Relevant bibliographies by topics / Approximate magnitudes

Academic literature on the topic 'Approximate magnitudes'

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Published: 10 December 2022
Last updated: 28 January 2023

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Journal articles on the topic "Approximate magnitudes"

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Sullivan, Jessica, and David Barner. "How are number words mapped to approximate magnitudes?" Quarterly Journal of Experimental Psychology 66, no. 2 (February 2013): 389–402. http://dx.doi.org/10.1080/17470218.2012.715655.

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Birol, İnanç, and Avadis Hacinliyan. "Signs and approximate magnitudes of Lyapunov exponents in continuous time dynamical systems." Journal of Mathematical Physics 38, no. 9 (September 1997): 4594–605. http://dx.doi.org/10.1063/1.532109.

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Obersteiner, Andreas, and Veronika Hofreiter. "Do we have a sense for irrational numbers?" Journal of Numerical Cognition 2, no. 3 (February 10, 2017): 170–89. http://dx.doi.org/10.5964/jnc.v2i3.43.

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Number sense requires, at least, an ability to assess magnitude information represented by number symbols. Most educated adults are able to assess magnitude information of rational numbers fairly quickly, including whole numbers and fractions. It is to date unclear whether educated adults without training are able to assess magnitudes of irrational numbers, such as the cube root of 41. In a computerized experiment, we asked mathematically skilled adults to repeatedly choose the larger of two irrational numbers as quickly as possible. Participants were highly accurate on problems in which reasoning about the exact or approximate value of the irrational numbers’ whole number components (e.g., 3 and 41 in the cube root of 41) yielded the correct response. However, they performed at random chance level when these strategies were invalid and the problem required reasoning about the irrational number magnitudes as a whole. Response times suggested that participants hardly even tried to assess magnitudes of the irrational numbers as a whole, and if they did, were largely unsuccessful. We conclude that even mathematically skilled adults struggle with quickly assessing magnitudes of irrational numbers in their symbolic notation. Without practice, number sense seems to be restricted to rational numbers.
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Guo, Yueming, Philip Nakashima, and Joanne Etheridge. "Structure factor measurement by 3-beam convergent beam electron diffraction." Acta Crystallographica Section A Foundations and Advances 70, a1 (August 5, 2014): C1623. http://dx.doi.org/10.1107/s2053273314083764.

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It has been shown mathematically that both the magnitudes and 3-phase invariants of the structure factors of a centrosymmetric crystal can be expressed explicitly in terms of the distances to specific features in the 3-beam convergent beam electron diffraction (CBED) pattern [1].This theoretical inversion can be implemented experimentally, enabling direct observations of 3-phase invariants and the approximate measurement of structure factor magnitudes. This method then enables a different approach to crystal structure determination, which is based on the observation of phases, rather than the measurement of amplitudes. It has been shown that by inspection of just a few phases using 3-beam CBED patterns, centrosymmetric crystal structures can be determined directly to picometre precision without the need to measure magnitudes [2]. Here, we will explore a different approach for measuring structure factor magnitudes from 3-beam CBED patterns. It has been demonstrated that the relative structure factor magnitudes can be determined directly from the ratio of the intensity distributions along specific lines within the CBED discs [3]. We will investigate the potential of using this approach for the relatively fast measurement of approximate structure factor magnitudes from nano-scale volumes of crystals.
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Ebaid, Abdelhalim, Weam Alharbi, Mona D. Aljoufi, and Essam R. El-Zahar. "The Exact Solution of the Falling Body Problem in Three-Dimensions: Comparative Study." Mathematics 8, no. 10 (October 8, 2020): 1726. http://dx.doi.org/10.3390/math8101726.

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Very recently, the system of differential equations governing the three-dimensional falling body problem (TDFBP) has been approximately solved. The previously obtained approximate solution was based on the fact that the Earth’s rotation (ER) is quite slow and hence all high order terms of ω in addition to the magnitude ω2R were neglected, where ω is the angular velocity and R is the radius of Earth. However, it is shown in this paper that the ignorance of such magnitudes leads, in many cases, to significant errors in the estimated falling time and other physical quantities. The current results are based on obtaining the exact solutions of the full TDFBP-system and performing several comparisons with the approximate ones in the relevant literature. The obtained results are of great interest and importance, especially for other planets in the Solar System or exterior planets, in which ω and/or ω2R are of considerable amounts and hence cannot be ignored. Therefore, the present analysis is valid in analyzing the TDFBP near to the surface of any spherical celestial body.
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Ganor-Stern, Dana. "Can Dyscalculics Estimate the Results of Arithmetic Problems?" Journal of Learning Disabilities 50, no. 1 (August 4, 2016): 23–33. http://dx.doi.org/10.1177/0022219415587785.

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The present study is the first to examine the computation estimation skills of dyscalculics versus controls using the estimation comparison task. In this task, participants judged whether an estimated answer to a multidigit multiplication problem was larger or smaller than a given reference number. While dyscalculics were less accurate than controls, their performance was well above chance level. The performance of controls but not of those with developmental dyscalculia (DD) improved consistently for smaller problem sizes. The performance of both groups was superior when the reference number was smaller (vs. larger) than the exact answer and when it was far (vs. close) from it, both of which are considered to be the markers of the approximate number system (ANS). Strategy analysis distinguished between an approximated calculation strategy and a sense of magnitude strategy, which does not involve any calculation but relies entirely on the ANS. Dyscalculics used the latter more often than controls. The present results suggest that there is little, if any, impairment in the ANS of adults with DD and that their main deficiency is with performing operations on magnitudes rather than with the representations of the magnitudes themselves.
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Stock, J., and C. Abad. "Recovery of the Astrographic Catalogue." Symposium - International Astronomical Union 133 (1988): 171–76. http://dx.doi.org/10.1017/s0074180900139580.

