The F test for comparing two normal variances: correct and incorrect calculation of the two-sided p-value?

This article illustrates that not all statistical software packages are correctly calculating a p-value for the classical F test comparison of two independent Normal variances. This is illustrated with a simple example, and the reasons why are discussed. Eight different software packages are considered.

Small time two-sided LIL behavior for Lévy processes at zero

We wish to characterize when a Lévy process X t crosses boundaries b(t), in a two-sided sense, for small times t, where b(t) satisfies very mild conditions. An integral test is furnished for computing the value of sup t→0|X t |/b(t) = c. In some cases, we also specify a function b(t) in terms of the Lévy triplet, such that sup t→0 |X t |/b(t) = 1.

On the principal eigenvalue of a Robin problem with a large parameter

We study the asymptotic behaviour of the principal eigenvalue of a Robin (or generalised Neumann) problem with a large parameter in the boundary condition for the Laplacian in a piecewise smooth domain. We show that the leading asymptotic term depends only on the singularities of the boundary of the domain, and give either explicit expressions or two-sided estimates for this term in a variety of situations.

Extended factorizations of exponential functionals of Lévy processes

Pardo, Patie, and Savov derived, under mild conditions, a Wiener-Hopf type factorization for the exponential functional of proper Lévy processes. In this paper, we extend this factorization by relaxing a finite moment assumption as well as by considering the exponential functional for killed Lévy processes. As a by-product, we derive some interesting fine distributional properties enjoyed by a large class of this random variable, such as the absolute continuity of its distribution and the smoothness, boundedness or complete monotonicity of its density. This type of results is then used to derive similar properties for the law of maxima and first passage time of some stable Lévy processes. Thus, for example, we show that for any stable process with $\rho\in(0,\frac{1}{\alpha}-1]$, where $\rho\in[0,1]$ is the positivity parameter and $\alpha$ is the stable index, then the first passage time has a bounded and non-increasing density on $\mathbb{R}_+$. We also generate many instances of integral or power series representations for the law of the exponential functional of Lévy processes with one or two-sided jumps. The proof of our main results requires different devices from the one developed by Pardo, Patie, Savov. It relies in particular on a generalization of a transform recently introduced by Chazal et al together with some extensions to killed Lévy process of Wiener-Hopf techniques. The factorizations developed here also allow for further applications which we only indicate here also allow for further applications which we only indicate here.

Application of the direct Liapunov method to the problem of symmetric stability in the atmosphere

The problem of symmetric stability is examined within the context of the direct Liapunov method. The sufficient conditions for stability derived by Fjørtoft are shown to imply finite-amplitude, normed stability. This finite-amplitude stability theorem is then used to obtain rigorous upper bounds on the saturation amplitude of disturbances to symmetrically unstable flows.By employing a virial functional, the necessary conditions for instability implied by the stability theorem are shown to be in fact sufficient for instability. The results of Ooyama are improved upon insofar as a tight two-sided (upper and lower) estimate is obtained of the growth rate of (modal or nonmodal) symmetric instabilities.The case of moist adiabatic systems is also considered.

A Wiener-Hopf type factorization for the exponential functional of Levy processes

For a Lévy process ξ=(ξt)t≥0 drifting to −∞, we define the so-called exponential functional as follows: Formula Under mild conditions on ξ, we show that the following factorization of exponential functionals: Formula holds, where × stands for the product of independent random variables, H− is the descending ladder height process of ξ and Y is a spectrally positive Lévy process with a negative mean constructed from its ascending ladder height process. As a by-product, we generate an integral or power series representation for the law of Iξ for a large class of Lévy processes with two-sided jumps and also derive some new distributional properties. The proof of our main result relies on a fine Markovian study of a class of generalized Ornstein–Uhlenbeck processes, which is itself of independent interest. We use and refine an alternative approach of studying the stationary measure of a Markov process which avoids some technicalities and difficulties that appear in the classical method of employing the generator of the dual Markov process.

Immersive Projection for biochemical pattern matching

In all biological processes, protein molecules and other small molecules interact to function and form transient macromolecular complexes. This interaction of two or more molecules can be described by a docking event. Docking is an important phase for structure-based drug design strategies, as it can be used as a method to simulate protein-ligand interactions. Various docking programs exist that allow automated docking, but most of them have limited visualization and user interaction. It would be advantageous if scientists could visualize the molecules participating in the docking process, manipulate their structures and manually dock them before submitting the new conformations to an automated docking process in an immersive environment, which can help stimulate the design/docking process. This also could greatly reduce docking time and resources. To achieve this, we propose a new virtual modelling/docking program, whereby the advantages of virtual modelling programs and the efficiency of the algorithms in existing docking programs will be merged.

