To evaluate the advantages of student satisfaction with and functionality of three digital teaching concepts during the SARS‐CoV‐2 pandemic compared to a conventional lecture setup.α = 0.05).This cross‐sectional study was a survey‐based e‐learning research among dental students in the clinical study phase of a department of prosthetic dentistry at a German university hospital. A total of 44 questions were answered in four main sections: 1. general technical components; 2. acceptance; 3. evaluation and functionality; and 4. overall evaluation and grades of the various digital concepts. The use of Zoom conference, livestream, and prerecorded PowerPoint was compared to the conventional lecture setup (control group/CG). Data were analyzed using the Kolmogorov‐Smirnov test, followed by an exploratory data analysis and Cronbach's alpha test (p ≤ 0.007), followed by Zoom conference, conventional lecture (CG), and livestream, while Zoom conference and the conventional lecture showed no significant difference (p = 0.784).Students were very satisfied with the provision, quality, and benefit of the digital concepts. The asynchronous concept was significantly more satisfying than the synchronous concepts in many aspects but was less successful in interactions. In the overall evaluation and grading, the asynchronous concept was rated significantly better than the other synchronous concepts (Students significantly preferred the asynchronous concept to the synchronous concepts. The results suggested that asynchronous concepts are an effective and functional form of distance education during a pandemic. In general, digital teaching concepts are currently widely accepted for maintaining university education. With this knowledge it may be possible to create a pandemic teaching concept for universities with a view to helping them to be better prepared for future pandemics. The hypothesis tested states that there is no difference in students’ satisfaction and the functionality of the diverse digital teaching concepts evaluated in the current time of the SARS‐CoV‐2 pandemic and social distancing.2During the pandemic period, the conventional lecture in the auditorium has been replaced by three digital teaching concepts. This cross‐sectional study was a survey‐based e‐learning research among 102 dental students in the clinical study phase (8th and 10th semester) of a department of prosthetic dentistry at a German university hospital.The series of lectures “Removable dental protheses I‐III” was presented through three different digital teaching concepts during the temporary closure of auditorium events in universities and compared with similar conventional lectures given the previous semester. All of the four teaching concepts Figure  and lectZoom conference: Zoom  is a communications technology that provides video telephony and can be used for distance education. The access link to the Zoom video conference was sent to the students via an already existing online learning platform (Moodle) of the university hospital. A Zoom conference enables the use of synchronous live video telephony conference for a variable number of students. The communication among the students is via the webcam of any computer, tablet computer, or smartphone. The teacher presented the lecture on a laptop with a webcam. The students followed the presentation slides and heard the teacher's voice as well as seeing the professor on a small screen. Questions were accepted via the Zoom conference integrated chat function and answered directly by the teacher via the microphone or a message. The students’ microphones were switched off to avoid an uncontrolled acoustic level.Livestream via vMix: vMix  is a software that allows the creation of productions by adding multiple cameras, videos, images, and audio to a web stream. The software offers to display, record, and stream the lecture at the same time. Livestream enables a digital teaching format that is close to the conventional auditorium. Access to the online livestream was sent to the students via the platform (Moodle). The link led directly to the livestream, and the professor was filmed during his lecture in the auditorium of the university and transmitted live with a delay of about 50 s. Questions were accepted via email and answered via livestream or email by a separate moderator during the lecture.Prerecorded PowerPoint presentation with audio explanation: The PowerPoint presentation was prerecorded and uploaded to the learning platform Moodle. The students could download the PowerPoint audio files with their access code and could watch the presentation offline. Questions about the presentation were answered via email communication.Conventional lecture in the auditorium: To compare digital teaching with a conventional lecture, the conventional lecture from the previous semester with the same professor (before the lockdown) was chosen as the comparison lecture (control).2.1A total of 102 students were invited for an online evaluation. The questionnaire was designed by the authors and developed in cooperation with the Chair of Didactics. Participation in the survey was voluntary and there was no compensation for participation. All students were dental students in the clinical study phase (8th and 10th semester). The questionnaire was created using an online survey platform called Questionstar  and consisted of 44 questions (Q), 37 of which were answered using a visual analog scale (VAS) and seven with fixed‐answer options  and declared harmless. The answers to the VAS questions were entered by the students with a scroll bar on a line, which reflected the range from 0% to 100%. The seven questions with fixed‐answer options were answered with a click.2.2p = 0.05. The verification of normal distribution of the answers was carried out with the Kolmogorov‐Smirnov test, followed by an exploratory data analysis. The median values of the questions and the range of deviation of the interquartile range (IQR) were used for the mean values. The IQR describes the dispersion of the data ‒ exactly 50% of the data were within the IQR. The Kruskal‐Wallis test for independent samples was used to compare the results (S4). An additional statistical reliability analysis  was carried out to secure the compilation of the questions and to test the internal consistency.The questionnaires were analyzed with the statistical program SPSS 25  with a significance level of 3Of the 102 students , all (100%) participated in the online survey with no dropout. None of the questions (0%) showed a normal distribution. Therefore, nonparametric tests with median values and IQR were applied. The results with median values and IQR are shown separately in Table 3.1The median value for S1Q1 showed that the students were well prepared for the digital teaching concepts in a short time . The students were satisfied with the quality of the digital media and the documents provided . Working the technical components of the media used was mostly trouble‐free . Thirty‐two students described problems with the transmission of digital data caused by a weak Internet connection (S1Q4). Almost no‐one felt disadvantaged due to missing hardware for digital education . All students (100%) had a digital device with which to participate. To view and use the different digital teaching concepts, 76.6% of the students used a computer, 17.8% a tablet computer, and 5.6% a smartphone (S1Q6). To follow the digital teaching online, 85.0% of the interviewed students used their private Internet connection (Wi‐Fi) from home; only 7.5% used their mobile data, 4.7% used public Wi‐Fi, and 2.6% another Internet service provider (S1Q7).3.2The provision of digital teaching courses not only encouraged learning within the university  but above all also promoted learning outside the university . The students’ agreement that the availability of digital courses increased their motivation toward the teaching content was based on a median of 92.0% with an IQR of 29.0 (S2Q3). With a median of 82.5% and an IQR of 46.8, students preferred digital teaching over conventional lectures (S2Q4); many students could concentrate better in their private environment than in the full auditorium . In general, the progress of knowledge through digital teaching concepts was evaluated positively . The lectures, which could be reviewed online at a later date, made it possible to deepen the learning content , which also meant that the students became more flexible in their time management . Missing the active discussion with the professor in the auditorium attracted widely dispersed views . The students evaluated the tools for online discussion as sufficient  and would like to see an increase in digital teaching concepts in the future .3.3In Section 3 the different teaching concepts were specifically compared and evaluated by the same questions.p < 0.001), with no significant differences (p > 0.999) between Zoom conference, livestream, and conventional lecture.In the first and second question S3Q1+S3Q2), concerning the transmission quality  from the other concepts. Zoom conference and conventional lecture (p = 0.618), and livestream, and conventional lecture, showed no significant differences (p = 0.356). Zoom conference and livestream were statistically significantly different (p = 0.002).For S3Q3, in terms of the potential of the various teaching concepts for future education, the prerecorded PowerPoint presentation was seen as significantly different (p > 0.999). Furthermore, Zoom conference and the prerecorded PowerPoint presentation presented no significant difference (p = 0.083).For S3Q4, in terms of interaction with the professor . The prerecorded PowerPoint presentation and livestream (p < 0.001) as well as Zoom conference and livestream (p = 0.001) differed significantly (p = 0.001).In S3Q5, the conventional lecture was excluded from the statistics because it was already a part of university teaching. As regards the integration of digital teaching concepts in future teaching, there was no significant difference between the prerecorded PowerPoint presentation and Zoom conference , for the specific follow‐up/debriefing of the learning content , and for the preparation for final examinations .With regard to future teaching in dentistry without the restrictions of the pandemic, the combination of conventional lectures and digital teaching concepts had the highest acceptance . Purely digital teaching would also be accepted . Entirely conventional teaching, however, should not dominate the teaching in future  . Zoom conference and conventional lecture showed no significant difference (p = 0.784) in the grade. The livestream was significantly different from the Zoom conference and prerecorded PowerPoint (p < 0.001) but not from the conventional lecture (p = 0.086).Cronbach's alpha (α) test: The compilation of the questions and the internal consistency of the questions in Section 4 were positive and could therefore be considered useful .4Due to the current situation of the SARS‐CoV‐2 pandemic, conventional lectures in dentistry had to be replaced by digital teaching concepts for theoretical content. The evaluation of the past semester under the SARS‐CoV‐2 