The Royal Dutch Dental Association (KNMT) developed a reporting code for dental professionals (RCD). Moreover, an e-learning module about DV has been developed. A web-survey was conducted to investigate how general dental practitioners (GDPs) deal with the RCD and what their experiences are with (signs of) DV and CA.On July 1In April 2014 1038 GDPs were invited by e-mail to participate in a web-survey consisting of 24 items, through the KNMT Data Stations Project. The data was analyzed using SPSS .Of all GDPs invited to participate 264 (25 %) responded. 82 % of these GDPs are aware of their obligation to use the reporting code. 54 % of the GDPs are in favor of this obligation. 76 % of the GDPs have taken notice of the KNMT’s RCD and 51 % of the GDPs have implemented the reporting code in one form or another in their practice. 24 % of the GDPs stated having suspected DV during the last twelve months in the case of 2.4 patients on average. 81 % took note of this in the patient’s record and 58 % also took action in different ways. 54 % wants to complete the e-learning module.Most GDPs are aware of the new legislation and have taken cognizance of the RCD. Even though the majority of GDPs are not opposed to using a reporting code, over half of them have not yet implemented the code in practice. An important factor in this regard seems to be that a substantial minority of the GDPs says they are not sufficiently informed about aspects of reporting a case and about the steps they have to take. Domestic violence (DV) can be defined as threatening behavior, violence or abuse between adults who are relatives, partners or ex-partners. It also includes violence or child abuse (CA) from adults to children or abuse from (adult) children to parents . It can DV is a serious public health problem, which particularly affects women. Overall, 30 to 35 % of women worldwide have experienced either physical and/or sexual abuse, most of which is intimate partner violence . In the In general, the majority of physical injuries from domestic and other forms of violence are inflicted to the head, face or neck , 9. BecaHow often primary care clinicians and in particular general dental practitioners (GDPs) suspect DV or CA cannot be concluded from available literature. Ramsay et al. (2012) state that 71 % of primary care clinicians in the United Kingdom have diagnosed one or more new cases of DV in the last 6 months . In 2010However, it appears that in many cases GDPs who suspect DV or CA do not report their suspicions , 17–20. st 2013. This act makes it compulsory for organizations and independent  professionals to have a reporting code that meets the statutory requirements [Meanwhile, in the United States reporting child abuse and neglect is mandatory for health professionals in all 50 states . In seveirements . MoreoveIn order to support oral health care professionals to fulfill their obligations according to the Act, the Royal Dutch Dental Association (KNMT) developed the reporting code for dental professionals (RCD). The RCD contains an information brochure which explains the different forms of DV and neglect, the new legislation, the judicial aspects, how to ask for advice and how to report abuse. The RCD also contains the five step action plan. In 2012 this RCD was sent to all dental practices in the Netherlands. It is up to the GDP to decide how to fulfill the requirements, how to tailor instructions and how to decide what kind of training the dental team needs. In cooperation with two other dental professional associations and with Augeo Academy, the KNMT developed an e-learning module about DV and the reporting code called ‘The Next Page’ . The modThe aim of this study is to investigate to which extent Dutch GDPs are aware of the RCD, if they have implemented the RCD and if so, how they implemented it. This study will also investigate how often dentists have had suspicions of DV or CA and how they dealt with their suspicions in the most recent case.By means of its Data Stations Project the KNMT periodically collects data on delivery of oral health care, on practice management and on GDPs’ opinions and views regarding current issues in dentistry in the Netherlands . For thiThe online questionnaire covered 24 items. GPDs were asked about their acquaintance with the RCD and whether or not they had actually perused this or a different reporting code, how they evaluated the content and the ‘look and feel’ of it and if they had implemented the RCD in their practice. Subsequently, their opinions on the effect of the RCD were gauged using four Likert type items. Furthermore, questions were asked about any suspicions of DV or CA in the last 12 months. If GDPs stated that they have had suspicions, some specific details were asked about their professional behavior concerning the most recent case in which suspicion of DV or CA was raised. GDPs who did not respond after 2 weeks and consecutively after 5 weeks, received a reminder e-mail.p < 0.05), but all associations proved to be very weak (Cramèr’s V < 0.10 and eta2 < 0.05).Ultimately, 264 (25 %) of the 1038 GDPs in the sample completed the questionnaire. With regard to some individual characteristics, the total group of respondents proved to be fairly representative for the population of GDPs in the Netherlands  in order to determine if one or more additive scales could be formed.A Cronbach’s alpha of 0.80 or greater was considered as a criterion for a reliable scale.Chi-square tests were used to test the correlation between nominal items and by analysis of variance differences between group means were tested.st, 2013, dentists and other care workers are compulsory to adhere to a reporting code in case of suspicion of DV or CA. It appears that 54 % is more or less positive about this obligation, while 35 % holds a neutral position. All others (11 %) are negative about the obligation to use a reporting code, most of whom (69 %) stated that they regard themselves not adequately equipped to judge on DV and CA.Most (82 %) respondents stated that they were aware of the fact that since July 1The majority (76 %) of GDPs indicated that they received information in some way about the brochure and/or the action plan of the RCD Table . Most GDp < 0.01). They also more often answered that they are sufficiently informed about the background of the reporting code , the aim of the reporting code , the various forms of DV and CA , the difference between asking advice and reporting a case  and the implications of reporting a case . Furthermore they more reported to be well informed about the five steps .Table All in all, 30 % of GDPs stated that the RCD had influenced their alertness and the way in which they take action Table . Almost n = 58) stated that they have had suspicions of DV or CA in the last 12 months in the case of 2.4 patients on average. These GDPs are more often female  and on average younger  than GDPs who have not had any suspicions of DV or CA. Moreover, these GDPs have implemented the RCD much more often .Twenty-four percent of the GDPs (Table p < 0.01) and have implemented it in their practice more often .GDPs who did not take action said they felt unsure about whether or not their suspicions were correct (88 %). GDPs who wrote down their suspicions of DV or CA in the patient’s record and/or took action are, in comparison to those who did not, more often aware of the RCD . Moreover, they have implemented the RCD more often  and they have had suspicions of DV or CA in the last 12 months . In more cases, they take a positive stance with regard to the legal obligation to use the reporting code . The RCD also has had more influence on them .Sixty-one percent of GDPs wants to complete the e-learning module ‘The Next Page’ and/or thinks it is important that their team complete the module Table . These GThis study shows that a large majority of GDPs was aware of the obligation to use a reporting code in 2014. Over 50 % of GDPs viewed this as positive. Those who were not positive usually felt unsure about the issue of DV and dealing with it. Most GDPs are also aware of the RCD. The majority of GDPs who have had suspicions of DV or CA took some form of action.The study gives some insight in why almost half of the GDPs have not implemented the reporting code into their practice. It appeared that these GDPs more often failed to take notice of the RCD than those who implemented the code. Moreover, there seems to be a connection between failure to implement and the information in the RCD. After all (proportionately) many GDPs who did not implement stated that the RCD insufficiently informed them about the background and aim of the reporting code, about the various forms of DV and CA, about aspects regarding asking advice and reporting a case and about the five steps they have to take.The information in the RCD is apparently not able to clarify the issue to all GDPs. Admittedly, Dutch legislation is complicated. GDPs, even though they are not qualified to diagnose DV or CA, are expected to judge suspicions based on their own observations and to follow the guideline which consists of five rather difficult steps. This starts with ‘identifying the signs’. According to this study, a large number of GDPs are unsure about the correctness of their suspicions. They are required to talk about their suspicions with experts. But the apparent unclarity regarding the task and the function of the Advice and Reporting Centers can form a barrier here and the same holds true for the judicial aspects of the confidentiality agreement. The next step is talking to the patient or their parents. This is not an easy task either when it comes to suspicions of DV or CA. Lastly, the GDP is supposed to decide whether or not to report his or her suspicions. What is best for the patient? How can I make sure not to damage the relationship with the patient and between the patient and their family? And are the signals strong enough to justify taking action? As becomes clear from the literature, GDPs and caretakers from other countries are also wrestling with these problems. For example Scottish GDPs, whose failure to take action is related to lack of certainty of the diagnosis  and or fThis does not change the fact that the reporting code is a legal obligation and that the inspectorate can ask individual GDPs to provide concrete details of how they implemented the code in their practice, what they have done to train the dental team in order to promote awareness and use of the reporting code and what their plans are for the coming year. It is therefore important for GDPs to be aware of their obligations. The KNMT should inform GDPs about these matters. Offering practical support with regard to using the RCD is also of pivotal importance when it comes to helping the GDP and the dental team in the diagnosis and documentation . After aFurthermore, it appears that educational interventions such as online tutorials and an