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

Worldview, the credit crisis and the ‘unity of life’. From ‘framework’ to ‘deep commitment’

The term ‘worldview’ harbours different dimensions that are not always clearly distinguished. A worldview can be considered to be a personal matter, but it may also be a more collective phenomenon, as it can manifest itself for example within a certain sphere of life (e.g. politics or economics) as a full-blown ideology or a more implicit ‘embedded worldview’. A second distinction can be made between the dimension of a deep, existential commitment and that of an encompassing mental framework, between spiritual inspiration and a more or less intellectually coherent system. There may be tensions between these various dimensions. Having a worldview as a person may imply being in conflict with other worldviews that are embodied in certain social fields. How can people deal with these conflicts? One can easily be seduced to avoid the conflicts and to shift gears between them. With the credit crisis and economics used as an illustration, this article explores some of the techniques that people – consciously, semi-consciously or unconsciously – may employ to navigate the differences between various social domains and their inherent worldviews. In order to support people to regain some unity, the notion of worldview may still be helpful, but interpreted primarily as ‘deep commitment’

Examination of the material removal mechanisms during the lapping process of advanced ceramic rolling elements

Two types of HIPed Si3N4 bearing ball blanks with different surface hardness and fracture toughness were lapped under various loads, speeds, and lubricants using a novel eccentric lapping machine. The lapped surfaces were examined by optical microscope and SEM. The experimental results show that the material removal rate for type I ball blanks were 3-4-fold of type 2 in most cases. Different lapping fluids affected the material removal rate at lower lapping loads, but they had much less influence on the material removal rate at higher lapping loads. The SEM micrographs reveal that the grain pullout prevailed on the lapped surface of type I ball blanks, and the surface of type 2 featured bulk material removal by microcracking. Under extreme high lapping load, surface cracks and damages were found, and SEM with EDX disclosed steel from the lapping plate had transferred to the ceramic ball surface. The preliminary conclusion is that the material removal mechanism during the lapping process of silicon nitride balls using this eccentric lapping machine is mainly mechanical abrasive wear. Lawn and Wilshaw's indentation model on brittle materials is used to explain the difference in material removal rate for the two types of ball blanks

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)

Detection superiority of 7 T MRI protocol in patients with epilepsy and suspected focal cortical dysplasia

In 11 adult patients with suspicion of Focal cortical dysplasia (FCD) on 1.5 T (n = 1) or 3 T (n = 10) magnetic resonance imaging (MRI), 7 T MRI was performed. Visibility, extent, morphological features and delineation were independently rated and subsequently discussed by three observers. Additionally, head-to-head comparisons with corresponding 3 T images were made in the eight patients with a previous 3 T MRI and sustained suspicion of FCD. Comparison with histopathology was done in the five patients that underwent surgery. All lesions, seen at 1.5 and 3 T, were also recognized on 7 T. At 7 T FLAIR highlighted the FCD-like lesions best, whereas T2 and T2* were deemed better suited to review structure and extent of the lesion. Image quality with the used 7 T MRI setup was higher than the quality with the used 3 T MRI setup. In 2 out of 11 patients diagnosis changed, in one after re-evaluation of the images, and in the other based on histopathology. With the used 7 T MRI setup, FCD-like lesions can be detected with more confidence and detail as compared to lower field strength. However, concordance between radiologic diagnosis and final diagnosis seems to be lower than expected

Surface plasmon resonance biosensing: Approaches for screening and characterising antibodies for food diagnostics

Research in biosensing approaches as alternative techniques for food diagnostics for the detection of chemical contaminants and foodborne pathogens has increased over the last twenty years. The key component of such tests is the biorecognition element whereby polyclonal or monoclonal antibodies still dominate the market. Traditionally the screening of sera or cell culture media for the selection of polyclonal or monoclonal candidate antibodies respectively has been performed by enzyme immunoassays. For niche toxin compounds, enzyme immunoassays can be expensive and/or prohibitive methodologies for antibody production due to limitations in toxin supply for conjugate production. Automated, self-regenerating, chip-based biosensors proven in food diagnostics may be utilised as rapid screening tools for antibody candidate selection. This work describes the use of both single channel and multi-channel surface plasmon resonance (SPR) biosensors for the selection and characterisation of antibodies, and their evaluation in shellfish tissue as standard techniques for the detection of domoic acid, as a model toxin compound. The key advantages in the use of these biosensor techniques for screening hybridomas in monoclonal antibody production were the real time observation of molecular interaction and rapid turnaround time in analysis compared to enzyme immunoassays. The multichannel prototype instrument was superior with 96 analyses completed in 2 h compared to 12 h for the single channel and over 24 h for the ELISA immunoassay. Antibodies of high sensitivity, IC(50)'s ranging from 4.8 to 6.9 ng/mL for monoclonal and 2.3–6.0 ng/mL for polyclonal, for the detection of domoic acid in a 1 min analysis time were selected. Although there is a progression for biosensor technology towards low cost, multiplexed portable diagnostics for the food industry, there remains a place for laboratory-based SPR instrumentation for antibody development for food diagnostics as shown herein