Applied sciences

Bulletin of the Polish Academy of Sciences: Technical Sciences

Content

Bulletin of the Polish Academy of Sciences: Technical Sciences | Early Access |

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Abstract

The paper presents the fusion approach of different feature selection methods in pattern recognition problems. The following methods are examined: nearest component analysis, Fisher discriminant criterion, refiefF method, stepwise fit, Kolmogorov-Smirnov criteria, T2-test, Kruskall-Wallis test, feature correlation with class, and SVM recursive feature elimination. The sensitivity to the noisy data as well as the repeatability of the most important features are studied. Based on this study, the best selection methods are chosen and applied in the process of selection of the most important genes and gene sequences in a dataset of gene expression microarray in prostate and ovarian cancers. The results of their fusion are presented and discussed. The small selected set of such genes can be treated as biomarkers of cancer.
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Authors and Affiliations

Fabian Gil
Stanislaw Osowski
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Abstract

Epilepsy is a neurological disorder that causes seizures of many different types. The article presents an analysis of heart rate variability (HRV) for epileptic seizure prediction. Considering that HRV is nonstationary, our research focused on the quantitative analysis of a Poincare plot feature, i.e. cardiac sympathetic index (CSI). It is reported that the CSI value increases before the epileptic seizure. An algorithm using a 1D-convolutional neural network (1D-CNN) was proposed for CSI estimation. The usability of this method was checked for 40 epilepsy patients. Our algorithm was compared with the method proposed by Toichi et al. The mean squared error (MSE) for testing data was 0.046 and the mean absolute percentage error (MAPE) amounted to 0.097. The 1D-CNN algorithm was also compared with regression methods. For this purpose, a classical type of neural network (MLP), as well as linear regression and SVM regression, were tested. In the study, typical artifacts occurring in ECG signals before and during an epileptic seizure were simulated. The proposed 1D-CNN algorithm estimates CSI well and is resistant to noise and artifacts in the ECG signal.
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Authors and Affiliations

Marcin Kołodziej
Andrzej Majkowski
Paweł Tarnowski
Remigiusz Jan Rak
Andrzej Rysz
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Abstract

Magnetic nanoparticle’s different applications in nanomedicine, due to their unique physical properties and biocompatibility, were intensively investigated. Recently, Fe3O4 nanoparticles, are confirmed to be the best sonosensitizers to enhance the performance of HIFU (high intensity focused ultrasound). They are also used as thermo-sensitizers in magnetic hyperthermia. A new idea of dual, magneto-ultrasound, coupled hyperthermia allows the ultrasound intensity to be reduced from the high to a moderate level. Our goal is to evaluate the enhancement of thermal effects of focused ultrasound of moderate intensity due to the presence of nanoparticles. We combine experimental results with numerical analysis. Experiments are performed on tissue-mimicking materials made of the 5% agar gel and gel samples containing Fe3O4 nanoparticles with φ  = 100 nm with two fractions of 0.76 and 1.53% w/w. Thermocouples registered curves of temperature rising during heating by focused ultrasound transducer with acoustic powers of the range from 1 to 4 W. The theoretical model of ultrasound-thermal coupling is solved in COMSOL Multiphysics. We compared the changes between the specific absorption rates (SAR) coefficients determined from the experimental and numerical temperature rise curves depending on the nanoparticle fractions and applied acoustic powers.We confirmed that the significant role of nanoparticles in enhancing the thermal effect is qualitatively similarly estimated, based on experimental and numerical results. So that we demonstrated the usefulness of the FEM linear acoustic model in the planning of efficiency of nanoparticle-mediated moderate hyperthermia.
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Authors and Affiliations

Barbara Gambin
Eleonora Kruglenko
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Abstract

