We show how to apply forward and reverse mode Combinatory Homomorphic Automatic Differentiation (CHAD) (Vákár (2021). ESOP, 607–634; Vákár and Smeding (2022). ACM Transactions on Programming Languages and Systems 44 (3) 20:1–20:49.) to total functional programming languages with expressive type systems featuring the combination of

• • tuple types;

• • sum types;

• • inductive types;

• • coinductive types;

• • function types.

We achieve this by analyzing the categorical semantics of such types in $\Sigma$-types (Grothendieck constructions) of suitable categories. Using a novel categorical logical relations technique for such expressive type systems, we give a correctness proof of CHAD in this setting by showing that it computes the usual mathematical derivative of the function that the original program implements. The result is a principled, purely functional and provably correct method for performing forward- and reverse-mode automatic differentiation (AD) on total functional programming languages with expressive type systems.

Based on the fact that the follicular phase in the menstrual cycle has length variation, it has been assumed that the duration of oestrogen (E2) administration could also be variable; therefore, for the first time, this randomized clinical trial study was conducted to investigate and compare the duration of estradiol administration and the effect on pregnancy outcomes in the cleavage-stage frozen embryo transfer (FET) cycle. We included women aged 20–40 with a normal uterus on hysteroscopy between September and December 2022 and who were divided randomly into three groups: group A [n = 79; 8–11 days of oestrogen before progesterone (P4) supplementation], group B (n = 78; 12–14 days of oestrogen before P4 supplementation), and group C (n = 76; 15–18 days of estrogen before P4 supplementation). Serum levels for E2 on the initial progesterone day and P4 on the transfer day were measured. The effect of the duration of E2 administration on clinical pregnancy and pregnancy loss was investigated. We found no significant differences between the three groups in the clinical pregnancy rate (P = 0.696) and clinical abortion rate (P = 0.925) according to the duration of the E2. There was no significant difference in the E2, P4 levels, and endometrial thickness in pregnant vs. non-pregnant women. The mean of the E2 and P4 levels was 300.03 ± 22.21 and 25.36 ± 5.78, respectively. Our findings suggest that variation in the length of E2 administration (8–18 days) before progesterone initiation in day 3 FET cycles does not affect pregnancy outcome and transfer time can be flexibly arranged.

This article argues that the ante mortem dreams of Alcibiades and Demosthenes articulate key themes of moral doubt in Plutarch’s biography of each man. Alcibiades’ dream of being dressed as a courtesan alludes to his uneasy stance between masculine and feminine postures; Demosthenes’ dream of himself as a failed tragic actor draws upon his lifelong concern with performance and insincerity. In these two Lives, Plutarch deploys the ambiguity and uncertainty of dreams to pose an interpretive problem for the reader which can never fully be resolved, particularly appropriate to these unpredictable and untrustworthy men.

The least squares Monte Carlo method has become a standard approach in the insurance and financial industries for evaluating a company’s exposure to market risk. However, the non-linear regression of simulated responses on risk factors poses a challenge in this procedure. This article presents a novel approach to address this issue by employing an a-priori segmentation of responses. Using a K-means algorithm, we identify clusters of responses that are then locally regressed on their corresponding risk factors. The global regression function is obtained by combining the local models with logistic regression. We demonstrate the effectiveness of the proposed local least squares Monte Carlo method through two case studies. The first case study investigates butterfly and bull trap options within a Heston stochastic volatility model, while the second case study examines the exposure to risks in a participating life insurance scenario.

In studies of singletons, a range of early-life characteristics have been reported to be associated with handedness, but some of these associations have failed to replicate. We examined associations between 23 early life characteristics with handedness in a large sample of 37,495 5-year-old twins. We considered three definitions of handedness: left-handedness (LH), mixed-handedness (MH), and non-right-handedness (NRH). Our main aim was to test whether the associations with sex, birth weight, gestational age, and season of birth — as reported in singletons — replicate in twins, and to examine twin-specific variables, including zygosity, chorionicity, birth order, and intertwin delivery time. Compared to previously published data from adults born as singletons (7.23%), the prevalence of NRH was higher in both twins (16.19%) and their parents (15.09%). In the twins, LH and NRH were associated with parents’ LH. Male sex and lower gestational age were associated with NRH, and LH was associated with not being breastfed. MH was related to neurodevelopmental delays and higher externalizing problems later in childhood. Other previously reported associations were not replicated, and no twin-specific characteristics were related to handedness. These results emphasize the importance of considering multiple definitions of handedness and indicate a small number of replicated associations across studies.

