We use bounds of character sums and some combinatorial arguments to show the abundance of very smooth numbers which also have very few nonzero binary digits.

In a conventional experiment, scientists typically aim to learn about target systems by manipulating source systems of the same material type. In an analogue quantum simulation, by contrast, scientists typically aim to learn about target quantum systems of one material type via an experiment on a source quantum system of a different material type. In this article, we argue that such inferences can be justified by reference to source and target quantum systems being of the same empirical type. We illustrate this novel experimental practice of wavefunction engineering with reference to the example of Bose–Hubbard systems.

This piece aims to assess the potential contribution and the scope and structure of a Catalan Centre for Business and Human Rights to supervise the fulfilment of the corporate responsibility to respect human rights and to hold businesses operating in Catalonia accountable for human rights abuses within the autonomous community and abroad. It also examines how this proposal fits into the regional and national regulatory landscape for mandatory human rights due diligence.

Folate, also known as vitamin B9, is a water-soluble vitamin. Previous studies on dietary folate intake in severe headache patients were equivocal. Therefore, we conducted a cross-sectional study to elucidate the relationship between folate intake and severe headache. This cross-sectional study used data from participants over 20 years old who participated in the National Health and Nutrition Examination Survey (NHANES) from 1999 to 2004. The diagnosis of severe headache was made through participants’ self-report in the NHANES questionnaire section. We performed multivariate logistic regression and restricted cubic spline (RCS) regression to explore the relationship between folate intake and severe headache. A total of 9859 participants took part in the study, 1965 of whom were severe headache patients and the rest were non-severe headache. We found that dietary folate intake was significantly and inversely associated with severe headache. Compared with participants with lower folate intake Q1 (≤ 229·97 ug/d), the adjusted OR values for dietary folate intake and severe headache in Q2 (229·98–337 ug/d), Q3 (337·01–485 ug/d) and Q4 (≥ 485·01 ug/d) were 0·81 (95 % CI: 0·67, 0·98, P = 0·03), 0·93 (95 % CI: 0·77, 1·12, P = 0·41) and 0·63 (95 % CI: 0·49, 0·80, P < 0·001), respectively. For women aged 20–50 years, there was a non-linear association between folate intake and severe headache in the RCS. Women aged 20–50 years should have higher awareness of dietary folate and increase their dietary intake of folate, which may aid in preventing severe headache.

Mammalian oocytes not fertilized immediately after ovulation can undergo ageing and a rapid decline in quality. The addition of antioxidants can be an efficient approach to delaying the oocyte ageing process. Onion peel extract (OPE) contains quercetin and other flavonoids with natural antioxidant activities. In this study, we investigated the effect of OPE on mouse oocyte ageing and its mechanism of action. The oocytes were aged in vitro in M16 medium for 16 h after adding OPE at different concentrations (0, 50, 100, 200, and 500 μg/ml). The addition of 100 μg/ml OPE reduced the oocyte fragmentation rate, decreased the reactive oxygen species (ROS) level, increased the glutathione (GSH) level, and improved the mitochondrial membrane potential compared with the control group. The addition of OPE also increased the expression of SOD1, CAT, and GPX3 genes, and the caspase-3 activity in OPE-treated aged oocytes was significantly lower than that in untreated aged oocytes and similar to that in fresh oocytes. These results indicated that OPE delayed mouse oocyte ageing by reducing oxidative stress and apoptosis and enhancing mitochondrial function.

Trilobites from the upper Guzhangian of the southern Argentine Precordillera, preliminarily described by Carlos Rusconi in the 1950s, are revised herein. The specimens studied were collected from an allochthonous limestone block of La Cruz Olistoliths at 200 m northwest of Estancia San Isidro locality (San Isidro area, Mendoza). Taxa comprise Kormagnostus seclusus (Walcott, 1884), Cedaria prolifica Walcott, 1924, C. puelchana Rusconi, 1954, Tricrepicephalus texanus (Shumard, 1861), Meteoraspis metra (Walcott, 1890), Coosia conicephala (Rusconi, 1954) new combination, Coosella texana? Resser, 1942, Nasocephalus cf. N. nasutus Wilson, 1954, and Olenoides proa (Rusconi, 1954) new combination. The North American genera Meteoraspis Resser, 1935 and Nasocephalus Wilson, 1954 are reported confidently from South America for the first time. This assemblage is representative of the Cedaria prolifica Zone, which correlates with the lower Crepicephalus Zone of the traditional North American genus-based zonation. Most of the genera and species identified were previously described exclusively from Canada, the United States, and northwestern Mexico, a fact that provides new support to an allochthonous Laurentian origin of the Argentine Precordillera.

