The structure of Borel reducibility for equivalence relations on $\omega _1$ is determined.

Seven accelerator mass spectrometry radiocarbon (AMS 14C) dates (7260±106∼7607±95 BP averaged 7444±103 BP) on a giant oyster shell, collected from an ancient shore of the Taipei Basin, are similar to the LSC (liquid scintillation counting) 14C age (7260±46 BP) of a grass sample inside the shell. The calibrated 14C ages of the C. gigas by Marine20 are 7490±240∼7805±230 cal BP (average 7660±96 cal BP), generally agreed with the calibrated LSC 14C ages of the grass and the oyster shell. Combined with other 14C ages of shoreline samples in the Taipei Basin, it is evident that sea level rose from 8600 to 7600 cal BP and reached a stand higher than modern sea level. During this marine transgression, the sedimentation rate along the shoreline was very high because 14C dating was not able to detect age differences for 4–5 m thick sediment sequences. Sixty-nine analyses of δ18O and δ13C from the oldest part of the shell exhibit clear seasonal cycles, with a 4-year period of growth in the 5.5-cm section. According to the δ18O values, the ancient oyster grew in a warmer-than-present shoreline environment, suggesting that the current absence of the giant oyster in Taiwan is not due to warming conditions.

KCNT1 mutations are associated with childhood epilepsy, developmental delay, and vascular malformations. We report a child with a likely pathogenic KCNT1 mutation (c.1885A>C, p.Lys629Glu) with recurrent pulmonary haemorrhage due to aortopulmonary collaterals successfully managed with coil embolisation followed by right upper lobectomy.

Every Thurston map $f\colon S^2\rightarrow S^2$ on a $2$-sphere $S^2$ induces a pull-back operation on Jordan curves $\alpha \subset S^2\smallsetminus {P_f}$, where ${P_f}$ is the postcritical set of f. Here the isotopy class $[f^{-1}(\alpha )]$ (relative to ${P_f}$) only depends on the isotopy class $[\alpha ]$. We study this operation for Thurston maps with four postcritical points. In this case, a Thurston obstruction for the map f can be seen as a fixed point of the pull-back operation. We show that if a Thurston map f with a hyperbolic orbifold and four postcritical points has a Thurston obstruction, then one can ‘blow up’ suitable arcs in the underlying $2$-sphere and construct a new Thurston map $\widehat f$ for which this obstruction is eliminated. We prove that no other obstruction arises and so $\widehat f$ is realized by a rational map. In particular, this allows for the combinatorial construction of a large class of rational Thurston maps with four postcritical points. We also study the dynamics of the pull-back operation under iteration. We exhibit a subclass of our rational Thurston maps with four postcritical points for which we can give positive answer to the global curve attractor problem.

Let $f(z)=\sum _{n=0}^{\infty }a_n z^n \in H(\mathbb {D})$ be an analytic function over the unit disk in the complex plane, and let $\mathcal {R} f$ be its randomization:

$$ \begin{align*}(\mathcal{R} f)(z)= \sum_{n=0}^{\infty} a_n X_n z^n \in H(\mathbb{D}),\end{align*} $$

where $(X_n)_{n\ge 0}$ is a standard sequence of independent Bernoulli, Steinhaus, or Gaussian random variables. In this note, we characterize those $f(z) \in H(\mathbb {D})$ such that the zero set of $\mathcal {R} f$ satisfies a Blaschke-type condition almost surely:

$$ \begin{align*}\sum_{n=1}^{\infty}(1-|z_n|)^t<\infty, \quad t>1.\end{align*} $$

Inspired by a result in T. H. Colding. (16). Acta. Math. 209(2) (2012), 229-263 [16] of Colding, the present paper studies the Green function $G$ on a non-parabolic $\operatorname {RCD}(0,\,N)$ space $(X,\, \mathsf {d},\, \mathfrak {m})$ for some finite $N>2$. Defining $\mathsf {b}_x=G(x,\, \cdot )^{\frac {1}{2-N}}$ for a point $x \in X$, which plays a role of a smoothed distance function from $x$, we prove that the gradient $|\nabla \mathsf {b}_x|$ has the canonical pointwise representative with the sharp upper bound in terms of the $N$-volume density $\nu _x=\lim _{r\to 0^+}\frac {\mathfrak {m} (B_r(x))}{r^N}$ of $\mathfrak {m}$ at $x$;

\[ |\nabla \mathsf{b}_x|(y) \le \left(N(N-2)\nu_x\right)^{\frac{1}{N-2}}, \quad \text{for any }y \in X \setminus \{x\}. \]

$y \in X \setminus \{x\}$

$N$

$\operatorname {RCD}(N-2,\, N-1)$

$x$

$N$

$N$

$\mathbb {R}^N$

$\operatorname {RCD}(0,\,N)$

We establish a generalized Rieffel correspondence for ideals in equivalent Fell bundles.

In this paper, we classify simple smooth modules over the mirror Heisenberg–Virasoro algebra ${\mathfrak {D}}$, and simple smooth modules over the twisted Heisenberg–Virasoro algebra $\bar {\mathfrak {D}}$ with non-zero level. To this end we generalize Sugawara operators to smooth modules over the Heisenberg algebra, and develop new techniques. As applications, we characterize simple Whittaker modules and simple highest weight modules over ${\mathfrak {D}}$. A vertex-algebraic interpretation of our result is the classification of simple weak twisted and untwisted modules over the Heisenberg–Virasoro vertex algebras. We also present a few examples of simple smooth ${\mathfrak {D}}$-modules and $\bar {\mathfrak {D}}$-modules induced from simple modules over finite dimensional solvable Lie algebras, that are not tensor product modules of Virasoro modules and Heisenberg modules. This is very different from the case of simple highest weight modules over $\mathfrak {D}$ and $\bar {\mathfrak {D}}$ which are always tensor products of simple Virasoro modules and simple Heisenberg modules.