The unsteady flow of a weakly compressible fluid in a thin porous layer. I: Two-dimensional theory

We consider the problem of determining the pressure and velocity fields for a weakly compressible fluid flowing in a two-dimensional reservoir in an inhomogeneous, anisotropic porous medium, with vertical side walls and variable upper and lower boundaries, in the presence of vertical wells injecting or extracting fluid. Numerical solution of this problem may be expensive, particularly in the case that the depth scale of the layer h is small compared to the horizontal length scale l. This is a situation which occurs frequently in the application to oil reservoir recovery. Under the assumption that epsilon=h/l<<1, we show that the pressure field varies only in the horizontal direction away from the wells (the outer region). We construct two-term asymptotic expansions in epsilon in both the inner (near the wells) and outer regions and use the asymptotic matching principle to derive analytical expressions for all significant process quantities. This approach, via the method of matched asymptotic expansions, takes advantage of the small aspect ratio of the reservoir, epsilon, at precisely the stage where full numerical computations become stiff, and also reveals the detailed structure of the dynamics of the flow, both in the neighborhood of wells and away from wells.

Optimal inverter design for an induction machine using resonant frequency matching

The frequency responses of two 50 Hz and one 400 Hz induction machines have been measured experimentally over a frequency range of 1 kHz to 400 kHz. This study has shown that the stator impedances of the machines behave in a similar manner to a parallel resonant circuit, and hence have a resonant point at which the Input impedance of the machine is at a maximum. This maximum impedance point was found experimentally to be as low as 33 kHz, which is well within the switching frequency ranges of modern inverter drives. This paper investigates the possibility of exploiting the maximum impedance point of the machine, by taking it into consideration when designing an inverter, in order to minimize ripple currents due to the switching frequency. Minimization of the ripple currents would reduce torque pulsation and losses, increasing overall performance. A modified machine model was developed to take into account the resonant point, and this model was then simulated with an inverter to demonstrate the possible advantages of matching the inverter switching frequency to the resonant point. Finally, in order to experimentally verify the simulated results, a real inverter with a variable switching frequency was used to drive an induction machine. Experimental results are presented.

Generalized matching networks and their properties

In this paper, we introduce two kinds of graphs: the generalized matching networks (GMNs) and the recursive generalized matching networks (RGMNs). The former generalize the hypercube-like networks (HLNs), while the latter include the generalized cubes and the star graphs. We prove that a GMN on a family of k-connected building graphs is -connected. We then prove that a GMN on a family of Hamiltonian-connected building graphs having at least three vertices each is Hamiltonian-connected. Our conclusions generalize some previously known results.

EDITOR'S CHOICE: REVIEW: Trait matching of flower visitors and crops predicts fruit set better than trait diversity

Understanding the relationships between trait diversity, species diversity and ecosystem functioning is essential for sustainable management. For functions comprising two trophic levels, trait matching between interacting partners should also drive functioning. However, the predictive ability of trait diversity and matching is unclear for most functions, particularly for crop pollination, where interacting partners did not necessarily co-evolve. World-wide, we collected data on traits of flower visitors and crops, visitation rates to crop flowers per insect species and fruit set in 469 fields of 33 crop systems. Through hierarchical mixed-effects models, we tested whether flower visitor trait diversity and/or trait matching between flower visitors and crops improve the prediction of crop fruit set (functioning) beyond flower visitor species diversity and abundance. Flower visitor trait diversity was positively related to fruit set, but surprisingly did not explain more variation than flower visitor species diversity. The best prediction of fruit set was obtained by matching traits of flower visitors (body size and mouthpart length) and crops (nectar accessibility of flowers) in addition to flower visitor abundance, species richness and species evenness. Fruit set increased with species richness, and more so in assemblages with high evenness, indicating that additional species of flower visitors contribute more to crop pollination when species abundances are similar. Synthesis and applications. Despite contrasting floral traits for crops world-wide, only the abundance of a few pollinator species is commonly managed for greater yield. Our results suggest that the identification and enhancement of pollinator species with traits matching those of the focal crop, as well as the enhancement of pollinator richness and evenness, will increase crop yield beyond current practices. Furthermore, we show that field practitioners can predict and manage agroecosystems for pollination services based on knowledge of just a few traits that are known for a wide range of flower visitor species.