restrictions supplies important and future‐oriented information for universities regarding the functionality of, and satisfaction with, digital concepts in regard to the ongoing pandemic and in the case of future pandemics. Universities and dental schools need to review and re‐evaluate this knowledge in order to guarantee professional and satisfactory education in the medical sector without quality loss or deficiencies in theoretical teaching. With this knowledge, not only can digital concepts be evaluated, but the data can also provide helpful information for the design of future teaching. Until the end of the year, teaching at universities in Germany will still take place online with digital concepts. Afterward, the situation and the infection rate must be reassessed before deciding whether a continuation of teaching at universities is justifiable. The current situation and the high infection rates suggest that theoretical teaching will continue to take place online in 2021.The survey showed a high level of acceptance among the interviewed students in the clinical study phase, indicating that the implementation of digital teaching concepts is a current and highly important topic. In recent years, clinical dentistry has seen strong growth in computer technology and digital concepts,In general, the survey confirms that all dentistry students who participated in the study own a digital device, have an Internet connection and were well prepared for the conversion from conventional to digital teaching under the circumstances of the pandemic. This means that the basic requirement for functioning digital teaching should be met. This contrasted with the fact that 32 of the 102 students complained that their Internet connectivity was too unstable to follow the live lectures in high quality and without interruption, which indicates that there are still deficits in the development, availability, and provision of fast Internet for students in the age of digitalization.To the authors’ best knowledge, there are few data on the comparison of asynchronous and synchronous digital teaching concepts during pandemics. The present study can therefore only be compared to a certain extent with other investigations, as there has never before been a pandemic on this scale in the age of digitalization. In the present survey, there was a high level of acceptance of digital teaching courses in times of contact restrictions. The digital environment led to increasing motivation for the lecture topic of removable dental protheses, as almost all students attended the lecture, which was not compulsory. Similar results have been shown in other studies, such as a generally positive attitude toward digital dental coursesThe main objective of this study was to compare and evaluate the different digital teaching concepts with each other and compare them with the conventional lecture in terms of functionality, acceptance and satisfaction, in order to develop a professional teaching concept.Despite the spontaneous change from conventional to purely digital teaching, there were generally no major problems. Theoretical teaching could be kept consistent, which was reflected in the results of the present study. In terms of transmission quality, the prerecorded PowerPoint presentation presented better results than the other teaching concepts (S3Q1). This may be due to the simplicity of the asynchronous format; after downloading the file, the lecture is available in the highest quality on the students’ digital devices, which enables a geographic and temporal flexibility of place and timeOne of the main reasons for the wide acceptance of digital teaching is that the content can be viewed again at a time and place of one's choosing,In a direct comparison of the concepts by school grades from 1 to 6 (very good to insufficient), the PowerPoint presentation was rated significantly best, followed in the ranking by Zoom conference, conventional lecture, and livestream Table . HoweverOn the one hand, a strength of the present survey is that all four teaching concepts were presented by the same professor over a short period, thus minimizing the influence of different personalities on the evaluation. The design, motivation, and interaction of the professor can influence students’ satisfaction and acceptance. On the other hand, some limitations of the present investigation should be mentioned. Both synchronous formats offer asynchronous replay in the post‐processing, which the majority of respondents took advantage of, whereas the asynchronous lectures were not digitally captured, therefore adding the limitation of memory. Additionally, for the control group it was assumed that students had to rely on their memory/experience of attending a conventional pre‐pandemic lecture. These memories may be biased by the time, and this was therefore assessed as a limitation. The survey took place at one single institution, so the results may be difficult to generalize. Furthermore, the influence of one professor on the result cannot be assessed. Poor teaching by the professor would probably bias the results negatively, so it would be interesting if the results were similar in a multi‐center study at different dental universities with different professors. The theoretical outcome of the different concepts was not evaluated either, leading to subjective outcomes. In addition, there is significantly increased mental stress among university students during the pandemic compared to normal education.5This study found that theoretical dental education through digital teaching has worked satisfactorily in times of a global pandemic. Despite the spontaneous switch from conventional to digital education, students were very satisfied with the teaching provided by the various digital teaching concepts. The results reflected the teaching situation during a global pandemic and can only be compared to a certain extent with other studies considering digital education. Within the limitations of the investigation, this study found that students significantly preferred the asynchronous PowerPoint presentation to synchronous concepts in many aspects. This may be due to the simplicity of the asynchronous format: flexibility in time and place and easy handling without technical problems. The result perhaps does suggest that asynchronous consumption of content is favored over live consumption and offers effective distance education in times of pandemics. Universities should remain focused on developing and improving synchronous and asynchronous concepts, especially in the area of interaction, as a significant part of teaching thrives through direct faculty/student and student/student interactions. Additional research is needed to compare lecture formats of different universities for the preclinical and clinical didactic teaching of dental students.The authors declare that there is no conflict of interest that could be perceived as prejudicing the impartiality of the research reported.


Nonlinear dynamical systems serving reservoir computing enrich the physical implementation of computing systems. A method for building physical reservoirs from electrochemical reactions is provided, and the potential of chemical dynamics as computing resources is shown. The essence of signal processing in such systems includes various degrees of ionic currents which pass through the solution as well as the electrochemical current detected based on a multiway data acquisition system to achieve switchable and parallel testing. The results show that they have respective advantages in periodic signals and temporal dynamic signals. Polyoxometalate molecule in the solution increases the diversity of the response current and thus improves their abilities to predict periodic signals. Conversely, distilled water exhibits great computing power in solving a second‐order nonlinear problem. It is expected that these results will lead to further exploration of ionic conductance as a nonlinear dynamical system and provide more support for novel devices as computing resources. Information processing ability of physical reservoirs utilizing electrochemical reactions in faradic current is investigated. Strong redox reactions of the acidic molecule exhibit advantage for the interpretation of periodic signals. Distilled water exhibits great computing ability for solving higher‐order nonlinear problems. The simplicity of such a system will blaze a trail for developing computing systems based on electrochemical ions reactions. Another attractive aspect of RC is that the hidden layer is replaced by a massive number of nonlinear nodes coupled with one another (referred to as reservoir), as shown in Figure  In fact, any dynamical system has the potential to be a reservoir for information processing. This basic concept introduces the concepts of arbitrariness and diversity in the choice of a reservoir and leads to the thriving development of physical reservoir computing. Hardware implementation of RC utilizes a variety of physical systems, devices and materials, and introduces more possibilities for hardware breakthroughs. Different feats displayed by different systems or designed schemes have been discussed extensively during recent years, among which organic electrochemical devices began to attract an attention. There is a study using semi‐conductive dendritic organic electrochemical networks for bio‐signal classification, proved that the nonlinearities created by electrolyte when electrically excited could be an advantage in RC. However, rich dynamic properties of electrochemical reactions have not been widely studied, and their greater application potential deserves to be further explored.It is becoming increasingly difficult to satisfy the requirements of high efficiency for computing power and storage capacity while developing hardware systems in artificial neural networks. Reservoir computing (RC) originates from recurrent neural networks (RNNs) with input, hidden, and output layers, and has attracted considerable attention owing to its unique advantages.1 Firs2 According to this conjecture, we discussed a reservoir construction method that can take advantage of the current‐to‐voltage property presented by molecules in the following research, further demonstrating the ability of chemical dynamics in the field of computing. Based on the prior studies, in this paper we build a physical RC system to utilize diverse electrochemical reactions of actual materials and experimentally analyze their computing ability. This section gives the concept of physical RC and the realization scheme of our system.Neuromorphic devices based on molecular dynamics or chemical reactions have great advantages in reducing power consumption and area reduction. The possibility of constructing complex neural networks based on molecular devices has been discussed in our previous research.20 Acc2.1 Such a physical dynamical system could act as nonlinear nodes in the traditional reservoir with varying degrees of data processing. Therefore, the physical dynamical system should have sufficiently rich dynamics with high effective dimension to enable diverse responses of the system to the same input. However, to