Fundamental challenge of imaging through a scattering media has been resolved by various approaches in the past two decades. Optical wavefront shaping technique is one such method in which one shapes the wavefront of light entering a scattering media using a wavefront shaper such that it cancels the scattering effect. It has been the most effective technique in focusing light inside a scattering media. Unfortunately, most of these techniques require direct access to the scattering medium or need to know the scattering properties of the medium beforehand. Through the novel scheme presented on this paper, both the illumination module and the detection are on the same side of the inspected object and the imaging process is a real time fast converging operation. We model the scattering medium being a biological tissue as a matrix having mathematical properties matched to the physical and biological aspects of the sample. In our adaptive optics scheme, we aim to estimate the scattering function and thus to encode the intensity of the illuminating laser light source using DMD  with an inverse scattering function of the scattering medium, such that after passing its scattering function a focused beam is obtained. We optimize the pattern to be displayed on the DMD using Particle Swarm Algorithm (PSO) which eventually help in retrieving a 1D object hidden behind the media. With the advent of technological advancements, several techniques came into existence that allowed imaging through these media, despite light scattering. Techniques such as Optical Coherence Tomography (OCT)4 and two photon microscopy6, use ballistic photons (photons which are not scattered) to image through the media. However, the media produces abundant scattering, and these techniques are less efficient due to lower number of ballistic photons. There are other techniques that utilize the scattered photons. Diffuse optical tomography7 is one such method that spatial resolution is limited, due to the scattering depth.Random scattering of light creates serious hindrance in imaging through a scattering medium like biological tissues. There was a widespread need felt to image through these scattering media for various applications ranging from biomedical to astronomical imaging. In the late 1960s, several works were suggested by Goodman Optical Memory Effect’. It was exploited in several works to obtain this most desirous goal of imaging through the perturbed media10. Freund12 introduced this concept of using a scattering media as a lens based on speckle intensity correlation. Bertolotti et al.13 extended this idea to image a fluorescent object behind the media. Katz et al.8 introduced a single-shot imaging technique to retrieve image of a hidden object. His concept was based on the intensity correlation of the speckle being identical to that of the object. Hence, he used Fienup’s phase retrieval algorithm14 to reconstruct the object behind the media. However, the quality of the reconstructed image faced artifacts, mainly due to the initial guess involved in the phase retrieval algorithm. Later, Sing et al.15 came up with the idea of using a reference point source along with the object in which the point source serves as a reference. The advantage of using simple autocorrelation of the camera intensity allowed the image to be reconstructed, hence avoiding the use of a phase retrieval algorithm. Ghost imaging also helped to retrieve the information of an unknown object18. However, a reference beam was also required for its implementation.Speckle produced when a beam of light is incident on scattering media remains correlated even if there is a small tilt in the incident wavefront over a specific area on the media. This effect is known as ‘et al.19 focused light through a thick chicken breast tissue using OPC, and proved that the width of the reconstructed focus spot is independent of the thickness of the sample. Holographic methods have also been used in improving images perturbed by the presence of scattering medium. One such method done by Vittorio et al.20 utilized the Brownian movement of colloidal particle to obtain multiple uncorrelated holograms, and later combined them to reduce the speckle contrast. Later through his other work21, he used the same technique to tackle the problem of imaging transparent samples that were hidden behind biological occluding objects in microfluidic platforms. Whereas, Melania et al.22 used the doppler frequency shift experienced by the photons scattered by the flowing colloidal particles, which do not contribute to the recorded hologram.Optical wavefront shaping technique has been proven to be a very effective technique in focusing light through a scattering medium. The discovery of Spatial Light Modulators (SLM) brought out a huge impact in this field. Optical Phase Conjugation (OPC) is one, among the wavefront shaping techniques, that is being extensively used to image through a scattering medium. Zahit et al.23 performed wavefront shaping using an SLM to obtain a focused spot behind a scattering medium. In their optical scheme, the scattering medium is illuminated by a light source whose phase is modulated by an SLM. A camera is placed behind the scattering medium and this acts as a feedback to the SLM. Finally through optimization, a focused spot is obtained on the camera. Later, Popoff et al.24 came up with the idea of measuring the transmission matrix of a scattering media and using it to introduce the inverse phase on the SLM to get a focused spot behind the scattering media. In 2014, Youngwoon Choi25 demonstrated that a scattering medium can be used as a lens to image objects behind it by exploiting the transmission matrix. He performed an endoscopic imaging through a single multimode optical fiber (acts like a scattering medium) as a lens. This method requires an initial calibration to find the complete transmission matrix. There were several works done by using SLM, as a phase compensator, to image through a scattering medium36. In spite of all the advantages of all the aforementioned techniques, most of them require some sort of feedback from behind the medium, hence making it unsuitable for non-invasive imaging through the medium.Vellekoop see Fig. MATLAB simulation that we can focus light through a scattering medium in a non-invasive manner, and implement it through experiments to reconstruct a 1-D object hidden behind a scattering medium.We propose a novel wavefront shaping scheme which we call ‘Reverse Response Wavefront Shaping Technique’ (RRWST), in which the illumination and detection is on the same side of the inspected tissue see Fig. . In thisIn our adaptive optics scheme, we aim to estimate the scattering function to encode the wavefront of the illuminating laser light source with an inverse scattering function of the scattering medium in such that after passing its scattering function, a focused beam is obtained. This wavefront was obtained after passing twice through the same scattering medium (on the way forward and on the way back).dz, being the average scattering length in the inspected tissue. This couple of operators is repeated, until the number of repeats equals to M = L/dz –where L is the distance of the target behind the media from the point of illumination. Thus, by modeling the 1-D case  due to cause of simplicity, the forward scattering matrix A can be written as:Fij] and [Fij]* are Fourier and inverse Fourier matrix. Hence,In order to estimate the encoded inverse wavefront that will be focused after passing the above-mentioned scattering medium, we use the following modeling: we assume that the scattering medium can be modeled by a sequence of operators multiplications –while the first is an operator of random phase and the second is an operator of short free space propagation of distance of A is unitary, since it is the product of multiplication of two unitary matrices. The operator matrix A was applied twice as there is a double passing through the scattering medium (on the way forward and on the way back). On the way back, the scattering is in inverse order and this is the reason that the transpose operation was applied on the matrix A. To find the input field distribution vector Ein (which e.g. can be a phase only distribution) after one passage when a focus is obtained, i.e. the operator A produces a delta function in the middle of the spatial axis (zero position coordinate):It is to be noted that the matrix N is the number of spatial sampling points along the output axis.Thus, one can extract that:in equals to the middle column of the matrix operator of inverse A:A is a unitary matrix, because it is a product of two unitary matrices. . There is a known relation between A transpose (At) and inverse of A (A−1).A denoting its conjugate transpose. By combining Eqs st passage through the medium. A pictorial representation of the above presented mathematical steps that can be seen as two steps described inFig. From Eq. Equation st pass. Hence, there are two ways of obtaining the focal spot by this optimization. Either by using phase modulation –where the Eq. MATLAB simulations, the validity of the method using phase modulation is verified and equally valid for amplitude modulation as well. However, to prove the concept, experimentally, amplitude modulation was chosen for more simple alignment and for ease of this experiment.Obviously, the above described model is an approximation and the obtained analytical result is only the starting iteration point of the distribution to be displayed on the wavefront shaping device –around which a close loop convergence process needs to be applied to achieve the focus, after the 137. In computational sense, PSO finds an optimum solution for a problem by iteratively improving the solution from a set of candidate solutions being random guess solutions to a problem. In technical terms, these solutions are called ‘particles’. Each particle is assigned a ‘position’ and a ‘velocity’ vector. The search space is known as ‘swarm’. Hence, the name PSO. The flowchart describing the steps involved in PSO is displayed in Fig. MaxIt’. However, the termination criteria could be set by calcualting a specific cost function value, below where the iteration continues and above where the iteration stops. Our supplementary material shows simulation results based on the aforementioned criteria.We used Particle Swarm Optimization Scheme (PSO) to perform the iterations. It is a stochastic optimization technique that mimics the social behavior of birds flocking together or fish schooling. It was introduced by Kennedy, Eberhart and ShiMATLAB simulations were performed to serve as a proof of concept for our proposed (RRWST) technique. A 100 × 100 pixels for simulation was chosen. Since the modeling is in 1-D, the effective area of the illumination was kept on the scattering medium minimal, i.e. a line illumination was chosen. There are 100 pixels whose phase values can be changed from 0 to 2π along the vertical axis. Along the horizontal direction, 6-pixel columns were chosen for the line illumination. The