The analysis of the video shot in basketball games and the edge detection of the video shot are the most active and rapid development topics in the field of multimedia research in the world. Video shots' temporal segmentation is based on video image frame extraction. It is the precondition for video application. Studying the temporal segmentation of basketball game video shots has great practical significance and application prospects. In view of the fact that the current algorithm has long segmentation time for the video shot of basketball games, the deep learning model and temporal segmentation algorithm based on the histogram for the video shot of the basketball game are proposed. The video data is converted from the RGB space to the HSV space by the boundary detection of the video shot of the basketball game using deep learning and processing of the image frames, in which the histogram statistics are used to reduce the dimension of the video image, and the three-color components in the video are combined into a one-dimensional feature vector to obtain the quantization level of the video. The one-dimensional vector is used as the variable to perform histogram statistics and analysis on the video shot and to calculate the continuous frame difference, the accumulated frame difference, the window frame difference, the adaptive window's mean, and the superaverage ratio of the basketball game video. The calculation results are combined with the set dynamic threshold to optimize the temporal segmentation of the video shot in the basketball game. It can be seen from the comparison results that the effectiveness of the proposed algorithm is verified by the test of the missed detection rate of the video shots. According to the test result of the split time, the optimization algorithm for temporal segmentation of the video shot in the basketball game is efficiently implemented. With the new development of computer technology, a video contains more abundant and vivid information and has become one of the important information carriers in the Internet . The popIn , the timThe analysis of the video shot in basketball games and the edge detection of the video shot are the most active and rapid development topics in the field of multimedia research in the world. Video shots' temporal segmentation is based on video image frame extraction. It is the precondition for video application. Studying the temporal segmentation of basketball game video shots has great practical significance and application prospects.Analyze the concept and conversion type of the video shot of the basketball games. The conversion type of the shots can be divided into fade in, fade out, overlap, and sweep.Using the threshold and the model method to detect the boundary of the video shot of the basketball games. The single-frame image of the video is processed, and the video image is reduced in dimension. The quantized dimensionality-reduced one-dimensional vector is used as a variable to perform histogram statistics and analysis on the video shots of basketball games, and the dynamic threshold is set to realize the temporal segmentation optimization of the video shots in basketball games.The accuracy and efficiency of the optimized segmentation of the shots are tested to verify the effectiveness of the proposed method.Summarize the research content.The research box of the temporal segmentation optimization algorithm for the video shot of basketball games based on the histogram algorithm is as follows:The introduction to various methods and detailed literature has been presented in the current section. The various methods and techniques used for detection and interpretation of information from images and videos are presented in Section 2 under the heading “Materials and Methods.” Section 3 includes the work environment, and all the results obtained from experimentation are described in this section. Sections The shot, as the most suitable unit of retrieval, is a sequence of frames that are continuously taken by the same camera. Most of the videos are connected because of the limited ability to describe the shot. These videos are mirrored to reflect what happens at different locations or times . The typFade in: gradually strengthen the pictureFade out: slowly reduce the picture until it disappearsOverlay: while the previous lens is gradually weakened, the image of the next lens is gradually strengthenedScanning: starting from a certain part of the screen, the previous lens is gradually replaced by the next lensThe conversion of the basketball video shot can be divided into two categories: shear and gradient. Switching into a shot directly converts to the next shot with no delay in time; the gradient includes stacking, fade in, fade out, and sweep. Among them, fade in and fade out can be used as the special case of stacking.The above four types are the most commonly used and most studied basketball game video shot conversion types, and video editors often create some complex shots' conversion types based on subjective intentions.f(t) of the basketball game video at a certain time t exceeds the threshold or is within a certain range, it is considered that the video shot changes at this time. One of the easiest ways to do this is to use the global threshold whose expression is as follows:The basic idea of the threshold method is that when the character t can be calculated by the following formula:In general, global thresholds that apply to all video and shot transitions do not exist. If the threshold is set too high, many missed conditions will occur, and setting the threshold too low will result in a higher false positive rate. Therefore, global thresholds  should bw frames before and after the current frame being examined. If the feature value of the checked frame is the maximum value within the window range and the ratio between the feature value and the average value of the feature values in the window is greater than the threshold a, then the frame is considered to have a shot shear, which uses the following expression:The current dynamic threshold is calculated using the video feature values in the window consisting of the S and kth frame and the k+lth frame, the game video belongs to the same shot and the shot changes. z is the nonsimilarity between the two frames. P(z|S) and Pka(S) means the probability that S is true in the current situation.The adaptive threshold is expressed by probability, which minimizes the average error rate. The expression is as follows:At some point in time, the occurrence of shot shear shows the very prominent nonsimilarity feature, while the shot gradation occurs in a period of time, and the characteristics of each frame are not obvious. The double-threshold method is used to judge the shear and gradation of the shot. The expressions areTh is used to detect the shear of the video shot in the basketball game. If the feature value of the video frame is greater than Th at a certain time, it is considered that the shear occurs at this time; during the period from ts to te, if the feature values of all video frames are greater than the lower threshold Tl and the sum of their feature values is greater than Th, then it is considered that the video has a lens gradation during this time period.Set two thresholds: the higher threshold fout means the color attribute of the t moment at the  position during the fade out process and g represents the color attribute of the screen whose picture is faded out at the  position at the time t; when the faded picture is still, g is the fixed value. a(t) represents a function that describes the color of the screen as the video shot fades out during the basketball game. During the process of fade out, a(t)=(1 − t)/T. The fade-in process of the shot is expressed by the following formula:β(t)=t/T.In the process of fading out the black screen, the video is dimmed and darkened, and the color gradually becomes black. It can be described asIn the linear fade-in process, the video shot's stacking process can be seen as the combination of fade-out and fade-in processes:x, y, t)=−(1/T)a(t), which is a time function that is independent of the position . It can detect the gradual process of the video shot of the basketball game based on the constant graph curve. Both of the above methods can complete the detection of the video shot boundary of the basketball game.In order to detect the change model of the basketball game video footage, a constant graph is defined to describe the color change on each frame of the video shot:The frame of the video image is further processed on the