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1

Franke, Richard H. The use of observed data for the initial value problem in numerical weather prediction. Naval Postgraduate School, 1987.

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2

Abarbanel, Henry. Predicting the Future: Completing Models of Observed Complex Systems. Springer New York, 2013.

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3

Kaufmann, Liane, Karin Kucian, and Michael von Aster. Development of the numerical brain. Edited by Roi Cohen Kadosh and Ann Dowker. Oxford University Press, 2014. http://dx.doi.org/10.1093/oxfordhb/9780199642342.013.008.

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This article focuses on typical trajectories of numerical cognition from infancy all the way through to adulthood (please note that atypical pathways of numerical cognition will be dealt in‘Brain Correlates of Numerical Disabilities’). Despite the fact that developmental imaging studies are still scarce to date there is converging evidence that (1) neural signatures of non-verbal number processing may be observed already in infants; and (2) developmental changes in neural responsivity are characterized by increasing functional specialization of number-relevant frontoparietal brain regions. It
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4

Noël, Marie-Pascale. When Number Processing and Calculation is Not Your Cup of Tea. Edited by Roi Cohen Kadosh and Ann Dowker. Oxford University Press, 2014. http://dx.doi.org/10.1093/oxfordhb/9780199642342.013.62.

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This section of this volume deals with the study of numerical impairment occurring either after brain damage (i.e., acquired acalculia) or during development without any known brain damage (i.e., dyscalculia). The chapters in this section will report the research aiming at characterizing those difficulties. The study of atypical number processing and calculation in acalculia has contributed importantly to the understanding of how our brain is structured to process number and to calculate. The study of dyscalculia has shed light on the numerical bases for arithmetic learning. This research has
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5

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-
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6

(Contributor), G. Brasseur, W. Cramer (Contributor), M. Ehrendorfer (Contributor), et al., eds. Observed Global Climate (Landolt-Bornstein: Numerical Data and Functional Relationships in Science and Technology - New Series). Springer, 2005.

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7

Huffaker, Ray, Marco Bittelli, and Rodolfo Rosa. Empirically Detecting Causality. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198782933.003.0008.

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Phenomenological models mathematically describe relationships among empirically observed phenomena without attempting to explain underlying mechanisms. Within the context of NLTS, phenomenological modeling goes beyond phase space reconstruction to extract equations governing real-world system dynamics from a single or multiple observed time series. Phenomenological models provide several benefits. They can be used to characterize the dynamics of variable interactions; for example, whether an incremental increase in one variable drives a marginal increase/decrease in the growth rate of another,
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8

Edwalds, Eric. A numerical study of sulfur and nitrogen scavenging in a mesoscale rainband observed in the GALE experiment. 1987.

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9

Andres, Michael, and Mauro Pesenti. Finger-based representation of mental arithmetic. Edited by Roi Cohen Kadosh and Ann Dowker. Oxford University Press, 2014. http://dx.doi.org/10.1093/oxfordhb/9780199642342.013.028.

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Human beings are permanently required to process the world numerically and, consequently, to perform computations to adapt their behaviour and they have developed various calculation strategies, some of them based on specific manipulations of the fingers. In this chapter, we argue that the way we express physically numerical concepts by raising fingers while counting leads to embodied representations of numbers and calculation procedures in the adult brain. To illustrate this, we focus on number and finger interactions in the context of simple arithmetic operations. We show that the fixed orde
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10

Mas, André, and Besnik Pumo. Linear Processes for Functional Data. Edited by Frédéric Ferraty and Yves Romain. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780199568444.013.3.

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This article provides an overview of the basic theory and applications of linear processes for functional data, with particular emphasis on results published from 2000 to 2008. It first considers centered processes with values in a Hilbert space of functions before proposing some statistical models that mimic or adapt the scalar or finite-dimensional approaches for time series. It then discusses general linear processes, focusing on the invertibility and convergence of the estimated moments and a general method for proving asymptotic results for linear processes. It also describes autoregressi
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11

Rusconi, Elena, and Carlo Umiltà. Mathematics and TMS. Edited by Charles M. Epstein, Eric M. Wassermann, and Ulf Ziemann. Oxford University Press, 2012. http://dx.doi.org/10.1093/oxfordhb/9780198568926.013.0033.

