Noting a curious link between Andrews’ even-odd crank and the Stanley rank, we adopt a combinatorial approach building on the map of conjugation and continue the study of integer partitions with parts separated by parity. Our motivation is twofold. Firstly, we derive results for certain restricted partitions with even parts below odd parts. These include a Franklin-type involution proving a parametrized identity that generalizes Andrews’ bivariate generating function, and two families of Andrews–Beck type congruences. Secondly, we introduce several new subsets of partitions that are stable (i.e. invariant under conjugation) and explore their connections with three third-order mock theta functions $\omega (q)$, $\nu (q)$, and $\psi ^{(3)}(q)$, introduced by Ramanujan and Watson.

There is a dearth of women judges sitting on international courts and tribunals. This contribution pays attention to the question of why judicial gender matters. Demonstrating that sex-based differences play an important part in judging has challenged even the most committed essentialists. Legitimacy-based arguments are deemed inadequate in so far as they fail to address the structures of power and discrimination that create exclusions. In this contribution, I argue that the dearth of women judges matters because it is both symptom and cause of the highly gendered way in which international law and international institutions operate. Drawing on Erika Rackley’s early work in which metaphor is used to reveal the gendered nature of the judicial role, I call forth the idea of the totemic judge of international law whose male gender is rendered invisible and unremarked and who functions to enrobe the gendered norms and institutions of international law. The female judge, conversely, is a disruptive force as her very presence places gender in the frame. Drawing on accounts from international courts and from the Feminist Judgments in International Law project, this contribution concludes that an approach to judging that acknowledges and challenges structures of power – including gender – contains transformative potential. However, it is potential that must find a way to operate within significant institutional and normative constraints.

Women’s ability to negotiate for safer sex has effects on their sexual and reproductive health. This study investigated the association between safer sex negotiation and parity among women in sub-Saharan Africa. The data were sourced from the Demographic and Health Surveys of 28 sub-Saharan African countries conducted from 2010 to 2019. A total of 215,397 women aged 15–49 were included in the study. Multilevel logistic analysis was conducted to examine the association between safer sex negotiation and parity among women in sub-Saharan Africa. The results were presented as adjusted odds ratios (aOR) and the significance level set at p<0.05. The overall prevalences of safer sex negotiation and high parity among women in sub-Saharan Africa were 82.7% and 52.1%, respectively. The prevalence of high parity ranged from 32.3% in Chad to 72.1% in Lesotho. The lowest prevalence of safer sex negotiation was in Chad (16.8%) while the highest prevalence was recorded in Rwanda (99.7%). Women who had the capacity to negotiate for safer sex were less likely to have high parity compared with those who had no capacity to negotiate for safer sex (aOR = 0.78, CI: 0.75–0.81). Other factors that were associated with high parity were age, educational level, marital status, exposure to media, contraceptive use, religion, wealth quintile, sex of household head, and place of residence. The study identified significant association between safer sex negotiation and high parity among women of reproductive age in sub-Saharan Africa. It is worth noting that women’s ability to negotiate for safer sex could reduce high parity among women in sub-Saharan Africa. Therefore, policies and programmes aimed at birth control or reducing high parity among women could be targeted at improving their capacity to negotiate for safer sex through education.

This article investigates the representativeness of news coverage when there are nearly as many female candidates as there are male candidates by considering the 2018 Québec Election, in which 47 per cent of candidates were women. We are interested not only in the magnitude of the coverage (that is, the volume of press coverage received by each candidate) but also in its tone (if the press coverage is negative or positive) and whether these parameters fluctuate based on the gender of the candidates. We know that the quality of the news coverage, and more specifically its tone, can affect voting intentions. We also know that journalists routinely portray politics as a masculine activity, but we know very little about the coverage that local female candidates receive in the context of parity in North America. We find that in spite of exceptional circumstances, female candidates received significantly less coverage than men.

