This paper is devoted to the study of the propagation dynamics of a mutualistic model of mistletoes and birds with nonlocal dispersal. By applying the theory of asymptotic speeds of spread and travelling waves for monotone semiflows, we establish the existence of the asymptotic spreading speed $c^*$, the existence of travelling wavefronts with the wave speed $c\ge c^*$ and the nonexistence of travelling wavefronts with $c\lt c^*$. It turns out that the spreading speed coincides with the minimal wave speed of travelling wavefronts. Moreover, some lower and upper bound estimates of the spreading speed $c^*$ are provided.

Reward processing dysfunctions are considered a candidate mechanism underlying anhedonia and apathy in depression. Neuroimaging studies have documented that neurofunctional alterations in mesocorticolimbic circuits may neurally mediate these dysfunctions. However, common and distinct neurofunctional alterations during motivational and hedonic evaluation of monetary and natural rewards in depression have not been systematically examined. Here, we capitalized on pre-registered neuroimaging meta-analyses to (1) establish general reward-related neural alterations in depression, (2) determine common and distinct alterations during the receipt and anticipation of monetary v. natural rewards, and, (3) characterize the differences on the behavioral, network, and molecular level. The pre-registered meta-analysis (https://osf.io/ay3r9) included 633 depressed patients and 644 healthy controls and revealed generally decreased subgenual anterior cingulate cortex and striatal reactivity toward rewards in depression. Subsequent comparative analyses indicated that monetary rewards led to decreased hedonic reactivity in the right ventral caudate while natural rewards led to decreased reactivity in the bilateral putamen in depressed individuals. These regions exhibited distinguishable profiles on the behavioral, network, and molecular level. Further analyses demonstrated that the right thalamus and left putamen showed decreased activation during the anticipation of monetary reward. The present results indicate that distinguishable neurofunctional alterations may neurally mediate reward-processing alterations in depression, in particular, with respect to monetary and natural rewards. Given that natural rewards prevail in everyday life, our findings suggest that reward-type specific interventions are warranted and challenge the generalizability of experimental tasks employing monetary incentives to capture reward dysregulations in everyday life.

An example of a nonfinitely based involution monoid of order five has recently been discovered. We confirm that this example is, up to isomorphism, the unique smallest among all involution monoids.

Experiments on divergent Richtmyer–Meshkov (RM) instability at a heavy gas layer are performed in a specially designed shock tube. A novel soap-film technique is extended to generate gas layers with controllable thicknesses and shapes. An unperturbed gas layer is first examined and its two interfaces are found to move uniformly at the early stage and be decelerated later. A general one-dimensional theory applicable to an arbitrary-thickness layer is established, which gives a good prediction of the layer motion in divergent geometry. Then, six kinds of perturbed SF$_6$ layers with various thicknesses and shapes surrounded by air are examined. At the early stage, the amplitude growths of the inner interface for various-thickness layers collapse quite well and also can be predicted by the Bell model for cylindrical RM instability at a single interface, which indicates a negligible interface coupling effect. Later, a rarefaction wave accelerates the inner interface, causing a dramatic rise in the growth rate. It is found that a thicker gas layer will result in a larger extent that the rarefaction wave can promote the instability growth. A modified Bell model accounting for both Rayleigh–Taylor (RT) instability and interface stretching caused by a rarefaction wave is established, which well reproduces the quick instability growth. At late stages, reverberating waves inside the layer are negligibly weak such that the inner interface growth is dominated by RM instability and RT stability. The major factors driving the outer interface development are a compression wave and interface coupling. A new interface coupling phenomenon existing uniquely in divergent geometry caused by the gradual thinning of the gas layer is observed and also modelled.

Circulating n-3 PUFA, which integrate endogenous and exogenous n-3 PUFA, can be better used to investigate the relationship between n-3 PUFA and disease. However, studies examining the associations between circulating n-3 PUFA and colorectal cancer (CRC) risk were limited, and the results remained inconclusive. This case–control study aimed to examine the association between serum n-3 PUFA and CRC risk in Chinese population. A total of 680 CRC cases and 680 sex- and age-matched (5-year interval) controls were included. Fatty acids were assayed by GC. OR and 95 % CI were calculated using multivariable logistic regression after adjustment for potential confounders. Higher level of serum α-linolenic acid (ALA), docosapentaenoic acid (DPA), DHA, long-chain n-3 PUFA and total n-3 PUFA were associated with lower odds of CRC. The adjusted OR and 95 % CI were 0·34 (0·24, 0·49, Pfor trend < 0·001) for ALA, 0·57 (0·40, 0·80, Pfor trend < 0·001) for DPA, 0·48 (0·34, 0·68, Pfor trend < 0·001) for DHA, 0·39 (0·27, 0·56, Pfor trend < 0·001) for long-chain n-3 PUFA and 0·31 (0·22, 0·45, Pfor trend < 0·001) for total n-3 PUFA comparing the highest with the lowest quartile. However, there was no statistically significant association between EPA and odds of CRC. Analysis stratified by sex showed that ALA, DHA, long-chain n-3 PUFA and total n-3 PUFA were inversely associated with odds of CRC in both sexes. This study indicated that serum ALA, DPA, DHA, long-chain n-3 PUFA and total n-3 PUFA were inversely associated with odds of having CRC in Chinese population.

We present experimental results of irregular long-crested waves propagating over a submerged trapezoidal bar with the presence of a background current in a wave flume. We investigate the non-equilibrium phenomenon (NEP) induced by significant changes of water depth and mean horizontal flow velocity as wave trains pass over the bar. Using skewness and kurtosis as proxies, we show evidence that an accelerating following current could increase the sea-state non-Gaussianity and enhance both the magnitude and spatial extent of the NEP. We also find that below a ‘saturation relative water depth’ $k_p h_2 \approx 0.5$ ($k_p$ being the peak wavenumber in the shallow area of depth $h_2$), although the NEP manifests, the decrease of the relative water depth does not further enhance the maximum skewness and kurtosis over the bar crest. This work highlights the nonlinear physics according to which a following current could provoke higher freak wave risk in coastal areas where modulation instability plays an insignificant role.

Boundary conditions at a liquid–solid interface are crucial to dynamics of a liquid film coated on a fibre. Here, a theoretical framework based on axisymmetric Stokes equations is developed to explore the influence of liquid–solid slip on the Rayleigh–Plateau instability of a cylindrical film on a fibre. The new model not only shows that the slip-enhanced growth rate of perturbations is overestimated by the classical lubrication model, but also indicates a slip-dependent dominant wavelength, instead of a constant value obtained by the lubrication method, which leads to larger drops formed on a more slippery fibre. The theoretical findings are validated by direct numerical simulations of Navier–Stokes equations via a volume-of-fluid method. Additionally, the slip-dependent dominant wavelengths predicted by our model agree with the experimental results provided by Haefner et al. (Nat. Commun., vol. 6, issue 1, 2015, 7409).