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.

Spectral asymmetry of the massless Dirac operator on a 3-torus

Consider the massless Dirac operator on a 3-torus equipped with Euclidean metric and standard spin structure. It is known that the eigenvalues can be calculated explicitly: the spectrum is symmetric about zero and zero itself is a double eigenvalue. The aim of the paper is to develop a perturbation theory for the eigenvalue with smallest modulus with respect to perturbations of the metric. Here the application of perturbation techniques is hindered by the fact that eigenvalues of the massless Dirac operator have even multiplicity, which is a consequence of this operator commuting with the antilinear operator of charge conjugation (a peculiar feature of dimension 3). We derive an asymptotic formula for the eigenvalue with smallest modulus for arbitrary perturbations of the metric and present two particular families of Riemannian metrics for which the eigenvalue with smallest modulus can be evaluated explicitly. We also establish a relation between our asymptotic formula and the eta invariant.

Business cycle asymmetries: characterisation and testing based on Markov-switching autoregressions

Tests for business cycle asymmetries are developed for Markov-switching autoregressive models. The tests of deepness, steepness, and sharpness are Wald statistics, which have standard asymptotics. For the standard two-regime model of expansions and contractions, deepness is shown to imply sharpness (and vice versa), whereas the process is always nonsteep. Two and three-state models of U.S. GNP growth are used to illustrate the approach, along with models of U.S. investment and consumption growth. The robustness of the tests to model misspecification, and the effects of regime-dependent heteroscedasticity, are investigated.

Use of batch culture and a two-stage continuous culture system to study the effect of supplemental a-lactalbumin and glycomacropeptide on mixed populations of human gut bacteria

Certain milk factors can promote the growth of a host-friendly gastrointestinal microflora. This may explain why breast-fed infants experience fewer intestinal infections than their formula-fed counterparts. The effect of formula supplementation with two such factors was investigated in this study. Infant faecal specimens were used to ferment formulas supplemented with glycomacropeptide and α-lactalbumin in a two-stage compound continuous culture model. Bacteriology was determined by fluorescence in situ hybridisation. Vessels that contained breast milk as well as α-lactalbumin and glycomacropeptide had stable counts of bifidobacteria while lactobacilli increased significantly only in vessels with breast milk. Bacteroides, clostridia and Escherichia coli decreased significantly in all runs. Acetate was the principal acid found along with high amounts of propionate and lactate. Supplementation of infant formulas with appropriate milk proteins may be useful in simulating the beneficial bacteriological effects of breast milk.

Threshold autoregressive and Markov switching models: an application to commercial real estate

Although financial theory rests heavily upon the assumption that asset returns are normally distributed, value indices of commercial real estate display significant departures from normality. In this paper, we apply and compare the properties of two recently proposed regime switching models for value indices of commercial real estate in the US and the UK, both of which relax the assumption that observations are drawn from a single distribution with constant mean and variance. Statistical tests of the models' specification indicate that the Markov switching model is better able to capture the non-stationary features of the data than the threshold autoregressive model, although both represent superior descriptions of the data than the models that allow for only one state. Our results have several implications for theoretical models and empirical research in finance.

Noisy Monte Carlo: convergence of Markov chains with approximate transition kernels

Monte Carlo algorithms often aim to draw from a distribution π by simulating a Markov chain with transition kernel P such that π is invariant under P. However, there are many situations for which it is impractical or impossible to draw from the transition kernel P. For instance, this is the case with massive datasets, where is it prohibitively expensive to calculate the likelihood and is also the case for intractable likelihood models arising from, for example, Gibbs random fields, such as those found in spatial statistics and network analysis. A natural approach in these cases is to replace P by an approximation Pˆ. Using theory from the stability of Markov chains we explore a variety of situations where it is possible to quantify how ’close’ the chain given by the transition kernel Pˆ is to the chain given by P . We apply these results to several examples from spatial statistics and network analysis.

