On the generalized eigenvalue problem for the Rossby wave vertical velocity in the presence of mean flow and topography

In a series of papers, Killworth and Blundell have proposed to study the effects of a background mean flow and topography on Rossby wave propagation by means of a generalized eigenvalue problem formulated in terms of the vertical velocity, obtained from a linearization of the primitive equations of motion. However, it has been known for a number of years that this eigenvalue problem contains an error, which Killworth was prevented from correcting himself by his unfortunate passing and whose correction is therefore taken up in this note. Here, the author shows in the context of quasigeostrophic (QG) theory that the error can ulti- mately be traced to the fact that the eigenvalue problem for the vertical velocity is fundamentally a non- linear one (the eigenvalue appears both in the numerator and denominator), unlike that for the pressure. The reason that this nonlinear term is lacking in the Killworth and Blundell theory comes from neglecting the depth dependence of a depth-dependent term. This nonlinear term is shown on idealized examples to alter significantly the Rossby wave dispersion relation in the high-wavenumber regime but is otherwise irrelevant in the long-wave limit, in which case the eigenvalue problems for the vertical velocity and pressure are both linear. In the general dispersive case, however, one should first solve the generalized eigenvalue problem for the pressure vertical structure and, if needed, diagnose the vertical velocity vertical structure from the latter.

Type-1 error inflation in the traditional by-participant analysis to metamemory accuracy: a generalized mixed-effects model perspective

In order to examine metacognitive accuracy (i.e., the relationship between metacognitive judgment and memory performance), researchers often rely on by-participant analysis, where metacognitive accuracy (e.g., resolution, as measured by the gamma coefficient or signal detection measures) is computed for each participant and the computed values are entered into group-level statistical tests such as the t-test. In the current work, we argue that the by-participant analysis, regardless of the accuracy measurements used, would produce a substantial inflation of Type-1 error rates, when a random item effect is present. A mixed-effects model is proposed as a way to effectively address the issue, and our simulation studies examining Type-1 error rates indeed showed superior performance of mixed-effects model analysis as compared to the conventional by-participant analysis. We also present real data applications to illustrate further strengths of mixed-effects model analysis. Our findings imply that caution is needed when using the by-participant analysis, and recommend the mixed-effects model analysis.

The full infinite dimensional moment problem on semi-algebraic sets of generalized functions

We consider a generic basic semi-algebraic subset S of the space of generalized functions, that is a set given by (not necessarily countably many) polynomial constraints. We derive necessary and sufficient conditions for an infinite sequence of generalized functions to be realizable on S, namely to be the moment sequence of a finite measure concentrated on S. Our approach combines the classical results about the moment problem on nuclear spaces with the techniques recently developed to treat the moment problem on basic semi-algebraic sets of Rd. In this way, we determine realizability conditions that can be more easily verified than the well-known Haviland type conditions. Our result completely characterizes the support of the realizing measure in terms of its moments. As concrete examples of semi-algebraic sets of generalized functions, we consider the set of all Radon measures and the set of all the measures having bounded Radon–Nikodym density w.r.t. the Lebesgue measure.

Accurate delay analysis in prioritised wireless sensor networks for generalized packet arrival

This letter presents an accurate delay analysis in prioritised wireless sensor networks (WSN). The analysis is an enhancement of the existing analysis proposed by Choobkar and Dilmaghani, which is only applicable to the case where the lower priority nodes always have packets to send in the empty slots of the higher priority node. The proposed analysis is applicable for any pattern of packet arrival, which includes the general case where the lower priority nodes may or may not have packets to send in the empty slots of the higher priority nodes. Evaluation of both analyses showed that the proposed delay analysis has better accuracy over the full range of loads and provides an excellent match to simulation results.

Generalized convective quasi-equilibrium principle

A generalization of Arakawa and Schubert's convective quasi-equilibrium principle is presented for a closure formulation of mass-flux convection parameterization. The original principle is based on the budget of the cloud work function. This principle is generalized by considering the budget for a vertical integral of an arbitrary convection-related quantity. The closure formulation includes Arakawa and Schubert's quasi-equilibrium, as well as both CAPE and moisture closures as special cases. The formulation also includes new possibilities for considering vertical integrals that are dependent on convective-scale variables, such as the moisture within convection. The generalized convective quasi-equilibrium is defined by a balance between large-scale forcing and convective response for a given vertically-integrated quantity. The latter takes the form of a convolution of a kernel matrix and a mass-flux spectrum, as in the original convective quasi-equilibrium. The kernel reduces to a scalar when either a bulk formulation is adopted, or only large-scale variables are considered within the vertical integral. Various physical implications of the generalized closure are discussed. These include the possibility that precipitation might be considered as a potentially-significant contribution to the large-scale forcing. Two dicta are proposed as guiding physical principles for the specifying a suitable vertically-integrated quantity.

Generalized drivers in the mammalian endangerment process

An important challenge for conservation today is to understand the endangerment process and identify any generalized patterns in how threats occur and aggregate across taxa. Here we use a global database describing main current external threats in mammals to evaluate the prevalence of distinct threatening processes, primarily of anthropogenic origin, and to identify generalized drivers of extinction and their association with vulnerability status and intrinsic species' traits. We detect several primary threat combinations that are generally associated with distinct species. In particular, large and widely distributed mammals are affected by combinations of direct exploitation and threats associated with increasing landscape modification that go from logging to intense human land-use. Meanwhile, small, narrowly distributed species are affected by intensifying levels of landscape modification but are not directly exploited. In general more vulnerable species are affected by a greater number of threats, suggesting increased extinction risk is associated with the accumulation of external threats. Overall, our findings show that endangerment in mammals is strongly associated with increasing habitat loss and degradation caused by human land-use intensification. For large and widely distributed mammals there is the additional risk of being hunted.

Schatten class Toeplitz operators on generalized Fock spaces

In this paper we characterize the Schatten p class membership of Toeplitz operators with positive measure symbols acting on generalized Fock spaces for the full range p>0.

Renormalized time scale for anticipating and lagging synchronization

Anticipating synchronization has been recently proposed as a mechanism of interaction in dynamical systems which are able to bring about predictions of future states of a driver system. We suggest that an interesting insight into the anticipating synchronization can be obtained by the renormalization of the time scale in the driven system. Our approach directly links the feedback delay of the driven system with the renormalized time scale of the driven system, identifying the main component in the anticipating synchronization paradigm and suggesting an alternative method to generate the anticipating and the lagging synchronization.