In this paper, we analyze the influence of corruption perception, experiences of corruptive behavior, and healthcare autonomy on the public trust in Montenegrin healthcare, by surveying the general population before and after the global COVID-19 pandemic. By providing a quasi-replication of a previous empirical study of corruption and trust in the Croatian public healthcare sector, we introduce the COVID-19 pandemic as a new research context. Before the pandemic, we found a consistent and significant negative influence of the corruptive practices and the generally perceived level of corruption  on the trust in public healthcare. The emergence of COVID-19 had mixed effects: while there is a slightly higher effect of corruption salience to the preference of public healthcare, corruptive experiences still matter but are tolerated much higher than before the pandemic. Public assessment of the autonomy of the health system increases preference for public healthcare, both before and after the pandemic, although the emergence of COVID-19 somewhat lowers this effect. The obtained results point to the most significant challenges of the ‘post-COVID-19’ social context to public health policymaking and management of public healthcare institutions. These include focusing the public healthcare reforms on corruption, reducing waiting times for different diagnostics and medical procedures in the public healthcare system, and regulating the ‘dual practice’ . Corruption and public trust are the topics of choice when discussing the public sector and its legitimacy, as they drive the political and socioeconomic outcomes of the public sector’s functioning . In the However, another relevant issue has not been adequately discussed in the emerging literature: does the COVID-19 pandemic context make the citizens more tolerant of public healthcare corruption, which could lead to the severe (mis)uses of public trust under claims of addressing the crisis? Along with the lower availability of public healthcare services, as the system becomes overburdened with COVID patients, the implied and highly tolerated corruption could also lower the quality of public healthcare.This presents a powerful argument in favor of the empirical research of corruption and social trust in the public healthcare sector and the identification of factors potentially contributing to the change of public perceptions before and after the emergence of the COVID-19 pandemic. The social dynamics of public trust matter in times of pandemic, as the higher trust in the health care system correlates with the long-term acceptance of the public health mandates, such as avoiding unnecessary travel . As showIt could be expected that the same applies to the case of the COVID-19 pandemic. In addition, it would be most helpful to identify the potential predictors of such patterns, which has not been done in the extant literature.We chose to address the research question of how the perceived level of corruption , the experience of corruption, and the perception of the public healthcare system’s independence from political/government pressures  affect the trust in the public healthcare system. The dynamics of the distrust in the healthcare system have been linked to poor governance and politically influenced decision-making, especially related to investments in healthcare infrastructure, equipment and pharmaceutical products . TherefoThis research is significant for theory-building and relevant for policymaking and medical practice. In our research arena, located in the South East European (SEE) region, other studies have pointed to corruption as one of the primary public health concerns –11. BeyoIn this paper, we analyzed data from two periods-before and after the emergence of COVID-19-on a nationally representative sample of adult citizens of Montenegro. We found a considerable increase in corruption salience and corruptive practices in healthcare in the post-COVID period. There are also significant differences in how medical autonomy and corruption influence the public trust in the healthcare sector before and after COVID-19. In the pre-COVID period, the conventional view of medical autonomy as increasing and the corruption as decreasing the public trust in healthcare are empirically confirmed. In the post-COVID period, the general level of perceived corruption in the public healthcare sector still reduces public trust, while the actual corruptive practices are more tolerated. The public perception of medical autonomy does not significantly influence public trust. While the doctors and the nurses could have been applauded for their contributions to public health, such public acts of support did not make any real change to the healthcare system.The empirical results are believed to be essential for public policy and management of public healthcare in Montenegro and other developing countries, which will be further analyzed in the discussion section of this study.In their meta-analysis of the potential policy interventions, Gaitonde et al.  define cDifferent stakeholders could be involved in the corruptive practices in the healthcare sector, although the generic ones include the insured citizens/patients; service providers; payers–whether public or private; regulators and other relevant government entities; and drugs/equipment providers . AlthougCorruption is one of the vital issues negatively impacting the global health outcomes, as it might completely discourage citizens from seeking healthcare services or lead to an informal ‘two-tiered’ system within the public healthcare sector , especiaThe adverse outcomes of corruption are confirmed by empirical results, linking its level to health outcomes and other quality of life indicators. In European countries, with a higher level of corrupted health systems and lower levels of income, health for citizens older than 50, in terms of chronic diseases, is significantly worsened . The heaPublic trust in institutions can be defined in terms of how citizens perceive social institutions’ work, compared to the widely shared normative expectations , 30. It As Radin  argued, Regardless of the causal direction, an association between trust in institutions and corruption is based on a strong coupling of perceptions related to the social acceptance of corruption and the legal systems’ and public institutions’ lack of legitimacy . SupposePublic trust is critical in crises, such as the pandemic of the COVID-19 caused by the novel coronavirus. High levels of social cohesion, denoting a high level of trust in institutions, lead to more effective solutions to crises, including health crises. This is demonstrated by the high-trust societies reaching the inflection point of the COVID-19 infection curve more quickly than the low-trust ones . High trIn addition, in crises, including the emergence of COVID-19, public spending is heavily increased. In the case of the pandemic, it is required to procure drugs and equipment and alleviate economic consequences caused by the closures of businesses and lost jobs and incomes across multiple economic sectors –44. As eBoth causal paths of the public trust-corruption relationship provide opportunities to develop negative scenarios during the pandemic crises. With a view of public trust in institutions as a cause of corruption, there could be an initial strengthening of public trust as the government takes the first steps to improve the existing situation. However, this initial impulse seems to wear off quickly if the public expectations are not met in the long term. Only consistent policy choices and government response matter to increase trust and reduce the threat of corruption during the crises , 47. On This study aims to assess the empirical relationships between public trust in institutions, the autonomy of the healthcare system, and healthcare corruption—including corruption perceptions and the experience of corruptive behavior in public healthcare before and after the COVID-19 pandemic. The research design replicates a previous study on public trust and healthcare corruption in Croatia, using the elections as its social context. To achieve such an objective, we added the items used by Radin  and the Following the recommendations by Bettis, Helfat & Shaver , our appPrimary data have been collected by using a nationally representative public opinion survey on the general population of Montenegro. Although public opinion can be shaped by media and powerful social actors’ narratives , there aWe use logistics regression for statistical analysis, following the choice of methods in the original study  and its The public healthcare sector in Montenegro comprises a network of healthcare institutions matching the country’s demographic parameters. The network consists mainly of state health institutions and a few private health institutions.The network of public (state-owned) health institutions consists of 18 health centers on the primary level. The Public Health Institute provides services of primary health protection. There are eight hospitals—providers of comprehensive healthcare services. In addition to general and special hospitals, hospitals that provide health care at the secondary and tertiary level are Codra Hospital, Tesla Medical polyclinic in Berane, and the Clinical Center of Montenegro. The Emergency Medical Service provides emergency medical care at the primary level, while the Office for Blood Transfusion covers the transfusion activities. The state-owned company, the Pharmacies of Montenegro “Montefarm,” regulates the field of medicines (and other pharmacies that have signed an agreement with the Pension and Insurance Fund). At the same time, “Rudo Montenegro” supplies medical and technical devices .The system is relatively centralized: most public health institutions’ managers are appointed and dismissed by the Minister of Health .Funding is entrusted to the Health Insurance Fund of Montenegro, an independent financial institution for health care funding and the exercise of other rights related to health insurance. Despite the health system relying predominantly on public health facilities, citizens would prefer the private sector if given an option. Although the market share of public health institutions is dominant, private health institutions position themselves by providing specialists’ services (28.4% of the market). The only area where private health institutions record a lower user rating compared to public health institutions is the cost of services .The latest available report of the European Health Consumer Index–EHCI ranked the health system Montenegro in the twenty-third position out of thirty-five. Despite the shortcomings, the waiting time for examination in public health institutions is not excessive. As many as 82.5% of users of health institutions say their appointment with chosen physicians is made within less than a week. Moreover, citizens of Montenegro rate their general satisfaction with the health system with a high mark . However, many physicians leave the public health system, move to other countries, or get employment with privately-owned health providers. In the context of this study, it should be noted that, due to the lack of personnel and identified problems in the system , physicians in the public sector often work extra hours in private health institutions as a part of the ‘dual practice’ .Due to the quasi-replication research design, preference for the public over private healthcare service was adopted as a dependent variable from the original study conducted by Radin . Her argThe described choice of measuring public trust in  institutions is not without limitations since not everyone might not have the means to afford private healthcare services. However, we used an unambiguous wording for the survey item: ‘If I could choose, I would prefer to obtain the treatment in…’ . Respondents’ preference is based on the trust in the public (or private) healthcare sector, rather than the ability to pay or some other factors, limiting the actual choices of healthcare facilities in everyday life.Several independent variables were used: salience (perception) of corruption in the public healthcare sector, demands for illicit payments (bribes), being diverted/referred to the private practice of a health provider, engagement in ‘dual practice,’ and the perception of public healthcare autonomy.Formulations of survey items for all variables can be found in the supporting files–in their original form and English translation.Some of those are adopted from the original study , which uAn additional independent variable of being diverted/referred from public to private healthcare provided was introduced to capture a practice that might not be recognized as corruptive in the current social context. The involuntary choice of private healthcare provider  has already been discussed in the introduction section, as well as reflected in our wording of the survey item: ‘Have you ever experienced a situation, in which a physician, employed at a public healthcare facility, refers you to a specific private clinic, to obtain a paid service, which should be available for free at a public facility?’