Wigner’s theorem characterizes isometries of the set of all rank one projections on a Hilbert space. In metric geometry, nonexpansive maps and noncontractive maps are well-studied generalizations of isometries. We show that under certain conditions Wigner symmetries can be characterized as nonexpansive or noncontractive maps on the set of all projections of rank one. The assumptions required for such characterizations are injectivity or surjectivity and they differ in the finite and the infinite-dimensional case. Motivated by a recently obtained optimal version of Uhlhorn’s generalization of Wigner’s theorem, we also give a description of nonexpansive maps which satisfy a condition that is much weaker than surjectivity. Such maps do not need to be Wigner symmetries. The optimality of all presented results is shown by counterexamples.

Semperula wallacei (Issel, 1874) is a species of terrestrial slug that occurs in southeast China and the Pacific Basin and is the only species of its genus that occurs beyond the Oriental region and to the east of Wallace’s line in the Australian region, where it has probably been introduced. In this study, we report for the first time S. wallacei as an intermediate host for Angiostrongylus cantonensis (Chen, 1935) based on histological and molecular analyses of slugs from Tuamasaga, Samoa, deposited at the Medical Malacological Collection (Fiocruz-CMM). DNA was obtained from the deparafinized tissues scraped from specimen slides. Polymerase chain reaction and restriction fragment length polymorphism (PCR-RFLP) targeted to the internal transcribed spacer 2 (ITS2) region were carried out using the restriction enzyme Cla I. The RFLP profile observed for our larval specimen of S. wallacei was identical to the profile previously established for A. cantonensis, demonstrating that S. wallacei can be naturally infected with A. cantonensis and is likely to be an intermediate host for this parasitic nematode species in the field. The potential for geographical range expansion of S. wallacei in the Pacific Basin, its small size, and the general role of veronicellids as crop pests and hosts of nematodes, indicate the significance of S. wallacei as an invasive species in the Pacific Basin. Our work also highlights the importance of biological collections for investigating the environmental impact of invasive species on agriculture, public health, and biodiversity conservation.

Healthy dietary patterns such as the Mediterranean diet (MeDi), Dietary Approaches to Stop Hypertension (DASH) and the Mediterranean-DASH Intervention for Neurodegenerative Delay (MIND) have been evaluated for their potential association with health outcomes. However, the lack of standardisation in scoring methodologies can hinder reproducibility and meaningful cross-study comparisons. Here we provide a reproducible workflow for generating the MeDi, DASH and MIND dietary pattern scores from frequently used dietary assessment tools including the 24-h recall tool and two variations of FFQ. Subjective aspects of the scoring process are highlighted and have led to a recommended reporting checklist. This checklist enables standardised reporting with sufficient detail to enhance the reproducibility and comparability of their outcomes. In addition to these aims, valuable insights in the strengths and limitations of each assessment tool for scoring the MeDi, DASH and MIND diet can be utilised by researchers and clinicians to determine which dietary assessment tool best meets their needs.

This commentary applauds Haveman, Joseph-Goteiner, and Li's (2023) efforts to build arguments around institutional logics to explain China’s remarkable economic progress since 1978. But it also calls for broadening the focus of this inquiry so it can more generally explain why and how some societies are able to build connections between cultures and institutions that enable widespread societal progress, while other countries fail to do so. In particular, I suggest that this line of inquiry would benefit from drawing more deeply on the extensive body of writings by economic historians who have compared the economic progress of different societies over a long period.

Carbonated soft-drink consumption is detrimental to multiple facets of adolescent health. However, little is known about temporal trends in carbonated soft-drink consumption among adolescents, particularly in non-Western countries. Therefore, we aimed to examine this trend in representative samples of school-going adolescents from eighteen countries in Africa, Asia and the Americas. Cross-sectional data from the Global School-based Student Health Survey 2009–2017 were analysed. Carbonated soft-drink consumption referred to drinking carbonated soft-drinks at least once per day in the past 30 d. The prevalence of carbonated soft-drink consumption was calculated for each survey, and crude linear trends were assessed by linear regression models. Data on 74 055 students aged 12–15 years were analysed (mean age 13·9 (sd 1·0) years; 49·2 % boys). The overall mean prevalence of carbonated soft-drink consumption was 42·1 %. Of the eighteen countries included in the study, significant decreasing, increasing and stable trends of carbonated soft-drink consumption were observed in seven, two and nine countries, respectively. The most drastic decrease was observed in Kuwait between 2011 (74·4 %) and 2015 (51·7 %). Even in countries with significant decreasing trends, the decrease was rather modest, while some countries with stable trends had very high prevalence across time (e.g. Suriname 80·5 % in 2009 and 79·4 % in 2016). The prevalence of carbonated soft-drink consumption was high in all countries included in the present analysis, despite decreasing trends being observed in some. Public health initiatives to reduce the consumption of carbonated soft-drink consumption among adolescents are urgently required.