A joint state and parameter estimation scheme for nonlinear dynamical systems

We present a novel algorithm for concurrent model state and parameter estimation in nonlinear dynamical systems. The new scheme uses ideas from three dimensional variational data assimilation (3D-Var) and the extended Kalman filter (EKF) together with the technique of state augmentation to estimate uncertain model parameters alongside the model state variables in a sequential filtering system. The method is relatively simple to implement and computationally inexpensive to run for large systems with relatively few parameters. We demonstrate the efficacy of the method via a series of identical twin experiments with three simple dynamical system models. The scheme is able to recover the parameter values to a good level of accuracy, even when observational data are noisy. We expect this new technique to be easily transferable to much larger models.

The impact of westerly wind bursts and ocean initial state on the development, and diversity of El Niño events

Westerly wind bursts (WWBs) that occur in the western tropical Pacific are believed to play an important role in the development of El Niño events. Here, following the study of Lengaigne et al. (Clim Dyn 23(6):601–620, 2004), we conduct numerical simulations in which we reexamine the response of the climate system to an observed wind burst added to a coupled general circulation model. Two sets of twin ensemble experiments are conducted (each set has control and perturbed experiments). In the first set, the initial ocean heat content of the system is higher than the model climatology (recharged), while in the second set it is nearly normal (neutral). For the recharged state, in the absence of WWBs, a moderate El Niño with a maximum warming in the central Pacific (CP) develops in about a year. In contrast, for the neutral state, there develops a weak La Niña. However, when the WWB is imposed, the situation dramatically changes: the recharged state slides into an El Niño with a maximum warming in the eastern Pacific, while the neutral set produces a weak CP El Niño instead of previous La Niña conditions. The different response of the system to the exact same perturbations is controlled by the initial state of the ocean and the subsequent ocean–atmosphere interactions involving the interplay between the eastward shift of the warm pool and the warming of the eastern equatorial Pacific. Consequently, the observed diversity of El Niño, including the occurrence of extreme events, may depend on stochastic atmospheric processes, modulating El Niño properties within a broad continuum.

A genome-wide test of the differential susceptibility hypothesis reveals a genetic predictor of differential response to psychological treatments for child anxiety disorders

Background: The differential susceptibly hypothesis suggests that certain genetic variants moderate the effects of both negative and positive environments on mental health and may therefore be important predictors of response to psychological treatments. Nevertheless, the identification of such variants has so far been limited to preselected candidate genes. In this study we extended the differential susceptibility hypothesis from a candidate gene to a genome-wide approach to test whether a polygenic score of environmental sensitivity predicted response to Cognitive Behavioural Therapy (CBT) in children with anxiety disorders. Methods: We identified variants associated with environmental sensitivity using a novel method in which within-pair variability in emotional problems in 1026 monozygotic (MZ) twin pairs was examined as a function of the pairs’ genotype. We created a polygenic score of environmental sensitivity based on the whole-genome findings and tested the score as a moderator of parenting on emotional problems in 1,406 children and response to individual, group and brief parent-led CBT in 973 children with anxiety disorders. Results: The polygenic score significantly moderated the effects of parenting on emotional problems and the effects of treatment. Individuals with a high score responded significantly better to individual CBT than group CBT or brief parent-led CBT (remission rates: 70.9%, 55.5% and 41.6% respectively). Conclusions: Pending successful replication, our results should be considered exploratory. Nevertheless, if replicated, they suggest that individuals with the greatest environmental sensitivity may be more likely to develop emotional problems in adverse environments, but also benefit more from the most intensive types of treatment.

