This article examines the politics of restitution within the Black Atlantic through the case of the Restitution Study Group’s legal challenge to the Smithsonian Institution’s return of Benin bronzes to Nigeria. While most scholarship frames restitution as a struggle between Western museums and postcolonial states, this article shifts the lens to intra-Black debates that complicate inherited frameworks of return, foregrounding the unresolved legacies of slavery and the claims of Black American and broader diasporic communities. At the same time, it situates these debates within the larger global landscape in which Western institutions and nation-states continue to define the terms and tempo of restitution. By challenging the assumption that restitution is solely a matter between source nations and former colonial powers, the Restitution Study Group brings attention to how African elites’ historical participation in the transatlantic slave trade and the ongoing marginalization of diaspora communities shape contemporary claims. The article also places these interventions alongside disputes within Nigeria over custodianship between the federal government, Edo State, and the Benin royal court. By tracing these overlapping histories, ethical claims, and political stakes, the article argues that returns of looted artifacts are not simply acts of restitution, but processes of decolonial repair that reconfigure authority, belonging, and historical responsibility across diasporic and national contexts.

Vertically symmetric alternating sign matrices (VSASMs) of order $2n+1$ are known to be equinumerous with lozenge tilings of a hexagon with side lengths $2n+2,2n,2n+2,2n,2n+2,2n$ and a central triangular hole of size $2$ that exhibit a cyclical as well as a vertical symmetry, but finding an explicit bijection proving this belongs to the most difficult problems in bijective combinatorics. Towards constructing such a bijection, we generalize the result by introducing certain natural extensions for both objects along with $n+3$ parameters and show that the multivariate generating functions with respect to these parameters coincide. This is a significant step from a constant number of equidistributed statistics to a linear number of statistics in n. The equinumeracy of VSASMs and the lozenge tilings is then an easy consequence of this result, which is obtained by specializing the generating functions to signed enumerations for both types of objects and then applying certain sign-reversing involutions. Another main result concerns the expansion of the multivariate generating function into symplectic characters as a sum over totally symmetric self-complementary plane partitions, which is in perfect analogy to the situation for ordinary ASMs where the Schur expansion can be written as a sum over totally symmetric plane partitions. This is exciting as it is reminiscent of the well-known Cauchy identity, and the Cauchy identity does have a bijective proof using the Robinson-Schensted-Knuth correspondence, and thus the result raises the question of whether there is a variation of the Robinson–Schensted–Knuth correspondence that does eventually lead to a bijective proof.

Building on the correspondence between finitely axiomatised theories in Łukasiewicz logic and rational polyhedra, we prove that the unification type of the fragment of Łukasiewicz logic with $n\geqslant 2$ variables is nullary. This solves a problem left open by V. Marra and L. Spada [Ann. Pure Appl. Logic 164 (2013), pp. 192–210]. Furthermore, we refine the study of unification with bounds on the number of variables. Our proposal distinguishes the number m of variables allowed in the problem and the number n in the solution. We prove that the unification type of Łukasiewicz logic for all $m,n \geqslant 2$ is nullary.

Yogurt acid whey (YAW) contains significant amounts of calcium as well as small amounts of protein, thus the idea of its reintroduction, especially of its calcium content, to the food chain is attractive. Calcium in milk is mainly complexed with casein micelles, whereas YAW contains only small amounts of protein, with no caseins at all, differing substantially from milk in the form in which calcium occurs. Therefore, the objective of the present research paper was to evaluate whether calcium bioavailability differs between YAW and milk. Following the INFOGEST protocol for simulated digestion and by coupling it with the Caco-2 model for intestinal absorption, calcium in YAW had higher bioaccessibility than calcium in milk. However, there were no differences in calcium transport by the intestinal cells and the transcription level of calcium absorption-related genes (VDR, TRPV6, S100G and PMCA1). Lastly, there were no differences in calcium bioaccessibility and the transcription of the calcium absorption-related genes between YAW samples of bovine, ovine or caprine origin obtained from Greek dairy products enterprises. In conclusion, despite the major differences in the protein profile between YAW and milk, there were no differences in calcium transport by the cells, but YAW was associated with higher calcium bioaccessibility, which ultimately may result in higher amount of absorbed calcium.