. It should also be mentioned that the unrealistic waiting times for public healthcare services  further The perception of public healthcare autonomy has been introduced to capture the public evaluation of the healthcare professionals’ skills and competencies , as oppoBased on the original study  and the H1. Both corruption salience and experiences negatively affect trust in the public healthcare system.H2. Perception of healthcare providers’ autonomy positively affects trust in the public healthcare system.H3. The emergence of the COVID-19 pandemic introduces new empirical patterns into the relationship between trust and corruption in the public healthcare system.Computer-Assisted Personal Interviewing) method. Data has been collected by trained interviewers, using the tablets for data input, allowing for simultaneous storage on a remote server and control of the process in real-time. The sampling frame was constructed using publicly available data on the number of registered voters in different districts. We used a two-stage random sampling design stratified by voting districts. The sample size equals 1,769 citizens aged 18 and over. The selection of respondents within each stratum has been performed using a random selection algorithm, with the strata size reflecting the size of the adult population of each district. The data was collected in 180 Montenegrin voting districts, thus guaranteeing national representativeness. For this sample size and the total population of Montenegro of 620,739, the confidence interval of 95%, with an incidence of 50%, equals ± 2.33%.Two waves of data collection were performed for this study, with the same research instrument used to ensure the longitudinal comparability of empirical results. In the first round, i.e., before the COVID-19 outbreak, data were collected through personal interviewing, from May 24 to June 15, 2019, using the CAPI  based on the regions , gender, and age. As both samples had the same number of randomly selected male and female respondents and the same number of respondents from different age groups and three Montenegrin regions, the principle of nationwide representation, according to the criteria of gender, age, and place of residence, is satisfied.Given that the target population in both samples consists of Montenegro residents aged 18 and older and that we use the same sample size as a starting point, the estimated parameters obtained from the samples are comparable.The study, data collection, and statistical analysis methods were reviewed and approved for compliance with ethical standards of the University of Montenegro–Faculty of Economics. The practice of faculty administration in this matter includes the review of the objectives of empirical research, the nature of data collection, and the private information collected (if any), leading to the decision to (dis)approve the planned survey and the research design. In both waves of research, participation was entirely voluntary and anonymous. Our survey(s) did not include any opportunities to identify the individual responses and link them to the respondents’ identities. Answers to demographic data, which were asked from the participants, were optional. A written introduction, uploaded on a tablet device, was shown to the participants before the beginning of interviews in the first wave of data collection. The same introduction has been placed as the first (Web) page of the Internet-based survey in the second wave of data collection. It consisted of statements related to the data collection policy, management of demographic data, and the guarantee of anonymity and the cumulative  reporting of research results.Since no stratification has been applied to the education and income groups, the post-Covid survey, performed entirely online, is somewhat skewed toward the higher income brackets and highly educated individuals. This is a limitation of the research, which logically follows from the availability of Internet access and information technology skills required to fill in the Web-based questionnaire.Descriptive statistics of the public trust and the perceived corruption in Montenegrin public healthcare are presented in After the COVID-19 emergence, provider preference has changed slightly toward private healthcare facilities. The corruption salience and the illicit payments made show a higher level of perceived corruption after COVID-19. Regardless of why the service has not been performed in a public facility, referrals from the public to the private sector have risen significantly. In contrast, the perceived autonomy of public healthcare seems to be rising, as well, after COVID-19.Interdependence of corruption salience and corruptive experiences, including diverting patients to private healthcare facilities, can be confirmed for the pre-COVID period by the simple linear correlation results, showing a modest but significant positive association (at the 0.01 level). On the other hand, medical autonomy proved to have a slight negative association with both salience and experiences of corruption, which was also significant at the 0.01 level. In other words, respondents reporting greater perceptions of corruption were also more likely to report being asked to provide illicit payments (bribes) or to state they were diverted from public to private healthcare providers. Respondents reporting higher levels of the public healthcare autonomy were, simultaneously, less likely to report both perception of corruption and the experiences of corruptive behavior. The same pattern could be observed in the post-COVID survey, although linear association strength proved somewhat higher.In analogy with Radin , we perfA range of interesting conclusions can be drawn from the empirical results of the pre-COVID survey see . Female As expected, Model A indicates that an increase in corruption salience for one unit  decreases the odds of preferring public healthcare by 1.096. Model B results show that providing illicit payments to healthcare staff decreases trust in public healthcare: an increase of experience related to providing illicit payments, for one unit, decreased public healthcare preference by a factor of 2.544. Experiencing diverting from public to private healthcare facilities as a result of the ‘dual practice’ system also has negative implications for public trust, although somewhat less severe than the illicit payments. Namely, for each unit of the increasing experience of this issue by the general public, public healthcare preference decreases by a factor of 1.675.In both models, one unit of increased perception of medical autonomy by the general public  increased public healthcare preference by 1.291 (Model A) or 1.319 (Model B).Unlike Radin , for herWe used the same two binary logistics regression models in the post-COVID survey see . The difAfter the emergence of COVID-19, the consistent influence of all demographic variables on the public healthcare preference can be observed: female respondents, as well as those, who are younger, more educated, and wealthier, have an increased odds of preferring the public healthcare system. Patterns of corruption influence on public trust have not changed. There is ample empirical support for the influence of corruption salience on the preference of public providers, as a salience increase for one unit decreases the odds of preferring public healthcare by 1.36 (Model A). An increase in experience related to providing illicit payments, for one unit, decreased public healthcare preference by a factor of 1.66. In comparison, one unit of increased experience related to diverting from public to private healthcare facilities decreased public healthcare preference by 1.41 (Model B).Even after the COVID pandemic, there is consistent support for hypotheses H1 and H2 since public healthcare preference is increased by 1.126 (Model A) or 1.180 (Model B) for each unit of increased perception of medical autonomy.Comparing the empirical results before and after the emergence of the COVID-19 provides empirical support for hypothesis H3, as the corruption salience has a more significant effect than before. It is somewhat surprising that the corruption experience, both in terms of providing illicit payments and being diverted to private healthcare facilities, has lower effects on public trust than before the emergence of COVID-19. Although we have not directly measured the tolerance of corruptive behavior in the public healthcare system, the fact that people reporting their own experiences of corruption have a higher trust in the public healthcare system could be interpreted in terms of a higher tolerance of corruption.Simultaneously, after the emergence of COVID-19, there is a lower influence of the perception of medical autonomy on the trust in the public healthcare system.Although somewhat paradoxical, the empirical results support all three hypotheses and create an excellent background for their discussion in the next section.Our research takes place in the public health system of Montenegro, which shares many similar characteristics to the other SEE public health systems.Comparative results of research conducted in 2012 and 2019 suggest that the level of corruption in the health system of Montenegro is at a similar level in both periods. While as many as 11.5% of Montenegrin citizens claimed in 2012 that there is no corruption in health care , only 5%Descriptive statistics show that the pandemic fuels the rise of both illicit payments and the ‘dual practice’-driven diverting of patients toward private facilities, where public healthcare employees earn personal income. In the post-COVID period, increased corruption, both in terms of its salience and the actual experiences of corruptive behavior, still decreases the public trust in the public healthcare system. Still, this effect is much lower than in the pre-COVID period. These empirical results lead to the point that the corruptive window of opportunity is created by the weakness of public healthcare systems in developing countries to simultaneously accommodate many inflowing COVID-19 patients and provide quality care to the existing patients. In such a situation, it is straightforward to divert the patients, ready to provide out-of-pocket payments for the healthcare services, from public to private healthcare facilities. In a ‘dual practice’ system, this could be perfectly legal but with disastrous effects on the public trust for patients with pre-existing medical issues. We do not consider the government response to COVID-19 in this context, where private providers could be integrated into the pandemic response to meet the limitations of the public sector. We are, instead, considering the availability of medical services to the existing patients. They seem to be denied medical service since the pandemic response overwhelms the public healthcare system. In such a situation, patients with pre-existing and acute conditions might have no choice but to provide illicit payments to public sector physicians or use the private healthcare service providers.Our empirical results support the hypothesis of the negative relationship between corruption and trust in the public healthcare system. However, the COVID pandemic makes this effect even more prominent regarding a higher tolerance of corruptive behavior. Those results could even be interpreted in terms of citizens feeling the lack of realistic, non-corruptive choices when obtaining health services during the pandemic.As previously mentioned, linkages between inefficient public healthcare governance and pandemic responses have already been studied . HoweverFrom this viewpoint, our empirical results could be compared to the previous research in the same geographical region conducted by Radin  in her 2It could also be argued that the private healthcare facilities in the SEE region rarely provide services aimed at treating acute conditions, which was the case with the COVID-19 pandemic. They tend to focus on less risky and complex diagnostics/procedures, which require long waiting times in the public healthcare system. Therefore, some corruption in the ‘dual practice’ system could even be seen as a way of securing long-term relationships with the staff of the public healthcare system, perceived as ‘gate-keepers’ to complex, life-saving medical procedures.This study, based on two nationally representative samples of Montenegrin citizens (before and after the COVID-19 pandemic), confirmed that both corruption salience and experiences negatively affect the trust in the public healthcare system (H1). It was also confirmed that the perception of healthcare provider autonomy positively affects public trust in the healthcare system (H2). Finally, the longitudinal nature of the study revealed that the outbreak of the COVID-19 pandemic had introduced new empirical patterns into the relationship between trust and corruption in the public healthcare system (H3).Empirical findings suggest a significant increase in the salience of corruption in public healthcare after the COVID-19 pandemic, which also applies to the experience of corruptive practices. The percentage of the general population that prefers the public to the private health care system decreased from 32.9% to 30.7%. Our results also suggest that the corruption salience after the pandemic had a more negative impact on trust in the public health system than before the pandemic. However, after the emergence of COVID-19, the negative impact of illicit payments on public trust has been reduced, along with the negative impact of referring patients to private health facilities by medical doctors from the public health sector.These findings lead to some recommendations for public policy and management of public healthcare institutions. Anti-corruption efforts should focus on the future reforms of public healthcare systems in Montenegro and the rest of the SEE region. Special attention must be paid to the regulation of ‘dual practice,’ which contributes to medical service availability in the context of long waiting lines for different procedures in public healthcare. Still, it raises concerns about hidden corruption, i.e., referring patients to specific private clinics and using the same medical staff, who previously made it difficult, or impossible to obtain service at a public healthcare institution. At the level of individual public healthcare institutions, the waiting times for different diagnostics and procedures should be analyzed and reduced, along with the (re)consideration of the permissions to the medical staff to engage in additional work in private clinics, as a part of the ‘dual practice’ patterns.There are several limitations of the study. Firstly, our intention to replicate a previous study  indirectIn addition, its results are based on data obtained from a single, small European country, with the discussion based on the previous studies in the same, culturally homogenous region. The emergence of COVID-19 could have also influenced the attitudes and perceptions of the Montenegrin general population in the ways that still need to be recognized and described. Therefore, it would be helpful to further replicate the described research design in different and culturally heterogeneous social environments and recognize fundamental mechanisms influencing the social dynamics during the COVID-19 pandemic.S1 File(XLSX)Click here for additional data file.S2 File(XLSX)Click here for additional data file.S3 File(DOCX)Click here for additional data file.S4 File(DOCX)Click here for additional data file.


