Gyalolechia fruticum, a new epiphytic species with a Mediterranean-Macaronesian distribution, is described. It differs in molecular data and in ecology from two closely related calcicolous species, G. luteococcinea and G. marmorata, both formerly called Caloplaca subochracea auct. The new species grows on coastal shrubs (rarely on wood), accompanied by species-rich communities of maritime epiphytic lichens. The typical habitat is undisturbed sand dunes, under dry conditions with frequent spells of humid air from the sea. The species is so far known from Greece, Italy, Tunisia, the Canary Islands and probably mainland Spain. We consider this conspicuous lichen an umbrella species of endangered and declining epiphytic communities of ancient shrub vegetation on well-developed sand dunes along Mediterranean coasts affected by touristic overexploitation.

We prove new statistical results about the distribution of the cokernel of a random integral matrix with a concentrated residue. Given a prime p and a positive integer n, consider a random $n \times n$ matrix $X_n$ over the ring $\mathbb{Z}_p$ of p-adic integers whose entries are independent. Previously, Wood showed that as long as each entry of $X_n$ is not too concentrated on a single residue modulo p, regardless of its distribution, the distribution of the cokernel $\mathrm{cok}(X_n)$ of $X_n$, up to isomorphism, weakly converges to the Cohen–Lenstra distribution, as $n \rightarrow \infty$. Here on the contrary, we consider the case when $X_n$ has a concentrated residue $A_n$ so that $X_n = A_n + pB_n$. When $B_n$ is a Haar-random $n \times n$ matrix over $\mathbb{Z}_p$, we explicitly compute the distribution of $\mathrm{cok}(P(X_n))$ for every fixed n and a non-constant monic polynomial $P(t) \in \mathbb{Z}_p[t]$. We deduce our result from an interesting equidistribution result for matrices over $\mathbb{Z}_p[t]/(P(t))$, which we prove by establishing a version of the Weierstrass preparation theorem for the noncommutative ring $\mathrm{M}_n(\mathbb{Z}_p)$ of $n \times n$ matrices over $\mathbb{Z}_p$. We also show through cases the subtlety of the “universality” behavior when $B_n$ is not Haar-random.

Over the last three years, Larry Gostin, I, and many others have urged world leaders to open their minds toward specific subsets of reform in the interest of pandemic response, including mechanisms for transparency, accountability, and, crucially, financial buy-in. With negotiations for a new pandemic accord still incomplete, our focus must remain on reaching global agreement, and keeping at top of mind the immense stakes if that is not possible.

Ramsey’s theorem guarantees for every graph H that any 2-edge-coloring of a sufficiently large complete graph contains a monochromatic copy of H. In 1962, Erdős conjectured that the random 2-edge-coloring minimizes the number of monochromatic copies of $K_k$, and the conjecture was extended by Burr and Rosta to all graphs. In the late 1980s, the conjectures were disproved by Thomason and Sidorenko, respectively. A classification of graphs whose number of monochromatic copies is minimized by the random 2-edge-coloring, which are referred to as common graphs, remains a challenging open problem. If Sidorenko’s conjecture, one of the most significant open problems in extremal graph theory, is true, then every 2-chromatic graph is common and, in fact, no 2-chromatic common graph unsettled for Sidorenko’s conjecture is known. While examples of 3-chromatic common graphs were known for a long time, the existence of a 4-chromatic common graph was open until 2012, and no common graph with a larger chromatic number is known.

We construct connected k-chromatic common graphs for every k. This answers a question posed by Hatami et al. [Non-three-colourable common graphs exist, Combin. Probab. Comput. 21 (2012), 734–742], and a problem listed by Conlon et al. [Recent developments in graph Ramsey theory, in Surveys in combinatorics 2015, London Mathematical Society Lecture Note Series, vol. 424 (Cambridge University Press, Cambridge, 2015), 49–118, Problem 2.28]. This also answers in a stronger form the question raised by Jagger et al. [Multiplicities of subgraphs, Combinatorica 16 (1996), 123–131] whether there exists a common graph with chromatic number at least four.

Purulia, a district in the southwestern part of West Bengal, is popular for the renowned chhou dance. Despite the prevalent notion that chhou is exclusively a war dance, it dynamically incorporates contemporary social and political issues, and has undergone significant changes such as new musical instruments and technologies, lighting, costume transformations, and female performers.

Overweight and obesity are growing health concerns globally. Technological advances drive interest in smartphone applications as possible health behaviour interventions to promote lifestyle change in these conditions. This article critically appraises a Cochrane Review of 18 studies (2703 participants) of smartphone app interventions for overweight or obesity in adolescents and adults and considers its relevance to clinical practice and research. The review's results suggest that there may be minimal benefit to the use of smartphone apps, but the evidence is very uncertain, lacking high-quality, replicable studies.

The Inflation Reduction Act (IRA) creates a new process to cap Medicare Part D branded drug prices. It prohibits Medicare from paying more than a specified discount from average private market prices and requires that CMS negotiate with manufacturers to agree on a maximum fair price that Medicare will pay that is lower than the specified discount. This article analyzes the cause of high drug prices and how negotiations to set the maximum fair price might unfold. It compares Medicare’s new pricing process to the way drug prices are set in Medicaid, the Veterans Administration, U.S. private insurers, and European nations. It analyzes how negotiations to set the maximum fair price might unfold in light of negotiation theory and the practices to negotiate prices employed in Europe. It draws inferences from the initial published data on the first round of negotiated prices.

Critically engaging with the works of Roger Brownsword, Mireille Hildebrandt and William Lucy, the article addresses the increasing reliance on computer codes and intelligent physical infrastructure as behavioural control tools and its implications for modern state law. It is argued that, if we look at the new developments in the context of broader social and institutional trends (like the rise of Internet platforms), instead of the prospect of code superseding the law, we face complex practical challenges related to the dynamic balance between different modes of guiding and controlling behaviour in legal regulation.