A reappraisal of Baskerville's Greek types

Ιn the eighteenth century the printing of Greek texts continued to be central to scholarship and discourse. The typography of Greek texts could be characterised as a continuation of French models from the sixteenth century, with a gradual dilution of the complexity of ligatures and abbreviations, mostly through printers in the Low Countries. In Britain, Greek printing was dominated by the university presses, which reproduced conservatively the continental models – exemplified by Oxford's Fell types, which were Dutch adaptations of earlier French models. Hindsight allows us to identify a meaningful development in the Greek types cut by Alexander Wilson for the Foulis Press in Glasgow, but we can argue that in the middle of the eighteenth century Baskerville was considering Greek printing the typographic environment was ripe for a new style of Greek types. The opportunity to cut the types for a New Testament (in an twin edition that included a generous octavo and a large quarto version) would seem perfect for showcasing Baskerville's capacity for innovation. His Greek type maintained the cursive ductus of earlier models, but abandoned complex ligatures and any hint of scribal flourish. He homogenised the modulation of the letter strokes and the treatment of terminals, and normalised the horizontal alignments of all letters. Although the strokes are in some letters too delicate, the narrow set of the style composes a consistent, uniform texture that is a clean break from contemporaneous models. The argument is made that this is the first Greek typeface that can be described as fully typographic in the context of the technology of the time. It sets a pattern that was to be followed, without acknowledgement, by Richard Porson nearly a century and a half later. The typeface received little praise by typographic historians, and was condemned by Victor Scholderer in his retrospective of Greek typography. A survey of typeface reviews in the surrounding decades establishes that the commentators were mostly reproducing the views of an arbitrary typographic orthodoxy, for which only types with direct references to Renaissance models were acceptable. In these comments we detect a bias against someone considered an arriviste in the scholarly printing establishment, as well as a conservative attitude to typographic innovation.

Tidal friction in close-in satellites and exoplanets: The Darwin theory re-visited

This report is a review of Darwin`s classical theory of bodily tides in which we present the analytical expressions for the orbital and rotational evolution of the bodies and for the energy dissipation rates due to their tidal interaction. General formulas are given which do not depend on any assumption linking the tidal lags to the frequencies of the corresponding tidal waves (except that equal frequency harmonics are assumed to span equal lags). Emphasis is given to the cases of companions having reached one of the two possible final states: (1) the super-synchronous stationary rotation resulting from the vanishing of the average tidal torque; (2) capture into the 1:1 spin-orbit resonance (true synchronization). In these cases, the energy dissipation is controlled by the tidal harmonic with period equal to the orbital period (instead of the semi-diurnal tide) and the singularity due to the vanishing of the geometric phase lag does not exist. It is also shown that the true synchronization with non-zero eccentricity is only possible if an extra torque exists opposite to the tidal torque. The theory is developed assuming that this additional torque is produced by an equatorial permanent asymmetry in the companion. The results are model-dependent and the theory is developed only to the second degree in eccentricity and inclination (obliquity). It can easily be extended to higher orders, but formal accuracy will not be a real improvement as long as the physics of the processes leading to tidal lags is not better known.

C(k)-solvability near the characteristic set for a class of planar complex vector fields of infinite type

This paper deals with semi-global C(k)-solvability of complex vector fields of the form L = partial derivative/partial derivative t + x(r) (a(x) + ib(x))partial derivative/partial derivative x, r >= 1, defined on Omega(epsilon) = (-epsilon, epsilon) x S(1), epsilon > 0, where a and b are C(infinity) real-valued functions in (-epsilon, epsilon). It is shown that the interplay between the order of vanishing of the functions a and b at x = 0 influences the C(k)-solvability at Sigma = {0} x S(1). When r = 1, it is permitted that the functions a and b of L depend on the x and t variables, that is, L = partial derivative/partial derivative t + x(a(x, t) + ib(x, t))partial derivative/partial derivative x, where (x, t) is an element of Omega(epsilon).

Gevrey solvability near the characteristic set for a class of planar complex vector fields of infinite type

We study the Gevrey solvability of a class of complex vector fields, defined on Omega(epsilon) = (-epsilon, epsilon) x S(1), given by L = partial derivative/partial derivative t + (a(x) + ib(x))partial derivative/partial derivative x, b not equivalent to 0, near the characteristic set Sigma = {0} x S(1). We show that the interplay between the order of vanishing of the functions a and b at x = 0 plays a role in the Gevrey solvability. (C) 2008 Elsevier Inc. All rights reserved.

