Physics-Informed Neural Networks (PINNs) have emerged as a robust framework for solving Partial Differential Equations (PDEs) by approximating their solutions via neural networks and imposing physics-based constraints on the loss function. Traditionally, Multilayer Perceptrons (MLPs) have been the neural network of choice, with significant progress made in optimizing their training. Recently, Kolmogorov-Arnold Networks (KANs) were introduced as a viable alternative, with the potential of offering better interpretability and efficiency while requiring fewer parameters. In this paper, we present a fast JAX-based implementation of grid-dependent Physics-Informed Kolmogorov-Arnold Networks (PIKANs) for solving PDEs, achieving up to 84 times faster training times than the original KAN implementation. We propose an adaptive training scheme for PIKANs, introducing an adaptive state transition technique to avoid loss function peaks between grid extensions, and a methodology for designing PIKANs with alternative basis functions. Through comparative experiments, we demonstrate that the adaptive features significantly enhance solution accuracy, decreasing the L2 error relative to the reference solution by up to 43.02%. For the studied forward PDE problems, our methodology approaches or surpasses the results obtained from architectures that utilize up to 8.5 times more parameters, highlighting the potential of adaptive, grid-dependent PIKANs as a superior alternative in scientific and engineering applications.

Corticosteroids are commonly used in empirical treatment of Behçet's disease (BD), a systemic inflammatory condition associated with reversible endothelial dysfunction. In the present study we aimed to dissect the effects of clinical disease activity and chronic or short-term corticosteroid treatment on endothelial function in patients with BD. In a case-control, cross-sectional study, we assessed endothelial function by endothelium dependent flow mediated dilatation (FMD) at the brachial artery of 87 patients, who either were or were not receiving chronic corticosteroid treatment, and exhibiting variable clinical disease activity. Healthy individuals matched for age and sex served as controls. Endothelial function was also assessed in a prospective study of 11 patients before and after 7 days of treatment with prednisolone given at disease relapse (20 mg/day). In the cross-sectional component of the study, FMD was lower in patients than in control individuals (mean ± standard error: 4.1 ± 0.4% versus 5.7 ± 0.2%, P = 0.003), whereas there was a significant interaction between the effects of corticosteroids and disease activity on endothelial function (P = 0.014, two-factor analysis of variance). Among patients with inactive BD, those who were not treated with corticosteroids (n = 33) had FMD comparable to that in healthy control individuals, whereas those treated with corticosteroids (n = 15) had impaired endothelial function (P = 0.023 versus the respective control subgroup). In contrast, among patients with active BD, those who were not treated with corticosteroids (n = 20) had lower FMD than control individuals (P = 0.007), but in those who were receiving corticosteroids (n = 19) the FMD values were comparable to those in control individuals. Moreover, FMD was significantly improved after 7 days of prednisolone administration (3.7 ± 0.9% versus 7.6 ± 1.4%, P = 0.027). Taken together, these results imply that although corticosteroid treatment may impair endothelial function per se during the remission phase of the inflammatory process, it restores endothelial dysfunction during active BD by counteracting the harmful effects of relapsing inflammation.

This paper proposes a method to generalize the equations estimating the inductance of square-shape planar windings to rectangle shape. This is done by utilizing the optimal $p$ -norm of the Generalized Mean Value or Power Mean (PM). Three well-established equations with verified accuracy are examined, namely Wheeler's, Rosa's, and the Monomial, which by definition consider only regular polygons. One critical parameter of the original equations is the outer-side length of the winding, which for the rectangle case, can be substituted by the PM of the two outer-side lengths, without the need for any further modifications. A methodology to select the optimal $p$ -norm for the PM is presented in terms of achieving the best accuracy for this estimation. The selection of the optimal $p$ is based on results from datasets containing more than 2600 simulations of different rectangle-shaped windings. Finally, the estimation accuracy is verified by laboratory measurements for a selection of planar inductors.

This paper deals with the interconnection of a small wind turbine with the low voltage distribution grid and the implementation of an improved control scheme, which also serves educational purposes. Initially the subsystems—wind turbine, rectifying bridge, interleaved boost converter, three-phase inverter, interconnection inductors, lifting transformer, filtering capacitors—are investigated, in order to explain their selection, based on the LEMEC (Laboratory of Electromechanical Energy Conversion, Department of Electrical Engineering, UoP) educational policy. Afterwards, the three-phase inverter control scheme, which is responsible for controlling its input voltage (voltage of the DC Bus) and consequently the active power, as well as the reactive power injected into the grid (VQ control) is analyzed. This is accomplished through DQ transformation and PI controllers which are responsible for generating the appropriate reference signals, to generate the required Space Vector Pulse Width Modulation (SVPWM) pulses to drive the semiconductor switches of the inverter. In addition, it is explained how this particular control method can compensate reactive power in the grid, even in apnea, by automatically charging the DC Bus. Finally, simulation and experimental results are given to prove the proposed control method effectiveness.

This paper proposes a simple and accurate monomial-like equation for estimating the inductance of Multilayer Rectangle-shaped Planar Windings (MLRPWs) for high-frequency, high-power applications. The equation consists of the power product of the geometrical dimensions, raised at individual power coefficients. The coefficients are generated via Multiple Linear Regression (MLR), based on a large set of approximately 6,000 simulated windings, with an 80/20 training/evaluation sample ratio. The resulting mean error value is 0%, with a standard deviation below 1.8%. The accuracy of the inductance estimation is confirmed on several experimental samples, with dimensions both within and outside the initial training dataset.

This paper proposes a simple and accurate monomial-like equation for estimating the inductance of Multilayer Rectangle-shaped Planar Windings (MLRPWs) for high-frequency, high-power applications. The equation consists of the power product of the geometrical dimensions, raised at individual power coefficients. The coefficients are generated via Multiple Linear Regression (MLR), based on a large set of approximately 6,000 simulated windings, with an 80/20 training/evaluation sample ratio. The resulting mean error value is µ=0%, with a standard deviation below 1.8%. The accuracy of the inductance estimation is confirmed on several experimental samples, with dimensions both within and outside the initial training dataset.