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An almost fully automatic scheme has been developed which produces final positions in the system determined by the reference catalogue, cross identifications, and approximate magnitudes in a standard system. A plate-overlap method is used which permits inclusion of higher order terms either plate by plate or common to a subset of plates. Magnitude dependent errors are also included. The system has already been applied to more than 500 plates, most of them of the Paris zone, with smaller sets of the Oxford, Potsdam, and Helsingfors zones. The Paris zone yields consistent higher order and magnitude terms over the entire set analyzed so far.
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Kuhn, Jörg-Tobias. "Developmental Dyscalculia." Zeitschrift für Psychologie 223, no. 2 (July 10, 2015): 69–82. http://dx.doi.org/10.1027/2151-2604/a000205.

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Developmental dyscalculia (DD) is a specific learning disorder that affects the acquisition of arithmetic skills and number processing in children. A high comorbidity between DD and other neurodevelopmental disorders (e.g., dyslexia, attention-deficit/hyperactivity disorder [ADHD]) as well as substantial heterogeneity in cognitive profiles have been reported. Current studies indicate that DD is persistent, has a genetic component, and is related to functional and structural alterations of brain areas involved in magnitude representation. Recent neuronal and behavioral evidence is presented, showing that DD entails (a) impairments in two preverbal core systems of number, an approximate system for estimating larger magnitudes and an exact system for representing small magnitudes, (b) deficits in symbolic number processing, (c) aberrant and nonadaptive neuronal activation in basic magnitude processing and calculation, (d) dysfunctional arithmetic fact retrieval and persistent use of counting strategies in calculation, and (e) deficits in visuospatial working memory and the central executive. Finally, open research questions, including the role of domain-general cognitive resources in DD, causes and developmental consequences of comorbidity, as well as design and evaluation of interventions for DD, are briefly discussed.
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Hyde, Daniel C., and Justin N. Wood. "Spatial Attention Determines the Nature of Nonverbal Number Representation." Journal of Cognitive Neuroscience 23, no. 9 (September 2011): 2336–51. http://dx.doi.org/10.1162/jocn.2010.21581.

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Coordinated studies of adults, infants, and nonhuman animals provide evidence for two systems of nonverbal number representation: a “parallel individuation” system that represents individual items and a “numerical magnitude” system that represents the approximate cardinal value of a group. However, there is considerable debate about the nature and functions of these systems, due largely to the fact that some studies show a dissociation between small (1–3) and large (>3) number representation, whereas others do not. Using event-related potentials, we show that it is possible to determine which system will represent the numerical value of a small number set (1–3 items) by manipulating spatial attention. Specifically, when attention can select individual objects, an early brain response (N1) scales with the cardinal value of the display, the signature of parallel individuation. In contrast, when attention cannot select individual objects or is occupied by another task, a later brain response (P2p) scales with ratio, the signature of the approximate numerical magnitude system. These results provide neural evidence that small numbers can be represented as approximate numerical magnitudes. Further, they empirically demonstrate the importance of early attentional processes to number representation by showing that the way in which attention disperses across a scene determines which numerical system will deploy in a given context.
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Du, Qinghui, and Chaoli Wang. "Convergence Analysis of Semi-Implicit Euler Methods for Solving Stochastic Age-Dependent Capital System with Variable Delays and Random Jump Magnitudes." Mathematical Problems in Engineering 2014 (2014): 1–12. http://dx.doi.org/10.1155/2014/460530.

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We consider semi-implicit Euler methods for stochastic age-dependent capital system with variable delays and random jump magnitudes, and investigate the convergence of the numerical approximation. It is proved that the numerical approximate solutions converge to the analytical solutions in the mean-square sense under given conditions.
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Dissertations / Theses on the topic "Approximate magnitudes"

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Riddervold, Sandberg Eva. "Neural Substrates Correlated with Magnitude Processing in Children and Adults : An fMRI study examining the Triple Code Model of numerical cognition." Thesis, Linköpings universitet, Institutionen för beteendevetenskap och lärande, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-158156.

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The Triple Code Model (TCM) of numerical cognition has become one of the most predominantly theories for how humans perceive, manipulate, and communicate numerical information. It builds on the notion that there exist three functionally distinct but neurologically connected codes that handle manipulations of different numerical input (non-symbolic magnitudes, symbolic representations, and verbal number words). In this study, we add a developmental perspective by collecting child data and comparing it to existing adult data. The main question is whether or not children elicit the same neural correlates as adults while performing three different number comparison tasks in line with TCM. Neuroimaging data using fMRI were collected for a total of 20 participants (ten children and ten adults). The results suggest that children rely on more right-lateralized regions and that a developmental shift towards the left hemisphere and associated language areas occur during acquisition of mathematical proficiency.

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Starr, Ariel. "From Magnitudes to Math: Developmental Precursors of Quantitative Reasoning." Diss., 2015. http://hdl.handle.net/10161/9842.

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The uniquely human mathematical mind sets us apart from all other animals. Although humans typically think about number symbolically, we also possess nonverbal representations of quantity that are present at birth and shared with many other animal species. These primitive numerical representations are thought to arise from an evolutionarily ancient system termed the Approximate Number System (ANS). The present dissertation aims to determine how these preverbal representations of quantity may serve as the foundation for more complex quantitative reasoning abilities. To this end, the five studies contained herein investigate the relations between representations of number, representations of other magnitude dimensions, and symbolic math proficiency in infants, children, and adults. The first empirical study, described in Chapter 2, investigated whether infants engage the ANS to represent the full range of natural numbers. The study presented in Chapter 3 compared infants' acuity for detecting changes in contour length to their acuity for detecting changes in number to assess whether representations of continuous quantities are primary to representations of number in infancy. The study presented in Chapter 4 compared individual differences in acuity for number, line length, and brightness in children and adults to determine how the relations between these magnitudes may change over development. Chapter 5 contains a longitudinal study investigating the relation between preverbal number sense in infancy and symbolic math abilities in preschool-aged children. Finally, the study presented in Chapter 6 investigated the mechanisms underlying the maturation of the number sense and determined which features of the number sense are predictive of symbolic math skill. Taken together, these findings confirm that number is a salient feature of the environment for infants and young children and suggest that approximate number representations are fundamental for the acquisition of symbolic math.