pixel size was set at 1 µm. Ideally, it would mean that a line of light, whose phase is modulated along the vertical direction, is incident on a scattering media. Since the scattering contribution from other areas of the scattering sample is undesired, the rest of the area was blocked on the scatterer, aside from the illumination area  is allowed to pass through the medium which then scatters and illuminates the target plane at 0.5 mm with speckle. The light that bounces back off of the target plane returns in phase opposition through the same medium. We simulate this situation and encode the phase of the output light (Eout) that has passed twice through the medium. From Eq. Ein and Eout*.see Fig. . The phaparticle in our scheme comprises of 100 variables, whose phase values change from 0 to 2π. It was started with 20 such random particles. Hence, the population of our swarm is 20. MaxIt is set at 4000. The algorithm starts with finding the best solution, ‘pbest’, corresponding to each particle in the swarm. The cost function value corresponding to it is known as ‘pbsestcost’. In the entire swarm, there would be one particle whose cost/merit function would be the best. This particle is termed as ‘gbest’. The cost function value corresponding to it is known as ‘gbestcost’. This is one iteration.Since there are an infinite number of solutions for the optimization to converge to a spot, the solution space was resticted. In the target plane, a binary mask was introduced in the form of a barcode with alternating black and white lines. Each white space is 10 pixels in its width (5 such white spaces of 10 pixel width). This serves as the hidden object in this simulation. The aim is to focus light on this object. Each iteration would yield a focus at different spatial location. An angular spectrum propagation method was used to propagate the light from the scatterer to the object and back. A single particle’s position and velocity are updated by using the formula given below:w is the inertial weight, C1 and C2 = 2 (constriction coefficient), k refers to the current iteration number. Now, the procedure is repeated for k = MaxIt. In our case, MaxIt = 4000. Figure In the second iteration, the and it but can still be scattered in the other direction as seen in Fig. Figure Figure nd iteration are illustrated in Fig. The results of the 2As previously mentioned, the most appropriate way to show it experimentally is to perform a phase modulation. However, considering the ease with experiment we chose to perform amplitude modulation for our experimental proof of concept.Texas Instruments was used as an amplitude modulator in the experiment. A diode pumped solid-state laser at 532 nm, collimated using a collimator passes through a polarizer and illuminates the DMD  (1280 × 800 pixels with pixel size 7.6 µm) from see Fig. .Figure 9st and 3rd white bar is 180 microns, and the second white bar is 84 microns. This white bar allows the light to passthrough it. The black bar absorbs light.We have used a very thin slice of chicken breast tissue of approximate thickness 20 microns as the scattering sample. It has scattering properties alike human tissue. We quantified the medium by using speckle contrast.  is used to image the target plane onto the detector with the help of a tube lens.MaxIt = 100. Number of particles used is 20. Number of variables optimized is 40. The captured intensity of the output is captured using D1 and it has 216 × 52 pixels. It is resized to 40 × 52 pixels and averaged along the 52 pixels to get a 1-D form of the output light. It is, then, correlated against the 1-D version of intensity of the input amplitude mask applied on the DMD. This is the cost function in this optimization. The optimization produces a converged spot, after N = 100 iterations. This was continued for 3 cycles, until 3 converged spots were obtained on 3 white bars that are hidden behind the sample.PSO runs for Figure : This only verifies that convergence was achieved at the desired locations. However, the nature of the optimization issue of having more than one solution remains, as there are minor peaks associated with each sharp peak.Figure st peak is about 189 microns –being close to its actual dimension at 180 microns. FWHM of the 2nd peak is 94 microns –being close to its original size at 84 microns. Finally, the 3rd peak has a FWHM of 213 microns. All reconstructed dimensions are very close to the actual width values with small deviations.We have added all 3 ouput intensities, resize, and average along the 52 pixels to get a 1-D plot, as shown in the Fig. We presented a unique, reference-free, non-invasive, reverse response-based wavefront shaping technique to image through s scattering medium. Since our illumination system and the detection system are on the same side of the object, it does not require the direct access behind the medium nor use a feedback from there.The application of our novel concept can be utilized mainly in biological imaging as a non-invasive diagnostic tool.Supplymentary Materials


The complex task of Electric Powered Wheelchairs (EPW) prescription relies mainly on personal experience and subjective observations despite standardized processes and protocols. The most informative measurements come from joystick monitoring, but recording direct joystick outputs require to disassemble the joystick. We propose a new solution called “SenseJoy” that is easy to plug on a joystick and is suitable to characterize the driver behavior by estimating the joystick command.SenseJoy is a pluggable system embedded on EPW built with a 3D accelerometer and a 2D gyrometer placed within the joystick and another 3D accelerometer located at the basis of the joystick. Data is sampled at 39 Hz and processed offline. First, SenseJoy sensitivity is assessed on wheelchair driving tasks performed by a group of 8 drivers  in a lab environment. Direct joystick measurements are compared with SenseJoy estimations in different driving exercises. A second group of 5 drivers is recorded in the ecological context of a rehabilitation center . The measurements from all groups of drivers are evaluated with an unsupervised statistical analysis, to estimate driving profile clusters.The SenseJoy is able to measure the EPW joystick inclination angles with a resolution of 1.31% and 1.23% in backward/forward and left/right directions respectively. A statistical validation ensures that the classical joystick-based indicators are equivalent when acquired with the SenseJoy or with a direct joystick output connection. Using an unsupervised methodology, based on a similarity matrix between subjects, it is possible to characterize the driver profile from real data.SenseJoy is a pluggable system for assessing the joystick controls during EPW driving tasks. This system can be plugged on any EPW equipped with a joystick control interface. We demonstrate that it correctly estimates the performance indicators and it is able to characterize driving profile. The system is suitable and efficient to assist therapists in their recommendation, by providing objective measures with a fast installation process. Chronic conditions that impede the mobility have an impact on the quality of life. One can rely on mobility assistive devices to improve the well-being, such as manual wheelchairs, power wheelchairs, scooters or other motorized vehicles . A correTherapists play a central role in wheelchair prescription, ensuring the efficient interaction between individuals and their technical aids. The prescription task is a complex and challenging intervention, in order to select the appropriate wheelchair with correct settings. This complexity arises from the relationship between the wheelchair users – characterized by their needs, abilities and preferences – the available technology and the constraints of the considered environment for mobility . PrescriSeveral solutions exist to assist and improve the technical aid prescription: standardized processes , guideliWheelchair data loggers are increasingly popular, they provide a quantitative assessment of wheelchair users’ activities , 11. ThoSenseJoy for monitoring and assessing the joystick controls during driving tasks, as shown on Fig. We propose in this study a novel pluggable solution named An easy-to-plug system, compatible with any joystick-driven EPWA novel clustering method to characterize the driver profile, based on the WST results.Our contributions are twofold:These contributions are supported by a metrological validation and an analysis with 13 subjects, including 7 people with disabilities. The ecological part of the evaluation is conducted in the occupational therapy department of Bobigny rehabilitation center (France).The SenseJoy solution is a stick to mount in place of any joystick grip part, with a remote component placed on the side. The pluggable part is designed to ensure the precise location of sensors and is 3D-printed. The system integrates two 3D analog accelerometers  and a 2D analog gyrometer (ITG1215 from Invensense). An accelerometer  and two angular velocities , as indicated on Fig. Digital data acquisition is made by a microcontroller card, designed in our lab and based on PIC18F2550 from Microchip. The sampling frequency is 39 Hz. Each sample is composed of eight values : six 3D accelerometer components . The first step is to normalize the 3D accelerometer components between -1 and +1. This normalization requires a calibration step to determine the minimum and maximum values measured with the EPW parked on a horizontal ground. In a second step, the difference between accelerometers 1 and 2 minimize the effects of EPW acceleration on the joystick:This simple processing does not remove completely the effects of the EPW movements in all situations, especially when translation and rotation movements are combined, but reduces them. This simple yet effective processing yields recording with a sufficient precision for an assessment during a WST protocol. The resulting vector could be seen as an approximation of the linear accelerations of user’s actions on the joystick. After applying a one-dimensional median filter (order 20) to remove outlier values, we determine the angular variation for each axis of the bidirectional joystick as follows:θx express the angular variation of the joystick in the left/right direction and θy in the backward/forward direction. To improve the angular variation estimation, we combine the acceleration data from accelerometers and the angular velocity data from the gyrometer with a complementary filter that is described on Fig. where Kp and Ki are the proportional-integral gains, where Complementary filters or Kalman filters are state-of-the-art in inertial-based system data fusion and attitude estimation –17. The In order to assess the driving performances of users, we borrowed seven indicators from  to charaThe joystick excursion is estimated as:for direct joystick outputs case andfor the SenseJoy one. The joystick direction is computed as:in the direct joystick outputs case andotherwise. The number