The gauge action, DG Lie algebra and identities for Bernoulli numbers

In this paper we prove a family of identities for Bernoulli numbers parameterized by triples of integers $(a,b,c)$ with $a+b+c=n-1$, $n\ge 4$. These identities are deduced while translating into homotopical terms the gauge action on the Maurer Cartan Set which can be seen an abstraction of the behaviour of gauge infinitesimal transformations in classical gauge theory. We show that Euler and Miki's identities, well known and apparently non related formulas, are linear combinations of our family and they satisfy a particular symmetry relation.Comment: Small modifications. To appear in Forum Mathematicu

Behavioural and physiological responses of laying hens to automated monitoring equipment

Automated monitoring of behaviour can offer a wealth of information in circumstances where observing behaviour is difficult or time consuming. However, this often requires attaching monitoring devices to the animal which can alter behaviour, potentially invalidating any data collected. Birds often show increased preening and energy expenditure when wearing devices and, especially in laying hens, there is a risk that individuals wearing devices will attract aggression from conspecifics. We studied the behavioural and physiological response of 20 laying hens to backpacks containing monitoring devices fastened with elastic loops around the wing base. We hypothesised that backpacks would lead to a stress-induced decrease in peripheral temperature, increased preening, more aggression from conspecifics, and reduced bodyweights. This was evaluated by thermography of the eye and comb (when isolated after fitting backpacks), direct observations of behaviour (when isolated, when placed back into the group, and on later days), and weighing (before and after each 7-day experimental period). Each hen wore a backpack during one of the two experimental periods only and was used as her own control. Contrary to our hypothesis, eye temperature was higher when hens wore a backpack (No backpack: 30.2 °C (IQR: 29.0–30.6) vs. Backpack: 30.9 °C (IQR: 30.0–32.0), P < 0.001). Eye temperature of hens wearing a backpack was strongly correlated to the time spent preening (rs = 0.8, P < 0.001), suggesting that the higher temperatures may have been due to preening itself, or to a low head position or decreased heat dissipation when preening under the wings. Aggressive behaviour was very rare and no effect of the backpacks was found. In line with our hypothesis, backpacks increased preening on the day of fitting, both when isolated (No backpack: 0% (IQR: 0–1) vs. Backpack: 22% (IQR: 1–43), P < 0.01) and when back in the group (No backpack: 0% (IQR: 0–27) vs. Backpack: 43% (IQR: 5–77), P < 0.001). However, no effect on preening was observed 2–7 days afterwards. Other behavioural changes suggested that on the day of fitting hens prioritized attempts to (re)move the backpack and were less attentive to their surroundings. However, only equipment pecking (i.e., pecking the backpack or leg rings) was still affected 2–7 days after fitting (No backpack: 0 pecks/hen/minute (IQR: 0–0), vs. Backpack: 0 (IQR: 0–0.07), P < 0.05). We found no effect of our backpacks on bodyweight. In conclusion, our backpacks seem suitable to attach monitoring equipment to hens with only a very minor effect on their behaviour after a short acclimation period (≤2 days)

Dynamic shipments of inventories in shared warehouse and transportation networks

In shared warehouse and transportation networks, dynamic shipments of inventories are carried out based on up-to-date inventory information. This paper studies the effect of network structures on optimal decision-making. We propose a discrete time modeling framework with stochastic demand, capturing a wide variety of network structures. Using Markov decision processes, we obtain optimal order and dynamic shipment decisions for small networks. We compare optimal solutions of different four-node network structures. Results indicate product characteristics significantly influence the effectiveness of network structures. Surprisingly, two-echelon networks are occasionally costlier than any other network. Moreover, dynamic shipments yield considerable gains over static shipments

The analysis of longitudinal quality of life measures with informative drop-out: a pattern mixture approach

The analysis of longitudinal health-related quality of life measures (HRQOL) can be seriously hampered due to informative drop-out. Random effects models assume Missing At Random and do not take into account informative drop-out. We therefore aim to correct the bias due to informative drop-out. Analyses of data from a trial comparing standard-dose and high-dose chemotherapy for patients with breast cancer with respect to long-term impact on HRQOL will serve as illustration. The subscale Physical Function (PF) of the SF36 will be used. A pattern mixture approach is proposed to account for informative drop-out. Patterns are defined based on events related to HRQOL, such as death and relapse. The results of this pattern mixture approach are compared to the results of the commonly used random effects model. The findings of the pattern mixture approach are well interpretable, and different courses over time in different patterns are distinguished. In terms of estimated differences between standard dose and high dose, the results of both approaches are slightly different, but have no consequences for the clinical evaluation of both doses. Under the assumption that drop-out is at random within the patterns, the pattern mixture approach adjusts the estimates to a certain degree. This approach accounts in a relatively simple way for informative drop-out

Unfolding-Based Process Discovery

This paper presents a novel technique for process discovery. In contrast to the current trend, which only considers an event log for discovering a process model, we assume two additional inputs: an independence relation on the set of logged activities, and a collection of negative traces. After deriving an intermediate net unfolding from them, we perform a controlled folding giving rise to a Petri net which contains both the input log and all independence-equivalent traces arising from it. Remarkably, the derived Petri net cannot execute any trace from the negative collection. The entire chain of transformations is fully automated. A tool has been developed and experimental results are provided that witness the significance of the contribution of this paper.Comment: This is the unabridged version of a paper with the same title appearead at the proceedings of ATVA 201

