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A three-hidden-layer neural network with super approximation power is introduced. This network is built with the floor function ( ⌊ x ⌋ ), the exponential function ( 2 x ), the step function ( 1 x ≥ 0 ), or their compositions as the activation function in each neuron and hence we call such networks as Floor-Exponential-Step (FLES) networks. For any width hyper-parameter N ∈ N + , it is shown that FLES networks with width max { d , N } and three hidden layers can uniformly approximate a Holder continuous function f on [ 0 , 1 ] d with an exponential approximation rate 3 λ ( 2 d ) α 2 − α N , where α ∈ ( 0 , 1 ] and λ > 0 are the Holder order and constant, respectively. More generally for an arbitrary continuous function f on [ 0 , 1 ] d with a modulus of continuity ω f ( ⋅ ) , the constructive approximation rate is 2 ω f ( 2 d ) 2 − N + ω f ( 2 d 2 − N ) . Moreover, we extend such a result to general bounded continuous functions on a bounded set E ⊆ R d . As a consequence, this new class of networks overcomes the curse of dimensionality in approximation power when the variation of ω f ( r ) as r → 0 is moderate (e.g., ω f ( r ) ≲ r α for Holder continuous functions), since the major term to be concerned in our approximation rate is essentially d times a function of N independent of d within the modulus of continuity. Finally, we extend our analysis to derive similar approximation results in the L p -norm for p ∈ [ 1 , ∞ ) via replacing Floor-Exponential-Step activation functions by continuous activation functions.

Photon Scattering Profiles in a turbid media were investigated through numerical simulation based on Monte Carlo-Mie method, at this present work. Using Wolfram Mathematics in the program algorithm. Photon Scattering was treated using electromagnetic spherical harmonics waves, in three-dimensional scattering. The proposal, as an alternative to the Henyey-Greensein phase approximation, was defining an unit vector that represents a phase distribution, as an equivalent function with three vector components, within the turbid media. Associating the step component, as projection using Legendre polynomials and for the transverse plane components were defining as vector bases in terms of Legendre-Hankel functions, according to Gustav Mie theory. This composite vector was defined as a step function and was evaluated within Monte Carlo algorithm, obtaining simulations of light scattering. Backscatter profiles were compared for different geometric dimensions of the spherical particles within the turbid media, including a validation of the model with an experimental Lidar signal from low clouds, obtaining physical properties of the turbid media by the proposed theoretical model.

The preview-based leader-following consensus control of distributed multi-agent systems (MAS) with a directed acyclic graph is investigated in this paper. The external disturbance considered in this paper is the step function that can be previewed, and the information of the leader can be obtained in advance. The leader-following consensus control of MAS is solved by using the state augmentation technique and the preview control method that transforms the consensus control problem into the finite horizon linear quadratic regulator (LQR) problem and the infinite horizon LQR problem. In the finite horizon, the minimum principle is utilized to design the optimal controller. In the infinite horizon, the standard infinite horizon LQR is applied to devise the corresponding controller. Assuming the original systems are stabilisable and detectable, the distributed consensus controller guarantees the asymptotic consensus of the preview MAS. The simulation illustrates the effectiveness of the distributed leader-following consensus controller designed in this paper.

We investigate, both analytically and numerically, dispersive fractalisation and quantisation of solutions to periodic linear and nonlinear Fermi–Pasta–Ulam–Tsingou systems. When subject to periodic boundary conditions and discontinuous initial conditions, e.g., a step function, both the linearised and nonlinear continuum models for FPUT exhibit fractal solution profiles at irrational times (as determined by the coefficients and the length of the interval) and quantised profiles (piecewise constant or perturbations thereof) at rational times. We observe a similar effect in the linearised FPUT chain at timestwhere these models have validity, namelyt= O(h−2), wherehis proportional to the intermass spacing or, equivalently, the reciprocal of the number of masses. For nonlinear periodic FPUT systems, our numerical results suggest a somewhat similar behaviour in the presence of small nonlinearities, which disappears as the nonlinear force increases in magnitude. However, these phenomena are manifested on very long time intervals, posing a severe challenge for numerical integration as the number of masses increases. Even with the high-order splitting methods used here, our numerical investigations are limited to nonlinear FPUT chains with a smaller number of masses than would be needed to resolve this question unambiguously.