of joystick actions is defined as the number of times where the joystick excursion exceeded the threshold of 10% maximum amplitude from the joystick’s center position during a trial. The total time required to execute each trial is determined as the time from the first joystick action to the last. The direction is computed as a vector with a unique origin positioned on the joystick’s center. Each vector determines the direction for a sample. The average joystick direction is the average vector. The standard deviation of the direction vectors is also estimated. The velocity of the EPW in backward/forward direction is calculated by integrating the linear acceleration on the Y-axis of the accelerometer 2.Two measurement campaigns have been made with different drivers and wheelchair using the same experimental protocol. A first data logging collection is conducted in a lab environment on a unique EPW equipped with SenseJoy and with a direct monitoring of the joystick outputs. This first measurement campaign is designed to make a thorough comparison with ground truth recording, with a direct joystick outputs setting, to validate the signal quality and the accuracy of the measurements. A second measurement campaign is conducted in a rehabilitation center on the personal EPW of individuals equipped with SenseJoy only. This second set of measurements is designed to demonstrate and to validate that our system is pluggable and compatible with any EPW driven by a joystick interface.The EPW used in the first measurement campaign comes from Invacare, it is a "Mistral" model. It has a rear-wheel drive system and a bidirectional joystick control interface placed on the right side, as shown on Fig. We apply the same experimental protocol in each measurement campaign, based on the WST  because The analyses are carried out with two populations. The objective of the first measurement campaign is to compare the performance of the direct joystick outputs system and the SenseJoy solution. It is conducted in the lab, with 8 individuals (labeled D1 to D8) that are assessed on the EPW shown on Fig. The objective for the second measurement campaign is to test the robustness and precision of our SenseJoy system, in an ecological context associating disabled EPW users with different levels of practice. Five individuals (labeled D9 to D13), mean age in years of the group is 41.4±10.5 years, have been recruited in a rehabilitation center. They are assessed on their own EPW equipped with SenseJoy, therefore there is no ground truth value for these recordings.Table Before using SenseJoy, a calibration step is necessary to determine the maximum amplitudes of the bidirectional joystick of each EPW. The calibration step is conducted to ensure the correct parameterization of the offline analysis. The joystick is positioned in the maximum rear position and then in maximum front position followed by the maximum left position and the maximum right position, as visible on Fig. We can deduce two metrological parameters, resolution and response time. The resolution is defined by the standard deviation of the measurement noise. For each axis X and Y, the system is assumed to be recorded in static position. The recorded data is thus assumed to be characteristic of the static position with an additional white noise, due to the measurement chain. After verifying that the noise follows a Gaussian distribution, the standard deviations are respectively estimated to 1.31% and 1.23% for the X- and Y-axis. The response time is measured to be the time of the sensor response to reach 95% of the step. It has been measured averaged over multiple samples and is estimated to 95 ms.The SenseJoy equipment includes Micro Electro Mechanical System (MEMS) sensors that measure linear accelerations and angular velocities. In consequence the dynamic of the wheelchair has a noticeable impact on the joystick angular estimations. Figure Figure For more complex exercises with more actions on the joystick several sources of error could impede the joystick angle estimations, for example: prediction error, overshoot, noise, peaks or delay time, all of which are visible on Fig. Prediction errors made by the SenseJoy system is imputable to the simple yet limited model of the system, which relies on a direct subtraction of the two accelerometer components. A direct subtraction is not accurate for movements combining rotations and translations and the wheelchair acceleration is only partially removed from joystick acceleration. A more advanced mechanical approach could improve the results but this version provide suitable results as they are close to the baseline directly measured on the joystick.ηT elements characterized by its mean and standard deviation  and a reference population of ηR elements characterized by . By defining a region bounded by a lower ΔL and an upper ΔU bounds, we could test a composite null hypothesis that combines H01={μT−μR≤ΔL} and H02={μT−μR≥ΔH} hypotheses. If we could reject both H1 and H2, we could conclude that ΔL<μT−μR<ΔH and that the considered measurements are close enough to be considered as equivalent [ΔH=−ΔL with objective values, they proposed to use λ=4.581. We considered tighter bounds with λ=2 to ensure a stricter equivalence in our study.In order to properly evaluate SenseJoy against a baseline obtained from direct measurements, we averaged each indicator by users on Fig. uivalent . Followiuivalent  to set ΔΔH=0.2 and p≈1×10−5, for an average time ΔH=1.5 and p≈3×10−4, for average direction ΔH=4.7 and p≈2×10−3 and for average standard deviation of direction ΔH=5 and p≈1×10−5. We can conclude that for all indicators SenseJoy yields results that are equivalent to the direct reference.The following results are obtained: for average joystick actions k-means clustering with k=4 classes and 300 iterations is conducted on each exercise using the indicator values as input. These values are chosen for their robustness, i.e. adding more iterations or clusters do not qualitatively change the results. A similarity matrix S is built by counting in the number of exercises for which two drivers are in the same cluster and by dividing the results by the total number of exercises. If we denote by ηE the number of exercises and by k-means for the user u and the exercise e, the similarity matrix Sij entries are defined by:The driver behavior could be characterized by the indicators derived from the joystick interactions . We propδxy is the Kronecker delta function, that is equal to 1 if x=y and 0 otherwise. This matrix S holds all the information regarding the similarity between two drivers across all considered exercises. For this second experiment, we have estimated S for the nE=13 exercises and for all the drivers of the groups 1 and 2. As this matrix account for high dimension data, a dimensionality reduction method could be applied to visualize the results. We choose the Laplacian Eigenmaps [S as it is best suited to work with similarity matrices. This clustering method shows on Fig. where igenmaps  to proceIn this study, SenseJoy is designed and 3D-printed as a stick with an external diameter of 30 mm. While standard diameters are usually smaller, circa 20 mm, we could not meet this condition due to the size of the electronic card for the inertial sensors. As we rely on retail available hardware and components, it was not possible to reduce significantly this electronic part. Future development of this system will rely on miniaturized components to be embedded in standard diameters.2 and this value is still smaller than The first experiment shows on Fig. The estimation of the joystick angle is obtained with a crude computation to remove the wheelchair acceleration. While this approach is correct in the case of the rectilinear movement, more complex driving situations combining rotation and rectilinear movement are more error prone for the system. To ensure that our system is robust, we add a specific exercise to generate these situations, that is the slaloms between two studs. The average results per exercises on Fig. Even if SenseJoy is equivalent from a statistical point of view to the direct recording of a joystick, some discrepancy are visible under close examination. The high variability of the signal requires to apply filters to remove noise sources and perturbations. We propose to rely on specific filtering method, called complementary filter, that is known to work well on systems like SenseJoy. Even if the complementary filter is well adapted for the joystick measurements, all filters remove some informative data. This could be seen on the joystick actions shown Fig. For the second experiment, the objective is to validate that the precision of SenseJoy allows to characterize the user behavior and is able to detect the expertise in EPW driving. One can note that the experiment is conducted on the two groups of drivers that have been recorded in two different locations. On Fig. In this study we propose an easy-to-plug equipment to assess the joystick controls during EPW driving tasks. This equipment can be plugged on any EPW equipped with a joystick control interface. We have demonstrated it is possible to collect the data and to estimate the driving indicators from the literature. These indicators help caregivers in rehabilitation centers to objectively quantify the driving behavior based on the direct measure of joystick actions. We have demonstrated that our system is robust and accurate with thorough and ecological tests. It is comparable to the direct output of the joystick, both quantitatively, as it is validated by a statistical equivalence test, and qualitatively, as we could extract the expert/novice driving profile with an automatic clustering method. This is an important advance as previous studies relying on the analysis of the joystick behavior required a dismantling procedure to directly record the joystick signal, a procedure that could not be conducted in rehabilitation centers. Our system allows to record any EPW without any destructive procedure and provides the opportunity to test a large cohort of EPW drivers in an ecological context.There are several interests for pluggable system like SenseJoy. It allows to evaluate the capability and usage-related performances of a driver using the subject equipment without altering it. These ecological measurements allow to identify driver profiles, as described in . It is tIt is limited in its present design to specific situations, that is a joystick-controlled EPW, as other types of controller like touch interface, sip-and-puff or forehead/chin joystick are not supported. Also, SenseJoy may not be suited for subjects with motion-impairement that exhibit spastic movements. This could be the subject of following evaluation to investigate those points.The actual version could be improved by a mechanical approach avoiding the impact of the EPW movement on the joystick actions measurements. We also plan to develop other pluggable tools to measure other driving-related data, thus completing the analysis of EPW driver’s profile.


