We derive an explicit formula for the N-point correlation $F_N(s)$ of the van der Corput sequence in base $2$ for all $N \in \mathbb {N}$ and $s \geq 0$. The formula can be evaluated without explicit knowledge about the elements of the van der Corput sequence. This constitutes the first example of an exact closed-form expression of $F_N(s)$ for all $N \in \mathbb {N}$ and all $s \geq 0$ which does not require explicit knowledge about the involved sequence. Moreover, it can be immediately read off that $\lim _{N \to \infty } F_N(s)$ exists only for $0 \leq s \leq 1/2$.

The new UK internal market, as embodied in the UK Internal Market Act 2020 and the common frameworks, is the latest example of market integration, but it is far from being the only one. A myriad of composite market structures exists across the world, including in Australia, Canada, Germany, Spain, Switzerland, the US and the EU. This article investigates how the UK internal market compares to other internal markets: to what extent does it follow pre-existing paths, to what extent does it depart from them? It is argued that the UK has diverged from international blueprints in several important aspects. Despite drawing on methods that are frequently employed for achieving economic integration, it reinterprets and combines these in a unique way. The result is an internal market which is defined by an unusual degree of centralisation, strong trade rights and a high potential for deregulation.

In this article, we introduce an innovative approach to examining campaign themes in Italy, by performing an original corpus linguistic analysis of the party manifestos related to the crucial 2022 election. Through its systematicity and flexibility, our approach allows us to gauge theory-driven propositions using a large amount of so far unexplored textual data. As anticipated, the 2022 Italian party manifestos are characterised by a somewhat balanced configuration of emphasis across a variety of themes, of which some are more controversial and others more widely shared among voters and parties. Further, we also corroborate that parties primarily focus on those themes that historically fit them best, ideologically and in terms of perceived competence. Lastly, salient ‘issues of the day’ are differently emphasised by Italian parties, which particularly avoid devoting considerable attention to the highly sensitive Russian-Ukrainian war.

This article introduces a bundle of active learning activities for an introductory undergraduate course in research methods. In particular, the activities aim to help students develop core knowledge and skills that provide a foundation for reading and conducting quantitative and qualitative research. Active learning is a pedagogical practice with well-established benefits such as better student attitudes and improved content comprehension and application. I build on this conventional wisdom by applying a student-centred evaluation method, demonstrating that students perceive active learning as an effective complement to traditional lecturing and assignments for learning core methodological topics in political science.

Framed within discussions on how law operationalizes race and ethnicity, the authors provide a description of how anti-Semitic racially exclusionary legislation identified, classified, and operationalized the Jewry in Hungary between 1920 and 1944.

It is increasingly easy to acquire a large amount of data about a problem before formulating a hypothesis. The idea of exploratory data analysis (EDA) predates this situation, but many researchers find themselves appealing to EDA as an explanation of what they are doing with these new resources. Yet there has been relatively little explicit work on what EDA is or why it might be important. I canvass several positions in the literature, find them wanting, and suggest an alternative: exploratory data analysis, when done well, shows the expected value of experimentation for a particular hypothesis.

The spatial and seasonal variability of the microphytoplankton and ciliates communities in relation to the environmental factors were studied in the southern coastal area of Sfax. Results revealed a striking difference between seasons regarding pH, with strong acidification in autumn generated by industrial activity. Spatial distribution of pH in autumn impacted the microorganisms in different ways: acidic stations to the south showed significant correlations with Cyanobacteria, dinoflagellates and loricate ciliates whereas higher pH values in spring (pH > 8) were linked to diatoms richness. The high availability of inorganic phosphate is associated with the high release of phosphate due to residue from a phosphate treatment manufacture along the coast; consequently, N/P ratios were low (1.34–13.43) suggesting nitrogen limitation. Microphytoplankton abundance shifted from dinoflagellates dominance in autumn to dominance of diatoms during winter and of Euglenophyceae in summer. Loricate ciliates accounted for the largest proportion of the ciliates community while aloricate ciliates were relatively scarce during all seasons. Variability of ciliate community appeared not directly linked to environmental conditions, but significant positive relationships between abundance of loricate ciliates and microphytoplankton suggest that these ciliates may feed on microphytoplankton.

