Relevant bibliographies by topics / Numerical representations

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Numerical representations'

Author: Grafiati
Published: 4 June 2021
Last updated: 26 April 2022

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Journal articles on the topic "Numerical representations"

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Siegler, Robert S., and John E. Opfer. "The Development of Numerical Estimation." Psychological Science 14, no. 3 (2003): 237–50. http://dx.doi.org/10.1111/1467-9280.02438.

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We examined children's and adults' numerical estimation and the representations that gave rise to their estimates. The results were inconsistent with two prominent models of numerical representation: the logarithmic-ruler model, which proposes that people of all ages possess a single, logarithmically spaced representation of numbers, and the accumulator model, which proposes that people of all ages represent numbers as linearly increasing magnitudes with scalar variability. Instead, the data indicated that individual children possess multiple numerical representations; that with increasing age and numerical experience, they rely on appropriate representations increasingly often; and that the numerical context influences their choice of representation. The results, obtained with second graders, fourth graders, sixth graders, and adults who performed two estimation tasks in two numerical contexts, strongly suggest that one cause of children's difficulties with estimation is reliance on logarithmic representations of numerical magnitudes in situations in which accurate estimation requires reliance on linear representations.
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Zhang, Jiajie, and Hongbin Wang. "The Effect of External Representations on Numeric Tasks." Quarterly Journal of Experimental Psychology Section A 58, no. 5 (2005): 817–38. http://dx.doi.org/10.1080/02724980443000340.

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This article explores the effect of external representations on numeric tasks. Through several minor modifications on the previously reported two-digit number comparison task, we obtained different results. Rather than holistic comparison, we found parallel comparison. We argue that this difference was a reflection of different representational forms: The comparison was based on internal representations in previous studies but on external representations in our present study. This representational effect is discussed under a framework of distributed number representations. We propose that in numerical tasks involving external representations, numbers should be considered as distributed representations, and the behaviour in these tasks should be considered as the interactive processing of internal and external information through the interplay of perceptual and cognitive processes. We suggest that theories of number representations and process models of numerical cognition should consider external representations as an essential component.
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Hauser, M. D., P. MacNeilage, and M. Ware. "Numerical representations in primates." Proceedings of the National Academy of Sciences 93, no. 4 (1996): 1514–17. http://dx.doi.org/10.1073/pnas.93.4.1514.

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Cohen, Dale J. "Numerical representations are neither abstract nor automatic." Behavioral and Brain Sciences 32, no. 3-4 (2009): 332–33. http://dx.doi.org/10.1017/s0140525x09990549.

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AbstractIn this commentary, I support and augment Cohen Kadosh & Walsh's (CK&W's) argument that numerical representations are not abstract. I briefly review data that support the non-abstract nature of the representation of numbers between zero and one, and I discuss how a failure to test alternative hypotheses has led researchers to erroneously conclude that numerals automatically activate their semantic meaning.
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Buijsman, Stefan, and Carlos Tirado. "Spatial–numerical associations: Shared symbolic and non-symbolic numerical representations." Quarterly Journal of Experimental Psychology 72, no. 10 (2019): 2423–36. http://dx.doi.org/10.1177/1747021819844503.

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During the last decades, there have been a large number of studies into the number-related abilities of humans. As a result, we know that humans and non-human animals have a system known as the approximate number system that allows them to distinguish between collections based on their number of items, separately from any counting procedures. Dehaene and others have argued for a model on which this system uses representations for numbers that are spatial in nature and are shared by our symbolic and non-symbolic processing of numbers. However, there is a conflicting theoretical perspective in which there are no representations of numbers underlying the approximate number system, but only quantity-related representations. This perspective would then suggest that there are no shared representations between symbolic and non-symbolic processing. We review the evidence on spatial biases resulting from the activation of numerical representations, for both non-symbolic and symbolic tests. These biases may help decide between the theoretical differences; shared representations are expected to lead to similar biases regardless of the format, whereas different representations more naturally explain differences in biases, and thus behaviour. The evidence is not yet decisive, as the behavioural evidence is split: we expect bisection tasks to eventually favour shared representations, whereas studies on the spatial–numerical association of response codes (SNARC) effect currently favour different representations. We discuss how this impasse may be resolved, in particular, by combining these behavioural studies with relevant neuroimaging data. If this approach is carried forward, then it may help decide which of these two theoretical perspectives on number representations is correct.
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Falter, Christine M., Valdas Noreika, Julian Kiverstein, and Bruno Mölder. "Concrete magnitudes: From numbers to time." Behavioral and Brain Sciences 32, no. 3-4 (2009): 335–36. http://dx.doi.org/10.1017/s0140525x09990045.