A variety of ancient sources suggest that there was more than one Aristophanic play entitled Πλοῦτος, and the scholia on the extant Plutus show that one ancient commentator erroneously thought that he was working on a comedy of 408 BC when in reality he had the comedy of 388 BC in front of him. This error, which most likely arose because there were two similar versions of the late Plutus, has often been attributed to the first-century BC scholar Didymus Chalcenterus. It is here argued that the basis for this ascription is weak and that there are in fact substantial counter-arguments. Instead of Didymus, a later commentator such as the second-century AD scholar Symmachus may have been responsible for the mistake, which probably had more to do with the evolving transmission history of Aristophanes’ comedies than with careless scholarship.

Confirmation, one of the seven sacraments in Lombard’s schedule, was retained by the English Reformers, but not as a sacrament and without any distinctive quasi-sacramental grace attributed to it. It became a ceremony to complete the catechizing process for children who, having been baptized as infants, were at the age of discretion now to come to holy communion. The reformers thought that a post-baptismal laying on of hands had been practised from apostolic times, and so commended the ceremony for their church practice. This requirement enabled later generations, such as Gregory Dix, to bid up its significance, teaching that confirmation completes baptism, and thus that water-baptism is of itself incomplete. The underlying premise has been that from the apostles onwards a requisite second initiatory ceremony invariably followed baptism. Both Bible and early church history contradict this thesis, not least the eight post-apostolic authors of the first two centuries who mention baptism. All eight testify to the use of water without any further ceremony. Thus, any insistence upon a two-stage sacramental initiation today lacks historical foundations; Anglicans ought to review residual texts and practices which reflect such a pattern.

The Minkowski functionals, including the Euler characteristic statistics, are standard tools for morphological analysis in cosmology. Motivated by cosmic research, we examine the Minkowski functional of the excursion set for an isotropic central limit random field, whose k-point correlation functions (kth-order cumulants) have the same structure as that assumed in cosmic research. Using 3- and 4-point correlation functions, we derive the asymptotic expansions of the Euler characteristic density, which is the building block of the Minkowski functional. The resulting formula reveals the types of non-Gaussianity that cannot be captured by the Minkowski functionals. As an example, we consider an isotropic chi-squared random field and confirm that the asymptotic expansion accurately approximates the true Euler characteristic density.

It is very challenging for robots to perform grinding and polishing tasks on surfaces with unknown geometry. Most existing methods solve this problem by modeling the relationship between the force sensing information and surface normal vectors by analyzing the forces on special end tools such as spherical tools and cylindrical tools and simplified friction model. In this paper, we propose a normal vectors learning method to simultaneously control end-effector force and direction on unknown surfaces. First, the relation that mapping the force sensing information to the surface normal vectors is learned from the demonstrated data on the known plane using locally weighted regression. Next, the learned relation is used to estimate surface normal vectors on the unknown surface. To improve the force control precision on the unknown geometry surface, the adaptive force control is developed. To improve the direction control precision due to friction, the iterative learning control is developed. The proposed method is verified by comparative simulations and experiments using the Franka robot. Results show that the end-effector can be controlled perpendicular to the surface with a certain force.

Child maltreatment is a pathogenic relational experience that creates risk for physical and psychological health difficulties throughout the lifespan. The Reminiscing and Emotion Training intervention (RET) was developed to support maltreated children’s healthy development by improving parenting behavior among maltreating mothers. Here, we evaluated whether RET was associated with reductions in child welfare reinvolvement over the course of two years. The sample included 165 maltreating and 83 nonmaltreating mothers and their 3- to 6-year-old children who were enrolled in a longitudinal randomized controlled trial of RET. Maltreating mother–child dyads were randomly assigned to receive RET or an active control condition (community standard [CS]). Nonmaltreating dyads were a separate control group (nonmaltreating control). Comparing CS and RET dyads, there was a significant effect of RET on frequency of child welfare reinvolvement (substantiations and unsubstantiated assessments) during the two years following dyads’ enrollment in the intervention, t(163) = 2.02, p < .05, Cohen’s d = 0.32. There was a significant indirect effect of RET on child welfare reinvolvement through maternal sensitive guidance during reminiscing [95% CI −0.093, −0.007]. Results provide support for the efficacy of RET in preventing child welfare reinvolvement.