Il Grand Tour, viaggio culturale ed educativo intrapreso dalle élite europee tra il XVI e il XIX secolo, ha svolto un ruolo fondamentale nella formazione dell’identità culturale europea. Questo fenomeno, che aveva come meta privilegiata l’Italia, si trasformò progressivamente con l’ascesa della borghesia, evolvendo verso forme di turismo più moderne. William Barnard Clarke (1806–1865), architetto e antiquario inglese, compì un Grand Tour tra il 1838 e il 1840, attraversando Francia e Italia. Fino al 2020, la sua esperienza era poco documentata, ma la riscoperta di 39 disegni ha offerto nuove prospettive sul suo viaggio. Le sue raffigurazioni, incentrate su siti architettonici e archeologici, forniscono testimonianze visive preziose, come nel caso della città romana di Veleia. Clarke, membro attivo della Society for the Diffusion of Useful Knowledge, contribuì in modo significativo alla cartografia e agli studi architettonici, con l’obiettivo di diffondere il sapere oltre i circoli accademici. Il suo rapporto con i reperti antichistici si estese anche oltre i suoi viaggi, come testimonia la sua militanza tra le fila dell’Instituto di Corrispondenza Archeologica di Roma. Il suo viaggio segna la transizione dal Grand Tour aristocratico a un approccio più strutturato e scientifico allo studio del patrimonio culturale, evidenziando il suo ruolo di documentarista e promotore di una conoscenza più accessibile delle antichità europee.

Let $K^r_n$ be the complete $r$-uniform hypergraph on $n$ vertices, that is, the hypergraph whose vertex set is $[n] \, :\! = \{1,2,\ldots ,n\}$ and whose edge set is $\binom {[n]}{r}$. We form $G^r(n,p)$ by retaining each edge of $K^r_n$ independently with probability $p$. An $r$-uniform hypergraph $H\subseteq G$ is $F$-saturated if $H$ does not contain any copy of $F$, but any missing edge of $H$ in $G$ creates a copy of $F$. Furthermore, we say that $H$ is weakly $F$-saturated in $G$ if $H$ does not contain any copy of $F$, but the missing edges of $H$ in $G$ can be added back one-by-one, in some order, such that every edge creates a new copy of $F$. The smallest number of edges in an $F$-saturated hypergraph in $G$ is denoted by ${\textit {sat}}(G,F)$, and in a weakly $F$-saturated hypergraph in $G$ by $\mathop {\mbox{$w$-${sat}$}}\! (G,F)$. In 2017, Korándi and Sudakov initiated the study of saturation in random graphs, showing that for constant $p$, with high probability ${\textit {sat}}(G(n,p),K_s)=(1+o(1))n\log _{\frac {1}{1-p}}n$, and $\mathop {\mbox{$w$-${sat}$}}\! (G(n,p),K_s)=\mathop {\mbox{$w$-${sat}$}}\! (K_n,K_s)$. Generalising their results, in this paper, we solve the saturation problem for random hypergraphs $G^r(n,p)$ for cliques $K_s^r$, for every $2\le r \lt s$ and constant $p$.

The idea of a ‘late colonial state’ has been surprisingly durable. It is also the case that the meaning and significance of decolonisation – indeed our understanding of when it took place and how long it lasted – has been widened and deepened. We no longer tend to think of it as a purely political let alone constitutional event, but as a much broader shift in the relations between the ‘colonial world’ and its (former) masters and as having many more dimensions: economic, cultural, demographic among them. Needless to say, we are no closer to an agreed explanation than we were twenty-five or fifty years ago: the primacy of nationalist resistance, or of metropolitan politics or of geopolitical change still have their adherents even if it was the ricochet effect of all three on each other that offers the most plausible analysis. However, regardless of which account is favoured it seems clear that the nature of the ‘end game’ of the colonial state is the best place in which to search for answers. The late colonial state still has work to do.

In the present study, we observe interesting profiles and fluctuations in a quasi-two-dimensional thermal convection system filled with low-Prandtl-number liquid metal. A high-precision thermistor, which can be precisely controlled to move up and down, is used to measure the temperature distribution along the centreline of a convection cell. As the thermistor probes move away from the heated wall surface, the measured temperatures initially decrease to values below the central temperature of the cell, then recover to the central temperature, indicating an inverse temperature gradient. Furthermore, by analysing the root-mean-square temperature ($\sigma _T (z)$) along the centreline, we find a second peak away from the wall location, which has never been reported before, in addition to the first peak associated with the thermal boundary thickness. This phenomenon is also confirmed by the results of third- and fourth-order moments of temperature. Experimental results, together with insights from previous studies, suggest that in liquid metal, the distinct flow organisation arising from the large thermal diffusivity plays an important role in shaping the observed temperature distribution.