e-learning module seem to have positive effects in particular when it comes to knowledge of DV and recognizing it –32. BaseMoreover, the Mandatory Reporting Code DV and CA makes it compulsory for health professionals like GDPs to promote the awareness and use of the code within their practice. This means that by offering an e-learning method the KNMT meets these educational needs. Most GDPs appear to appreciate this initiative.Finally, a critical evaluation of the results of this study is needed. The relatively high number of non-response raises questions. Regardless of a certain ‘research fatigue’ GDPs may experience (which plays a role in every survey), the subject of this research may also have been a reason not to respond. For example because of disinterest, but more importantly, insecurities regarding how to handle suspicions of DV and CA and fear of acting legally insufficient may play a role. Presumably, the percentage of GDPs in the Netherlands that have not implemented the reporting code in their practice is higher than the 49 % this study found. In relation to this, a certain amount of ‘socially acceptable answers’ should be taken into consideration. This is likely with regard to for example implementing the reporting code in their practice as well as taking action when GDPs have suspicions of DV or CA.All in all, it can be concluded that the large number of GDPs who do not (yet) comply with the new legislation do not fail to do so because of unwillingness, but merely because of inexperience and insecurities with regard to handling signs of DV and CA. This survey shows that a reporting code like the RCD can be a good support to GDPs and can encourage them to be alert on signs of DV and to report these. Moreover, the survey shows that the KNMT should pay close attention to the ways in which GDPs are coping with their legal obligations and to possible problems that may arise. Meanwhile, the legislation in the Netherlands has been adjusted in a number of ways. The KNMT is working on an updated version of the RCD, which will be published in 2015. In this version, partly in response to the conclusions of this study, clear information on the new legislation and steps that need to be taken is of pivotal importance.st 2015 the Dutch government transferred the responsibility for the approach of DV and CA to municipalities. They have to make their own agreements with certified agencies responsible for child protection measures in their region, which leads to regional differences. Fortunately, the Dutch government is aware of the importance of monitoring this issue. In 2015, the Ministry of Health Welfare and Sport (VWS) ran a quick scan in order to investigate the workings of the Mandatory Reporting Code DV and CA. This quick scan should provide insight into how professionals experience work with the Reporting Code.In the future the KNMT should investigate whether or not GDPs are better informed as a consequence of the updated RCD and whether or not they meet the legal requirements. In this context, the KNMT should also take stock of possible problems regarding dealing with (suspicions of) DV and CA. However, this is also a public health issue, and more attention should be paid to making this an issue of public interest. When society regards these issues as highly important, it will be easier for GDPs to implement this new legislation in their daily practice. Future research should then focus on the effect of (early) reporting DV and CA. A complicating factor is that on January 1


Image pair is often aligned initially based on a rigid or affine transformation before a deformable registration method is applied in medical image registration. Inappropriate initial registration may compromise the registration speed or impede the convergence of the optimization algorithm. In this work, a novel technique was proposed for prealignment in both monomodality and multimodality image registration based on statistical correlation of gradient information. A simple and robust algorithm was proposed to determine the rotational differences between two images based on orientation histogram matching accumulated from local orientation of each pixel without any feature extraction. Experimental results showed that it was effective to acquire the orientation angle between two unregistered images with advantages over the existed method based on edge-map in multimodalities. Applying the orientation detection into the registration of CT/MR, T1/T2 MRI, and monomadality images with respect to rigid and nonrigid deformation improved the chances of finding the global optimization of the registration and reduced the search space of optimization. Image registration is the spatial mapping of corresponding locations between different images with broad applications in neurosurgery and radiotherapy . MedicalIt was previously reported that orientation difference estimation based on edge information  with CanIn this study, the feasibility of calculating the orientation difference between two unregistered images is explored to facilitate the image registration without any feature extraction. The challenges lie in the lack of abundant corresponding characteristics between multimodality images. Tissue boundaries may vary in corresponding multimodality images, but the distribution of gradient information often has considerable similarities. The orientation difference between multimodality images is expected to be determined by the orientation histogram of gradient information. Gradient information has been widely used in the field of image registration –21. HistContrast to all previously proposed methods based on gradient information, gradient information is adopted to estimate the global orientation difference between images in this work. The estimation of global rotational difference is casted as the problem of gradient magnitude weighted orientation histogram matching. A robust technique for histogram matching based on L1 norm and L2 norm is also provided, which is robust to local deformation, partial occlusion, and illumination change in addition to noise in images. Normalizing the gradient magnitude weighted orientation histogram allows estimating the orientation difference across scale differences of images. The main contribution of the work lies in the fact that the global orientation is estimated based on the accumulation of local gradient information, and the global orientation difference is formulated as the problem of robust matching of gradient magnitude weighted orientation histograms.The prealignment for multimodality images mainly consists of two components: (1) estimating the rotation and (2) estimating the translation. f/∂x is the gradient in the x direction and ∂f/∂y is the gradient in the y direction. The gradient magnitude is calculated by the following formula:The local orientation in the image is obtained by calculating the first derivatives in two orthogonal directions and the orientation is determined using the gradient expression illustrated as (1)∇f=∂fThe gradient direction is calculated asx and y directions. To reduce the effect of noisy directions, the partial derivatives in the image are calculated by filtering the image in the x and y direction with the filters that implement the derivatives of the Gaussian functions. This is achieved by filtering the image with 1D operators that are computed using the expression by the following formula:σ is the standard deviation of the Gaussian function. After calculating the partial derivatives, the weak edges response are eliminated by applying a nonmaximal suppression procedure and the orientation at each pixel is determined by the expression in . To clearly observe the accumulation of histograms in different orientation bins, the type of bar was adopted for histogram presentation rather than using the conventional type of line. Magnitudes weighted orientation histograms with different orientation bins were created in In HA and HB are the magnitudes weighted orientation histograms of the reference image and the moving images, respectively. Histogram matching is to determine the optimal translation that minimizes the cost function TD of two histograms HA and HB, that is, to find TD(j) = ∑i=0K−1(|HA(i) − HB(i + j)|) for j = 0,…, K − 1. Then find J such that TD(J) = min(TD(j)) for j = 0,…, K − 1, where J is the estimation of rotational difference between two images and K is the number of bins for the orientation histogram. Note that this shift of histogram matching is done cyclically, so that if i + j > K − 1, then i + j is replaced with i + j − (K − 1). The matching metric is L1 norm of HA and HB. In addition, L2 norm is also performed for the histogram matching TD(j) = ∑i=0K−1(|HA(i)−HB(i+j)|2).Since two images may not cover exactly the same parts of anatomic structures, in order to maximize the area of overlap between the two images, areas within largest circular regions centered at the images are used in the orientation histogram accumulation. To maximize the area of overlap between the images, only areas within largest circular regions centered at the images are used for the accumulation. The orientation histogram of one image is cyclically slided over the other orientation histogram from the other image, and the position where the two histograms best match is used to determine the rotational difference between the images, assuming j = 0,…, K − 1. K was chosen as 9 to generate the magnitudes weighted orientation histogram for orientation bins for brain T2 MR. The shift j was considered as 2 and 5, respectively. The histogram matching values of TD with shift j from 0 to K − 1 were recorded, and the global minimum value of TD was considered as the position of the best match. In the implementation, a figure of TD with all shifts was plotted for better observation, where the horizontal axis was the shift j from 0 to K − 1, and the vertical axis was the histogram matching value TD. In order to improve the robustness of histogram matching and eliminate the noise in orientation histograms, 1-dimensional Gaussian smoothing with small standard deviation was performed for two histograms before the matching process. Finally, interpolation methods were used to improve the accuracy of orientation difference estimation. The point which corresponded to the global minimum value and its nearest neighborhood points in the histogram of TD were fitted as a curve to generate the minimum in the continuous domain.Fourier transform based on Fourier shift theorem was used to efficiently compute the sum of absolute difference (L1 norm) or the sum of squared difference (L2 norm) for all possible shifts cyclically for A synthetic example of determining the rotational difference between two brain T1 MRI and T2 MRI images was presented to demonstrate the detailed performance of the proposed algorithm in To demonstrate the accuracy and robustness of the proposed method for global orientation