A generalised extreme value distribution for r largest order statistics is fitted to the annual maxima. This is performed in an effort to study the behaviour of the r largest order statistics. The method of maximum likelihood is used in estimating the target parameters and the frequency of occurrences of the hottest days is assessed. The study presents a case study of South Africa in which the data for the non-winter season (September–April of each year) are used. The meteorological data used are the AMDT that are collected by the South African Weather Service and provided by Eskom. The estimation of the shape parameter reveals evidence of a Weibull class as an appropriate distribution for modelling AMDT in South Africa. The extreme quantiles for specified return periods are estimated using the quantile function and the best model is chosen through the use of the deviance statistic with the support of the graphical diagnostic tools. The Entropy Difference Test (EDT) is used as a specification test for diagnosing the fit of the models to the data.Natural hazards  are established in the literature as major causes of various massive and destructive problems worldwide. The occurrences of earthquakes, floods and heat waves affect millions of people through several impacts. These include cases of hospitalisation, loss of lives and economic challenges. The focus of this study was on the risk reduction of the disasters that occur because of extremely high temperatures and heat waves. Modelling average maximum daily temperature (AMDT) guards against the disaster risk and may also help countries towards preparing for extreme heat. This study discusses the use of the  Most of the classical statistical techniques that are frequently used in the energy sector and meteorological analysis are classified into regression analysis, time series, state space and Kalman filtering  in South Africa is discussed. This approach is an extension of the block maxima approach. The primary purpose is to present a modelling approach that is suitable for modelling the frequency of the occurrence of extremely high temperatures and heat waves as one of the natural hazards. The meteorological data that are used comprise the daily average maximum temperatures that are collected by the South African Weather Service over the period 2000−2010. The daily average maximum temperatures are specified in this study by defining the non-winter season as the period from September to April of each year. The problem to be addressed is the demonstration of the modelling approach that contributes towards disaster risk reduction as far as the occurrence of extreme high temperatures is concerned. The R package that is used for modelling the r largest order statistics in this article is the ismev package  that is developed by Heffernan and Stephenson  is fitted to the average maximum temperature. This is performed in an effort to assess the asymptotic behaviour of the r largest order statistics within the blocks of equal lengths. The use of the generalised extreme value (GEV) approach in modelling temperature gains attention worldwide. Wang et al. (r = 1) is criticised in the literature in favour of the r largest order statistics model (r > 1). Bader, Yan and Zhang  gains preference over the ordinary GEV distribution for block maxima. Coles  as an alternative EVT approach is that it avoids blocking and hence uses as much as possible the available data. However, the motivation for studying the block maxima approach in this study is based on Ferreira and De Haan  on the AMDT. Our objectives include, among others, the use of the maximum likelihood estimation (MLE) method in estimating the target parameters, the choice of the best model out of several nested models using the likelihood ratio test that is based on the deviance statistic, the use of entropy difference test (EDT) in assessing the goodness of fit of the models as well as the estimation of the return levels using the quantile function.This study is aimed at fitting the GEV distribution for 1,…,Xn constitutes a random sample of size n that is chosen from the random variable X whose marginal distribution function is F. Let Mn = max{X1,…,Xn}, then the extremal types theorem states that for the suitable normalising constants {an > 0} and {bn}, the distribution function of the re-scaled block maxima The GEV distribution is discussed by Fisher and Tippett  as the mG, then G belongs to a unified GEV distribution family that is given by:for a non-degenerate distribution function defined for μ < ∞ is the location parameter, σ > 0 is the scale parameter and − ∞ < γ < ∞ is the shape parameter.where − ∞ < γ. When γ = 0, γG(x) reduces to a type I or a short-tailed unbounded Gumbel family of distributions  is thin-tailed and we get a type II family which is the Weibull class of distributions with an upper bound given by  belongs to a type III family which is a heavy-tailed Frèchet class of distributions that is bounded below by  and rearranging By letting p → 0 and As r largest order statistics within annual blocks, for fixed values of r. We initially define:The quantile function given in k, as n → ∞. If k:and then identify the limiting behaviour of this variable, for fixed defined on where:with:r largest order statistics:The GEV distribution for the is the joint probability density function given in Coles  as:∞ < μ < ∞, σ > 0 and − ∞ < γ < ∞;xr)( ≤ xr–1)( ≤ …≤ x(1); and:valid for − k = 1,2,…,r.r largest order statistics model when γ = 0 is given by:The likelihood function for the defined for r largest order statistics depends on the choice of the number of order statistics r, which is critical. If r is too large, the asymptotic support for the model is likely to be violated, leading to the occurrence of bias , for i = 1,…,10, have led to the maximum likelihood estimates of the target parameters as illustrated in r ≤ 6 order statistics as a result of the reasonable doubt on the validity of the model for r ≥ 7. The maximised negative log-likelihood estimates (λi) seem to be stable for r ≤ 6 and start decreasing significantly when r ≥ 7. The standard errors of estimates increase significantly when r ≥ 7, implying poor fit of the model when r ≥ 7. According to Soares and Scotto  is given in d Scotto , the abor. A negative value of the shape parameter in classical EVT implies that the GEV distribution converges towards the Weibull class of distributions. All estimates of r largest asymptotic GEV distribution are given for each value of r in r = 2, 3 and 4 display the dots that are near linear. There is doubt on the fit of the model at r ≥ 6. The model fitted for r = 4 with λ4 = − 8.5826 seems to be the one that possesses a reasonably good fit. The graphical diagnostics which are the P–P, Q–Q, return level and the density plots are given for r = 4 in γ is estimated for all values of r. All the point estimates of the shape parameter γ are found to be negative values. It is important to compare the outcomes of point estimation with the results of interval estimation. If indeed the point estimates of the shape parameter are negative values, then they must be bounded below and above by the negative confidence limits. For example, the confidence interval for γ considering r = 1 is given by:The sufficient evidence of the validity of the Weibull distribution family towards modelling of AMDT in South Africa is revealed by the estimates of the shape parameter for all values of γ is expected to be enclosed within the interval , which makes sense because r = 1. The confidence interval for γ is then estimated for all r values, and it is noted that all the upper limits are negative values, and hence enclose the point estimates This leads us to conclude that at a 95% level of confidence, the value of the shape parameter r for r largest order statistics (r > 1). This is derived as the difference in entropy of GEVr and GEVr-1 models. Considering a continuous random variable X with density function f, the entropy difference is given by:There are various tests that are considered in the literature as relevant to assess the goodness of fit of the models to the data. The Anderson–Darling test is suitable for assessing the goodness of fit of the heavy-tailed distributions. In this article, we use the EDT that is discussed in Bader et al.  as a sper − 1 top order statistics fit the GEVr-1 distribution. Then the difference in the log-likelihood between GEVr-1 and GEVr provides a measure of deviation from the null hypothesis i th block:which is the mean of the negative log-likelihood that is estimable by the sample average of the contribution to the log-likelihood from the observed data. Suppose that is given by:r distribution with a sequence of null hypotheses  R package of Bader and Yan  and λ(rj) are the maximum likelihood functions of ri and rj, respectively. A test of the validity of model based on ri relative to rj at the α level of significance is to reject ri if D > Cα, where Cα is the (1 – α) quantile of the where on Coles ./p are calculated using x0.04 = 32.15 is expected to be exceeded on average once every 25 years. For the greater accuracy in the estimation of the return level and parameters in the model for r = 4, profile log-likelihoods for µ, σ and γ are given in λ(r1) and λ(r2) is calculated as D = 2 (−15.9670 – (−12.5255)) = −6.88. Similar to Soares and Scotto , D and D. The comparison is invalid for D and D. The test for selecting the best model is conducted at 1% level of significance for which D and D, λ(r3) and λ(r5) are rejected as D > 6.64 and D > 6.64. It is therefore clear that D = 5.49 < 6.64 reveals failure to reject λ(r4), which implies the validity of r = 4 as an order statistic that possesses the reasonably good fit as suggested by the graphical diagnostic tools. The Q–Q and the P–P plots given in r = 4 possesses the most reasonable fit of the model out of the six order statistics. The point estimates d Scotto , the devx0.1 = 32.0 are then counted and found to be 2. For the observed number of exceedances, we get 0.1 × 44 = 4.4 ≈ 4, where 44 is the number of observations available in 11 years by four order statistics.The number of observations that are above the estimated tail quantile px = 32 °C, is the maximum temperature that is expected to be exceeded on average once every 10 years. This is the temperature above which we expect the occurrence of extreme heat that may lead to natural hazards such as hot spells or heat waves. From the viewpoint of energy demand forecasting, this is the maximum temperature above which the demand of electricity does not increase significantly.r distribution for r largest order statistics is fitted towards modelling AMDT in South Africa over the period 2000–2010. Of the 10 order statistics, r = 4 gives a reasonably good fit of the GEVr distribution to the data. The choice of r = 4 as the best model is based on the deviance statistic with the support of the diagnostic