Let $\Sigma$ be an alphabet and $\mu$ be a distribution on $\Sigma ^k$ for some $k \geqslant 2$. Let $\alpha \gt 0$ be the minimum probability of a tuple in the support of $\mu$ (denoted $\mathsf{supp}(\mu )$). We treat the parameters $\Sigma , k, \mu , \alpha$ as fixed and constant. We say that the distribution $\mu$ has a linear embedding if there exist an Abelian group $G$ (with the identity element $0_G$) and mappings $\sigma _i : \Sigma \rightarrow G$, $1 \leqslant i \leqslant k$, such that at least one of the mappings is non-constant and for every $(a_1, a_2, \ldots , a_k)\in \mathsf{supp}(\mu )$, $\sum _{i=1}^k \sigma _i(a_i) = 0_G$. In [Bhangale-Khot-Minzer, STOC 2022], the authors asked the following analytical question. Let $f_i: \Sigma ^n\rightarrow [\!-1,1]$ be bounded functions, such that at least one of the functions $f_i$ essentially has degree at least $d$, meaning that the Fourier mass of $f_i$ on terms of degree less than $d$ is at most $\delta$. If $\mu$ has no linear embedding (over any Abelian group), then is it necessarily the case that

\begin{equation*}\left | \mathop {\mathbb{E}}_{({\textbf {x}}_1, {\textbf {x}}_2, \ldots , {\textbf {x}}_k)\sim \mu ^{\otimes n}}[f_1({\textbf {x}}_1)f_2({\textbf {x}}_2)\cdots f_k({\textbf {x}}_k)] \right | = o_{d, \delta }(1),\end{equation*}

$\to 0$

$d \to \infty$

$\delta \to 0$

In this paper, we answer this analytical question fully and in the affirmative for $k=3$. We also show the following two applications of the result.

1. 1. The first application is related to hardness of approximation. Using the reduction from [5], we show that for every $3$-ary predicate $P:\Sigma ^3 \to \{0,1\}$ such that $P$ has no linear embedding, an SDP (semi-definite programming) integrality gap instance of a $P$-Constraint Satisfaction Problem (CSP) instance with gap $(1,s)$ can be translated into a dictatorship test with completeness $1$ and soundness $s+o(1)$, under certain additional conditions on the instance.

2. 2. The second application is related to additive combinatorics. We show that if the distribution $\mu$ on $\Sigma ^3$ has no linear embedding, marginals of $\mu$ are uniform on $\Sigma$, and $(a,a,a)\in \texttt{supp}(\mu )$ for every $a\in \Sigma$, then every large enough subset of $\Sigma ^n$ contains a triple $({\textbf {x}}_1, {\textbf {x}}_2,{\textbf {x}}_3)$ from $\mu ^{\otimes n}$ (and in fact a significant density of such triples).

Over the last two decades, Marxism has experienced a significant revival, including in the discipline of law. The 2003 Iraq War and, perhaps more obviously, the 2008 financial crisis posed questions about the relationship between law, capitalism and imperialism that mainstream legal scholarship had difficulty answering. One marked exception to this revival has been in the field of European Union (EU) law. EU law scholarship, perhaps understandably given that few Member States participated in the invasion, had little to say about the Iraq War. For its part, the 2008 financial crisis and its manifestation in Europe as the ‘Euro-Crisis’ prompted a ‘critical turn’ in EU legal studies.1 However, these two movements – the Marxist tradition and critical EU law scholarship – have largely failed to meet. Marxist analyses of EU law, let alone the development of a full-blown Marxist theory of EU law, remain almost non-existent.

This article examines historical perceptions of the territorial extent of Bod, the Tibetan toponym for ‘Tibet’. In a bid to establish what area second-millennium authors (and audiences) may have pictured when this toponym was invoked, we analyse instructive passages from five historiographical works, mostly dating from between the twelfth and seventeenth centuries. The rough-hewn maps of Bod ‘Tibet’ that emerge from this procedure differ quite radically from one work to the next, and at times even between different passages from a single source. While one work may see ‘Tibet’ as the territory directly centered on the Tibetan Plateau’s south-central river valleys, another source may forward an image of a ‘Tibet’ that is thrice as large. Works may also allow for shifts in its borders from one political period to the next, or incorporate multiple incongruous territorial descriptions. This material helps answer what ‘Tibet’ meant in different periods and places, and to different people—questions that have only poorly been studied outside of modern political history. One relevant finding, among others, is that the notion of a ‘Tibet’ that covers a large part of the Tibetan Plateau, incorporating for instance sites in contemporary eastern Qinghai, was not in fact a modern innovation.