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Books on the topic "Approximate magnitudes"

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Magee, Lonnie. Approximate magnitudes of LR, W, and LM test statistics. Louvain-la-Neuve: Center for Operations Research & Econometrics, 1985.

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Geary, David C. The Classification and Cognitive Characteristics of Mathematical Disabilities in Children. Edited by Roi Cohen Kadosh and Ann Dowker. Oxford University Press, 2014. http://dx.doi.org/10.1093/oxfordhb/9780199642342.013.017.

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Children in the bottom quartile of mathematics achievement are at high risk for underemployment in adulthood. These children include the roughly 7% of students with a mathematical learning disability (MLD) and another 10% of students with persistent low achievement (LA) that is not attributable to intelligence. The poor mathematics achievement of children who compose groups of MLD and LA students appears to be related to one or several deficits; specifically, (1) a delay in the development and poor fidelity of the system for representing approximate magnitudes; (2) difficulty mapping Arabic numerals, number words, and rational numbers onto associated quantities; (3) poor conceptual understanding of some arithmetic concepts; (4) developmental delay in the learning of mathematical procedures; and (5) difficulty committing basic arithmetic facts to or retrieving them from long-term memory. Children with MLD also have concurrent working memory deficits that exacerbate their mathematics-specific deficits and delays.
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Van Herwegen, Jo, and Annette Karmiloff-Smith. Genetic Developmental Disorders and Numerical Competence across the Lifespan. Edited by Roi Cohen Kadosh and Ann Dowker. Oxford University Press, 2014. http://dx.doi.org/10.1093/oxfordhb/9780199642342.013.031.

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Due to their frequent uneven cognitive profiles, genetic developmental disorders allow researchers to investigate which numerical sub-system of those present in typically developing infants best predicts subsequent numerical abilities. More importantly, they can provide evidence of which other cognitive abilities outside number are necessary for the successful development of these numerical sub-systems. We discuss evidence from cross-syndrome comparisons of adults, adolescents, children, and infants with Williams syndrome and those with Down syndrome to show that the approximate magnitude sub-system is crucial for later number development. In addition, we show that specific problems outside the number domain, and within basic-level visual and attention systems contribute to an explanation of the difficulties and proficiencies observed within each genetic disorder. Finally, we argue that a truly developmental approach is critical when using the cross-syndrome design in order to reveal subtle differences that impact over time on the development of cognitive abilities.
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Baloh, Robert W. Breuer Discovers How the Balance Portion of the Inner Ear Works. Oxford University Press, 2016. http://dx.doi.org/10.1093/med/9780190600129.003.0004.

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Josef Breuer presented his initial work on the inner ear to the Imperial Society of Physicians in 1873. His basic premise was that the semicircular canals sense angular movement of the head by movement of the fluid (endolymph) within them. The endolymph moves relative to the walls of the canals because of its inertia. In dissecting the semicircular canals of pigeons, he noted nerve endings contacting cells at the base of the ampulla and microscopic hairs extending from the top of the cells into a gelatinous bulb (the cupula). He hypothesized that movement of the endolymph fluid triggered by angular head movements bent the tiny hairs, activating the nerve endings at the base of the hair cells. The nerves in turn passed on signals reflecting the direction and magnitude of hair deflection to the central nervous system. At approximately the same time, Ernst Mach came to a similar conclusion.
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Chapple, David, Reid Tingley, Nicola Mitchell, Stewart Macdonald, J. Scott Keogh, Glenn Shea, Philip Bowles, Neil Cox, and John Woinarski. Action Plan for Australian Lizards and Snakes 2017. CSIRO Publishing, 2019. http://dx.doi.org/10.1071/9781486309474.

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Lizards and snakes (squamate reptiles) are the most diverse vertebrate group in Australia, with approximately 1000 described species, representing about 10% of the global squamate diversity. Squamates are a vital part of the Australian ecosystem, but their conservation has been hindered by a lack of knowledge of their diversity, distribution, biology and key threats. The Action Plan for Australian Lizards and Snakes 2017 provides the first comprehensive assessment of the conservation status of Australian squamates in 25 years. Conservation assessments are provided for 986 species of Australian lizards and snakes (including sea snakes). Over the past 25 years there has been a substantial increase in the number of species and families recognised within Australia. There has also been an increase in the range and magnitude of threatening processes with the potential to impact squamates. This has resulted in an increase in the proportion of the Australian squamate fauna that is considered Threatened. Notably over this period, the first known extinction (post-European settlement) of an Australian reptile species occurred – an indication of the increasingly urgent need for better knowledge and management of this fauna. Six key recommendations are presented to improve the conservation management and plight of Australian squamates. This Action Plan represents an essential resource for research scientists, conservation biologists, conservation managers, environmental consultants, policy makers from Commonwealth and State/Territory governments, and the herpetological community.
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Lachniet, Matthew S., and Juan Pablo Bernal-Uruchurtu. AD 550–600 Collapse at Teotihuacan. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780199329199.003.0006.