Recently, analysis of medical imaging is gaining substantial research interest, due to advancements in the computer vision field. Automation of medical image analysis can significantly improve the diagnosis process and lead to better prioritization of patients waiting for medical consultation. This research is dedicated to building a multi-feature ensemble model which associates two independent methods of image description: textural features and deep learning. Different algorithms of classification were applied to single-phase computed tomography images containing 8 subtypes of renal neoplastic lesions. The final ensemble includes a textural description combined with support vector machine and various configurations of Convolutional Neural Networks. Results of experimental tests have proved that such a model can achieve 93.6% of weighted F1-score (tested in 10-fold cross validation mode). Improvement of performance of the best individual predictor totalled 3.5 percentage points.
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Authors and Affiliations

Aleksandra Maria Osowska-Kurczab
Tomasz Markiewicz
Miroslaw Dziekiewicz
Malgorzata Lorent
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Abstract

For brain tumour treatment plans, the diagnoses and predictions made by medical doctors and radiologists are dependent on medical imaging. Obtaining clinically meaningful information from various imaging modalities such as computerized tomography (CT), positron emission tomography (PET) and magnetic resonance (MR) scans are the core methods in software and advanced screening utilized by radiologists. In this paper, a universal and complex framework for two parts of the dose control process – tumours detection and tumours area segmentation from medical images is introduced. The framework formed the implementation of methods to detect glioma tumour from CT and PET scans. Two deep learning pre-trained models: VGG19 and VGG19-BN were investigated and utilized to fuse CT and PET examinations results. Mask R-CNN (region-based convolutional neural network) was used for tumour detection – output of the model is bounding box coordinates for each object in the image – tumour. U-Net was used to perform semantic segmentation – segment malignant cells and tumour area. Transfer learning technique was used to increase the accuracy of models while having a limited collection of the dataset. Data augmentation methods were applied to generate and increase the number of training samples. The implemented framework can be utilized for other use-cases that combine object detection and area segmentation from grayscale and RGB images, especially to shape computer-aided diagnosis (CADx) and computer-aided detection (CADe) systems in the healthcare industry to facilitate and assist doctors and medical care providers.
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Authors and Affiliations

Estera Kot
Zuzanna Krawczyk
Krzysztof Siwek
Leszek Królicki
Piotr Czwarnowski
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Abstract

The paper is focused on automatic segmentation task of bone structures out of CT data series of pelvic region. The authors trained and compared four different models of deep neural networks (FCN, PSPNet, U-net and Segnet) to perform the segmentation task of three following classes: background, patient outline and bones. The mean and class-wise Intersection over Union (IoU), Dice coefficient and pixel accuracy measures were evaluated for each network outcome. In the initial phase all of the networks were trained for 10 epochs. The most exact segmentation results were obtained with the use of U-net model, with mean IoU value equal to 93.2%. The results where further outperformed with the U-net model modification with ResNet50 model used as the encoder, trained by 30 epochs, which obtained following result: mIoU measure – 96.92%, “bone” class IoU – 92.87%, mDice coefficient – 98.41%, mDice coefficient for “bone” – 96.31%, mAccuracy – 99.85% and Accuracy for “bone” class – 99.92%.
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Authors and Affiliations

Zuzanna Krawczyk
Jacek Starzyński
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Abstract

The article presents research on the use of Monte-Carlo Tree Search (MCTS) methods to create an artificial player for the popular card game “The Lord of the Rings”. The game is characterized by complicated rules, multi-stage round construction, and a high level of randomness. The described study found that the best probability of a win is received for a strategy combining expert knowledge-based agents with MCTS agents at different decision stages. It is also beneficial to replace random playouts with playouts using expert knowledge. The results of the final experiments indicate that the relative effectiveness of the developed solution grows as the difficulty of the game increases.
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Authors and Affiliations