difference estimation between multimodality medical images, both synthetic and clinical medical images were applied for the experiments. The performance of the proposed method on synthetic images was firstly tested as the ground truths of the rotational difference were known. The gold-standard rigid-body rotational difference for each registration was set by rotating one image in the image pair with respect to the other image. The proposed method was compared with the edge-based method for rotational estimation for challenging multimodality images. Finally, we incorporated the proposed orientation estimation for preregistration of multimodality images.The method was tested in three different medical image processing scenarios: brain T1WI and T2WI with scale difference , head CTThe test results of rotational differences between image pairs shown in Then, test results of image pairs in σ should be relatively large  in order to reduce the influence of interpolation artifacts from the bicubic interpolation. From the test results, the proposed method obtained promising results when the rotational difference was larger than 3°. However, the proposed method was not much sensitive to too small rotational differences, for example, <2°. When the rotational difference between two images was smaller than 2°, the obtained result was usually zero. Two reasons accounted for it. One was that the orientation resolution of histograms is 1° in the work, and it was so difficult to differentiate too small rotational differences from the orientation histogram. Another factor was that the precision was strongly related to the interpolation method, which in the case was bicubic interpolation. It was also very difficult to generate rotational images precisely with very small known rotational differences  by the bicubic interpolation. Therefore, when the rotational difference was very small , the test result may contain small errors . But these results with such small rotation errors were mostly accurate to guide the iterative optimization to obtain desired values, because the estimated value was very close to the desired value.In essence, the proposed method of rotational estimation is a general technique for image registration with wide ranges of rotational differences. In order to demonstrate the sensitivity of the method to smaller rotations and larger rotations, detailed simulation tests were presented with a smaller range of rotations, including 1°, 2°, 3°,…, 8°. Meanwhile, larger rotations were also tested, including 40° or 70°. Three medical images were selected for the test including brain T1 MRI, head CT, and prostate MR images as shown in The proposed orientation detection was experimentally incorporated into the registration of CT/MR and T1/T2 MRI images. Four clinical cases with multimodality images under affine transformation were registered. The image registration process was performed on a computer with CPU 3.3 GHz and 4G RAM. The computation time of the registration process with and without the proposed method was measured, and the time consuming of the proposed technique was also reported in An image pair is often aligned initially based on a rigid or affine transformation before a nonrigid transformation for deformable medical image registration. Therefore, registration results of clinical prostate images as shown in Since the goal of preregistration by the proposed method is to reduce the search space of the iteration optimization and increase the robustness of the process of the registration. The purpose of using SSD in Figures It is striking that the estimation of rotational differences is accurate and robust for very dissimilar images captured for the same scene. When there are large local differences, illumination changes, scale or rotational changes, the process of histogram matching generates promising results. The main reason is that the proposed method is computed based on the global distribution of local orientations weighted by gradient magnitudes, which seems to be robust to considerable image changes for multimodalities. The statistic orientation histogram matching is robust to capture the rotational differences between images. Since no high-level features in images are required in the process, the proposed method is very simple and robust to determine the rotational difference between two images. The proposed method for orientation differences estimation is able to be used for rigid registration directly. Since if the orientation difference between two images is known, the prealignment becomes significantly easier after eliminating the rotational difference between two images. The work left from translation estimation is then determined by mutual information-based , phase cj for j = 0,…, K − 1. The global minimum value was 349 (or 11°), which was same to the result in The overlapping area between two unregistered images is an important factor for general image registration. It is often assumed that the overlapping area is larger than 50% of the image area, and registration methods have to be robust to partial occlusion. In clinical medical images, the scan volumes to be registered often contain same anatomic structures of the patient but are often scanned at different time or in different scans. Therefore, it is assumed that the unregistered two images are almost contain the same scene in medical images, so the red circle in θ and θ + 180° should be considered for image registration. Since the rotational angle for clinical medical images is often not too large, the global minimum θ can be validated by this experience.Since the gradient orientations in a neighborhood of a straight pattern have (on average) opposite directions, the orientation histogram appears to be symmetric from 0 to 360° due to the fact that about half the gradient vectors have an opposite direction (180°) with respect to other halves for straight patterns in images. The major difference in the image registration with and without the proposed method is the computation iterations (efficiency) as well as the possibility of finding the global minimum of the optimization (robustness), rather than the accuracy. Thus, reducing the number of iterations of optimization (time consuming) is one advantage of the proposed method. More importantly, increasing the possibility of finding global minimum of optimization of image registration (robustness) is another advantage of the proposed method. Certainly, accuracy of registration is known to be most important in image registration, but the robustness and efficiency of registration are very important as well. Modern computers with more powerful performances may make the process of time reducing meaningless. However, the success rate of the registration (robustness) cannot be improved with powerful computers. Experiments have demonstrated that the proposed method can make the registration more reliable in the process of iterative optimization and reduced the chances of registration failure.V in 3D into three components V = {θ, Ψ, γ}, where θ, Ψ, and γ are the angles between the vector and the x, y, and z coordinate, respectively. The orientation difference in 3D is thus converted to the histogram matchings with respect to θ, Ψ, and γ, from which the final orientation difference between two 3D volumetric images is defined by synthesizing Δθ, ΔΨ and Δγ in the x-y-z coordinate system. Without loss of generality, the case of 2D image registration has been fully considered for explanation in the work.This application is expected to straightforwardly extend to 3D volumetric images, in which the local orientation is estimated based on the smoothed structure tensor  in a voxIn this work, a very simple and robust method was proposed to compute the rotational difference between two multimodality images and very dissimilar monomodality images. The proposed method is superior to the existed edge-map based method from the experimental comparison. Experimental results have demonstrated that orientation detection between images is reliable and robust to considerable deformations, slightly scale differences, and dissimilar image contents. Experimental results have also demonstrated that the incorporation of this method into image registration both enhances the robustness of registration and significantly speeds up the registration calculation. It is worthwhile to note that the proposed method of orientation detection is appropriate to be applied for image registration with rigid transformation and nonrigid transformation, which has very broad applications in medical image registration and other applications in general image registration.


Multilegged locomotion improves the mobility of terrestrial animals and artifacts. Using many legs has advantages, such as the ability to avoid falling and to tolerate leg malfunction. However, many intrinsic degrees of freedom make the motion planning and control difficult, and many contact legs can impede the maneuverability during locomotion. The underlying mechanism for generating agile locomotion using many legs remains unclear from biological and engineering viewpoints. The present study used a centipede-like multilegged robot composed of six body segments and twelve legs. The body segments are passively connected through yaw joints with torsional springs. The dynamic stability of the robot walking in a straight line changes through a supercritical Hopf bifurcation due to the body axis flexibility. We focused on a quick turning task of the robot and quantitatively investigated the relationship between stability and maneuverability in multilegged locomotion by using a simple control strategy. Our experimental results show that the straight walk instability does help the turning maneuver. We discuss the importance and relevance of our findings for biological systems and propose a design principle for a simple control scheme to create maneuverable locomotion of multilegged robots. Legged locomotion is one of the versatile forms of mobility for terrestrial animals and artifacts. Locomotor behaviors differ in accordance with the number of legs. The use of many legs has advantages, such as the ability to avoid falling and to tolerate leg malfunction123As an example, centipedes are arthropods that have a lot of legs. Although different species of centipedes have different numbers of legs, all have at least 15 pairs (some have 191 pairs) of legs as adults5So far, to elucidate adaptive motor control in arthropods, biomechanical and physiological studies have measured the activities of their exoskeletal, muscular, and nervous systems during locomotion7891011121314151718192021222425262728293032In our previous work34In the present study, we improved our previous robot and control system to perform turning locomotion to demonstrate the relationship between the stability induced by the passive properties in the body axis and the maneuverability in multilegged locomotion in the