The contributions of domain-general and numerical factors to third-grade arithmetic skills and mathematical learning disability

Explanations of the marked individual differences in elementary school mathematical achievement and mathematical learning disability (MLD or dyscalculia) have involved domain-general factors (working memory, reasoning, processing speed and oral language) and numerical factors that include single-digit processing efficiency and multi-digit skills such as number system knowledge and estimation. This study of third graders (N = 258) finds both domain-general and numerical factors contribute independently to explaining variation in three significant arithmetic skills: basic calculation fluency, written multi-digit computation, and arithmetic word problems. Estimation accuracy and number system knowledge show the strongest associations with every skill and their contributions are both independent of each other and other factors. Different domain-general factors independently account for variation in each skill. Numeral comparison, a single digit processing skill, uniquely accounts for variation in basic calculation. Subsamples of children with MLD (at or below 10th percentile, n = 29) are compared with low achievement (LA, 11th to 25th percentiles, n = 42) and typical achievement (above 25th percentile, n = 187). Examination of these and subsets with persistent difficulties supports a multiple deficits view of number difficulties: most children with number difficulties exhibit deficits in both domain-general and numerical factors. The only factor deficit common to all persistent MLD children is in multi-digit skills. These findings indicate that many factors matter but multi-digit skills matter most in third grade mathematical achievement.

The heuristic application of explanatory theories in international relations

Explanatory theorists increasingly insist that their theories are useful even though they cannot be deductively applied. But if so, then how do such theories contribute to our understanding of international relations? I argue that explanatory theories are typically heuristically applied: theorists’ accounts of specific empirical episodes are shaped by their theories’ thematic content, but are not inferred from putative causal generalizations or covering laws. These accounts therefore gain no weight from their purely rhetorical association with theories’ quasi-deductive arguments: they must be judged on the plausibility of their empirical claims. Moreover, the quasi-deductive form in which explanatory theories are typically presented obscures their actual explanatory role, which is to indicate what sort of explanation may be required, to provide conceptual categories, and to suggest an empirical focus. This account of how theoretical explanations are constructed subverts the nomothetic–idiographic distinction that is often used to distinguish International Relations from History.

Nutrient-limited toxin production and the dynamics of two phytoplankton in culture media: a mathematical model

In this paper we have proposed and analyzed a simple mathematical model consisting of four variables, viz., nutrient concentration, toxin producing phytoplankton (TPP), non-toxic phytoplankton (NTP), and toxin concentration. Limitation in the concentration of the extracellular nutrient has been incorporated as an environmental stress condition for the plankton population, and the liberation of toxic chemicals has been described by a monotonic function of extracellular nutrient. The model is analyzed and simulated to reproduce the experimental findings of Graneli and Johansson [Graneli, E., Johansson, N., 2003. Increase in the production of allelopathic Prymnesium parvum cells grown under N- or P-deficient conditions. Harmful Algae 2, 135–145]. The robustness of the numerical experiments are tested by a formal parameter sensitivity analysis. As the first theoretical model consistent with the experiment of Graneli and Johansson (2003), our results demonstrate that, when nutrient-deficient conditions are favorable for the TPP population to release toxic chemicals, the TPP species control the bloom of other phytoplankton species which are non-toxic. Consistent with the observations made by Graneli and Johansson (2003), our model overcomes the limitation of not incorporating the effect of nutrient-limited toxic production in several other models developed on plankton dynamics.