Bartosz Sawicki
Konrad Godlewski
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Adsorption cooling and desalination technologies have recently received more attention. Adsorption chillers, using eco-friendly refrigerants, provide promising abilities for low-grade waste heat recovery and utilization, especially renewable and waste heat of the near ambient temperature. However, due to the low coefficient of performance (COP) and cooling capacity (CC) of the chillers, they have not been wide commercialized. Although operating in combined heating and cooling (HC) systems, adsorption chillers allow more efficient conversion and management of low-grade sources of thermal energy, their operation is still not sufficiently recognized, and the improvement of their performance is still a challenging task. The paper introduces an artificial intelligence (AI) approach for the optimization study of a two-bed adsorption chiller operating in an existing combined HC system, driven by low-temperature heat from cogeneration. Artificial neural networks are employed to develop a model that allows estimating the behavior of the chiller. Two crucial energy efficiency and performance indicators of the adsorption chiller, i.e., CC and the COP, are examined during the study for different operating sceneries and a wide range of operating conditions. Thus this work provides useful guidance for the operating conditions of the adsorption chiller integrated into the HC system. For the considered range of input parameters, the highest CC and COP are equal to 12.7 kW and 0.65, respectively. The developed model, based on the neurocomputing approach, constitutes an easy-to-use and powerful optimization tool of the adsorption chiller operating in the complex HC system.
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Authors and Affiliations

Jarosław Krzywanski
Karol Sztekler
Marcin Bugaj
Wojciech Kalawa
Karolina Grabowska
Patryk Robert Chaja
Marcin Sosnowski
Wojciech Nowak
Łukasz Mika
Sebastian Bykuć
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Abstract

Boron nitride (BN) reinforced Al6061 aluminum-based composites are synthesized by conventional stir casting method followed by exposure to hot extrusion. The optical images confirmed the distribution of BN nanoparticles in the aluminum alloy matrix. The concentration of BN is varied from (0.5, 1.5, 3, 4.5, 6, 7.5, and 9 wt%) in the composites and its effect on the tensile strength was investigated. The results revealed that both extruded and heat-treated composites specimens showed enhanced toughness and tensile strength by increasing BN nanoparticle concentration. The heat-treated composite samples showed lower flexibility of up to 40%, and further, it exhibited 37% greater hardness and 32% enhancement in tensile strength over the extruded sample. The tensile properties of Al6061-BN composites were evaluated by temperature-dependent internal friction (TDIF) analysis and the results showed that the as-prepared composite’s strength increased with temperature.
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Authors and Affiliations

Y.B. Mukesh
Prem Kumar Naik
Rao R. Raghavendra
Vishwanath Nagaraj
Prema Nisana Siddegowda
H.N. Girish
Naik L. Laxman
Puttaswamy Madhusudan
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Abstract

The research was attempted to mimic the locomotion of the salamander which finds to be one of the main animals from evolutionary point of view. The design of the limb and body was started with the parametric studies of Pneumatic network (Pneu-Net). Pneu-Net is a pneumatically operated soft actuator that bends when a compressed fluid is passed inside the chamber. Finite Element Analysis software, ANSYS was used to evaluate the height of the chamber, number of chambers, the gap between chambers for both limb and body of the soft mechanism. The parameters were decided based on the force generated by the soft actuators. The assembly of the salamander robot was then exported to MATLAB for simulating the locomotion of the robot in physical environment. Sine based controller was used to simulate the robot model and the fastest locomotion of salamander robot was identified at 1Hz frequency, 0.3 second of signal delay for limb actuator and negative π phase difference for every contralateral side of limbs. Shin-Etsu KE-1603, a hyper elastic material was used to build the salamander robot and the series of experiments were conducted to record the bending angle, the respective generated force in soft actuators and the gait speed of the robot. The developed salamander robot was able to walk at 0.06774 m/s, almost similar pattern to the simulation.
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Authors and Affiliations

Elango Natarajan
Kwang Y. Chia
Ahmad A. Faudzi
Wei H. Lim
Chun Kit Ang
Ali Jafaari
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Abstract