The modeling of coils with ferromagnetic cores is considered. An attempt is made at the application of fractional derivatives because of the success in the modeling of real phenomena in various other fields. Three coils with ferromagnetic cores have been selected for the analysis. In order to obtain a basis for the study, measurements have been taken on a specially designed setup including an arbitrary function generator and a data acquisition device. The measurement process has been controlled by an original algorithm written in C#. The studied model has been considered in several varieties (various numbers of fractional coil and capacitor branches) in a ladder-like structure. The estimation process has been performed in an original program written in C#, applying the COBYLA method for constrained optimization. The modeling and simulation results have been compared through their frequency characteristics. A more critical approach has also been applied, where the measurements and simulations are compared for both a non-sinusoidal waveform and a step function on the source output.

Pulse-coupled neural network (PCNN) aims to control neuronal firing state automatically and complete related image processing tasks. This paper presents a pulse-number-adjustable MSPCNN model (PNA-MSPCNN) that can automatically acquire the firing times and the firing frequency of each neuron. Hereinto, synaptic weight matrix $W_{\mathrm {ijkl}}$ and decay factor $\alpha $ will generate an interaction value to determine the final calculation result of the internal activity $U$ . Dynamic threshold amplitude $V$ , step function $Q$ , and auxiliary parameter $P$ can precisely adjust the variation ranges of the dynamic threshold $E$ . Additionally, we propose a low-light image enhancement method based on the above PNA-MSPCNN and a modified low-light image enhancement (LIME). The proposed LIME algorithm focuses mainly on the parameter setting method of weight matrix $W_{\mathrm {mq}}$ , which will bring further improvement of testing image contrast. Experimental results demonstrate that our proposed method achieves better low-light image enhancement performances, compared to prevalent image enhancement methods, including SSIM of 0.8725, AMBE of 0.0550, MSE of 0.0092, and PSNR of 45.7764.

The development of highly efficient models of Photovoltaic (PV) cells and modules is essential for optimized performance, evaluation and control of solar PV systems. The accurate estimation of PV cells parameters is a challenging task because of their non-linear characteristics. In this paper, an improved variant of Flower Pollination Algorithm (FPA) is proposed for accurate estimation of PV cells and modules parameters. The proposed algorithm involves double exponential based dynamic switch probability and a dynamic step size function that mitigate the limitations of conventional FPA. The dynamic switch probability improves the overall performance of algorithm by maintaining a balance between local and global search, while dynamic step function controls the search speed which avoids premature convergence and local optima stagnation. Moreover, Newton Raphson Method is utilized for accurate computation of estimated current for optimum set of estimated parameters. The proposed methodology is evaluated using seven benchmark functions and three case studies; 1- RTC France silicon PV cell, 2- Photo-watt PWP-201 PV module and 3- a practical solar PV system (EAGLE PERC 60M 310W monocrystalline PV module) under different environmental conditions by estimating parameters for single and double diode models. The analysis of results indicates that, the proposed approach improves the convergence speed, precision, avoids premature convergence and stagnation in local optima of conventional FPA. Furthermore, comparative analysis of results illustrates that, the proposed approach is more reliable and efficient than many other techniques in literature.