This paper presents a method for extracting novel spectral features based on a sinusoidal model. The method is focused on characterizing the spectral shapes of audio signals using spectral peaks in frequency sub-bands. The extracted features are evaluated for predicting the levels of emotional dimensions, namely arousal and valence. Principal component regression, partial least squares regression, and deep convolutional neural network (CNN) models are used as prediction models for the levels of the emotional dimensions. The experimental results indicate that the proposed features include additional spectral information that common baseline features may not include. Since the quality of audio signals, especially timbre, plays a major role in affecting the perception of emotional valence in music, the inclusion of the presented features will contribute to decreasing the prediction error rate. One such practical application is improving human-robot interaction (HRI) quality with social robots. A robot can perceive the emotional state or mood of a user not only via the facial expressions of the user but also the types of music the user is listening to. The robot can then also recommend the user with a song according to the mood of the user or other contextual conditions  ,2.Emotions are expressed through music via many different musical characteristics. For example, different chord progressions are used in different musical genres and also associated with different emotional effects. At the same time, different songs with the same chord progression may have different emotional effects due to the different arrangements of musical instruments. For example, a rock version of Mozart’s Symphony No. 40 may be perceived differently in terms of emotions from the original version.Although each musical instrument has a unique timbre, it is very hard to separate individual instrumental sounds from a whole polyphonic mix of music. However, since a polyphonic signal has a specific spectral shape of its own , it has Since the sinusoidal transform coding (STC) method has been successful in modeling the spectral characteristics of audio signals –7, a STC2.In this work, the 1000 Songs Database .Two emotional dimensions, valence and arousal, are labeled in the range of , and the average sampling frequency of the annotation was 4.3 Hz. For the latest version of the database, the developers further resampled the annotation time series to 2 Hz sampling frequency. We have processed the continuous labels from annotators of the songs and averaged over each time window from the database. .3.One of the popular feature extraction toolkits for speech and audio analysis and classification is Technical University of Munich’s (TUM) open-source feature extractor (openSMILE) . The tooOnce the LLDs are calculated, supra-level features are calculated and used for training classifiers and regression models. The supra-level features are characterized by regression and statistical measures to model the trajectories of the LLDs over time whose duration is much longer than the length of the window used for the LLD calculations .In previous work , it was Deep CNNs could also act as a feature extractor for MER. The embedding vector is extracted by CNNs and a fully connected layer on top of the model is used for predicting different classes. In this study, the deep CNNs are the pre-trained models and transfer learning is utilized for our target task.3.1.In speech processing, a linear-predictive coefficient (LPC) is commonly used to model a spectral envelope, also known as a formant. However, it is not so trivial to find the spectral envelopes of musical signals due to their polyphonic nature. Because the spectral characteristics of high frequency content can be precisely represented using sinusoidal transform coding (STC) –6, a metmth analysis frame are then represented as follows:Ak(m) and fk(m) are the k-th amplitude and harmonic frequency at m-th frame, and no;k)((m) is the onset time of its corresponding k-th components Ak(m) and fk(m) , which are mapped onto a 2D-plane of arousal and valence. Some generated sample images from each class are shown in Several pre-trained deep networks were evaluated for classifying the spectrogram images. The purpose of using different deep networks for this study is to developdeveloping a guideline for choosing a deep learning model in future research. The present study aims to determine the better performance model for our target task, so all the hyper-parameters, optimizer, and loss function of the deep learning models are set to be the same. We set the training epochs to 60, and introduced the stochastic gradient descent optimizer to train the network, and used the cross-entropy function to evaluate the loss. For the reason that the deep models we used in this study were pre-trained on the ImageNet dataset which is not similar to our target dataset, we freeze all the layers of the networks and only train the last fully connected layer to avoid overfitting. As shown in 5.To enable fast and reliable emotion detection from music, the spectral features were extracted based on a sinusoidal model and evaluated for predicting the levels of arousal and valence in music. Since the extracted spectral features were designed to characterize the quality of audio signals such as timbre and harmonicity, an improvement in prediction accuracy was obtained as expected. When each feature set was tested separately, the STC-based feature set alone was not as effective as the baseline feature set; however, additional resolving power was revealed when the two feature sets were combined. The results indicate that the STC-based features include spectral characteristics that the baseline features may not include.We also applied the recent deep learning methods for classifying different emotional states based on the spectrogram images mapped onto the 2D domain of arousal and valence. The results were improved by employing the most advanced deep learning network structure combined with the spectral data extracted from music. However, in this study, only spectral features from short-time window were considered to classify the emotional states. An improvement in classification accuracy could be expected by introducing neural networks capable of learning memory-based relations in the time domain, such as the long short-term memory (LSTM) networks. The input of the LSTM would be a sequence of spectral features and the network output context vector will be used for classifying emotional states, and we aim to further analyze the implication of deep learning techniques in enhancing real-time affective audio perception.


