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Why Europe must stop appeasing Donald Trump and prepare for the end of Nato
No full textIt argues that Europe must urgently confront an uncomfortable reality: under Donald Trump, the United States no longer behaves as a reliable ally. Recent developments—from Venezuela to renewed talk of acquiring Greenland—underline the erosion of the transatlantic partnership and the risks of sustained European dependence on Washington.Europe, including the UK, must therefore prepare for a post‑transatlantic future. That means reducing strategic dependence on the US, ending appeasement of Trump, using Europe’s economic power more assertively, strengthening defence capabilities, and assuming greater responsibility for Ukraine’s security. Strategic emancipation is no longer a theoretical debate, but an urgent political necessity
Crystal structure prediction, a challenging and fundamental problem
No full textIn this papers, we highlight recent work done on one of the most fundamental problems in computational chemistry, Crystal Structure Prediction. In CSP, the goal is to find a configuration of ions in 3D space that yields the lowest (i.e. the greatest negative) pairwise potential energy. This problem has only recently been formalised as a mathematical problem, leaving many interesting open problems. This abstract will highlight the recent work between computer science and chemistry, as well as presenting several interesting open problems. In particular, we show that this problem is undecidable in the general case and NP-hard when the size of the period defining the crystal is given. Further, we give an overview of the combinatorial results on these structures that may provide future tools for solving this problem in some restricted cases. Finally, we provide an integer programming model for solving this problem in the case of a fixed-size period
Distributed weak independent sets in hypergraphs:upper and lower bounds
No full textIn this paper, we consider the problem of finding weak independent sets in a distributed network represented by a hypergraph. In this setting, each edge contains a set of r vertices rather than simply a pair, as in a standard graph. A k-weak independent set in a hypergraph is a set where no edge contains more than k vertices in the independent set. We focus on two variations of this problem. First, we study the problem of finding k-weak maximal independent sets, k-weak independent sets where each vertex belongs to at least one edge with k vertices in the independent set. Second we introduce a weaker variant that we call (α,β)-independent sets where the independent set is β-weak, and each vertex belongs to at least one edge with at least α vertices in the independent set. Given a hypergraph H of rank r and maximum degree Δ, we provide a LLL formulation for finding an (α,β)-independent set when (β-α)2/(β+α)≥6log(16rΔ), an O(Δr/(β-α+1)+log∗n) round deterministic algorithm finding an (α,β)-independent set, and a O(Δ2(r-k)logr+Δlogrlog∗r+log∗n) round algorithm for finding a k-weak maximal independent set. Additionally, we provide zero round randomized algorithms for finding (α,β) independent sets, when (β-α)2/(β+α)≥6clogn+6 for some constant c, and finding an m-weak independent set for some m≥r/2k where k is a given parameter. Finally, we provide lower bounds of Ω(Δ+log∗n) and Ω(r+log∗n) on the problems of finding k-weak maximal independent sets for some values of k.</p
Metatheology:the foundations of divinity
No full textThis work examines some of the most pressing problems facing contemporary systematic theology. Crisp provides an overview of the contemporary landscape in the area of theological methodology and assessment of the strengths and weaknesses of each approach surveyed. This positive contribution to the field offers a clear and concise assessment of the methodologies on offer for students and scholars alike. It lays the groundwork for a vision of a common theological project across varied theological approaches. These include the importance of metaphysics and divine revelation, and the key doctrines of the Christian faith such as the Trinity and Incarnation. Crisp also sets out a constructive proposal for addressing the question of how we understand the relationship between the different levels of theological authority. This leads to a powerful sketch of a programme in systematic theology that is both respectful to the Christian tradition, as well as constructive in nature
Words after the storm:elite rhetoric and the limits of de-escalation in postreferendum Catalonia
No full textWhen does a secessionist crisis end? What drives political elites to shift from hostility to moderation? This article examines the prospects of rhetorical de-escalation in the aftermath of a secessionist dispute through the paradigmatic case of Catalonia. We analyse elite rhetoric on X (formerly Twitter) between 2017 and 2023, focusing on how parties and civil society organisations portrayed their opponents. Using sentiment analysis, thematic coding and the Thomas–Kilmann conflict model, we show that antagonism remained the predominant mode of communication, particularly among nationalist civil society organisations. Yet some moderation emerged among parties, particularly the Catalan Socialist Party (PSC), Esquerra Republicana de Catalunya (ERC) and Comuns, who adopted more conciliatory tones during moments of coalition formation and budget negotiation. These episodes were tactical rather than ideological, reflecting the pressures of parliamentary arithmetic. De-escalation, we suggest, is driven more by political need than by political will