This article explores the systems of policing that emerged in the early Cape Colony (1652–1830). Contrary to previous historical scholarship that understood the institution to be largely nonexistent or of marginal importance to the colony’s political economic development, this article argues that the Cape colony’s systems of policing, which doubled as ad hoc military organizations, were not so much weak as privatized. It shows how this persistent tendency was motivated by the Dutch East India Company’s desire to maximize profits—though it manifested differently in different parts of the colony. Moreover, this article demonstrates that the mercantile economy that the company installed at the Cape ensured that private policing would become a vehicle of indigenous dispossession. In doing so, it seeks to contribute to the field of African carceral studies and understandings of processes of racialization in the early Cape.

This article is the introduction to the Special Issue on The Constitution of Political Economy. It provides an overview of six articles which in distinctive yet overlapping ways explore three key issues. First, how the economy and the polity are embedded in society. Second, how interdependence shapes institutional arrangements. Third, how different levels of aggregation determine levels of policy-making, notably the importance of intermediate institutions.

We derive the scale-by-scale uncertainty energy budget equation and demonstrate theoretically and computationally the presence of a self-similar equilibrium cascade of decorrelation in an inertial range of scales during the time range of power-law growth of uncertainty in statistically stationary homogeneous turbulence. This cascade is predominantly inverse and driven by compressions of the reference field’s relative deformation tensor and their alignments with the uncertainty velocity field. Three other subdominant cascade mechanisms are also present, two of which are forward and also dominated by compressions and one of which, the weakest and the only nonlinear one of the four, is inverse. The uncertainty production and dissipation scalings which may follow from the self-similar equilibrium cascade of decorrelation lead to power-law growths of the uncertainty integral scale and the average uncertainty energy which are also investigated. Compressions are key not only to chaoticity, as previously shown, but also to stochasticity.

Common milkweed is a creeping perennial weed that is problematic in row crops and pastures. Its ability to readily reproduce via adventitious root buds enables it to persist, and full control often requires several growing seasons of management. Although it is a troublesome agricultural weed, common milkweed is ecologically important due to its use as a food source for many arthropod species. Declines in common milkweed populations in North America have been correlated with and blamed for declines in monarch butterfly populations. This review summarizes available information on the biology, ecology, and management of common milkweed, as well as its potential uses and provisioning of ecosystem services.

A new species of Blastulospongia Pickett and Jell, 1983 from the middle Cambrian Devoncourt Limestone, Georgina Basin, Australia exhibits distinct perforation patterns characteristic of sphinctozoans. Recognition as a sphinctozoan-grade sponge confirms the poriferan affinity of this enigmatic genus, which appeared prior to the development of other hypercalcified sponge forms of chaetetids and stromatoporoids. Blastulospongia bouliaensis new species occurs together with four species of primitive spicular radiolarians: Echidnina irregularis Won in Won and Iams, 2002, Parechidnina aspinosa Won in Won and Below, 1999, Palaeospiculum reedae Won in Won and Below, 1999, and Palaeospiculum devoncourtensis Won in Won and Below, 1999. Micro-computed tomographic (MCT) analysis of Parechidnina aspinosa reveals its skeletal construction through the fusion of unirayed spicules, indicating a close phylogenetic link with archeoentactinids. Blastulospongia bouliaensis n. sp. and Palaeospiculum devoncourtensis represent promising Miaolingian accessory species for biostratigraphy during the Drumian-Guzhangian interval.

UUID: http://zoobank.org/a74cdd4d-6bc3-427b-bf4c-d4f0b79a5c91

A large empirical literature examines how judges’ traits affect how cases get resolved. This literature has led many to conclude that judges matter for case outcomes. But how much do they matter? Existing empirical findings understate the true extent of judicial influence over case outcomes since standard estimation techniques hide some disagreement among judges. We devise a machine learning method to reveal additional sources of disagreement. Applying this method to the Ninth Circuit, we estimate that at least 38% of cases could be decided differently based solely on the panel they were assigned to.