Hidden Markov analysis describes dive patterns in semiaquatic animals

Existing methods of dive analysis, developed for fully aquatic animals, tend to focus on frequency of behaviors rather than transitions between them. They, therefore, do not account for the variability of behavior of semiaquatic animals, and the switching between terrestrial and aquatic environments. This is the first study to use hidden Markov models (HMM) to divide dives of a semiaquatic animal into clusters and thus identify the environmental predictors of transition between behavioral modes. We used 18 existing data sets of the dives of 14 American mink (Neovison vison) fitted with time-depth recorders in lowland England. Using HMM, we identified 3 behavioral states (1, temporal cluster of dives; 2, more loosely aggregated diving within aquatic activity; and 3, terminal dive of a cluster or a single, isolated dive). Based on the higher than expected proportion of dives in State 1, we conclude that mink tend to dive in clusters. We found no relationship between temperature and the proportion of dives in each state or between temperature and the rate of transition between states, meaning that in our study area, mink are apparently not adopting different diving strategies at different temperatures. Transition analysis between states has shown that there is no correlation between ambient temperature and the likelihood of mink switching from one state to another, that is, changing foraging modes. The variables provided good discrimination and grouped into consistent states well, indicating promise for further application of HMM and other state transition analyses in studies of semiaquatic animals.

Decomposition of surface electromyographic signal using Hidden Markov Model

The detection of physiological signals from the motor system (electromyographic signals) is being utilized in the practice clinic to guide the therapist in a more precise and accurate diagnosis of motor disorders. In this context, the process of decomposition of EMG (electromyographic) signals that includes the identification and classification of MUAP (Motor Unit Action Potential) of a EMG signal, is very important to help the therapist in the evaluation of motor disorders. The EMG decomposition is a complex task due to EMG features depend on the electrode type (needle or surface), its placement related to the muscle, the contraction level and the health of the Neuromuscular System. To date, the majority of researches on EMG decomposition utilize EMG signals acquired by needle electrodes, due to their advantages in processing this type of signal. However, relatively few researches have been conducted using surface EMG signals. Thus, this article aims to contribute to the clinical practice by presenting a technique that permit the decomposition of surface EMG signal via the use of Hidden Markov Models. This process is supported by the use of differential evolution and spectral clustering techniques. The developed system presented coherent results in: (1) identification of the number of Motor Units actives in the EMG signal; (2) presentation of the morphological patterns of MUAPs in the EMG signal; (3) identification of the firing sequence of the Motor Units. The model proposed in this work is an advance in the research area of decomposition of surface EMG signals.

The uniqueness of signature problem in the non-Markov setting

We establish a general framework for a class of multidimensional stochastic processes over [0,1] under which with probability one, the signature (the collection of iterated path integrals in the sense of rough paths) is well-defined and determines the sample paths of the process up to reparametrization. In particular, by using the Malliavin calculus we show that our method applies to a class of Gaussian processes including fractional Brownian motion with Hurst parameter H>1/4, the Ornstein–Uhlenbeck process and the Brownian bridge.

Edge effects as the principal cause of area effects on birds in fragmented secondary forest

Bird communities in tropical forests are strongly affected by both patch area and habitat edges. The fact that both effects are intrinsically confounded in space raises questions about how these two widely reported ecological patterns interact, and whether they are independent or simply different spatial manifestations of the same phenomenon. Moreover, do small patches of secondary forest, in landscapes where the most sensitive species have gone locally extinct, exhibit similar patterns to those previously observed in fragmented and continuous primary forests? We addressed these questions by testing edge-related differences in vegetation structure and bird community composition at 31 sites in fragmented and continuous landscapes in the imperilled Atlantic forest of Brazil. Over a two-year period, birds were captured with mist nets to a standardized effort of 680 net-hours at each site (similar to 22 000 net-hours resulting in 3381 captures from 114 species). We found that the bird community in patches of secondary forest was degraded in species composition compared to primary continuous forest, but still exhibited a strong response to edge effects. In fragmented secondary forests, edge and area effects also interacted, such that the magnitude of edge to interior differences on bird community composition declined markedly with patch size. The change in bird species composition between forest interiors and edges was similar to the change in community composition between large and small patches (because species had congruent responses to edge and area), but after controlling for edge effects community composition was no longer affected by patch area. Our results show that although secondary forests hold an impoverished bird community, ecological patterns such as area and edge effects are similar to those reported for primary forests. Our data provide further evidence that edge effects are the main drivers of area effects in fragmented landscapes.