Robust tori in a double-waved Hamiltonian model

A Hamiltonian system perturbed by two waves with particular wave numbers can present robust tori, which are barriers created by the vanishing of the perturbed Hamiltonian at some defined positions. When robust tori exist, any trajectory in phase space passing close to them is blocked by emergent invariant curves that prevent the chaotic transport. Our results indicate that the considered particular solution for the two waves Hamiltonian model shows plenty of robust tori blocking radial transport. (C) 2010 Elsevier B.V. All rights reserved.

Extensive Bilayer Perforation Coupled with the Phase Transition Region of an Anionic Phospholipid

At low ionic strength dimyristoylphosphatidylglycerol (DMPG) exhibits a broad phase transition region characterized by several superimposed calorimetric peaks. Peculiar properties, such as sample transparency, are observed only in the transition region. In this work we use differential scanning calorimetry (DSC), turbidity. and optical microscopy to study the narrowing of the transition region with the increase of ionic strength (0-500 mM NaCl). Upon addition of salt, the temperature extension of the transition region is reduced, and the number of calorimetric peaks decreases until a single cooperative event at T(m) = 23 degrees C is observed in the presence of 500 mM NaCl. The transition region is always coupled with a decrease in turbidity, but a transparent region is detected within the melting process only in the presence of up to 20 mM NaCl. The vanishing of the transparent region is associated with one of the calorimetric peaks. Optical microscopy of giant vesicles shows that bilayers first rupture when the transition region is reached and Subsequently lose optical contrast. Fluorescence microscopy reveals a blurry and undefined image in the transparent region, suggesting a different lipid self-assembly. Overall sample turbidity can be directly related to the bilayer optical contrast. Our observations are discussed in terms of the bilayer being perforated along the transition region. In the narrower temperature interval of the transparent region, dependent on the ionic strength, the perforation is extensive and the bilayer completely loses the optical contrast.

Reentrant quantum Hall effect in bilayer system at high filling factors

We report on the measurements of the quantum Hall effect states in double quantum well structures at the filling factors v = 4N + 1 and 4N + 3, where N is the Landau index number, in the presence of the in-plane magnetic field. The quantum Hall states at these filling factors vanish and reappear several times. Repeated reentrance of the transport gap occurs due to the periodic vanishing of the tunneling amplitude in the presence of the in-plane field. When the gap vanishes, the transport becomes anisotropic. The anisotropy persist at half-odd filling factors, when bilayer quantum Hall states are recovered with increase of the tilt angle. (C) 2007 Elsevier B.V. All rights reserved.

Crystallization and Preliminary Crystallographic Analysis of Laminarinase from Rhodothermus marinus: A Case of Pseudomerohedral Twinning

Thermophilic endo-1,3(4)-beta-glucanase (laminarinase) from Rhodothermus marinus was crystallized by the hanging-drop vapor diffusion method. The needle-like crystals belong to space group P2(1) and contain two protein molecules in the asymmetric unit with a solvent content of 51.75%. Diffraction data were collected to a resolution of 1.95 angstrom and resulted in a dataset with an overall R-merge of 10.4% and a completeness of 97.8%. Analysis of the structure factors revealed pseudomerohedral twinning of the crystals with a twin fraction of approximately 42%.

Footemineite, the Mn-analog of atencioite, from the Foote mine, Kings Mountain, Cleveland County, North Carolina, USA, and its relationship with other roscherite-group minerals