real world. We first clarified the stability properties of a robot walking in a straight line in accordance with the body axis flexibility and then investigated how the stability properties influence the turning maneuverability by defining evaluation criteria to quantitatively investigate the relationship between stability and maneuverability. Our robot experimental results show that the body flexibility changes the stability of straight walking and that the straight walk instability does help the turning mobility, similar to the results of the modeling study of cockroaches. In this paper, we discuss the importance and relevance of our findings to understanding the underlying mechanisms in biological systems for manipulating the turning maneuverability and we propose a design principle for a simple control scheme to create maneuverable locomotion of multilegged robots.k). Each leg has two pitch joints to walk and the legs in the first body segment have an additional yaw joint to control the walking direction by a laser range scanner. Although the body segments are passively connected, the leg joints are controlled by motors. The leg pitch joints are controlled so that the leg tips follow the desired movement composed of two parts: half of an elliptical curve, and a straight line . We set all the body segments parallel to each other as the initial condition and the leg yaw joints in the first module were fixed.Our previous study using a computer simulation of a robot model and a Floquet analysis with a simple physical model34k = 7.3, 8.7, 11, and 15 and not for k = 21, 41, and 450 Nmm/deg. k−1 calculated by the Fourier transform. The data points and error bars correspond to the means and standard errors, respectively, of the results of five experiments. These amplitudes vary with k−1 and show the Hopf bifurcation. These results were fitted by the square root of k−1 to evaluate the bifurcation point When we used large spring constants for torsional springs in the body-segment yaw joints, the robot kept walking in a straight line as expected, and the body segments were aligned without producing body undulations . Howeverx-y plane). The leg yaw joints θ1 and θ2 of the first module were controlled based on the relative angle θt between the first module and the target monitored by the laser range scanner , which was the smallest spring constant in our experiments, neighboring body segments easily clashed and our robot could not achieve the turning task well.ectively ,4–5. Wheectively , the robectively , it tookectively , althougε1, ε2, and ε3. k−1, where the data points and error bars correspond to the means and standard errors, respectively, of the results of five experiments, and the gray regions indicate that the straight walk is unstable, as estimated from ε1 shows the time that our robot took to reduce the relative target angle to less than 10% of the initial value; the time is used to evaluate how quickly our robot changes the walking direction to point to the target. The second criterion ε2 is the integration of the absolute value of the relative target angle during the turning task; the integration is used to estimate how quickly and stably our robot is oriented to the target. The third criterion ε3 indicates the deviation of the first module trajectory on the floor from the line between the initial position and the target ; the deviation is used to evaluate how small the overshoot of the robot trajectory is to approach the target. For these criteria, smaller values indicate better turning performance. As shown in the figures, when the spring constant is large so that walking in a straight line is stable, these criteria have large values. Although these criteria decrease as the spring constant decreases, they show an increase, especially ε2 and ε3, at k−1 = 0.115. This means that the turning performance increases as the straight walk becomes unstable, but that a large instability degrades the performance.To quantitatively clarify the turning performance in accordance with the spring constant, we employed three evaluation criteria, As should be clear by now, stability and maneuverability are important factors for evaluating locomotor performance. The stability is related to the capability in the moving direction to resist and recover from disturbances. In contrast, the maneuverability is related to the ability to voluntarily change the direction. These properties have a strong connection in locomotion. The connection prominently appears in locomotion generated through the dynamic interactions of aerodynamics and hydrodynamics. For example, some aquatic animals and aircrafts utilize instability to enhance their maneuverability. Sea lions have relatively large flippers and highly flexible bodies, and execute turning by body flexion and using their flippers. Their flippers are located near the center of gravity and their morphology promotes rotational and translational instabilities, which enhances turning performanceLegged locomotion is characterized by the dynamic interactions between the feet and the contact surface and by the intermittency of the interactions due to the discrete events of foot contact and lift-off in periodic leg movement. Mammals with erect legs have a high center of mass and use body leaning to enhance their turning maneuverability3332In centipede locomotion, body undulations are absent at slow speeds and appear at faster speeds13433233Although our robot has only six pairs of legs, adult centipedes have at least 15 pairs of legs (some have 191 pairs of legs)534Even though the instability helps the turning maneuver, stability and maneuverability are generally a trade-off45464742In the present study, the stability changed through a bifurcation via the body axis flexibility. Bifurcation plays an important role in various motor behaviors in terrestrial animals, such as gait transition50515254For the control design of the locomotion of artifacts, maneuverability is an important factor. In particular, biologically inspired robots that use the body axis for propulsion in locomotion, such as snake and fish robots, have achieved maneuverable locomotion comparable to that of animals47565758Even when all robot movements are planned in real time through huge computations based on the robot model, and when tasks and planned motions are generated, robust locomotion against uncertainties, such as modeling errors and environmental variations, is not necessarily produced. Locomotor performance degrades as the robot and the environment become more complex. Designing a simple control system based on fundamental dynamical principles is more useful for legged robots than a control system based on such precise motion planning and control. For example, biped robots based on passive dynamic walking272863In general, the design of the controller of artifacts focuses on the stabilization of the systems. However, our robot experiments show that the active use of instability leads to improvement of locomotor functions. Such instability is useful, as shown for artifacts such as aircraft38k = 7.3, 8.7, 11, 15, 21, 41 and 450 Nmm/deg) to investigate the dependence of walking performance on the straight walk stability. Module 1 has a laser range scanner  to find the relative position of a target for turning. Our multilegged robot consists of six body segment modules (Modules 1–6), as shown in The robot was controlled by an external host computer  with 2 ms intervals, and both computer control and electric power were provided via external cables. During the experiments, the computer control and electric power cables were kept slack and suspended to avoid influencing the robot’s locomotor behavior. The robot walked on a wooden flat floor with a vinyl floor mat to suppress slipping.π/3 rad. When the leg yaw joint angles of Module 1 were fixed so that the leg tip trajectories were parallel to the body segment, our robot was expected to walk in a straight line while keeping the body segments parallel to each other, because torsional springs were installed on the body-segment yaw joints and the leg tips moved parallel to the body segments at an identical speed for all legs.To produce straight walking of the robot, we controlled the leg movement by using the two pitch joints in each leg to follow the desired movement, which consists of two parts: half of an elliptical curve that starts from the posterior extreme position (PEP) and ends at the anterior extreme position (AEP), and a straight line from the AEP to the PEP . In the θt of the first module measured by the laser range scanner and the leg yaw joints θ1 and θ2 of the first module ) byFor a quick turn task of our robot, we made the robot approach a target located on the floor in a largely different direction from where the robot was oriented . For that module . Specifitstart and tend were set to 40% and 80%, respectively, of the duration of the half elliptical curve of the leg tip trajectory (=0.12 and 0.23 s). This means that each leg changed its yaw direction to the target only during the swing phase with 5° of the maximum turning angle for one gait cycle. The robot iterated this procedure in the legs of the first module for the gait cycles (after t = 5 s), and the turning task was complete when θt converged to 0. We performed robot experiments of this turning task for various spring constants of the torsional springs to investigate the dependence of the turning mobility on spring constant k. We used θt = 80° and 4 m for the distance between the first module and target and set all body-segment yaw joint angles to zero as the initial condition.where ε1, ε2, and ε3. For the first criterion, ε1, we examined the time needed for our robot to reduce the relative angle θt to less than 10% of the initial value in order to evaluate how quickly the robot changed the walking direction to point to the target. We defined the second criterion ε2 byTo quantitatively investigate the turning performance of our robot, we defined three evaluation criteria, t1 = 5 s (start time of turning) and t1 = 55 s (θt sufficiently converges to 0 for stable cases and shows some oscillations for unstable cases by this time). This criterion estimated how quickly and stably our robot was oriented to the target. For the third criterion, ε3, we usedwhere y = f(x) is the trajectory of the first module on the floor during the turning task, x = y = 0 is the initial position, y = ax is the line connected from the initial position to the target (a = tan10°), x1 = x(t1), and x2 = x(t2). The position of the first module on the floor was calculated by measuring not only the target but also other landmarks located on the floor by using the laser range scanner. The third criterion calculated the area enclosed by the trajectory of the first module (y = f(x)) and the line (y = ax) to evaluate how much the first module deviated from the line (y = ax) and how small the overshoot was to approach the target .