Ecological niche modeling and principal component analysis of Krameria Loefl. (Krameriaceae)

Krameria plants are found in arid regions of the Americas and present a floral system that attracts oil-collecting bees. Niche modeling and multivariate tools were applied to examine ecological and geographical aspects of the 18 species of this genus, using occurrence data obtained from herbaria and literature. Niche modeling showed the potential areas of occurrence for each species and the analysis of climatic variables suggested that North American species occur mostly in deserted or xeric ecoregions with monthly precipitation below 140 mm and large temperature ranges. South American species are mainly found in deserted ecoregions and subtropical savannas where monthly precipitation often exceeds 150 mm and temperature ranges are smaller. Principal Component Analysis (PCA) performed with values of temperature and precipitation showed that the distribution limits of Krameria species are primarily associated with maximum and minimum temperatures. Modeling of Krameria species proved to be a useful tool for analyzing the influence of the ecological niche variables in the geographical distribution of species, providing new information to guide future investigations. (C) 2011 Elsevier Ltd. All rights reserved.

An extension of the concept of gradient semigroups which is stable under perturbation

In this article we introduce the concept of a gradient-like nonlinear semigroup as an intermediate concept between a gradient nonlinear semigroup (those possessing a Lyapunov function, see [J.K. Hale, Asymptotic Behavior of Dissipative Systems, Math. Surveys Monogr., vol. 25, Amer. Math. Soc., 1989]) and a nonlinear semigroup possessing a gradient-like attractor. We prove that a perturbation of a gradient-like nonlinear semigroup remains a gradient-like nonlinear semigroup. Moreover, for non-autonomous dynamical systems we introduce the concept of a gradient-like evolution process and prove that a non-autonomous perturbation of a gradient-like nonlinear semigroup is a gradient-like evolution process. For gradient-like nonlinear semigroups and evolution processes, we prove continuity, characterization and (pullback and forwards) exponential attraction of their attractors under perturbation extending the results of [A.N. Carvalho, J.A. Langa, J.C. Robinson, A. Suarez, Characterization of non-autonomous attractors of a perturbed gradient system, J. Differential Equations 236 (2007) 570-603] on characterization and of [A.V. Babin, M.I. Vishik, Attractors in Evolutionary Equations, Stud. Math. Appl.. vol. 25, North-Holland, Amsterdam, 1992] on exponential attraction. (C) 2009 Elsevier Inc. All rights reserved.

Stability of gradient semigroups under perturbations

In this paper we prove that gradient-like semigroups (in the sense of Carvalho and Langa (2009 J. Diff. Eqns 246 2646-68)) are gradient semigroups (possess a Lyapunov function). This is primarily done to provide conditions under which gradient semigroups, in a general metric space, are stable under perturbation exploiting the known fact (see Carvalho and Langa (2009 J. Diff. Eqns 246 2646-68)) that gradient-like semigroups are stable under perturbation. The results presented here were motivated by the work carried out in Conley (1978 Isolated Invariant Sets and the Morse Index (CBMS Regional Conference Series in Mathematics vol 38) (RI: American Mathematical Society Providence)) for groups in compact metric spaces (see also Rybakowski (1987 The Homotopy Index and Partial Differential Equations (Universitext) (Berlin: Springer)) for the Morse decomposition of an invariant set for a semigroup on a compact metric space).

Semilinear elliptic problems near resonance with a nonprincipal eigenvalue

We consider the Dirichlet problem for the equation -Delta u = lambda u +/- (x, u) + h(x) in a bounded domain, where f has a sublinear growth and h is an element of L-2. We find suitable conditions on f and It in order to have at least two solutions for X near to an eigenvalue of -Delta. A typical example to which our results apply is when f (x, u) behaves at infinity like a(x)vertical bar u vertical bar(q-2)u, with M > a(x) > delta > 0, and I < q < 2. (C) 2007 Elsevier Inc. All rights reserved.