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AbstractCohen Kadosh & Walsh (CK&W) present convincing evidence indicating the existence of notation-specific numerical representations in parietal cortex. We suggest that the same conclusions can be drawn for a particular type of numerical representation: the representation of time. Notation-dependent representations need not be limited to number but may also be extended to other magnitude-related contents processed in parietal cortex (Walsh 2003).
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Prather, Richard. "Individual differences in numerical comparison is independent of numerical precision." Journal of Numerical Cognition 5, no. 2 (2019): 220–40. http://dx.doi.org/10.5964/jnc.v5i2.164.

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Numeracy, as measured by performance on the non-symbolic numerical comparison task, is a key construct in numerical and mathematical cognition. The current study examines individual variation in performance on the numerical comparison task. We contrast the hypothesis that performance on the numerical comparison task is primarily due to more accurate representations of numbers with the hypothesis that performance dependent on decision-making factors. We present data from two behavioral experiments and a mathematical model. In both behavioral experiments we measure the precision of participant’s numerical value representation using a free response estimation task. Taken together, results suggest that individual variation in numerical comparison performance is not predicted by variation in the precision of participants’ numerical value representation.
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Smilde, Age K., and Thomas Hankemeier. "Numerical Representations of Metabolic Systems." Analytical Chemistry 92, no. 20 (2020): 13614–21. http://dx.doi.org/10.1021/acs.analchem.9b05613.

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Zhao, Jiaying, and Ru Yu. "Statistical regularities compress numerical representations." Journal of Vision 15, no. 12 (2015): 390. http://dx.doi.org/10.1167/15.12.390.

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Pesenti, Mauro, and Michael Andres. "Common mistakes about numerical representations." Behavioral and Brain Sciences 32, no. 3-4 (2009): 346–47. http://dx.doi.org/10.1017/s0140525x09990835.

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AbstractCohen Kadosh & Walsh (CK&W) argue that recent findings challenge the hypothesis of abstract numerical representations. Here we show that because, like many other authors in the field, they rely on inaccurate definitions of abstract and non-abstract representations, CK&W fail to provide compelling evidence against the abstract view.
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Dissertations / Theses on the topic "Numerical representations"

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Thompson, Clarissa Ann. "The Representational Alignment Hypothesis of Transfer of Numerical Representations." The Ohio State University, 2008. http://rave.ohiolink.edu/etdc/view?acc_num=osu1211376719.

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Davies, Nigel Howard. "Numerical representations of fluid mixing." Thesis, University of South Wales, 1993. https://pure.southwales.ac.uk/en/studentthesis/numerical-representations-of-fluid-mixing(3bf1cb31-ec80-49f2-95ae-a2f56eeeeec2).html.

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The work contained within this thesis is concerned with a theoretical investigatiop of both laminar and thermally driven types of cavity flow, together with an analysis of their associated mixing processes which find applications to Industrial mixing and also to the environment. The mixing efficiency has been viewed from two perspectives namely the tracking of a selection of fluid particles, and also the simulation of the dispersive mixing of a coloured fluid element as carried along by the flow. This thesis also incorporates features of both Newtonian and a wide range of non-Newtonian fluids.
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Mitchell, Thomas. "Activation of numerical representations : sources of variability." Thesis, University of Aberdeen, 2015. http://digitool.abdn.ac.uk:80/webclient/DeliveryManager?pid=227222.

