ANOVA kernels and RKHS of zero mean functions for model-based sensitivity analysis

Given a reproducing kernel Hilbert space (H,〈.,.〉)(H,〈.,.〉) of real-valued functions and a suitable measure μμ over the source space D⊂RD⊂R, we decompose HH as the sum of a subspace of centered functions for μμ and its orthogonal in HH. This decomposition leads to a special case of ANOVA kernels, for which the functional ANOVA representation of the best predictor can be elegantly derived, either in an interpolation or regularization framework. The proposed kernels appear to be particularly convenient for analyzing the effect of each (group of) variable(s) and computing sensitivity indices without recursivity.

Kernels and Designs for Modelling Invariant Functions: From Group Invariance to Additivity

We focus on kernels incorporating different kinds of prior knowledge on functions to be approximated by Kriging. A recent result on random fields with paths invariant under a group action is generalised to combinations of composition operators, and a characterisation of kernels leading to random fields with additive paths is obtained as a corollary. A discussion follows on some implications on design of experiments, and it is shown in the case of additive kernels that the so-called class of “axis designs” outperforms Latin hypercubes in terms of the IMSE criterion.

Tree-level contribution to B[over ¯]→X_{d}γ using fragmentation functions

We evaluate the most important tree-level contributions connected with the b→uu ¯ ¯ dγ transition to the inclusive radiative decay B ¯ ¯ ¯ →X d γ using fragmentation functions. In this framework the singularities arising from collinear photon emission from the light quarks (u , u ¯ ¯ , and d ) can be absorbed into the (bare) quark-to-photon fragmentation function. We use as input the fragmentation function extracted by the ALEPH group from the two-jet cross section measured at the large electron positron (LEP) collider, where one of the jets is required to contain a photon. To get the quark-to-photon fragmentation function at the fragmentation scale μ F ∼m b , we use the evolution equation, which we solve numerically. We then calculate the (integrated) photon energy spectrum for b→uu ¯ ¯ dγ related to the operators P u 1,2 . For comparison, we also give the corresponding results when using nonzero (constituent) masses for the light quarks.

Calculating track thrust with track functions

In e+e− event shapes studies at LEP, two different measurements were sometimes performed: a “calorimetric” measurement using both charged and neutral particles and a “track-based” measurement using just charged particles. Whereas calorimetric measurements are infrared and collinear safe, and therefore calculable in perturbative QCD, track-based measurements necessarily depend on nonperturbative hadronization effects. On the other hand, track-based measurements typically have smaller experimental uncertainties. In this paper, we present the first calculation of the event shape “track thrust” and compare to measurements performed at ALEPH and DELPHI. This calculation is made possible through the recently developed formalism of track functions, which are nonperturbative objects describing how energetic partons fragment into charged hadrons. By incorporating track functions into soft-collinear effective theory, we calculate the distribution for track thrust with next-to-leading logarithmic resummation. Due to a partial cancellation between nonperturbative parameters, the distributions for calorimeter thrust and track thrust are remarkably similar, a feature also seen in LEP data.

Influence of Gestational Age and Parental Education on Executive Functions of Children Born Very Preterm

Background: Children born very preterm (<32 weeks’ gestational age; VPT) and/or very low birth weight (<1500 g; VLBW) are at high risk of deficits in executive functions, namely inhibition, working memory, and shifting. Both, gestational age and socioeconomic factors, such as parental education, are known to influence executive functions, with children born at lower gestational age and with lower educated parents displaying worse executive skills. This study aimed to investigate if maternal and paternal education moderated the relationship between gestational age and executive functions in VPT/VLBW children aged 8-12 years. It was hypothesised that the disadvantageous effect of low gestational age could be buffered more easily in families with higher educational background. Methods: Sixty VPT/VLBW children born in the cohort of 1998-2003 were recruited. All children completed executive function tasks (inhibition, working memory, and shifting). Results: There was a significant dose-response-relationship between gestational age and inhibition, with children being born at earlier gestational age showing worse inhibition. However, neither maternal nor paternal education moderated the relationship between gestational age and executive functions significantly. Conclusion: children than parental education. The disadvantageous effect of low gestational age was equal in children with higher and lower educated parents. However, the impact of gestational age and parental education on executive functions may differ depending on the socioeconomic spectrum of the study sample.

Executive functions and their differential contribution to sustained attention in 5- to 8-year-old children

ABSTRACT Everyday routine in general and school settings in particular make high demands on children's abilities to sustain their focus of attention over longer time periods. School tasks thus require the child to accomplish the task on an appropriate level of performance while maintaining the focus of attention even under repetitious or distracting conditions. However, sustained attention (SA) may be a more heterogeneous construct than commonly assumed as it requires the individual not only to sustain attentional capacities but also to store and maintain the task rule (working memory), to inhibit inappropriate responses (inhibition), and to switch according to requirements (switching). It might thus involve processes counted among executive functions (EF). In the present study, performance in EF tasks (covering the core components inhibition, switching, and working memory) and in a SA task was assessed in 118 children, aged between 5;0 and 8;11 years. Similar age-dependent performance trajectories were found in EF components and SA, indicating ongoing performance improvements between 5 until at least 8 years of age in SA and in EF. Interrelations between single EF components and SA showed to be small to moderate. Finally, different patterns of SA performance predictions were found in age-homogeneous subgroups with inhibition being crucial for SA performance in the youngest and switching in the oldest age group. Taken as a whole, even though similarities in assumed developmental trajectories and substantial interrelations point to common underlying processes in EF and SA, age-dependent patterns of explained variance indicate clear discriminability.

Personality factors in elementary school children: Contributions to academic performance over and above executive functions?

Unique contributions of Big Five personality factors to academic performance in young elementary school children were explored. Extraversion and Openness (labeled “Culture” in our study) uniquely contributed to academic performance, over and above the contribution of executive functions in first and second grade children (N = 446). Well established associations between Conscientiousness and academic performance, however, could only be replicated with regard to zero-order correlations. Executive functions (inhibition, updating, and shifting), for their part, proved to be powerful predictors of academic performance. Results were to some extent dependent on the criterion with which academic performance was measured: Both personality factors had stronger effects on grades than on standardized achievement tests, whereas the opposite was true for executive functions. Finally, analyses on gender differences revealed that Extraversion and Openness/Culture played a more dominant role in girls than in boys, but only regarding grades.

Executive functions in 5- to 8-year olds: Developmental changes and relationship to academic achievement

Pronounced improvements in executive functions (EF) during preschool years have been documented in cross-sectional studies. However, longitudinal evidence on EF development during the transition to school and predictive associations between early EF and later school achievement are still scarce. This study examined developmental changes in EF across three time-points, the predictive value of EF for mathematical, reading and spelling skills and explored children's specific academic attainment as a function of early EF. Participants were 323 children following regular education; 160 children were enrolled in prekindergarten (younger cohort: 69 months) and 163 children in kindergarten (older cohort: 78.4 months) at the first assessment. Various tasks of EF were administered three times with an interval of one year each. Mathematical, reading and spelling skills were measured at the last assessment. Individual background characteristics such as vocabulary, non-verbal intelligence and socioeconomic status were included as control variables. In both cohorts, changes in EF were substantial; improvements in EF, however, were larger in preschoolers than school-aged children. EF assessed in preschool accounted for substantial variability in mathematical, reading and spelling achievement two years later, with low EF being especially associated with significant academic disadvantages in early school years. Given that EF continue to develop from preschool into primary school years and that starting with low EF is associated with lower school achievement, EF may be considered as a marker or risk for academic disabilities.