Gilt progeny (GP) are born and weaned lighter than sow progeny (SP) and tend to have higher rates of mortality and morbidity. This study quantified the lifetime growth performance differences between GP and SP and, additionally, evaluated whether segregating GP and SP in the grower–finisher period compared to mixing them within common pens reduced this variation. It was hypothesised that GP would be lighter than SP at every stage and segregation would improve growth performance of both GP and SP. All piglets born to 61 gilts (parity 1) and 47 sows (parities 2 to 7; mean 3.5 ± 0.2) were allocated to four treatments at 10 weeks of age: (i) GP housed together (GG), (ii) GP mixed (M) with SP (GM), (iii) SP housed together (SS) and (iv) SP mixed with GP (SM). The GM and SM pigs were housed together in common pens after movement into the grower–finisher facility. Individual live weight of all progeny was recorded at birth, weaning (WWT), 10 weeks of age (10WT) and sale (SWT). Individual hot carcass weight (HCW), fat depth at the head of the last rib (P2) and dressing percentage were measured at slaughter. Gilt progeny were lighter at birth (P = 0.038), weaning (P < 0.001) and through to sale (P = 0.001) than SP. Nursery and grower–finisher performance differences in GP were highly attributable to their lower WWT compared to SP (P < 0.001 when fitted as a covariate). Segregation of GP and SP increased grower–finisher average daily gain (ADG) in SP but decreased ADG and SWT in GP (P < 0.10). Segregated SP had increased average daily feed intake but only in males (P = 0.007); HCW (P < 0.001) and P2 fat depth (P = 0.055) were higher in mixed female GP, but there was no difference (P > 0.10) in female SP, or in males. In conclusion, GP were lighter at every stage than SP and differences after weaning were highly related to the lighter WWT of GP. Under the conditions of this study, overall segregation of GP and SP showed no consistent advantages in growth performance for both groups and differed significantly between males and females.

Body condition score (BCS) is a subjective assessment of the proportion of body fat an animal possesses and is independent of frame size. There is a growing awareness of the importance of mature animal live-weight given its contribution to the overall costs of production of a sector. Because of the known relationship between BCS and live-weight, strategies to reduce live-weight could contribute to the favouring of animals with lesser body condition. The objective of the present study was to estimate the average difference in live-weight per incremental change in BCS, measured subjectively on a scale of 1 to 5. The data used consisted of 19 033 BCS and live-weight observations recorded on the same day from 7556 ewes on commercial and research flocks; the breeds represented included purebred Belclare (540 ewes), Charollais (1484 ewes), Suffolk (885 ewes), Texel (1695 ewes), Vendeen (140 ewes), as well as, crossbreds (2812 ewes). All associations were quantified using linear mixed models with the dependent variable of live-weight; ewe parity was included as a random effect. The independent variables were BCS, breed (n=6), stage of the inter-lambing interval (n=6; pregnancy, lambing, pre-weaning, at weaning, post-weaning and mating) and parity (1, 2, 3, 4 and 5+). In addition, two-way interactions were used to investigate whether the association between BCS and live-weight differed by parity, a period of the inter-lambing interval or breed. The association between BCS and live-weight differed by parity, by a period of the inter-lambing interval and by breed. Across all data, a one-unit difference in BCS was associated with 4.82 (SE=0.08) kg live-weight, but this differed by parity from 4.23 kg in parity 1 ewes to 5.82 kg in parity 5+ ewes. The correlation between BCS and live-weight across all data was 0.48 (0.47 when adjusted for nuisance factors in the statistical model), but this varied from 0.48 to 0.53 by parity, from 0.36 to 0.63 by stage of the inter-lambing interval and from 0.41 to 0.62 by breed. Results demonstrate that consideration should be taken of differences in BCS when comparing ewes on live-weight as differences in BCS contribute quite substantially to differences in live-weight; moreover, adjustments for differences in BCS should consider the population stratum, especially breed.