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We analyze a 2400-year rainfall reconstruction from an ultra-high-resolution absolutely-dated stalagmite (JX-6) from southwestern Mexico (Lachniet et al., 2012). Oxygen isotope variations correlate strongly to rainfall amount in the Mexico City area since 1870 CE, and for the wider southwestern Mexico region since 1948, allowing us to quantitatively reconstruct rainfall variability for the Basin of Mexico and Sierra Madre del Sur for the past 2400 years. Because oxygen isotopes integrate rainfall variations over broad geographic regions, our data suggest substantial variations in Mesoamerican monsoon strength over the past two millennia. As a result of low age uncertainties (≤ 11 yr), our stalagmite paleoclimate reconstruction allows us to place robust ages on past rainfall variations with a resolution an order of magnitude more precise than archeological dates associated with societal change. We relate our new rainfall reconstruction to the sequence of events at Teotihuacan (Millon, 1967; Cowgill, 2015a) and to other pre-Colombian civilizations in Mesoamerica. We observe a centuries long drying trend that culminated in peak drought conditions in ca. 750 CE related to a weakening monsoon, which may have been a stressor on Mesoamerican societies. Teotihuacan is an ideal location to test for links between climate change and society, because it was located in a semi-arid highland valley with limited permanent water sources, which relied upon spring fed irrigation to ensure a reliable maize harvest (Sanders, 1977). The city of Teotihuacan was one of the largest Mesoamerican cities, which apparently reached population sizes of 80,000 to 100,000 inhabitants by AD 300 (Cowgill, 1997; 2015a). Following the “Great Fire”, which dates approximately to AD 550, population decreased to lower levels and many buildings were abandoned (Cowgill, 2015). Because of the apparent reliance on rainwater capture (Linn é, 2003) and spring-fed agriculture in the Teotihuacan valley to ensure food security and drinking water, food production and domestic water supplies should have been sensitive to rainfall variations that recharge the surficial aquifer that sustained spring discharge prior recent groundwater extraction.
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Book chapters on the topic "Approximate magnitudes"

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Gemel, Aleksander, and Paula Quinon. "Magnitude and Number Sensitivity of the Approximate Number System in Conceptual Spaces." In Conceptual Spaces: Elaborations and Applications, 183–203. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-12800-5_10.

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Goubault, Eric, and Sylvie Putot. "RINO: Robust INner and Outer Approximated Reachability of Neural Networks Controlled Systems." In Computer Aided Verification, 511–23. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-13185-1_25.

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AbstractWe present a unified approach, implemented in the RINO tool, for the computation of inner and outer-approximations of reachable sets of discrete-time and continuous-time dynamical systems, possibly controlled by neural networks with differentiable activation functions. RINO combines a zonotopic set representation with generalized mean-value AE extensions to compute under and over-approximations of the robust range of differentiable functions, and applies these techniques to the particular case of learning-enabled dynamical systems. The AE extensions require an efficient and accurate evaluation of the function and its Jacobian with respect to the inputs and initial conditions. For continuous-time systems, possibly controlled by neural networks, the function to evaluate is the solution of the dynamical system. It is over-approximated in RINO using Taylor methods in time coupled with a set-based evaluation with zonotopes. We demonstrate the good performances of RINO compared to state-of-the art tools Verisig 2.0 and ReachNN* on a set of classical benchmark examples of neural network controlled closed loop systems. For generally comparable precision to Verisig 2.0 and higher precision than ReachNN*, RINO is always at least one order of magnitude faster, while also computing the more involved inner-approximations that the other tools do not compute.
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"Approximate Magnitudes in Some Typical Plasmas." In Fundamentals of Plasma Physics, 702. Elsevier, 1986. http://dx.doi.org/10.1016/b978-0-08-033923-8.50032-x.

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Peters, Ellen. "The Approximate Number System (ANS) and Discriminating Magnitudes." In Innumeracy in the Wild, 127–39. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780190861094.003.0011.

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This chapter, “The Approximate Number System (ANS) and Discriminating Magnitudes,” discusses our intuitive, rather than deliberative, understanding of numbers. Humans are born with an innate sense of number and an ability to perform simple arithmetic operations with sets of objects without counting. We share this intuitive sense of numeric magnitude (how big one quantity is relative to another) with other species. Non-human animals cannot count as humans do. However, they have a keen sense of quantity that allows them to tell quickly and efficiently which quantity is bigger so that they can make better choices about food, mates, and safety. In humans, this intuitive sense of numbers develops from infancy to adulthood, and it appears to underlie the emergence of symbolic math ability (objective numeracy) in children.
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Criss, Robert E., and Anne M. Hofmeister. "How spin down and radioactive decay drive rocky planet evolution." In In the Footsteps of Warren B. Hamilton: New Ideas in Earth Science. Geological Society of America, 2022. http://dx.doi.org/10.1130/2021.2553(19).

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ABSTRACT Most differences in the gross surface morphologies, tectonic styles, overall geologic histories, and atmospheres of the rocky bodies in the solar system can be explained by contributions and dissipation of gravitational and radiogenic energy over geologic time. These two energy sources are large and measurable and can be extrapolated back in time. Accretion was likely cold, and directly converted gravitational potential energy into axial spin, a prominent feature of planets that is otherwise unexplained. Impact heating was mostly limited to planetary surfaces in the final stages of accretion. Frictional dissipation of spin contributed sufficient energy to ignite the primordial Sun and heated Earth and Venus by nearly as much as has the radioactive decay of K, U, and Th over geologic time. Energy inputs have been continuously offset by loss of heat to the surroundings. The magnitudes of most important energy contributions depend on the planet radius R and also on the distance r to the Sun. Quantitative, albeit approximate, relationships show that the net specific energy (kJ/kg) contributed to the rocky bodies over geologic time goes as: Earth ~ Venus >> Mars ~ Mercury ~ Moon >> asteroids. Net energy inputs increased the average internal temperatures of Earth and Venus by ~3000 K but heated asteroids by only a few hundred kelvins.
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Glusker, Jenny Pickworth, and Kenneth N. Trueblood. "The derivation of trial structures. I. Analytical methods for direct phase determination." In Crystal Structure Analysis. Oxford University Press, 2010. http://dx.doi.org/10.1093/oso/9780199576340.003.0017.

