We determine the order of the k-core in a large class of dense graph sequences. Let $G_n$ be a sequence of undirected, n-vertex graphs with edge weights $\{a^n_{i,j}\}_{i,j \in [n]}$ that converges to a graphon $W\colon[0,1]^2 \to [0,+\infty)$ in the cut metric. Keeping an edge (i,j) of $G_n$ with probability ${a^n_{i,j}}/{n}$ independently, we obtain a sequence of random graphs $G_n({1}/{n})$. Using a branching process and the theory of dense graph limits, under mild assumptions we obtain the order of the k-core of random graphs $G_n({1}/{n})$. Our result can also be used to obtain the threshold of appearance of a k-core of order n.

After 78 years of democracy, Italy continues to grapple with its recent past in the political, social, and cultural spheres. Its experience of fascism under Mussolini, its dual participation in the Second World War, and the continuous and still existent connections between the ideological factions of the 1930s–1940s and now render the country a rich case for the study of public history and memory. The specificity of these characteristics has often made Italian history and memory look like an outlier, shaped by circumstances difficult to compare with those of other countries'. This paper argues that contemporary Italian memory politics are in reality a valuable source of information about the kind of mnemonic discourses that may arise in other (Western) European countries, given the increasingly polarised and populist European landscape. Our study of discourses put forwarded by the post-fascist party Fratelli d'Italia reveals a set of mnemonic tools with which they successfully banalise fascism and chip at Italian public discourse slowly but surely. The comparison between this discourse and that of VOX and AfD in Spain and Germany, respectively, shows that these tools, ranging from nativism to policy (de)legitimation linked to fascist imagery, has started to transfer to other countries' political strategies.

We settle the noninner automorphism conjecture for finite p-groups ($p> 2$) with certain conditions. Also, we give an elementary and short proof of the main result of Ghoraishi [‘On noninner automorphisms of finite nonabelian p-groups’, Bull. Aust. Math. Soc. 89(2) (2014) 202–209].

Let p be a prime number. Let $n\geq 2$ be an integer given by $n = p^{m_1} + p^{m_2} + \cdots + p^{m_r}$, where $0\leq m_1 < m_2 < \cdots < m_r$ are integers. Let $a_0, a_1, \ldots , a_{n-1}$ be integers not divisible by p. Let $K = \mathbb Q(\theta )$ be an algebraic number field with $\theta \in {\mathbb C}$ a root of an irreducible polynomial $f(x) = \sum _{i=0}^{n-1}a_i{x^i}/{i!} + {x^n}/{n!}$ over the field $\mathbb Q$ of rationals. We prove that p divides the common index divisor of K if and only if $r>p$. In particular, if $r>p$, then K is always nonmonogenic. As an application, we show that if $n \geq 3$ is an odd integer such that $n-1\neq 2^s$ for $s\in {\mathbb Z}$ and K is a number field generated by a root of a truncated exponential Taylor polynomial of degree n, then K is always nonmonogenic.

Warren Nutter’s work as director of the National Bureau of Economic Research’s (NBER) Soviet growth project is his best-known contribution to economics and public affairs. Many histories of Sovietology note the oddity of Nutter’s selection as project director, given his apparent lack of prior experience studying the Soviet Union. This paper provides new context for Nutter’s selection to lead the NBER effort. From 1951 to 1952 Nutter was the acting chief of the Economic Capabilities Branch of the CIA’s Office of Research and Reports (ORR), and chairman of the Economic Analysis Subcommittee of the interagency Economic Intelligence Committee. In this capacity he managed at least three major research efforts, including an input-output analysis of the Soviet Union and contributions to two national intelligence estimates. Nutter may have been proposed as director of the NBER project by Robert Amory, the Deputy Director of Intelligence, in 1953. Nutter’s research for the CIA cultivated new analytic capacities for the agency and provided a foundation for his own work on the Soviet Union.

Obsessive-compulsive disorder (OCD) and eating disorders (ED) are compulsive disorders with overlapping symptoms. However, weight loss and over-exercise causing secondary medical complications are rarely seen in OCD. We report the case of a 15-year-old male who presented with atypical symptoms of OCD leading to severe medical compromise. Covid-19 related team sport restrictions led to compulsive exercise associated with intrusive thoughts. The onset of stress fractures limited exercise ability, prompting compensatory food restriction. Bradycardia, hypothermia and hypoglycaemia resulted from severe malnourishment and weight loss in the context of OCD. His weight was 85.8% of ideal body weight on admission, reflective of a weight 10–15 kg lower than his premorbid weight. During admission, he developed exercise-induced rhabdomyolysis with significantly elevated creatinine kinase and required intensive care unit treatment. Psychotropic medication included lamotrigine, olanzapine and high dose fluoxetine alongside cognitive-behavioural therapy. Medical stabilisation and weight restoration allowed discharge to an outpatient Child and Adolescent Mental Health Service. This atypical case of OCD highlights the potentially life-threatening risks associated with excessive exercise and malnutrition. This paper highlights the complexities of treatment in a patient who cannot adhere to bed rest and the differential diagnoses of anorexia nervosa, orthorexia nervosa and exercise addiction.