This paper empirically investigates wage inequality within the group of skilled workers in the recent four decades in the USA using CPS data and finds evidence that the trend of wage growth of the top and bottom 10th percentile of skilled workers significantly diverged starting from 2000. Using a task-based framework of occupation, I find that the changing trend of wage inequality was entirely driven by one category of occupation, namely the nonroutine analytic occupation. Then, I consider in a model task reallocation between two broad task categories, namely the routine and abstract task, induced by an ongoing investment-specific technical change. In my model, the labor in the routine task is replaced by cheaper machines due to investment-specific technical change, then workers that are less productive in the abstract task enter abstract occupations. As a result, the wage inequality in the abstract task widens because of the reallocation of less productive workers from the routine task to the abstract task, that is, the “composition effect.” In addition, since economic agents tend to postpone the investment in machines after the ongoing investment-specific technical change takes place for a while, the expansion path of wage inequality is not linear but features an acceleration of wage dispersion in the middle of the technical change. The quantitative results suggest that the model is able to provide a well-matched timing and magnitude of the nonlinear expansion path in wage inequality that is observed in the data.

Over the course of the period from the end of 2022 to early 2023, requests for advisory opinions on climate change were, for the first time, made to the International Court of Justice (ICJ), the International Tribunal for the Law of the Sea (ITLOS), and the Inter-American Court of Human Rights (IACtHR).

Polychaetes from tropical ecosystems of the eastern Pacific have been poorly studied; thus, the aim of this study was to analyse their taxonomic composition in the southern Mexican Pacific shelf and to examine their biogeographic affinities. A total of 3741 specimens from 82 species, 52 genera, and 27 families were identified from 38 stations at 42–109 m depth. The Sedentaria group was more diverse (40 species, 48.8%) and abundant (1753 ind., 46.9%) compared to the Errantia (36 species, 43.9%; 346 ind., 9.2%) and the Basal Annelida groups (6 species, 7.3%; 1642 ind., 43.9%). The families Onuphidae (14 spp.), Spionidae (8 spp.), and Paraonidae (8 spp.) were the most diverse. The Amphinomidae and Spionidae accounted for 72.6% of the fauna; the remarkably high abundance of both families together is unusual in the tropical eastern Pacific. The polychaete species had high biogeographic affinities with the Mexican tropical Pacific ecoregion (45.1%), which has tropical conditions, and the Cortezian (29.3%), which has warm-temperate characteristics. Twelve amphiamerican species and ten with worldwide distribution were found. The tropical eastern Pacific is one of the world regions with the lowest number of polychaete records, thus underlining the importance of the taxonomic and biogeographic information provided here. The sampling effort should increase, since the non-parametric estimators indicated that 116–138 species were expected, instead of the 82 species actually found.

I defend a novel account of scientific progress centered around justification. Science progresses, on this account, where there is a change in justification. I consider three options for explicating this notion of change-in-justification. This account of scientific progress dispels with a condition for scientific progress that requires accumulation of truth or truth-likeness, and it emphasizes the social nature of scientific justification.

I propose the “Propositional Account” of effective quantum field theories. According to the Propositional Account, each effective quantum field theory expresses propositions about various physical items: fields, interactions, and more. In addition, two effective quantum field theories are physically equivalent just in case they express the same propositions. As I explain, the Propositional Account is scientifically naturalistic, since it invokes terms and principles from the empirical science of linguistics. And the Propositional Account avoids problems faced by other accounts of the physical contents of effective theories.

In 2008, Tóth and Vető defined the self-repelling random walk with directed edges as a non-Markovian random walk on $\unicode{x2124}$: in this model, the probability that the walk moves from a point of $\unicode{x2124}$ to a given neighbor depends on the number of previous crossings of the directed edge from the initial point to the target, called the local time of the edge. Tóth and Vető found that this model exhibited very peculiar behavior, as the process formed by the local times of all the edges, evaluated at a stopping time of a certain type and suitably renormalized, converges to a deterministic process, instead of a random one as in similar models. In this work, we study the fluctuations of the local times process around its deterministic limit, about which nothing was previously known. We prove that these fluctuations converge in the Skorokhod $M_1$ topology, as well as in the uniform topology away from the discontinuities of the limit, but not in the most classical Skorokhod topology. We also prove the convergence of the fluctuations of the aforementioned stopping times.