Blenders are special hyperbolic sets used to produce various robust dynamical phenomena that appear fragile at first glance. We prove that for $C^r$ diffeomorphisms ($r=2,\ldots ,\infty ,\omega $), blenders naturally exist (without perturbation) near non-degenerate heterodimensional cycles of coindex 1, and the existence is determined by arithmetic properties of moduli of topological conjugacy for diffeomorphisms with heterodimensional cycles. In particular, we obtain a dichotomy for the dynamics in any small neighborhood U of a non-degenerate heterodimensional cycle: either there exist infinitely many blenders accumulating on the cycle, forming robust heterodimensional dynamics in most cases, or there are no orbits, other than those constituting the cycle, lying entirely in U.

Invasive fruit flies have the potential to exert a profound influence on agroecosystems, given their capacity to displace native species and modify host-use dynamics. In northwestern Argentina, Anastrepha fraterculus and Ceratitis capitata are the most significant fruit fly pests. This study synthesised infestation data by A. fraterculus and C. capitata on host plant species in northwestern Argentina, and explored how land use and altitude modulate infestation patterns. The findings demonstrated that A. fraterculus exhibited significantly higher and more variable infestation levels, particularly on native hosts belonging to the families Myrtaceae and Juglandaceae. Infestation levels exhibited significant variation among the landscape units, increasing with altitude. Conversely, C. capitata exhibited lower and more homogeneous infestation levels, with no substantial disparities related to host plant origin or landscape unit, although a notable non-linear relationship with elevation was observed. The findings indicate ecological niche partitioning between the two species and highlight the necessity of integrating host use, environmental gradients, and landscape context into fruit fly management. By integrating biotic and abiotic drivers of infestation across multiple environmental contexts, our systematic study provides a novel, landscape-scale perspective on the ecology of both native and invasive fruit flies, suggesting practical implications for improving pest surveillance and control strategies through habitat-based approaches tailored to species-specific ecology.

Schiller’s hunch was correct: spoken drama must overcome history in order to produce the effect of history (when portrayed monumentally) originally had. But the historical drama should not be antiquarian at any price; Shakespeare was correct to let his Romans appear on stage as Englishmen. […] However, one should not measure it according to the highest artistic expectations; we should make out of drama a rhetorical work of art.1

The recent surge of attacks on diversity, equity, and inclusion (DEI) has prompted urgent questions about the past, present, and future of such initiatives. In this HEQ policy dialogue, Kevin Kumashiro and Michael Olneck take up those questions directly, tracing how contemporary assaults—beginning with criticisms of the 1619 Project, critical race theory, and gender studies—have broadened into a campaign aimed at reshaping curriculum, institutions, and civic understanding. They probe the power of narrative and counter-narrative, asking what stories about democracy, citizenship, and education are being advanced and whether progressive educators and advocates have offered compelling alternatives.

Drawing on historical examples and political theory, their conversation situates today’s moment within longer struggles over who belongs in the American civic imaginary—from early twentieth-century immigrant restrictionism to competing visions of liberty voiced in nineteenth-century abolitionist and Reconstruction debates. Kumashiro and Olneck consider how new social imaginaries are articulated and disseminated, and what educators might do to cultivate aspirations about the kind of society and schools we aim to build.

Michael Olneck is Professor Emeritus in the departments of Educational Policy Studies and Sociology at the University of Wisconsin-Madison and the author of Culture Wars in American Education: Past and Present Struggles Over the Symbolic Order, along with numerous articles and book chapters on multiculturalism in American education. Kevin Kumashiro is former dean of the School of Education at the University of San Francisco and cofounder of the national network Education Deans for Justice and Equity; he is the author or editor of ten books on education and justice.

HEQ policy dialogues are, by design, intended to promote an informal, free exchange of ideas between scholars. The transcript of this dialogue has been lightly edited for clarity and consistency.

We study the semi-infinite Neumann problem, which models the variation law of a cline in a semi-infinite habitat. Using the bifurcation analysis method, we find that there is a unique solution curve emanating from $(\arctan \alpha ,0)$ with $\alpha> 0$, which is strictly increasing and approaches $1$ in $C[0,+\infty )$. Furthermore, we show that any cline (bifurcation solution) is stable, thereby providing a confirmed answer to a conjecture. Moreover, we also establish the stability of the trivial solution. Our conclusions are consistent with the related numerical results and biological reality.

The Fontan circulation is defined by unique physiological constraints that limit preload, elevate systemic venous pressure, and reduce the capacity to compensate for stress or injury. Traditional paradigms for managing biventricular heart failure are often misaligned with the pathophysiology of this preload-limited, non-pulsatile system. In this editorial, we propose a conceptual reframing of medical therapy in the Fontan circulation, centred on preserving physiological reserve and long-term durability rather than reversing established failure. We introduce a serial constraints model that emphasises the interconnected roles of the pulmonary vascular bed, ventricular filling, systemic output, venous and lymphatic function, and end-organ tolerance. As limitations shift over time, therapeutic focus must also evolve from pulmonary vasodilation in early stages to addressing ventricular dysfunction, venous congestion, and fibrosis later in the trajectory. We review emerging applications of phosphodiesterase type 5 inhibitors, sodium-glucose cotransporter-2 inhibitors, nonsteroidal mineralocorticoid receptor antagonists and exercise within this framework, while cautioning against routine use of conventional renin-angiotensin-aldosterone system inhibition or beta-blockers in the absence of clear comorbid indications. Antithrombotic strategies remain important due to a persistent thrombo-inflammatory milieu. We advocate for a shift from reactive to trajectory-preserving therapy, targeting flow under stress, organ protection, and reserve conservation. This physiology-aligned, evidence-informed approach provides a rationale for earlier intervention and testable hypotheses for future Fontan-specific trials.