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This thesis presents an investigation into sources of variability in activating and processing numerical information. Chapter 1 provides an overview of research literature exploring the ways in which magnitude information can be represented, and how models relating to number information have developed. These theoretical models are addressed in relation to the neural representation of number, and the range of behavioural markers which suggest an association between spatial and numerical processing. Chapter 2 using a dual-task paradigm investigated whether magnitude information is accessed on perceiving numbers, or if this information is linked to response selection or execution. Previous research studies investigating this question produced inconsistent findings (Oriet, Tombu & Jolicoeur, 2005; Sigman & Dehaene, 2005) with regard to the locus of magnitude processing; the findings of Experiments 1-3 reliably support access to magnitude information during response selection. Chapter 3 explored the activation of spatial-numerical response associations, where response-irrelevant magnitude information was not represented by a single stimulus (i.e. an Arabic digit) but by a numerosity representation. Experiments 4-7 found a strong association between spatial-orientation processing and numerical magnitude, but no association with perceptual-colour processing, extending previous work by Fias, Lammertyn and Lauwereyns (2001) regarding the neural overlap between the attended and irrelevant stimulus dimensions. However the strength of this association was found to be inconsistent across the number range. Chapter 4 investigated the impact of healthy aging on the presence of neural-overlap in processing spatial-numerical information, further developing the paradigm used in Chapter 3, and addressed direct predictions from the literature as to how age should influence these associations (Wood, Willmes, Nuerk & Fischer, 2008). Experiments 8-11 found evidence for spatial-numerical associations across the lifespan, but that the strength of these effects were moderated by 5 task instruction. Chapter 5 was designed to assess aging differences in numerical and spatial processing with a battery of tests and the extent to which other sources of individual difference (sex, embodiment) have a measureable impact. A range of standardised measures were used to assess verbal ability, mathematical processing, and spatial working memory alongside behavioural measures of spatial numerical associations. Experiment 12 provided evidence of aging and sex differences in different cognitive tasks and a marginal impact of embodiment on spatial-numerical processing; however the effect of embodiment was not supported in a larger more homogenous sample in Experiment 13. Chapter 6 reflects on the current findings and provides contextual information on how they align with previous research, outlining how evidence from the thesis extend current research paradigms and provides new evidence regarding the maintenance of spatial-numerical associations in healthy aging. Methodologies developed in the thesis are considered with relation to how they may be applied to assess individual differences in early number acquisition in children. Finally the discussion outlines methods and controversies within the field of numerical cognition, with consideration of new methods for measuring the strength of spatial-numerical associations (Pinhas, Tzelgov, & Ganor-Stern, 2012), alongside the potential application of modelling techniques to investigate individual differences in task performance.
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Shen, Tianrui. "Mental abacus and innate non-verbal numerical representations." Thesis, University of Cambridge, 2010. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.608681.

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Marciani, Francesca. "Numeric Memory: Developing Representations." The Ohio State University, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=osu1365697597.

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Lou, Zhenjun. "Kinematic representations and numerical methods in precision position synthesis of mechanisms." Thesis, King's College London (University of London), 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.429316.

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Ferres, Forga Nuria 1968. "Improving mathematical abilities by training numerical representations in children : the relation between learning mathematics and numerical cognition." Doctoral thesis, Universitat Pompeu Fabra, 2018. http://hdl.handle.net/10803/663849.

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Improving mathematical abilities is important for educational systems and for society overall. We present two training regimes based on numerical representations. In Study 1, we show that a three-week computer-based quantity discrimination training, focused on enhancing the accuracy of the Approximate Number System (ANS), improved mathematics performance in low-performing 7-to-8-year-old children. In Study 2, we show that a novel numerical estimation training enhancing mappings between Arabic digits and quantities, improved overall mathematical competence in all children, going beyond the improvements obtained by training ANS. In Study 3, we show that performance in both trainings correlate, in different extend, with school math marks, but we especially found a consistent and extended relation between the ability of mapping digits to quantities and the school math marks in pupils from 8 to 13 years of age. Thus, training the precision of the digit-quantity relation may improve mathematical competence, particularly in the first crucial years of exposure to formal mathematics.<br>La millora de les habilitats matemàtiques es un objectiu important pels sistemes educatius i per la societat en general. Aquí presentem dos entrenaments basats en representacions numèriques. A l’estudi 1, mostrem com entrenant la discriminació de quantitats durant tres setmanes amb la intenció de fer més precís el Sistema d’Aproximació Numèric (ANS), millora el rendiment matemàtic del nens de 7-8 anys de baix perfil acadèmic A l’estudi 2, mostrem com un inèdit entrenament d’estimació numèrica dissenyat per incrementar la precisió en relacionar els dígits Aràbics amb les quantitats que representen, provoca una millora generalitzada de la competència matemàtica en tots els perfils acadèmics en nens de 7 a 8 anys. A l’estudi 3, mostrem com el rendiment en els dos entrenaments correlaciona amb les notes de matemàtiques a l’escola encara que en diferent mesura, essent l’habilitat de relacionar els dígits amb les quantitats, la que correlaciona amb les notes en més cursos escolars, des dels 8 anys fins als 13. Així, entrenar la precisió en relacionar els dígits amb quantitats provoca una millora de la competència matemàtica, sobretot en els primers anys crucials d'exposició a les matemàtiques formals.
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Koutoumbas, Anastasios M. "Bidirectional and unidirectional spectral representations for the scalar wave equation." Thesis, Virginia Tech, 1990. http://hdl.handle.net/10919/41904.