make the reservoir works successfully, there is one prerequisite, that is, the reproducibility of the input–output relation, which is also termed an echo state property. When the system becomes chaotic and exhibits considerable dynamics, it loses the echo state in general and its relevance to the input data, making it an unreliable computing resource. When this condition is satisfied, the output signals behave like a series of signals synchronized with the input series.From Figure 18 Sucy^ should be trained to be as close as possible to the target signal y by adjusting the output weights Wout, and the optimal values can be obtained by a linear regression algorithm, such as the least‐squares method . Therefore, at the temporal unit t, the output signal y^(t) and reservoir state x(t) can be expressed as followsfres is the nonlinear function of reservoir, Win and Wres are the input weights and weights between nodes, respectively. u(t) is the input value at the current temporal unit, while x(t − 1) represents the reservoir state at the previous temporal unit. To quantize the deviation between the target signal and the testing signal as well as to evaluate the performance of RC, mean square error (MSE) is generally used. With the testing data a length of M, the expression of MSE is as followsThe working principle of RC can be described as follows. The output signal Based on this expression, the normalized mean square error (NMSE) is defined to measure the mean relative scatter and reflect the random errors, expressed as follows2.2 Therefore, selection of appropriate node definition is also one of the most important explorations in physical RC system, and the work in this paper also covers this.Figure 21 The3Figure  In this study, we utilize the electrochemical current in the solution, of which complex and large nonlinear response is expected even at low voltages owing to the high and multiple redox activities of POMs. A simple signal prediction test was performed first to verify the effectiveness of our system and POM molecule, and the general process is shown in Figure  The concentration of the molecule is not specified in this study because the specific concentration values do not result in discernable difference within a certain range. The solution concentrations between 1–3 mg mL−1, used for the performance tests, do not affect the results of the experiment; this conclusion is proved succinctly in the last section of Supporting Information.Polyoxometalate (POM) exhibits several advantages owing to the unique structure, as shown in Figure 25 In u(t) is a sinusoidal signal with a period of 1.8 s, while the target signals are sine wave signals with quadruple frequency of input signal, saw tooth wave signals and square wave signals of the frequency same to input signal, respectively. The response currents were normalized to the range of  as the training and testing data, respectively. To evaluate the performance, we calculated the MSEs between the predicted and target values. The response of DI water  is a random signal with a step width of 6 ms, the prediction performance of the POM solution is inferior to that of DI water. The NMSE was introduced to evaluate the NARMA2 performance, and the calculated results were 0.2106 and 0.3865 for DI water and POM solution, respectively (with 112 nodes). Figure For periodic signal prediction, the input r Figure , right tr Figure , left ex MCk corresponds to the squared correlation coefficients between the current reservoir states  and kth unit of past input , where k ∈ ), which ranges from 0 to 1. It reflects the extent to which the current states can be explained from past inputs. From this calculation, we found two coefficients in showed significant differences in this task. The results of DI water and POM solution are plotted in Figure 0 and MC1, which play the most important roles in the NARMA2 task, are higher in DI water than in POM solution and yield a better performance in NARMA2  test was performed.28 MCFigure I–V amplifier. The input voltage range and magnitude factor of the amplifier were adjusted to make the output from all nodes the most adequate value on average. Compared with the gradual trend during the entire response of DI water, the response of the POM solution was more intense in the initial response. The abrupt initial spike was caused by the double layer on the electrode surface and by an interaction of the capacitive resistance circuits within the parallel external circuit, as explained in the first section of Supporting Information. It is considered that the intense capacitive current led to a poor POM solution computing power at early sampling times.The response waveform of the samples shows different transient characteristics. Specifically, the upper and lower voltage limits are due to the limitation of the  There is no doubt, however, that proton migration plays a positive role in this process, as the system computing power deteriorates in the case of non‐protonic solvent dimethylformamide (see the first section of Supporting Information).From the observation of the response waveform, we speculated that the performance of this system may be affected by the length of the reaction time, so it was necessary to further control the parameters of the time. This is also the exploration of the more appropriate node definition that mentioned earlier. To clarify how the reaction time of the solution affects the computing power, we tested the performance of the NARMA2 task in terms of the test period and sampling time, and the statistical results are plotted in Figure 30 TheFigure qP(t − k) in order to calculate the MC of higher order nonlinearities, where q is the degree of polynomial. The sum of MCk values at the same q of past units (t – k) is labeled as MCq. This expression was used to extend the MC measurement for evaluating the nonlinear memory capacities, and the results are shown in the insets of Figure 1 , especially the MC11 and MC21 , could be greatly increased by adjusting the sampling time. It did not affect the MCq of the POM solution for higher‐order signals , but it had an adverse effect on the higher‐order MCq of DI water.From the above analysis, we fixed the response period to 6 ms and repeated the same tests many times. Finally, we got the conclusion that better computational performance can be achieved by selecting better reading time points. For example, in NARMA2 task, NMSE of DI water was decreased from 0.2106 to 0.0624, and that of POM solution greatly decreased from 0.3865 to 0.0947.  PAM is well known to exhibit hysteresis, and to estimate its length, we need to consider the history of applied pressures. Therefore, this task is appropriate to evaluate the memory‐required computational capability. In order to perform the investigation, 3000 data points were chosen from the open‐source data file provided by Akashi et al. The training and testing processes were maintained the same to the NARMA2 task, and NMSE was used to represent the error. The results from Figure The information processing capability of our system was evaluated using a real‐world task which was pneumatic artificial muscle (PAM) length prediction.31 PAMI–V characteristics of these samples at two periods equal to 4 and 10 ms, respectively. The current curves plotted in Figure  However, the shapes are not exactly the same with respect to the peak position and magnitude ratio. The two‐terminal measurement lost definitive control of the potential at the working electrode surface; therefore, the chemical reaction in our system took place at input voltages which deviated slightly from the norm at each pair of electrodes with different distances. The complex but reproducible higher nonlinearity of the current from the POM solution was advantageous in the periodic signal reconstruction task. Conversely, the I–V characteristics of DI water exhibit less nonlinearity but greater help to higher order tasks. This is directly reflected in NARMA2 task and PAM length task: the dynamics offered by chemical reactions of POM were less helpful to performance than proton migration in DI water.To explore the effect of reaction time on the current‐to‐voltage response, we tested the n Figure 32 How the detected signal is the electrical current flowing through an organic‐ionic‐electronic conductor, where the organic fibers within the electrolyte create strong nonlinear responses corresponding to multiple input signals. Our system detects the formation and transients of the electric double layer along with the electrochemical reaction. This results in good computing performance even at fast measurement speeds, and the power consumption is also expected to reduce owing to the dynamics of ions. Considering the high sensitivity of the computing power of electrochemical reaction to various factors, a more rigorous exploration ought to be conducted to maximize its computing ability, and to enhance the coupling of the functionality of complex chemical reactions and the dynamics of light ions.Our system provides a novel perspective on the reservoir application of Faradic currents in solution. Although an organic‐electrochemical‐reservoir has recently been reported,19 the4I–V characteristics of molecules, this condition was achieved by introducing external parameters of “feedforward gain.” We think this is a natural advantage of our system and deserves further development and exploitation. Moreover, we found that the complex and diverse chemical reactions of POM molecules contributed to the enhancement of information processing ability for periodic signals and memory in higher‐order, nonlinear systems, but the computing power of higher‐order tasks has not been fully utilized. Conversely, DI water showed strong computing power in the NARMA2 task. Other studies have shown that good performance in time‐serials prediction task also enables handwriting font recognition, isolated word recognition, and other classification tasks. Therefore, our proposed device has the potential to serve as a computing system. Furthermore, in this device with the solution sample, electrons barely flow from the electrodes to the surface of the material owing to the fact that protons travel much faster than ions. Based on this discovery, it may be possible to design a more powerful computing system using the proton or ion transfer with minimal electrochemical reactions within very fast time sequential range to provide a low‐cost, low‐power consumption, and highly integrated hardware devices for increasingly important edge computing. We hope that our research provides a new perspective combining chemical properties for the future development of hardware computing systems with low‐power consumption.With the help of a multiway data acquisition system and electronic circuits, we realized a physical RC system based on ionic current or proton migration. This system displayed “feedforward connection” between nodes, which was proved to be independent of sample selection in this study. However, in our previous scheme, which was designed according to the nonlinear rd gain.”21 We The authors declare no conflict of interest.Supporting InformationClick here for additional data file.