Synchronization of a complex chaotic network of permanent magnet synchronous motor systems has increasing practical importance in the field of electrical engineering. This article presents the control design method for hybrid synchronization and parameter estimation of ring connected complex chaotic network of permanent magnet synchronous motor systems. The design of the desired control law is a challenging task for control engineers due to parametric uncertainties and chaotic responses to some specific parameter values. Controllers are designed based on the adaptive integral sliding mode control to ensure hybrid synchronization and estimation of uncertain terms. To apply the adaptive ISMC, firstly the error system is converted to a unique system consisting of a nominal part along with unknown terms which are computed adaptively. The stabilizing controller incorporating nominal control and compensator control is designed for the error system. The compensator controller, as well as the adapted laws, are designed to get the first derivative of the Lyapunov equation strictly negative. To give an illustration, the proposed technique is applied to 4-coupled motor systems yielding the convergence of error dynamics to zero, estimation of uncertain parameters, and hybrid synchronization of system states. The usefulness of the proposed method has also been tested through computer simulations and found to be valid.
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Authors and Affiliations

Nazam Siddique
Fazal UR Rehman
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Abstract

This work presents an automatic system for generating kidney boundaries in computed tomography (CT) images. This paper presents the main points of medical image processing, which are the parts of the developed system. The U-Net network was used for image segmentation, which is now widely used as a standard solution for many medical image processing tasks. An innovative solution for framing the input data has been implemented to improve the quality of the learning data as well as to reduce the size of the data. Precision-Recall analysis was performed to calculate the optimal image threshold value. To eliminate false-positive errors, which are a common issue in segmentation based on neural networks, the volumetric analysis of coherent areas was applied. The developed system allows for a fully automatic generation of kidney boundaries as well as the generation of a three-dimensional kidney model. The system can be helpful for people who deal with the analysis of medical images, medical specialists in medical centers, especially for those who perform the descriptions of CT examination. The system works fully automatically and can help to increase the accuracy of the performed medical diagnosis and reduce the time of preparing medical description.
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Authors and Affiliations

Tomasz Les
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Abstract

Real time simulators of IEC 61850 compliant protection devices can be implemented without its analogue part, reducing costs and increasing versatility. Implementation of Sampled Values (SV) and GOOSE interfaces to Matlab/Simulink allows for interaction with protection relays in closed loop during power system simulation. Properly configured and synchronized Linux system with Real Time (RT) patch, can be used as a low latency run time environment for Matlab/Simulink generated model. Number of overruns during model execution using proposed SV and GOOSE interfaces with 50 μs step size is minimal. The paper discusses the implementation details and time synchronization methods of IEC 61850 real time simulator implemented in Matlab/Simulink that is built on top of run time environment shown in authors preliminary works and is the further development of them. Correct operation of the proposed solution is evaluated during the hardware-in-the-loop testing of ABB REL670 relay.
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Authors and Affiliations

Karol Kurek
Łukasz Nogal
Ryszard Kowalik
Marcin Januszewski
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Abstract

This article considers the problem of the rise in temperature of the windings of an induction motor during startup. Excessive growth of thermal stresses in the structure of a cage winding increases the probability of damage to the winding of the rotor. For the purpose of analysis of the problem, simplified mathematical relationships are given, enabling the comparison of quantities of energy released in a rotor winding during startup by different methods. Also, laboratory tests were carried out on a specially adapted cage induction motor enabling measurement of the temperature of a rotor winding during its operation. Because there was no possibility of investigating motors in medium- and high-power drive systems, the authors decided to carry out tests on a low-power motor. The study concerned the startup of a drive system with a 4 kW cage induction motor. Changes in the winding temperature were recorded for three cases: direct online startup, soft starting, and the use of a variable-frequency drive (VFD). Conclusions were drawn based on the results obtained. In high-power motors, the observed phenomena occur with greater intensity, because of the use of deep bar and double cage rotors. For this reason, indication is made of the particular need for research into the energy aspects of different startup methods for medium- and high-power cage induction motors in conditions of prolonged startup.
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Authors and Affiliations

Jan Mróz
Piotr Bogusz
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Abstract