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<p>The Cauchy problem associated with the scalar wave equation in free space is used as a vehicle for a critical examination and assessment of the bidirectional and unidirectional spectral representations. These two novel methods for synthesizing wave signals are distinct from the superposition principle underlying the conventional Fourier method and they can effectively be used to derive a large class of localized solutions to the scalar wave equation. The bidirectional spectral representation is presented as an extension of Brittingham's ansatz and Ziolkowski's Focus Wave Mode spectral representations. On the other hand, the unidirectional spectral representation is motivated through a group-theoretic similarity reduction of the scalar wave equation.</p><br>Master of Science
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Hurst, Michelle Ann Roddy. "Exploring Attention to Numerical Features in Proportional Reasoning: The Role of Representations, Context, and Individual Differences." Thesis, Boston College, 2017. http://hdl.handle.net/2345/bc-ir:107599.

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Thesis advisor: Sara Cordes<br>Human infants show relatively sophisticated abilities to track and use proportional information. However, by the age of 6, children tend to make predictable errors in their proportional reasoning and later encounter significant challenges in many aspects of formal fraction learning. Thus, one of the central questions motivating this research is to identify the factors leading to these difficulties, in light of evidence of early intuitions about these concepts. In the current dissertation, I address this question by investigating the tradeoff between attending to proportional magnitude information and discrete numerical information about the components (termed “numerical interference”) across both spatial (i.e., area models, number lines) and symbolic (fractions, decimals) representations of proportion information. These explorations focus on young children (5-7 year olds) who have yet to receive formal fraction instruction, older children (9-12 year olds) who are in the process of learning these concepts, and adults who have already learned formal fractions. In Project 1, I investigated how older children and adults map between symbolic and spatial representations, particularly focusing on their strategies in highlighting componential information versus magnitude information when solving these mapping tasks. In Projects 2 and 3, I explore the malleability of individual differences in this numerical interference in 4- to 7-year-old children. Across the three projects, I suggest that although numerical interference does impact proportional reasoning, this over-attention to number can be reduced through modifying early experiences with proportional information. These findings have implications for education and the way we conceptualize numerical interference more generally<br>Thesis (PhD) — Boston College, 2017<br>Submitted to: Boston College. Graduate School of Arts and Sciences<br>Discipline: Psychology
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Harries, Tony, and Patrick Barmby. "The importance of using representations to help primary pupils give meaning to numerical concepts." Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2012. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-82542.

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Books on the topic "Numerical representations"

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Blackett, Norman. Developing understanding of trigonometry in boys and girls using a computer to link numerical and visual representations. typescript, 1990.

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Canada. Defence Research Establishment Atlantic. Numerical Representation of Hulls with Knuckles. s.n, 1986.

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Myers, Cory S. Signal representation for symbolic and numerical processing. Massachusetts Institute of Technology, Research Laboratory of Electronics, 1986.

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Walmsley, N. The numerical representation of pump-turbine performance characteristics. typescript, 1986.

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Emanuel, Kerry A., and David J. Raymond, eds. The Representation of Cumulus Convection in Numerical Models. American Meteorological Society, 1993. http://dx.doi.org/10.1007/978-1-935704-13-3.

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Stone, Dan N. Numeric and linguistic information representation in multiattribute choice. College of Commerce and Business Administration, University of Illinois at Urbana-Champaign, 1989.

