Weighted overconstrained least-squares mixed finite elements for hyperelasticity

The present contribution aims to improve the least-squares finite element method (LSFEM) with respect to the approximation quality in hyperelasticity. We consider a geometrically nonlinear elastic setup and here especially bending dominated problems. Compared with other variational approaches as for example the Galerkin method, the main drawback of least-squares formulations is the unsatisfying approximation quality in terms of accuracy and robustness of especially lower-order elements, see e.g. SCHWARZ ET AL. [1]. In order to circumvent these problems, we introduce an overconstrained first-order stress-displacement system with suited weights. For the interpolation of the unknowns standard polynomials for the displacements and vector-valued Raviart-Thomas functions for the approximation of the stresses are used. Finally, a numerical example is presented in order to show the improvement of performance and accuracy. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Monotonicity for excited random walk in high dimensions

We prove that the drift θ(d, β) for excited random walk in dimension d is monotone in the excitement parameter ${\beta \in [0,1]}$ , when d is sufficiently large. We give an explicit criterion for monotonicity involving random walk Green’s functions, and use rigorous numerical upper bounds provided by Hara (Private communication, 2007) to verify the criterion for d ≥ 9.     

Long-term characteristics of analogical processing in high-school students with high fluid intelligence: an fMRI study

Intelligence is known to predict scholastic achievement and enables high performance in cognitive tasks. Fluid intelligence is strongly related to analogical reasoning abilities, which are fundamental to mathematical thinking. Geometric analogical reasoning is a prototypical measure of fluid intelligence. However, the cerebral correlates of geometric analogical reasoning and their developmental modulation over time are still rarely investigated. We report a 1-year follow-up functional magnetic resonance imaging study of a geometric analogical reasoning task in high fluid intelligence high-school students. This study was designed to characterise the cerebral correlates of geometric analogical reasoning and to improve our knowledge about the impact of general cognitive development on behavioural performance and on cerebral mechanisms underlying geometric analogical reasoning in adolescents. Our data indicate that a fronto-parietal network comprising the left and right parietal lobes and the left middle frontal gyrus was equally modulated by task difficulty at both measuring time points. At the behavioural level, however, participants showed improvements in performance at the second measuring time point. The behavioural improvements point to a more efficient task processing. As this is not accompanied by differential recruitment of fronto-parietal brain regions, the data suggest an increase in neural efficiency for these brain regions.     

The Penalty Functions Method and Multiplier Rules Based on the Mordukhovich Subdifferential

We show that the finite-dimensional Fritz John multiplier rule, which is based on the limiting/Mordukhovich subdifferential, can be proved by using differentiable penalty functions and the basic calculus tools in variational analysis. The corresponding Kuhn–Tucker multiplier rule is derived from the Fritz John multiplier rule by imposing a constraint qualification condition or the exactness of an ?₁ penalty function. Complementing the existing proofs, our proofs provide another viewpoint on the fundamental multiplier rules employing the Mordukhovich subdifferential.     

Approximated Bayes and empirical Bayes confidence intervals—The known variance case

In this paper hierarchical Bayes and empirical Bayes results are used to obtain confidence intervals of the population means in the case of real problems. This is achieved by approximating the posterior distribution with a Pearson distribution. In the first example hierarchical Bayes confidence intervals for the Efron and Morris (1975, J. Amer. Statist. Assoc., 70, 311–319) baseball data are obtained. The same methods are used in the second example to obtain confidence intervals of treatment effects as well as the difference between treatment effects in an analysis of variance experiment. In the third example hierarchical Bayes intervals of treatment effects are obtained and compared with normal approximations in the unequal variance case.Financially supported by the CSIR and the University of the Orange Free State, Central Research Fund.     

Topological degree of a family of convex functions and localization of nash equilibrium points

We define the degree of a family of convex functionsf _x, wherex , and prove that, if this degree is different from zero, one has at least one Nash equilibrium point in . This is a criterion of localization of such equilibrium points.