basis of the boundary detection. The processing of images of a single frame is roughly divided into the following steps:One is to cut the source video image; the second is to extract the Canny boundary; the third is to optimize the boundary to remove impurities; the fourth is to search the curve in the optimized boundary and record the coordinate value of the point on the curve.Through the above research, it can be found that the top of each frame of the image contains the viewer's picture. Influenced by factors such as clothes color or skin color, the Canny boundary is very messy, which seriously affects the subsequent research . TherefoThe OTSU algorithm is used to binarize the extracted video frame image of the basketball game. The specific cropping scale is more suitable for retaining the bottom end of the source video image 7/10. The cut video of the basketball game video is shown in The Canny operator does not only determine whether a pixel is an edge point by the gradient operation. When determining whether a pixel is an edge point, it is necessary to consider the influence of other pixels at the same time. It is also not a simple boundary tracking. When looking for edge points, it needs to be judged based on the current and previously processed pixels . It convThe Canny edge indicator is an edge location administrator that utilizes a multistage calculation to distinguish a wide scope of edges in pictures. It was created by John F. Shrewd in 1986. Shrewd additionally created a computational hypothesis of the edge location clarifying why the strategy works. Canny edge detection is a strategy to extract helpful underlying data from images, and it drastically reduces the requirement of information and hence the processing. It has been broadly applied in different PC vision frameworks. Watchful has tracked down that the prerequisites for the utilization of edge recognition on assorted vision frameworks are somewhat comparable. In this way, edge recognition answer for addressing these necessities can be executed in a wide scope of circumstances.The Canny boundary in d is incremented by 1, and the corresponding point in the result graph is set to 0.Determine whether the pixel value of the current point is greater than zero. If it is greater than 0, proceed to step 2; otherwise, the left distance d is greater than the distance threshold, proceed to step 3; otherwise, reset the left distance to 0, and set the corresponding point in the result graph to 0.If the left distance d to 0, and then, determine whether the number of nonzero points on the left boundary is less than 5. If yes, enter step 4; otherwise, set the value of the corresponding point in the result graph to the rightmost point of the left boundary to 0, and set the current point in First set the left distance It is judged whether the number of zeros between the double lines is less than 6 and greater than 2. If yes, go to step 5. Otherwise, set the value of the rightmost point of the corresponding point to the zero-point sequence in the result graph to 0, and set the current point in Determine whether the number of nonzero points on the right boundary is less than 5. If it is less, the process proceeds to step 6. Otherwise, the value of the corresponding point in the result graph to the rightmost point of the right boundary is set to 0, and the current point in d for the number of subsequent zeros; otherwise, the value of the corresponding point in the result graph to the rightmost point of the subsequent zero sequence is set to 0, and the current point in A.Determine whether the number of subsequent zero points is greater than the distance threshold. If so, the value of the current point in In The overall shape of the three-point line is similar to the parabolaThe boundary points of the three-point line are relatively concentrated and relatively long, while most of the other boundary points are very scatteredThe optimization boundary of the basketball game video shot is ideal, which has two characteristics:Based on these two characteristics, the two methods are, respectively, designed to accurately locate the boundary curve that meets the requirements and record the coordinates of the points on the curve for later use .(1) Hough Transform. The Hough transform is a component extraction method utilized in picture investigation, PC vision, and advanced picture processing. The reason for using this technique is that it helps to discover blemished cases of articles inside a specific class of shapes. This d technique is done in a boundary space, from which article up-and-comers are gotten as nearby maxima in a purported collector space that is expressly built by the calculation for processing the Hough change. Hough transform is used, and according to feature on the parabola, and then, the tangential direction of the parabola at this point is dx′/dy′=2a′(y′ − y0′). Let the angle between the tangent of the parabola at this point and the y′ axis be θ; then, there is tan  θ=dx′/dy′. According to the above analysis, the following expression can be obtained:Take any point ; for any edge point  in the basketball game video image, it is to use the edge gradient direction prediction value θ and change the value a′ to calculate  by formula  Scanning Method. According to proposed feature , reset the corresponding point value in the marked video image to 1, and finally, set the current point to the nonzero point; go to ⑥; otherwise, exit ⑥ and restore the current point to the original current point position, and then, continue to traverse the next point.A, which can be used as the basis for subsequent video shot segmentation optimization.Finally, the result map of the basketball game video is the boundary curve extracted from Based on the above analysis, the overall framework for video segmentation of basketball games is established. The video data is converted from the RGB space to the HSV space by the boundary detection of the video shot of the basketball game and the processing of the image frames, in which the histogram statistics are used to reduce the dimension of the video image, and the three-colors components in the video are combined into a one-dimensional feature vector to obtain the quantization level of the video. The one-dimensional vector is used as the variable to perform histogram statistics and analysis on the video shot and to calculate the continuous frame difference, the accumulated frame difference, the window frame difference, the adaptive window's mean, and the superaverage ratio of the basketball game video. The calculation results are combined with the set dynamic threshold to optimize the temporal segmentation of the video shot in the basketball game.The overall framework of the temporal segmentation of the basketball game video shot is shown in H is divided into 8 parts, and the saturation S and the brightness V space are, respectively, divided into 3 parts, and the following expression is obtained:The basketball game video is generally represented by RGB values, which need to be converted from RGB space to HSV space. When performing histogram statistics, the amount of calculation is too large, so it needs to be dimension-reduced. According to the human visual resolution, the color QSand QV represent the quantization levels of the components S and V, respectively, and QS=3, and QV=3. It can be converted toAccording to the above quantization level, the three-color components in the basketball game video are combined into one-dimensional feature vector, and the expression is as follows:H, S, and V are distributed on the one-dimensional vector G, the value of G ranges from . Using the one-dimensional vector G after the quantized dimensionality reduction as a variable, the histogram statistical analysis of the basketball game video shot also needs to calculate the continuous frame difference of the basketball game video, the accumulated frame difference, the window frame difference, the adaptive window's mean, and superaverage ratio.While the three components of I1, I2, I3,…, In} as a sequence of video frames for the basketball game video, the corresponding histograms are {h1, h2, h3,…, hn}. The continuous frame difference of the basketball game video is calculated as the difference value of the histograms of consecutive adjacent frames. The calculation formula isProvided {HDi′(G) represents the histogram difference between the video frame i′ − 1 and the frame i′ of the basketball game, which is called the continuous frame difference of the frame i′.In the formula, i′th frame of image Ii′ in the video sequence as the