Many bioheat transfer problems involve linear/non-linear equations with non-linear or time-dependent boundary conditions. For heat transfer problems, the presence of time and space-dependent functions under Neumann and Mixed type boundary conditions characterize trivial applications in bioengineering, such as thermotherapies, laser surgeries, and burn studies. This greatly increases the complexity of the numerical solution in several problems, requiring fast and accurate numerical solutions. This paper has a main objective evaluate an adaptive mesh refinement radial basis function method strategy for the classical Penne's bioheat transfer modeling. Our numerical results had errors of ~0.1% compared to analytical solutions. Thus, the proposed methodology is accurate and has a low computational cost. For step function heating, two RBF shape parameters were applied, again achieving excellent results. The distributions of the nodes in the solution domain show that the primary source of error in the numerical solutions came from the boundary conditions. This finding should arouse the interest of engineers and scientists in the development of new strategies for problems involving boundary conditions with periodic functions.

Recently, wind energy is one of energy sources most have been devoted much awareness as result of shortage of energy. This study shows loads which are formed in the rotating shaft of wind turbine (WT). These loads cause disturbances on the blades, which leads to damage the blades. these loads can be exceeded, and the amount of productive energy can be controlled by using a good control unit that adjusts the angle of the WT blade. For the previous purpose, independent electric motor is used to control blade pitch, this process called pitch control (PC) system. This paper presents a mathematical model of PC system that is controlled by using two different controllers in MATLAB/Simulink; proportional -integral-derivative controller (PID) and proportional -integral-derivative-acceleration (PIDA). In this system three different function are used as reference pitch angle; unit step function, sinewave function and step change signal which are used on control system without any controller and it is found that output system isn’t reached to a reference value for three functions. The steady state error equal to 76% when step function is used, so the controller is needed for a system. When PID and PIDA controllers are used, the time domain specification of output is improved. The steady state error in PID and PIDA controllers is 9% and 0.014% respectively. It is found that the better time domain specification is given by PIDA. PID and PIDA controllers are tested with sinewave and step change, PIDA is also produced the best response.

Background Electrocardiogram (ECG) signal, an important indicator for heart problems, is commonly corrupted by a low-frequency baseline wander (BW) artifact, which may cause interpretation difficulty or inaccurate analysis. Unlike current state-of-the-art approach using band-pass filters, wavelet transforms can accurately capture both time and frequency information of a signal. However, extant literature is limited in applying wavelet transforms (WTs) for baseline wander removal. In this study, we aimed to evaluate 5 wavelet families with a total of 14 wavelets for removing ECG baseline wanders from a semi-synthetic dataset. Methods We created a semi-synthetic ECG dataset based on a public QT Database on Physionet repository with ECG data from 105 patients. The semi-synthetic ECG dataset comprised ECG excerpts from the QT database superimposed with artificial baseline wanders. We extracted one ECG excerpt from each of 105 patients, and the ECG excerpt comprised 14 s of randomly selected ECG data. Twelve baseline wanders were manually generated, including sinusoidal waves, spikes and step functions. We implemented and evaluated 14 commonly used wavelets up to 12 WT levels. The evaluation metric was mean-square-error (MSE) between the original ECG excerpt and the processed signal with artificial BW removed. Results Among the 14 wavelets, Daubechies-3 wavelet and Symlets-3 wavelet with 7 levels of WT had best performance, MSE = 0.0044. The average MSEs for sinusoidal waves, step, and spike functions were 0.0271, 0.0304, 0.0199 respectively. For artificial baseline wanders with spikes or step functions, wavelet transforms in general had lower performance in removing the BW; however, WTs accurately located the temporal position of an impulse edge. Conclusions We found wavelet transforms in general accurately removed various baseline wanders. Daubechies-3 and Symlets-3 wavelets performed best. The study could facilitate future real-time processing of streaming ECG signals for clinical decision support systems.

The classical Grüss inequality has spurred a range of improvements, generalizations, and extensions. In this article, we provide new functional bounds that ultimately lead to two elementary proofs of the inequality that might be of interest. Our results are motivated by the extreme cases where the equality is reached, namely step functions of equal support. Our first proof is based on the standard Cauchy-Schwarz inequality and a simple bound on the variance of a function. Its simplicity would be of particular interest to those who are new to the study of functional inequalities. Our second proof utilizes non-intuitive and novel bounds on functionals defined on L∞(0, 1). As a result, we provide a detailed and new insight into the nature of the Grüss inequality.

