A perturbative approach to the spectral zeta functions of strings, drums and quantum billiards

We have obtained an explicit expression for the spectral zeta functions and for the heat kernel of strings, drums and quantum billiards working to third order in perturbation theory, using a generalization of the binomial theorem to operators. The perturbative parameter used in the expansion is either the small deformation of a reference domain (for instance a square), or a small variation of the density around a constant value (in two dimensions both cases can apply). This expansion is well defined even in presence of degenerations of the unperturbed spectrum. We have discussed several examples in one, two and three dimensions, obtaining in some cases the analytic continuation of the series, which we have then used to evaluate the corresponding Casimir energy. For the case of a string with piecewise constant density, subject to different boundary conditions, and of two concentric cylinders of very close radii, we have reproduced results previously published, thus obtaining a useful check of our method.Comment: 23 pages, 5 figures, 2 tables; version accepted on Journal of Mathematical Physic

Resistant protein. Forms and functions

Several global health risks are related to our dietary lifestyle. As a consequence of the overconsumption of ultra-processed and highly digestible protein (150–200% of the recommended value), excess dietary proteins reach the colon, are hydrolysed to peptides and amino acids by bacterial proteases and fermented to various potentially toxic end products. A diet reformulation strategy with reduced protein content in food products appears to be the most effective approach. A potential approach to this challenge is to reduce food digestibility by introducing resistant protein into the diet that could positively influence human health and gut microbiome functionality. Resistant protein is a dietary constituent not hydrolysed by digestive enzymes or absorbed in the human small intestine. The chemical conformation and the amino acid composition strictly influence its structural stability and resistance to in vivo proteolysis and denaturation. Responding to the important gap in our knowledge regarding the digestibility performance of alternative proteins, we hypothesise that resistant proteins can beneficially alter food functionality via their role in improving metabolic properties and health benefits in human nutrition, similar to fibres and resistant starches. A multidisciplinary investigation of resistant protein will generate tremendous scientific impact for other interlinked societal, economic, technological and health and wellbeing aspects of human life

Zone-plate focusing of Bose-Einstein condensates for atom optics and erasable high-speed lithography of quantum electronic components

We show that Fresnel zone plates, fabricated in a solid surface, can sharply focus atomic Bose-Einstein condensates that quantum reflect from the surface or pass through the etched holes. The focusing process compresses the condensate by orders of magnitude despite inter-atomic repulsion. Crucially, the focusing dynamics are insensitive to quantum fluctuations of the atom cloud and largely preserve the condensates' coherence, suggesting applications in passive atom-optical elements, for example zone plate lenses that focus atomic matter waves and light at the same point to strengthen their interaction. We explore transmission zone-plate focusing of alkali atoms as a route to erasable and scalable lithography of quantum electronic components in two-dimensional electron gases embedded in semiconductor nanostructures. To do this, we calculate the density profile of a two-dimensional electron gas immediately below a patch of alkali atoms deposited on the surface of the nanostructure by zone-plate focusing. Our results reveal that surface-induced polarization of only a few thousand adsorbed atoms can locally deplete the electron gas. We show that, as a result, the focused deposition of alkali atoms by existing zone plates can create quantum electronic components on the 50 nm scale, comparable to that attainable by ion beam implantation but with minimal damage to either the nanostructure or electron gas.Comment: 13 pages, 7 figure

The influence of protein concentration on key quality attributes of chickpea-based alternatives to cheese

In response to consumer demands, plant protein ingredients are increasingly being used in the formulation of plant-based alternatives to cheese. The aim of this study was to determine the influence of protein concentration on key quality attributes of chickpea-based alternatives to cheese. Moreover, the age-induced changes in such attributes were assessed, with samples analysed after 1 month of storage. After characterisation of the ingredients, the chickpea-based formulations were prepared by blending chickpea flour and protein concentrate in different proportions to obtain four samples of increasing protein content (i.e., 8.68–21.5%). Formulations were developed at pH ∼4.5, and a moisture content of 50%, with shea butter used to obtain 15% fat content. The differential scanning calorimetry thermograms of the samples showed a main peak around 30 °C, corresponding to transition of the shea butter, and a smaller peak around 70 °C related to starch gelatinisation. Analysis of microstructure showed formation of a protein matrix with more extensive protein structure at high protein concentration. Furthermore, none of the chickpea-based samples melted under the testing conditions and all samples showed increasing values for adhesiveness, springiness and cohesiveness with increasing protein content. However, hardness was the highest for the sample with the lowest protein content, likely due to starch retrogradation. After storage, hardness increased further for all samples. This work improves our understanding of the role of chickpea protein in developing plant-based alternatives to cheese and the challenges therein

