Relations between the Atiyah–Patodi–Singer rho invariant and signatures of links have been known for a long time, but they were only partially investigated. In order to explore them further, we develop a versatile cut-and-paste formula for the rho invariant, which allows us to manipulate manifolds in a convenient way. With the help of this tool, we give a description of the multivariable signature of a link $L$ as the rho invariant of some closed three-manifold $Y_L$ intrinsically associated with $L$. We study then the rho invariant of the manifolds obtained by the Dehn surgery on $L$ along integer and rational framings. Inspired by the results of Casson and Gordon and Cimasoni and Florens, we give formulas expressing this value as a sum of the multivariable signature of $L$ and some easy-to-compute extra terms.

Sea-ice drift in the Antarctic marginal ice zone (MIZ) is discussed using data from a 4-month-long drift of a buoy deployed on a pancake ice floe during the winter sea-ice expansion. We demonstrate increased meandering and drift speeds, and changes in the dynamical regimes of the absolute dispersion during cyclone activity, together with high correlations between drift velocities and wind from atmospheric reanalyses. This indicates a dominant physical control of wind forcing on ice drift and the persistence of free-drift conditions. These conditions occurred despite the buoy remaining largely in >80% ice concentrations and at distances >200 km from the estimated ice edge. The drift is additionally characterised by a strong inertial signature at 13.47 h, which appears initiated by passing cyclones. A wavelet analysis of the buoy's velocity confirms that the momentum transfer from winds at the multi-day frequencies is due to atmospheric forcing, while the initiation of inertial oscillations of sea ice has been identified as the secondary effect. Propagating storm-generated waves may initiate inertial oscillations by increasing the mobility of floes and enhance the drag of the inertial current. This analysis indicates that the Antarctic MIZ in the Indian Ocean sector remains much wider and mobile, during austral winter-to-spring, than defined by sea-ice concentration.

The ocean is a central site of escape, danger, and rescue for refugees. It is also a place where oceanic humanitarianism is enacted. In histories of refugee migration, the combination of the ocean, weather, and climate in determining the fate of refugees has not been adequately examined. This article provides a critical analysis of a Vietnamese refugee boat journey in 1982, to demonstrate the paradoxical nature of the ocean as both a site of danger and saviour. Conventional historical methodologies alone cannot capture the complex role of the ocean and the weather in determining boat refugee journeys and rescues. Interdisciplinary research between historians and ocean engineers provides new evidence and understanding of how the ocean and weather influences the outcomes of refugees seeking asylum by boat. Numerical model predictions of sea state and ship motion – which enables the vessel's journey in past environmental conditions to be understood – integrated within historical analysis contributes to a fuller and more complex understanding of the nexus between environmental conditions and forced migration journeys. Ocean engineering produces a scientific narrative that historians can use, alongside oral histories and other sources, to theorize the ocean as an active agent.

The aim of this study was to evaluate the production of bovine embryos in vitro when supplemented with l-carnitine for 24 h beginning on day 5 (d 5) under two different oxygen tensions (20% or 5%) and the relationship of nitric oxide (NO) in in vitro culture (IVC) medium to embryo development. Cumulus–oocyte complexes (COC; n = 837) were matured in vitro for 24 h and fertilization was performed for 18 h. Zygotes were cultured in vitro for 9 days after in vitro fertilization in synthetic oviductal fluid (SOF) medium with 5% fetal calf serum. At d 5 the plates were assigned to one of four treatment groups: high (20%) or low (5%) O2 tension either with or without the addition of 3.03 mM l-carnitine (High-Cont, High-Lcar, Low-Cont, Low-Lcar). The concentration of NO in the culture medium was evaluated on d 5, d 6 and d 9. On d 7, parts of the embryos were submitted for evaluation of intracellular lipid droplets. The cleavage rate was similar (P > 0.05) between high and low O2 tension and the blastocyst rate was similar in all conditions evaluated. The hatching rate was higher (P < 0.05) for Low-Cont. The NO concentration was higher at d 9 under low O2 tension (P < 0.1). The addition of 3.03 mM l-carnitine between d 5 and d 6 of IVC was not efficient in reducing cytoplasmic lipid content of bovine embryos. Additionally, IVC at a low oxygen tension without l-carnitine promoted better conditions for embryo development. A higher concentration of NO in medium was observed under low O2 tension.