An ostium secundum atrial septal defect (ASD) is a CHD that can be treated percutaneously since 1974, mostly cases with only one main defect. In cases with fenestrations close to the main defect, a single occluder can be used for treatment because the discs extend beyond the waist of the device. In some cases where the defects are far from each other, they may require either more than one device or surgical closure. We present two patients in whom we observed fenestrations far from the primary defect. Initially, the main ASDs were closed with an ASD occluder, and then the fenestrations were closed with a patent ductus arteriosus (PDA) coil, resulting in complete closure of both defects. This shows that closing small fenestrations that are far away from the primary interatrial defect without rims and using other devices instead, such as a PDA coil, is feasible and can avoid the need for an open-heart surgical procedure; moreover, it is important to note that leaving these fenestrations open can have the same physiology as a patent foramen oval.

We provide decadal estimates of GDP per capita for the Russian Empire from the 1690s to the 1880s, making it possible for the first time to compare the economic performance of one of the world’s largest economies with other countries. Significant Russian economic growth before the 1760s resulted in catching-up on northwest Europe, but this was followed by a period of negative growth between the 1760s and 1800s and stagnation from the 1800s to the 1880s, leaving late-nineteenth century Russia further behind the West than at the beginning of the eighteenth century.

Biofortification – the process of increasing the concentrations of essential nutrients in staple crops – is a means of addressing the burden of micronutrient deficiencies at a population level via existing food systems, such as smallholder farms. To realise its potential for global impact, we need to understand the factors that are associated with decisions to adopt biofortified crops and food products. We searched the literature to identify adoption determinants, i.e. barriers to (factors negatively associated) or facilitators of (factors positively associated) adoption, of biofortified crops and food products. We found 41 studies reporting facilitator(s) and/or barrier(s) of adoption. We categorised the factors using the Consolidated Framework of Implementation Research 2.0, resulting in a set of factors that enable or constrain adoption of biofortified foods across twenty-four constructs and five domains of this meta-theoretical determinant framework from implementation science. Facilitators of orange sweet potato adoption included knowledge about importance, relative advantage, efficient production and management practices; barriers included lacking timely access to quality vines and market remoteness (28 studies total). Facilitators of vitamin A cassava adoption included awareness of its benefits and access to information; barriers included poor road networks and scarcity of improved technology including inadequate processing/storage facilities (8). Facilitators of high-iron bean adoption included farmers’ networking and high farming experience; barriers included low knowledge of bean biofortification (8). Barriers to vitamin A maize adoption included low awareness and concerns regarding yield, texture and aflatoxin contamination (1). These barriers and facilitators may be a starting point for researchers to move towards testing implementation strategies and/or for policymakers to consider before planning scale-up and continuous optimisation of ongoing projects promoting adoption of biofortified crops and food products.

This article analyses a selection of archival material written by Paul Tillich, particularly his early parish sermons and sermons from World War I. Although the themes of ‘eternity’ and ‘the soul’ are rare in the early parish sermons and only appear in the context of death or suffering, they play a predominant role in the World War I sermons. This article suggests that this is because, for Tillich, suffering became the interpretative key. Through his sermons amidst the suffering and devastation of war Tillich employed what he called the immanent way of theology.

Feature-based models of sign language use distinctive features to describe the phonological structure of signs. We use near-minimal pairs and phonological phenomena like productivity and neutralisation in French Sign Language to show that the feature [web], which refers to the webbing part of the fingers, should be (re)introduced into the list of phonologically active features. In discussing potential cases of [web] in other sign languages and the impact on the shape of phonological inventories, we first offer an account of [web] in terms of a location feature in line with most traditional feature-geometry models. We then offer some speculations on why a more uniform characterisation of [web] and the features in the same subclass in terms of the orientation type results in more economical models.

Lunatic Asylums, published 130 years ago, is a fascinating insight into how these institutions were managed in the late Victorian era. This brief article considers what it reveals about the zeitgeist of the time and the book's author, the remarkable Charles Mercier.

One variant of the q-Catalan polynomials is defined in terms of Gaussian polynomials by

$$ \begin{align*}\mathcal{C}_k(q)=\bigg[\begin{matrix}{2k}\\ {k}\end{matrix}\bigg]_q-q \bigg[\begin{matrix}{2k}\\ {k+1} \end{matrix}\bigg]_q.\end{align*} $$

Liu [‘On a congruence involving q-Catalan numbers’, C. R. Math. Acad. Sci. Paris 358 (2020), 211–215] studied congruences of the form $\sum _{k=0}^{n-1} q^k\mathcal {C}_k$ modulo the cyclotomic polynomial $\Phi _n(q)^2$, provided that $n\equiv \pm 1\pmod 3$. Apparently, the case $n\equiv 0\pmod 3$ has been missing from the literature. Our primary purpose is to fill this gap. In addition, we discuss a certain fascinating link to Dirichlet character sum identities.