Due to the coexistence of continuity and discreteness, the energy management of the multi-mode power split hybrid electric vehicle (HEV) can be considered as a typical hybrid system. Therefore, the hybrid system theory is applied to investigate the optimal energy distribution strategy of a power split multi-mode HEV. In order to obtain a unified description of the continuous/discrete dynamics including both steady power distribution process and mode switching behaviors, the mixed logical dynamical (MLD) modeling is adopted to build the control-oriented model. Moreover, the linear piecewise affine (PWA) technology is applied to deal with the nonlinear characteristics in MLD modeling. The MLD model is finally obtained through a high level modeling language—HYSDEL. Based on the MLD model, hybrid model predictive control (HMPC) strategy is proposed, where a mixed integer quadratic programming (MIQP) problem is constructed for optimal power distribution. Simulation studies under different driving cycles demonstrate that the proposed control strategy can realize superior control effect compared with a rule based control strategy.
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Authors and Affiliations

Shaohua Wang
Sheng Zhang
Dehua Shi
Xiaoqiang Sun
T. Yang
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Abstract

To improve the curve driving stability and safety under critical maneuvers for four-wheel-independent drive autonomous electric vehicles, a three-stage direct yaw moment control (DYC) strategy design procedure is proposed in this work. The first stage conducts the modeling of the tire nonlinear mechanical properties, i.e. the coupling relationship between the tire longitudinal force and the tire lateral force, which is crucial for the DYC strategy design, in the STI (Systems Technologies Inc.) form based on experimental data. On this basis, a 7-DOF vehicle dynamics model is established and the direct yaw moment calculation problem of the four-wheel-independent drive autonomous electric vehicle is solved through the nonsingular fast terminal sliding mode (NFTSM) control method, thus the optimal direct yaw moment can be obtained. To achieve this direct yaw moment, an optimal allocation problem of the tire forces is further solved by using the trust-region interior-point method, which can effectively guarantee the solving efficiency of complex optimization problem like the tire driving and braking forces allocation of four wheels in this work. Finally, the effectiveness of the DYC strategy proposed for the autonomous electric vehicles is verified through the CarSim-Simulink co-simulation results.
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Authors and Affiliations

Xiaoqiang Sun
Yujun Wang
Yingfeng Cai
Pak Kin Wong
Long Chen
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Abstract

In the ceramic industry, quality control is performed using visual inspection in three different product stages: green, biscuit, and the final ceramic tile. To develop a real-time computer visual inspection system, the necessary step is successful tile segmentation from its background. In this paper, a new statistical Multi-Line Signal Change Detection (MLSCD) segmentation method based on signal change detection (SCD) method is presented. Through experimental results on seven different ceramic tile image sets, MLSCD performance is analyzed and compared with the SCD method. Finally, recommended parameters are proposed for optimal performance of the MLSCD method.
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Authors and Affiliations

Filip Sušac
Tomislav Matić
Ivan Aleksi
Tomislav Keser
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Abstract

The paper sums up and presents the research and technical aspects of the modernization of the cutting tool of the dredger. Improper adjustments of the cutting elements not adjusted to the characteristics of excavated material is not uncommon situation, Causes of that are versatile geological conditions. Relocation of the machines from one pit to another may result in the significant influence to the excavation process (wear, output, etc). Common practice, is the field try and error approach to obtain desired machine performance. In the paper authors present the approach with aid of cutting edge technologies. Coupled DEM and kinematic simulations supported by the reverse engineering technologies of laser scanning were the fundamental drivers for final adjustments of the cutting tool at its present operational conditions.
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Authors and Affiliations

Jakub Andruszko
Przemyslaw Moczko
Damian Pietrusiak
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Abstract

Bridge inspections are a vital part of bridge maintenance, and the main information source for Bridge Management Systems used for decision-making regarding repairs. Both can no doubt benefit from the implementation of Building Information Modelling philosophy. To fully harness BIM potential in this area, we have to develop tools that will provide inspection information accurately, fast and with ease. In this paper, we present an example of how such a tool can utilise tablets coupled with the latest generation RGB-D cameras for data acquisition, how these data can be processed to extract the defect surface area and create a 3D representation, and finally embed these information into the BIM model. Additionally, the study of depth sensor accuracy is presented along with surface area accuracy tests and exemplar inspection of bridge pillar column.
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Authors and Affiliations