Outcome and risk factors for recurrence of early onset fracture-related infections treated with debridement, antibiotics and implant retention:Results of a large retrospective multicentre cohort study

Introduction: Early Fracture-Related Infections (FRIs) are a common entity in hospitals treating trauma patients and are often treated with a Debridement, Antibiotics and Implant Retention (DAIR) procedure. Aims of this study were to 1) evaluate the recurrence rate after DAIR procedures for early onset FRI, 2) establish the number of surgical procedures to gain control of the initial infection and 3) identify independent predictors for recurrence in this cohort. Methods: A retrospective multicentre cohort study was conducted in two level 1 trauma centres. Consecutive patients who underwent a DAIR procedure between January 1st 2015 and July 1st 2020 for confirmed FRI with an onset of <6 weeks after the latest osseous operation were included. Recorded data included patient demographics, treatment characteristics and follow-up. Univariate and multivariate logistic regression analyses were performed to assess predictors for recurrent FRI. Results: A total of 141 patients with early FRI were included in this study with a median age of 54.0 years (interquartile range (IQR) 34.5–64.0). The recurrence rate of FRI was 13% (n = 19) at one year follow-up and 18% (n = 25) at 23.1 months (IQR 15.3–36.4) follow-up. Infection control was achieved in 94% (n = 127/135) of cases. In total, 73 patients (52%) underwent at least two surgical procedures to treat the ongoing initial episode of FRI, of whom 54 patients (74%) required two to three procedures and 17 patients (23%) four to five procedures. Predictors for recurrent FRI were use of an intramedullary nail during index operation (odds ratio (OR) 4.0 (95% confidence interval (CI) 1.1–13.8)), need for additional surgical procedures to treat ongoing infection during the treatment period following the first presentation of early FRI (OR 1.9 (95% CI 1.1–3.5)) and a decreased Injury Severity Score (ISS) (inverted OR 1.1 (95% CI 1.0–1.1)). Conclusion: The recurrence rate after treatment of early onset FRI in patients treated with a DAIR procedure was 18% at 23.1 months follow-up. At least two surgical procedures to gain control of the initial infection were needed in 52% of patients. Independent predictors for recurrent FRI were the use of an intramedullary nail during index operation, need for additional surgical procedures and a decreased ISS

Influence of Cremophor El on the bioavailability of intraperitoneal paclitaxel

It has been hypothesized that the paclitaxel vehicle Cremophor EL (CrEL) is responsible for nonlinear drug disposition by micellar entrapment. To gain further insight into the role of CrEL in taxane pharmacology, we studied the pharmacokinetics of paclitaxel in the presence and absence of CrEL after i.p. and i.v. dosing. Patients received an i.p. tracer dose of [G-(3)H]paclitaxel in ethanol without CrEL (100 microCi diluted further in isotonic saline) on day 1, i.p. paclitaxel formulated in CrEL (Taxol; 125 mg/m(2)) on day 4, an i.v. tracer of [G-(3)H]paclitaxel on day 22, and i.v. Taxol (175 mg/m(2)) on day 24. Four patients (age range, 54-74 years) were studied, and serial plasma samples up to 72 h were obtained and analyzed for total radioactivity, paclitaxel, and CrEL. In the presence of CrEL, i.v. paclitaxel clearance was 10.2 +/- 3.76 liters/h/m(2) (mean +/- SD), consistent with previous findings. The terminal disposition half-life was substantially prolonged after i.p. dosing (17.0 +/- 11.3 versus 28.7 +/- 8.72 h), as was the mean residence time (7.28 +/- 2.76 versus 40.7 +/- 13.8 h). The bioavailability of paclitaxel was 31.4 +/- 5.18%, indicating insignificant systemic concentrations after i.p. treatment. CrEL levels were undetectable after i.p. dosing (<0.05 microl/ml), whereas after i.v. dosing, the mean clearance was 159 +/- 58.4 ml/h/m(2), in line with earlier observations. In the absence of CrEL, the bioavailability and systemic concentrations of i.p. paclitaxel were significantly increased. This finding is consistent with the postulated concept that CrEL is largely responsible for the pharmacokinetic advantage for peritoneal cavity exposure to total paclitaxel compared with systemic delivery

Relativistically rotating dust

Dust configurations play an important role in astrophysics and are the simplest models for rotating bodies. The physical properties of the general--relativistic global solution for the rigidly rotating disk of dust, which has been found recently as the solution of a boundary value problem, are discussed.Comment: 18 pages, 11 figure

Learning through social spaces: migrant women and lifelong learning in post-colonial London

This article shows how migrant women engage in learning through social spaces. It argues that such spaces are little recognised, and that there are multiple ways in which migrant women construct and negotiate their informal learning through socialising with other women in different informal modes. Additionally, the article shows how learning is shaped by the socio-political, geographical and multicultural context of living in London, outlining ways in which gendered and racialised identities shape, construct and constrain participation in lifelong learning. The article shows that one way in which migrant women resist (post)colonial constructions of difference is by engaging in informal and non-formal lifelong learning, arguing that the benefits are (at least) two-fold. The women develop skills (including language skills) but also use their informal learning to develop what is referred to in this article as 'relational capital'. The article concludes that informal lifelong learning developed through social spaces can enhance a sense of belonging for migrant women