tools, which are the Q–Q plots and the EDT. The asymptotic behaviour of the r largest order statistics model reveals the Weibull family as an appropriate distribution that can be used for modelling AMDT in South Africa. Inference is performed by analysing several return levels corresponding to the return periods as well as plotting the profile log-likelihoods for the parameters of the best model.Natural hazards are established in the literature as major causes of various massive and destructive problems worldwide. The occurrence of extremely high temperatures, heat waves and hot spells affects millions of people through several impacts. These include cases of hospitalisation, loss of lives and economic challenges. It is important that countries should always be prepared for natural hazards that cause actual disasters as uncertain events. One of the steps towards the preparation is to manage the risk of the occurrence of heat waves, which is performed in this study through modelling the frequency of the occurrence of extremely high temperatures. A brief discussion of actual disasters together with their corresponding impacts is given in this study. The main focus is on the reduction of disaster risk that could occur as a result of extreme heat. This study has demonstrated the modelling approach that is relevant for guarding against the disaster risk that could occur as a result of extreme high temperatures. The GEVThe methodology and results of this study are important to disaster risk managers as the modelling framework demonstrated in this article is valid for modelling occurrence of extreme heat. This may be useful for guarding against risk of disasters that may occur as a result of hot spells and heat waves. The use of statistical approaches that concentrate on the mean instead of the tails of the distributions is not recommendable for modelling the occurrence of extreme temperatures. The Weibull family of distributions is recommended for modelling AMDTs in South Africa. This study is also important for power utility companies such as Eskom, South Africa’s power utility company, as demand for electricity significantly increases during a heat wave period. This will therefore help system operators to determine the amount of electricity that is consumed during a heat wave period, which will then help them to schedule and dispatch the increased demand in electricity. Extreme high temperatures cause transmission lines to sag. Combination of extreme heat and the added demand for electricity to run air conditioning causes transmission line temperatures to rise.r largest order statistics and the POT approaches is recommended for application in meteorology and energy demand forecasting. Areas for future research include the use of multivariate non-stationary EVT models with the parameters that are estimated based on the Bayesian estimation framework including an analysis of the duration a hot spell would last if it occurs in future, the area it will cover and how it will vary with climate and impact on mortality.The use of extreme value analysis techniques such as the GEV distribution for


Today, many companies develop modular systems to realise considerable product differentiation and variation while simultaneously reducing costs through economies of scale [1]. Designing these modular systems to be lasting and robust in a highly dynamic environment [2], avoiding subsequent modification cost  and staying innovative over the product lifecycle is crucial for sustainable success in an increasingly competitive market [5]. Two closely related surveys were carried out on the initial situation described above. The first survey deals with the major conflict between planning reliability and flexibility with regard to future boundary conditions that the described challenges lead to. The data presented in this article on the first survey was collected from German companies, mainly from the automotive industry, developing and manufacturing complex products using modular systems. Other represented companies operate in the machine and plant construction industry. The survey comprises the answers of 39 participants, gathered via online questionnaire. The 17 questions of the survey are divided into two topics: characteristics of the participants, and the problem description of modular systems in highly dynamic environments and the management thereof. The second survey deals with the anticipation of innovations in the design of modular systems and the selection of the right choice from a variety of possible innovations to be considered. The data presented in this article on the second survey was collected from German automotive manufacturers, which develop and manufacture complex products using modular systems. The survey comprises the answers of 501 participants, gathered via online questionnaire. The 14 questions of the survey are divided into two topics: characteristics of the participants, and the problem description of modular systems and the management thereof. The data obtained allows the identification of existing deficits and dedicated research on solutions. From November 2017 to March 2018, 39 Participants from numerous internationally active companies from Germany were interviewed 17 questions in an online questionnaire against the background of several hypotheses. The gathered data of the survey is divided into two consecutive modules. In the first part, the sample of the survey is presented and characterised. The second module deals with the problem description of modular systems. The data predominantly consists of ordinally scaled variables, either representing the participants' degree of consent to a statement, or a self-assessment of their situation and capabilities. The full dataset (Q1-17) is provided as supplementary material in [dataset] 1.2The survey was conducted to determine the status quo of modular systems in dealing with innovations and the specified need for action in practice. From May 2017 to July 2017, 501 participants from internationally active German automotive manufacturers were interviewed using 14 questions in an online questionnaire against the background of several hypotheses. The survey data collected is divided into two successive modules. In the first part, the sample of the survey is presented and characterized. The second module deals with the problem description of modular systems. The data consist predominantly of ordinal-scaled variables that represent either the degree of agreement of participants to a statement or a self-assessment of their situation and capabilities. The full dataset (Q1-Q14) is provided as supplementary material in [dataset] 22.12.1.1The first part of the questionnaire is intended to characterise the sample of the survey. As the data in On average, more than 30,001 people are employed in the companies in which the participants work See . On the In order to be able to assess the economic situation of the participating companies, the annual turnover was used as a benchmark. As can be seen in The business areas in which the survey participants work are as follows: 19% of the participants work in predevelopment, 70% in development, three percent in strategy and three percent in sales and after-sales. Another five percent are listed under the term “Other areas” and an example of this would be data and product management, as can be seen in The roles of the survey participants are manifold: 41% of the survey participants are specialists, 43% are active in lower management, 13% in middle management and three percent in top management See .Fig. 5RoThe survey participants come from the following areas, as shown in 2.1.2In the second part of the survey, the participants are confronted with various statements as to whether and where companies see challenges through modular systems. Further statements deal in particular with the current situation and the challenges for modular systems in a highly dynamic environment. The number of samples for all studies is n = 39, unless otherwise specified.“The diversity of your company's product range will continue to increase in the future due to more individual customer requirements (market pull).” In “The diversity of your company's product range will continue to increase in the future due to rapidly overtaking technologies and innovations (technology push).” The majority (77%) of participants agree with this statement, 13% rate this statement neutrally and only 10% disagree.In the beginning, the participants are asked to rate their approval of two statements regarding the diversity of the product range. First they were asked if In the next question, the participants are confronted with two statements as to whether the economies of scale generated by modular systems achieve economic advantages on both the process and product sides.As can be seen in “Modular systems are an important means of achieving the innovation leadership of your products in an economically compatible manner." in As already described in the introduction, the literature states that innovation is crucial for the company's success in securing the competitiveness of its own products . TherefoThe vast majority (77%) of the participants confirm that the innovation leadership of their products can be achieved in an economically compatible manner by modular systems (26% strongly). There is a 20% rating on the neutral statement and only three percent disagree with the statement.“The use of modular systems makes it more difficult to implement innovations in the product in the area in which you work.” and there are significant differences in the evaluation between specialists and managers, as described in the paragraph below . With a percentage of 48%, managers disagree more with the statement than the specialists with 12%. The neutral evaluation is at a nearly similar percentage level for both comparison groups.“Change and cancellation costs over the award period of modular systems ensure that the initial and production costs planned when the contract was awarded cannot be realised”.Change and cancellation costs reduce company profits, as they have a negative impact on the margins of the affected products each time they occur ,7. Becau“The current modular systems development process loses relevance for modular systems that are in a highly dynamic environment, as it is therefore difficult to adequately consider future boundary conditions”.All of the following statements focus on the challenges of modular systems in a highly dynamic environment. In The answers show that 42% of the participants agree and eight percent strongly agree with the presented statement. A share of 32% of the participants rated the statement neutrally and 18% disagree. The number of samples for this statement is n = 38.