The rolling sphere method for air termination placement on a structure is easy to apply, but it cannot be used to determine the probability of lightning strike to different points on the structure. The dynamic electro-geometrical model (DEGM) using numerical methods can be implemented to evaluate the interception efficiency of various air termination systems. The DEGM is implemented using the probability function of lightning current distribution which has a discontinuity at 20 kA. This study proposes a way to remove the discontinuity by the introduction of a continuous step function. The effectiveness of various centrally positioned air terminations on structures was also examined. Mesh air terminations are typically installed directly on the roof of protected structures. Using DEGM concept, result shows that lifting the mesh network by the penetration depth does not significantly improve the interception efficiency of the air termination network for a gable roof structure.

This paper investigates the flow behavior of a viscous, incompressible and electrically conducting fluid in a long channel subjected to a time-varied oblique magnetic field B 0 ( t ) = B 0 f ( t ) . The time-dependent MHD equations are solved by using the dual reciprocity boundary element method (DRBEM). The transient level velocity and induced magnetic field profiles are presented for moderate Hartmann number values, several direction of applied magnetic field and for several functions f(t) as polynomial, exponential, trigonometric, impulse and step functions. It is observed that, when f(t) is a polynomial or exponential function, the velocity magnitude increases up to a certain time level where the flow shows an elliptical elongation and then starts to decrease for all values of Hartmann numbers. For the trigonometric function f(t), the flow repeats its behavior with a period. An impulse function changes flow behavior with an elongation at the level where the impulse is applied to the magnetic field. Then, it behaves as if a uniform magnetic field is applied. Having a step function f(t), the behavior of the flow shows both impulse and polynomial functions features. This study shows that time-varied magnetic field changes the flow behavior significantly at all the transient levels.

The same term “dose-response curve” describes the relationship between the number of ingested microbes or their logarithm, and the probability of acute illness or death (type I), and between a disinfectant’s dose and the targeted microbe’s survival ratio (type II), akin to survival curves in thermal and non-thermal inactivation kinetics. The most common model of type I curves is the cumulative form of the beta-Poisson distribution which is sometimes indistinguishable from the lognormal or Weibull distribution. The most notable survival kinetics models in static disinfection are of the Chick-Watson-Hom’s kind. Their published dynamic versions, however, should be viewed with caution. A microbe population’s type II dose-response curve, static and dynamic, can be viewed as expressing an underlying spectrum of individual vulnerabilities (or resistances) to the particular disinfectant. Therefore, such a curve can be described mathematically by the flexible Weibull distribution, whose scale parameter is a function of the disinfectant’s intensity, temperature, and other factors. But where the survival ratio’s drop is so steep that the static dose-response curve resembles a step function, the Fermi distribution function becomes a suitable substitute. The utility of the CT (or Ct) concept primarily used in water disinfection is challenged on theoretical grounds and its limitations highlighted. It is suggested that stochastic models of microbial inactivation could be used to link the fates of individual viruses or bacteria to their manifestation in the survival curve’s shape. Although the emphasis is on viruses and bacteria, most of the discussion is relevant to fungi, protozoa, and perhaps worms too.

The fast and stable inner current loop in the permanent magnet synchronous motor control system is the key factor that ensures the torque control performance of the motor. The deadbeat predictive current control has good dynamic response performance, but it depends heavily on the precise mathematical model of the controlled object. The parameter mismatch will degrade the control performance. A deadbeat predictive current control method based on online parameter identification is proposed in this study. This method does not need to inject additional d-axis current to identify the parameters during the operation of the motor; it only needs to make full use of the inherent phenomenon that the q-axis current changes when the load of the motor changes during operation, and perform parameter identification. Aiming at the problem that the effect of parameter identification is easily affected by motor speed, a new variable step-size neural network algorithm is designed in this study. The speed factor is introduced into step function to ensure the performance of the identification algorithm at a different speed. Finally, based on the new online parameter identification algorithm, the deadbeat predictive current control method is used to verify the experiment.