Tool condition monitoring can be employed to ensure safe and full utilization of the cutting tool. Hence, remaining useful life (RUL) prediction of a cutting tool is an important issue for an effective high-speed milling process-monitoring system. However, it is difficult to establish a mechanism model for the life decreasing process owing to the different wear rates in various stages of cutting tool. This study proposes a three-stage Wiener-process-based degradation model for the cutting tool wear estimation and remaining useful life prediction. Tool wear stages classification and RUL prediction are jointly addressed in this work in order to take full advantage of Wiener process, as this three-stage Wiener process definitely constitutes to describe the degradation processes at different wear stages, based on which the overall useful life can be accurately obtained. The numerical results obtained using extensive experiment indicate that the proposed model can effectively predict the cutting tool’s remaining useful life. Empirical comparisons show that the proposed model performs better than existing models in predicting the cutting tool RUL. Cutting tool plays an important role in the machining system and its wear causes an increase in friction and heat generation in the machining process. Wear of cutting tools not only affects the quality of machined surface and the machining precision but also results in increasing machining cost. Moreover, unnecessary tool replacement that aims at preventing the decrease in surface quality will increase the downtime and machining cost in high-speed milling. Tool condition monitoring can be employed to ensure safe and full utilization of a cutting tool. Hence, the remaining useful life (RUL) prediction of a cutting tool is an important issue for an effective high-speed milling process-monitoring system.In the past few decades, various studies have been devoted to predicting the cutting tool RUL in both academia research and industry. According to the preliminary research, these studies were developed based on the consideration of physics-based and data-driven models. The Taylor model  and the Although these aforementioned methods appear to obtain not so bad RUL estimation results, it is still difficult to describe the nonmonotonic dynamic characteristics of system. Fortunately, the Wiener process has shown to be the optimal degradation process modeling tool for explaining the physical behavior of a dynamic system, due to its excellent mathematical properties and physical interpretations . GhorbanThe above research studies ignore the mechanism of degradation and regard it as an overall process. However, the degradation process  exhibits multiple stages characteristics in practice due to the environmental working condition, internal materials and so on. Lim et al.  proposedAccording to the literature review given above, the aim of this study is to develop a three-stage Wiener-process-based degradation model that can predict the tool’s remaining useful life in high-speed milling processes. First, the time domain, frequency domain and time–frequency domain features are extracted from raw sensor data , and then the stacked denoising autoencoder (SDAE) is utilized to automatically select the most relevant features. Second, tool wear stages and corresponding wear value are estimated with the extreme learning machine (ELM). Third, the degradation process of each wear stage is established based on Wiener process and the overall useful life is estimated with the stage RUL prediction. Additionally, multi-source variabilities  are considered and quantified in the modeling process of each stage, which helps describe the physical behavior of tool wear process more precisely and significantly improves the accuracy of RUL prediction.In most existing research studies, the degradation mechanism was assumed as stationary over the entire life of a cutting tool, which was characterized with a fixed model. However, the degradation process of a cutting tool exhibits multiple-stage characteristics in practice due to the environmental working condition, internal materials and so on. It can be seen from Motivated by this phenomena, three models were developed to characterize the features into different stages. It can be seen from In practice, the wear process of a cutting tool usually exhibits a stochastic behavior with nonlinearity and multiple variability sources. The Wiener process has proved to be effective in characterizing the degradation signals due to its great mathematical properties. In order to quantify the multi-source variabilities  and characterize the degradation process of each stage, a three-stage Wiener-process-based model considering multi-source variabilities was proposed in this subsection.Let To define the lifetime and predict the RUL, a concept of first hitting time (FHT) is adopted. According to the concept of FHT, the lifetime Usually, the degradation state of a cutting tool cannot be measured directly, but formulated with the health indicator (HI) generated from the observable sensor data. The relationship between degradation state and HI can be expressed as follows:After the Kalman filter algorithm, RTS is used to obtain the optimal estimation of the preceding conditional expectations. The smoothing algorithm is summarized as follows in The RUL prediction framework is presented in this section and the overall architecture of this framework is depicted in Feature extraction is conducted to reduce noise interference and remove irrelevant signals from the original signals. Statistical features in the time domain and frequency domain are extracted from force signals, vibration signals in each direction  and acoustic emission signals. In total, 16 kinds of time domain features namely mean, standard deviation, variance, peak value, peak to peak, root mean square error (RMSE), skewness, kurtosis, kurtosis factor, average absolute value, shape factor, crest factor, impact factor, margin factor, skewness factor and bias factor are extracted from seven channels, respectively. A total of 112 features can be obtained and these features are listed in Eight frequency domain features are also extracted from raw sensor signals. These statistical features are listed in The wavelet packet decomposition (WP) is a kind of time–frequency domain analysis tool and is propitious to analyze the non-stationary and time-varying signal. It can decompose the raw signal into multiple levels and each level consists of several frequency bands, in which abundant information can be obtained. In this study, three channels of force, three channels of vibration and one channel acoustic emission signals are decomposed into seven levels by WP. The energy of a signal can be expressed as Equation (11), in which fficient . The sumIn total, 175 features are extracted in Current wear stages are determined and health indictor is constructed based on the feature vector. Conventionally, this step can be conducted with a machine-learning-based or deep-learning-based algorithm. In this subsection, we adopt ELM to perform the classification and regression task, while other intelligent algorithms  can also be used as an alternative. ELM was first proposed by Huang in 2006  and thenThen the probability The objective function of Equation (16) can be rewritten asFinally, probabilistic outputs In this subsection, the initial parameters of the proposed model are first estimated with the historical sensor data and wear label and then updated online with the new sensory data. Benefit from the offline estimation, the parameters that update by our algorithm can converge quickly and obtain remarkable performances.According to the proposed three-stage mode in Supposing there are For the convenience of calculation and simplification of expression, we define two intermediate variables Then, the log-likelihood function can be expressed as:To estimate the parameters Then the estimated parameters The log-likelihood function of parameters Furthermore, the estimation parameters Substituting the model parameters and omitting the variables that are unrelated to the estimated parameters, we can obtain the expectation of log-likelihood function.Then, the estimation procedure consists of two steps: expectation step (E-step) and maximization step (M-step).E-Step: Calculating the expectation of log-likelihood function based on the Then M-Step: Calculating the parameter Equation (30) can be divided into two parts:The parameters After the model parameter estimation, the overall lifetime and remaining useful life to a specific moment and their corresponding PDFs can be obtained.PDF of lifetimeThe PDF of lifetime can be described as follows:PDF of RUL up to Model parameters, underlying wear state In this section, the proposed tool wear model is demonstrated with a practical experimental study based on the dataset from the 2010 Prognostic and Health Management (PHM) competition  .In the conducted experiment as shown in In this study, to obtain the most representative features, the selection of node sizes in the SDAE was researched. The node number of the hidden layer was chosen from 10 to 160 with the interval of 10 in the first DAE and from 5 to 50 with the interval of 10 in the second DAE, respectively. Given different combinations of node sizes, the pre-classify accuracy results can be obtained and presented in In this study, each group of experiment data describe the whole wear process of a cutter and can be divided into three stages according the to the Taylor tool life curve . We randParameters of the proposed three-stage Wiener-process-based model were estimated with the experimental data. The key model parameters of each stage are list in (1)Stage-1(2)Stage-2(3)Stage-3The whole life of each cutter is 315 cutting passes and each cutting pass lasts four seconds. RUL prediction result of three cutters with our proposed model and three other models are present in To further investigate the superiority of the proposed three-stage Wiener-process-based degradation model, the PDFs of RUL at different wear stages are calculated. Take Cutter #1 as an example, In order to compare the proposed three-stage model with other models more clearly, the prediction errors are calculated and the error result of Cutter #1 is present in To quantitatively compare the RUL prediction accuracy between the proposed model and the other three models, we list the mean square error (MSE), mean absolute error (MAE) and coefficient of determination ((1)MSE(2)MAE(3)To further explore the inherent reasons for the performance gap between the proposed model and the other three models, a comparative study is carried out. PDFs of Cutter #1 were calculated with different models. This study proposes a three-stage Wiener-process-based degradation model for the cutting tool wear and remaining useful life prediction. Taking full advantage of the Wiener process to describe the degradation processes and ELM to classify tool wear stages, joint implementation of tool wear stage classification and RUL prediction is carried out. Moreover, considering multi-source variabilities in the modeling process of each stage, the proposed model can describe the physical behavior of the tool wear process more precisely and significantly improve the accuracy of RUL prediction. The numerical results obtained using extensive experiments indicate that the proposed model can effectively predict the tool’s remaining useful life in high-speed milling processes. Empirical comparisons show that the proposed three-stage Wiener-process-based model performs better compared to existing models in predicting the tool’s RUL while also providing the analytical form of the RUL distribution that is very useful for the health management of the cutting tool.Although the experimental studies in this study show that our model can accurately predict the RUL and estimate the wear value of the cutting tool, there are still several issues that need to be studies further. Firstly, the three stages of a cutting tool are assumed mutually independent, which leads to the saltatory prediction result at the boundary of different stages. Therefore, the correlation between different stages needs to be considered. Secondly, we mainly concentrate on the gradual and continuous wear process of a cutting tool; however, the sudden failures of the cutting tool  also need to be considered in the practical application. It is worth pursuing this research direction in our future work.


