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)

Teelt van herfstchrysanten

Mét de toegenomen belangstelling voor de teelt van snijbloemen in het algemeen, is ook de interesse voor de teelt van herfstchrysanten toegenomen. En ook nu is deze teelt favoriet als nateelt op tal van groentebedrijven. Er is echter in de loop der jaren veel veranderd; ook met betrekking tot de teelt van herfstchrysanten. De mogelijkheden in teelttechnisch opzicht zijn belangrijk vergroot, maar ook de eisen voor een goede kwaliteit zijn verscherpt. Deze teelthandleiding geeft onder andere informatie over de economische aspecten, de kasteelt, arbeid, teeltmethoden, gewasbescherming en bemesting

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

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

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