A mathematical model of crystallization in an emulsion

A mathematical model incorporating many of the important processes at work in the crystallization of emulsions is presented. The model describes nucleation within the discontinuous domain of an emulsion, precipitation in the continuous domain, transport of monomers between the two domains, and formation and subsequent growth of crystals in both domains. The model is formulated as an autonomous system of nonlinear, coupled ordinary differential equations. The description of nucleation and precipitation is based upon the Becker–Döring equations of classical nucleation theory. A particular feature of the model is that the number of particles of all species present is explicitly conserved; this differs from work that employs Arrhenius descriptions of nucleation rate. Since the model includes many physical effects, it is analyzed in stages so that the role of each process may be understood. When precipitation occurs in the continuous domain, the concentration of monomers falls below the equilibrium concentration at the surface of the drops of the discontinuous domain. This leads to a transport of monomers from the drops into the continuous domain that are then incorporated into crystals and nuclei. Since the formation of crystals is irreversible and their subsequent growth inevitable, crystals forming in the continuous domain effectively act as a sink for monomers “sucking” monomers from the drops. In this case, numerical calculations are presented which are consistent with experimental observations. In the case in which critical crystal formation does not occur, the stationary solution is found and a linear stability analysis is performed. Bifurcation diagrams describing the loci of stationary solutions, which may be multiple, are numerically calculated.

Organizing for sustainable procurement: theories, institutions and practice

That construction procurement needs to be re-organized to make it more sustainable implies that there is a problem with the current situation. Starting from this assumption, an overview of construction procurement sets the scene for a discussion of some recent developments relating to organizational frameworks for sustainable construction procurement. Emergent theories dealing with sustainable procurement are considered. There is a plethora of standards and guidance documents for organizing sustainable procurement, originating from a variety of organizations involved. These considerations form the context for approaches being used in practice to achieve sustainable procurement. The Chapter concludes with reflections on why current approaches are insufficient. It seems difficult to persuade clients to spend less money over the life cycle of their buildings. Future directions needed to translate sustainable procurement from rhetoric to reality include the development of suitable incentives and appropriate organizational structures.

A mathematical model of the sterol regulatory element binding protein 2 cholesterol biosynthesis pathway

Cholesterol is one of the key constituents for maintaining the cellular membrane and thus the integrity of the cell itself. In contrast high levels of cholesterol in the blood are known to be a major risk factor in the development of cardiovascular disease. We formulate a deterministic nonlinear ordinary differential equation model of the sterol regulatory element binding protein 2 (SREBP-2) cholesterol genetic regulatory pathway in an hepatocyte. The mathematical model includes a description of genetic transcription by SREBP-2 which is subsequently translated to mRNA leading to the formation of 3-hydroxy-3-methylglutaryl coenzyme A reductase (HMGCR), a main precursor of cholesterol synthesis. Cholesterol synthesis subsequently leads to the regulation of SREBP-2 via a negative feedback formulation. Parameterised with data from the literature, the model is used to understand how SREBP-2 transcription and regulation affects cellular cholesterol concentration. Model stability analysis shows that the only positive steady-state of the system exhibits purely oscillatory, damped oscillatory or monotic behaviour under certain parameter conditions. In light of our findings we postulate how cholesterol homestasis is maintained within the cell and the advantages of our model formulation are discussed with respect to other models of genetic regulation within the literature.

An experimental comparison between rival theories of rapid automatized naming performance and its relationship to reading

Two studies investigated the degree to which the relationship between Rapid Automatized Naming (RAN) performance and reading development is driven by shared phonological processes. Study 1 assessed RAN, phonological awareness and reading performance in 1010 children aged 7-10 years. Results showed that RAN deficits occurred in the absence of phonological awareness deficits. These were accompanied by modest reading delays. In structural equation modeling, solutions where RAN was subsumed within a phonological processing factor did not provide a good fit to the data, suggesting that processes outside phonology may drive RAN performance and its association with reading. Study 2 investigated Kail's (1991) proposal that speed of processing underlies this relationship. Children with single RAN deficits showed slower speed of processing than closely matched controls performing normally on RAN. However, regression analysis revealed that RAN made a unique contribution to reading even after accounting for processing speed. Theoretical implications are discussed.