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Madej, Łukasz. Development of the modelling strategy for the strain localization simulation based on the digital material representation. AGH University of Science and Technology Press, 2010.

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Pawlak, Zdzisław. Rough sets: Theoretical aspects of reasoning about data. Kluwer Academic Publishers, 1991.

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David, Hutchison. Transactions on Computational Science V: Special Issue on Cognitive Knowledge Representation. Springer Berlin Heidelberg, 2009.

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Spadacini, Lorenzo. Regole elettorali e integrità numerica delle Camere: La mancata assegnazione di alcuni seggi alla Camera nella 14. legislatura. Promodis Italia, 2003.

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Book chapters on the topic "Numerical representations"

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Turner, Peter R. "Number Representations and Errors." In Guide to Numerical Analysis. Macmillan Education UK, 1989. http://dx.doi.org/10.1007/978-1-349-09784-5_1.

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Regoli, Giuliana. "Rational Comparisons and Numerical Representations." In Decision Theory and Decision Analysis: Trends and Challenges. Springer Netherlands, 1994. http://dx.doi.org/10.1007/978-94-011-1372-4_8.

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Wahab, M. A. "Unit Cell Symmetries and Their Representations." In Numerical Problems in Crystallography. Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-15-9754-1_6.

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Wahab, M. A. "Unit Cell Representations of Miller Indices." In Numerical Problems in Crystallography. Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-15-9754-1_4.

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Gay, David M. "Revisiting Expression Representations for Nonlinear AMPL Models." In Numerical Analysis and Optimization. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-90026-1_5.

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Gatermann, Karin. "Linear Representations of Finite Groups and The Ideal Theoretical Construction of G-Invariant Cubature Formulas." In Numerical Integration. Springer Netherlands, 1992. http://dx.doi.org/10.1007/978-94-011-2646-5_2.

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Delfour, Michel C. "Representations, Composition, and Decomposition of C 1,1-hypersurfaces." In International Series of Numerical Mathematics. Birkhäuser Basel, 2009. http://dx.doi.org/10.1007/978-3-7643-8923-9_5.

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Pop, G. P., and E. Onaca. "Numerical Representations in Alpha Satellite DNA Analysis." In IFMBE Proceedings. Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-04292-8_48.

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Platen, Eckhard, and Nicola Bruti-Liberati. "Martingale Representations and Hedge Ratios." In Numerical Solution of Stochastic Differential Equations with Jumps in Finance. Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-13694-8_15.

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Wiśniewski, K. "Operations on tensors and their representations." In Lecture Notes on Numerical Methods in Engineering and Sciences. Springer Netherlands, 2009. http://dx.doi.org/10.1007/978-90-481-8761-4_2.

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Conference papers on the topic "Numerical representations"

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Jaroszewicz, Szymon, and Marcin Korzeń. "Approximating Representations for Large Numerical Databases." In Proceedings of the 2007 SIAM International Conference on Data Mining. Society for Industrial and Applied Mathematics, 2007. http://dx.doi.org/10.1137/1.9781611972771.55.

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Rajković, Milan, Milena Stanković, Ivica Marković, et al. "A Template Engine for Parsing Objects from Textual Representations." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2011: International Conference on Numerical Analysis and Applied Mathematics. AIP, 2011. http://dx.doi.org/10.1063/1.3636860.

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Szwabowicz, Marek L., Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "Medial Representations for Shells of Variable Thickness." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS: International Conference on Numerical Analysis and Applied Mathematics 2009: Volume 1 and Volume 2. AIP, 2009. http://dx.doi.org/10.1063/1.3241478.

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Sozen, Yasar. "Reidemeister torsion of Hitchin representations of PSp[sub 2n](R)." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2012: International Conference of Numerical Analysis and Applied Mathematics. AIP, 2012. http://dx.doi.org/10.1063/1.4756196.

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Keller, Jaime, and Pierre Anglès. "Representations of the Clifford Algebra Cl(1,4) and their relevance for Physics." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS: International Conference on Numerical Analysis and Applied Mathematics 2008. American Institute of Physics, 2008. http://dx.doi.org/10.1063/1.2991014.

