Functionals and the Quantum Master Equation

The quantum master equation is usually formulated in terms of functionals of the components of mappings from a space-time manifold M into a finite-dimensional vector space. The master equation is the sum of two terms one of which is the anti-bracket (odd Poisson bracket) of functionals and the other is the Laplacian of a functional. Both of these terms seem to depend on the fact that the mappings on which the functionals act are vector-valued. It turns out that neither this Laplacian nor the anti-bracket is well-defined for sections of an arbitrary vector bundle. We show that if the functionals are permitted to have their values in an appropriate graded tensor algebra whose factors are the dual of the space of smooth functions on M, then both the anti-bracket and the Laplace operator can be invariantly defined. Additionally, one obtains a new anti-bracket for ordinary functionals.Comment: 21 pages, Late

Broadening the phenotypic and molecular spectrum of FINCA syndrome: Biallelic NHLRC2 variants in 15 novel individuals

FINCA syndrome [MIM: 618278] is an autosomal recessive multisystem disorder characterized by fibrosis, neurodegeneration and cerebral angiomatosis. To date, 13 patients from nine families with biallelic NHLRC2 variants have been published. In all of them, the recurrent missense variant p.(Asp148Tyr) was detected on at least one allele. Common manifestations included lung or muscle fibrosis, respiratory distress, developmental delay, neuromuscular symptoms and seizures often followed by early death due to rapid disease progression.Here, we present 15 individuals from 12 families with an overlapping phenotype associated with nine novel NHLRC2 variants identified by exome analysis. All patients described here presented with moderate to severe global developmental delay and variable disease progression. Seizures, truncal hypotonia and movement disorders were frequently observed. Notably, we also present the first eight cases in which the recurrent p.(Asp148Tyr) variant was not detected in either homozygous or compound heterozygous state.We cloned and expressed all novel and most previously published non-truncating variants in HEK293-cells. From the results of these functional studies, we propose a potential genotype-phenotype correlation, with a greater reduction in protein expression being associated with a more severe phenotype.Taken together, our findings broaden the known phenotypic and molecular spectrum and emphasize that NHLRC2-related disease should be considered in patients presenting with intellectual disability, movement disorders, neuroregression and epilepsy with or without pulmonary involvement

Modeling of the Response of a Hot-Wire Anemometer with Neural Nets under Various Air Densities

The sensors, which use the convective heat transfer at hot wires in order to measure the flow rate of gases, are well known. Hot-Wire Anemometry (HWA), which is operated in either constant-current mode or in constant temperature mode, represents the most popular methods to measure the velocity and the flow rate of the fluid flow. Generally, the hot-wire sensors are calibrated against the flow velocity under atmospheric pressure conditions. To calibrate hot-wire sensors under different air densities; a special calibration test rig is needed. In the present paper, calibrations are shown to yield the same hot-wire response curves for density locations in the range of 1 to 7 kg/m3 and its usable mass flow rate range (rU) is 0.1 to 25 kg/m²s. Also, a neural network has been trained with the output data for the hot-wire sensor and tested on our measurements. It was observed that the quality of the results depends on the number of hidden neurons. The predicted values are close to the real ones which indicate the neural net model gives a good approximation for the calibration curves of the hot-wire anemometer under different flow densities. The hot-wire sensor that used in the present study has 5 mm diameter and 1.25 mm length so its aspect ratio is 250

Taguchi optimization of hardness and scratch adhesion strength of multilayer Ti/TiN coatings on Ti- 51 at%Ni alloy deposited via magnetron sputtering technique

The near equiatomic Ti-51at %Ni alloy has excellent corrosion resistance, strength, shape memory and pseudo-elastic behaviour. However, it is lacking biocompatibility due to the release of hazardous Ni-ions when used as an implant. Thus, this research proposes optimizing the fabrication of multilayer Ti/TiN coating on Ti-51at %Ni alloy using magnetron sputtering. The hardness and adhesion strength are crucial properties to sustain external bearing loads and to ensure the durability of the coating. The process parameters of magnetron sputtering were optimized using Taguchi method. The analysis showed that optimum adhesion strength was obtained at 370 W, 100 °C, 50 V and 5 sccm with respect to DC power, substrate temperature, bias voltage and nitrogen flow, respectively. Whereas, the optimum hardness was obtained at 370 W, 150 °C, 75 V and 5 sccm. The confirmation test evidenced the hardness and adhesion strength improvement by 6.83 % and 10.74 %, respectively. The results of the optimized substrate surface showed a dense and compact growth of the deposited layer with the absence of cracks and pores. Finally, this research demonstrated a promising durable multilayer Ti/TiN coating on Ti-51at %Ni for biomedical applications

A defect in the retromer accessory protein, SNX27, manifests by infantile myoclonic epilepsy and neurodegeneration

The composition of the neuronal cell surface dictates synaptic plasticity and thereby cognitive development. This remodeling of the synapses is governed by the endocytic network which internalize transmembrane proteins, then sort them back to the cell surface or carry them to the lysosome for degradation. The multi-protein retromer complex is central to this selection, capturing specific transmembrane proteins and remodeling the cell membrane to form isolated cargo-enriched transport carriers. We investigated a consanguineous family with four patients who presented in infancy with intractable myoclonic epilepsy and lack of psychomotor development. Using exome analysis, we identified a homozygous deleterious mutation in SNX27, which encodes sorting nexin 27, a retromer cargo adaptor. In western analysis of patient fibroblasts, the encoded mutant protein was expressed at an undetectable level when compared with a control sample. The patients’ presentation and clinical course recapitulate that reported for the SNX27 knock-out mouse. Since the cargo proteins for SNX27-mediated sorting include subunits of ionotropic glutamate receptors and endosome-to-cell surface synaptic insertion of AMPA receptors is severely perturbed in SNX27−/− neurons, it is proposed that at least part of the neurological aberrations observed in the patients is attributed to defective sorting of ionotropic glutamate receptors. SNX27 deficiency is now added to the growing list of neurodegenerative disorders associated with retromer dysfunction