The current risk model for percutaneous coronary intervention (PCI) in the UK is based on outcomes of patients treated in a different era of interventional cardiology. This study aimed to create a new model, based on a contemporary cohort of PCI treated patients, which would: predict 30 day mortality; provide good discrimination; and be well calibrated across a broad risk-spectrum.The model was derived from a training dataset of 336,433 PCI cases carried out between 2007 and 2011 in England and Wales, with 30 day mortality provided by record linkage. Candidate variables were selected on the basis of clinical consensus and data quality. Procedures in 2012 were used to perform temporal validation of the model. The strongest predictors of 30-day mortality were: cardiogenic shock; dialysis; and the indication for PCI and the degree of urgency with which it was performed. The model had an area under the receiver operator characteristic curve of 0.85 on the training data and 0.86 on validation. Calibration plots indicated a good model fit on development which was maintained on validation.We have created a contemporary model for PCI that encompasses a range of clinical risk, from stable elective PCI to emergency primary PCI and cardiogenic shock. The model is easy to apply and based on data reported in national registries. It has a high degree of discrimination and is well calibrated across the risk spectrum. The examination of key outcomes in PCI audit can be improved with this risk-adjusted model. Since 2005, BCIS has incorporated patient-level data in its long running annual audit of all percutaneous coronary intervention (PCI) procedures performed in the UK. This audit is used for benchmarking performance to help improve services and underpin clinical governance The British Cardiovascular Intervention Society  model has been used for risk-adjusted outcome surveillance since 2006 The aim of this study was to produce an updated robust risk adjustment model with good discrimination and correct calibration for contemporary PCI practise in the UK. A similar updating exercise has recently been undertaken in the National Cardiovascular Data Registry in the US 22.1The BCIS database comprises 113 variables describing baseline demographics, clinical presentation, procedural details and outcomes to hospital discharge. Data for all procedures performed in the UK are collected at each PCI centre, encrypted and then uploaded to servers now hosted by the National Institute for Clinical Outcomes Research (NICOR) based at University College London Although there is no independent validation of data entry, a number of range checks and assessments of internal validity are applied as data are uploaded to NICOR. We performed a sequence of further procedures to clean the dataset. A number of exclusion criteria were applied . We limiA total of 1112 procedures were identified as likely duplicate entries and were also excluded. These were identified by comparing records across age, gender, pseudonymised hospital identifier, pseudonymised patient identifier, pseudonymised date of operation, month of operation, time of operation, urgency, clinical indication for procedure and status at discharge. Data used for the final model are available from the authors where the requester has sought permission from NICOR.2.2Of the available fields in the BCIS dataset, a shortlist of 10 candidate risk factors was identified by the authors on the basis of clinical consensus and data quality. As the model was intended to be used to predict outcome before the start of a procedure, variables relating to decisions or events occurring during or after the procedure were excluded.Age at procedure was given in years and months. For modelling, age was mean-centred within the development cohort (mean = 64.8 years); a quadratic age term was also explored. Diabetes was defined as present whether patients were diet controlled, or treated with medication including insulin. Serum creatinine levels were only recently added to the dataset and were therefore missing in earlier years of the development cohort. However, a binary variable indicating whether creatinine measures were greater than 200 μmol/l was available throughout the time period, so this was used as the measure of renal function. Use of dialysis for acute or chronic renal failure was also recorded, and if both this and a creatinine measure of > 200 μmol/l were present, the patient was assigned to the ‘dialysis’ group. Patients with functioning transplants were grouped with those who had no renal impairment, unless on dialysis or with a creatinine > 200 μmol/l.www.ucl.ac.uk/nicor/audits/adultpercutaneous/datasets). Clinical indication for PCI procedure is recorded as one of 12 possible options in the database. For the purposes of this model we derived a simpler five-group classification to combine the clinical indication and the urgency of the procedure, to avoid the problem of collinearity between these two variables. These groups are described in Definitions of the fields are available online  and the ability of the model to correctly separate those who went on to have the outcome from those who did not (discrimination). We used visual inspection of calibration plots derived from calculating the Hosmer–Lemeshow statistic, as opposed to relying on P values for this statistic, which are often unreliable with large datasets To improve the calibration of the model, we also explored interaction terms. A selection of clinically plausible interactions was tested by introducing them individually into the model. Those which gave a statistically significant contribution to the model were then introduced in a forward stepwise manner with manual selection on the basis of Akaike information criterion. In the interests of maintaining parsimony, we restricted the number of interaction terms to three.The selected model was then validated on data from 2012  and calibration and discrimination tests were performed as above.33.1Of the 336,443 procedures included in the model development dataset from 2007 to 2011, a total of 5722 patients died within 30 days of their procedure (1.7%). The final model is shown in There were three interaction terms introduced to improve the calibration of the model: clinical indication and cardiogenic shock, centred age and cardiogenic shock and centred age and diabetes. The negative coefficients associated with these interactions effectively correct for over estimation of risk in patients who have both risk factors in the interaction pair. The quadratic term for age did not improve the model so it was not included.Risk prediction is carried out by summing constant and all coefficients where a risk factor is present to derive the log odds. 64.8 is subtracted from age before multiplying by coefficient. Interaction coefficients are used when both interacting features are present.For example, a 75-year old male with diabetes, in urgency group 2 would have log-odds = − 6.089 + 0.071*(75–64.8) + 0.524 + 1.004 + (− 0.016) × (75–64.8) = − 4.000. This can be converted to a probability: P = 100/(1 + exp.(−(− 4.000))) = 1.80%.3.2The validation data from 2012 comprised 75,234 procedures with a 30 day mortality of 2.09%. The validation cohort was similar to the development cohort in terms of patient characteristics though patients in the validation cohort were on average slightly older  and a far higher percentage of the patients who died within 30 days had been classified as salvage procedures (36.2% compared with 17.1% in the development cohort).Calibration plots at a range of quantile thresholds indicated a good model fit with the development data. 3.3We examined different approaches to handling missing data. Complete case analysis was performed by examining the performance of the above model only in people who had information available for all the included variables . Of the development cohort, 264,053 (78.5%) of people fulfilled this criterion. The model coefficients and intercept were broadly similar. There was an increase in the coefficient for indication-urgency group 5 but a decrease in the coefficient for cardiogenic shock. The area under the ROC curve for the complete case model was 0.789. This drop in model discrimination may lend support for the inclusion of non-complete cases under an imputation framework.Multiple imputation was conducted as a sensitivity analysis to see if there was any additional benefit in using this approach. Overall the model coefficients remained broadly consistent under multiple imputation, though the coefficient for cardiogenic shock decreased from 3.82 to 3.73 (with a corresponding drop in odds ratio of 45.47 to 41.76). There was no difference in the AUC between ‘missing assumed absent’ and multiple imputation, as assessed using either the training or validation datasets, nor did calibration plots noticeably differ.Inclusion of LVEF as a variable in the model under different missing data handling frameworks identified that worsening LVEF was associated with a higher odds of 30 day mortality. However, the estimated size of the effect was sensitive to the method used. When the model was trained only on cases where LVEF data were present, ‘fair’ LVEF (30–50%) was assigned a coefficient of 0.84  and ‘poor’ LVEF (< 30%) had a coefficient of 1.67 . Where multiple imputation was used, however, the estimates shrunk: fair LVEF gave 0.28  and poor LVEF gave 0.79 . A comparison of models where LVEF was or was not included indicated only a small incremental improvement in overall model discrimination on its inclusion: in the full training set a model without LVEF had an AUC of 0.848 while a model with LVEF had an AUC of 0.852. We decided not to include LV function in our model for a number of reasons. We wanted the model to be as parsimonious as possible. The analysis above has shown only a small improvement in AUC. Our model needed to be as robust as possible in the setting of a National data collection programme, where the majority of PCI is performed in an acute setting, the likelihood of a significant improvement in data collection for LV function was low in the short term, and the variability of LV function in this setting acknowledged but poorly defined.44.1We have created a contemporary PCI mortality model that encompasses a wide range of clinical risk, from stable elective PCI to emergency primary PCI and cardiogenic shock. It has a high degree of discrimination and is well calibrated across the risk spectrum.The overriding aim of clinical audit is to drive up standards of care. This requires that important aspects of care are measured so they can be assessed. Robust risk adjustment underpins any clinical audit that is used to assess institutional or individual operator performance.There are several outcomes by which the quality of PCI might be measured. While symptom relief is undoubtedly important in patients with stable angina, over 70% of patients in the UK are treated in the context of an acute coronary syndrome 4.2The model presented here represents a tool which better reflects contemporary UK clinical practise than existing published models. The previous UK NWQIP model It is possible that the discrimination of this model would improve with the addition of further risk factors. Lack of sufficient data on left ventricular ejection fraction (LVEF) was a notable limitation of our data resource. The Toronto PCI in-hospital mortality score, which has an AUC of 0.96, incorporates a binary measure of LVEF, assigning an odds ratio of 1.40 to patients with LVEF of < 20% 4.3Clinical performance measurement is moving into an era of greater openness, transparency and candour. It is no longer acceptable for measures of outcome to be used only within professional bodies. Public reporting of outcomes of individual operators is intended to drive up standards, and uncloak what has been perceived as professional secrecy. In providing patients with much more information, it aims to help a rational selection of treatment choices, and to promote a better understanding of expected outcomes. It demonstrates to the public that quality of care is being actively monitored and improved where necessary. Public reporting also encourages healthcare organisations to focus on recording and providing more complete and accurate information.An important problem with public reporting is that it can precipitate risk-averse clinical decisions, disadvantaging the sickest patients who have the most to benefit from interventions 4.4Although the BCIS audit programme applies to all UK procedures, the model was fit using only data from England and Wales, since record linkage via the Office for National Statistics is available only for these patients. This does, however, present opportunity for validation studies in Scotland and Northern Ireland; these regions may have different patterns of risk factors and mortality, adding useful heterogeneity to the extended validation of this model. Further temporal validation should be conducted in future years to ensure the performance of the model remains acceptable, with recalibration performed as necessary Our practise of replacing missing categorical values with null values may lead to biased estimates of individual patient risk. This will cause bias if some centres or operators are systematically under-reporting the presence of risk factors. However, we found no benefit to be had from conducting multiple imputation, and it may be more productive to focus efforts on reducing missing data at source in future years of the audit. Given the additional complexity of applying the model in a multiple imputation framework, and the fact that data may be missing in patterns other than random, our approach is appropriate at this time.Due to limitations imposed by the data sharing framework, we did not have access to un-pseudonymised procedure date. It was therefore not possible to identify redo procedures (i.e. those which were a second attempt), which may have led to some double counting of procedures or potential underestimation of the mortality burden of the index procedure in cases where a patient died following a redo procedure. We hope that the establishment of “safe havens” for analysis by national organisations such as the Farr Institute will enable such analyses in the future, better serving patients with proportionate governance of their information 4.5We intend to validate the model further, and monitor the calibration and discrimination performance over time, updating as necessary. Future updates of the model will likely incorporate established or emerging risk factors that we were not able to include in this version.In addition, we are investigating dynamic modelling approaches that will run continuous statistical surveillance of model performance and prompt the clinical audit team over possible calibration drift and potential structural deterioration of the model. Where factors such as renal function are under-represented due to data quality they can be kept on watch for fuller inclusion as the data are better collected. In addition, there is a need to study the effects of different forms of audit feedback on data collection and quality.4.6We have generated a new parsimonious and contemporary model for predicting risk of 30-day mortality in patients undergoing PCI in the UK. It shows good discrimination and calibration across a wide spectrum of risk. It takes into account the marked changes to the performance of PCI in recent years and is independent of variations in completeness of adverse event reporting and therefore is a more appropriate choice of model for the BCIS national audit programme.The authors report no relationships that could be construed as a conflict of interest.