“For modular systems in a highly dynamic environment, it is a challenge to resolve the tension between planning reliability (= robustness against changes and new developments) and flexibility with regard to future boundary conditions” was presented. As the data in Subsequently, the proposition In the next question, the causal categories for the difficulties of reacting to future boundary conditions for modular systems in a highly dynamic environment are analysed.“For modular systems in a highly dynamic environment, it is currently difficult to react to future boundary conditions, as their effects are not taken into account in the product or its architecture in the concept design phase.” In “For modular systems in a highly dynamic environment, it is currently difficult to react to future boundary conditions, as their effects are not taken into account in the business case over its life cycle.” Eight percent of participants strongly agree with this statement, 37% agree, 31% rate this statement neutrally and 24% disagree (3% strongly). Third they were asked if “For modular systems in a highly dynamic environment, it is currently difficult to react to future boundary conditions, as their effects are not taken into account in purchasing, in the awarding of contracts.” It can be seen that 39% of the participants agree or strongly agree with this statement. 45% rate this statement neutrally, 13% disagree and only three percent strongly disagree.First they were asked if In “There is currently no efficient approach to coordinate or synchronise the different life and change cycles of modular systems that are in a highly dynamic environment, their products and architectures.” was presented and the participants are asked for their opinion on this statement. It can be derived from Next, the proposition “There is currently no holistic, business case-minded procedure for calculating the consideration of future boundary conditions in the modular systems development process of modular systems that are in a highly dynamic environment.” With an agreement of 70% (59% agree and eleven percent strongly agree), the participants confirm the statement below. 24% gave a neutral assessment, three percent disagreed and three percent strongly disagreed. The number of samples for the statement of In the last question of the second part the participants are asked for their degree of agreement with the statement 2.22.2.12.2.1.1The first part of the questionnaire is intended to characterise the sample of the survey. As the data in The roles of the survey participants are manifold, as shown in As can be seen in The participants' length of service with their company are as follows: 31% of the participants have been with their company for 0–5 years, 25% for 5–10 years, 18% for 10–15 years, 15% for 15–20 years, four percent for 20–25 years, another four percent for 25–30 years and three percent for 30–35 years. There are no participants with a length of service with their company of over 35 years See . The num2.2.1.2In the second part of the survey, participants are confronted with various statements about whether and where companies see challenges posed by modular systems. Further statements refer in particular to the current situation and the challenges for modular systems in the realization of innovations. In this context, the temporal and content-related focus of this survey will be established. The survey focuses on stage 2 of the standard stage gate process according to COOPER . This ph•Degree of maturity 0 “Idea”: The project idea and the goals are described and evaluated with regard to feasibility, customer benefits and the market potential.•Degree of maturity 1 “Predevelopment maturity”: The basic technological and economic feasibility is presented. A recommendation on the part of the department for predevelopment is available. Technical killer criteria have been listed.•Degree of maturity 2 “Proof of feasibility - Qualitative”: A solution for the function/property is identified and evaluated . Current requirements regarding the target product line are met. First prototype samples are available.•Degree of maturity 3 “Proof of feasibility - Quantitative”: The technology is controllable and the integration risk is known and assessable. Quantified statements about e.g. operating strengths and costs can be made.•Degree of maturity 4 “Concept maturity”: The technical implementation and integration risk, business aspects, affordability, and resource planning are roughly assessed by the responsible departments.•Degree of maturity 5 “Integration-ready”: The technical implementation and integration risk, business aspects, affordability and resource planning are assessed in detail by the responsible departments.On the basis of maturity level management, JAHN has defined six degrees of maturity that support an efficient and targeted transfer of innovations into the development process of modular systems at an early stage, as can be seen in At each degree of maturity of the innovation process, different parameters are taken into account that represent the progress of the project. In this study, five criteria were defined on the basis of which a statement can be made about the feasibility at the respective levels. Due to similar goals of the described maturity levels, the levels 0 and 1, levels 2 and 3 and levels 4 and 5 were combined in order to keep the response effort for the participants low.First the participants were asked how important it is that “Technical contents and concepts are realizable” at the different levels of maturity. “The business case of the project meets the objectives” at the different levels of maturity. In the maturity levels 0 and 1, three percent of the participants rate the statement as crucial, 16% as highly important, 40% as fairly important, 32% as not very important and nine percent as not important at all. The number of samples is n = 498. In the maturity levels 2 and 3, the crucial rating rises up to twelve percent. The statement is rated as highly important by 37%, fairly important by 41%. Ten percent rated it as not important . The number of samples is n = 498. At the maturity levels 4 and 5, 44% of the participants rate this statement as crucial, 41% as highly important, 13% as fairly important and only two percent as not very important. The number of samples is n = 495  rate the statement as undecided and two percent disagree. The number of samples is n = 495. A share of 31% of the respondents strongly agree and 48% agree with the statement regarding the diffusion of innovations. There are 18% of the participants who are undecided and three percent who disagree (one percent strongly). The number of samples is n = 478.In “anticipated legislative changes require the implementation of innovations”. In predevelopment projects, 61% of participants strongly agree with the statement, 31% agree, six percent consider it undecided and two percent disagree (one percent strongly). The number of samples is n = 496. For the diffusion of innovations, 91% of the respondents agree with the statement, 55% strongly. Seven percent gave an undecided assessment and the remaining two percent split equally between disagreement and strong disagreement with the statement. The number of samples is n = 476 . A further 13% are undecided about the statement and one percent disagree. The number of samples is n = 494. For the diffusion of innovation it can be observed in In the last question of the second part, the participants are asked about their degree of agreement with the statement


For data collected on a circular rather than linear scale, a very common procedure is to test whether the underlying distribution appears to deviate from circular uniformity. Rao’s spacing test is often used to evaluate the support the data offers for the null hypothesis of uniformity. Here we demonstrate that the traditional version of this test fails to adequately control type I error rate when the data is non-continuous . To overcome this issue, we provide a numerically-intensive simulation version of the test.We use a simulation study to explore the performance of the traditional and our novel variant on Rao’s spacing test, both in terms of control of type I error rate and statistical power.When data is measured on a continuous circular scale then both methods offer good control of type I error and similar statistical power. If the data is rounded , however, the traditional method produces highly inflated type I error rates, particularly with high sample sizes, that make it inappropriate for application to such data. In contrast, our simulation method retains good control of type I error while offering levels of statistical power similar to the traditional Rao test.The traditional method of applying Rao’s spacing test should be replaced by the simulation-based variant introduced here. The two methods offer similar performance but only the simulation method retains good control of the type I error rate when circular data is rounded to a finite set of values (likely due to limited precision of measuring equipment). Adoption of the simulation variant will substantially improve the reliability of this regularly-used test in the commonplace situation where data values are rounded.The online version of this article (10.1186/s40462-019-0160-x) contains supplementary material, which is available to authorized users. The test statistic is based on the sum of the deviations of the actual arc lengths from this expectation, and a sufficiently high test statistic suggests departure from uniformity.Circular data is commonly generated whenever researchers measure angles (such as the distribution of compass directions that seeds disperse from a parent plant) or have hypotheses related to cyclic behaviour . Such data needs different treatment to data measured on linear scales, and a number of monographs are available on the statistical treatment of circular data . We further assume that the observations are ordered from smallest to largest: ϕ1 < ϕ2 < …. < ϕn-1 < ϕn. We can then define the set of n arc lengths between neighbouring points asWe define the test for U is then the sum of the differences between the actual arc lengths and their expected values under uniformity (2π/n).The test statistic U exceeds a critical value then the null hypothesis of uniformity is rejected. Based on the moments of the underlying distribution, Russell & Levitin [rao.spacing.test in the package circular, and all implementations of the test we have seen in the literature . We then generate NR samples from a continuous uniform distribution, each with the same sample size as the original sample. For each of these simulated samples we calculate the value of the test statistic, and calculate the number Ne of these simulated samples that produce a test statistic value equal to or greater than Uo. The estimated p value is then (Ne+ 1)/(NR + 1). In our simulations we used NR = 10,000. In the case of discrete (rounded) data, this approach needs to be modified because the restrained number of options the random distribution can be drawn from (e.g. 360 when rounded