the three control tasks, they indicated the side on which dimming occurred. A conjunction analysis between the three subtractions (comparison task-control task) revealed a site in left IPS that is specifically responsive when two stimuli have to be compared quantitatively, irrespective of stimulus format. The results confirm the hypothesis that quantity is represented by a common mechanism for both symbolic and nonsymbolic stimuli in IPS. In addition, the interaction between task and type of stimulus identified a region anterior to the conjunction site, not specific for quantitative processing, but reflecting general processes loaded by number processing.

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Rousselle, Laurence, and Marie-Pascale Noël. "Basic numerical skills in children with mathematics learning disabilities: A comparison of symbolic vs non-symbolic number magnitude processing." Cognition 102, no. 3 (March 2007): 361–95. http://dx.doi.org/10.1016/j.cognition.2006.01.005.

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North, Michael. "The Sea as Site of Memory: The Danish Sound and the Dardanelles in Comparison." Romanian Journal for Baltic and Nordic Studies 6, no. 1 (December 15, 2014): 65–79. http://dx.doi.org/10.53604/rjbns.v6i1_3.

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This paper introduces the concept of the sea as lieu de mémoire into maritime history. Pierre Nora has developed his „Lieux de mémoire” in France. According to Nora „a lieu de mémoire is any significant entity, whether material or non-material in nature […] which has become a symbolic element of the memorial heritage of any community”. Nora thus highlights symbolic values, hitherto often separated from historical sciences and reduced to historical narratives. In my paper I shall focus on shared memories, divided memories and entangled histories, but especially shared sites of memory. These – material or immaterial – „lieux de mémoire divisés” constitute symbolic intersections between cultures, spaces and times. They simultaneously affect not only the neighbouring countries and the national cultures of memory, but also societies and ethnic or religious groups. In two comparative case studies on the straits of the Sound (Oresund) and Dardanelles I shall try to test the application of the concept with respect to the various memories of the seafaring nations and ethnic communities, settling at the entrance of the Baltic Sea and the Black Sea.

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Oriet, Chris, Michael Tombu, and Pierre Jolicoeur. "Symbolic distance affects two processing loci in the number comparison task." Memory & Cognition 33, no. 5 (July 2005): 913–26. http://dx.doi.org/10.3758/bf03193085.

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Foggia, P., R. Genna, and M. Vento. "Symbolic vs. connectionist learning: an experimental comparison in a structured domain." IEEE Transactions on Knowledge and Data Engineering 13, no. 2 (2001): 176–95. http://dx.doi.org/10.1109/69.917559.

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Ferent, Cristian, and Alex Doboli. "Symbolic Matching and Constraint Generation for Systematic Comparison of Analog Circuits." IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 32, no. 4 (April 2013): 616–29. http://dx.doi.org/10.1109/tcad.2012.2234826.

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Khan, Rao F. H., and N. Ahmad. "A comparison of symbolic solution of radioactive decay chains using Mathematica." ACM SIGSAM Bulletin 33, no. 3 (September 1999): 20. http://dx.doi.org/10.1145/347127.347336.

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Mussolin, Christophe, Sandrine Mejias, and Marie-Pascale Noël. "Symbolic and nonsymbolic number comparison in children with and without dyscalculia." Cognition 115, no. 1 (April 2010): 10–25. http://dx.doi.org/10.1016/j.cognition.2009.10.006.

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Sasanguie, Delphine, Ian M. Lyons, Bert De Smedt, and Bert Reynvoet. "Unpacking symbolic number comparison and its relation with arithmetic in adults." Cognition 165 (August 2017): 26–38. http://dx.doi.org/10.1016/j.cognition.2017.04.007.

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Pełka, Marcin, and Andrzej Dudek. "The Comparison of Fuzzy Clustering Methods for Symbolic Interval-Valued Data." Przegląd Statystyczny 62, no. 3 (September 30, 2015): 301–19. http://dx.doi.org/10.5604/01.3001.0014.1755.

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Interval-valued data can find their practical applications in such situations as recording monthly interval temperatures at meteorological stations, daily interval stock prices, etc. The primary objective of the presented paper is to compare three different methods of fuzzy clustering for interval-valued symbolic data, i.e.: fuzzy c-means clustering, adaptive fuzzy c-means clustering and fuzzy k-means clustering with fuzzy spectral clustering. Fuzzy spectral clustering combines both spectral and fuzzy approaches in order to obtain better results (in terms of Rand index for fuzzy clustering). The conducted simulation studies with artificial and real data sets confirm both higher usefulness and more stable results of fuzzy spectral clustering method, as compared to other existing fuzzy clustering methods for symbolic interval-valued data, when dealing with data featuring different cluster structures, noisy variables and/or outliers.

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Whitehead, Andrew L., and Christopher P. Scheitle. "We the (Christian) People: Christianity and American Identity from 1996 to 2014." Social Currents 5, no. 2 (August 17, 2017): 157–72. http://dx.doi.org/10.1177/2329496517725333.

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Religious identity, and specifically Christian identity, has long been a dominant symbolic boundary marker for inclusion into American society. But how has the salience of this boundary marker changed in recent years and in comparison to other boundary markers? Using multiple waves of the General Social Survey, we investigate temporal variation in the use of religion and other markers in constructing symbolic boundaries around American identity. First, we find that the Christian symbolic boundary both increased from 1996 to 2004 and declined from 2004 to 2014. Second, this pattern was not unique; in addition to the Christian symbolic boundary, Americans used a variety of both civic and ascriptive boundary markers to define American identity. However, our analysis also demonstrates that in 2004, the Christian symbolic boundary was significantly linked to national identity in a unique way while the other boundary markers were not. These results suggest that period effects and cultural events can influence the salience of religion in creating national symbolic boundaries. We discuss each of these findings, their relationship to the study of symbolic boundaries and American identity, and their societal implications.

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Journal articles on the topic 'Symbolic comparison'

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