Bartosz Wójcik
Mateusz Żarski
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Abstract

The optimum combination of blade angle of runner and guide vane opening with Kaplan turbine can improve the hydroelectric generating set’s operation efficiency and oscillations suppression capability. Due to the time-economy cost limitation and complex operation mechanism of the Kaplan turbine, the coordination tests data is insufficient, making it challenging to obtain the whole curves at each head under the optimum coordination operation by field tests. The field test data is employed to propose a least-squares support vector machine (LSSVM)-based prediction model for Kaplan turbine coordination tests. Considering the small sample characteristics of the Kaplan turbine’s coordination tests data, the LSSVM parameters are optimized by an improved grey wolf optimization (IGWO) algorithm with mixed non-linear factors and static weights. The grey wolf optimization (GWO) algorithm has some deficiencies, such as the linear convergence factor, which inaccurately simulates the actual situation, and the position updating indeterminately reflects the absolute leadership of the leader wolf. The IGWO algorithm is employed to overcome the mentioned problems. The prediction model is simulated to verify the effectiveness of the proposed IGWO-LSSVM. The results show high accuracy with small samples, a 2.59% relative error in coordination tests, and less than 1.85% relative error in non-coordination tests under different heads.
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Authors and Affiliations

Fannie Kong
Jiahui Xia
Daliang Yang
Ming Luo
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Abstract

Outdoor lighting is an important element in creating an evening and night image of urban spaces. Properly designed and constructed lighting installations provide comfort and security to residents. One way to improve energy efficiency of road lighting installation is to replace electromagnetic control gear (ECG) with electronic ballasts (EB). The main purpose of this article is to provide an in-depth comparative energy efficiency and performance analysis of HPS lamps with ECG and EB. It will compare their performance under sinusoidal and nonsinusoidal voltage supply conditions for the four most commonly used HPS lamps of 70 W, 100 W, 150 W and 250 W. The number of luminaires supplied from one circuit was determined on the basis of the value of permissible active power losses. With the use of the DIALux program projects of the road lighting installation were developed. On this basis, energy performance indicators, electricity consumption, electricity costs and CO 2 emissions were calculated for one-phase and three-phase installations. The obtained results indicate that the HPS lamp with EB is better than the HPS lamp with ECG in terms of energy quality, energy savings and environmental impact. The results of this analysis are expected to assist in the choice of HPS lighting technology.
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Authors and Affiliations

Roman Sikora
Przemysław Markiewicz
Paweł Rózga
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Abstract

This paper presents a new approach to the design methodology of road routes often referred to in the literature as polynomial alignment. The author proposes the use of the so-called general transition curves that have been described in detail in his earlier research papers. General transitions curves employ only one curvature extremum, and the whole curved transition between two extreme points of zero curvature value is described by a single equation. As a result, the curves are very useful for the creation of route geometry in accordance with the principles of polynomial alignment. The paper describes the main concept of polynomial alignment and presents equations of curves which can be used in the proposed alignment procedure. In addition, the paper gives a detailed description of design procedures.
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Authors and Affiliations

Andrzej Kobryń
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Abstract

Here, we present the first vertical-cavity surface-emitting lasers (VCSELs) designed, grown, processed, and evaluated in Poland. The lasers emit at »850 nm, which is the most commonly used wavelength for short-reach (<2 km) optical data communication across multiple-mode optical fiber. Our devices show state-of-the-art electrical and optical parameters, e.g. high room-temperature maximum optical powers of over 5 mW, laser emission at heatsink temperatures up to at least 95°C, low threshold current densities (<10 kA/cm2), and wall-plug efficiencies exceeding 30%. The VCSELs can be adjusted easily to reach emission wavelengths of around 780 to 1090 nm.
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Authors and Affiliations