reference frame, and the histogram difference value between each frame and the reference frame is calculated. So, the obtained difference value of the series is the accumulated frame difference of the i′th frame Ii′ image in the basketball game video as follows:i′j′(G) represents the histogram difference value of the basketball game video between frame Ij′ and frame Ii′, j′=i′+k′.The accumulated frame difference of the basketball game video refers to the FWn is the window frame difference for the video, n is the size of window, Ii′ is the start frame of the window, and Ij′ is the sequence of frames within the window, j′=i′+k′.It refers to the ratio of the continuous frame difference of each frame to the continuous frame difference of the first window frame in a window, and the maximum value of the ratio is the frame difference of the window. Its expression isn frame size at the assumed gradient start frame position, taking the mean value of each successive frame difference in the window. Its calculation formula is as follows:WAn is the mean value of the adaptive window of the window with n frame.It refers to adaptively opening a window of ηn represents the window's superaverage ratio and ∂j′ represents the ratio factor. Through the calculation of the continuous frame difference, the accumulated frame difference, the window frame difference, the adaptive window's mean, and the superaverage ratio of the basketball game video, the time segmentation of the video footage of the basketball game is paved, and the video shot of the basketball game is analyzed, in order to do segmentation optimization.It means that, in the set window, the continuous frame difference of each frame image is larger than the average of the adaptive window mean. The ratio obtained compared with the window size is the superaverage ratio of the window. The calculation formula isHDi′(G) of the basketball game video sequence can be obtained in turn, and two dynamic thresholds T1′ and T2′ are set, where T1′=b∗HDi′−1 and T2′=b∗HDi′+1, b are coefficients. Combining the dynamic threshold with the above calculation results can optimize the time domain segmentation of the video shot of the basketball game. The expression isThe change of the shots refers to the switching between one shot and the other shot. Through the calculation of equation , the conδ is obtained, and the optimization of the temporal segmentation of the video shot in the basketball game is completed.The optimal solution μ), and the result is shown in The experiment selects the CPU with 2 GB memory, the running software is MATLAB, and the running system is Windows7. In order to verify the effectiveness of the proposed algorithm, a temporal segmentation optimization algorithm based on the histogram algorithm, a temporal segmentation optimization algorithm based on interframe difference distribution and gradual model, and a temporal segmentation optimization algorithm based on boundary categorization are used to test the missed detection rate (ignoring the effect of the ratio factor and setting the ratio factor to be constant expressed in Analysis of Using the segmentation time of the video shot to further study the efficiency of video shot temporal segmentation optimization, the shorter the segmentation time is, the higher the efficiency is, and the test results are shown in In Through the test of the missed detection rate of the basketball game video shot, the accuracy of the video shot temporal segmentation optimization of the proposed algorithm is verified. Based on the histogram algorithm, the research focuses on the optimization of the temporal segmentation algorithm for video shot of basketball games. It is divided into two stages: using the missed detection rate of the basketball game video shot to test the accuracy of temporal segmentation optimization, which verifies that the proposed algorithm can accurately optimize the video segmentation. Using the segmentation time of the video shot of the basketball game to test the efficiency of temporal segmentation optimization, and it is verified that the proposed algorithm can efficiently complete the temporal segmentation optimization of the basketball game video shot.


The contactless estimation of vital signs using conventional color cameras and ambient light can be affected by motion artifacts and changes in ambient light. On both these problems, a multimodal 3D imaging system with an irritation-free controlled illumination was developed in this work. In this system, real-time 3D imaging was combined with multispectral and thermal imaging. Based on 3D image data, an efficient method was developed for the compensation of head motions, and novel approaches based on the use of 3D regions of interest were proposed for the estimation of various vital signs from multispectral and thermal video data. The developed imaging system and algorithms were demonstrated with test subjects, delivering a proof-of-concept. Conventional devices for such tasks mostly take contact-based measurement approaches. However, contact measurement has several disadvantages. Above all, contact with the body and skin raises the risk of skin irritation and germ contamination. Moreover, contact-based devices significantly limit the freedom of body movement of the patients, and hence, it could lead to severe discomforts. Therefore, the contactless estimation of vital signs using image sensors has continuously gained importance because of its advantages regarding hygiene and patient-friendliness.The measurement of vital signs such as heart rate, oxygen saturation  measurement of skin using a color camera. In the representative works ,2,3,4, v2 conversion are to be empirically determined.The estimation of oxygen saturation begins with the extraction of the pulsatile (AC) and nonpulsatile (DC) components of blood flow at two different channels of the color camera. These AC and DC components can be calculated either from extracted PPG signals ,6,7 or dFor the estimation of respiration rate, there are two different approaches. As the low-frequency components in raw PPG signals are caused mainly by respiration, the respiration rate could be estimated from low-pass-filtered PPG signals ,6,11,12.These existing approaches and methods for vital sign estimation can deliver reliable values at patients with little motion and under homogeneous and steady illumination. However, there exist two major problems in the practical implementation of these approaches and methods. The motion of patients, especially the head rotation, can disturb the selection of ROIs, which should be located at the same local position on the face in each video frame. In  and 10]10], methNext to the problem due to head motion, the practical lighting conditions could cause another problem, especially in the estimation of heart rate and oxygen saturation. The approaches using color cameras are based on the uncontrolled ambient light; thus, the change in the intensity of ambient light could induce artefacts, or rather, distortions in the extracted PPG signals, which can hardly be perfectly filtered out or corrected. Consequently, strong changes in ambient light intensity may lead to the true vital signs being covered by noise and artefacts in the PPG signals.In order to solve the first problem concerning motion artefacts, 3D imaging technology offers a promising approach. Compared to 2D imaging, with perspective distortion of objects, the 3D sensor always delivers 3D surface shape data independent of perspective. With a 3D sensor, it is possible to accurately capture the head motion with all six degrees of freedom. Thus, it is feasible to realize the alignment of the head poses in different video frames using 3D rigid body transformations. On this basis, 3D ROIs could be used for vital sign estimation and tracked across all video frames, and the problem of head motion could be significantly mitigated.A simple but effective solution to the problem of unstable light conditions is the usage of active illumination instead of ambient light. Considering the reduction in eye strain for patients, the active illumination should be irritation-free as possible. Thus, it could be conceived to light the patients using illuminators in the invisible near-infrared (NIR) spectral range. Previous investigations  show thaThe integration of different imaging modalities into one system yields the so-called multimodal imaging. In recent years, a lot of multimodal imaging systems ,18,19,20In this work, a multimodal imaging system was designed for the implementation of both approaches mentioned above for