In this article, the authors describe the 1-stage surgical technique that has been used by the senior author since 1990 for all his primary grade 2 and grade 3 augmentation-mastopexies. The article provides a safe, simple, and reproducible approach to a challenging procedure, one that tends to be the most litigious in aesthetic breast surgery. The key points of this technique are simple preoperative markings; the augmentation is performed with a true submuscular placement of smooth implants; and the mastopexy is performed with an inferior pedicle technique with unlimited skin flap undermining and no limitation of nipple elevation. Seventy-eight consecutive cases of augmentation mastopexy performed since 1999 by a single surgeon (V.S.) using the same technique were reviewed. The age range was 26-62 years old; the range of implant volume was 150-375 cc; and the follow-up time period was from 1 year to 22 years. After an extensive patient case review, the authors enforce true extended submuscular augmentation (TESMA) as a reliable augmentation technique that can be used as the first procedure in any grades 2 and 3 ptosis, 1-stage augmentation-mastopexies including bariatric cases. The authors believe that the split inferior pedicle for the mastopexy in combination with the TESMA is a breakthrough approach that eliminates the second stage for any augmentation mastopexy procedure. No major complications such as nipple necrosis, implant bottoming, malpositioning, or extrusions were observed. It is a safe, simple, and reproducible procedure.  In our view, the augmentation-mastopexy is a procedure that has been plagued by the notion of the opposing forces resulting from the combination of the 2 procedures.3-11 The problem originates from the persistent use of the dual plane,12 subglandular, and subfascial13 augmentation as part of the procedure which is then combined most often with a superior pedicle flap for the mastopexy.14-16 When these types of augmentation are used, the implant lacks muscle support at the inferior pole, and, therefore, the “gravity effect” of the implant opposes the intended mastopexy lifting effect. This process creates the “opposing forces” of the augmentation and the mastopexy, which contributes to results that are not long-lasting, early postoperative complications, reoperations, and technically difficult problems to solve. These problems can be circumvented by preserving true muscular coverage at the inferior pole. By supporting the implants with a true submuscular pocket at the inferior pole, the mastopexy is performed using an inferior pedicle that allows wide undermining without any vascular compromise and excellent parenchymal redistribution. The inferior pedicle in combination with the muscular closure of the augmentation gives additional tissue coverage for the implant at the inferior pole eliminating the possibility of the implant extrusion and development of a low double bubble (LDB).Since first described by Gonzalez-UlloaThe “split inferior pedicle” technique was developed by the senior author (V.S.) in 1990. The technique consists of a combination of a true extended submuscular augmentation (TESMA) followed by an inferior pedicle mastopexy. The pedicle is split transversely by the augmentation incision and, therefore, is referred to as a “split inferior pedicle.”17 for all his primary augmentations but then progressed to developing an inferiorly based muscle cuff for full muscle coverage which he refers to as a TESMA. This technique is done strictly only through the inframammary fold (IMF) approach.18 It allows a wide range of implant sizes to be used and provides long-lasting natural results in all his primary augmentations. With an unwavering commitment to the TESMA technique, and striving to perform a safe and long-lasting 1-stage augmentation-mastopexies, he developed the “split inferior pedicle” technique. For over 30 years, the “split inferior pedicle” augmentation mastopexy has been proven to be safe, reliable, and reproducible with long-lasting results without experiencing any major complications such as nipple-areola complex (NAC) necrosis, implant bottoming, malpositioning, or extrusions.4-11The senior surgeon originally performed submusculofascial augmentations as described by Bostwick,19 regarding the ethical treatment of human patients in research were followed. The only exclusion criterion for the mastopexy is the history of any previous breast surgery including biopsies. The follow-up range of the study is 1 to 22 years, and the age range was 26 to 62 years old  smooth round moderate and moderate plus silicone implants. The size of the implant is limited only by the need for complete muscle coverage and in our practice ranges from 150 to 375 cc (μ = 270 cc).The preoperative markings  consist 23 original true submuscular technique.There are 3 variations of submuscular breast augmentation: the submusculofascial, dual plane, and TESMA. The submusculofascial and dual plane techniques can be done either by IMF or by periareolar access . The TESIn the Wise pattern, the augmentation incisions correspond transversely at the base of the inferior pedicle, therefore creating a “split inferior pedicle.”With the patient in the upright position, the implants in place, and the augmentation incision closed to the subcutaneous level, the Wise pattern is drawn with 7 cm vertical limbs . The NACThe procedure to be performed is an inferior pedicle mastopexy with unlimited undermining of flaps and elevation of the NAC as it is typically done with a breast reduction . We elecThe de-epithelialized inferior pedicle is then plicated to a total vertical length of 6 cm marking horizontally 3 cm from the areola and 3 cm from the IMF . The pliA total of 78 patients were reviewed. From 1990 to 1999, another 52 patients were lost to follow-up due to the relocation of our practice from Florida to Greece and were not included in the study , 1 mastopexy hematoma (1.28%), 4 superficial “T” point sloughings (5.13%), 6 marginal areoral sloughing (7.69%), and 14 minor scar revisions under local anesthesia (17.95%).The procedure described is an inferior pedicle mastopexy with unlimited undermining of flaps and elevation of the NAC with the use of smooth round implants of any size that can be covered completely by muscle. The procedure is versatile and is used for all primary grades 2 and 3 ptosis.As we discuss the procedure, a reference to the augmentation needs to be further analyzed. The TESMA augmentation should not be done by the periareolar approach for 2 reasons. Firstly, by using the periareolar approach and dissecting through the breast tissue, the viability of the flap is compromised. However, by using the IMF approach, the surgeon is able to bypass the breast tissue during the augmentation; therefore, the attachment of the breast to the pectoralis major muscle and the perforators to the NAC remain undisturbed. Secondly, with the IMF access, the inferiorly based muscle cuff is easily developed to provide complete muscle coverage at the inferior pole.The complete muscle coverage is achieved by suturing the inferiorly based muscle cuff to the opposing edge of the transected pectoralis major. By doing so, the inferior muscle cuff is stretched and overlaps the gap between the insertion of the pectoralis major and the insertion of the rectus abdominis, subsequently creating a true submuscular pocket. This technique counteracts the opposing forces of the augmentation and mastopexy procedures. Therefore, the use of the periareolar approach, dual plane, subfascial, or subglandular augmentation is not compatible with this technique.The inferior muscle cuff does not allow the development of an LDB. LDB can only be an iatrogenic result of the uneven deepening of the inferior cuff. If an LDB develops and needs to be corrected, the lower aspect of the pocket always has muscular coverage of the implant.The advantages of using this technique for 1-stage augmentation mastopexy can be divided into 3 parts: technique, postoperative quality of life, and long-term effects.The implant gravity effect is counteracted by the muscle closure—an inherent problem to all existing techniques.Any size implant can be used provided that there is complete muscle coverage. Our implant size range has been 150-375 cc (μ = 270 cc).We always used round silicone smooth implants of moderate or moderate plus profile. Saline implants can also be used. Smooth implants are not palpable and have movement within the muscle pocket. Smooth implants are also preferred due to the current anaplastic large cell lymphoma issue.No muscle animation, upper pole ridging, or medial and lateral rippling are seen. The pectoralis major muscle is sutured and stabilized inferiorly to the muscle cuff and remains stretched. This stretching of the pectoralis major creates a tenting effect over the implant. The wide undermining of the inferior pedicle allows the breast tissue to be freely redistributed superiorly, anterior to the implant, thus creating an additional layer of tissue to make the implant almost unnoticeable and not palpable. Importantly, the pinch test is not a guiding indicator for our procedure.The implants never extrude due to the muscle coverage. Even in cases of “T” sloughing or skin flap necrosis, the implants will never be exposed.Due to the muscle support, there is no loss of cleavage, implant malpositioning, and bottoming even after pregnancies and lactation.The inferior pedicle mastopexy and the absence of the periareolar approach for the augmentation leave the breast tissue intact for lactation. Therefore, there is no ductal obstruction and lactation is uneventful.Any degree of breast ptosis, including bariatric cases, can be corrected with this 1-stage technique. There is no vascular compromise to the inferior pedicle with the procedure, and, therefore, there is no limitation of the length of the pedicle, the length of the vertical excess, and the nipple elevation.This technique provides a tight skin envelope over the redistributed parenchyma, due to the wide undermining, and makes the result long lasting.The plication of the inferior pedicle provides support to the inferior pedicle and reduces the degree of breast tissue bottoming. It is also an easy way to correct breast asymmetry.No need for staging. No need for early-stage reoperations for corrective purposes as reported in 1-stage augmentation-mastopexies using other techniques.Accellular Dermal Matrix (ADM) are not used. The presence of muscular support and capsular tissue makes ADMs unnecessary for this procedure and for any long-term revisions.The stabilization of the pectoralis muscle decreases the postoperative pain. The patient is able to fully extend their arms without pain in 3 days and requires minimal opioids for pain management for the first 24 hours. We believe that this is due to the stabilization of the pectoralis muscle to the muscle cuff.There is no need for the use of a postoperative bra because an internal muscular bra has been constructed. The patient may choose to wear a soft bra or a sports bra electively for comfort for as long as they prefer. However, the postoperative result is not affected by the use of the bra.With the true submuscular placement, the smooth implants are not palpable, and the patients can barely feel their presence. Palpability is a parameter that is hardly discussed in the literature of breast surgery with implants. The implants that are palpable after the augmentation and “dance under the skin” at the inferior pole in the upright position is an issue that is not addressed and leaves the patients dissatisfied.Long-term effects such as the naturally aging breast, capsular contracture, high double bubble, waterfall phenomenon, or bottoming of breast tissue due to poor quality of the skin, especially in bariatric cases, can be safely corrected by always maintaining the true submuscular pocket and combining any of the following modalities. It is noteworthy that the combination of the following modalities does not run the risk of vascular compromise or extrusion of the implants, as long as the muscle pocket is respected.Anterior and peripheral capsulotomy/partial capsulectomy/ capsulorrhaphy.Change of implant size: The submuscular pocket stretches and the size of the implants can be increased easily an average of 100-125 cc and sometimes more, after a 4- to 6-month period, maintaining the muscle pocket intact. Smaller implants can be used in cases of excessive weight gain.Permanent explantation with crescentic excision of the lower pole if the nipples are in a proper place, or explantation with redo of the inferior pedicle in the unlikely event the position of the nipples needs to be revised.Lowering of IMF by deepening the muscle cuff in order to improve small lower pole ptosis due to aging and sagging breast.Crescentic excision of the lower pole without vascular compromise.No need for 2-stage revisions or staging a temporary explantation. ADMs are not required for any revisional surgery of this procedure.The major benefits of this technique for a long-lasting result are derived from the complete muscular coverage of the implants and the versatility of the tightening of the skin envelope that the inferior pedicle allows. The procedure makes it also technically easy, without the use of ADMs, to perform any future maintenance procedures of the aging breast without running the risk of implant bottoming, malpositioning, extrusion, or tissue necrosis.We strongly believe that this is a breakthrough approach to the 1-stage augmentation mastopexy procedure for primary grades 2 and 3 ptosis of any size including bariatric breast ptosis. The prerequisite for the split inferior pedicle mastopexy is the use of the TESMA for the augmentation. It has been proven in our practice to be a safe, simple, and reproducible procedure that is easy to be taught and very reliable without any major complications.