Understanding how critical sow live-weight and back-fat depth during gestation are in ensuring optimum sow productivity is important. The objective of this study was to quantify the association between sow parity, live-weight and back-fat depth during gestation with subsequent sow reproductive performance. Records of 1058 sows and 13 827 piglets from 10 trials on two research farms between the years 2005 and 2015 were analysed. Sows ranged from parity 1 to 6 with the number of sows per parity distributed as follows: 232, 277, 180, 131, 132 and 106, respectively. Variables that were analysed included total born (TB), born alive (BA), piglet birth weight (BtWT), pre-weaning mortality (PWM), piglet wean weight (WnWT), number of piglets weaned (Wn), wean to service interval (WSI), piglets born alive in subsequent farrowing and sow lactation feed intake. Calculated variables included the within-litter CV in birth weight (LtV), pre-weaning growth rate per litter (PWG), total litter gain (TLG), lactation efficiency and litter size reared after cross-fostering. Data were analysed using linear mixed models accounting for covariance among records. Third and fourth parity sows had more (P<0.05) TB, BA and heavier BtWT compared with gilts and parity 6 sow contemporaries. Parities 2 and 3 sows weaned more (P<0.05) piglets than older sows. These piglets had heavier (P<0.05) birth weights than those from gilt litters. LtV and PWM were greater (P<0.01) in litters born to parity 5 sows than those born to younger sows. Sow live-weight and back-fat depth at service, days 25 and 50 of gestation were not associated with TB, BA, BtWT, LtV, PWG, WnWT or lactation efficiency (P>0.05). Heavier sow live-weight throughout gestation was associated with an increase in PWM (P<0.01) and reduced Wn and lactation feed intake (P<0.05). Deeper back-fat in late gestation was associated with fewer (P<0.05) BA but heavier (P<0.05) BtWT, whereas deeper back-fat depth throughout gestation was associated with reduced (P<0.01) lactation feed intake. Sow back-fat depth was not associated with LtV, PWG, TLG, WSI or piglets born alive in subsequent farrowing (P>0.05). In conclusion, this study showed that sow parity, live-weight and back-fat depth can be used as indicators of reproductive performance. In addition, this study also provides validation for future development of a benchmarking tool to monitor and improve the productivity of modern sow herd.

On parity views of mere addition if someone (or a group of people) is added to the world at a range of well-being levels – or ‘neutral range’ – leaving existing people unaffected, addition is on a par with the initial situation. Two distinct parity views – ‘rough equality’ and fitting-attitudes views – defend the ‘intuition of neutrality’. The first can be interpreted or adjusted so that it can rebut John Broome's objection that the neutral range is wide. The two views respond in distinct ways to two of Broome's other objections. Both views can, nonetheless, be plausibly defended against these objections.

In this Research Communication we assessed factors affecting colostrum quality of dairy Lacaune ewes using the Brix-refractometer. Colostrum from 536 lambings from one commercial intensive dairy Lacaune farm were analysed for the following factors with potential influence in colostrum quality: (1) ewe parity (n = 84–132), (2) length of previous dry period (PDP) (n = 23–214), (3) age at first lambing (AFL) of primiparous ewes (n = 9–88), (4) lambing season (n = 192 or 344), and (5) year (2011–2013, n = 142–203). Parity significantly affected colostrum quality, with primiparous ewes showing the highest Brix refractometer values (22·6 ± 5·6%, P < 0·0001), though values were similar among multiparous ewes. PDP length also significantly affected colostrum quality: ewes with the shortest PDP showed the worst quality (16·8 ± 4·2%, P < 0·0001), with quality gradually rising with PDP length. Colostrum quality was significantly higher in 2011 (21·0 ± 5·2%) than in 2012 or 2013 (P < 0·0001); this likely reflects the several-fold greater proportion of animals with long PDP in 2011. In contrast, neither AFL nor lambing season significantly affected colostrum quality. These results suggest that parity and PDP length can substantially affect ovine colostrum quality of dairy ewes under intensive management conditions and they further show the usefulness of the Brix refractometer for providing a rough estimation of colostrum quality on-farm. However, further studies are needed to determine a validated cut-off Brix value for identifying good-quality colostra in ovine species.