In this paper we consider a portfolio selection problem defined for irregularly spaced observations. We use the Independent Component Analysis for the identification of the dependence structure and continuous-time GARCH models for the marginals. We discuss both estimation and simulation of market prices in a context where the time grid of price quotations differs across assets. We present an empirical analysis of the proposed approach using two high-frequency datasets that provides better out-of-sample results than competing portfolio strategies except for the case of severe market conditions with frequent rebalancements. Conditional heteroskedasticity is a well-known stylized fact observed in financial time series. Generalized Autoregressive Conditional Heteroskedastic (GARCH) models have been widely used since their introduction in Bollerslev . The maiThe Continuous GARCH model where the independent non-Gaussian signals are assumed to follow a COGARCH process. In the literature, a similar approach in discrete-time context has been proposed in Broda and Paolella  where th, 1 modelThe objective function in the portfolio selection problem is a combination of the expected terminal wealth and a specific risk measureResults of the portfolio selection problem are presented for different risk aversion profiles. We discuss the results of a rolling window strategy both from an in-sample and from the out-of-sample point of view. The proposed approach provides better out-of-sample results than competing portfolio strategies except for the case of financial turmoils as observed recently during the COVID19-induced crisis.The outline of the paper is as follows. In Sect. l et al.  and press and t, q-vector. Using the theory of stochastic recurrence equations, it is possible to establish sufficient conditions for the stationarity of a COGARCH process, for the positivity of the variance process Let l et al. , the stamentclass2pt{minimmentclass2pt{minimf system .n, we consider a sequence of natural numbers p, q) model based on the assumption of normality for We quickly review a result given in Iacus et al. , particuentclass1pt{minimaSzimayer  . The independent components are determined by looking for a W such that:S and the linear transformation matrix W based for example on maximum likelihood or maximization of any non-Gaussianity measure. In particular, the Fast Fixed Point algorithm FastICA proposed in Hyvarinen and Oja  introduced in Comon  is a sta and Oja  is an itThe ICA-COGARCH datasets composed of prices of the components in the FTSE 100 Index in 2018 and 2020. Intraday prices are collected every five minutesThe analysis performed revolves around two main parts. We first determine optimal weights using the methodology described in Sect. Figure The first dataset is composed of 14078 points of successive time instants where we have price quotations for at least one asset in the portfolio. We have 7927 points in the original grid with at least one missing data for the components of the FTSE 100 IndexThe second dataset is composed of 14086 points of successive time instants: we have 29110 missing data over the total 1422686 points  and we have 5705 time instants with at least one missing data for the components. If we follow the strategy of removing the whole row that contains a missing data we have a loss of about 40% of the original observations; the dataset of 2020 is composed of 846,481 observations with a similar behavior of the first dataset in terms of the maximum distance (160 min) within a trading day. Again we introduce use linear interpolation to complete the dataset.In both cases, the final grid is still irregular and reflects the grid of most liquid components of the FTSE 100 Index.X and Y  model to the independent componentsWe discuss the stability of portfolio weights using two measures, namely the Modified Herfindahl Index Table t. A value close to zero denotes a stability of the weights. From Table The portfolio Turnover Index Figures To investigate further the out-of-sample results, we consider the maximum drawdown index Based on the results of the first dataset presented in Tables Tables Table In this study, we use continuous-time models for the dynamics of the independent components extracted from real market time series. The independence of the components and the estimation algorithm for COGARCH(s et al.  constituThe advantage of our approach is found in the formulation of a mathematical problem for portfolio selection that incorporates information generated both from price level and time distribution of market quotations. Compared to recent machine learning techniques that look for patterns of asset dynamics useful in price prediction, we have a direct interpretation of model parameters that allows to perform a sensitivity analysis.


D,  a state we call socially distanced. , they remain at their current node next period; with complementary probability p which achieves social distance in the least expected time, which is the absorption time of a Markov chain. We observe that the same Markov chain, with different goals (absorbing states), models the gathering, or multi-rendezvous problem . Allowing distinct laziness for two types of agents (searchers and hider) extends the existing literature on predator–prey search games to multiple searchers. We consider only special networks: line, cycle and grid.During epidemics, the population is asked to socially distance, with pairs of individuals keeping two meters apart. We model this as a new optimization problem by considering a team of agents placed on the nodes of a network. Their common aim is to achieve pairwise graph distances of at least  Each agent adopts a lazy random walk (LRW) which stays at his current node with a probability p  and moves to a random adjacent node with complementary probability speed). In the common interest game, we seek a common value of p which minimizes the time for all pairs of players to be at least D nodes apart . Once p is adopted by all, the positions of the agents on the network  follow a Markov chain, with distanced states as absorbing. Standard elementary results on absorption times for Markov chains are used to optimize p, to find the value of p which if adopted by all agents minimizes the absorption time. This work can be seen as an extension to networks of the spatial dispersion problem introduced by Alpern and Reyniers [any two locations. That paper also allowed agents knowledge of populations at other locations, whereas here agents have no knowledge of the whereabouts of other agents. To combat epidemics, three actions are recommended to the public: mask wearing, hand washing, social distancing. This paper models the last of these in an abstract model of mobile agents on a network. Social distancing can be considered a group goal (common-interest game) or individual goal . We consider both goals in a dynamic model where agents (players) walk on a network (graph). A group of Reyniers , where asticky form of the problem, where agents who meet coalesce into a single agent and move together subsequently. Rendezvous problems were introduced by Anderson and Weber [We observed that by changing the states which we call absorbing , we can usefully model other existing problems. For example, by taking the absorbing states as those where all agents occupy a common node, we model the multi-rendezvous (or gathering) problem, and our results extend known results for entclass1pt{minimaentclass1pt{minimand Weber . See alsnd Weber , Howard nd Weber  and Webend Weber . A survend Weber , 4.searchers and hiders (or predators and prey), who can choose different speeds. Here, the payoff is related to the search or capture time (when a searcher coincides with a hider), with the searchers as minimizers and the hiders as maximizers in a two-person team search game. These problems were proposed by Isaacs [We also consider a model with two types of agents called y Isaacs  and firsy Isaacs , Alpern y Isaacs  and Gal y Isaacs , and laty Isaacs  and Alpey Isaacs  for mononlocations  with n agents placed randomly on them. The aim to obtain a dispersed situation with one agent at each location . This would correspond to a value of pairwise distance at least k agents at each location. After each period, the distribution of agents over the locations becomes common knowledge. That problem modeled a situation where drivers can take any of n bridges, let us say from New Jersey into Manhattan, and the distribution of yesterday’s traffic is announced every night. The aim is to equalize traffic over the bridges for the common good. Grenager et al [As mentioned above, the forerunner to social distancing problems is the related spatial dispersion problem of Alpern and Reyniers . They coer et al  extendeder et al  to econoer et al .It is clear that ours is an extremely abstract approach to the problem of social distancing. For a very recent practical analysis of the impact of social distancing on deaths from Covid-19, including a monetary equivalent, see Greenstone and Nigam . For menn players start together an end of a line graph, each choosing their own laziness in a lazy random walk. At the first time periods where some agents are alone at their node, these agents split a unit prize. When any pair This paper is organized as follows. Section m agents in our model move on a connected network Q with n nodes, n. While we could do this analysis on a general network with arbitrary arc lengths, we take a graph theoretic assumption where all arc lengths are 1,  so we will from now on call Q a graph. In this section, we describe the dynamic model that we use throughout the paper. We do this in three stages: states, motion of agents, the resulting Markov chain. Since we will restrict the arc length to 1 here  we will henceforth use the term graph instead of network.The state of the system. A general way is to write square brackets i,  with population of node i. We could also use a notation j is occupying, but in this paper we have no need to know this. Attached to every state is a number d denoting the minimum distance between two agents, where we use the graph distance between nodes (the number or arcs in a shortest path). For example, if we number the nodes of the line graph d,  it is called socially distanced if D is a parameter of the problem. For example, the state There are several ways to denote the The unifying idea of this paper is the use of agent motions of the following type.Q,  with laziness parameter p  for an agent on the graph For various problems considered in the paper, random walks or loop-random walks will be optimal, in terms of minimizing the mean time to reach the desired state.p,  i.e., our main assumption, then a Markov chain is thereby defined on the state space m (number of agents), D desired distancing and Q (the connected graph), where it is possible for having distanced states. For example, the triple D distanced nodes) is at least m. If If all the agents in the model follow independent LRWs with the same value of Reyniers , an impoQ (with n nodes), m and D,  there is a Markov chain on the state space B denote the i to state j. Let t be the vector i. The n matrix of 1s and t is given byp,  so these times p. This use of the fundamental matrix to calculate absorption times , we wish to know the probability that a particular absorbing state is reached (which searcher finds the hider). Formulae for this problem are also known, but in the event we find a more direct way to determine this. This will be made clear in Sect. In most cases, we consider the problem of finding the laziness value k of agents at their node, the population of the node. This case may allow a laziness k. For example, if I find myself at a node with three other agents, I stay there with probability p regardless of the population of the node.A useful variation is to allow agents to see the number j between the agents. State j covers all configurations where this distance is n,  there are (up to symmetry) two non-absorbing states (1 and 2) and a single absorbing state 3.Generally, we will consider problems with at least mentclass2pt{minimT from state 2 when adopting a random walk However, there is a variation of the gathering problem on s and the hider chooses a laziness h. In this instance, we take the point that the searchers are a team, mother and father to a hungry infant. They have the common aim of minimizing the time T taken to find the hider, who wants to maximize T. Here, T is the first time that one of the searchers finds the hider, it does not matter which searcher it is.  