Well-Posedness and Symmetries of Strongly Coupled Network Equations

We consider a diffusion process on the edges of a finite network and allow for feedback effects between different, possibly non-adjacent edges. This generalizes the setting that is common in the literature, where the only considered interactions take place at the boundary, i. e., in the nodes of the network. We discuss well-posedness of the associated initial value problem as well as contractivity and positivity properties of its solutions. Finally, we discuss qualitative properties that can be formulated in terms of invariance of linear subspaces of the state space, i. e., of symmetries of the associated physical system. Applications to a neurobiological model as well as to a system of linear Schroedinger equations on a quantum graph are discussed.Comment: 25 pages. Corrected typos and minor change

Reply to Jensen, O.K. On the Use of Quantitative Sensory Testing to Estimate Central Sensitization in Humans. Comment on "Schuttert et al. The Definition, Assessment, and Prevalence of (Human Assumed) Central Sensitisation in Patients with Chronic Low Back Pain: A Systematic Review. J. Clin. Med. 2021, 10, 5931":A Systematic Review. J. Clin. Med. 2021, 10, 5931"

We thank Dr. Jensen for his interest [...]

Deep mid-infrared observations of Lyman-break galaxies

As part of the In-Orbit Checkout activities for the Spitzer Space Telescope, the IRAC team carried out a deep observation (average integration time ~8 hours) of a field surrounding the bright QSO HS 1700+6416. This field contains several hundred z~3 Lyman-break galaxy candidates, and we report here on their mid-infrared properties, including the IRAC detection rate, flux densities and colors, and the results of fitting population synthesis models to the optical, near-infrared, and IRAC magnitudes. The results of the model-fitting show that previous optical/near-infrared studies of LBGs were not missing large, hidden old stellar populations. The LBG candidates' properties are consistent with those of massive, star-forming galaxies at z~3. Other IRAC sources in the same field have similar properties, so IRAC selection may prove a promising method of finding additional high-redshift galaxies.Comment: ApJS in press (Spitzer special issue); 13 pages, 3 figure

First-time patellar dislocation with resultant habitual dislocation two years later, which was not demonstrated on plain X-rays halfway: a case report

We present an instructive case of habitual left patellar dislocation in which the patella had appeared odd due to lateral tilt relative to contralateral side, but had been radiologically confirmed to be on the trochlea at 1 year prior to the referral. An 11-year-old girl presented to our hospital 2 years after the left patella had dislocated with a 'giving way' when cutting to the left. Our physical and radiological examinations confirmed that the left patella was laterally tilted in the patellar groove with the knee in extension but was dislocated in flexion beyond 45°. In spite of these findings, she had been untreated at the previous hospital since all plain X-rays, including a skyline patellar view, had failed to demonstrate the dislocation. Consequently, in addition to reconstruction of medial patellofemoral ligament, she had to undergo a lateral retinacular release, which might have been unnecessary if treated earlier. This case illustrates that first-time patellar dislocation can gradually lead to habitual dislocation subsequently, and that cautious physical examinations in regard to patella tracking are essential since radiological examinations do not always reveal the pathophysiology of patellar instability

Cell specific quantitative iron mapping on brain slices by immuno-µPIXE in healthy elderly and Parkinson’s disease

Iron is essential for neurons and glial cells, playing key roles in neurotransmitter synthesis, energy production and myelination. In contrast, high concentrations of free iron can be detrimental and contribute to neurodegeneration, through promotion of oxidative stress. Particularly in Parkinson's disease (PD) changes in iron concentrations in the substantia nigra (SN) was suggested to play a key role in degeneration of dopaminergic neurons in nigrosome 1. However, the cellular iron pathways and the mechanisms of the pathogenic role of iron in PD are not well understood, mainly due to the lack of quantitative analytical techniques for iron quantification with subcellular resolution. Here, we quantified cellular iron concentrations and subcellular iron distributions in dopaminergic neurons and different types of glial cells in the SN both in brains of PD patients and in non-neurodegenerative control brains (Co). To this end, we combined spatially resolved quantitative element mapping using micro particle induced X-ray emission (mu PIXE) with nickel-enhanced immunocytochemical detection of cell type-specific antigens allowing to allocate element-related signals to specific cell types. Distinct patterns of iron accumulation were observed across different cell populations. In the control (Co) SNc, oligodendroglial and astroglial cells hold the highest cellular iron concentration whereas in PD, the iron concentration was increased in most cell types in the substantia nigra except for astroglial cells and ferritin-positive oligodendroglial cells. While iron levels in astroglial cells remain unchanged, ferritin in oligodendroglial cells seems to be depleted by almost half in PD. The highest cellular iron levels in neurons were located in the cytoplasm, which might increase the source of non-chelated Fe3+, implicating a critical increase in the labile iron pool. Indeed, neuromelanin is characterised by a significantly higher loading of iron including most probable the occupancy of low-affinity iron binding sites. Quantitative trace element analysis is essential to characterise iron in oxidative processes in PD. The quantification of iron provides deeper insights into changes of cellular iron levels in PD and may contribute to the research in iron-chelating disease-modifying drugs