the enhancement of contactless vital sign estimation. In this system, a high-speed 3D sensor based on the structured light technique is aligned with various 2D cameras , providing a comprehensive data basis with pixel-wise registration of different image data. Based on this system, efficient novel algorithms were developed for the preprocessing of video data and the estimation of heart rate, oxygen saturation, respiration rate, and body temperature in real-time. At the end, the imaging system and algorithms were demonstrated with test subjects, and a proof-of-concept could be provided with test results.2 and, thus, within the eye safety limits [y limits . The higThis multimodal 3D imaging system was calibrated using the method in  in orderBased on color image data collected from 30 volunteers in the laboratory, a procedure of face analysis was designed. In the color image of the first frame, the frontal face and its eye regions are detected using the Viola-Jones detector . FurtherFor the purpose of face tracking, a set of 2D feature points, which are shown as green points in N ₌ 100) and comparing them with a set of predefined thresholds. When strong head movements are detected, the face tracking is terminated, and the next video frame is indexed with number 1 again.From the second video frame, the Shi–Tomasi 2D feature points detected in the first video frame are first tracked in the 2D color image using the Lucas–Kanade tracker . Then, tIn each valid video frame, the 3D ROIs generated in the first frame are registered with the face in the current video frame by transforming them into the local 3D coordinate system of the current frame using the head pose corrected by the Kalman filter. After that, the ROIs are aligned with the 3D face in the current video frame, and the 3D points of these 3D ROIs can be projected onto the images from the NIR cameras and the thermal camera in order to assign NIR and thermal grey values to these 3D ROI points. As shown in For the estimation of respiration frequency, the mean thermal grey value of the nostrils’ ROI is calculated in each video frame. The resulting respiration signal composed of temporal mean thermal grey values is filtered using a 128-order finite impulse response (FIR) band-pass filter with a passband between 0.15 and 1 Hz. The power density spectrum of the filtered respiration signal is calculated based on discrete Fourier transformation, whereby zero-padding is performed in order to improve the resolution of frequency. Finally, the frequency of the highest peak in the power density spectrum is regarded as the estimated value of respiration rate.The estimation of heart rate and oxygen saturation is based on the NIR cameras at 780 and 940 nm, as well as the forehead ROI. Here, there is a challenge that the signal-to-noise ratio (SNR) of the PPG measurement is comparatively low, because the skin reflectance variation is very small and could be easily corrupted by temporal noise in the NIR cameras. An approach for the improvement of the SNR of PPG signals is the Eulerian video magnification (EVM) method ,34,35,36For the estimation of heart rate, the PPG signal is obtained from the amplified periodic variations in skin reflectance. For this, the amplified signals of all the 3D points of the forehead ROI are averaged at first, so that two primary PPG signals are generated at 780 and 940 nm, as shown in For the estimation of oxygen saturation, the band-limited amplified skin reflectance variations at the 3D forehead ROI points are added to their original grey value variations, resulting in enhanced NIR grey value signals, as shown in 2 value, can be calculated by calculating the AC and DC components at both 780 and 940 nm. In order to improve the stability of oxygen saturation estimation, the RR values should be averaged over a certain time window.In the end, the ratio of ratios RR, which should be linear to the SpOThe algorithms were implemented in the C++ programming environment with the use of image processing libraries OpenCV and Point Cloud Library. The compiled program realized a real-time processing of multimodal 3D image data at a frame rate of 15 Hz. In the analysis of respiration signal, PPG signal, and signal of RR values, a 10 s sliding window was applied to estimate respiration rate, heart rate, and oxygen saturation at every video frame after the initial period. For the evaluation of the continuous estimation of vital signs, videos of test subjects with natural moderate head motions were captured in the laboratory under natural daylight, and the video duration lied between 20 and 80 s. In order to introduce variations in ground truth values of oxygen saturation, the test subjects were encouraged to hold their breath for a while during the video capturing.For the quantitative evaluation of estimated heart rate and oxygen saturation values, a pulse oximeter “PULOX PO-200 Solo” was used as a reference device. During the acquisition of multimodal video data, the display of the pulse oximeter was captured with a webcam at a frame rate of 1 Hz. The images from the webcam were labeled with time stamps, so that the ground truth values for heart rate and oxygen saturation could be assigned to the respective frames of multimodal videos.The results of respiration rate estimation are shown in Overall, the mean absolute deviation in estimated heart rate from the pulse oximeter across all video frames was 2.56 bpm, while the maximal absolute deviation was 9 bpm. Moreover, the agreement between the contactless heart rate estimation and the pulse oximeter was assessed using the method proposed by Bland and Altman . For thi2 values and calculated RR values within 65 s. Both these variations are qualitatively consistent with each other in the course of time, and the Pearson moment correlation coefficient between them is 0.867. In 2 values is shown. In general, a linear relation can be found and the prediction of SpO2 values based on RR is possible, though the data appear to be somewhat noisy and the coefficient of determination R2 of the linear statistical model is 0.7521. Based on SpO2 values estimated from the RR values using this linear model, the limits of agreement were determined according to the Bland–Altman method and are shown in 2 conversion model were also used for the determination of LoAs, and the 95% confidence LoAs were −4.26% and 4.26%. Based on 2 values by more than 5% could be detected with high reliability.In this work, a real-time multimodal 3D imaging system and a hybrid approach are proposed for the enhancement of contactless estimation of heart rate, oxygen saturation, respiration rate, and body temperature. Based on real-time 3D image data, global head motions can be precisely compensated by performing 3D face tracking, while strong head movements can be detected for the assessment of measurement condition. Via the 3D sensor, multispectral and thermal image data from different 2D cameras are pixel-synchronously aligned with each other, enabling an accurate transfer of ROI among different 2D cameras and the estimation of vital signs with combined use of image data in different modalities. The demonstration shows that a real-time vital sign estimation is possible at a frame rate of 15 Hz, and the estimation of desired vital signs at subjects with moderate motions is successful in principle. What is more, further cameras could be integrated into this imaging system in order to simultaneously estimate additional vital signs such as bilirubin  and blooIn the experiments, it is noticed that the estimated oxygen saturation values are a little noisy. The reasons for this may be the imperfection in the illumination regarding spatial uniformity and remaining spectral crosstalk in the NIR cameras. On this problem, we will try to improve the LED array in order to create a more homogenous lighting and equip the NIR cameras with band-pass optical filters with narrower passbands.Moreover, the correlation and mutual interferences between different vital signs, e.g., between heart rate and respiration, should also be systematically investigated. A joint analysis of the variations in different vital signs may offer the possibility for posterior correction of estimated values or the recognition of estimation errors.This work presents only a demonstrative test of the system and algorithms. As preparation for the practical use, a more comprehensive evaluation in the clinical setting is planned; the estimated values will be compared with more accurate and reliable ground truth values obtained using contact-based clinical measurement devices.