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As indicated at the start of Chapter 4, after the diffraction pattern has been recorded and measured, the next stage in a crystal structure determination is solving the structure—that is, finding a suitable “trial structure” that contains approximate positions for most of the atoms in the unit cell of known dimensions and space group. The term “trial structure” implies that the structure that has been found is only an approximation to the correct or “true” structure, while “suitable” implies that the trial structure is close enough to the true structure that it can be smoothly refined to give a good fit to the experimental data. Methods for finding suitable trial structures form the subject of this chapter and the next. In the early days of structure determination, trial and error methods were, of necessity, almost the only available way of solving structures. Structure factors for the suggested “trial structure” were calculated and compared with those that had been observed. When more productive methods for obtaining trial structures—the “Patterson function” and “direct methods”—were introduced, the manner of solving a crystal structure changed dramatically for the better. We begin with a discussion of so-called “direct methods.” These are analytical techniques for deriving an approximate set of phases from which a first approximation to the electron-density map can be calculated. Interpretation of this map may then give a suitable trial structure. Previous to direct methods, all phases were calculated (as described in Chapter 5) from a proposed trial structure. The search for other methods that did not require a trial structure led to these phaseprobability methods, that is, direct methods. A direct solution to the phase problem by algebraic methods began in the 1920s (Ott, 1927; Banerjee, 1933; Avrami, 1938) and progressed with work on inequalities by David Harker and John Kasper (Harker and Kasper, 1948). The latter authors used inequality relationships put forward by Augustin Louis Cauchy and Karl Hermann Amandus Schwarz that led to relations between the magnitudes of some structure factors.
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Gautam, Usha, and Tarun Kumar Rawat. "Analysis of Wideband Second-Order Microwave Integrators." In Innovations in Ultra-Wideband Technologies. IntechOpen, 2021. http://dx.doi.org/10.5772/intechopen.94843.

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This chapter presents the implementation of stable, accurate, and wideband second-order microwave integrators (SOMIs). These SOMI designs are obtained by the use of various cascading combinations of transmission line sections and shunt stubs. In order to obtain the optimal values of the characteristic impedances of these line elements, the particle swarm optimization (PSO), cuckoo search algorithm (CSA) and gravitational search algorithm (GSA) are used to approximate the magnitude response of the ideal second-order integrator (SOI). Based on magnitude response, absolute magnitude error, phase response, convergence rate, pole-zero plot, and improvement graph, the performance measure criteria for the proposed SOMIs are performed. The results of the simulation and statistical analysis reveal that GSA exceeds the PSO and CSA in order to approximate the ideal SOI in all state-of-the-art eligible for wide-band microwave integrator. The designed SOMI is compact and suitable for applications covering ultra-wideband (UWB). The designed SOMI structure is also simulated on Advanced Design Software (ADS) in the form of a microstrip line on a dielectric constant 2.2 RT/Duroid substrate with a height of 0.762 mm. In the 3–15 GHz frequency range, the simulated magnitude result agrees well with the ideal one.
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Hammell, Robert J., Julie Hoksbergen, James Wood, and Mark Christensen. "Computational Intelligence for Information Technology Project Management." In Machine Learning, 1601–24. IGI Global, 2012. http://dx.doi.org/10.4018/978-1-60960-818-7.ch606.

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With the growing complexity of information technology (IT) projects, the management of these projects is proving to be a daunting task. The magnitude of this problem is underscored by the assertion that approximately 70% of IT projects fail to meet their objectives (Lewis, 2007). Computational intelligence (CI) is an area of research focused on developing intelligent systems to help with complex problems. Specifically, CI seeks to integrate techniques and methodologies to assist in problem domains in which information, data and perhaps even the problem itself are vague, approximate, and uncertain. It would seem that research aimed at leveraging the power of CI against IT project management problems is critical if IT project success rates are to be improved. This work examines the core CI technologies – fuzzy logic, neural networks, and genetic algorithms – and looks at current and potential future applications of these techniques to assist IT project managers.
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R. Ciric, Ioan. "Using Matrix Differential Equations for Solving Systems of Linear Algebraic Equations." In Matrix Theory - Classics and Advances [Working Title]. IntechOpen, 2022. http://dx.doi.org/10.5772/intechopen.104209.

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Various ordinary differential equations of the first order have recently been used by the author for the solution of general, large linear systems of algebraic equations. Exact solutions were derived in terms of a new kind of infinite series of matrices which are truncated and applied repeatedly to approximate the solution. In these matrix series, each new term is obtained from the preceding one by multiplication with a matrix which becomes better and better conditioned tending to the identity matrix. Obviously, this helps the numerical computations. For a more efficient computation of approximate solutions of the algebraic systems, we consider new differential equations which are solved by simple techniques of numerical integration. The solution procedure allows to easily control and monitor the magnitude of the residual vector at each step of integration. A related iterative method is also proposed. The solution methods are flexible, permitting various intervening parameters to be changed whenever necessary in order to increase their efficiency. Efficient computation of a rough approximation of the solution, applicable even to poorly conditioned systems, is also performed based on the alternate application of two different types of minimization of associated functionals. A smaller amount of computation is needed to obtain an approximate solution of large linear systems as compared to existing methods.
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R. Ciric, Ioan. "Using Matrix Differential Equations for Solving Systems of Linear Algebraic Equations." In Matrix Theory - Classics and Advances [Working Title]. IntechOpen, 2022. http://dx.doi.org/10.5772/intechopen.104209.

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Various ordinary differential equations of the first order have recently been used by the author for the solution of general, large linear systems of algebraic equations. Exact solutions were derived in terms of a new kind of infinite series of matrices which are truncated and applied repeatedly to approximate the solution. In these matrix series, each new term is obtained from the preceding one by multiplication with a matrix which becomes better and better conditioned tending to the identity matrix. Obviously, this helps the numerical computations. For a more efficient computation of approximate solutions of the algebraic systems, we consider new differential equations which are solved by simple techniques of numerical integration. The solution procedure allows to easily control and monitor the magnitude of the residual vector at each step of integration. A related iterative method is also proposed. The solution methods are flexible, permitting various intervening parameters to be changed whenever necessary in order to increase their efficiency. Efficient computation of a rough approximation of the solution, applicable even to poorly conditioned systems, is also performed based on the alternate application of two different types of minimization of associated functionals. A smaller amount of computation is needed to obtain an approximate solution of large linear systems as compared to existing methods.
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Conference papers on the topic "Approximate magnitudes"

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Wilson, Dennis, and Michael R. Sheller. "The Effect of Unsteady Compression and Expansion Waves on a Compressible Boundary Layer." In ASME 1988 International Gas Turbine and Aeroengine Congress and Exposition. American Society of Mechanical Engineers, 1988. http://dx.doi.org/10.1115/88-gt-117.

