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.

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.

Learning enjoyment in early adolescence

There is empirical evidence showing that positive emotional and motivational factors in formal learning contexts decrease at the stage of young adolescence. According to Stage-Environment-Fit Theory and Self-Determination Theory, this change should be explained by a non-fulfilment of students' needs. By combining two different methods (questionnaires and day-to-day diaries) and applying a longitudinal design, this study aimed to explore the change in and the determinants of habitual and actual learning enjoyment. The sample consisted of 356 students. Quantitative results indicated that learning enjoyment and classroom practices decreased between Grades 6 and 7. Path analyses revealed that classroom practices are the source of students' learning enjoyment, while self-efficacy functions as a partial mediator. Data from students' diaries showed that a teacher's neglect of students' needs for competence and relatedness were significant sources of impeded learning enjoyment. Practical implications suggest the relevance of adjusting learning conditions to the needs of young adolescents in order to provide a facilitating basis for learning enjoyment.

Convolution roots and differentiability of isotropic positive definite functions on spheres

We prove that any isotropic positive definite function on the sphere can be written as the spherical self-convolution of an isotropic real-valued function. It is known that isotropic positive definite functions on d-dimensional Euclidean space admit a continuous derivative of order [(d − 1)/2]. We show that the same holds true for isotropic positive definite functions on spheres and prove that this result is optimal for all odd dimensions.

Combining Wireless Sensor Networks and Machine Learning for Flash Flood Nowcasting

This paper addresses an investigation with machine learning (ML) classification techniques to assist in the problem of flash flood now casting. We have been attempting to build a Wireless Sensor Network (WSN) to collect measurements from a river located in an urban area. The machine learning classification methods were investigated with the aim of allowing flash flood now casting, which in turn allows the WSN to give alerts to the local population. We have evaluated several types of ML taking account of the different now casting stages (i.e. Number of future time steps to forecast). We have also evaluated different data representation to be used as input of the ML techniques. The results show that different data representation can lead to results significantly better for different stages of now casting.

Executive functions after pediatric mild traumatic brain injury: A prospective short-term longitudinal study

Traumatic brain injuries (TBIs) occur frequently in childhood and entail broad cognitive deficits, particularly in the domain of executive functions (EF). Concerning mild TBI (mTBI), only little empirical evidence is available on acute and postacute performance in EF. Given that EF are linked to school adaptation and achievement, even subtle deficits in performance may affect children's academic careers. The present study assessed performance in the EF components of inhibition, working memory (WM), and switching in children after mTBI. Regarding both acute and postacute consequences, performance trajectories were measured in 13 patients aged between 5 and 10 years and 13 controls who were closely matched in terms of sex, age, and education. Performance in the EF components of inhibition, switching, and WM was assessed in a short-term longitudinal design at 2, 6, and 12 weeks after the mTBI. Results indicate subtle deficits after mTBI, which became apparent in the longitudinal trajectory in the EF components of switching and WM. Compared with controls, children who sustained mTBI displayed an inferior performance enhancement across testing sessions in the first 6 weeks after the injury in switching and WM, resulting in a delayed deficit in the EF component of WM 12 weeks after the injury. Results are interpreted as mTBI-related deficits that become evident in terms of an inability to profit from previous learning opportunities, a finding that is potentially important for children's mastery of their daily lives.

The block numerical range of analytic operator functions

We introduce the block numerical range Wn(L) of an operator function L with respect to a decomposition H = H1⊕. . .⊕Hn of the underlying Hilbert space. Our main results include the spectral inclusion property and estimates of the norm of the resolvent for analytic L . They generalise, and improve, the corresponding results for the numerical range (which is the case n = 1) since the block numerical range is contained in, and may be much smaller than, the usual numerical range. We show that refinements of the decomposition entail inclusions between the corresponding block numerical ranges and that the block numerical range of the operator matrix function L contains those of its principal subminors. For the special case of operator polynomials, we investigate the boundedness of Wn(L) and we prove a Perron-Frobenius type result for the block numerical radius of monic operator polynomials with coefficients that are positive in Hilbert lattice sense.

Continued fractions built from convex sets and convex functions

In a partially ordered semigroup with the duality (or polarity) transform, it is pos- sible to define a generalisation of continued fractions. General sufficient conditions for convergence of continued fractions are provided. Two particular applications concern the cases of convex sets with the Minkowski addition and the polarity transform and the family of non-negative convex functions with the Legendre–Fenchel and Artstein-Avidan–Milman transforms.

Linking executive functions and procedural metacognition

Traditionally, researchers have discussed executive function and metacognition independently. However, more recently, theoretical frameworks linking these two groups of higher order cognitive processes have been advanced. In this article, we explore the relationship between executive function and procedural metacognition, and summarize theoretical similarities. From a developmental perspective, the assumed theoretical resemblances seem to be supported, considering development trajectories and their substantial impact on areas that include learning and memory. Moreover, empirical evidence suggests direct relationships on the task level, on the level of latent variables, and in terms of involved brain regions. However, research linking the two concepts directly remains rare. We discuss evidence and developmental mechanisms, and propose ways researchers can investigate links between executive function and procedural metacognition.

Differentiating the Multipoint Expected Improvement for Optimal Batch Design

This work deals with parallel optimization of expensive objective functions which are modelled as sample realizations of Gaussian processes. The study is formalized as a Bayesian optimization problem, or continuous multi-armed bandit problem, where a batch of q > 0 arms is pulled in parallel at each iteration. Several algorithms have been developed for choosing batches by trading off exploitation and exploration. As of today, the maximum Expected Improvement (EI) and Upper Confidence Bound (UCB) selection rules appear as the most prominent approaches for batch selection. Here, we build upon recent work on the multipoint Expected Improvement criterion, for which an analytic expansion relying on Tallis’ formula was recently established. The computational burden of this selection rule being still an issue in application, we derive a closed-form expression for the gradient of the multipoint Expected Improvement, which aims at facilitating its maximization using gradient-based ascent algorithms. Substantial computational savings are shown in application. In addition, our algorithms are tested numerically and compared to state-of-the-art UCB-based batchsequential algorithms. Combining starting designs relying on UCB with gradient-based EI local optimization finally appears as a sound option for batch design in distributed Gaussian Process optimization.

How gender fair are German schoolbooks in the twenty-first century? An analysis of language and illustrations in schoolbooks for mathematics and German

Schoolbooks convey not only school-relevant knowledge; they also influence the development of stereotypes about different social groups. Particularly during the 1970s and 1980s, many studies analysed schoolbooks and criticised the overall predominance of male persons and of traditional role allocations. Since that time, women’s and men’s occupations and social functions have changed considerably. The present research investigated gender portrayals in schoolbooks for German and mathematics that were recently published in Germany. We examined the proportions of female and male persons in pictures and texts and categorized their activities, occupational and parental roles. Going beyond previous studies, we added two criteria: the use of gender-fair language and the spatial arrangements of persons in pictures. Our results show that schoolbooks for German contained almost balanced depictions of girls and boys, whereas women were less frequently shown than men. In mathematics books, males outnumbered females in general. Across both types of books, female and male persons were engaged in many different activities, not only gendertyped ones; however, male persons were more often described via their profession than females. Use of gender-fair language has found its way into schoolbooks but is not used consistently. Books for German were more gender fair in terms of linguistic forms than books for mathematics. For spatial arrangements, we found no indication for gender biases. The results are discussed with a focus on how schoolbooks can be optimized to contribute to gender equality.