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This article introduces the relationship between mathematical cognition and transcranial magnetic stimulation (TMS). The mental number line is located in the parietal lobe. Studies employing TMS have explored issues related to the mental number line. This article reviews the studies centered on the magnitude code. The results show that even though the parietal activation is nearly always present in both hemispheres, it is often asymmetric, being greater in the right hemisphere when quantification of nonverbal and nonsymbolic material is required. Neuropsychological studies confirm the relation
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12

Zeitlin, Vladimir. RSW Modons and their Surprising Properties: RSW Turbulence. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198804338.003.0009.

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By using quasi-geostrophic modons constructed in Chapter 6 as initial conditions, rotating-shallow-water modons are obtained through the process of ageostrophic adjustment, both in one- and in two-layer configurations. Scatter plots show that they are solutions of the rotating shallow-water equations. A special class of modons with an internal front (shock) is shown to exist. A panorama of collision processes of the modons, leading to formation of tripoles, nonlinear modons, or elastic scattering is presented. The modon solutions are then used for initialisations of numerical simulations of de
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13

Cheng, Russell. Change-Point Models. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198505044.003.0011.

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This chapter investigates change-point (hazard rate) probability models for the random survival time in some population of interest. A parametric probability distribution is assumed with parameters to be estimated from a sample of observed survival times. If a change-point parameter, denoted by τ‎, is included to represent the time at which there is a discrete change in hazard rate, then the model is non-standard. The profile log-likelihood, with τ‎ as profiling parameter, has a discontinuous jump at every τ‎ equal to a sampled value, becoming unbounded as τ‎ tends to the largest observation.
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14

Zeitlin, Vladimir. Wave Turbulence. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198804338.003.0013.

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Main notions and ideas of wave (weak) turbulence theory are explained with the help of Hamiltonian approach to wave dynamics, and are applied to waves in RSW model. Derivation of kinetic equations under random-phase approximation is explained. Short inertia–gravity waves on the f plane, short equatorial inertia–gravity waves, and Rossby waves on the beta plane are then considered along these lines. In all of these cases, approximate solutions of kinetic equation, annihilating the collision integral, can be obtained by scaling arguments, giving power-law energy spectra. The predictions of turbu
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15

Saha, Prasenjit, and Paul A. Taylor. The Astronomers' Magic Envelope. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198816461.001.0001.

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This is a conceptual introduction to astrophysical processes, at the advanced-undergraduate level. Topics are developed in more or less their historical order of discovery, but from a modern perspective. The book begins with orbits, gradually building in complexity to chaos, relativistic orbits and gravitational lensing, and eventually a semi-classical treatment of gravitational-wave sources. The second part is about how stars work, including related topics like the mass—radius relations for planets and stellar remnants. The third part is about the expanding universe and its history, the concl
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16

Dowker, Ann. Individual Differences in Arithmetical Abilities. Edited by Roi Cohen Kadosh and Ann Dowker. Oxford University Press, 2014. http://dx.doi.org/10.1093/oxfordhb/9780199642342.013.034.

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This chapter discusses individual differences in arithmetic. It deals relatively briefly with the findings about the general large extent of such differences in both children and adults. It then discusses findings that indicate that it is inadequate to speak of arithmetical ability as a single characteristic. Rather, it is made up of many components, which may correlate, but also show significant functional independence. Discrepancies between any two such components, in both directions, can be frequently observed. There is evidence for this from many sources, including studies of patients with
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17

Loporcaro, Michele. The older stages of the Romance languages. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780199656547.003.0006.

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The chapter explores the earliest attested stages of the different Romance branches, elaborating on the picture which has emerged in Chapter 4 and showing that the traces of more-than-binary gender contrasts grow increasingly significant, and geographically widespread, as one proceeds backwards in time. Thus, even Northern Italo-Romance and Gallo-Romance, which have no traces of a functional neuter today, still featured in their medieval stage not only a non-lexical neuter adjective inflection for default/agreement with non-lexical controllers (Gallo-Romance), but neuter agreement on (overdiff
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18

Tibaldi, Stefano, and Franco Molteni. Atmospheric Blocking in Observation and Models. Oxford University Press, 2018. http://dx.doi.org/10.1093/acrefore/9780190228620.013.611.

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The atmospheric circulation in the mid-latitudes of both hemispheres is usually dominated by westerly winds and by planetary-scale and shorter-scale synoptic waves, moving mostly from west to east. A remarkable and frequent exception to this “usual” behavior is atmospheric blocking. Blocking occurs when the usual zonal flow is hindered by the establishment of a large-amplitude, quasi-stationary, high-pressure meridional circulation structure which “blocks” the flow of the westerlies and the progression of the atmospheric waves and disturbances embedded in them. Such blocking structures can hav
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