In the vein of important observations made by several scholars, in this article I discuss a variegated corpus of early sefirotic passages attesting to the prevalence and conventionality of spherical perceptions of the sefirot, already at the earliest stages of the sefirotic literature known to us. First, I show that for at least a substantial number of the earliest authors, seeing the sefirot as a set of concentric, hierarchical spherical divine entities was a self-evident premise. Second, I offer a tripartite division of the material, based on the different types of inner hierarchies characterizing the spherical descriptions. For each of these types I offer a relevant ideational context, related to contemporary cosmological conventions as well as to various theological notions.

Historically, trans people have been excluded from politics. Despite political under representation, trans interests increasingly appear on the political agenda in the Netherlands and Germany. In 2021, trans women were elected to the Dutch and German parliaments for the first time. However, increased trans visibility is accompanied by backlash and transphobia. The political representation of trans people does not follow a familiar pattern from elected descriptive representatives to increased substantive representation of interests. What mechanisms shape the political representation of trans people? We argue that symbolic representation shapes possibilities for descriptive and substantive representation of trans people. The analysis of symbolic representation of transpeople draws on a combination of 1) qualitative text analysis of Dutch and German parliamentary documents, research reports, and trans activists’ publications and 2) in-depth interviews with trans andcisgender representatives, candidates, and activists. The findings demonstrate how political spaces are not only gendered, but also cisgendered and heteronormative.

In this paper, we prove a cocycle version of marked length spectrum rigidity. There are two consequences: the first one is marked length pattern rigidity for arithmetic hyperbolic locally symmetric manifolds, and the second one is a strengthened marked length spectrum rigidity for surfaces and closed locally symmetric manifolds.

Let $F$ be a non-archimedean local field of characteristic different from 2 and residual characteristic $p$. This paper concerns the $\ell$-modular representations of a connected reductive group $G$ distinguished by a Galois involution, with $\ell$ an odd prime different from $p$. We start by proving a general theorem allowing to lift supercuspidal $\overline {\mathbf {F}}_{\ell }$-representations of $\operatorname {GL}_n(F)$ distinguished by an arbitrary closed subgroup $H$ to a distinguished supercuspidal $\overline {\mathbf {Q}}_{\ell }$-representation. Given a quadratic field extension $E/F$ and an irreducible $\overline {\mathbf {F}}_{\ell }$-representation $\pi$ of $\operatorname {GL}_n(E)$, we verify the Jacquet conjecture in the modular setting that if the Langlands parameter $\phi _\pi$ is irreducible and conjugate-selfdual, then $\pi$ is either $\operatorname {GL}_n(F)$-distinguished or $(\operatorname {GL}_{n}(F),\omega _{E/F})$-distinguished (where $\omega _{E/F}$ is the quadratic character of $F^\times$ associated to the quadratic field extension $E/F$ by the local class field theory), but not both, which extends one result of Sécherre to the case $p=2$. We give another application of our lifting theorem for supercuspidal representations distinguished by a unitary involution, extending one result of Zou to $p=2$. After that, we give a complete classification of the $\operatorname {GL}_2(F)$-distinguished representations of $\operatorname {GL}_2(E)$. Using this classification we discuss a modular version of the Prasad conjecture for $\operatorname {PGL}_2$. We show that the ‘classical’ Prasad conjecture fails in the modular setting. We propose a solution using non-nilpotent Weil–Deligne representations. Finally, we apply the restriction method of Anandavardhanan and Prasad to classify the $\operatorname {SL}_2(F)$-distinguished modular representations of $\operatorname {SL}_2(E)$.

Scholarship on early modern English Catholic music after the reformations tends to focus on the activities of male musicians and male institutions. Despite increased study of English convent culture by scholars of religious, social, and literary history, there remains little specialist examination of music at post-Reformation English convents in exile, and their role in wider musical networks in early modern Europe is markedly under-acknowledged. This article aims to highlight how complex miscellanies with links to English monastic institutions in exile can offer insight into the convents’ otherwise elusive musical world. Using a hitherto unanalysed miscellany – Douai Ms 785 – this article will show how codicological study of manuscripts, combined with study of concordances and unica, can illuminate the role of English convents in early modern musical networks. In doing so, it will demonstrate the need to understand miscellanies like Douai Ms 785 as witness to interacting, overlapping musical and religious ecosystems in early modern Europe.

All the known non-self-referential paradoxes share a reference pattern of Yablo’s paradox in that they all necessarily contain infinitely many sentences, each of which refers to infinitely many sentences. This raises a question: Does the reference pattern of Yablo’s paradox underlie all non-self-referential paradoxes, just as the reference pattern of the liar paradox underlies all finite paradoxes? In this regard, Rabern et al. [J Philos Logic 42(5): 727–765, 2013] prove that every dangerous acyclic digraph contains infinitely many points with an infinite out-degree. Building upon their work, this paper extends Rabern et al.’s result to the first-order arithmetic language with a primitive truth predicate, proving that all reference digraphs for non-self-referential paradoxes contain infinitely many sentences of infinite out-degree (called “social sentences”). We then strengthen this result in two respects. First, among these social sentences, infinitely many appear in one ray. Second, among these social sentences, infinitely many have infinitely many out-neighbors, none of which will eventually get to a sink. These observations provide helpful information towards the following conjecture proposed by Beringer and Schindler [Bull. of Symb. Logic 23(4): 442–492, 2017]: every dangerous acyclic digraph contains the Yablo digraph as a finitary minor.

We develop a new class of spatial voting models for binary preference data that can accommodate both monotonic and non-monotonic response functions, and are more flexible than alternative “unfolding” models previously introduced in the literature. We then use these models to estimate revealed preferences for legislators in the U.S. House of Representatives and justices on the U.S. Supreme Court. The results from these applications indicate that the new models provide superior complexity-adjusted performance to various alternatives and that the additional flexibility leads to preferences’ estimates that more closely match the perceived ideological positions of legislators and justices.

We study the multifractal properties of the uniform approximation exponent and asymptotic approximation exponent in continued fractions. As a corollary, we calculate the Hausdorff dimension of the uniform Diophantine set

$$ \begin{align*} {\mathcal{U}(\hat{\nu})}= &\ \{x\in[0,1)\colon \text{for all }N\gg1,\text{ there exists }n\in[1,N],\\&\ \ \text{ such that }|T^{n}(x)-y| < |I_{N}(y)|^{\hat{\nu}}\} \end{align*} $$

$y\in [0,1)$