Twisted products of monoids
No full textA twisting of a monoid S is a map Φ : S × S → ℕ satisfying the identity Φ(a, b) + Φ(ab, c) = Φ(a, bc) + Φ(b, c). Together with an additive commutative monoid M, and a fixed q ∈ M, this gives rise a so-called twisted product M ×qΦ S, which has underlying set M × S and multiplication (i, a)(j, b) = (i + j + Φ(a, b)q, ab). This construction has appeared in the special cases where M is ℕ or ℤ under addition, S is a diagram monoid (e.g. partition, Brauer or Temperley-Lieb), and Φ counts floating components in concatenated diagrams. In this paper we identify a special kind of ‘tight’ twisting, and give a thorough structural description of the resulting twisted products. This involves characterising Green’s relations, (von Neumann) regular elements, idempotents, biordered sets, maximal subgroups, Schützenberger groups, and more. We also consider a number of examples, including several apparently new ones, which take as their starting point certain generalisations of Sylvester’s rank inequality from linear algebra
Toward an improved understanding of dyslexia:reflections on a new consensus definition and its implications
No full textInconsistencies in the definition and diagnosis of dyslexia continue to impede research, assessment, and intervention. This paper, authored by members of the UK Specific Learning Difficulties Network, critically examines a recent effort to establish a consensus definition and guidance for assessment and intervention for dyslexia, which involved 58 experts from academia, practice and lived experience. The resulting framework offers a developmental, multifactorial and continuum-based perspective. It expands on prevailing definitions by highlighting the influence of multiple genetic, environmental and cognitive factors, as well as developmental changes in dyslexia profiles. However, unresolved issues remain, including ambiguity around prevalence and the role of general cognitive functioning, and a lack of clear guidance for educators. The definition also lacks clarity on assessment and intervention, especially in global contexts where teaching practice may be highly variable. Co-occurrence with language and mathematics difficulties is acknowledged but underexplored, limiting implications for practice. Whilst the Delphi method provides useful consensus, we also reflect on its limitations, including potential bias in the composition of the panel. Overall, the framework is a valuable step forward, but unresolved issues remain both from a research perspective and in terms of practical implementation
(Re-)setting the world stage:role theory and transitional orders
No full textThis article offers a role theoretical perspective on transitional orders, the liminal space between one order and the next. Role theory understands international order as an evolving role system, in which states seek and reject roles for themselves and others. We argue that established international orders can be destabilized by widespread role change dynamics, giving rise to transitional orders that are marked by deep uncertainty about available and appropriate roles in the role system. We identify the spread of order-related domestic role contestation and the weakening of international role socialization as the main mechanisms driving towards transitional orders. These two interlinked processes—domestic contestation and international socialization—are also entwined with particular role dynamics within transitional orders. Specifically, we propose that the uncertainty of order transitions results in three types of role dynamics: Transitional orders confront role holders with dilemmas that require them to interrogate existing role relationships; put order-related questions at the center of role-seeking behaviors; and elevate existential sovereignty concerns, both domestically and internationally. In these ways, role dynamics shape the major features of transitional orders, including their intentionality, fluidity and temporality
Impossible worlds are here to stay
No full textI address objections to impossible worlds (IWs) by Timothy Williamson and Kit Fine. Two species of IWs Mark Jago and I had in our Impossible Worlds book were FDE worlds (worlds used in the semantics of the nonclassical logic of First Degree Entailment) and open worlds (worlds not closed under any non-trivial logical consequence relation). Williamson attacks the idea that propositional contents are sets of open worlds; but we explicitly disavowed that very idea. He endorses uses of IWs we developed, except he calls these ‘pseudo-worlds’. In Angellic Content (AC), Fine champions a truthmaker semantics and in Constructing the Impossible advocates its superiority over IWs. But his semantics also includes states that are IWs, as characterized in the literature: representations of absolute impossibilities. They are like Barwise and Perry’s situations — which is how FDE worlds have been interpreted for decades. A key difference between AC and FDE is that only the latter validates ‘absorption principles’ one may find unwelcome in a characterization of propositional content. But a more topic-sensitive FDE can make them fail. Williamson has also objected to the idea of giving truth(making) and falsity(making) conditions separately, as in both AC and FDE. But FDE can work with truth conditions only and the compatibility semantics for negation. AC can work the same way
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