Latvia’s far right has had a great deal of political influence since the late 1980s, when nativist movements played a key role in mobilizing political opposition to Soviet power. Far-right parties have been in 16 of the 22 government coalitions in Latvia between 1993 and 2023. Since 2010, the National Alliance (NA), a merger between an established far-right party and a more youthful political party, has come to dominate Latvia’s far right and has been a part of every government coalition from 2011-2023. This article begins with a discussion of Europeanization, the Europeanization of political parties, and the qualitative methodology used in the article to examine the impact of Latvia’s membership in the European Union on NA’s international links and program. The article then outlines the development and influence of Latvia’s far-right. The following sections examine links between Latvia’s far right and Europe’s far right and the impact of Europe on NA’s ideology and program. It finds little evidence of Europeanization of Latvia’s far right. Latvia’s far right is more hawkish toward Russia than the West European right and also enjoys greater domestic influence and respectability. “New nativist” anti-immigration and cultural Marxism themes have lower salience in Latvia where Russian-speakers are perceived as a bigger and more immediate threat than Muslims or “Woke” activists.

Since 1997, the Canadian province of Quebec has put in place a heavily subsidized universal childcare program for all children under the school age. The present paper examines how the level of competition among individual providers associates with the quality of childcare in Quebec. The quality of childcare is measured by the number of violations and penalties recorded in the inspections conducted by the Quebec Ministry of Family Affairs. The analysis indicates that the intensity of parental competition for daycare spots, as opposed to childcare centres’ competition to attract parents, negatively associates with the quality of childcare. Critically, this association is mainly driven by less affluent neighbourhoods. In addition, these associations are found to be stronger for more serious violations. The policy implications for both childcare quality and childcare equality are discussed.

We document the unique structure of the peer-to-peer lending market. Originally designed as decentralized, the market has become highly, but not fully, reintermediated. The platforms’ software now performs essentially all tasks related to loan evaluation, whereas most lenders are passive and automatically fund most applications on offer. Yet unlike banks, and in contrast to theories predicting full reintermediation, the platforms provide detailed loan information, and some active loan pickers coexist with passive investors. We argue that while intermediation attracts unsophisticated passive investors, transparency in the presence of active investors resolves the lending platform’s moral hazard problem inherent in intermediated markets.

Although individuals born at extremely low birth weight (ELBW; ≤1000 g) are known to be at greater risk for mental health problems than individuals born at normal birth weight (NBW; ≥2500 g), contributions of postnatal growth to these relations have not been fully explored. We compared individual differences in the Ponderal Index [(PI; weight(kg)/height(m3)] and head circumference (HC) in predicting internalizing and externalizing behaviors in childhood and adolescence in a cohort of ELBW survivors (N = 137) prospectively followed since birth. Baseline models indicated that infants who were born thinner or with smaller HC showed greater PI or HC growth in the first 3 years. Latent difference score (LDS) models showed that compensatory HC growth in the first year (ΔHC = 20.72 cm), controlled for birth HC, predicted ADHD behaviors in adolescence in those born with smaller HC. LDS models also indicated that the PI increased within the first year (ΔPI = 1.568) but decreased overall between birth and age 3 years (net ΔPI = −4.597). Modeling further showed that larger increases in the PI in the first year and smaller net decreases over 3 years predicted more internalizing behaviors in adolescence. These findings suggest early growth patterns prioritizing weight over height may have negative effects on later mental health in ELBW survivors, consistent with developmental programming theories.

We develop an effective version of the Chabauty–Kim method which gives explicit upper bounds on the number of $S$-integral points on a hyperbolic curve in terms of dimensions of certain Bloch–Kato Selmer groups. Using this, we give a new ‘motivic’ proof that the number of solutions to the $S$-unit equation is bounded uniformly in terms of $\#S$.