We compute a Hirzebruch-Riemann-Roch type formula for the invariant Riemann-Roch number of a quantizable Hamiltonian $S^1$-manifold $(M,\omega ,{ \mathcal J})$, allowing $0$ to be a singular value of the moment map ${ \mathcal J}:M\to {\mathbb R}$. Our formula represents an instance of the Guillemin-Sternberg principle, which states that quantization should commute with reduction. The conceptual novelty of our result is that the involved reduced system only depends on the symplectic data of M. To establish this, we derive a complete singular stationary phase expansion of the Witten integral without appealing to any kind of desingularization. As a consequence, our formula expresses the invariant Riemann-Roch number purely in terms of symplectic invariants of the singular symplectic quotient. In particular, it involves a new explicit symplectic invariant of the singularities.

Macroeconomic models often have multiple equilibria. Nonetheless, a popular view on inflation targeting posits that this policy helps to coordinate agents’ expectations and actions. This paper provides a rationalization for this notion. I consider an infinitely repeated game, built on the Barro-Gordon model, in which the central bank incurs a fixed penalty whenever the actual inflation rate differs from the announced target and study how changes in the penalty impact its equilibria. I conclude that, in consonance with the aforementioned view, an inflation-targeting policy lessens the problem of equilibrium multiplicity. However, by itself, it is unlikely to achieve uniqueness.

Martin-Löf’s identity types provide a generic (albeit opaque) notion of identification or “equality” between any two elements of the same type, embodied in a canonical reflexive graph structure $(=_A, \mathbf{refl})$ on any type A. The miracle of Voevodsky’s univalence principle is that it ensures, for essentially any naturally occurring structure in mathematics, that the resultant notion of identification is equivalent to the type of isomorphisms in the category of such structures. Characterisations of this kind are not automatic and must be established one-by-one; to this end, several authors have employed reflexive graphs and displayed reflexive graphs to organise the characterisation of identity types. We contribute reflexive graph lenses, a new family of intermediate abstractions lying between families of reflexive graphs and displayed reflexive graphs that simplifies the characterisation of identity types for complex structures. Every reflexive graph lens gives rise to a (more complicated) displayed reflexive graph, and our experience suggests that many naturally occurring displayed reflexive graphs arise in this way. Evidence for the utility of reflexive graph lenses is given by means of several case studies, including the theory of reflexive graphs itself as well as that of polynomial type operators. Finally, we exhibit an equivalence between the type of reflexive graph fibrations and the type of univalent reflexive graph lenses.

Cette contribution examine la production des voyelles nasales du français chez les apprenants néerlandophones belges. Elle innove en ce qu’elle allie l'« intelligibilité » des voyelles non natives, évaluée par des auditeurs représentant Paris et Liège, à une analyse acoustique centrée sur la « nativité phonétique ». Les stimuli sont des mots monosyllabiques de haute fréquence produits par 20 apprenants néerlandophones. Les résultats indiquent que l’intelligibilité des nasales non natives est plutôt élevée, exception faite de /ɑ̃/. En outre, les deux groupes d’auditeurs ne diffèrent pas dans leur compréhension des voyelles, à l’exception de /ε̃/, que les Liégeois identifient plus souvent. Cette différence peut être liée à l’impact de (i) la variation en L1 ou (ii) la familiarité des auditeurs belges avec la parole néerlandaise. Enfin, l’étude montre que ce n’est pas tant la nasalité même qui pose des difficultés de production aux apprenants néerlandophones, mais l’interaction avec le timbre vocalique.

Faced with the pressures of digital transformation, media organizations in China are undergoing a “think-tank turn,” in which Public Opinion Monitoring Services (POMS) are playing an integral role. This study uses POMS as a case to examine the digital transformation of Chinese media organizations and to explore the broader shifts in the political economy of Chinese media in the digital age. Combining in-depth interviews, fieldwork and analysis of secondary documents, this qualitative research study identifies the emergence of consulting as a “third role” of Chinese media, supplementing the traditional roles of news reporting and ideological propagation. This new role caters to the government’s need to govern the online space and manage public opinion through three primary operations: “timely firefighting” against dissident voices, “regular monitoring” of public opinion and the “periodic training” of information officials. In this context, POMS not only enable media organizations to navigate financial challenges but also significantly reshape their role and relationship with the state.

This paper analyzes the structure of Noun Phrases with repeater classifiers (i.e., numeral classifiers that are only used with the single noun they are form-identical with). I show that a previous attempt to account for repeaters in terms of syntactic head movement encounters both empirical and theoretical problems. I suggest that repeaters emerge in the post-syntactic component, via a melody copying operation, which I characterize as a type of syntactic reduplication.

Yào in Mandarin, typically a modal, has subjunctive-like uses in complement clauses. Such uses are textual in that they signal interclausal modal cohesion between the main verb and the complement clause in a construction known as the pivotal manipulative construction. They fall into three types, depending on the relationship between yào and the main verb. All three likely originate from complement clauses negated by prohibitives. However, despite a common origin, two of the types are diachronically later and more contentful, rather than procedural. Therefore, it is proposed that the development of uses in complement clauses out of modality proper does not necessarily involve unidirectional increases in procedural meaning, as is often hypothesized.