Growing evidence suggests that the presence of C4 photosynthesis alone is insufficient to account for drought resilience in grasses, pointing to other adaptations as contributing to tolerance traits. The majority of grasses from the Chloridoideae subfamily are tolerant to drought, salt, and desiccation, making this subfamily a hub of resilience. Here, we discuss the evolutionary innovations that make C4 grasses so resilient, with a particular emphasis on grasses from the Chloridoideae (chloridoid) and Panicoideae (panicoid) subfamilies. We propose that a baseline level of resilience in chloridoid ancestors allowed them to colonize harsh habitats, and these environments drove selective pressure that enabled the repeated evolution of abiotic stress tolerance traits. Furthermore, we suggest that a lack of evolutionary access to stressful environments is partially responsible for the relatively poor stress resilience of major C4 crops compared to their wild relatives. We propose that chloridoid crops and the subfamily more broadly represent an untapped reservoir for improving resilience to drought and other abiotic stresses in cereals.Grasslands dominate the terrestrial landscape, and grasses have evolved complex and elegant strategies to overcome abiotic stresses. The C Chloridoid grasses have evolved unique adaptations to adverse environments and represent an untapped reservoir for improving resilience to drought and other abiotic stresses in cereals. Pooideae is the largest subfamily of grasses and includes the temperate cereals wheat (Triticum aestivum), barley (Hordeum vulgare), oat (Avena sativa), and rye , as well as most pasture grasses. All BOP clade grasses utilize the C3 pathway of photosynthesis, and most independent origins of frost tolerance in grasses are found within the Pooideae , maize (Zea mays), sorghum (Sorghum bicolor), and various millets are in Panicoideae and the under-resourced grain crops finger millet (Eleusine coracana) and teff (Eragrostis tef) are in the Chloridoideae. In this review, we focus on the PACMAD grasses and the evolution of the abiotic stress tolerance that empowered their dominance and diversification. We ask which factors fostered the evolution of stress tolerance in these grasses, and why all C4 PACMAD grasses are not drought-tolerant.The majority of species in the grass family falls into two evolutionarily and phenotypically distinct clades, BOP  and PACMAD , named for the subfamilies they contain . Most spPooideae . Conversolerance . The agr4 grasses in the United Nations Food and Agriculture Organization global crop production database, only two, finger millet and teff, are chloridoid grasses  leading all other plants in terms of global production. Water availability is thought to have been a major driving force of C4 grass evolution and diversification  and Oropetium capense, are able to equilibrate to low atmospheric moisture for months without dying, while other C4 species such as switchgrass (Panicum hemitomon) are semi-aquatic, requiring regular flooding to survive , increased leaf hydraulic conductance results in lower WUE  catalyzes the reaction fixing inorganic bicarbonate (HCO3), which is in equilibrium with CO2, into organic acids. These organic acids are then transported to bundle sheath cells where they are decarboxylated, raising the bundle sheath CO2 concentration and allowing Rubisco to operate more efficiently , NAD-dependent malic enzyme (NAD-me), and phosphoenolpyruvate carboxykinase (PCK). In NADP-me plants, malate is the primary C4 acid being transported between mesophyll and bundle sheath cells, while aspartate is the primary transported acid in NAD-me and PCK C4 grasses. WUE is correlated with the C4 subtype, with NAD-me grasses having higher WUE under drought stress than NADP-me grasses  and fonio millet (Digitaria exilis) use far less water  in a semi-arid environment revealed that maize is the highest yielding crop, followed by sorghum, with pearl millet having the lowest yield , African rice (Oryza glaberrima), pearl millet, and cowpea (Vigna unguiculata) were domesticated around the Niger River, likely in the early Holocene when the “green Sahara” slowly desertified  and iburu (D. iburua) were domesticated in the central delta and Jos plateau of Nigeria, respectively, and drought-tolerant iburu is intercropped with fonio as a fail-safe under low rainfall  and by predoctoral training award T32-GM110523 from the National Institute of General Medical Sciences of the NIH (to J.P.).Conflict of interest statement. None declared.


Understanding unidirectional and topological wave phenomena requires the unveiling of intrinsic geometry and symmetry for wave dynamics. This is essential yet challenging for the flexible control of near-field evanescent waves, highly desirable in broad practical scenarios ranging from information communication to energy radiation. However, exploitations of near-field waves are limited by a lack of fundamental understanding about inherent near-field symmetry and directional coupling at sub-wavelengths, especially for longitudinal waves. Here, based on the acoustic wave platform, we show the efficient selective couplings enabled by near-field symmetry properties. Based on the inherent symmetry properties of three geometrically orthogonal vectors in near-field acoustics, we successfully realize acoustic Janus, Huygens, spin sources and quadrupole hybrid sources, respectively. Moreover, we experimentally demonstrate fertile symmetry selective directionality of those evanescent modes, supported by two opposite meta-surfaces. The symmetry properties of the near-field acoustic spin angular momenta are revealed by directly measuring local vectorial fields. Our findings advance the understanding of symmetries in near-field physics, supply feasible approaches for directional couplings, and pave the way for promising acoustic devices in the future. It is essential yet challenging to achieve flexible control of near-field evanescent waves, highly desirable in broad practical scenarios. Here, we show the efficient symmetry selective couplings for near-field acoustics The near-field waves are confined in the close region around objects, that is scatters, sources and waveguides, which usually decay exponentially with distance from objects . Owing tAlong with the transverse wave, the curl-free longitudinal wave as the other fundamental component in wave families also plays an indispensable role in many engineering applications or practical scenarios, i.e. acoustic wave, compression elastic wave and P-type seismic wave. Yet, the exploitations of near-field longitudinal waves are severely limited by a lack of fundamental understanding about symmetry essences. And some geometrical and dynamic properties about longitudinal waves are usually overlooked, for example the acoustic spin angular momentum, which was not considered until recently . TherefoIt is worth emphasizing the many fundamental differences between acoustics and optics: (1) A longitudinal acoustic wave has different physical origin, dynamic equation and geometrical properties from a transverse optical wave. The acoustic wave originates from the regular collective motions of molecules, satisfies the dynamic equation based on Newtonian mechanics, and has a geometrical curl-free nature. In contrast, the optical wave is described by relativistic Maxwell equations, composed of the synchronized oscillated electric and magnetic fields, of a geometrical divergence-free nature. (2) Basic properties of source elements are totally different. There is a monopole for acoustics, but, generally, this does not hold for optics. Besides, unlike acoustics, there are two dual types of multipoles in optics: the electric and magnetic multipoles. (3) There is NO optical magnetic vector field counterpart in acoustics. As such, some necessary requirements of electric and magnetic fields in optical sources ,28 cannoIn this paper, based on the acoustic wave platform, we unveil the inherent symmetry and geometric properties of near-field waves experimentally. Based on symmetry analysis, it is possible to achieve selective near-field longitudinal wave coupling. The near-field acoustics can be universally associated with three geometrically orthogonal physical vectors: time-average energy flow (Poynting vector), reactive power and spin angular momentum (SAM) , even fo0 is the amplitude of acoustic velocity field, τ is the decay rate of the evanescent wave in y direction, and ω is the frequency. To describe the dynamic features of near-fields, we can exploit three vectorial quantities  = iεijkSk.Introducing the state vector about acoustic field, y = 0 as the interface between air and effective media):c1 and c2 are the acoustic speeds, ρ1 and ρ2 are the mass densities, specially ρ2 < 0, k is wave vector. The acoustic wave satisfies the dispersion relationship : k: S > 0 for k > 0, S < 0 for k < 0, as shown in Fig.S5 of the Supplementary data, which has similar properties to that in quantum spin Hall effect (QSHE) [For Fig. nted as:\documentt (QSHE)  and 3D tt (QSHE) . Thus tht (QSHE) ,27. Simi media):\documentBased on the acoustic SAM, e in Eq.  can be wIn this section, we will supply one feasible experimental scheme to achieve a general near-field acoustic source, and give a practical example to realize Janus, Huygens and spin sources.A scheme to achieve a general near-field acoustic source is shown in Fig. x, βy will be responsible for achieving these sources. Thus, we can design such a source device shown in Fig. 0 plays the role of acoustic monopole M. The other four speakers φ1, φ2, φ3, φ4 will behave as effective acoustic dipoles Dx, Dy when they are set as:To exemplify one experimental scheme, we will exploit speaker array to realize the Janus, Huygens and spin sources in the main text. The physical mechanism of these sources can be understood as a linear combination of different kinds of basic acoustic sources nwaa040_Supplemental_FileClick here for additional data file.