It is not clear a priori that there will be a saddle point. However in the event, we show that there is one, with h about .51 and s about .28. Thus, the searcher moves more frequently than the hider. Ruckle [n nodes) when there is a single searcher and a single hider.We now consider a search game played by two mobile searchers and a mobile hider on y Isaacs  and study Isaacs , Alpern mentclass2pt{minimy Isaacs . For a cy Isaacs  and Alpey Isaacs . We plac. Ruckle  has consThere are four states : states 1 and 2 are non-absorbing (hider is not caught), states 3 and 4 are absorbing (the hider has been caught). See Fig. B  curve shows that the payoff T is at least V for any value of V if V when adopting h.Numerical approximation of the critical point T. Perhaps a male and female who will bring the captured prey back to their offspring, and it does not matter which one makes the kill. A different approach (Payoff function) could model a competition between the two searchers, as carried out in the next section.This analysis considers the two searchers as a team which wishes to minimize the capture time T when one or both searchers coincide with the hider. The hider’s payoff is simply T. A searcher gets payoff 1 if he is the unique player to find the hider; 1/2 if both searchers find the hider at the same time and 0 if the other searcher finds the hider alone. This element of competition between the searchers has been studied in Nakai [T to reach an absorbing state.We now model the problem of two searchers and one hider as a three person game, rather than considering the two searchers as a single player (team). As in the previous subsection, the game ends at the first time in Nakai  and Duvoin Nakai , but herr, searcher 2 by s and of the hider by h. Let j,  assuming it starts randomly. Player 2’s payoff is equal to r and h such thats.The probabilities that an absorbing Markov chain ends at each absorbing state are easily calculated but we use a qualitative idea to avoid this calculation on a five-state chain. Instead we show that there is a dominating search strategy (depending on h but not the other search strategy) that ensures always capturing in the next period with maximum probability. Such a strategy clearly maximizes the searcher’s payoff, regardless of what the other searcher is doing.We seek a Nash equilibrium that is symmetric with respect to the two searchers. Denote the laziness of searcher 1 by To calculate the optimal response of the hider to a symmetric pair h. If a searcher can always maximize the probability of finding the hider in the current period, he guarantees doing at least as well as the other searcher. What is the best value of s to maximize this probability? If h,  the capture probability in the next period iss will be 1 if s will be 0 if s give the same capture probability. Note that h give the same expected capture time from a random start. So Suppose the hider adopts strategy h is an optimal response to s if 0,  contradicting our assumption.To see that this equilibrium is unique, suppose The unique searcher-symmetric Nash equilibrium to the competitive search game on To see why the team solution given in the previous subsection is not an equilibrium with respect to the searchers, note that against n. We may use the symmetry of the network to reduce that state to three numbers . Let j denote the distance between the two closest agents and let k denote the distance between the second closest pair. Thus, the arcs between the three agents have distances j,  k and Suppose three agents are located on the cycle network In general, for three agents on n,  the states for three agents will be more numerous and from state For larger values of This figure indicates the complexity of analyzing even three agents for larger cycle graphs and explains why will use simulation techniques to obtain approximate solutions for larger cycle graphs.The gathering problem is defined in the same way on p  asThe non-absorbing states (rows) for our transition matrix are thus p for The expected time to absorption for the different initial states are shown in Fig. d are not attainable on j is by definition the minimum pairwise distance between agents. We renumber the remaining states as For the social distancing problem on mentclasspt{minimaIt is intuitive that social distancing takes the longest when the agents are in the gathered position. When two are at the same location it takes longer to disperse when the third is closest to them. The random starting process takes a shorter time because there is already a high probability (13/25) that they are dispersed, in which case the dispersal time is 0.n players start together at the end location 1 on the line graph i has a single strategic variable, her laziness probability In this section, we consider the game territoriality, a player who is alone at her node becomes the owner of it. This means she stays there forever and anyone else who lands there immediately moves away randomly in the next period. So the game considered here can be thought of as the beginning of a dispersal problem with territoriality.We can consider this game as a selfish form of the social distancing problem with any pair This is an almost trivial case. For any p,  they all have expected payoff of 1/3. We will show that when any two players adopt the same p,  the remaining player can get more than 1/3 by a suitable strategy, and hence there is no symmetric equilibrium. The algebra involved in the proof is greatly simplified if we consider the “modified payoff” M to the single player  adopting q when the other two adopt p. It is modified from the actual payoff by not giving her the prize of 1/3 when there is a tie. So it will be enough to show that player 1 can always find a q (for any p adopted by the others) with By symmetry, it is clear that when all players adopt stay probability Suppose two players use a common strategy p is given by the expression O be the event exactly one moves and B be the event both move, N be the event none moves. The winning sequences for are B, NB, NNB, .. . Since B has probability N has probability It suffices to show that his payoff for general Suppose two players use a common strategy p,  starting, respectively, with all agents at location 1 (or 3) and all agents at the middle location 2,  assuming this player does not accept the payment of 1/3 in case of a tie. This last assumption simplifies the algebra. From position A , the remaining player must go to location 2, so there are three possible subsequent states: all go to middle location 2 (payoff B), the other players stay at location 1 (payoff 1) or if he alone stays at location 1. Other outcomes lead to payoff 0 and can be ignored. This gives the formula A),  both of the other players go to the other end (payoff 1). The other states are either have payoff 0 or have payoff 1/3, which we are reducing to 0 in this calculation. So we have A,  starting from an end, which isLet There is no symmetric Nash equilibrium for the game Lemma p’s, there might be a symmetric equilibrium.Of course in this analysis, the laziness strategies should be thought of as pure strategies. If the players use mixed strategies which are distributions of m and n,  we determine expected time to reach social distancing with m agents in some specified initial locations on the network. Then we have them move independently according to LRW’s with the same p value. After each step, we find the minimum pairwise distance d between agents in the current state. If T. We carry out 5, 000 trials and record the mean. Contrary to our earlier results, we find for the line and the two-dimensional grid that it is optimal for the agents to follow (independent) random walks, n is very small, it takes a little longer to reach social distancing.For larger problems with respect to In practice, social distancing is often to be achieved by individuals in a planar region. A good network model for this is the two-dimensional grid graph p spaced at distance 0.2. Note that for all the four values of k,  the mean times to reach distance p. The means that the random walk, k,  It takes a bit longer for the k, the times do not appear to depend much on k.A natural starting state is the one with all agents at a corner node  or all at the center. We find that the common value of p should be 0,  that is, the agents should adopt independent random walks. Figure The graph D. While different motions and information could be given to the agents for this problem, we give them only local knowledge of the graph and no knowledge of locations of other agents. So they know only the degree of their current node and lack memory. These assumptions limit the motions of the agents to lazy random walks. We showed how to optimize their common laziness value p to achieve social distancing in the least expected number of steps. We considered various graphs and both exact and simulated methods. In some cases, the optimal motion was a random walk . One goal is multi rendezvous, or gathering, where the common goal is for all agents to occupy a common node. This extended earlier result limited to two agents. Another problem is the search game where agents come in two types, searchers and hiders, with obvious associated goals. Here, our methods extend known results to multiple searchers. Many other results in search games could usefully be extended in a similar way.We expect this area of research to be enlarged to other assumptions:In this first paper on social distancing, we have restricted ourselves to considering only some simple classes of graph and small sizes. It is to be hoped that further research in this area will find new and stronger methods able to study general graphs.


