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The main goal of our target article was to provide concrete recommendations for improving the replicability of research findings. Most of the comments focus on this point. In addition, a few comments were concerned with the distinction between replicability and generalizability and the role of theory in replication. We address all comments within the conceptual structure of the target article and hope to convince readers that replication in psychological science amounts to much more than hitting the lottery twice.
We consider systems of Euler-Lagrange equations with two degrees of freedom and with Lagrangian being quadratic in velocities. For this class of equations the generic case of the equivalence problem is solved with respect to point transformations. Using Lie's infinitesimal method we construct a basis of differential invariants and invariant differentiation operators for such systems. We describe certain types of Lagrangian systems in terms of their invariants. The results are illustrated by several examples.
The two and k-sample tests of equality of the survival distributions against the alternatives including cross-effects of survival functions, proportional and monotone hazard ratios, are given for the right censored data. The asymptotic power against approaching alternatives is investigated. The tests are applied to the well known chemio and radio therapy data of the Gastrointestinal Tumor Study Group. The P-values for both proposed tests are much smaller then in the case of other known tests. Differently from the test of Stablein and Koutrouvelis the new tests can be applied not only for singly but also to randomly censored data.
Prosody and information status in typological perspective - Introduction to the Special Issue
(2015)
Background: Several equipment interventions like optimizing seat position or optimizing shoe/insole/pedal interface are suggested to reduce overuse injury in cycling. Data analyzing clinical or biomechanical effects of those interventions is sparse. Foot orthoses out of carbon fiber are one possibility to alter the interface between foot and pedal. The aim of this study was therefore to analyze plantar pressure distribution in carbon fiber foot orthoses in comparison to standard insoles of commercially available cycling shoes. Materials and Methods: 11 pain-free triathletes (Age: 29 +/- 9, 1.77 +/- 0.04 m, 68 5 kg) were tested on a cycle ergometer at 60 and 90 rotations per minute (rpm) at workloads of 200 and 300 Watts. Subjects wore in randomized order a cycling shoe with its standard insole (control condition CO) or the shoe with carbon fiber foot orthoses (Condition CA). Mean peak pressure out of 30 movement cycles were extracted for the total foot and specific foot regions (rear, mid, fore foot (medial, central, lateral) and toe region). Three-factor ANOVAs (factor foot orthoses, rpm, workload) for repeated measures (alpha = 0.05) were used to analyze the main question of a foot orthoses effect on peak in-shoe plantar pressure. Results: Peak pressures in the total foot were in a range of 70-75 kPa for 200 Watts (W) (300 W: 85-110 kPa). The carbon fiber foot orthoses reduced peak pressures by -4,1% compared to the standard insole (p = 0,10). In the foot regions rear(-16,6%, p<0.001), mid (-20,0%, p<0.001) and fore foot (-5.9%, p < 0.03)CA reduced peak pressure compared to CO. In the toe region, peak pressure was higher in CA (+16,2%) compared to CO (p<0,001). The lateral fore foot showed higher peak pressures in CA (+34%) and CO (+59%) compared to medial and central fore foot. Conclusion: Carbon fiber can serve as a suitable material for foot orthoses manufacturing in cycling. Plantar pressures do not increase due to the stiffness of the carbon. Individual customization may have the potential to reduce peak pressure in certain foot areas.
We introduce a theoretical framework for performing statistical hypothesis testing simultaneously over a fairly general, possibly uncountably infinite, set of null hypotheses. This extends the standard statistical setting for multiple hypotheses testing, which is restricted to a finite set. This work is motivated by numerous modern applications where the observed signal is modeled by a stochastic process over a continuum. As a measure of type I error, we extend the concept of false discovery rate (FDR) to this setting. The FDR is defined as the average ratio of the measure of two random sets, so that its study presents some challenge and is of some intrinsic mathematical interest. Our main result shows how to use the p-value process to control the FDR at a nominal level, either under arbitrary dependence of p-values, or under the assumption that the finite dimensional distributions of the p-value process have positive correlations of a specific type (weak PRDS). Both cases generalize existing results established in the finite setting, the latter one leading to a less conservative procedure. The interest of this approach is demonstrated in several non-parametric examples: testing the mean/signal in a Gaussian white noise model, testing the intensity of a Poisson process and testing the c.d.f. of i.i.d. random variables. Conceptually, an interesting feature of the setting advocated here is that it focuses directly on the intrinsic hypothesis space associated with a testing model on a random process, without referring to an arbitrary discretization.
We prove statistical rates of convergence for kernel-based least squares regression from i.i.d. data using a conjugate gradient algorithm, where regularization against overfitting is obtained by early stopping. This method is related to Kernel Partial Least Squares, a regression method that combines supervised dimensionality reduction with least squares projection. Following the setting introduced in earlier related literature, we study so-called "fast convergence rates" depending on the regularity of the target regression function (measured by a source condition in terms of the kernel integral operator) and on the effective dimensionality of the data mapped into the kernel space. We obtain upper bounds, essentially matching known minimax lower bounds, for the L^2 (prediction) norm as well as for the stronger Hilbert norm, if the true
regression function belongs to the reproducing kernel Hilbert space. If the latter assumption is not fulfilled, we obtain similar convergence rates for appropriate norms, provided additional unlabeled data are available.