Arteriovenous malformation (AVM) of the brain is a congenital vascular abnormality, in which the arterial and venous blood pools are intertwined and directly connected. This dangerous disease causes a high risk of intracranial hemorrhage and disrupts brain functioning. The preferred method of AVM treating is embolization, which is the endovascular filling of abnormal AVM vessels with a special embolic agent. Despite the fact that this method is widely used in neurosurgery, in some cases its use is accompanied by perioperative AVM vessels rupture. In this regard, the aim of this work is to study the optimal scenarios for multi-stage AVM embolization from the effectiveness and safety of the procedure point of view. Mathematically, the joint movement of blood and embolic agent in the AVM body is described on the basis of a one-dimensional two-phase filtration model, which takes into account the redistribution of blood to surrounding healthy vessels. For the numerical solution of the resulting integro-differential system of equations, a monotonic modification of the CABARET scheme is used. To find optimal embolization scenarios, the optimal control problem with phase constraints arising from medicine is formulated. A modified particle swarm optimization method is used to solve this problem numerically. This technique is used to obtain optimal embolization scenarios on the basis of real patients clinical data collected during neurosurgical operations. By type of pathological blood vessels, connecting the arterial and venous pools, AVMs can be divided into racemic pathology  and fistula one (consisting of large vessels). The resistance of the corresponding part of circulatory system is reduced due to the capillary network absence. This causes changes in both the hemodynamic parameters (flow rate and pressure) and the strength properties of the blood vessels5. AVMs have a complex effect on intracranial hemodynamics, which varies with changes in morphology and angioarchitecture, especially with different treatment methods. Endovascular embolization is the filling of abnormal blood vessels with a special embolic agent in order to shut them off from the bloodstream. Due to the minimal invasiveness and the possibility of operating in deep, functionally significant brain areas, embolization is one of the most effective methods at the current level of medical development6. Despite the fact that this method is widely used, the risk of perioperative vascular rupture is still a serious danger7. Therefore, the study of optimal scenarios for multi-stage AVM embolization from the effectiveness and safety of neurosurgical surgery point of view remains an urgent task.Currently, the most common methods of AVM treatment are microsurgical, endovascular and radiosurgical8. There are works in which the equations describing flows in pipes with rigid and elastic boundaries are analytically investigated10. Viscous fluid flow in a network of soft tubes is also modeled on the basis of a one-dimensional approximation of mass and momentum conservation laws13. Numerical simulation of hemodynamics for large blood vessels based on 3D–1D coupled flow is also considered16.For the mathematical description of blood flow, a one-dimensional approximation of the Navier–Stokes equations is widely used, obtained by averaging these equations over blood vessel cross-section19. Such models allow us to assess the impact of various embolization scenarios on blood flow redistribution and are consistent with the general medical view on pathology hemodynamics. Various approaches are used to describe the joint flow of blood and embolic agent, for example, a two-phase flow model was used to simulate a viscous fluid drop movement of embolic agent through a bifurcation point or multifurcation point based on dimensionless Navier–Stokes equations for incompressible liquids20. A model of AVM embolization was proposed based on the concept of two-fluid modeling and scalar transport, where embolic agent and blood interaction along with its hardening is simulated by viscosity increase21. Another approach to the description of the embolization process is based on the two-phase filtration model in the authors’ work22. The present paper is a extension of this work. In comparison to the present work in22 blood flow into the adjacent healthy vessels was not considered, the cross-section area and porosity were assumed to be constant, and embolization was modeled without taking into account embolic agent solidification between the stages of surgery (simplified one-stage case). The optimal control problem22 differs in form from the one described below, but is essentially the same, namely, it requires performing the operation in the most efficient way in compliance with safety constraints. The formulation of the optimal control problem in present paper is obtained from the control problem22 by interchanging the constraint and the objective functional, which is typical of extremum search problems with constraints. In the work22, the search for an extremum of the functional was based on the calculation of its value on the grid in the three-dimensional control parameter space with subsequent interpolation. While present work uses the global optimization method - the particle swarm method, which significantly accelerates calculations, increases their accuracy and allows us to explore the control parameter space of a larger dimension. Despite the large number of publications dedicated to the AVM hemodynamics, research expansion in this direction is a great scientific interest.The interaction of AVM and blood flow in the surrounding vessels is often studied in analogy with electric and hydraulic networksIn this paper, mathematical modeling of AVM embolization is carried out as follows: the flow of blood and embolic agent through the AVM body is considered as filtration flow based on Darcy’s law, taking into account the redistribution of blood to healthy vessels. This approach is justified for small-vascular racemic AVM compartments embolization description. It is assumed that both liquids are Newtonian with constant viscosity, incompressible and immiscible, while ignoring the interfacial capillary forces, the effect of embolic agent adsorption, as well as the deformation and permeability of the vessel walls.24. For numerical calculations real blood and embolic agent (ONYX18) viscosities were used. To find optimal embolization scenarios, the optimal control problem of multi-stage embolization with phase constraints arising from medicine is formulated. To solve this problem numerically a particle swarm optimization method is used26, which is specially modified in order to adapt it to the problem under consideration. The proposed technique is used to obtain optimal embolization scenarios on the basis of real patients clinical data collected during neurosurgical operations27.As a result, the mathematical description of the joint movement of blood and embolic agent in the AVM body is based on a one-dimensional two-phase filtration model that takes into account the redistribution of blood to surrounding healthy vessels. For the numerical solution of the resulting system of integro-differential equations, a monotonic modification of the CABARET scheme is used, which localizes with high accuracy the strong and weak discontinuities that occur when solving this problemIn the next section, a mathematical formulation of the one-stage embolization problem is given, leading to an initial-boundary value problem for a system of integro-differential equations, including a hyperbolic partial differential equation, which is a quasilinear scalar conservation law with a nonconvex flux. Then the optimal control problem of one-stage AVM embolization is formulated, where the control is a time function setting the boundary condition of the problem and is included in the coefficients of the equation. The objective functional is the integral of the initial-boundary value problem solution at terminal time. The phase constraints on the control function represent additional integral and algebraic relations. The objective functional and constraints are selected according to medical indications. We introduce a class of piecewise