This article was republished on May 19, 2014, to replace Figure 3 with a version which is available under the Creative Commons CC0 public domain dedication. The figure caption was also amended to clarify this is the case. Please download this article again to view the correct version.


To calculate the intensity of x-ray emission in electron beam microanalysis requires a knowledge of the energy distribution of the electrons in the solid, the energy variation of the ionization cross section of the relevant subshell, the fraction of ionizations events producing x rays of interest and the absorption coefficient of the x rays on the path to the detector. The theoretical predictions and experimental data available for ionization cross sections are limited mainly to K shells of a few elements. Results of systematic plane wave Born approximation calculations with exchange for K, L, and M shell ionization cross sections over the range of electron energies used in microanalysis are presented. Comparisons are made with experimental measurement for selected K shells and it is shown that the plane wave theory is not appropriate for overvoltages less than 2.5 V. I is the distribution of electrons in the specimen as a function of energy E and position r, σX(E) is the ionization cross section for the relevant subshell, fX is the fraction of ionization events producing x rays in the line of interest and σX is the absorption coefficient for the x rays on their path to the detector at position r0. The integration is over all electrons that can ionize the subshell of interest, energy EI, and over the volume of the specimen. For TEM this expression can be considerably simplified as specimens are so thin that energy loss is negligible.  The cross section is then just the ionization cross sections for electrons at the beam energy.The intensity of x rays emitted when an electron beam strikes a sample depends on the energy distribution of the electrons in the solid, the energy variation of the ionization cross section of the relevant subshell, the fraction of ionization events that give x rays in the line of interest and the absorption coefficient of the x rays on the path to the detector. This can be summarized as IX=∫EIE0Φ(ρz), that is a function of depth in spatially homogeneous specimens [Φ(ρz) function [In microanalysis the ionization cross section for production of x rays and the electron energy distribution are often multiplied together to form a new function pecimens .IX=∫ϕ(r|r0−r|)drϕ(r)=∫E1The energy distribution of electrons in the specimen can be modeled either from numerical solutions of the Boltzmann transport equations  or MonteThe fraction of events giving x rays in the line of interest is a product of the fluorescence yield and the fraction of x rays in a particular line. Reliable calculations for fluorescence yield and x-ray emission rates based on atomic physics are readily available ,7,8,9. Axn is the number of electrons in the subshell and xb and xc are parameters to be determined by fitting to experimental data or other calculation. An obvious shortcoming with this expression is that it fails for electron energies less than cXEI when xc is greater than 1 . The same problem arises in the expression for the stopping power and Joy and Luo [In practice microanalysts use cross sections based on the Powell  paramete and Luo  have pro and Luo  was aime3 ionisation cross sections were tabulated from sulfur, and M5 cross sections from strontium. The high binding energy limit was set at about 40 kV which meant that K cross sections were calculated up to promethium and all L3 and M5 cross sections up to uranium were tabulated. The cross sections were calculated for a range of energies from the binding energy or 5 kV, whichever was lower, up to 400 kV. This represents the range of electron energies used in both scanning electron microscopes and transmission electron microscopes. The steps were chosen to correspond to typical step sizes on electron microscopes, though of course intermediate values could be estimated by interpolation.I have now completed systematic calculations of the electron ionization cross sections from all subshells that might be relevant for microanalysis. The plane wave Born approximation with the Ockhur  approximA selection of the results is presented and they are compared with experimental measurement and other previously reported calculations.E ionizes an inner shell with binding energy EB, and in the process is scattered by a wave vector q emerging with energy E′ and ejecting an electron of energy ε from the atom. Conservation of energy requires thatψi(r1) represents the incident electron, φi(r2) the inner shell electron, fψ (r1) the scattered electron and fφ (r2) the ejected electron. The constant a0, the Bohr radius, gives the scale of the interaction and γ is the relativistic correction factor. Expanding The complete theory is given elsewhere  so in thgiven by d2σdΩdε=ψi(r1) and the scattered wave fψ (r1) can be represented by plane waves exp(ikir) and exp(ikfr) respectively. The momentum transfer, q, is just the difference between the initial and scattered wavevectors.fk the scattered wave vector isF defined byq and ε, known as a Bethe surface [ε is about 4 EB the ejected electron can be represented by a plane wave with wave vector q. The GOS tends to a Gaussian shape known as the Bethe Ridge with a half width in nm−1 approximately given by EB the binding energy is in Hartrees. The GOS values were tabulated to a momentum transfer of −1 over an energy range of 4 EB. Above this energy the scaled form of the Bethe Ridge was used. It was found that exponential grids in both wave vector and electron energy gave the minimum error in the numerical integration, and 64 points in q and 64 for ε were sufficient to assure numerical convergence to better than 2 %.The incident wave attering qmin=ki2 surface . In the FB. The GOS in An approximate expression for the exchange scattering due to Ochkur  also assEB and then slowly falls off [U, the ratio of the electron energy to the binding energy.It is well known that the ionization cross section typically rises from threshold to a maximum at about 3 alls off ,17. Sinc3 and uranium M5 are plotted as a function of electron energy. The dashed curves are the direct contribution only, the solid curves incorporate the effects of exchange with the approximate theory. Exchange not surprisingly has a larger effect near threshold and typically can lower the ionization cross section by 20 % in the region of the peak at about 3 EB. At higher energies typical of transmission electron microscopes the exchange correction is less important, making a 3 % difference for inner shells with binding energy of about 3.5 kV, and an 8 % difference for inner shells with binding energies of about 11.5 kV. The corresponding figures for a 400 kV accelerating voltage are 1 % and 3 %, respectively.In 3 and uranium M5 are all shown as Since this is the first time that M cross sections have been explicitly calculated it is interesting to compare them with K and L cross sections for subshells with comparable binding energy. The cross sections for potassium K cadmium LThere have been very few systematic calculations of cross sections reported in the literature, the most comprehensive being those published by Scofield . He was While comparison with theory is limited to very high energies, the experiments are confined to low energies, very often not even covering the peak of the cross section. Nearly all the results are for K shell ionization of transition element thin films, no doubt because they are easy to prepare. There are additional complications from backscattered electrons generating x rays when the film is lying on a substrate. Luo et al. , have usIn his work on the relative cross sections for electron and positron emission Hippler  argued tEB, then it is inconsistent to treat the scattered wave as a plane wave at these energies since electrons are indistinguishable. A correct formulation would represent all the electrons as radial solutions of the appropriate energy of the Shrodinger equation with the atomic self-consistent potential. The theory would look very different and the direct them would then bej symbols and r> and r< mean the greater or lesser of r1 and r2, respectively. The exchange term, g, is identical apart from switching r1 and r2 in The problems arise from an incorrect treatment of the wavefunctions for low energies above threshold. If it is wrong to treat the ejected electron as a plane wave for energies less than 4 A selection of results from a comprehensive set of calculations for K, L, and M shell ionization cross sections relevant for microanalysis has been presented. The theory is based on the plane wave Born approximation with the Ochkur  expressiEB. There is good agreement with both Scofield’s [The cross sections have been tabulated over an energy range from 5 kV to 400 kV appropriate for both scanning and transmission electron microscopes. The cross sections show similar behavior with energy, showing a peak at about 3 ofield’s  calculat


Sub-pixelic resolution is obtained thanks to a structured pattern placed on the target. The pattern is made of twin periodic grids with slightly different periods. The periodic frames are suited for Fourier-like phase calculations—leading to high resolution—while the period difference allows the removal of phase ambiguity and thus a high range-to-resolution ratio. The paper presents the measurement principle as well as the processing algorithms . The theoretical and experimental performances are also discussed. The processing time is around 3 μs for a line of 780 pixels, which means that the measurement rate is mostly limited by the image acquisition frame rate. A 3- It restricts the unambiguous measurement range to a single stripe period. The measurement range and measurement resolution are thus dependent on each other and the number of resolved positions is equal to K = 2π/δΦ, where δΦ is the resolution of the phase determination. The only adjustment parameter is P that affects range and resolution in inverse proportions and thus does not affect the range-to-resolution ratio. The latter can only be improved through the phase computation performances. In practice, image digitizing, electronic noise and environmental disturbances form irreducible noise sources. As explained below, the use of a second stripe period is an alternative way to extend the measurement range without decreasing the resolution.where 2.2.R; i.e., when the stripes have the same position with respect to each other as at the left side of the image. Thanks to the progressive mismatch between the two stripe sets, phase ambiguities can be removed and the unambiguous range switches from a single period to a new value Λ given by:The use of a second stripe set with a slightly different