A numerical model, based on the two-phase incompressible Navier–Stokes equations, is used to study transmission of regular water waves by a thin floating plate in two dimensions. The model is shown to capture the phenomenon of waves overwashing the plate, and the generation of turbulent bores on the upper plate surface. It is validated against laboratory experimental measurements, in terms of the transmitted wave field and overwash depths, for a set of incident wave periods and steepness values. Corresponding simulations are performed for a thick plate that does not experience overwash, which are validated using experiments where an edge barrier prevents thin-plate overwash. The model accurately reproduces (i) the linear relationship between the transmitted and incident amplitudes for the thick plate, and (ii) the decrease in proportion of incident-wave transmission for the thin plate, as incident steepness increases. Model outputs are used to link the decreasing transmission to wave-energy dissipation in the overwash, particularly where bores collide, and in the surrounding water, particularly at the plate ends. It is shown that most energy dissipation occurs in the overwash for the shortest incident waves tested, and in the surrounding water for the longer incident waves. Further, evidence is given that overwash suppresses plate motions, and causes asymmetry in plate rotations.

This curated collection of The Americas explores revolution and revolutionary movements in Latin American history from the colonial period to the present. This theme embraces events and processes contributing to the courses, outcomes, and reactions to both moments conventionally labeled “revolutions” in Latin American history, such as large-scale events like the Mexican Revolution, and more disparate efforts to secure—or resist—sociopolitical change.

The aim of this article is to investigate the roles of commutative diagrams (CDs) in a specific mathematical domain, and to unveil the reasons underlying their effectiveness as a mathematical notation; this will be done through a case study. It will be shown that CDs do not depict spatial relations, but represent mathematical structures. CDs will be interpreted as a hybrid notation that goes beyond the traditional bipartition of mathematical representations into diagrammatic and linguistic. It will be argued that one of the reasons why CDs form a good notation is that they are highly mathematically tractable: experts can obtain valid results by ‘calculating’ with CDs. These calculations, take the form of ‘diagram chases’. In order to draw inferences, experts move algebraic elements around the diagrams. It will be argued that these diagrams are dynamic. It is thanks to their dynamicity that CDs can externalize the relevant reasoning and allow experts to draw conclusions directly by manipulating them. Lastly, it will be shown that CDs play essential roles in the context of proof as well as in other phases of the mathematical enterprise, such as discovery and conjecture formation.

A series of experiments were conducted in a wave basin (50 m long, 10 m wide and 5 m deep) generating two waves propagating at an angle by a directional wavemaker. When the two waves were selected from a resonant triplet, an initially non-existing wave grew as the waves propagated down the tank. The linear growth rate of the resonating wave agreed well with third-order resonance theory based on Zakharov’s reduced gravity equation. Additional experiments with opposing and coflowing mean current with large temporal and spatial variations were conducted. As the flow rate increased, the linear growth was suppressed. As reproduced numerically with Zakharov’s equation, the resonant interaction saturated at time scales inversely proportional to the magnitude of the forced random resonance detuning. It is conjectured that the resonance is detuned by the variation and not by the mean of the current field due to wavelength-dependent Doppler shift and to the refraction of wave rays. Further analysis of the spectral evolution revealed that while discrete peaks appear at high frequencies as a result of dynamical cascading, a continuously saturated spectrum develops in the background as the current speed increases. Additional experiments were conducted studying the evolution of the random directional wave on a dynamical time scale under the influence of current. Due to random resonance detuning by the current, the spectral tail tended to be suppressed.

A theoretical model of water wave overwash of a thin floating plate is proposed. The nonlinear shallow-water equations are used to model the overwash, and the linear potential-flow/thin-plate model to force it. Model predictions are compared with overwash depths measured during a series of laboratory wave basin experiments. The model is shown to be accurate for incident waves of low steepness or short length.

