Recently, there has been much progress in understanding stationary measures for colored (also called multi-species or multi-type) interacting particle systems, motivated by asymptotic phenomena and rich underlying algebraic and combinatorial structures (such as nonsymmetric Macdonald polynomials). In this paper, we present a unified approach to constructing stationary measures for most of the known colored particle systems on the ring and the line, including (1) the Asymmetric Simple Exclusion Process (multi-species ASEP, or mASEP); (2) the $q$-deformed Totally Asymmetric Zero Range Process (TAZRP) also known as the $q$-Boson particle system; (3) the $q$-deformed Pushing Totally Asymmetric Simple Exclusion Process ($q$-PushTASEP). Our method is based on integrable stochastic vertex models and the Yang–Baxter equation. We express the stationary measures as partition functions of new ‘queue vertex models’ on the cylinder. The stationarity property is a direct consequence of the Yang–Baxter equation. For the mASEP on the ring, a particular case of our vertex model is equivalent to the multiline queues of Martin (Stationary distributions of the multi-type ASEP, Electron. J. Probab. 25 (2020), 1–41). For the colored $q$-Boson process and the $q$-PushTASEP on the ring, we recover and generalize known stationary measures constructed using multiline queues or other methods by Ayyer, Mandelshtam and Martin (Modified Macdonald polynomials and the multispecies zero range process: II, Algebr. Comb. 6 (2022), 243–284; Modified Macdonald polynomials and the multispecies zero-range process: I, Algebr. Comb. 6 (2023), 243–284) and Bukh and Cox (Periodic words, common subsequences and frogs, Ann. Appl. Probab. 32 (2022), 1295–1332). Our proofs of stationarity use the Yang–Baxter equation and bypass the Matrix Product Ansatz (used for the mASEP by Prolhac, Evans and Mallick (The matrix product solution of the multispecies partially asymmetric exclusion process, J. Phys. A. 42 (2009), 165004)). On the line and in a quadrant, we use the Yang–Baxter equation to establish a general colored Burke’s theorem, which implies that suitable specializations of our queue vertex models produce stationary measures for particle systems on the line. We also compute the colored particle currents in stationarity.

We study the behaviour of the norm of the resolvent for non-self-adjoint operators of the form $A := -\partial_x + W(x)$, with $W(x) \ge 0$, defined in ${L^2}({\mathbb{R}})$. We provide a sharp estimate for the norm of its resolvent operator, $\| (A - \lambda)^{-1} \|$, as the spectral parameter diverges $(\lambda \to +\infty)$. Furthermore, we describe the C0-semigroup generated by −A and determine its norm. Finally, we discuss the applications of the results to the asymptotic description of pseudospectra of Schrödinger and damped wave operators, and also the optimality of abstract resolvent bounds based on Carleman-type estimates.

Exchange rate manipulation—the active devaluation of a currency through intervention in the foreign exchange market—is a frequent trigger of international disputes. Yet it is not an obvious policy choice: as a blunt tool to boost export competitiveness, it is disliked by citizens and importers because of the loss of purchasing power it entails, and because it benefits those with investment abroad at the expense of those with savings at home. It is thus notable that a group of East Asian countries, from Japan and Korea to Thailand, undertake frequent and often large interventions to devalue their currencies. What explains their policy choice? We provide evidence that exchange rate depreciations are undertaken at the behest of export industries. Because lobbying activities in East Asian countries are not directly observable, we focus on Japan and Korea and construct a proxy measure of lobbying by exporters, drawing on news reports. We use machine learning to scale daily reports of industry demands in the two leading financial newspapers, the Japanese Nihon Keizai Shimbun and, in a robustness check, the Korean Hankyung, over twenty-five years. We find evidence that mounting public pressure by organized economic interest groups precedes intervention and induces currency depreciation.

Given the ongoing global extinction crisis, preserving genetic diversity is critical for long-term ecosystem resilience. A large, openly available DNA barcoding database could support this goal by allowing the identification of ‘genetic hotspots’ for conservation planning. We studied 77 woody species in the Monte Desert, South America’s largest dryland, using ITS2 and rbcLa markers to identify haplotypes for each species. We modified a previously published genetic diversity criterion, which prioritizes uniqueness, to also consider species ubiquity. We then mapped this genetic diversity metric, calculated Faith’s phylogenetic diversity (PD) index and overlaid our map with protected areas and permanent plantations. We identified five robust genetic hotspots, three of which coalesced into a central ‘mega-hotspot’. Alarmingly, most hotspots lay outside existing protected areas, and two overlapped with permanent plantations. As expected, high PD did not consistently align with high genetic diversity or species richness, suggesting that in the Monte Desert current protected areas overlook key genetic and PD. Our study highlights the importance of integrating DNA barcoding from understudied geographic regions into conservation plans.