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This abstract summarizes the results of an investigation into the effects of finite amplitude acoustic disturbances or weak compression and expansion waves on compressible boundary layers. Specifically, the goal is to provide a theoretical model which predicts the increased heat transfer and skin friction associated with unsteady pressure disturbances. These pressure disturbances, which are produced by combustion instabilities, are present in most combustors. The magnitude of the fluctuating component relative to the stagnation pressure varies from the low acoustic range (0.05 %) to the weak shock range (5 %). The frequencies range from a few hundred Hz. for the longitudinal mode to a few thousand Hz. for the transverse mode. A simple but accurate theoretical model which predicts the enhanced heat transfer and skin friction for a wide range of frequencies and magnitudes is presented. The formulation yielded an unexpected result in that an approximate analytical solution is possible for the laminar flow case.
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Khoshnoud, Farbod, and Clarence W. de Silva. "Modal Analysis of Systems Using a Neuro-Fuzzy Approach." In ASME 2010 International Mechanical Engineering Congress and Exposition. ASMEDC, 2010. http://dx.doi.org/10.1115/imece2010-37798.

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A novel method of modal analysis for vibration modeling of systems is presented in this paper. In the developed method, first, mode shapes of the structure that is being analyzed are approximated. The approximate mode shapes are expressed by fuzzy sets where approximate deflections or displacement magnitudes of the mode shapes are described by fuzzy linguistic terms such as Zero, Medium, and Large. Fuzzy membership functions provide a means of dealing with the imprecisely defined system and it gives access to a large repertoire of tools available in the field of fuzzy reasoning. Second, fuzzy representations of the approximate mode shapes, called Fuzzy Mode Shapes in this paper, are updated using modal analysis data as obtained through experimentation. Finally, artificial neural networks are used as a tool to obtain an accurate version of the mode shape data by learning the target set of the data. An appropriate analogy of the application of Fuzzy Mode Shapes in the first step is the Starting Mode Shape Vectors in numerical eigenvector problem where the starting vector is updated through an iterative process. In this paper iterative updating process of mode shapes is carried out for the application of experimental modal testing. In this approach the differences between the fuzzy mode shapes and the corresponding measured modal testing data are minimized through an iterative process. In validating the developed technique for vibration modeling of one-dimensional and two-dimensional elastic bodies and structures, modeling of elastic beams, a clamped-free-clamped-free plate and a frame are used as illustrative examples. The solutions of the corresponding simulations are compared with the results from finite element computations and analytical model solutions. The good agreement of the results obtained for these models justifies the application of the developed method in experimental vibration modeling of systems. Use of the fuzzy-neural approach as developed in the paper expands the coverage of experimentally measured data, which is normally limited to a small number of measurement sets due to the limited number of available vibration sensors in the analyzed system. Neural networks provide a satisfactory interpolation of two sets of data including a) modal test data, which is accurate but is normally available only for a few measured points, and b) Fuzzy Mode Shapes, which are available for large number of points but are approximate.
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Sansone, Anthony, Jeff A. Webster, Rusi P. Taleyarkhan, and Brian Archambault. "Tensioned Metastable Fluid Detectors for High Efficiency Thermal and Fast Neutron Sensitivity." In 2016 24th International Conference on Nuclear Engineering. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/icone24-60757.

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Advancements in tension metastable fluid detector (TMFD) technology have led to an extension in detector sensitivity to now also detect and distinguish thermal energy (∼.02 eV) neutrons in addition to fast neutrons — spanning 109 orders of magnitude. The unique nature of detector operation and inherent detection mechanism in TMFDs offers a distinct advantage over conventional systems. TMFDs now posses the capabilities for simultaneous sensitivity to fast and thermal neutrons with high intrinsic efficiency, ascertaining directional and spectroscopic source information, all while remaining completely blind to background gamma and beta irradiation. The additional of thermal energy sensitivity was enabled via inclusion of boron in the detection fluid mixture; a compound composed of decaflouropentane (DFP), trimethyl borate (TMB) and methanol. Experimental benchmarking studies were conducted using the spontaneous fission based neutron source 252Cf, in conjunction with theoretical assessments using the nuclear particle transport package MCNP. Source neutron thermalization was accomplished through submersion of the source in a block of ice, such that the moderated spectrum contained an approximate 1:1 ratio between the fast and thermal flux magnitudes. Experimental results show that borated detection fluids yielded up to 6x improvements in the detection rate over their non-borated counterparts. Implications of the current results in regards to the applicability of TMFDs in the field of special nuclear material (SNM) interrogation and detection are discussed.
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Shareghi, Ehsan, Gholamreza Haffari, and Trevor Cohn. "Compressed Nonparametric Language Modelling." In Twenty-Sixth International Joint Conference on Artificial Intelligence. California: International Joint Conferences on Artificial Intelligence Organization, 2017. http://dx.doi.org/10.24963/ijcai.2017/376.

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Hierarchical Pitman-Yor Process priors are compelling for learning language models, outperforming point-estimate based methods. However, these models remain unpopular due to computational and statistical inference issues, such as memory and time usage, as well as poor mixing of sampler. In this work we propose a novel framework which represents the HPYP model compactly using compressed suffix trees. Then, we develop an efficient approximate inference scheme in this framework that has a much lower memory footprint compared to full HPYP and is fast in the inference time. The experimental results illustrate that our model can be built on significantly larger datasets compared to previous HPYP models, while being several orders of magnitudes smaller, fast for training and inference, and outperforming the perplexity of the state-of-the-art Modified Kneser-Ney count-based LM smoothing by up to 15%.
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Thomas, B. C., and Victor W. Wong. "Engine-Component Wear Modeling With Consideration of Growth and Removal of Surface Films: Computational Framework and Preliminary Results." In ASME 2008 Internal Combustion Engine Division Spring Technical Conference. ASMEDC, 2008. http://dx.doi.org/10.1115/ices2008-1693.