period provides complementary and independent phase data that can be used for the removal of phase ambiguities. The principle is illustrated in P1 and P2 are the stripe set periods .where P is replaced by Λ. In fact, because of the phase subtraction, noise is magnified in the same proportion as the unambiguous range and a supplementary step is necessary to improve the range-to-resolution ratio. This step consists in using synthetic data to determine the correct 2kπ constant to apply to the phase shift observed for either stripe set. From a computational point of view, the phase relative to the synthetic period Λ is simply given by the subtraction between the two elementary phases  after ph1 is the phase shift for the chosen stripe set, k1 the number of periods derived from the synthetic phase and xk an unknown number of periods Λ that represents the new ambiguity range. The range-to-resolution improvement resulting from this twin period method is equal to Λ/P1.in which ΔΦP1 and P2. We notice however that large values of Λ are obtained with small period differences. In such cases the effects of noise are significantly enlarged and, at some level, the determination of k1  and I2(l) (l pixel index) are extracted and associated with stripe sets of period P1 and P2 respectively.This preprocessing task aims to determine the image lines to be used for the phase computation for each stripe set. Since our aim is to measure only 1D displacements, the hardware is set in such a way that the stripes are perpendicular to the displacement and the camera lines are parallel to the stripes. With this setting, stripes move only in the horizontal direction of the recorded images and this task has to be performed only once. Since the used pattern is repetitive, there are several possibilities and for instance the stripes sets between the red lines can be chosen cf.. At this3.2.I(l) is the windowed intensity vector, l and s are reciprocal variables and N is the number of image pixels per line. m of the maximum DFT magnitude within a spectral interval . This interval aims to remove background intensity and high frequency noise.This second step aims to determine the spatial frequency of each stripe set in the recorded images. This task has also to be performed only once since the imaging magnification is not affected by 1D lateral target displacements. Furthermore m in order to get a better localization of the maximum, such as:Since the log of a Gaussian produces a parabola, we use a quadratic interpolation on the points around P in the pattern image is then given byi.e., once for each stripe set and thus periods P1 and P2 are obtained.The stripe period 3.3.Z1(l) defined by a Gaussian envelop and a periodic signal at the period of the stripe set  by the intensity distribution I1(l):We notice that the analysis functions have also to be defined only once. The expected phase Φ2 related to the second stripe set is computed in the same way by applying this procedure with P2 instead of P1 and I2(l) instead of I1(l). We then obtain the synthetic phase Φ related to the current image by: Φ = Φ1 − Φ2 which has to be unwrapped in the interval ]−π, π] by adding ±2π where necessary  instead of that of the synthetic period Λ is obtained by rounding (k1 = round(k̂1) where round(x) returns the integer the closest to x) k̂1 to the closest integer k1. The high-resolution displacement measurement is finally provided by inserting the computed value of k1 in xk = 0. This procedure leads to the final displacement value with a range-to-resolution ratio RRR of:From a theoretical point of view, 4.Without considerations for the material used, the ultimate capabilities of the method would be determined by the physics phenomena involved and, in our case, would imply quantum statistics of the light source of illumination and of photon conversion on the image sensor. Such fundamental sources of noise are responsible for extremely low error levels as expected for instance in gravitation wave detection interferometers. In the case of applications based on scientific grade instrumentation as aimed here, the ultimate performances are determined by material and environmental specifications. The most influential error sources in such visual experiments are thus due to digitizing and to the signal-to-noise ratio of the detected images. Environmental disturbances are also detrimental to high resolution displacement measurements and may be found to be the most restrictive parameter. They remain however independent of the intrinsic method capabilities and thus form extrinsic error sources.cf. Section 2). The square grids were digitized using area sampling with a fill factor equal to one emulating a perfect CCD sensor . The standard deviation of digitizing errors is of 10−4 pixel at this digitizing depth. The red curve was obtained without digitalization but by adding a gaussian noise to the generated grid with a standard deviation equal to 1% of the square amplitude. The resulting errors present a different distribution but approximately with the same peak-to-peak amplitude. The error standard deviation due to gaussian noise is equal to 9.6 × 10−5 pixel. These simulation results determine the best resolutions that can be expected experimentally with these parameters that correspond to typical specifications of usual image sensors.Differences observed between the reconstructed positions and the ones used for image generation provide the actual method detection errors. N and the grid period. The best resolution is achieved when this ratio corresponds to an integer number—as indicated by the red vertical lines - which corresponds to the best representation of an infinite periodic signal as considered in continuous Fourier transforms.i.e., if the grid period remains the same; then after error conversion from pixels to actual distance, the resolution becomes independent of the period value as represented in If the period increase is due to an increase of the vision system magnification; These numerical evaluations of the method capabilities can be used to match the setup design with the expected system performances. For instance, if sufficient free space has to be kept between the lens and the target, a larger grid period can be chosen to be suited with a low magnification objective and a large working distance. The resolution loss due to period increase can then be compensated by the use of a higher grade camera with improved signal-to-noise ratio and digitizing depth. Such an elementary period increase may also be chosen to enlarge the unambiguous measurement range as defined by 5.5.1.P = Λ = 168 μm . The blue curve is obtained from P1 after compensation for 2π phase jumps. The gain in resolution can be evaluated in σ precision of 5 nm. It could be compared to the 55 pm found as the optimal resolution of the method in these conditions, in Section 4. This gap is the result of environmental disturbances : a 5 nm noise is normal for a macro-setup used in non-controlled atmosphere.5.2.Z direction; i.e., perpendicularly to the beams, result in 1D displacements of the shuttle. Such a device allows force-to-displacement transduction with a proportion ratio that is a function of the beam stiffness. A grid pattern was fixed onto the shuttle and observed by means of the vision system. The camera was replaced by a fast Firewire camera (Allied Vision Technology Pike F-032B). The exposure time was reduced to 18 μs and a region of interest of 320 × 26 pixels was selected in the image in order to increase the acquisition rate. A frame grabbing of 1389.5 fps was achieved with these parameters and a common computer . The C++ software developed (Provided as supplementary data to this paper.) was able to process the image flow in real time as demonstrated in i.e., 5 times the elementary grid pattern period, the continuity of the shuttle displacement is perfectly reconstructed thanks to the slightly different periods of the twin grids. The 1389.5 fps sampling rate allows for a high quality description of the 19.7 ms period of the shuttle vibration as observed in the zoom of 3 Hz on this machine.Finally the experimental setup was used to characterize the free oscillations of a compliant shuttle as shown in 6.http://www.mdpi.com/) and from the website of the VERNIER project (http://www.femto-st.fr/vernier/).In order to permit the reproducibility of results and the development of new applications, we provide the source code of the presented algorithms within a library called VERNIER along with the paper. The library is distributed under the GNU General Public License in the hope that it will be useful. The package can be downloaded from the website of MDPI (http://opencv.org/) is a widely-used library of programming functions mainly aimed at real-time computer vision. VERNIER also uses FFTW routines to compute the discrete Fourier transforms. FFTW (http://www.fftw.org/) is one of the fastest libraries for computing the discrete Fourier transform in one or more dimensions [While developing VERNIER, our goal was to allow a portable (independent from the hardware), fast, and reliable code. We also wanted to provide a package that is suitable for real-time implementation and that allows to obtain good performances with both simulations and real experiments from the same code. Therefore, we chose the C++ language for the implementation. VERNIER is built upon the cross-platform OpenCV library that provides a large compatibility with many image processing applications. OpenCV  by matching the actual values of the grid periods and of the vision system magnification accordingly. These conversion parameters from the object space domain to the image domain remains indeed ignored by the image processing routines that consider images only. Secondly as presented in the principle and numerical performance sections, the method resolution and unambiguous measurement range can be chosen almost independently from each other through the suitable choice of the grid period difference and of the camera signal-to-noise ratio and digitizing depth; provided that environmental disturbances remain sufficiently low. Thirdly, the vision system magnification does not have to be calibrated since the knowledge of the grid periods provides a size reference that is sufficient to convert pixels into actual distances in the reconstructed displacements.These specifications make the method very attractive for a wide range of applications especially in robotics and automation. At present time a single direction is addressed and this point is one of the few limitations of the method. The extension of the proposed principle to measurements versus multi-degrees of freedom can however be envisaged for instance by using stereovison and/or multiple grid patterns. In this prospect, the capabilities of grid processing to comply with defocus is of particular interest .