Instabilities and fluctuations of the plasma jet in a thermal spray process can have a significant influence on the particle in-flight temperatures and velocities, affecting the properties of resulting plasma-sprayed coatings. Presented in this paper is a novel method for capturing the effects particles are exposed to in the plasma spraying process. High-speed camera images of a plasma jet generated by a cascaded three-cathode plasma generator (TriplexPro-210) were recorded for varying operating conditions. The images are processed using the inverse Abel transform. This transformation accounts for the fact that the images represent a 2D projection of the 3D jet and generates more accurate intensity values that the sprayed particles would experience. These images are then combined with particle tracks resulting from CFD simulations of the plasma jet to match the particles path with the recorded plasma jet. This new method allows a precise description of the plasma intensity experienced by individual particles with a high temporal resolution. The results show a high sensitivity of the method, even detecting the influence on the particles of the plasma jet originating from the cascaded triple arc plasma generator, which is considered as rather stable. First developed in the 1910s and 1920s  Ref . The proA major issue in describing this process is the large number of interactions that would need to be described to capture each step in this process: the electron–gas interactions that create the plasma, the plasma–particle interactions when the feedstock is introduced to the plasma jet and finally the particle–substrate interactions when the coating material impacts on the substrate Ref . There aOne approach used to improve the stability of the jet has been the introduction of multiple arcs and the cascaded anode design. The cascaded design of the anode increases the distance between the electrodes thus raising the arc voltage rather than the arc current in order to achieve the necessary power. At the same time, the movement of the arc is restricted, which also reduces the fluctuation of the power output. By combining this measure with the division into three arcs, the stability of the power output can be further increased, resulting in a very stable plasma jet Ref , 10.However, even this rather stable plasma jet is affected by turbulence and thus continues to exhibit fluctuations. These varying jet sizes and movements affect the temperatures experienced by the individual particles as they pass through the plasma. An approach to generally describe the instability of plasma jets, including observations of fluctuations in the electric arc and the effect this has on the plasma jet and resulting coatings, has already been performed in literature Ref , 12. HowAdvances in camera hardware have allowed for new optical approaches to describe the plasma spraying process. Many of these focus on the particles in flight after they have passed through the plasma jet Ref , 14. It The approach of this paper was to now apply a high-speed camera to capture the plasma jet fluctuations and its possible influence on the particles in plasma spraying. This was carried out on the assumed stable cascaded multi cathode plasma generator, to evaluate whether this type of plasma generator can still lead to varying particle properties. Attempting to follow individual particles’ flight paths as they pass through the plasma jet presents some unique challenges however. The extreme brightness of the plasma makes it impossible to follow the particle flight paths using standalone high-speed imaging. For this reason, a previously developed CFD simulation was used to calculate the particle trajectories within the plasma jet. These trajectories were then mapped onto the high-speed recordings of the jet. By combining the recordings and the particle tracks, the possible effect of the plasma jet fluctuations on individual particles was assessed.I = 200, 350 and 500 A, while the plasma gas flow rate took the following steps The cascaded triple arc plasma generator used in this study is the TriplexPro-210 Plasma Spray Gun . The torch was equipped with a 9 mm diameter nozzle. As mentioned earlier, this plasma gun exhibits an increased plasma stability compared to commonly used non-cascaded single-arc models like the F4 or SG-100. Pure argon was used as plasma gas. The electric current was varied at the levels High-speed videos of the plasma jet emerging from the plasma generator were recorded perpendicular to the torch axis. The camera used is a Fastcam model SA-Z by Photron, which was mounted with an Irix 150 mm f/2.38 macro-lens. Higher frame rates can only be achieved with the Photron Fastcam by reducing the maximum image size and thus the field of view. For this investigation, a frame rate of 210,000 fps was used, along with an exposure time of 1.25 μs. This allowed for a resolution of 384 × 160 pixels , resulting in a field of view large enough to capture the entire length of the plasma jet while maximizing the frame rate. A neutral density filter (ND64) was used to decrease the intensity of the recorded imaging to 1.5% of the original, preventing overexposure. An additional ultraviolet filter was also used as a customary protection of the lens. During this analysis, the powder feeding was deactivated. For clarity, the complete experimental setup with plasma torch and high-speed camera is illustrated in Fig. dp = 37.7 µm and standard deviation of σp = 11 µm, representing the particle size distribution − 45 +22 µm of the commercially available feedstock AMDRY 6062 . The trajectories of the particles are calculated using a steady-state approach. The gas flow is calculated by assuming a turbulent flow, describing the turbulences using the shear-stress-transport model. The particle velocities are calculated using the following drag coefficient (CD) correlation:The particle trajectories were calculated using an existing CFD simulation in Ansys CFX. The simulations are composed of two different steady-state models. The first model shown in Fig. CD values are depending on the particles Reynolds number Rep following the relations proposed in :The shown d in Ref -22. In tIn this model, the particles are assumed to be one-dimensional solid particle. The heat transfer and the melting degree are calculated using subroutines in ANSYS. Yet these processes are not described in detail as they are not relevant for the particle’s trajectories. The used mesh consists of 2,363,272 elements, using tetrahedra, pyramids, wedges and hexahedra as element types which exhibit an edge length ranging between 0.3 and 2 mm. Further details and more information of this model can be found in Ref . Both moIn contrast to the recorded images, the particle trajectories were calculated only for one process parameter. The reason for this is that the method is novel and in this first step we only wanted to investigate the possible influence of different process parameters on the particle properties. If the process parameters, current and gas flow were also varied in the simulations, the injector gas flow would also need to be adjusted. This would create a chain of interdependencies that would be difficult to trace. In order to not affect the comparability of the presented results, only the process parameters of the recorded images were varied.I = 500 A and a plasma gas flow rate of x-, y- and z- components for the particles’ location and the respective time. Since the camera images only have two dimensions, the particles were projected onto a plane that lies along the axis of the injector and the plasma torch, thus reducing the dimensions as well. Figure A current of An inverse Abel transformation, as shown in the equation below, was carried out on the high-speed camera images in order to correct for the fact that they are a 2D projection of the plasma jet.It is necessary to apply this transformation to the plasma jet images before the mapping can be done. This is because the camera captures a 2D projection of an originally 3D plasma jet. The inverse Abel transform restores the 3D object from its 2D projection. If this transformation would not be applied the captured intensities of the plasma jet would not correctly represent the reality. The transformation was done in Python, using a package called PyAbel Ref . This paThe instability of the plasma jet makes carrying out the transform difficult, as a prerequisite to carry it out is cylindrical symmetry. In order to overcome this issue, the Abel inversion is applied individually on the columns of the images using its individual center of intensity. The complete effect of this pre-processing is illustrated in Fig. The inverse Abel transformation is then applied to the image as shown in Fig. direction was set to inverse as we wish to apply the inverse Abel transform to the 2D projection of the plasma jet that is our image. The symmetry_axis is used to specify in your image which axis is the symmetrical axis around which to apply the transformation, 0 being the vertical axis which we need. The use_quadrants variables can be adjusted to take only specific quadrants of the image into account and to adjust when data quality is poor/obscured in part of the image. As we wanted to make use of all the recorded data, this was all set to True. The symmetrize_method can be set to “average” or “Fourier.” It was not found that “Fourier” resulted in improved results, so the default method “average” was applied.Due to the extremely high frame rate used in this study, the number of files is in the thousands, and so an efficient algorithm is advantageous. A thorough investigation of the different transform algorithm methods is already available Ref , both foThe calculated particle trajectories and high-speed imaging can then be combined in order to determine the potential plasma intensities profile single particles would experience. A full illustration of the complete image processing method carried out can be seen in Fig. It must be noted that the CFD simulation has a longer flight path than the trajectory presented in Fig. I = 200 A and I = 500 A and I = 200 A barely show a plasma jet at all. This is due to the deliberately chosen consistent parameters during recording, which lead to a strong attenuation of the images’ brightness. This is especially true for the higher gas flow rate. Therefore, the results of these parameters are omitted in the following.A sample of the plasma jet images for each of the arc current and gas flow parameters is shown in Fig. I = 500 A and two different gas flow rates Figure I = 500 A, t = 0.6 ms, the intensity begins to increase and only little fluctuations can be observed. These variations could be caused by the inherent fluctuations in the plasma jet, probably resulting from instabilities in the electric arc. The observable fluctuations become greater as the particle continues its flight, as turbulence impacts the jet more and more. Eventually, the particle exits the jet completely and continues out of frame. It must be remembered that the Triplex plasma gun used is considered to be a stable plasma jet and the particle only stayed in the apparent plasma jet for about t = 0.4 ms. However, as made clear in Fig. As mentioned, 1000 particles were included in the CFD simulation. The intensity profiles for each of these particles were calculated for different plasma gas flows and arc currents. A typical example of the intensity profile of a single particle of trial 9 (The key concern in this case is the fact that not all particles