This article aims to further our understanding of the mechanics of physical weed control, specifically the mechanism of using a cutting blade to cut weeds. Research on weed stem cutting is sparse, so this paper draws on examples of plant stem cutting. It reviews the factors that affect the plant stem cutting process. Among the, Cutting speed, blade sharpness, and moisture content, factors that can easily be controlled, are discussed. The indicators for evaluating the cutting process and the methods for measuring the influencing factors are introduced as well. Finally, different blade designs, examples of the application of mechanisms that affect the cutting process of plant stems are provided. This review argues that, under conditions of high cutting speed, high blade sharpness, and high moisture content, plastic deformation would be reduced and the stems would exhibit brittle material characteristics. This would help to reduce the cutting force and energy, but excessive brittleness can cause stem fragmentation and degrade cutting quality. This paper also lists some possible future research directions. First, friction behavior during the cutting process of fresh plant stems. Another, cutting blade design based on the comprehensive application of cutting speed, blade wedge angle, and sliding cutting angle on the cutting process. At present, the mechanism of plant stem cutting process is still not clear. Further research is needed.

To what extent can intellectual humility be formalized? One natural idea links humility to open-mindedness, captured by a regularity principle: no coherent hypothesis should get probability zero. While debates over regularity often concern infinities, my objection is different. Regularity is feasible only for ideally rational, logically omniscient agents. Yet on a common view, humility involves appreciating our limitations—including our failure to be such agents. So whatever its merits for ideal cognition, regularity is a poor model for human humility. Indeed, taking it as such would itself be un-humble, by failing to appreciate our own epistemic limitations.

The decision to work is an important yet understudied facet of women’s economic empowerment. This study explores the relationship between married women’s agency over the decision to work, workforce participation, and control over financial resources, using cross-sectional survey data collected in 2022 in India’s three most populous states: Bihar, Uttar Pradesh, and Maharashtra. Employing logistic regression, inverse probability weighting, and partial identification approaches, we demonstrate that married women in all three states are significantly more likely to engage in paid work when they alone have the final say over the decision to work, compared to when their spouse is the primary decision-maker. We also find that sole decision-making about paid work is positively related to married women’s control over money in Bihar and Maharashtra, and with savings and remittances in Maharashtra. In Maharashtra, women who jointly decide about employment with their spouse are also more likely to work than women whose husbands are the sole decision-makers. Joint decision-making is positively associated with women’s control over money in all three states. Our study highlights work-related agency as an important pathway to married women’s economic opportunities and inclusion in India, and is among the first to empirically examine the relationship between women’s work-related decision-making and economic outcomes. These results align with existing evidence on the positive relationship between women’s household bargaining power and health and human capital outcomes, and offer support for designing programmes to promote women’s participation in the workforce.

The Llandoverian (Telychian) Schoolcraft Formation of Schoolcraft County in the Upper Peninsula of Michigan includes several intervals of exceptional preservation marked by abundant specimens of the noncalcified macroalga Thalassocystis striata Taggart and Parker, 1976. Here, two new noncalcified macroalgal species are described from one of these algal-Lagerstätten intervals. The monopodial thallus of Archaeobatophora gulliverensis new species resembles that of the living dasycladalean green alga Batophora Agardh, 1854 and consists of a cylindrical main axis bearing whorls of branched laterals. It is the second species to be assigned to Archaeobatophora Nitecki, 1976, the type species of which is known only from the Upper Ordovician of neighboring Delta County and the diagnosis of which is emended herein. The thallus of Earltonella swinehartii new species consists of a horizontal stolon that bears a series of upright pinnate fronds. This taxon broadly resembles the living bryopsidalean green alga Caulerpa Lamouroux, 1809 and is the second species to be assigned to Earltonella LoDuca in LoDuca et al., 2023, a genus otherwise known only from approximately age-equivalent strata in the Lake Timiskaming area of Ontario. Additionally, a new Thalassocystis striata occurrence is reported from the Schoolcraft Formation in neighboring Mackinac County, extending eastward the geographic range of this Codium-like bryopsidalean taxon within the Michigan Basin. Viewed in broader terms, the two new species show complex thallus morphologies consistent with a previously documented large-scale morphological pattern in the early Paleozoic evolutionary history of macroalgae and contribute to an emerging understanding of major early Paleozoic radiations of both dasycladalean and bryopsidalean algae that produced, by the mid-Silurian, diverse floras of siphonous green macroalgae broadly similar to those that thrive today in Florida Bay and the Bahama Banks.