Mathematical solutions for electricity networks in a low carbon future

Smart meters are becoming more ubiquitous as governments aim to reduce the risks to the energy supply as the world moves toward a low carbon economy. The data they provide could create a wealth of information to better understand customer behaviour. However at the household, and even the low voltage (LV) substation level, energy demand is extremely volatile, irregular and noisy compared to the demand at the high voltage (HV) substation level. Novel analytical methods will be required in order to optimise the use of household level data. In this paper we briefly outline some mathematical techniques which will play a key role in better understanding the customer's behaviour and create solutions for supporting the network at the LV substation level.

A genome wide association study of mathematical ability reveals an association at chromosome 3q29, a locus associated with autism and learning difficulties: a preliminary study

Mathematical ability is heritable, but few studies have directly investigated its molecular genetic basis. Here we aimed to identify specific genetic contributions to variation in mathematical ability. We carried out a genome wide association scan using pooled DNA in two groups of U.K. samples, based on end of secondary/high school national academic exam achievement: high (n = 419) versus low (n = 183) mathematical ability while controlling for their verbal ability. Significant differences in allele frequencies between these groups were searched for in 906,600 SNPs using the Affymetrix GeneChip Human Mapping version 6.0 array. After meeting a threshold of p<1.5×10-5, 12 SNPs from the pooled association analysis were individually genotyped in 542 of the participants and analyzed to validate the initial associations (lowest p-value 1.14 ×10-6). In this analysis, one of the SNPs (rs789859) showed significant association after Bonferroni correction, and four (rs10873824, rs4144887, rs12130910 rs2809115) were nominally significant (lowest p-value 3.278 × 10-4). Three of the SNPs of interest are located within, or near to, known genes (FAM43A, SFT2D1, C14orf64). The SNP that showed the strongest association, rs789859, is located in a region on chromosome 3q29 that has been previously linked to learning difficulties and autism. rs789859 lies 1.3 kbp downstream of LSG1, and 700 bp upstream of FAM43A, mapping within the potential promoter/regulatory region of the latter. To our knowledge, this is only the second study to investigate the association of genetic variants with mathematical ability, and it highlights a number of interesting markers for future study.

Rerum cognoscere causas: part I - How do the ideas of system dynamics relate to traditional social theories and the voluntarism/determinism debate?

This is the first half of a two-part paper which deals with the social theoretic assumptions underlying system dynamics. The motivation is that clarification in this area can help mainstream social scientists to understand how our field relates to their literature, methods and concerns. Part I has two main sections. The aim of the first is to answer the question: How do the ideas of system dynamics relate to traditional social theories? The theoretic assumptions of the field are seldom explicit but rather are implicit in its practice. The range of system dynamics practice is therefore considered and related to a framework - widely used in both operational research (OR) and systems science - that organises the assumptions behind traditional social theoretic paradigms. Distinct and surprisingly varied groupings of practice are identified, making it difficult to place system dynamics in any one paradigm with any certainty. The difficulties of establishing a social theoretic home for system dynamics are exemplified in the second main section. This is done by considering the question: Is system dynamics deterministic? An analysis shows that attempts to relate system dynamics to strict notions of voluntarism or determinism quickly indicate that the field does not fit with either pole of this dichotomous, and strictly paradigmatic, view. Part I therefore concludes that definitively placing system dynamics with respect to traditional social theories is highly problematic. The scene is therefore set for Part II of the paper, which proposes an innovative and potentially fruitful resolution to this problem.

Testing substorm theories: The need for multipoint observations

The requirement for multipoint observations to test theories of magnetospheric substorms is reviewed. A wide variety of such theories have been proposed, but these cannot be properly evaluated because we do not understand how the various features of a substorm are causally linked. In terms of explaining certain substorm features, some theories may be mutually-exclusive rivals. But this is not always the case, making it possible that theories may be either combined into a synthesis model or loosely connected in a more modular view of substorms. Some key questions are defined which require multipoint in-situ measurements, combined with remote sensing observations, of the development and relationship of the major substorm features.