experience the same intensity profile, as the plasma jet fluctuates both in position and intensity, and small differences in particle trajectory (see CFD simulation flight paths in Fig. I = 500 A. It is obvious that there are strong variations between the integrated intensities of the individual particles. However, in this display, no statement can be made about the differences between the process parameters.However, the fluctuation of intensities within the particle trajectories could be irrelevant if they result in the same particle properties like the temperature. It is easy to imagine that, for example, a moment of a particle in a very hot region of the plasma jet can be balanced again by a very cold one, resulting in no effect of the observed fluctuation. The particles are influenced over the entire path, therefore only the total absorbed energy from the plasma jet plays is important for its temperature. The same applies for its velocity. While the velocity cannot be considered with the here presented method, the temperature should correlate with the experienced intensity of the particles. Therefore, it seems reasonable to estimate the influence of the jet fluctuations onto the particles by integrating the particles’ intensity over its entire flight. Figure To investigate this further the particle CFD simulation flight paths for all 1000 particles were applied to the plasma jet images with various parameters, as described previously. By analyzing the large number of particles, it is possible to carry out a statistical evaluation in order to assess the parameters quantitatively. As Fig. σ when operating under different plasma jet parameters is particularly pronounced for the measurements with an arc current of I = 500 A. A similar, if less pronounced, trend is apparent for the electrical current of I = 350 A. The second observable trend is that as the current decreases, the standard deviation decreases as well. However, the trends observed here should not be overrated. Since the particle trajectories all originate from the simulation of the same parameter (I = 500 A, Figure High-speed imaging proves to be a useful approach to analyze the plasma spraying process in detail. The fluctuations in the plasma jet are reduced by adjustments such as the implementation of cascaded electrode systems, however the particles still experience significant sudden plasma jet intensity fluctuation, in particular as they move in the jet toward the substrate and turbulence that cannot be avoided. This fluctuation is not considered if a plasma jet is assumed to heat homogeneously and not time dependently. By combining particle flight paths from a CFD simulation and high-speed imaging of a plasma jet under several operating conditions, the possible effect of such fluctuations was identified.One key result of this investigation is that turbulence-induced fluctuations of plasma jet generated by the cascaded triple arc plasma generator, which is assumed to be stable, have the potential to affect the particle in-flight properties. The presented method has also shown that it will be able to detect differences between varying parameters in the future. With the help of further simulations, such investigations can be carried out in a next step. In addition, the results presented here still need to be further substantiated by investigations, such as measurements of particles’ in-flight properties.


The cervical extension of the thymus is the most common variation. However, this may be mistaken for a soft tissue mass in the neck particularly by the radiologists who are not familiar with the pediatric population and not aware of this variation, leading to unnecessary surgery and increased medical costs. Since the rates of cervicaly extended thymus in children in clinical practice are lacking in Turkey, this study aimed to evaluate the prevalence of cervical extension of the normal thymus in the pediatric population.This descriptive cross-sectional study included all pediatric patients who were referred to the radiology department for neck ultrasonography between August–October 2018. A high-frequency probe was implemented and 220 patients  with a mean age of 8.7 ± 4.39 years (ranging from 1 month to 18 years of age) were examined.Cervical extension of the thymus was detected in 103 patients (46.8%). The age of the patients was found to be significantly lower than the age of the patients whose thymus was not extended . The mean craniocaudal length of the thymus that cervically extended was 6.41 ± 2.31 mm. There was no significant difference in the length of the thymus between males, females (6.48 ± 2.12 mm and 6.37 ± 2.46 mm. p = 0.924), and different age groups (p = 0.442).Approximately half of the children have the cervical extension of the thymus. Thus, radiologists and clinicians should be aware of this entity to avoid unnecessary imaging studies and interventional procedures. •The cervical extension of the thymus in children is the common anatomic variation.•It may be mistaken for a soft tissue mass in the neck.•The clinicians should be aware of this entity to avoid unnecessary imaging and intervention. It is formed by the fusion of the right and left thymic rudiments, originating from the ectoderm of the third branchial cleft and the endoderm of the third branchial pouch, and moves caudally and medially from the pharyngeal region to the superior anterior mediastinum . DefectiAccording to our clinical experience of neck ultrasound (US), the cervical extension of the thymus is the most common variation of the thymus. This may be mistaken for a soft tissue mass in the neck particularly by radiologists who are not familiar with the pediatric population and not aware of this variation, potentially leading to unnecessary surgery and increased medical costs ,4. To ou2This descriptive cross-sectional, single-centered study was approved by the Institutional Review Board for Ethical Issues in Clinical Research and is compatible with the Declaration of Helsinki. The patients referred to the radiology department for the neck US with various clinical indications between August–October 2018 were included in the study. The informed consent was taken from the parents of the patients. The patients who had any systemic illness, treated for malignancy, or had a history of lower neck or chest surgery, were excluded.The neck US was performed by two radiologists . The scan was performed using a 7–12 MHz high-frequency linear transducer on the Aplio-500 US device . The probe was placed perpendicular in the suprasternal notch in the transverse plane. Without any angulation towards the mediastinum, the cervical extension of the thymus was considered to be ‘positive’, when the thymus-located in the anterior mediastinum abutted the upper border of the manubrium sterni through the neck. The thymus was distinguished with its homogeneous hypoechoic background echogenicity compared to the thyroid with scattered hyperechoic foci resembling a ‘starry sky’. With increasing age, due to physiological fatty replacement, the echogenicity of the cervically extended thymus could increase.The length of the extended thymus, from the upper margin of the manubrium to the superior edge of the thymic tissue on the transverse plane was measured in millimeters and recorded. The images containing the most upper extent of the thymus at midline or near the left or right of the midline were used for measurement.Patients were grouped according to sex and age intervals  and compared statistically in terms of the length of the cervically extended thymus.Statistical analysis of the data was performed in SPSS, Version 25 program . Pearson Chi-Square Test was used in comparing categorical data between groups. Due to the lack of normal distribution of continuous data, Kruskal Wallis H was implemented for comparisons between more than two groups and Mann Whitney U statistical analysis for comparisons between two groups. p<0.05 was considered statistically significant.This work has been reported in line with the STROCSS 2021 criteria .32 = 3.743, p = 0.442).220 patients  with a mean age of 8.7 ± 4.39 years were included in the study. 103 patients (46.8%) had cervically extended thymus. The location of the extended thymus was in the midline and inferior portion of the neck not exceeding the thyroid lobes . The ageIn 4 patients , and vascularity of any mass, as well as its relationship to nearby anatomic structures .With theIn the literature, there is a limited number of studies focusing on the cervical extension of the thymus. In a study reviewing PET/CT examinations acquired in children and young adults with malignancy and under the age of 20 years for 2 months, the superior thymic extension was reported as 11% . HoweverThe thymus has a unique US appearance, a homogeneous hypoechoic background echogenicity, compared to the thyroid, with scattered hyperechoic foci resembling ‘starry sky’ due to the mixture of lymphoid tissue and fat. Continuity with the thymus located in the anterior mediastinum and the US characteristics resembling normal thymus tissue is the features helping establish the diagnosis of 'cervically extended thymus' .The cervical thymic extension above the manubrium in the midline should not be confused with a pathologic condition. Criteria for differentiating the normal finding of cervical thymic extension from pathologic mass is that cervical extension appears as a soft tissue lobe, extending above the upper margin of the manubrium anterior to the trachea and great vessels with direct vicinity of the mediastinal thymic tissue and should not deform or compress vessels or airway ,15. In oIn the current study, we demonstrated no significant difference between the sex and age groups in terms of frequency of cervical extension. However, the patients without cervically extended thymus were significantly older than those in whom cervical extension was detected. The increased echogenicity of the thymus due to increasing fatty replacement with the age may interfere with discrimination of the thymus from the fatty tissue of the neck .Fig. 2ThThere were several limitations in this study. Although this study, to our knowledge, is one of the few studies implementing the US to determine the prevalence of superior cervical extension of the thymus in children, the study had a relatively small study population. Future US studies with a larger sample size would emphasize the entity of the cervical thymic extension. Since the echogenicity of the thymus increases with age due to fatty replacement, discrimination of the cervically extended thymus from surrounding adipous tissue may be challenging. More than half of the pediatric patients were older than ten years of age and this might have been interfering with the detection of cervical extension of the thymus.5The findings of our study shows that approximately 50% of the children have a cervical extension of the thymus. The extended thymus tissue is often located in the midline at the suprasternal notch level in the neck and continued with the mediastinal thymus, having the typical thymus echogenicity. However, with increasing age due to fatty replacement the thymus echogenicity increases and cervical extension may not be detected on US examination. Thus, radiologists and clinicians should be aware of the high frequency of cervical extension of the thymus as a variation in pediatric patients to avoid unnecessary imaging studies and interventional procedures.Not commissioned, externally peer reviewed.The authors declare no conflict of interest.