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The life of an automotive engine is often limited by the ability of its components to resist wear. The ability to predict wear, particularly for the effects of lubricant and additive characteristics, would greatly aid the development process of both engine components and lubricants. This paper addresses the development and function of thin solid films on rough surfaces and their effect on surface wear, as that occurring between contacting engine component surfaces. Completely deterministic modeling of such films may not be possible due to the complex interactions between the numerous mechanical, thermal, and chemical variables over disparate magnitudes of time and length scales. However, it is believed that useful predictions can be made by constructing a mechanistic model in which all of the most important effects are included, even if only at an approximate level. This work outlines the early stages of such a modeling effort in the context of zinc dialkyl-dithiophosphate (ZDDP) antiwear films on iron surfaces. The key concepts behind the theoretical model will be introduced, while its numerical implementation will be the focus of the discussion. Preliminary results from this effort are presented to illustrate feasibility and functionality on a qualitative level.
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Lou, Fangyuan, Douglas R. Matthews, Nicholas J. Kormanik, and Nicole L. Key. "Accounting for Circumferential Flow Nonuniformity in a Multi-Stage Axial Compressor." In ASME Turbo Expo 2021: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2021. http://dx.doi.org/10.1115/gt2021-59968.

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Abstract The flow field in a compressor is circumferentially non-uniform due to geometric imperfections, inlet flow nonuniformities, and blade row interactions. Therefore, the flow field, as represented by measurements from discrete stationary instrumentation, can be skewed and contribute to uncertainties in both calculated one-dimensional performance parameters and aerodynamic forcing functions needed for aeromechanics analyses. Considering this challenge, this paper documents a continued effort to account for compressor circumferential flow nonuniformities based on discrete, under-sampled measurements. First, the total pressure field downstream of the first two stators in a three-stage axial compressor was measured across half of the annulus. The circumferential nonuniformities in the stator exit flow, including vane wake variability, were characterized. In addition, the influence of wake variation on stage performance calculations and aerodynamic forcing functions were investigated. In the present study for the compressor with an approximate pressure ratio of 1.3 at design point, the circumferential nonuniformity in total pressure yields an approximate 2.4-point variation in isentropic efficiency and 54% variation in spectral magnitudes of the fundamental forcing frequency for the embedded stage. Furthermore, the stator exit circumferential flow nonuniformity is accounted for by reconstructing the full-annulus flow using a novel multi-wavelet approximation method. Strong agreement was achieved between experiment and the reconstructed total pressure field from a small segment of measurements representing 20% coverage of the annulus. Analysis shows the wake-wake interactions from the upstream vane rows dominate the circumferentially nonuniform distributions in the total pressure field downstream of stators. The features associated with wake-wake interactions accounting for passage-to-passage variations are resolved in the reconstructed total pressure profile, yielding representative mean flow properties and aerodynamic forcing functions.
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Miao, Jin, Andreas Gerstlauer, and Michael Orshansky. "Approximate logic synthesis under general error magnitude and frequency constraints." In 2013 IEEE/ACM International Conference on Computer-Aided Design (ICCAD). IEEE, 2013. http://dx.doi.org/10.1109/iccad.2013.6691202.

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Vaughan, David, Howard Levine, Paul Hassig, and Robert Smilowitz. "Evaluation of Airblast Loads on Structures in Complex Configurations." In ASME 2012 Pressure Vessels and Piping Conference. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/pvp2012-78728.

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A common terrorist threat worldwide is the use of large vehicle bombs to attack high value targets. Detonation of large yield devices can cause significant damage to nearby buildings, facilities and infrastructure with potentially high loss of life and large economic losses. Blast pressures can have major consequences on critical facilities such as nuclear power plants, causing economic loss, environmental damage and system failure. Closely spaced structures in a dense configuration provide a complicated setting for evaluating airblast pressures caused by explosive devices. The presence of multiple buildings can channel the airblast, resulting in significant effects on load magnitudes at range from the detonation. Buildings reflect propagating blast waves causing increased loading at some locations and reduced loads elsewhere due to shielding from direct blast waves. The complex interaction between structures, streets, alleys and geographical terrain can have a major impact on structural loads. Currently, the most common way to estimate airblast pressures resulting from above ground explosive detonations is to use fast running, approximate blast tools such as CONWEP. These simplified tools may not provide accurate guidance on airblast pressures in complex environments. The following paper illustrates the use of Computational Fluid Dynamics (CFD) calculations of complex building configurations to quantify the resulting blast environment. Comparisons with simplified methods are presented. An approach to using a database of CFD simulations, customized for a specific site, to provide a fast running blast assessment tool is described. This approach provides a convenient, fast running tool for designers and security planners to visualize and accurately quantify the hazard from any threat size and location within the area of interest.
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Bates, R. H., W. R. Fright, and P. H. Gardenier. "Gerchberg-Saxton Phase Retrieval When Image Magnitude Given Only Approximately." In 31st Annual Technical Symposium, edited by Paul S. Idell. SPIE, 1988. http://dx.doi.org/10.1117/12.942096.

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Mahmood, G. I., P. M. Ligrani, and S. Y. Won. "Spatially-Resolved Heat Transfer and Flow Structure in a Rectangular Channel With 45° Angled Rib Turbulators." In ASME Turbo Expo 2002: Power for Land, Sea, and Air. ASMEDC, 2002. http://dx.doi.org/10.1115/gt2002-30215.