Bilateral cleft hand syndrome is a rare congenital malformation with complex anatomy. Previous reports have mainly focused on the description of bone and soft tissue abnormalities, but information about innervation is scarce. Knowledge of the peripheral nerve anatomy is helpful for surgical treatment, optimizing the reconstruction, and preventing iatrogenic damage. Following clinical assessment and conventional radiologic imaging, we used high-resolution ultrasound of both hands and forearms to image the peripheral nerves in a patient with severe bilateral cleft hand syndrome. The patient presented with two ulnar digits, a deformed thumb on the right, and a rudimentary thumb appendage on the left. In keeping with the tissue elements present and absent, we found a severe bilateral nerve size reduction of the median nerves, sparing the anterior interosseous nerve fascicles. The radial nerve and end branches were intact, and a slightly smaller ulnar nerve was found that ended in two digital branches to a single digit. Our study shows that in cleft hand syndrome the peripheral nervous system anatomy exactly reflects the presence and absence of the corresponding muscle and skin innervation areas. This information is helpful for planning a surgical-reconstructive approach and suggests a potential role for nerve ultrasound in the assessment of complex limb malformations. A 25-year-old man presented to us with, in our opinion, a cleft hand syndrome. He had a bilateral complete absence of three fingers and metacarpus, with a bilateral long “ulnar finger,” a hypoplastic thumb with a highly unstable carpometacarpal joint and thenar hypoplasia on the right side, and only a short soft tissue stump at the end of radius at the radial side . The patCleft hand syndrome, or ectrodactyly, is a congenital malformation defined as a longitudinal deficiency with suppression of bone and soft tissue in the central elements of the hand, including the index, middle, and ring fingers . In the Reports of patients with cleft hands, both from cadaveric dissections and imaging studies, have mainly focused on descriptions of bone and soft tissue, such as muscle and tendons . HoweverThe patient underwent clinical assessment including photographic documentation, standard X-ray studies of the hands, and MRI of the forearms to assess the bony and musculotendinous anatomy. As a part of the pre-surgical workup, bilateral high-resolution nerve ultrasound of the superficial radial, ulnar, and median nerves bilaterally was performed, following the nerves from the proximal forearm to the distal branches, to better define the anatomical characteristics of the peripheral nervous system in this rare type of congenital malformation. We used a Canon Aplio i800 ultrasound machine  with a high-frequency 8–24 MHz linear matrix array probe with a 38 mm footprint, using a specifically created “nerve” preset set to 19 MHz center frequency, with focus and depth settings to match the course of the nerves during the examination.The ulnar finger on each hand had three phalanges and a metacarpal resting on the ulnar pillar of the carpus. On the ulnar side of the hand, the soft tissues of the palm were superfluous. The skin and nails of the fingers were intact . The hanThere was no history of congenital malformations in the patient's family. His parents were consanguineous with a second degree of kinship. He was exposed to an unknown drug during the first 3 months of intrauterine life. In addition to the hand deformities, the patient also presented with the following congenital malformations: bilateral hip dysplasia, hypospadias, gonadal retention (treated with orchidopexy), and hypopituitarism with hypocortisolism and hypoaldosteronism, which was treated with hydrocortisone and fludrocortisone replacement therapy. He also suffered from Perthes disease. His face and lower extremities demonstrated a shorter 3rd toe on the left foot  but no fAccording to the DAST functional classification of cleft hand , the patient presented a D-3 (three or more), A-0, S-1 , T-4 (4 is hypoplastic) score on the right side and a D-4, A-0, S-1, T-5 (floating thumb or agenesis) score on the left side. This score implied a severe cleft type that would most likely need reconstruction with a vascularized toe transfer on the left .For the X-ray  and MRI Scanning the forearm muscles and the soft tissues in the wrist regions confirmed the MRI appearance of muscles and tendons. The median nerve on both sides ran a normal anatomical course in the arm and forearm, but with a pronounced reduction of the cross-sectional area (CSA) of the median nerve proper, while the anterior interosseus nerve (AIN) fascicles had a normal size before and after branching. Ultrasonography could be seen as an inversion of the normal CSA ratio between the two nerve bundles at the elbow level, with an AIN branch that was larger than the main median nerve branch . After tThe ulnar and superficial radial nerves followed a regular anatomic course bilaterally from the forearm to the hand, with the ulnar nerve having a slightly smaller CSA when compared to normal values for the patients' age and sex. At wrist level, the ulnar nerve on the right ran through an area recognizable as the normal ultrasound configuration of Guyon's channel, to split into two branches that ran from the rudimentary palm of the hand to form the radial and ulnar digital branches of the single ulnar finger. On the left, the ulnar nerve passed a rudimentary entrance to Guyon's channel from which two branches emerged that ran in the rudimentary palm of the hand toward the single digit. The left and right superficial radial nerve branched out over the dorsum of the thumb and ended in different small end branches in the subcutis in this region.Our high-resolution nerve ultrasound study of these bilateral cleft hands showed nerve sizes and anatomical nerve courses that fit exactly with the presence of the remaining anatomical elements. This suggests that the peripheral nerve innervation in cleft hands can be expected to reflect and follow the presence and course of the remaining target muscles and skin innervation areas. The severe caliber reduction of the median nerve proper in the arm and forearm fits this hypothesis. In addition to the missing intrinsic hand muscles, is it known that the large majority of axons in the upper limb nerves are sensory axons , the lacIn the presented patient there is one finger on the left side and one finger with a hypoplastic thumb on the right side. In terms of classification, it needs to be differentiated from ulnar longitudinal deficiency or an oligodactylous type of symbrachydactyly. As the forearm bones, both are equally formed it is more likely not to be an ulnar longitudinal deficiency. Symbrachydactyly can present in the form of an oligodactylous type , but it Our innervation pattern findings are most likely explained by the reciprocal neuro-muscular-bone interaction necessary to correctly guide the embryogenesis of peripheral nerves . EmbryolThe anatomical description provided here can contribute useful information to correctly guide surgical-reconstructive management, for instance, if a vascular composite transfer is planned like a toe-to-hand transfer. Nerve ultrasound can help in the surgical planning if and where nerve connections can be made. Nerve ultrasound could also help guide other diagnostic or therapeutic techniques such as electrodiagnostic testing or selective peripheral nervous system (PNS) anesthetic blocks in patients with such complex anatomic abnormalities. We hope this report will encourage the use of nerve imaging in the workup of such patients. At the same time, we realize that this high-resolution nerve ultrasound requires training and specific operator expertise to be available. Alternatively, the innervation of these complex anatomic malformations can also be assessed with MR neurography and/or MR tractography when available. Our anatomical findings offer new insights into the anatomy of this rare malformation and may be useful for future pathophysiological studies.The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.Ethical review and approval was not required for the study on human participants in accordance with the local legislation and institutional requirements. The patients/participants provided their written informed consent to participate in this study. Written informed consent was obtained from the individual(s) for the publication of any potentially identifiable images or data included in this article.SH performed the clinical assessment and oversaw the conventional radiologic studies. PF and NA performed the ultrasound measurements. NA provided the figures. All authors contributed to writing the manuscript draft.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.