A new method was used to study the performance of pile across cave. This paper investigated the vertical bearing characteristics of piles cross caves using centrifugal model tests and a theoretical model of sensitivity. Twelve pile scenarios were selected, the first was a conventional pile, 24 cm long and 2.5 cm in diameter, with no karst cave as a control. In the other eleven scenarios the piles passed through karst caves of four different heights, of four different spans, and three different numbers of caves. The results reveal that increasing the height, span, and number of caves all are negative for vertical ultimate bearing capacity of piles. The axial force and unit shaft resistance of piles are great different. According to the ratios of the tip and shaft resistance, caves change the type of piles. The sensitivity of vertical ultimate bearing capacity to these factors from high to low is height, number, and span of caves. Importantly, the bearing characteristics of piles decrease faster once the height of the prototype karst cave is higher than 9 m, but decreases slowly when the cave’s span is greater than 9 m × 9 m. Three problem scenarios can occur when installing piles in terrain with karst caves: cave across pile, cave at side of pile, or cave under pile. Piles often need to pass through caves to ensure there is a stable bearing layer under pile tip for support. When the piles pass through the caves, the influence of karst cave on the bearing characteristics of piles is mainly affected by the cave’s height, span and number. A lack of rock surrounding the pile cross caves directly affects the bearing characteristics and load transfer laws of piles, which will affect the structure’s stability8. Others established simulated models to study them10. Feng and He predicted the ultimate bearing capacity of piles cross the caves in vertical load with the changing height and span of the caves using the high-accuracy grey theoretical model12. Su and Xiao analyzed the adverse effects of multi-layer karst caves’ diagram on the bearing performances of piles and proposed the shaft resistance of piles gradually decrease with the increasing diagrams of caves by the indoor test and finite element analysis14. The above studied were about the bearing capacity of piles cross caves, but the load transfer mechanism of end and shaft resistance was not clear. More scholars payed attention to the calculated methods of safety roof thickness and stability of the roof when the caves were under the pile.The bearing performance of piles in karst cave has attracted much attention from scholars. Some analyzed pile’s characteristics using indoor tests, static load tests or through theoretical derivation16. Lee and Zhang carried out the influence of five factors of underlying caves on the bearing capacity of piles using indoor test, and the results showed that with the increases of roof thickness and cave migration position, the ultimate bearing capacity increases gradually and the size order of sensitivities is cave diameter, roof thickness and equatorial radius, polar radius, cave position19. Wang established the finite limit models to study the single piles bearing force with different roof thickness, the cave’s diameter and the eccentric center of caves and carried out the roof thickness of cave was the key factor20. Wong and Xie studied the applicability of different types of basements in karst areas and numerically simulated four key factors of caves under piles to require the bearing characteristics, and they found that the shaft resistance was enhanced by the increasing cave’s size22. Fattah and Zhao experimentally studied the ultimate bearing force of piles under changes of two sizes of caves and established the simply supported mechanical model to get the destroy mode of the roof, when the roof is subjected to punching, shear and bending and tensile failure25. These numerous studies were all about the bearing capacity of piles cross caves or on a cave, the calculate method of the safe roof thickness and the stability of caves under the piles. However, there was very few researches about the load transfer mechanism and the shaft resistance and tip resistance of piles cross karst caves.Dong and Jiang implemented the load-settlement laws of piles in karst area to analyze the changing of the bearing capacity of piles by static load test, and a new calculation method of safe thickness of the cave roof was obtained using theoretical deduction30. Therefore, centrifugal model tests were used in this study to analyze the vertical bearing performance of pile across cave and sensitivity of three parameters. In this study, the effects of the cave’s height, span, and number on the bearing characteristics of piles were investigated by centrifugal tests and a theoretical model. The vertical bearing capacity were obtained under different caves. Meanwhile, the load transfer characteristics were studied under different scenarios including the axial force, unit shaft resistance and ratios of two resistances. Sensitivity of the vertical ultimate bearing pressure to above factors were calculated by a theoretical model.Centrifugal model tests were shorter test periods, lower costs, and are convenient. Furthermore, the high accuracy of centrifugal model test results has been proved by many researchesThe results were transformed into units corresponding to the prototype pile according to the similarity ratio. There are two methods requiring the ultimate vertical bearing force of piles from load-settlement curve according to the standard. The first calculates ultimate vertical bearing force as the load corresponding to the sudden change settlement. The other method is to calculate the value of 3% of the pile diameter and the value of 40 mm, then elect the smaller one to regard as the failure settlement. The load needed to produce this settlement is the bearing capacity of piles when the settlement does not mutate. Because no abrupt settlement is apparent in Fig. When the height is 3 m, span is 3 m × 3 m, and number of the karst caves is one, the vertical bearing capacities of the piles are reduced by 4.1 MN, 1.8 MN, and 4.1 MN, respectively, compared to piles with no karst cave. This shows that, in all scenarios, the ultimate vertical bearing capacity of piles passing through karst caves will be reduced.As shown in Figs. PA is the axial force; Ap is cross-sectional area; Es is elasticity modulus; and ε is shaft strain.The shaft strain of pile foundations was obtained from the recorded data. Then the axial force on the pile foundations was calculated using Eq. :1\documeIn Fig. The trends in axial force experienced by piles in soil and rock and karst caves with varying spans are similar as shown in Fig. The trends of the axial force of piles in soil and rock are similar for the tests with different numbers of karst caves in Fig. PT is unit shaft resistance of pile; PA is axial force; n is strain gauges’ number, increasing from pile top to tip; h is height of pile element between adjacent components; and d is diameter of pile.Equation  were appFigure The unit shaft resistance of piles with five kinds of cave’s spans can be seen in Fig. 33. The portion of the pile within the karst cave had no contact with load-transferring material, and as such could not transfer the load into the surrounding rock via shaft resistance as the cave was empty. As shown in Fig. Figure Qis is the shaft resistance; Qui is the ultimate bearing force; and Qti is the tip resistance; i is the condition number.The tip resistance of the piles under the ultimate vertical load was obtained by fitting through interpolation. The shaft resistance could be calculated by Eq. . The ratAs shown in Fig. As shown in Fig. As shown in Fig. The ratios of shaft resistance of the piles passing through karst caves are obviously smaller than those that does not pass through karst caves. The main reason is that the void creates by a cave does not squeeze the piles passing through it, and as such does not exert shaft resistance on the pile.P) represents the vertical ultimate bearing force under the three factors, as shown in Eq.  for 5 min. The load was increased after one loading period ended, then the centrifuge was closed and cycled again at 100 g for 5 min. Data were collected once per second and transmitted to the data receiver.The centrifuge model test processes can be seen as follows Fig. .AccordinThe parameters that are manipulated included the height, the span, and the number of karst caves that interact with piles. There are twelve total experimental treatments, including one with piles without karst caves (control), four different heights , four different spans , and three different numbers of caves . When the karstic number is manipulated, the size of each karst cave layer is 3 cm × 6 cm × 6 cm (the height is 3 cm). The heights of the caves are measured in the axial direction of the pile. The spans of the caves are measured in two directions perpendicular to the axial direction of the pile.