linear continuous and discontinuous functions used as controls for the AVM embolization process. Further, the optimal control problem of multi-stage AVM embolization is formulated, which leads to a chain of integro-differential initial-boundary value problems, in which each subsequent problem uses the results of solving the previous problem as parameters of a new system of equations.Next, we present a monotonic modification of the CABARET scheme, which localizes with high accuracy the strong and weak discontinuities that arise when solving the initial-boundary value problem under consideration. The modification of the particle swarm optimization method is proposed that is specially adapted to the considering problem in order to more fully investigate the admissible parameters area and accelerate the progress of the particle swarm to the absolute minimum. Numerical verification of the optimal control problem of multi-stage embolization using real patients clinical data was performed, on the basis of which AVM embolization optimal scenarios were obtained. Also we discusses the limitations of the proposed method, as well as the possibilities for its further development.29.In this paper, blood and embolic agent movement through small-vascular racemic AVM is modeled Fig.  as a two30 and will be further used in the optimal embolization control problem.Based on this initial-boundary value problem, it is set the task of finding the optimal regime of one-stage AVM embolization from the effectiveness and safety of neurosurgical surgery point of view. The objective functional and constraints that arise in the optimal control problem are selected according to medical indications. The control is a time function that determines the embolic agent injection at the AVM input. The embolization effectiveness is determined by the degree of blood displacement from the AVM by the embolic agent at the operation end. One of the possible risks of the operation complications is the embolic agent entering in the vein, as a which result the AVM or vein vessels rupture may occur. Also, during the operation, vascular network has an additional stress, since when the embolic agent is injected, the pressure in the arterial vessels increases. Excessive pressure build-up is dangerous. Both of these factors increase the brain hemorrhage riskA the AVM cross-section area available for the phase flows, by m the AVM body porosity, by Q the volume flow rate of two-phase mixture. These values can vary both in space and in time. Let f(S)29, which sets the distribution of the phases volume flow inside a porous medium and is equal to the flow fraction of displaced phase in the total two phases flow.Consider the one-dimensional joined filtration flow of blood and embolic agent through the AVM body. Denote by We derive the differential form of the integral conservation law of blood volume, assuming that the AVM walls are impermeable and the phases are incompressible fluids. The change in blood volume This change is due to the blood flow through the cross-sections at points m(x) and A(x) are given piecewise continuous functions of the spatial coordinate x. The differential form of the conservation law ,,2), we oS is considered in the class of piecewise continuous functions. We will assume that the Buckley–Leverett function Q(t) does not depend on the spatial coordinate x and is determined by the relationSince the Eq.  is hyper the Eq.  can be wL and T are some positive numbers. Since at the initial time The differential equation  is solveQ(t) of two-phase mixture inside the AVM, included in  is expressed in terms of boundary phase flows and is defined as followsS. It is important to emphasize that the control function Blood flow changes during the cardiac cycle is not taken into account due to the duration of the embolization process is significantly longer than the cardiac cycle duration, and the blood flow rate luded in , is deteequation  propagat the Eq.  one boun formula , 6), , , S inside the AVM, the mixture flow rate Q(t) and the pressure Taking into account the fact that ¯), Eqs. , 8) and and\docuS and the pressure Thus, in the optimal control problem, it is necessary to find a function nctional , which inctional , 6),  on on\docum formula .We consider a numerical solution of the problem , 8), ,  with iniFor the control class  and 15)15), timeol class  and 16)\documentAs a result, the optimal embolization problem is led to finding the control parameterst supply . The cort supply , 6), 17\documet supply  prohibitN. Mathematical modeling of multi-stage embolization is a generalization of the one-stage embolization described in the previous section. Between the stages there are time breaks, during which the embolic agent remains fixes inside the AVM and does not change its location in the following stages of embolization. For the mathematical modeling, we assume that the duration of these time breaks is zero. Taking this into account, embolization at each i-th stage occurs on the time interval i-th stage is denoted by m, absolute permeability K, relative phase permeability f. In the multi-stage case, the embolization process at each i-th stage is modeled similarly to the one-stage embolization case, which was described above. Thus, the initial-boundary value problem simulating the i-th embolization stage on the time interval A real neurosurgical operation for AVM embolization usually proceeds in several stages, the number of which is denoted by milar to , 6),  at  at N-th milar to , 12) ha haN-th sFor multi-stage embolization, we consider a control that at each stage similar to the control for one-stage embolization –16). Su. Su16). i-th embolization stage. Next, instead of the parameters  giv giv30\dot supply , which ct supply  and 26)30\documet supply  prohibit31, which has a second-order approximation on smooth solutions. This modification of the CABARET scheme was proposed in paper23 and is used to model the problems of hemodynamics32. The main advantages of this scheme are due to the fact that it is given on a compact spatial stencil and, when approximating linear equations, is time-reversible and accurate with two different Courant numbers 33.For the numerical solution of the initial boundary value problem , 23) fo fo23) foi-th stage. Let us divide the segment  on which the considered problem is solved into J equal parts of length h is a constant spatial step, and n-th time layer, determined from the CFL-stability condition at the i-th embolization stage. Let us denote by i-th stage. The CABARET scheme uses the flux Numerical simulation is carried out one after another at all stages of embolization, and the same difference scheme is applied at each stages. We present the algorithm of CABARET scheme for the n-th time layer is calculated. At the second stage, by approximating the Eqs.  at  at \docuondition :\documenthe Eqs. –21) wit wit\docuAt the third stage for n is replaced by the index At the fifth stage, using formula , in whicAt the beginning of the fourth stage, as a result of the second-order approximation of the integral boundary condition  on the li, which specifies the number of the embolization stage, is omitted for brevity.Further in the formulas of this section, the index The numerical fluxes 34 that the correction of fluxes (n-th time layer in the vicinity of the grid node It is shownf fluxes  is not sIf neither of the two conditions  or 39)  39) is ff, and At the beginning of the seventh stage, the flux variable value is found on the left boundary of the computational domainformulas  and 36)\document25. To apply this method, the optimal control problem  is  is 25. T26. The particle swarm method for minimizing the functional consists in setting the initial position of each particle and organizing the iterative process of moving these particles so that after a given finite number of iterations I all the particles end up in a small neighborhood of some point The required parameters nctional , are repnctional . At eachM bounded disjoint subdomains The search for the vector rameters  we allock-th step of the iteration. The values at the 26; The formulas The coordinates of the particle The formulas P, and in the set P is the given number.The set of all