When a single-degree-of-freedom underdamped system is subjected to a step function force in order that it eventually acquires a constant displacement, its response shows undershoots and overshoots. Since a step function force is difficult, if not impossible, to apply to many aerospace, civil, and mechanical engineering systems because of their inertias, this paper looks at simple forces that can be generated from a practical standpoint and are not instantaneously applied, that cause an underdamped oscillator to acquire a constant displacement without any overshoots and/or undershoots. These forces are ramped up (or down) over a short duration of time and held constant thereafter. A preliminary approach to the development of such force–time histories is presented by using a force given by a polynomial in time. Open-loop optimal control is next considered, and then closed-loop optimal control. The optimal control problem does not fall within the standard rubric of terminal control and a new approach for doing this is developed. These ideas are then woven into the development of a methodology that allows an undamped/underdamped single degree of freedom system to track a desired piecewise constant displacement time-history using forces that do not need to be instantaneously applied and that generate rippleless responses with no overshoots/undershoots. The methodology is also applicable to classically damped multi-degree-of-freedom systems with underdamped modes of vibration.

Given a set of n weighted points on the x – y plane, we want to find a step function consisting of k steps parallel to the x axis such that the maximum weighted vertical distance from any point to a step is minimized. Using the prune and search technique, we solve this problem in O ( 2 k 2 n ) time, thus in linear time in n when k is a constant. Our approach can be applied directly or with small modifications to solve other related problems, such as the minmax error histogram problem and the line-constrained k -center problem, in O ( n ) time when k is a constant.

We present a version of the John–Nirenberg inequality for a sub-class of BMO by estimating the corresponding mean oscillating distribution function via dyadic decomposition. The dominating functions are of the form of decreasing step functions which are finer than the classical exponential functions and might be much more efficient for some sophisticated analysis. We also prove that the modified BMO-norm is equivalent to the classical BMO-norm under the convexity assumption.

In the pitching motion, the unsteady transition and relaminarization position plays an important role in the dynamic characteristics of the airfoil. In order to facilitate the computer to automatically and accurately calculate the position of the transition and relaminarization, a Variable Slip Window Technology (VSWT) suitable for airfoil dynamic data processing was developed using the S809 airfoil experimental data in this paper and two calculation strategies, i.e., global strategy and single point strategy, were proposed: global strategy and single point strategy. The core of the VSWT is the selection of the window function h and the parameters setting in the h function. The effect of the VSWT was evaluated using the dimensionless pulse strength value (INB), which can be used to evaluate the signal characteristics, of the root mean square (RMS) value of the fluctuating pressure. It is found that: the h function characteristics have a significant influence on the VSWT. The suitable functions are Hn function constructed in this paper and step function. For the left boundary of the magnified area, the step function can obtain the largest INB value, but the robustness is not good. The H1 function (Gaussian-like function, n = 1) can show higher robustness while ensuring a large INB value. The two computing strategies, which are single point strategy and global strategy, have their own advantages and disadvantages. The former strategy, that is the single point strategy, can achieve a higher INB value, but the RMS magnification at the feature position needs to be known in advance. Although the INB value obtained by the latter strategy, that is the global strategy, is slightly smaller than the calculation results of the former strategy, it is not necessary to know the RMS magnification at the feature position in advance. So the global strategy has better robustness. The experimental data of NACA0012 airfoil was used to further validate the developed VSWT in this paper, and the results show that the VSWT developed in this paper can still double the INB value of the transition/relaminarization position. The VSWT developed in this paper has certain practicability, which is convenient for the computer to automatically determine the transition/relaminarization characteristics.

