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

Deep CNN-LSTM With Self-Attention Model for Human Activity Recognition Using Wearable Sensor

Human Activity Recognition (HAR) systems are devised for continuously observing human behavior - primarily in the fields of environmental compatibility, sports injury detection, senior care, rehabilitation, entertainment, and the surveillance in intelligent home settings. Inertial sensors, e.g., accelerometers, linear acceleration, and gyroscopes are frequently employed for this purpose, which are now compacted into smart devices, e.g., smartphones. Since the use of smartphones is so widespread now-a-days, activity data acquisition for the HAR systems is a pressing need. In this article, we have conducted the smartphone sensor-based raw data collection, namely H-Activity , using an Android-OS-based application for accelerometer, gyroscope, and linear acceleration. Furthermore, a hybrid deep learning model is proposed, coupling convolutional neural network and long-short term memory network (CNN-LSTM), empowered by the self-attention algorithm to enhance the predictive capabilities of the system. In addition to our collected dataset ( H-Activity ), the model has been evaluated with some benchmark datasets, e.g., MHEALTH, and UCI-HAR to demonstrate the comparative performance of our model. When compared to other models, the proposed model has an accuracy of 99.93% using our collected H-Activity data, and 98.76% and 93.11% using data from MHEALTH and UCI-HAR databases respectively, indicating its efficacy in recognizing human activity recognition. We hope that our developed model could be applicable in the clinical settings and collected data could be useful for further research.publishedVersio

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

MUTUAL INTERDEPENDENCE OF THE PHYSICAL PARAMETERS GOVERNING THE BOUNDARY-LAYER FLOW OF NON-NEWTONIAN FLUIDS

We consider non-Newtonian boundary-layer fluid flow, governed by a power-law OstwalddeWaele rheology. Boundary-layer flows of non-Newtonian fluids have far-reaching applications, and are very frequently encountered in physical, as well as, engineering and industrial processes. A similarity transformation results in a BVP consisting of an ODE and some boundary conditions. Our aim is to derive highly accurate analytical relationships between the physical and mathematical parameters associated with the BVP and boundary-layer flow problem. Mathematical analyses are employed, where the results are verified at the numerical computational level, illustrating the accuracy of the derived relations. A set of “Crocco variables” is used to transform the problem, and, where appropriate, techniques are used to deal with the resulting singularities in order to establish an efficient computational setting. The resulting computational setting provides an alternative, which is different from those previously used in the literature. We employ it to carry out our numerical computations