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Spatially-resolved Nusselt numbers and flow structure are presented for a stationary channel with an aspect ratio of 4 and angled rib turbulators inclined at 45° with perpendicular orientations on two opposite surfaces. The flow structure results include time-averaged distributions of streamwise velocity and total pressure, surveyed over flow cross-sectional planes, as well as flow visualization images and friction factors. Results are given at different Reynolds numbers based on channel height from 270 to 90,000. The ratio of rib height to hydraulic diameter is .078, the rib pitch-to-height ratio is 10, and the blockage provided by the ribs is 25 percent of the channel cross-sectional area. Spatially-resolved local Nusselt numbers are highest on tops of the rib turbulators, with lower magnitudes on flat surfaces between the ribs, where regions of flow separation and shear layer re-attachment have pronounced influences on local surface heat transfer behavior. Also important are intense, highly unsteady secondary flows and vortex pairs, which increase secondary advection and turbulent transport over the entire channel cross-section. The resulting augmented local and spatially-averaged Nusselt number ratios (rib turbulator Nusselt numbers normalized by values measured in a smooth channel) generally increase on the rib tops as Reynolds number increases. Nusselt number ratios decrease on the flat regions away from the ribs, especially at locations just downstream of the ribs, as Reynolds number increases. Globally-averaged Nusselt number ratios vary from 3.36 to 2.82 as Reynolds number increases from 10,000 to 90,000. Thermal performance parameters also decrease somewhat as Reynolds number increases over this range, with values in approximate agreement with, or slightly higher than 60° continuous rib data measured by other investigators in a square channel.
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Reports on the topic "Approximate magnitudes"

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Bent, A. L. A revised moment magnitude catalog of eastern Canada's largest earthquakes. Natural Resources Canada/CMSS/Information Management, 2022. http://dx.doi.org/10.4095/329612.

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Although there are many scales used to calculate earthquake magnitude, moment magnitude is currently considered the preferred magnitude scale for use in seismic hazard assessment in Canada. Historically, moment magnitude was not determined for eastern Canadian earthquakes although it has been routinely calculated for earthquakes of approximately magnitude 4.0 and greater, on regional magnitude scales, for the last decade. Thus, most moment magnitudes for eastern Canadian earthquakes must be obtained by converting from another magnitude scale or from felt information. This paper provides a moment magnitude catalog for the largest earthquakes in eastern Canada and vicinity. The study derives moment magnitudes for some events but also makes use of values from the published literature. Earthquakes are assessed individually using all available sources of information. The resulting catalog provides moment magnitudes for 254 events. Three additional events were evaluated but removed from the catalog as it is highly questionable whether they were earthquakes.
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Gopinath, Ranjani, Rajesh Bhatia, Sonalini Khetrapal, Sungsup Ra, and Giridhara R. Babu. Tuberculosis Control Measures in Urban India: Strengthening Delivery of Comprehensive Primary Health Services. Asian Development Bank, December 2020. http://dx.doi.org/10.22617/wps200409-2.

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Approximately 2.69 million tuberculosis (TB) cases—about a quarter of the global cases—were reported in India on The Global TB Report 2019. There are nearly half a million “missing” cases every year, either undiagnosed, unaccountable, or inadequately diagnosed and treated. This paper analyzes the magnitude of TB transmission and the quality of interventions in urban areas and migrant populations in India. It identifies key factors and areas that need to be further strengthened for the country to achieve its goal of eliminating TB by 2025. The study is aligned with the government’s objective to strengthen the provision of comprehensive primary health care services for the urban poor as part of India’s National Strategic Plan, 2017–2025.
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Gopinath, Ranjani, Rajesh Bhatia, Sonalini Khetrapal, Sungsup Ra, and Giridhara R. Babu. Tuberculosis Control Measures in Urban India: Strengthening Delivery of Comprehensive Primary Health Services. Asian Development Bank, December 2020. http://dx.doi.org/10.22617/wps200409-2.

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Approximately 2.69 million tuberculosis (TB) cases—about a quarter of the global cases—were reported in India on The Global TB Report 2019. There are nearly half a million “missing” cases every year, either undiagnosed, unaccountable, or inadequately diagnosed and treated. This paper analyzes the magnitude of TB transmission and the quality of interventions in urban areas and migrant populations in India. It identifies key factors and areas that need to be further strengthened for the country to achieve its goal of eliminating TB by 2025. The study is aligned with the government’s objective to strengthen the provision of comprehensive primary health care services for the urban poor as part of India’s National Strategic Plan, 2017–2025.
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Gutiérrez, José E., and Luis Fernández Lafuerza. Credit line runs and bank risk management: evidence from the disclosure of stress test results. Madrid: Banco de España, December 2022. http://dx.doi.org/10.53479/25006.

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As noted in recent literature, firms can run on credit lines due to fear of future credit restrictions. We exploit the 2011 stress test supervised by the European Banking Authority (EBA) and the Spanish Central Credit Register to explore: 1) the occurrence and magnitude of these runs after the release of negative stress test results; and 2) banks’ behaviour before and after the release of this information. We find that, following the release of the results, firms drew down approximately 10 pp more available funds from lines granted by banks that had a worse performance in the stress test. Moreover, before the release date, poorer performing banks were more likely to reduce the size of credit lines, while those with more significant balances of undrawn credit lines were more likely to cut term lending.
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Gutiérrez, José E., and Luis Fernández Lafuerza. Credit line runs and bank risk management: evidence from the disclosure of stress test results. Madrid: Banco de España, January 2023. http://dx.doi.org/10.53479/24998.

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As noted in recent literature, firms can run on credit lines due to fear of future credit restrictions. We exploit the 2011 stress test supervised by the European Banking Authority (EBA) and the Spanish Central Credit Register to explore: 1) the occurrence and magnitude of these runs after the release of negative stress test results; and 2) banks’ behaviour before and after the release of this information. We find that, following the release of the results, firms drew down approximately 10 pp more available funds from lines granted by banks that had a worse performance in the stress test. Moreover, before the release date, poorer performing banks were more likely to reduce the size of credit lines, while those with more significant balances of undrawn credit lines were more likely to cut term lending.
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