Marcin Gębski
Patrycja Śpiewak
Walery Kołkowski
Iwona Pasternak
W. Głowadzka
Włodzimierz Nakwaski
Robert P. Sarzała
Michał Wasiak
Tomasz Czyszanowski
Włodzimierz Strupiński
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Abstract

In E-Commerce applications, nowadays the Aspect-based sentiment analysis has become vital, and every consumer started focusing on various aspects of the product before making the purchase decision through online portals like Amazon, Walmart, Alibaba, etc. Hence, the enhancement of sentiment classification considering every aspect of product and services is in the limelight. In this proposed research, Aspect Based Sentiment Classification model has been developed employing Sentiment Whale Optimized Adaptive Neural Network (SWOANN) for classifying the sentiment of key aspects of products and services. The accuracy of sentiment classification of the product and services has been improved by the optimal selection of weights of the neurons of proposed model. The promising results are obtained by analyzing the mobile phone review dataset when compared with other existing sentiment classification approaches such as Support Vector Machine (SVM), Artificial Neural Network (ANN). The proposed work uses the key features such as the Positive Opinion Score, Negative Opinion Score, and the Term Frequency-Inverse Document Frequency (TF-IDF) for representing each aspect of products and services, which further to improve the overall effectiveness of the classifier. The proposed model can be compatible with any sentiment classification problem of products and services.
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Authors and Affiliations

Balaganesh Nallathambi
K. Muneeswaran
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Abstract

In times of the COVID-19, reliable tools to simulate the airborne pathogens causing the infection are extremely important to enable the testing of various preventive methods. Advection-diffusion simulations can model the propagation of pathogens in the air. We can represent the concentration of pathogens in the air by “contamination” propagating from the source, by the mechanisms of advection (representing air movement) and diffusion (representing the spontaneous propagation of pathogen particles in the air). The three-dimensional time-dependent advection-diffusion equation is difficult to simulate due to the high computational cost and instabilities of the numerical methods. In this paper, we present alternating directions implicit isogeometric analysis simulations of the three-dimensional advection-diffusion equations. We introduce three intermediate time steps, where in the differential operator, we separate the derivatives concerning particular spatial directions. We provide a mathematical analysis of the numerical stability of the method. We show well-posedness of each time step formulation, under the assumption of a particular time step size. We utilize the tensor products of one-dimensional B-spline basis functions over the three-dimensional cube shape domain for the spatial discretization. The alternating direction solver is implemented in C++ and parallelized using the GALOIS framework for multi-core processors. We run the simulations within 120 minutes on a laptop equipped with i7 6700 Q processor 2.6 GHz (8 cores with HT) and 16 GB of RAM.
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Authors and Affiliations

Marcin Łoś
Maciej Woźniak
Ignacio Muga
Maciej Paszynski
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Abstract

We analyze the Google-Apple exposure notification mechanism designed by the Apple-Google consortium and deployed on a large number of Corona-warn apps. At the time of designing it, the most important issue was time-to-market and strict compliance with the privacy protection rules of GDPR. This resulted in a plain but elegant scheme with a high level of privacy protection. In this paper we go into details and propose some extensions of the original design addressing practical issues. First, we point to the danger of a malicious cryptographic random number generator (CRNG) and resulting possibility of unrestricted user tracing. We propose an update that enables verification of unlinkability of pseudonymous identifiers directly by the user. Second, we show how to solve the problem of verifying the “same household” situation justifying exempts from distancing rules. We present a solution with MIN-sketches based on rolling proximity identifiers from the Apple-Google scheme. Third, we examine the strategies for revealing temporary exposure keys. We detect some unexpected phenomena regarding the number of keys for unbalanced binary trees of a small size. These observations may be used in case that the size of the lists of diagnosis keys has to be optimized.
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Authors and Affiliations

Adam Bobowski
Jacek Cichoń
Mirosław Kutyłowski

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