Piglet mortality is a major problem in organic pig production affecting both farm economy and animal welfare. Knowledge is scarce on the risk factors of piglet mortality in Danish commercial organic pig production. The objectives of this study were to evaluate season, litter size, parity, sow body condition and stillborn littermates as risk factors for early piglet mortality and crushing of liveborn piglets from parturition until castration at day 3 to 5 postpartum (pp). The study was conducted over a 1-year period in nine commercial Danish organic pig herds practicing outdoor farrowing all year round. Data included recordings on 3393 farrowings with 50 284 liveborn piglets of which 14.8% died before castration. A subset of the dead piglets were collected and necropsied to identify crushed piglets. The average number of liveborn piglets per litter was 14.8 (SD=3.7) and the average time from parturition until castration was 4.1 (SD=1.7) days. A negative binomial regression analysis was used to model the effect of the predictive variables on the early piglet mortality accounting for different time periods from parturition to castration. An increase in maternal body condition score (BCS) and parity significantly increased the risk of dying between parturition and castration. Early mortality was found to be lowest during spring (March to May) and highest during summer (June to August). Being born into a litter with one or more stillborn littermates increased the risk of early mortality. The risk factors for crushing of piglets were evaluated using a logistic analysis. A significant effect of parity and litter size was found where the odds of at least one piglet in a litter with mortality was diagnosed as crushed increased with increasing parity and litter size. In conclusion, being born during summer (June to August), high parity and maternal BCS and stillborn littermates were found to be risk factors for piglet mortality between parturition and castration. In addition, parity and increasing litter size were found to be risk factors for crushing of piglets in litters with mortality.

The objective of this study was to estimate the economic impact of subclinical ketosis (SCK) in dairy cows. This metabolic disorder occurs in the period around calving and is associated with an increased risk of other diseases. Therefore, SCK affects farm productivity and profitability. Estimating the economic impact of SCK may make farmers more aware of this problem, and can improve their decision-making regarding interventions to reduce SCK. We developed a dynamic stochastic simulation model that enables estimating the economic impact of SCK and related diseases (i.e. mastitis, metritis, displaced abomasum, lameness and clinical ketosis) occurring during the first 30 days after calving. This model, which was applied to a typical Dutch dairy herd, groups cows according to their parity (1 to 5+), and simulates the dynamics of SCK and related diseases, and milk production per cow during one lactation. The economic impact of SCK and related diseases resulted from a reduced milk production, discarded milk, treatment costs, costs from a prolonged calving interval and removal (culling or dying) of cows. The total costs of SCK were €130 per case per year, with a range between €39 and €348 (5 to 95 percentiles). The total costs of SCK per case per year, moreover, increased from €83 per year in parity 1 to €175 in parity 3. Most cows with SCK, however, had SCK only (61%), and costs were €58 per case per year. Total costs of SCK per case per year resulted for 36% from a prolonged calving interval, 24% from reduced milk production, 19% from treatment, 14% from discarded milk and 6% from removal. Results of the sensitivity analysis showed that the disease incidence, removal risk, relations of SCK with other diseases and prices of milk resulted in a high variation of costs of SCK. The costs of SCK, therefore, might differ per farm because of farm-specific circumstances. Improving data collection on the incidence of SCK and related diseases, and on consequences of diseases can further improve economic estimations.

What makes a choice hard? I discuss and criticize three common answers and then make a proposal of my own. Paradigmatic hard choices are not hard because of our ignorance, the incommensurability of values, or the incomparability of the alternatives. They are hard because the alternatives are on a par; they are comparable, but one is not better than the other, and yet nor are they equally good. So understood, hard choices open up a new way of thinking about what it is to be a rational agent.

According to Wlodek Rabinowicz's (2008) fitting-attitude analysis of value relations, two items are on a par if and only if it is both permissible to strictly prefer one to the other and permissible to have the opposite strict preference. Rabinowicz's account is subject, however, to one important objection: if strict preferences involve betterness judgements, then his analysis contrasts with the intuitive understanding of parity. In this paper, I examine Rabinowicz's three responses to this objection and argue that they do not succeed. I then propose an alternative solution. I argue that the objection can be avoided if we ‘relativize’ Rabinowicz's account and define parity in terms of opposite strict preferences between two items that are only relatively permissible, rather than permissible simpliciter. I argue that this account of parity can be defended if we take seriously the distinction between sufficient and decisive reason for a preference relation. I also show that, on the basis of this distinction, we can arrive at a more extensive taxonomy of value relations than the one proposed by Rabinowicz.