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

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

$y\in [0,1)$

We study the dynamics of dissipative billiard maps within planar convex domains. Such maps have a global attractor. We are interested in the topological and dynamical complexity of the attractor, in terms both of the geometry of the billiard table and of the strength of the dissipation. We focus on the study of an invariant subset of the attractor, the so-called Birkhoff attractor. On the one hand, we show that for a generic convex table with ‘pinched’ curvature, the Birkhoff attractor is a normally contracted manifold when the dissipation is strong. On the other hand, for a mild dissipation, we prove that, generically, the Birkhoff attractor is complicated, both from the topological and the dynamical points of view.

Does gender influence how candidates in the United States present their prior political experience to voters? Messaging one’s experience might demonstrate a history of power-seeking behavior, a gender role violation for women under traditional norms. As a result, men should be more likely to make experience-based appeals than women candidates. For evidence, we analyze the contents of 1,030 televised advertisements from 2018 state legislative candidates from the Wesleyan Media Project. We find that ads sponsored by experienced men are significantly more likely to highlight experience than ads sponsored by experienced women. However, we find that women’s and men’s ads are roughly equally likely to discuss work experience, suggesting that men’s greater emphasis on experience is limited to prior officeholding. The results contribute to our understanding of gender dynamics in political campaigns, the information available to voters, and how advertising shapes the criteria voters use to assess candidates.

Violence against women in politics is on the rise, threatening political achievements with respect to equality. Little research, however, has been conducted on the experiences of women from minority communities. This article, therefore, takes an intersectional approach to explore how gender, religion, and other categories of difference intersect when it comes to Muslim women’s experiences in the UK. Based on a longitudinal case study of Bradford West during the 2015, 2017, and 2019 general elections that combines participant observations, qualitative interviews, and a Twitter analysis, we argue that, in addition to the violence often experienced by women, Muslim women are also confronted with Islamophobic bias and abuse, as well as intersectional intimidation and harassment from within the Muslim community in their constituencies. Our case study approach, however, also reveals the existence of appreciation and support for Muslim women in politics that needs to be nurtured to counter abuse.

The state of the Free Exercise Clause in U.S. constitutional law is uncertain. With an opportunity in Fulton v. Philadelphia to clarify the vitality of the current standard from Employment Division v. Smith, the United States Supreme Court has declined to do so. The lasting impact of Smith has been to move away from directly requiring government justifications for infringing free exercise. Instead, courts now use neutrality and general applicability as heuristics for government justification. Yet, relying solely on neutrality and general applicability to proxy for government justification when infringing religious exercise distracts courts from conducting a fact-based inquiry. This article demonstrates how more scrutiny of the legislative facts in free exercise doctrine may serve as a viable alternative to Smith’s flawed approach for evaluating government justifications. The author first shows empirically how more factual scrutiny—directly requiring the government to justify its actions with evidence—can benefit government and religious claimants and then discusses the normative advantages of a fact-intensive approach to constitutional scrutiny. During a moment of sharp division over religious freedom and other competing rights, factual scrutiny can be a powerful tool for handling free exercise challenges and promoting responsible religious freedom.

We study the parameterized complexity of the problem to decide whether a given natural number n satisfies a given $\Delta _0$-formula $\varphi (x)$; the parameter is the size of $\varphi $. This parameterization focusses attention on instances where n is large compared to the size of $\varphi $. We show unconditionally that this problem does not belong to the parameterized analogue of $\mathsf {AC}^0$. From this we derive that certain natural upper bounds on the complexity of our parameterized problem imply certain separations of classical complexity classes. This connection is obtained via an analysis of a parameterized halting problem. Some of these upper bounds follow assuming that $I\Delta _0$ proves the MRDP theorem in a certain weak sense.

Ventriculocoronary connections develop most commonly in children with mitral stenosis/aortic atresia hypoplastic left heart. These connections can lead to myocardial ischaemia and dysfunction. We report a newborn with mitral stenosis/aortic stenosis hypoplastic left heart who endured systemic ventricular injury post-Norwood, secondary to a large ventriculocoronary fistula. He was treated medically and had favourable outcomes following bidirectional Glenn procedure.

Civic associations underpin American democracy. How can politically cross-cutting associations engage members who hold divergent viewpoints amidst increasing partisan polarization and nationalization of politics? I examine this question in the context of labor unions, studying how unions engage members who hold conservative views at odds with some of the union’s political actions. Using original surveys of local union presidents, members, and non-members along with in-depth interviews in selected local unions, I show how local union leaders can foster norms of participation among politically cross-pressured members. Norms of participation increase conservative members’ perceptions of political representation and engagement in politics, including participation in the union’s political action committee and support for union political mobilization. These findings have implications for understanding civic associations and participation in an era of political division, as well as the role unions continue to play in politics.

In [A. Capozzoli, C. Curcio, A. Liseno, MMS, Pizzo Calabro, Italy, 2022], the problem of modeling a source/scatterer using an equivalent radiator has been addressed and an approach has been given and numerically assessed.

Once dimensioned the radiating panel, a practical implementation can be provided by a non-uniform array. The element positions should be chosen so that the array is capable to approximate, with an adequate accuracy, the fields radiated by the equivalent radiator. Here, the array element positioning is performed by exploiting a quadrature rule which takes into account that the singular functions supported on the region of interest associated to the most significant singular values of the radiation operator are related to those supported on the equivalent panel by a radiation integral. The quadrature rule enables also to choose a set of weights which are essential in the definition of the element excitation coefficients from the knowledge of the source distribution on the equivalent panel. For simplicity, a one-dimensional problem with a Legendre quadrature rule is considered. The approach is numerically assessed by checking the capability of the array to radiate, with a satisfactory degree of accuracy, the singular functions associated to the region of interest.