We studied the neutron quantum states in the potential well formed by the Earth’s gravitational field and a horizontal mirror. The estimated characteristic sizes of the neutron wave functions in two lowest quantum states correspond to their expectations with an accuracy of ≈25 %. The spatial density distribution in a standing neutron wave above a mirror was measured for a set of a few lowest quantum states. A position-sensitive neutron detector with an extra high spatial resolution of 1 μm to 2 μm was developed and tested for this particular task. Although this experiment was not designed or optimized to search for an additional short-range force, nevertheless it allowed us to slightly improve the published boundary in the nanometer range of characteristic distances. We studied systematical uncertainties in the chosen “flow-through” method as well as the feasibility to improve further the accuracy in this experiment. A mirror can be approximated as an infinitely high and sharp potential step compared to other characteristic parameters of the problem. Note that the neutron energy in the lowest quantum state ≈10−12 eV is much lower than the effective potential of a mirror ≈10−7 eV, and the range of increase of this effective potential ≈1 nm is much shorter than the neutron wavelength in the lowest quantum state ≈10 μm.Quantum states of a particle with mass echanics . A possiechanics . The lowechanics . The enenE in a gravitational field can rise to the maximum height of nz = nE/mg. In the quantum mechanics, a probability to observe a neutron in nth quantum state with an energy nE at a height z equals the square of the modulus of its wave function |nψ (z)|2 in this quantum state. Formally, this value is not equal zero at any height z > 0. However, as soon as a height z is bigger than the characteristic size nz of the corresponding wave function, specific for every nth quantum state and precisely equal to the height of the neutron classical turning point, then a probability to observe a neutron approaches zero exponentially fast. Such a purely quantum effect of penetration of neutrons to a classically prohibited region is called the tunneling effect.In the classical mechanics, a neutron with an energy z between a horizontal mirror on bottom and a scatterer/absorber on top (referred to as a scatterer hereafter). If a scatterer is much higher than the turning point for the corresponding quantum state Δz ≫ nz, then neutrons pass such a slit without significant losses. As a slit size decreases, the neutron wave function nψ(z) starts touching the scatterer and the probability of neutron losses increases. If a slit size is smaller then the characteristic size of the neutron wave function in the lowest quantum state z1, then such a slit is not transparent for neutrons. Just this phenomenon was measured in our previous experiment [Such a wave-function shape allowed us to find a method to observe the neutron quantum states: to measure their transmission through a narrow slit Δperiment : the neu−12 eV). The degree of validity of each condition is not evident a priori and should be verified in respective experiments. Thus, the efficiency of scatterers was shown to be close to unity and the probability of non-specular reflection of neutrons from bottom mirrors was measured to be at least as low as ~1 %. The absolute distance between a mirror and a scatterer was measured using a “capacitor” method.The experimental installation and the method of measurement are analogous to those used in our previous work  see Fig. We measα-decay: the neutron loss rate is proportional to the probability of neutron tunneling through the gravitational barrier between the classically allowed region and the scatterer height multiplied by the frequency of neutron collisions with the gravitational barrier. Detailed justification of this approach will be given in a forthcoming publication. At the moment let’s just present the parameterization, which is used to analyze the experimental data within framework of this model:F is the neutron flux through the slit, α is the coefficient responsible for a finite scatterer efficiency and for the approximations used in the model, nβ is a population of nth quantum state, Vhor is a neutron horizontal velocity component, and L is the mirror length along the neutron beam axis. One can show that a scatterer does not disturb too much the neutron wave functions and that allows us to extract the values of non-disturbed critical heights nz with an uncertainty of about ±1.5 μm.Our installation is a precision one-component gravitational neutron spectrometer. The most important limit for its spatial resolution in the mode of scanning the neutron density with a scatterer follows from the finite sharpness of the gravitational barrier penetrability in function of a scatterer height. Our model is analogous to the well known model of nuclear F [The dependence of the neutron flux through a slit between a mirror and a scatterer versus the slit size was measured in an analogous way to that in Ref. , with beΔz,Vhor)  on the vχ2/dof = 0.9. In this calculation, the critical heights {nz, n > 2} corresponded to the above mentioned values for pure quantum states while the two lowest quantum heights z1 and z2 were fitted from the experimental data; the quantum state populations {nβ, n > 1} were supposed to be equal except for the lowest quantum state population β1, which was calculated from the experimental data; the scatterer efficiency α was defined from the data as well.The curve (2) in β1 ≈ 0.7 ± 0.1) is lower than populations of higher quantum states as this was measured as well in Ref. [z1 and z2  are equal to Comparison of this model with the experimental data shows that: 1) the lowest quantum state population  firs235UF4) described in Ref. [A direct measurement of the spatial density distribution in the neutron standing wave above a mirror is preferable compared to its study using a scatterer with a variable height. This so-called differential method is much more sensitive. Besides, a scatterer  unavoidably disturbs the measured quantum states: it deforms the wave functions and shifts the energy levels. A finite accuracy of the corresponding corrections causes systematic uncertainties, which finally limit an achievable accuracy of measurement of the quantum state’s parameters. These reasons make attractive the application of a position-sensitive detector in order to directly measure the probability to observe neutrons above a mirror. We developed such a detector and the method of measurement: a plastic track nuclear detector CR39) with a uranium coating . Systematic errors of the present method, as well as the ways to decrease them, were investigated. We showed that the spatial resolution of the method is close to its theoretical limit, defined by the sharpness of the neutron wave functions versus height, or, in other words, by the sharpness of the gravitational barrier permeability for neutrons versus height. The accuracy of this experiment could be improved by a few times if a more precise model of neutron interaction with a scatterer could be developed and the scatterer positioning accuracy could be improved. More significant increase in the accuracy of an experiment of such a kind could be achieved by means of long storage of neutrons in quantum states and by a measurement of the frequency of resonant transitions between them, which would allow one to calculate directly the energies of the corresponding quantum states.In the present work, we investigated the quantization of neutron states in the potential well formed by the Earth’s gravitational field and a horizontal mirror. The conclusion of work  about pr


The objective of the paper was to exhibit the range of qualitative behaviors that is possible when pMHCI/CD8 kinetics interacts with TCR/pMHCI kinetics and to show how varying levels of the co-receptor at the T-cell surface may be able to modulate the functional sensitivity of the T-cell to various ligands in a differential fashion. These qualitative phenomena remain very much the same when we choose parameter values that respect the constraint ν = γkinδ, as shown in the corrected figures that follow below  impose the following condition on the parameters: Figures –4. It isThe kinetic scheme  and the equations are all unaltered, except for a typographical error in the subscript of a quantity appearing in one of the equations. Specifically, equation (23) in the published text should read:We apologize profusely for any inconvenience our oversight may have caused.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.