to one degree) would otherwise create many identical distributions. To obtain a p-value for discrete (rounded) data by simulation the following approach was taken. First, we added very small random perturbations selected independently from a von Mises distribution with mean zero to each data-point in our sample. That is for data point ϕi we obtain a perturbation εi drawn from a von Mises with mean zero and with concentration parameter κ. We then calculate the value of the test statistics for the observed sample with added perturbations . Notice that if the sum of the original value and perturbation is outside of [0,2π) then we add or subtract 2π (modulo 360) as required to correct this prior to calculating the test statistic. We then generate NR samples from a continuous uniform distribution, each with the same sample size as the original sample. For each of these simulated samples we (i) round values to the same precision as the original sample, then (ii) add perturbations in the same way as we did for the original sample ), and then finally (iii) calculate the value of the test statistic for each perturbed simulated sample. We then calculate the number Ne of these perturbed simulated samples that produce a test statistic value equal to or greater than Uo. The estimated p value is then (Ne+ 1)/(NR + 1). In our simulations we used NR = 10,000, and κ = 1000. The higher the value of κ the more concentrated the distribution. A value should be chosen that is high enough that the perturbations are much smaller than the granularity of the imprecision. That is, if (for example) original values were obtained to the nearest 10 degrees, then a value of κ should be selected to ensure that almost all perturbations are less than 1 degree. See supplementary files for R codes for both simulation-based approaches . We evaluate the p-value both in the traditional way using the R function rao.spacing.test in the package circular and using our simulation approach. Because Rao’s spacing test considers the distribution of arcs between data points we might expect it to be sensitive to any rounding of the values due (for example) to finite precision of equipment used to record values. Therefore, we repeated this analysis using circular uniform distributions rounded to the next degree (360 bins) and to the next 10 degrees (36 bins), two situations, due to practical reasons, commonly encountered in biological studies.We estimate the type I error rate as the fraction of 10,000 samples each drawn from a uniform distribution that cause the test to generate a κ = 2, μ = pi) and skew normal distributions  with continuous data of different sample sizes and calculated the power as the fraction of 10,000 samples that generate a p-value equal to or less than 0.05, using both approaches. In a next step we rounded the von Mises distribution to the next degree and also the next 10 degrees and repeated the analysis using the simulation approach.We estimated the power of the different approaches to correctly detect deviation from uniform distribution. For this we first generated von Mises . Further, the statistical power of our new method could be explored for a broader range of shapes of deviation from uniformity. Finally, the sensitivity of our method to selection of the size of the perturbations added to data-points could be explored. However, our own preliminary explorations (not shown) give us no reason to expect that the results presented here are unrepresentative. We hope that our simulations provide the basis of further development of circular statistical methods and spark comprehensive evaluation of different methods. False positive results are a large concern in life sciences; our provided functions therefore might help to avoid some unintentional statistical mistakes, when dealing with circular data.R functions to perform this test by simulation in the two cases where sample values can be considered continuous or where the data is grouped into a specified number of equal divisions around the circle  then this causes inflation of type I error rates, i.e. the test is detecting the non-uniformity of rounding the data. Such rounding is very common throughout practical science. We show that this inflation of type I error rate can be very substantial even for moderate rounding (to the nearest degree or 10 degrees), and that the problem is exacerbated by large sample sizes. We advocate evaluation by simulation, comparing the sample to a test set of similar samples drawn from a uniform distribution. We demonstrate that this avoids type I error problems and maintains power. We provide Additional file 1:Figure S1. Power  of the traditional Rao and the simulation-based Rao test with different sample sizes on a skew normal distribution. (PDF 70 kb)Additional file 2:R code for the simulation-based Rao test. (R 5 kb)


To identify and describe triage category allocations and their associated patient pathway timeframes in four emergency centres of a large private healthcare group in the United Arab Emirates.The classification of patients in accordance with their acuity level is a complex task that requires quick and accurate allocation. Triage system categories have predetermined timeframes in which patients should be seen by a physician or treatment initiated for the best possible outcome.An observational, cross‐sectional study was conducted through the prospective capture and evaluation of medical records from patients triaged in each of the four emergency centres  over a period of a month. The STROBE statement was used as a reporting framework. Descriptive statistics were used to determine the timeframes associated with the patient pathway through each EC and contrasted against their allocated triage category.A total of 4,432 patient records were eligible for analysis from the four emergency centres. Triage category 4 (54.7%) was allocated the most with only a single category 1 patient seen between the four emergency centres. The median time from registration to triage was <10 min and triage to physician consult was <25 min. The overall length of stay of high‐acuity cases was between 1 hr 13 min–2 hr 44 min, compared with low‐acuity cases being 32–49 min. Overall time to physician was substantially lower than the targets set by the triage systems itself. The STROBE statement checklist See File  for repoMedical records from patients triaged in each of the four ECs over a period of 1 month were evaluated and considered for inclusion. Electronic and manual platforms were used to collect the required data. The initial electronic data were sourced through the hospital groups’ medical records department at the end of the 1‐month period. EC staff were instructed to specifically include electronic data fields that was set out for this study, in addition to the usual EC data they capture. The electronically captured data from the four ECs during the month were collated and provided in a single Microsoft Excel (2016) spreadsheet. This included triage category allocations and patient flow timeframes . It was necessary to capture manual data that were not contained in the hospitals electronic information system. The manual data were captured by the triage nurses completing a one‐page form during their triage assessment of patients presenting to their ECs. Entries included the triage category allocation, time of triage, time of physician consult and time the patient leaves the EC. Internal training by the EC unit managers was conducted to familiarize the staff with the content of the data collection form. Medical record stickers with patient identifiers were attached to the form so that the data could later be merged with the electronic data. Clerical staff from the four ECs captured the manual data daily from the forms onto a custom spreadsheet. The researcher collected the spreadsheets from the four ECs and used the patient identifiers to merge the electronic and manual data sets through the merge data function. Patient identifiers  were included in the data set shared with the researcher to provide an identifier for merging electronic data with manual data. Following this, all identifiers were stripped from the sample prior to analysis. The manual data capture forms were collected from the four ECs and handed back over to the hospital groups’ medical records department at the end of the study.Only records with all the relevant data points were included. Records with missing data points were identified, filtered and removed from the database prior to analysis. Removing records from the data set may have introduced exclusion bias that could have resulted in the removal of potential outliers such as high‐acuity cases. Removing incomplete records before analysis ensured that a complete data set was available with all the data points present. There were no obvious reasons for data points to be missing other than random omission from the staff to make entries and thus obtaining these missing data points would not be possible.The timeframes as patients moved through the ECs were captured at specific points in their journey from entering to leaving the EC by either being discharged or admitted to hospital. An observational analysis was done using non‐parametric descriptive statistics, with the median as a measure of central tendency as timeframes per triage category do not follow a normal distribution. Factors such as timestamp input delays, inaccurate time readings and adjusted time inputs that could have an impact on and alter these timeframes coupled with the uncertainty of their reliability and validity did not warrant in‐depth variance and relationship testing. Patient flow timeframes were contrasted against their allocated triage category, which in turn should have been guided by the triage systems themselves, as presented in Table 4N = 2,423; 54.7%). Conversely, category 1 was only allocated once , whereas high‐acuity cases (categories 1 and 2) only made up an extremely small proportion of allocations .There were a total of 7,311 electronic and 6,754 manual patient records captured from the four ECs. When the data were combined in a single spreadsheet, there were some records captured electronically but not manually and vice versa, thus resulting in a smaller, combined number of 6,320 records. Duplicate and missing entries were removed leading to a further loss of 1,888 records and a final sample of 4,432 records. Of the 4,432 sampled records, triage category 4 was allocated most often  and registration –> physician consult was <20 min (IQR 0–19 min)  strengthens the clinical ability of the unit to manage patients effectively.This study was conducted in the emergency centres of Mediclinic Middle East who highlighted triage as a vital component of their business model. The author declares no conflict of interest beyond the support provided by the management of Mediclinic Middle East to undertake this study. Click here for additional data file.