Interaction with an opposing current amplifies wave modulation and accelerates nonlinear wave focusing in regular wavepackets. This results in large-amplitude waves, usually known as rogue waves, even if the wave conditions are less prone to extremes. Laboratory experiments in three independent facilities are presented here to assess the role of opposing currents in changing the statistical properties of unidirectional and directional mechanically generated random wavefields. The results demonstrate in a consistent and robust manner that opposing currents induce a sharp and rapid transition from weakly to strongly non-Gaussian properties. This is associated with a substantial increase in the probability of occurrence of rogue waves for unidirectional and directional sea states, for which the occurrence of extreme and rogue waves is normally the least expected.

Jaw claudication (JC) results from ischemia of the masticatory muscles, typically caused by temporal arteritis and other arteriopathies affecting the external carotid artery (ECA).

We documented a case of JC resulting from cardioembolic occlusion of the ECA and searched both English and French literature on the Medline database (1966-October 2006) to identify previous reports. We combined the keywords “jaw claudication” with either “cardiogenic embolism”, “cardiac embolism”, “cardioembolism”, “etiology”, “cause”, or “carotid occlusion”.

The exchange of the extra-framework Na+ ions in Engelhard titanosilicate (ETS-10) with Ag+ and Ru3+ has been investigated theoretically by means of density functional theory (DFT) and experimentally, with the aim of elucidating its effects on the structural, electronic and vibrational properties of the Ti-O-Ti quantum wire. A comparison of theoretical findings and experimental Raman data in the region of Ti-O-Ti stretching reveals that the introduction of the Ag+ ions preserves the integrity of the wire to a large extent while Ru3+ ions cause large-scale distortions along with some loss in crystallinity.

Linear instability of two-dimensional wave fields and its concurrent evolution in time is here investigated by means of the Alber equation for narrow-banded random surface waves in deep water subject to inhomogeneous disturbances. The probability of freak waves in the context of these simulations is also discussed. The instability is first studied for the symmetric Lorentz spectrum, and continued for the realistic asymmetric Joint North Sea Wave Project (JONSWAP) spectrum of ocean waves with variable directional spreading and steepness. It is found that instability depends on the directional spreading and parameters $\alpha $ and $\gamma $ of the JONSWAP spectrum, where $\alpha $ and $\gamma $ are the energy scale and the peak enhancement factor, respectively. Both influence the mean steepness of waves with such a spectrum, although in different ways. Specifically, if the instability stops as a result of the directional spreading, increase of the steepness by increasing $\alpha $ or $\gamma $ can reactivate it. A criterion for the instability is suggested as a dimensionless ‘width parameter’, $\Pi $ . For the unstable conditions, long-time evolution is simulated by integrating the Alber equation numerically. Recurrent evolution is obtained, which is a stochastic counterpart of the Fermi–Pasta–Ulam recurrence obtained for the cubic Schrödinger equation. This recurrence enables us to study the probability of freak waves, and the results are compared to the values given by the Rayleigh distribution. Moreover, it is found that stability–instability transition, the most unstable mode, recurrence duration and freak wave probability depend solely on the dimensionless ‘width parameter’, $\Pi $ .

This article discusses the informal learning of English by non-native speakers with particular reference to the role of virtual communities. The concept of informal learning is presented and related to current areas of interest in the literature such as incidental learning, and dynamic systems theory. Our research investigates how non-specialist language learners use the Internet in their spare time to read and listen to English, and also communicate in English, notably in online communities through social networking websites. The study looks particularly at the dynamics of these phenomena by studying a small number of non-native users of English over a period of two months. The results of this research will be used to question the relevance of the learner autonomy paradigm, which has been a cornerstone of language learning policy in Europe for the past thirty years.