A curve-free, Bayesian decision-theoretic two-stage design is proposed to select biological efficacious doses (BEDs) for phase Ia/Ib trials in which both toxicity and efficacy signals are observed. No parametric models are assumed to govern the dose-toxicity, dose-efficacy, and toxicity-efficacy relationships. We assume that the dose-toxicity curve is monotonic non-decreasing and the dose-efficacy curve is unimodal. In the phase Ia stage, a Bayesian model on the toxicity rates is used to locate the maximum tolerated dose. In the phase Ib stage, we model the dose-efficacy curve using a step function while continuing to monitor the toxicity rates. Furthermore, a measure of the goodness of fit of a candidate step function is proposed, and the interval of BEDs associated with the best fitting step function is recommended. At the end of phase Ib, if some doses are recommended as BEDs, a cohort of confirmation is recruited and assigned at these doses to improve the precision of estimates at these doses. Extensive simulation studies show that the proposed design has desirable operating characteristics across different shapes of the underlying true toxicity and efficacy curves.

The stability of some simple density profiles in a vertically orientated two-dimensional porous medium is considered. The quasi-steady-state approximation is made so that the stability of the system can be approximated. As the profiles diffuse in time, the instantaneous growth rates evolve in time. For an initial step function density profile, the instantaneous growth rate was numerically found to decay like $$T^{-1/2}$$ for large times T, and the corresponding eigenfunctions scale with $$\mathrm{e}^{\omega \sqrt{T}}$$ where $$\omega $$ is a constant. For density profiles initially corresponding to a finite layer, the instantaneous growth rate eventually decayed like $$T^{-1}$$. This corresponds to an instability with algebraic growth, and the eigenfunctions scale with $$T^p$$ (where p is a constant) for large time. For a species initially linearly distributed in a finite layer, when the concentration has an increasing gradient in the downwards direction, the stability of the system was similar to that found for a uniformly distributed finite layer. However, when the concentration had a decreasing gradient in the downwards direction, the growth rates remained constant for a long period time, but eventually decayed in the same way as found in a uniformly distributed finite layer, for very large times. Numerical simulations were performed to validate the predictions made by the linear stability analysis.

We prove that the Parisi measure of the mixed p-spin model at zero temperature has infinitely many points in its support. This establishes Parisi's prediction that the functional order parameter of the Sherrington-Kirkpatrick model is not a step function at zero temperature. As a consequence, we show that the number of levels of broken replica symmetry in the Parisi formula of the free energy diverges as the temperature goes to zero., revised version; 20 pages

The ray-series (RS) method, which is practically more tractable and feasible than the transfer matrix (TM) method for the time-domain analysis, is examined and applied for investigation of temporal reflection and transmission responses of an $N$ -layer structure for a plane wave incidence. These responses are represented by reduced reflection and transmission coefficients associated with unit step functions with different effective time periods and weightings depending on electromagnetic properties of the layers constituting the $N$ -layer structure. Numerical and simulation analyses in line with the residue theorem and Bromwich integral were performed to validate our formalism and practically demonstrate its applicability for temporal analysis.