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Afanasieva, T., N. Yarushkina, and I. Sibirev. "Time series clustering using numerical and fuzzy representations." In 2017 Joint 17th World Congress of International Fuzzy Systems Association and 9th International Conference on Soft Computing and Intelligent Systems (IFSA-SCIS). IEEE, 2017. http://dx.doi.org/10.1109/ifsa-scis.2017.8023356.

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Pop, Petre G., and Alin Voina. "DNA repeats detection using numerical representations and dot plot analysis." In 2010 9th International Symposium on Electronics and Telecommunications (ISETC 2010). IEEE, 2010. http://dx.doi.org/10.1109/isetc.2010.5679258.

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Akhtar, Mahmood, Julien Epps, and Eliathamby Ambikairajah. "On DNA Numerical Representations for Period-3 Based Exon Prediction." In 2007 IEEE International Workshop on Genomic Signal Processing and Statistics. IEEE, 2007. http://dx.doi.org/10.1109/gensips.2007.4365821.

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Wei, Yiheng, YangQuan Chen, Peter W. Tse, and Songsong Cheng. "Analytical and numerical representations for discrete Grünwald–Letnikov fractional calculus." In 2020 Chinese Automation Congress (CAC). IEEE, 2020. http://dx.doi.org/10.1109/cac51589.2020.9327090.

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Bruns, Morgan, and Christiaan J. J. Paredis. "Numerical Methods for Propagating Imprecise Uncertainty." In ASME 2006 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2006. http://dx.doi.org/10.1115/detc2006-99237.

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Since engineering design requires decision making under uncertainty, the degree to which good decisions can be made depends upon the degree to which the decision maker has expressive and accurate representations of his or her uncertain beliefs. Whereas traditional decision analysis uses precise probability distributions to represent uncertain beliefs, recent research has examined the effects of relaxing this assumption of precision. A specific example of this is the theory of imprecise probability. Imprecise probabilities are more expressive than precise probabilities, but they are also more computationally expensive to propagate through mathematical models. The probability box (p-box) is an alternative representation that is both more expressive than precise probabilities, and less computationally expensive than general imprecise probabilities. In this paper, we introduce a method for propagating p-boxes through black box models. Based on two example models, a new method, called p-box convolution sampling (PCS), is compared with three other p-box propagation methods. It is found that, although PCS is less expensive than the alternatives, it is still relatively expensive and therefore only justifiable when the expected benefits are large. Several directions for further improving the efficiency of PCS are discussed.
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Reports on the topic "Numerical representations"

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Chacon, Luis, Guangye Chen, William Taitano, Andrei N. Simakov, and Daniel C. Barnes. Implicit, manifold-preserving numerical representations and solvers for multiscale kinetic simulations of plasmas. Office of Scientific and Technical Information (OSTI), 2019. http://dx.doi.org/10.2172/1496736.

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Goodman, I. R. Algebraic Representations of Linguistic and Numerical Modifications of Probability Statements and Inferences Based on a Product Space Construction. Defense Technical Information Center, 1996. http://dx.doi.org/10.21236/ada306334.

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Oppenheim, Alan. Numerical and Symbolic Signal Representation and Processing. Defense Technical Information Center, 1991. http://dx.doi.org/10.21236/ada235621.

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Repin, Dmitry, and Stephen Grossberg. A Neural Model of Multidigit Numerical Representation and Comparison. Defense Technical Information Center, 2001. http://dx.doi.org/10.21236/ada529819.

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Larson, Magnus, and Nicholas C. Kraus. SBEACH: Numerical Model for Simulating Storm-Induced Beach Change. Report 5: Representation of Nonerodible (Hard) Bottoms. Defense Technical Information Center, 1998. http://dx.doi.org/10.21236/ada354783.

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Tselioudis, George. Advancing cloud lifecycle representation in numerical models using innovative analysis methods that bridge arm observations over a breadth of scales. Office of Scientific and Technical Information (OSTI), 2016. http://dx.doi.org/10.2172/1240272.

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Kollias, Pavlos. Advancing Clouds Lifecycle Representation in Numerical Models Using Innovative Analysis Methods that Bridge ARM Observations and Models Over a Breadth of Scales. Office of Scientific and Technical Information (OSTI), 2016. http://dx.doi.org/10.2172/1319810.

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