Nonlinear modulational instability of wavepackets is one of the mechanisms responsible for the formation of large-amplitude water waves. Here, mechanically generated waves in a three-dimensional basin and numerical simulations of nonlinear waves have been compared in order to assess the ability of numerical models to describe the evolution of weakly nonlinear waves and predict the probability of occurrence of extreme waves within a variety of random directional wave fields. Numerical simulations have been performed following two different approaches: numerical integration of a modified nonlinear Schrödinger equation and numerical integration of the potential Euler equations based on a higher-order spectral method. Whereas the first makes a narrow-banded approximation (both in frequency and direction), the latter is free from bandwidth constraints. Both models assume weakly nonlinear waves. On the whole, it has been found that the statistical properties of numerically simulated wave fields are in good quantitative agreement with laboratory observations. Moreover, this study shows that the modified nonlinear Schrödinger equation can also provide consistent results outside its narrow-banded domain of validity.

A wave basin experiment has been performed in the MARINTEK laboratories, in one of the largest existing three-dimensional wave tanks in the world. The aim of the experiment is to investigate the effects of directional energy distribution on the statistical properties of surface gravity waves. Different degrees of directionality have been considered, starting from long-crested waves up to directional distributions with a spread of ±30° at the spectral peak. Particular attention is given to the tails of the distribution function of the surface elevation, wave heights and wave crests. Comparison with a simplified model based on second-order theory is reported. The results show that for long-crested, steep and narrow-banded waves, the second-order theory underestimates the probability of occurrence of large waves. As directional effects are included, the departure from second-order theory becomes less accentuated and the surface elevation is characterized by weak deviations from Gaussian statistics.

As the dimensions of interconnects shrink, the confinement effects associated with a very small grain size lead to a significant increase in the resistivity of the metal. Cu resistivity models have been proposed using the classical Fuch and Sondheimer approach for surface effect, and the Mayadas and Shatzkes approach for the grain boundary effect. In these models, three adjustable parameters must be used. Good agreement between experimental data and models can easily be obtained. However, numerous fitting parameter sets can be used with equivalent fitting quality and opposite physical meaning. In this work, experiments dedicated to model parameter extraction are proposed and released. They are based on the used of Cu lines with various line widths and heights. Classical resistivity increase with line width and line height decrease is observed. The resistivity behaviour is modelled. In this case, limited fitting parameter options are obtained. For Cu narrow lines confined with Ta, these parameters suggest maximum surface effect, medium grain boundary effect and low impurity content inside the lines.

Earlier analysis of the Italian population showed patterns of genetic differentiation that were interpreted as being the result of population settlements going back to pre-Roman times. DNA disease mutations may be a powerful tool in further testing this hypothesis since the analysis of diseased individuals can detect variants too rare to be resolved in normal individuals. We present data on the relative frequencies of 60 cystic fibrosis (CF) mutations in Italy and the geographical distribution of the 12 most frequent CF mutations screened in 3492 CF chromosomes originating in 13 Italian regions. The 12 most frequent mutations characterize about 73% of the Italian CF chromosomes. The most common mutation, ΔF508, has an average frequency of 51%, followed by N1303K and G542X, both with average frequencies around 5%. Multivariate analyses show that the relative frequencies of CF mutations are heterogeneous among Italian regions, and that this heterogeneity is weakly correlated with the geographical pattern of non-DNA ‘classical’ genetic markers. The northern regions are well differentiated from the central-southern regions and within the former group the western and eastern regions are remarkably distinct. Moreover, Sardinia shows the presence of mutation T338I, which seems absent in any other European CF chromosome. The north-western regions of Italy, characterized by the mutation 1717-1G→A, were under Celtic influence, while the north-east regions, characterized by the mutations R1162X, 2183AA→G and 711­5G→A, were under the influence of the Venetic culture.

In order to improve our ability to simulate the complex behavior of polymers, we introduce dynamical models in the class of Cellular Automata (CA). Space partitioning methods enable us to overcome fundamental obstacles to large scale simulation of connected chains with excluded volume by parallel processing computers. A highly efficient, two-space algorithm is devised and tested on both Cellular Automata Machines (CAMs) and serial computers. Preliminary results on the static and dynamic properties of polymers in two dimensions are reported.