In the current era of Noisy Intermediate-Scale Quantum (NISQ) technology, the practical use of quantum computers remains inhibited by our inability to aptly decouple qubits from their environment to mitigate computational errors. In this paper, we introduce an approach by which knowledge of a qubit’s initial quantum state and the standard parameters describing its decoherence can be leveraged to mitigate the noise present during the execution of a single-qubit gate. We benchmark our protocol using cloud-based access to IBM quantum processors. On ibmq_rome, we demonstrate a reduction of the single-qubit error rate by 38%, from  Among the various physical systems whose quantum properties can be harnessed for computation6, superconducting transmon qubits have demonstrated promise in their ability to realize scalable QCs9 and have accordingly been made available to the public via cloud-based services offered by private companies such as IBM, Rigetti Computing, and Amazon. Despite the recent increase in availability, in the current era of Noisy Intermediate-Scale Quantum (NISQ) technology10, our ability to utilize these machines to their full potential remains significantly inhibited by the computational errors that arise from interactions between the physical qubits and their environment.Four decades after the conception of a quantum computer (QC)11. Examples of software-based optimization protocols have been demonstrated across the full quantum computing stack, from high-level circuit depth compression via quantum-assisted quantum compiling12 down to the optimization of individual native gates-the default quantum operations calibrated by the hardware provider-through the use of pulse-level control15. Some notable examples include noise tailoring via randomized compiling16, dynamical decoupling of idle qubits17, optimized state preparation via active reset19, and measurement via excited state promoted readout21.While these detrimental interactions can be suppressed through the development of noise-resilient quantum hardware, the effective noise present during circuit execution can also be mitigated by optimizations in the compilation process22 experiments: (i) on the ibmq_rome23 quantum processor, we empirically determine the reduction of the single-qubit error rate offered by our optimization technique when the initial state of the input qubit is known, and (ii) on the ibmq_bogota24 quantum processor, we analyze the sensitivity of our approach to the accuracy and drifts of the device’s calibrated In this paper, we pioneer a software-based optimization protocol for fidelity improvements of general single-qubit gates by leveraging knowledge of the qubit decoherence parameters to generate an optimized noise-aware decomposition into native hardware gates. The optimization of native gates themselves is a complementary task and a powerful noise-mitigation tool in its own right, but it requires pulse-level control, a level of hardware access both unfamiliar and inaccessible to many users of NISQ devices. The goal of this paper is to demonstrate a reduction of single-qubit error rates without the need for this lower level of access. By optimizing the decomposition of single-qubit gates without improving the native gates themselves, we demonstrate the efficacy of a protocol that is straightforward to implement at the gate level and requires minimal knowledge of the underlying Hamiltonian governing the qubit dynamics during gate execution. Accordingly, it can be easily adapted for use in QCs based on arbitrary physical systems. Our results demonstrate that it is possible to significantly improve the fidelity of single-qubits gates by leveraging knowledge of the qubit’s initial state, along with its characteristic coherence times U on the Bloch sphere can be parameterized by its Euler angles25. Concretely, 26: rotations about the x-axis by integer multiples of 14, but in hopes of making our protocol easier to implement for those without this lower level of access, we maintain the standard native gate set described above. The decomposition outlined in Eq.  and dephasing, respectively characterized by IBM’s publicly reported 23 and ibmq_bogota24 were provided by IBM through Qiskit29 and are tabulated in the While there are a number of noteworthy sources of single-qubit decoherence, including leakageBased on the physical implementation of IBM’s native gates discussed above, we model the noisy application of an entclass1pt{minimaThe derivation of this expression is provided in the The variable  in Eqs. –5 are fuUsing the noise model given by Eqs. –5, we no30 library with the method L-BFGS-B. For the parameters used in both experiments performed on IBM’s hardware, the gradient descent to optimize a single gate could be performed in approximately 0.2 s on a standard computer.We find the optimal Euler angles that Eq.  has an e32.To provide some intuition for how the optimized operation improves the fidelity, we begin by noting that the effect of amplitude damping is most pronounced on the south pole of the Bloch sphere (excited state), and the effect of phase damping is most pronounced on the equator of the Bloch sphere . Thus, to best map the initial state to the target state, the optimizer finds a trajectory through the Bloch sphere that most aptly avoids these noisy regions. For the sake of visualization, we have included an example of an optimized (blue) and an unoptimized (red) trajectory through the Bloch sphere in Fig. We now experimentally validate the protocol outlined above on qubit 3 of the ibmq_rome device by empirically determining the reduction in the single-qubit error rate achieved by the optimizer. At the time of the experiment, the qubit had the following characteristics: 33. We then optimize each gate C. For each circuit C and d gates by d gates by applying d are then averaged over the 10 circuits. Readout errors were mitigated for all measurements made on ibmq_rome and ibmq_bogota by inverting a calibration matrix34 composed of IBM’s publicly reported readout error probabilities.We begin by generating a circuit composed of a sequence of randomized single-qubit gates The results from simulating the execution of the circuits using our noise model and from executing the circuits on ibmq_rome qubit 3 are displayed in Fig. 35. Nonetheless, we maintain our reported error rate reduction as an estimate for the degree to which the noise present during the execution of a single-qubit gate can be mitigated by leveraging knowledge of the initial state of the input qubit and a description of the noise present during gate execution. An experiment of identical structure was carried out on Rigetti’s Aspen-836 device and is detailed in the In the simulation and on the hardware, the optimized circuits outperformed the unoptimized circuits, thereby experimentally validating the optimization protocol put forth in this paper. Both the optimized and unoptimized circuits on the hardware have lower fidelities than in the simulation. We attribute this to two factors. First, our noise model only accounts for relaxation and dephasing, when in reality there are other noise channels present, such as sources of non-Markovian noise and leakage. Second, we made the approximation that a noisy single-qubit gate can be modeled as coherent evolution followed by decoherent evolution, when in reality the two occur simultaneously. We believe these two factors are the largest contributors to the lower fidelities observed on the hardware. Finally, from direct calculation of the optimized and unoptimized error rates defined by Eq. , we concAs an illustrative example application of the optimization protocol outlined above, we now analyze its ability to improve the preparation fidelity of a single-qubit state. Suppose that we wish to implement the target operation Without loss of generality, we set duce Eq.  to the fWe find the optimal Euler angles We now proceed by analyzing the relationship between the improvement in preparation fidelity offered by the optimizer and the amount of noise in the system. Since The above optimization protocol requires knowledge of the initial state to achieve an improvement in fidelity, as reflected in the fidelity function’s explicit dependence on the initial state’s Bloch sphere coordinates (see Eq. ). HoweveThe fidelity function d in Eq. . We findWe proceed by analyzing the expected fidelity improvement offered by our protocol as a function of the initial state uncertainty. We have already shown a nontrivial improvement in expected fidelity provided perfect knowledge  of the initial state The expected fidelity in this case is given byFurther analysis of Eq.  shows15\some knowledge of the initial state to improve expected fidelity. To further analyze this dependence, we examine the effect of maximizing the expected fidelity for a new probability density function:Regardless of the target operation and the amount of noise, the expected fidelity achieves a local maximum at The initial state is now uniformly distributed over the portion of the Bloch sphere with polar angle less than We quantify the degree to which an arbitrary single-qubit gate can be optimized as a function of the initial state uncertainty. To visualize this dependence, we begin by fixing the noise parameter t of Eq.  over theThe optimization protocol outlined in this paper reduces the error rate of a single-qubit gate by employing the k:In reality, the coherence times assumed by the optimizer are fixed, and the system’s coherence times are free to drift. However, since the system’s coherence times are not controllable parameters, we simulate the effect of a drift by intentionally providing the optimizer with inaccurate We justify this simplification in two ways. First, with limited reservable time on ibmq_bogota and limited computational resources for optimization, the experiment described in this section could only be made computationally feasible by reducing the scan of possible drifts from 2D to 1D. Second, though The results from simulating the execution of the circuits using our noise model and from executing the circuits on ibmq_bogota qubit 2 are displayed in Fig. k approaches 0, the optimizer assumes that there is no noise in the system. For any target rotation, in the absence of noise, the optimal rotation is the target rotation itself. Thus, as k approaches 0, we expect the fidelity offered by the optimizer to approach the unoptimized fidelity. This holds true in both the simulation data and the hardware data in Fig. k approaches As the factor some knowledge of the initial state of the input qubit-the more localized the initial state distribution, the more we can improve the expected fidelity. The technique can be applied as a means to improve the fidelity of state preparation, as well as to improve the fidelity of quantum circuits for which some knowledge of intermediate states of qubits can be inferred; the former is well-suited for use in variational quantum eigensolvers (VQE), while the latter is likely only applicable in the near-term. Our optimization technique is not limited to the native gate set of IBM quantum hardware and can be adapted for optimization over an arbitrary native gate set.The optimization protocol outlined in this work reduces the error rate of single-qubit gates by leveraging knowledge of the initial state of the input qubit, along with the level of decoherence in the system, defined via n-qubit gates by parameterizing all possible decompositions into an expanded native gate set (including entangling gates), and then proceeding as usual with the noise model and expected fidelity maximization for a specified distribution of n-qubit initial states. Since this work focused specifically on the optimization of single-qubit gates, gradient descent was sufficient for fidelity maximization; however, since the degrees of freedom required to parameterize an n-qubit gate are exponential in n, efficient alternatives to gradient descent are likely necessary to maximize the fidelity of larger n-qubit operations with more practical run-times.In the noise model employed in this work, we used the approximation that native gates are applied instantaneously and are followed by a period of decoherence over the time interval equal to the gate duration. This approximation can be avoided by deriving a noise model from master equations involving the system’s Hamiltonian during gate execution , which falls outside of the scope of this work. If the exact initial state of the input qubit is unknown, the optimization protocol can be modified to instead maximize the expected fidelity, averaged over the distribution of possible initial states. Our technique can also be adapted to optimize In the near-term, while the execution of quantum circuits can still be simulated by classical computers, one can track the state of each qubit and use our protocol to optimize an arbitrary gate embedded within a quantum circuit. While the target qubit to said gate will generally be entangled with other qubits in the circuit, its reduced density matrix can be recovered by tracing over the degrees of freedom introduced by the qubits with which it is entangled. Though this entanglement will cause the qubit’s initial state to be mixed, the optimization protocol can be easily adapted to accommodate mixed initial states, as is alluded to in the Supplementary Information.