Aufgrund der immer weiter steigenden Beliebtheit von erneuerbaren Energien und somit auch Photovoltaikanlagen, benötigt es immer mehr Zeit, diese zu warten. Da immer mehrere Photovoltaikmodule auf einem Wechselrichter, welcher zusätzlich ein Monitoring enthält, zusammengeschaltet sind, kann nicht genau gesagt werden, welches Modul fehlerhaft oder verschmutzt ist. Mithilfe von Wärmebildaufnahmen einer Drohne können diese Probleme jedoch identifiziert werden. Damit die Sichtung und Verifikation der Aufnahmen nicht noch zusätzliche personelle Ressourcen beansprucht, soll die Analyse der Aufnahmen in einem durch-gängigen, cloudbasierten Prozess durch eine serverlosen Microservice-Architektur abgebildet werden. Dadurch können sowohl die Vorteile der Cloud genutzt wer-den, wodurch beispielsweise keine Hardware angeschafft werden muss und nur die tatsächlich verwendeten Ressourcen bezahlt werden müssen. Weiters können auch die Vorteile einer serverlosen Architektur genutzt werden, wodurch beispielsweise keine Verwaltung der Hardwareressourcen übernommen werden muss, und die Vorteile einer Microservice Architektur, wodurch die einzelnen Komponenten leicht wartbar gemacht werden. Dadurch ergibt sich die Fragestellung „Ist eine Umsetzung einer innovativen automatisierten Pipeline anhand einer Serverless Microservice-Architektur zur Bildvorverarbeitung mithilfe der Ama-zon Web Services möglich?“. Wird der Prozess der Datenerfassung über den Input, das Preprocessing, die Detection bis hin zum Postprocessing betrachtet, liegt der Focus dieser Arbeit vor allem bei der Implementierung des Inputs und einem Teil des Preprocessings. Für den restlichen Teil des Preprocessings, die Detection und das Postprocessing wird die Architektur vorbereitet. Die technische Umsetzung wird in der AWS Cloud durchgeführt, da diese derzeit die Marktführerschaft besitzt und auch hohe Innovationen zu verzeichnen hat. Für die Umsetzung waren die AWS Lambda Services, die AWS Step Function, das Amazon Elastic File System sowie der Amazon Elastic Container Service und die Amazon Elastic Container Registry von essenziellem Wert. Werden nun Wärmebilder auf einer Website hochgeladen, werden diese zu einem Orthomosaik zusammengesetzt, in gleich große Patches zerteilt, normalisiert und es wird eine Erkennung durchgeführt. Im Orthofoto werden die fehlerhaften Module schlussendlich gekennzeichnet. Dadurch können Technikerinnen und Techniker gezielt Module, welche gekennzeichnet wurden, überprüfen oder so-fort austauschen, wodurch ebenso die Forschungsfrage verifiziert werden kann. Due to the ever-increasing popularity of renewable energies and therefore also photovoltaic systems, it takes more and more time to maintain them. Since several photovoltaic modules are always connected together on an inverter, which also contains a monitoring system, it is not possible to say exactly which module is faulty or dirty. However, with the help of thermal images taken by a drone, these problems can be identified. In order to prevent the sifting and verification of the images from requiring additional personal resources, the analysis of the images is to be mapped in an end-to-end, cloud-based process using a serverless microservice architecture. This allows both the advantages of the cloud to be used, whereby, for example, no hardware has to be purchased and only the resources actually used have to be paid for. Furthermore, the advantages of a serverless architecture can be used, whereby, for example, no administration of hardware resources has to be taken over, and the advantages of a microservice architecture, whereby the individual components are made easily maintainable. This leads to the question "Is it possible to implement an innovative automated pipeline using a serverless microservice architecture for image pre-processing with the help of Amazon Web Services? If the process of data acquisition, input, pre-processing, detection and post-processing is considered, the focus of this work is primarily on the implementation of the input and part of the pre-processing. For the remaining part of the pre-processing, the detection and the postprocessing, the architecture is prepared. The technical implementation is carried out in the AWS Cloud, as this is currently the market leader and has also recorded high innovations. The AWS Lambda Services, the AWS Step Function, the Amazon Elastic File System as well as the Amazon Elastic Container Service and the Amazon Elastic Container Registry were of essential value for the implementation. When thermal images are uploaded to a website, they are assembled into an orthomosaic, divided into patches of equal size, normalised and a detection is performed. Finally, the faulty modules are marked in the orthophoto. In this way, technicians can specifically check or immediately replace modules that have been marked, which also allows the research question to be verified. Verfasserin: Julia Gruber Abweichender Titel laut Übersetzung der Verfasserin/des Verfassers Masterarbeit FH JOANNEUM 2022