The ability to extract the direction of the other’s gaze allows us to shift our attention to an object of interest to the other and to establish joint attention. By mapping one’s own intentions on the object of joint attention, humans develop a Theory of (the other’s) Mind (TOM), a functional sequence possibly disrupted in autism. Gaze following of both humans and old world monkeys is orchestrated by very similar cortical architectures, strongly suggesting homology. Also new world monkeys, a primate suborder that split from the old world monkey line about 35 million years ago, have complex social structures and one member of this group, the common marmosets  are known to follow human head-gaze. However, the question is if they use gaze following to establish joint attention with conspecifics. Here we show that this is indeed the case. In a free choice task, head-restrained marmosets prefer objects gazed at by a conspecific and, moreover, they exhibit considerably shorter choice reaction times for the same objects. These findings support the assumption of an evolutionarily old domain specific faculty shared within the primate order and they underline the potential value of marmosets in studies of normal and disturbed joint attention. Like humans, gaze following of old world monkeys fulfills Fodor’s criteria of a domain specific function. Common marmosets are also well known for having a peculiar interest in faces3. Unlike macaques, the species of old world primates studied best, and other non-human primate species, they often engage in mutual gaze, for example in the context of joint action tasks4. Many individuals even seek eye contact with their human caretakers . Common marmosets also care about the orientation of a human face as demonstrated by the fact that human head-gaze biases choices in an object selection task5. While this latter behavior may indicate an inherent capacity for gaze following, it remains to be shown that it can also be triggered by conspecifics. By the same token the lack of high resolution behavioral data has as yet precluded well-founded inferences about the relationship of marmoset gaze following to gaze following exhibited by humans and rhesus monkeys, the two species of old world primates for which detailed behavioral and neuronal data are available6. Gaze following of macaques and humans is reflex-like in the sense that it is fast and hard to suppress, two features that have contributed to the assumption of a domain specific faculty12 based on a dedicated neural system13. Do marmosets follow the gaze of conspecifics in the same reflex-like manner? An affirmative response would support the notion that gaze following in extant primate lines is homologous, i.e. a reflection of shared ancestry.Gaze following is a an important social skill, which enables humans, great apes and old world primates to establish joint attention on an object of interest to the other. Although old world monkeys probably do not possess a TOM, namely they are not able to map one’s own intentions, desires and expectations on the object of interest, they follow the other’s gaze and they establish joint attentionIn order to address these questions, we trained 3 common marmosets  to execute a free choice task in a well-controlled experimental setup that allowed us to head-restrain the animals to precisely track eye movements. A conspecific’s face, oriented either to the left or to the right, was presented on a monitor for a variable time ranging between 100 and 600 ms in steps of 100 ms Fig.  and the 15. As shown in the right panel of Fig. 17. Yet, given the fact that the third animal exhibited a different pattern, characterized by an absence of a second gaze following peak and a constant choice at chance level after 300 ms, further studies will be needed to critically assess the possibility of periodicity.Figure All three animals exhibited individually different directional biases for the left and the right respectively, modifying their choice behavior on top of the influence of directional information provided by facial orientation. Directional biases became apparent when plotting the dependence of choice preference on head gaze direction for the three individual animals independently for head gaze to the left and to the right Fig. . For exaWhen the animals were confronted with direct gaze of a conspecific with the face turned straight or alternatively, with black or grey disks of a similar size, likewise lacking directional information, target choices of all three animals did not differ significantly from chance level at most exposure times with the exception of the shortest one Fig. , yet, noThe white ear tufts on the left and right of the darker central face of a straight ahead marmoset offer a symmetric luminance profile. Once the animal turns the head to the side, symmetry is lost as the visible area of the ear tuft on the side of the head turn will decrease, whereas the area of the other one will increase  exhibited latencies that were not different from the ones associated with incongruent choices to oriented faces. Interestingly, latencies of saccades associated with neutral disks showed an influence of exposure time that was qualitatively opposite to the influence on saccades for congruent choices: while being similar to saccades for straight faces for short presentation durations, they became shorter with increasing exposure time see Fig. . The sam18. As shown here, gaze following is also well developed in common marmosets, a new world monkey species. Marmoset gaze following is characterized by strong similarities with the gaze following behavior of the two old world primate species studied extensively, macaques and humans. The strongest argument for correspondence is the similar dependence on the time of exposure to the other’s gaze direction. In all three species the other’s gaze biases decisions on potential targets already after only 100 ms of exposure to the other’s gaze, too short to accommodate a more detailed scrutiny of the other’s face. However, given more time to explore the other’s face, the bias gets stronger in all three, in line with the assumption that primate gaze following is a faculty, consisting of an early reflex-line component that is complemented by a later, more flexible component, arguably also responsible for the more sophisticated emotional and cognitive control known to modulate gaze following21. The behavioral similarities between the gaze following behavior of marmosets, macaque monkeys and humans are in principle in line with the assumption of a homologous faculty, already available before the split of the new and old world monkey primate lines. This conclusion may strengthen the view that the marmoset may indeed become a useful model system for research into the underpinnings of disturbed human social interactions like autism, related to deficient gaze following and joint attention22. However, although compelling, the behavioral similarities established in our study may as well reflect behavioral convergence. Hence, comparative physiological and genetic studies of the underlying neural systems will be needed to strengthen the case for homology.Gaze following is prevalent among numerous species but its strength and flexibility varies substantially between themWe trained 3 adult common marmoset monkeys  to voluntarily enter a custom made monkey chair by means of positive reinforcement training and to accept the restriction of head movements through a head holder. Animals were all born in captivity and kept in a marmoset husbandry at approximately 26 °C, 40%–60% relative humidity and a 12 h:12 h light-dark cycle. Access to water was always ad libitum, while food intake was controlled according to body weight (weight loss never less than 10% of the ad libitum weight) and amount of reward received in the experiment. Food consisted in fresh fruits and vegetables and standard commercial chow. As additional treats the animals received mealworms and locusts on days of good performance in the behavioral training and experiments. Reward given in the experimental setup consisted in self prepared marshmallow juice  with the addition of a small amount of gum arabic, or only gum arabic diluted in water, according to the individual animal’s preference. Experimental procedures were approved and supervised by the regional state authorities  and are in agreement with the guidelines of the European Community for the care of laboratory animals.All the animals underwent the surgical implantation of a titanium headpost under general anesthesia with sevofluran (2.5–5%), propofol (0.05–2 mg/kg/min), remifentanil (0.06–0.1 mcg/kg/min) and tight control of vital parameters. The headpost was fixed with three upside down T-shaped anchors, whose arms were placed between the skull and the dura. This was achieved by cutting a small slit into the bone using an ultrasound bone-knife , allowing the insertion of the arms that were then rotated 90° under the bone. Two-component UV curing cement (ESPE Rely X Unicem 2) was used to close the bone slit and Super Bond C & B to glue the head post to the profiles protruding a few mm from the bone. After full recovery from surgery, the animals were gradually accustomed to head restraint through daily sessions of increasing duration, up to a maximum of 2 hours.The experiments were performed in a small sound proof room in daily sessions lasting between 30 min and 2 hours. The number of trials per session ranged from 50  up to 500 trials per session. The animals were sitting in a comfortable monkey chair that was placed on a table facing a computer screen , at a distance of 32 cm. Eye movements were tracked with the EyeScan System ETL-200, through a camera placed on the right side of the screen, and resampled at 1 kHz. Reward was delivered by means of a small cannula placed in front of the animals’ mouth, on or very close to the upper lip, depending on the animals’ preference. The delivery of rewards was controlled via a pump, set to release one drop of fluid for each correct answer or more (2–3 drops), depending on the animal’s motivation.Eye position was calibrated by asking the animal to pursue a human face (4 × 5°) that was slowly moving on a circular trajectory on the screen (circle diameter 5°) at a speed of 6°/s. In order to prevent the animal from losing interest in the face, we replaced it every 4 trials by another face, differing in identity and/or expression. The animals followed a novel moving face spontaneously with smooth pursuit eye movements with interspersed catch up saccades allowing us to calibrate the eye position records by fitting the target trajectory to the eye trace.Each trial started with the appearance of a small red dot (0.2°) in the center of the screen on a white background, available for a maximum of 500 ms to start fixation (fixation window (2° × 2°). Otherwise it disappeared and the trial was discarded. However, if fixation was acquired and maintained for 500 ms, the dot was replaced by the portrait of a conspecific portrait, in the main experiment randomly oriented towards a position at −5° or 5° on the horizontal, in 50% of the trials to the left side and in 50% to the right side. In the control experiments the oriented faces were replaced by a face of a marmoset looking straight at the experimental animal, a monochromous disk (black or grey), a bipartite-monochromous disk , or a black equilateral triangle oriented either to the left or to the right side respectively. Animals could freely explore the central images, as long as they kept the eye within the fixation window, which whose size corresponded to the image. Central images were presented for a variable duration of 100, 200, 300, 400, 500 or 600 ms. At the end of the image presentation time, the central image disappeared while at the same time a pair of 2 peripheral targets, human faces, looking straight and exhibiting a neutral expression (size 2 × 3°) appeared at + 5° and −5° from the center. The identity of the animal presented in the center and the identity of the pairs of human faces serving as targets were kept constant. The appearance of the targets served as go signal, telling the animals to perform a saccade to one of the two targets. All choices were rewarded, as long as the indicative saccade landed within a window of 2° × 3°centered on the targets and was not carried out later than 500 ms after the go signal. Intertrial intervals were kept constant at 1 second. As peripheral target we used a human face rather than a neutral object (e.g. a dot) as marmosets are attracted by faces much more than by any other object, thereby boosting an animal’s readiness to perform saccades to either of the two choice targets.The face stimuli used were based on photographs of the faces of marmoset conspecifics and humans that had been taken with a digital camera  and manually processed in Adobe Photoshop to unify their size and luminance. For the oriented face condition we used two different portraits of the same animal. The direct gaze stimuli were generated removing the peripheral white ear-tufts. The inner face feature were maintained and the resulting image was rescaled such as to match the spatial dimensions of the disk control stimuli.Saccades were identified by a Matlab routine as events characterized by an increase in instantaneous eye velocity above a threshold of 20°/s. The performance of the algorithm was double checked by eye in order to discard false hits. As expected selected saccades respected the main sequence, i.e. relationship between amplitude and velocity/duration.For the statistical analysis of the binary decisions of the experiments animals, all sessions per animal and condition were pooled, yielding a binomial distribution allowing the detection of significant deviations from chance level (50%). The pairwise comparison of the binomial distributions for individual animals was based on chi-square tests which were carried without Yates correction, given that the number of trials per condition was large (>200). Pooled reactions times were compared between the various conditions by Wilcoxon-test with Bonferroni correction.Supplementary Information