Vortex electromagnetic wave (VEMW) carrying orbital angular momentum (OAM), which is expected to introduce additional degrees of freedom in inverse synthetic aperture radar(ISAR) imaging. However, the current research about maneuvering targets is based on the "stop go" hypothesis, which does not apply to high-speed motion scenarios due to the intrapulse movement of the target. To improve the imaging quality, this letter proposes a VEMW-based high-speed maneuvering targets imaging method. Firstly, the ISAR imaging scenario of high-speed target is established. According to the spatial geometric relationship between radar and maneuvering target, the vortex echo is deduced and its characteristics are analyzed. Subsequently, a frequency modulation rate estimation method considering both calculation efficiency and high precision is proposed to realize the accurate estimation of target speed. Then, an adaptive azimuth image compensation method based on minimum entropy is proposed. Through the setting of threshold, the number of component signals in linear frequency modulation (LFM) signal is determined and compensated successively. Finally, the range profile and azimuth profile are combined to reconstruct the three-dimensional information. The simulation results demonstrate that this work can effectively eliminate the influence of high-speed motion on range and azimuth profile, also benefit the development of ISAR imaging technique of high-speed maneuvering targets. With the development of science and technology in recent years, ISAR imaging for non-cooperative targets, has been extensively studied by scholars at home and abroad because of its wide application in military and civil fields. The mechanism of ISAR imaging is to use the Doppler information generated by the target’s rotation to distinguish the echoes returned from different parts of the target. Therefore, when the relative motion between the target and the radar is insufficient, in order to improve the cross-range resolution of the traditional planar electromagnetic wave ISAR, it is necessary to transmit more pulses or a longer coherent processing interval (CPI). In this way, a large number of echo data will be generated in the imaging process, which will not only cause great pressure on the radar system, but also affect the real-time imaging of the target. For high-speed maneuvering targets, it will also bring problems such as phase tracking error and Doppler ambiguity.1, vortex electromagnetic wave has attracted increasing attention in the fields of rotation Doppler parameter estimation3, OAM modulated wireless communication6, quantum application7. In addition, when the moving target is irradiated by vortex radar, the unique wavefront shows the characteristic of angular diversity, the dual relationship between the OAM mode number and the azimuth angle, so the scattered echo in the target area will contain more relevant information, which make the electromagnetic vortex radar is expected to develop into a new imaging mechanism.In the past 30 years, due to unique spiral phase structure and orthogonal characteristics8 first discovered the Laguerre Gauss beam had a spatial spiral wavefront, and also determines the relationship between the wavefront structures and intrinsic values of OAM. In 2013, Guo et al. established a scattering point imaging model based on VEMW via the uniform circular array (UCA), and explained the relationship between OAM mode value and azimuth by using the spectrum characteristics of Bessel function, which proved the potential of vortex radar imaging9. Since then, domestic researchers have put forward a variety of motion imaging models of vortex radar and corresponding algorithms for these models, which realize the vortex imaging of moving targets. By analysing the relationship between the rotation Doppler and azimuth,then compensating the echo signal range profile, the azimuth imaging of rotating disk is realized10. A new method of vortex imaging based on improved back projection (BP) algorithm is proposed11. The influence of additional terms of vortex electromagnetic wave on azimuth phase is compensated by increasing azimuth modulation function. Besides, it also revealed the relationship between azimuth resolution and OAM mode number. The traditional synthetic aperture radar (SAR) imaging and the vortex radar are combined12, through adding Bessel term compensation and azimuth filtering in the traditional RD algorithm, the two-dimensional imaging of moving targets is realized, which demonstrates that the combined vortex imaging method has more advantages in azimuth resolution. The vortex radar is first applied to ISAR imaging13, the traditional Fast Fourier Transform (FFT) algorithm is replaced by the convolution back projection (CBP) and Power Spectrum Density (PSD) estimation, and the combination of CBP and PSD estimation is better than FFT from the simulation results. To improve the anti noise performance, an electromagnetic vortex imaging method based on the generation of fractional OAM beams is proposed14, which show that the method has strong noise resistance and effectively overcomes the shortcomings of poor imaging performance of low-order OAM beam.In 1992, Allen et al.15. Therefore, the intrapulse motion of high-speed target can not be ignored, and the problems such as range migration, Doppler dimension expansion and azimuth blur are also unavoidable16. To solve these problems, Ref.17 establish the imaging model of high-speed of ISAR and propose a joint estimation method for echo signal. Through the reconstruction of the target azimuth, the 3-D target imaging is finally realized. But the joint estimation method has its limitations. On the one hand, it has high precision to the model constructed in this paper; on the other hand, the estimated velocity still has some error with the actual velocity, which makes the constructed compensation phase inaccurate. Above all, the reference only considers the case that the Y-axis coordinate difference of scattering point is small, that is, when the value of error phase term is close, the common compensation method is used to realize the image quality improvement. But the target with great difference in position distribution is not studied in depth.From the current research results, most of the moving imaging of vortex radar is based on the "stop go" model, and the target motion speed is relatively slow. But with the development of high-speed aircraft, the speed of air target continues to increase. The existing supersonic aircraft can fly at more than five times the speed of sound17, this paper makes an in-depth analysis on the targets with large differences in the position distribution of scattering points. After that, through the frequency modulation rate estimation, the phase function is constructed to compensate the echo signal. Then the compensated phase error term is estimated by the least squares quadratic polynomial regression method (LSPR), so as to further accurately estimate the frequency modulation rate of the echo signal and the speed of moving target. Finally, according to the characteristics of a multi-component LFM signal, this paper carries out two-dimensional search and estimation of azimuth parameters based on the minimum entropy method and realizes adaptive compensation of component signals through the setting of threshold. Finally, the deterioration of range-azimuth imaging is overcome and simulation results realize three-dimensional information reconstruction.In this context, a VEMW-based high-speed maneuvering targets ISAR imaging method is proposed. Firstly, based on the papers published earlierThe rest of this paper is organized as follows. In section “19, and the center is located at O in the global coordinate system. The target with multiple scattering points moves at the speed v towards the direction of the angle Z-axis, the path of motion is in the XOZ plane and the intercept of this direction on the positive Z-axis is Z-axis is the pitch angle XOY plane and the positive X-axis.In this section, the imaging scenario for vortex radar ISAR is described and the signal model is deduced. As shown in Fig. 20, and the emission signal of each UCA element can be expressed ast,K is the linear frequency modulation ratio and l is the OAM mode value, and the modulation phase of the v, the instantaneous distance of the scattering point Assuming that the LFM signal is utilized to generate vortex EM wavesAccording to the above analysis, the echo signal after dechirping process is written asmodel in . The secv of multiple echos estimation can effectively eliminate variation error. After that, the parameters of azimuth profile are obtained by two-dimensional search, and the corresponding entropy is calculated. According to the principle of minimum entropy, the original signal is reconstructed and the estimated component signal is removed, and the ambiguity in azimuth profile is solved. Finally, the deterioration of two dimensional imaging is improved, and the 3D image is obtained according to the spatial geometric relationship.The flow chart of the imaging algorithm is shown in Fig. 17, the echo signals at different times are autocorrelated to find the maximum frequency under different sequence differences, and the rough frequency modulation value According to the estimation method proposed in Ref.c is much greater than the maneuvering speed v, so The phase compensation function  term in . The commentclasspt{minima between  and 9),,\documenrding to , the cormentclasspt{minimaThis section is used to verify the effectiveness of the proposed algorithm and its superiority in LFM signal parameter estimation compared with other references. The simulation parameters are set as shown in Table Figure In order to eliminate this phenomenon, 500 echo signals are extracted to estimate the ratio entclass1pt{minimaAs shown in Table entclass1pt{minimaAfter obtaining the precise estimation of frequency modulation ratio, Fig. Then, the ambiguity of azimuth profile needs to be compensated. As shown in Fig. E can be calculated. According to the results of many experiments, the threshold of this paper By searching for different azimuth angles and After 5 compensations of echo signal, the entropy value is 7.0228 and the variance is Figure Finally, the reconstruction information of each scattering point can be obtained, as shown in Table To validate the effectiveness of the proposed imaging method, the aircraft model constituted by multiple ideal scattering pints is utilized for simulation experiments, as shown in Fig. The algorithm proposed in this paper is used to estimate the frequency modulation ratio of the echo signal. According to the estimation results, 500 echoes are are randomly selected to calculate the velocity of the target, and then the broadening and shift of the one-dimensional range profile are compensated. The range profile results of the aircraft are shown in Fig. On this basis, the minimum entropy is utilized as the measurement standard to adaptively compensate the multi-component LFM signal, as shown in Fig. The two-dimensional information distribution of scattering points is obtained by combining the range and azimuth image information. The image focusing effect is significantly improved after algorithm compensation, as shown in Figs. A VEMW-based high-speed maneuvering targets ISAR imaging method design for eliminating range profile broadening and azimuth profile blur is proposed in this paper. The movement speed of the target is obtained by estimating the frequency modulation rate of the echo signal. Then adaptive compensation based on minimum entropy effectively eliminates the ambiguity of azimuth profile. Finally, theoretical analysis and simulation results verity the effectiveness of the proposed algorithm. The further work will focus on the VEMW-based parameter acquisition technology for high-speed targets.