We show that each local field $\mathbb{F}_q(\!(t)\!)$ of characteristic $p > 0$ is characterised up to isomorphism within the class of all fields of imperfect exponent at most 1 by (certain small quotients of) its absolute Galois group together with natural axioms concerning the p-torsion of its Brauer group. This complements previous work by Efrat and Fesenko, who analysed fields whose absolute Galois group is isomorphic to that of a local field of characteristic p.

The global political order that emerged from 1919 inscribed Jews into two distinct legal roles under the League of Nations system: a model national minority in the new nation-states of Eastern Europe, and a virtual national majority in British Mandatory Palestine. Despite extensive scholarship on each of these stories, we know precious little about how they interacted in the interwar Jewish political imagination. In this article I track several key East European Zionist intellectuals through the period between World War I and the aftermath of World War II as they attempted to imagine a new geometry of transnational nationhood via international law. This account of their pursuit of national self-determination beyond sovereignty reveals the promise and limits of interwar Jewish worldmaking and provides an index of the changing meaning of nationhood itself in the interwar period.

In this study, we argue that uncovering losses from public collections and making efforts to recover them is of fundamental importance concerning the responsible management of state assets and the maintenance of the cultural public interest. In recent times, the perception of museums has been in a constant state of flux, with international expectations associated with them sometimes appearing to be contradictory. While much attention has been paid to the diligence of care, museums must exercise in areas such as acquisition, deaccessioning policies, repatriation, and decolonization, an equally important function – but one less discussed in the international literature – which is the duty of public collections to safeguard and manage state-owned assets. In 2023, the Hungarian National Museum implemented a new initiative aimed at recovering cultural property that had disappeared from public collections under unknown circumstances. This procedure has already generated numerous insights that the current study analyzes, ranging from the difficulty of shedding light on decades-long ownership chains to the challenges of acquisition and the effectiveness of dispute resolution. The Hungarian initiative represents an additional approach to the protection of cultural property, addressing a significant gap in the Hungarian heritage protection system that has received less attention.

The Ninth Circuit's decision in Doe v. Cisco Systems, Inc. shows that there may yet be life in the Alien Tort Statute (ATS). The court held that Chinese practitioners of Falun Gong could bring claims of aiding and abetting human rights violations against Cisco Systems and its CEO for designing and building a surveillance system for the People's Republic of China. The Ninth Circuit denied rehearing en banc, more than a year after the original decision, with a long dissent joined by six judges. This introductory note discusses the panel opinion and the opinions on the petition for rehearing. The story may not be over yet, however, because Cisco has petitioned for Supreme Court review.

We study certain categories associated to symmetric quivers with potential, called quasi-Bogomol’nyi–Prasad–Sommerfield (BPS) categories. We construct semiorthogonal decompositions of the categories of matrix factorizations for moduli stacks of representations of (framed or unframed) symmetric quivers with potential, where the summands are categorical Hall products of quasi-BPS categories. These results generalize our previous results about the three-loop quiver. We prove several properties of quasi-BPS categories: wall-crossing equivalence, strong generation, and a categorical support lemma in the case of tripled quivers with potential. We also introduce reduced quasi-BPS categories for preprojective algebras, which have trivial relative Serre functor and are indecomposable when the weight is coprime with the total dimension. In this case, we regard the reduced quasi-BPS categories as noncommutative local hyperkähler varieties and as (twisted) categorical versions of crepant resolutions of singularities of good moduli spaces of representations of preprojective algebras. The studied categories include the local models of quasi-BPS categories of K3 surfaces. In a follow-up paper, we establish analogous properties for quasi-BPS categories of K3 surfaces.

We investigate the primitive recursive content of linear orders. We prove that the punctual degrees of rigid linear orders, the order of the integers $\mathbb {Z}$, and the order of the rationals $\mathbb {Q}$ embed the diamond (preserving supremum and infimum). In the cases of rigid orders and the order $\mathbb {Z}$, we further extend the result to embed the atomless Boolean algebra; we leave the case of $\mathbb {Q}$ as an open problem. We also show that our results for the rigid orders, in fact, work for orders having a computable infinite invariant rigid sub-order.