In this paper we consider a step function characterized by an arbitrary sequence of real -valued scalars and approximate it with a matching pursuit (MP) algorithm. We utilize a waveform dictionary with rectangular window functions as part of this algorithm. We show that the waveform dictionary is not necessary when all of the scalars are either non positive or non negative and the parameters of a wavelet dictionary on an integer lattice yields a closed-form solution for the initial optimization problem as part of the MP. Additionally, for any real-valued scalar sequence, we provide a solution with a related wavelet dictionary at each iteration of the algorithm. This allows for practical calculation of the approximating function, which we use to provide examples on simulated and real univariate time series data that display discontinuities in its underlying structure where the step function can be thought of as a sample from a signal of interest.(c) 2022 Elsevier B.V. All rights reserved.

This study revisits the mathematical equations for diffusive mass transport in 1D, 2D and 3D space and highlights a widespread misconception about the meaning of the regular and cumulative probability of random-walk solutions for diffusive mass transport. Next, the regular probability solution for molecular diffusion is applied to pressure diffusion in porous media. The pressure drop (by fluid extraction) or increase (by fluid injection) due to the production system may start with a simple pressure step function. The pressure perturbation imposed by the step function (representing the engineering intervention) will instantaneously diffuse into the reservoir at a rate that is controlled by the hydraulic diffusivity. Traditionally, the advance of the pressure transient in porous media such as geological reservoirs is modeled by two distinct approaches: (1) scalar equations for well performance testing that do not attempt to solve for the spatial change or the position of the pressure transient without reference to a well rate; (2) advanced reservoir models based on numerical solution methods. The Gaussian pressure transient solution method presented in this study can compute the spatial pressure depletion in the reservoir at arbitrary times and is based on analytical expressions that give spatial resolution without gridding-meaning solutions that have infinite resolution. The Gaussian solution is efficient for quantifying the advance of the pressure transient and associated pressure depletion around single wells, multiple wells and hydraulic fractures. This work lays the basis for the development of advanced reservoir simulations based on the superposition of analytical pressure transient solutions.

We consider the evolution of the solution of a class of scalar nonlinear hyperbolic reaction–diffusion equations which incorporate a relaxation time and with a reaction function given by a monostable cubic polynomial. An initial-value problem is studied when the prescribed starting data are given by a simple step function. It is established that the large-time structure of the solution is governed by the evolution of a propagating wave-front. The character of this front can be one of three forms, either reaction–diffusion, reaction–relaxation or reaction–relaxation–diffusion, which is relevant and depends on the particular values of the problem parameters that describe the underlying reaction polynomial.

Our legs act as our primary contact with the surrounding environment, generating external forces that enable agile motion. To be agile, the nervous system has to control both the magnitude of the force that the feet apply to the ground and the point of application of this force. The purpose of this study was to characterize the performance of the healthy human neuromechanical system in controlling the force-magnitude and position of an externally applied force. To accomplish this, we built an apparatus that immobilized participants but allowed them to exert variable but controlled external forces with a single leg onto a ground embedded force plate. We provided real-time visual feedback of either the leg force-magnitude or position that participants were exerting against the force platform and instructed participants to best match their real-time signal to prescribed target step functions. We tested target step functions of a range of sizes and quantified the responsiveness and accuracy of the control. For the control of force-magnitude and for intermediate step sizes of 0.45 bodyweights, we found a bandwidth of 1.8±0.5 Hz, a steady-state error of 2.6±0.9%, and a steady-state variability of 2.7±0.9%. We found similar control performance in terms of responsiveness and accuracy across step sizes and between force-magnitude and position control. Increases in responsiveness correlated with reductions in other measures of control performance, such as a greater magnitude of overshooting. We modelled the observed control performance and found that a second-order model was a good predictor of external leg force control. We discuss how benchmarking force control performance in young healthy humans aids in understanding differences in agility between humans, between humans and other animals, and between humans and engineered systems.