Footemineite, ideally Ca2Mn2+square Mn22+Be4(PO4)(6)(OH)(4)-6H(2)O, triclinic, is a new member of the roscherite group. It occurs on thin fractures crossing quartz-microcline-spodumene pegmatite at the Foote mine, Kings Mountain, Cleveland County, North Carolina, U.S.A. Associated minerals are albite, analcime, eosphorite, siderite/rhodochrosite, fairfieldite, fluorapatite, quartz, milarite, and pyrite. Footemineite forms prismatic to bladed generally rough to barrel-shaped crystals up to about 1.5 mm long and I mm in diameter. Its color is yellow, the streak is white, and the luster is vitreous to slightly pearly. Footemineite is transparent and non-fluorescent. Twinning is simple, by reflection, with twin boundaries across the length of the crystals. Cleavage is good on {0 (1) over bar1}) and {100}. Density (calc.) is 2.873 g/cm(3). Footemineite is biaxial (-), n(alpha) = 1.620(2), n(beta) = 1.627(2), n(gamma) = 1.634(2) (white light). 2V(obs) = 80 degrees, 2V(calc) = 89.6 degrees. Orientation: X boolean AND b similar to 12 degrees, Y boolean AND c similar to 15 degrees, Z boolean AND a similar to 15 degrees. Elongation direction is c, dispersion: r > v or r < v, weak. Pleochroism: beta (brownish yellow) > alpha = gamma (yellow). Mossbauer and IR spectra are given. The chemical composition is (EDS mode electron microprobe, Li and Be by ICP-OES, Fe3+:Fe2+ y Mossbauer, H2O by TG data, wt%): Li2O 0.23, BeO 9.54, CaO 9.43, SrO 0.23, BaO 0.24, MgO 0.18, MnO 26.16, FeO 2.77, Fe2O3 0.62, Al2O3 0.14, P2O5 36.58, SiO2 0.42, H2O 13.1, total 99.64. The empirical formula is (Ca1.89Sr0.03Ba0.02)Sigma(1.94)(Mn-0.90(2+)square(0.10))Sigma(1.00)(square 0.78Li0.17Mg0.05) Sigma(1.00)(Mn3.252+Fe0.432+ Fe0.093+Al0.03)Sigma(3.80) Be-4.30(P5.81Si0.08O24)[(OH)3.64(H2O)0.36]Sigma(4.00)center dot 6.00H(2)O . The strongest reflection peaks of the powder diffraction pattern [d, angstrom (1, %) (hkl)] are 9.575 (53) (010), 5.998 (100) (0 (1) over bar1), 4.848 (26) (021), 3.192 (44) (210), 3.003 (14) (0 (2) over bar2), 2.803 (38) ((1) over bar 03), 2.650 (29) ((2) over bar 02), 2.424 (14) (231). Single-crystal unit-cell parameters are a = 6.788(2), b = 9.972(3), c = 10.014(2) A, (x = 73.84(2), beta = 85.34(2), gamma = 87.44(2)degrees,V = 648.74 angstrom(3), Z = 1. The space group is P (1) over bar. Crystal structure was refined to R = 0.0347 with 1273 independent reflections (F > 2(5). Footemineite is dimorphous with roscherite, and isostructural with atencioite. It is identical with the mineral from Foote mine described as ""triclinic roscherite."" The name is for the Foote mine, type locality for this and several other minerals.

ABELIANIZED OBSTRUCTION FOR FIXED POINTS OF FIBER-PRESERVING MAPS OF SURFACE BUNDLES

Let f: M -> M be a fiber-preserving map where S -> M -> B is a bundle and S is a closed surface. We study the abelianized obstruction, which is a cohomology class in dimension 2, to deform f to a fixed point free map by a fiber-preserving homotopy. The vanishing of this obstruction is only a necessary condition in order to have such deformation, but in some cases it is sufficient. We describe this obstruction and we prove that the vanishing of this class is equivalent to the existence of solution of a system of equations over a certain group ring with coefficients given by Fox derivatives.

EQUIVARIANT PATH FIELDS ON TOPOLOGICAL MANIFOLDS

A classical theorem of H. Hopf asserts that a closed connected smooth manifold admits a nowhere vanishing vector field if and only if its Euler characteristic is zero. R. Brown generalized Hopf`s result to topological manifolds, replacing vector fields with path fields. In this note, we give an equivariant analog of Brown`s theorem for locally smooth G-manifolds where G is a finite group.

Periodic geodesics and geometry of compact Lorentzian manifolds with a Killing vector field

We study the geometry and the periodic geodesics of a compact Lorentzian manifold that has a Killing vector field which is timelike somewhere. Using a compactness argument for subgroups of the isometry group, we prove the existence of one timelike non self-intersecting periodic geodesic. If the Killing vector field is nowhere vanishing, then there are at least two distinct periodic geodesics; as a special case, compact stationary manifolds have at least two periodic timelike geodesics. We also discuss some properties of the topology of such manifolds. In particular, we show that a compact manifold M admits a Lorentzian metric with a nowhere vanishing Killing vector field which is timelike somewhere if and only if M admits a smooth circle action without fixed points.