Staged Fontan pathway treatment is a recognised surgical approach for managing congenital heart lesions with single ventricle physiology. Some patients necessitate communication between the tunnel and the atrium to maintain circulatory balance. During follow-up, adjustments to fenestration size may be required. While methods for enlarging or completely closing fenestrations are common, partially reducing flow through a fenestration remains challenging. We present an effective technique for partially reducing the size of a large, stented fenestration using a coronary stent and a vascular occluder.

If ${\mathcal {E}}, {\mathcal {F}}$ are vector bundles of ranks $r-1,r$ on a smooth fourfold X and $\mathop {\mathcal Hom}({\mathcal {E}},{\mathcal {F}})$ is globally generated, it is well known that the general map $\phi : {\mathcal {E}} \to {\mathcal {F}}$ is injective and drops rank along a smooth surface. Chang improved on this with a filtered Bertini theorem. We strengthen these results by proving variants in which (a) ${\mathcal {F}}$ is not a vector bundle and (b) $\mathop {\mathcal Hom}({\mathcal {E}},{\mathcal {F}})$ is not globally generated. As an application, we give examples of even linkage classes of surfaces on $\mathbb P^4$ in which all integral surfaces are smoothable, including the linkage classes associated with the Horrocks–Mumford surface.

A couple of years ago, a non-mathematician friend of mine who takes an interest in mathematics mainly as puzzles mentioned a problem of Euler.

There remain important questions about how personality shapes risk perceptions, willingness to engage in protective behaviors, and policy preferences during a changing pandemic. Focusing on the Big-5 and COVID-19 attitudes, we find associations between risk perceptions and negative emotionality and agreeableness, as well as between each Big-5 trait and protective behaviors and support for government restrictions. These associations are mostly stable over time, with instability pronounced for lockdown policy support, where agreeableness and conscientiousness diminish in importance as pandemic conditions improve. Negative emotionality, conscientiousness, and agreeableness reduce differences between the political left and right and between those who do and do not trust experts. We highlight the heterogeneous interplay between personality and political ideology to understand pandemic policy support, attitudes, and behaviors.

Computing mathematical expectation for an experiment involving a finite number of numerical outcomes is straightforward. Let X denote the random variable having n possible values x1, x2, x3,…, xn. Letting pk denote the probability of xk, the expected value of X is

$$E\,(X)\, = \,\sum\limits_{k\, = \,1}^n {{x_k}{p_k}} ,$$

which can be interpreted as a weighted average of all xk, where the weight of each outcome is represented by its probability. But caution is required when interpreting the sum if there are infinitely many outcomes and the series fails to converge absolutely.

Large language models based on machine-learning technologies are reshaping linguistic contexts and understandings of language. We explore these reconfigurations by investigating discursive positionings of traditional institutional guardians of power in language in response to these changes. Focusing on the discourse of the Real Academia Española (RAE), we show how RAE’s social functions, ways of asserting authority, and the nature, function, and rightful ownership of RAE’s standard language have been reimagined. Crucially, RAE presents itself as a professional soft power that protects the rights of Spanish speakers. Drawing on tropes of authenticity and endangerment, it conceptualises language generated by machine-learning technologies as inauthentic and as destroying the authentic Spanish of human Spanish speakers. We argue that these discourses are indexical of a power struggle where the role of traditional language norming institutions is reshaped in the face of sociotechnical innovations that are in the hands of global commercial companies. (Standard language, AI technology, language academies, authority in language, big tech, Real Academia Española)*

Pi (π) is a mathematical constant that represents the ratio of the circumference of a circle to its diameter. Although for calculations using the number π usually one only needs a few decimal places, mathematicians have devoted much effort to obtain as many decimal places as they have been able to calculate. For a general description of the methods used to approximate the value of π, see e.g. [1, 2].