particles For all When Let the values 25 in that a special initial particle distribution is selected and that at each algorithm iteration the positions of all particles are reinitialized with a certain probability P. This modification was required for a more complete examination of the admissible parameter domain and to accelerate the progress of the swarm to an absolute minimum.The proposed algorithm differs from the classical particle swarm optimization method27 using a Philips ComboMap system and the Philips ComboWire sensor (sensor diameter is 0.36 mm and its length is 1.85 m), which measures blood velocity and pressure inside the cerebral vessels near the pathology. This way the pressure and velocity at the AVM input were obtained before, during and after the embolization, as well as at the AVM output before and after the operation. To obtain the geometrical AVM parameters: the length L, the cross-section area A as well as input artery cross-section area, data from angiographic studies (perioperative X-ray tomography) were used  and m can be reduced to this case by scaling the time variable t. The initial cross-section area A is assumed to be constant and equal to the average cross-section of the AVM before embolization. It should be noted that the developed method can be used to numerically solve the problem of multi-stage embolization with variable values m(x) and A(x). To verify the proposed model, we consider the multi-stage embolization problems for patients K, S and P. The geometrical and filtration characteristics of the pathologies of these patients used for calculations are shown in Table Using the method proposed in the previous papersquations –23). In. In22, tquations –26), th, th22, tmentclass2pt{minimThe investigation was conducted in accordance with the Helsinki Declaration and approved by the Inspection Commission of the Meshalkin Clinic (Session No. 549). All included patients gave their informed consent.K, S and P based on the clinical data given above. For the calculations, a space-uniform difference grid was used  is isK, S aK, S is achieved in two embolization stages, and for patient P in three stages. A further increase in the number of embolization stages leads to smaller values of the objective functional. It should be noted that in a real neurosurgical operation, the number of stages can be more than three. To solve the optimal control problem of two-stage embolization by the particle swarm optimization method, the number of particles is chosen to be K, S and P.In order to be consistent with the clinical data, numerical calculations were performed in such a way that the objective functional value was entclass1pt{minimaK and S. At the same time, for the patient P, the behavior of the clinical and calculated pressures differs to a greater extent. This probably due to the fact that this patient has a difficult clinical case, as indicated by the rupture of AVM vessels after surgery. Thus, it can be assumed that the process of clinical embolization was not carried out in an optimal way for patient P. Figure K. For patients S and P, such distributions have a similar behavior.Figure A(x) and m(x). However, modern medical examination methods of reconstructing the AVM geometry, such as computed tomography, magnetic resonance imaging and cerebral angiography, allow us to determine in vivo vessels with an average diameter of at least 0.5 mm. This not enough to determine the detailed geometric structure of the AVM, which often consisting of a large number of conjoined intertwined thin vessels, the diameter of which can reach 0.1 mm. In addition, important information is provided by intraoperative intravascular measurements of hemodynamic parameters near the pathology. Such measurements are possible only in sufficiently large vessels adjacent to the AVM, and measurements directly inside the AVM are seriously difficult and often impossible. Due to the above limitations, the proposed mathematical model is simplified, but despite this, it demonstrates a good agreement between the behavior of the calculated pressure and the clinical one. It should be noted that the question of the theoretical justification of the existence and uniqueness of the optimal control problem solution under consideration requires additional study and can be the subject of another mathematical investigation. Since this theoretical study is not the subject of interest of our applied work, we obtain optimal control using numerical modeling.Despite the well-developed technique of embolization operations, the risk of perioperative vascular rupture is still a serious danger. In this regard, the development of new methods of mathematical modeling of the AVM embolization process remains an urgent task. For modeling, it is desirable to have detailed information about the AVM geometrical structure, which would allow you to define the functions K and S. Among the considered patients, patient P stands out, for which three-stage embolization was required to achieve the functional value K and S, for which such functional values were achieved in two stages. It should be noted that the patient P had a hemorrhage immediately after the neurosurgical operation, while the other patients did not have perioperative complications. This suggests that the properties of AVM and its surrounding vessels for patient P are significantly different from those of the other two patients. This is also evidenced by a significant difference in the behavior of the clinical and calculated pressure for this patient. It can be hypothesized that the need for a large number of embolization stages indicates a high probability of perioperative complications, and in this case, it is especially useful to find the optimal embolization regime. The appearance of optimal discontinuous controls (“bang-bang” control type) at the last stage for patients S and P is also interesting.On the basis of the mathematical model, it was possible to obtain a good correlation of the calculated and clinical pressure at the AVM input for patients In the considered model, the influence of surrounding healthy vessels on blood flow through the AVM is taken into account by setting the In this paper it is formulated and investigated the optimal control problem of multi-stage embolization, which arises in the simulation of neurosurgery on pathological blood vessels of the brain. This simulation is performed by describing the joint filtration flow of two phases: blood and embolic agent that thromboses the pathology, as well as taking into account the redistribution of blood into healthy vessels. As a result, an initial-boundary value problem arises for a system of integro-differential equations that includes a hyperbolic divergent partial differential equation with a nonconvex flow function. The numerical solution of this problem, obtained using a monotone modification of the CABARET scheme, is used to solve the optimal control problem of multi-stage embolization by a modified particle swarm method.In the numerical solution of the considered problem, the parameters and functions included in the system of integro-differential equations and the phase constraints of the optimal control problem are determined on the basis of data obtained for real patients during neurosurgical embolization operations. For the obtained solutions to the optimal control problem of multi-stage embolization, a good agreement between the calculated and clinical pressures is observed. The proposed mathematical model and numerical algorithm will be used to improve the methodology and the safety of neurosurgical operations.


The study explores how social network determinants relate to the prevalence and frequency of alcohol use among peer dyads. It is studied how similar alcohol habits co-exist among persons (egos) and their peers  when socio-demographic similarity , network composition and other socio-cultural aspects were considered. Data was ego-based responses derived from a Swedish national survey with a cohort of 23-year olds. The analytical sample included 7987 ego-alter pairs, which corresponds to 2071 individuals (egos). A so-called dyadic design was applied i.e., all components of the analysis refer to ego-alter pairs (dyads). Multilevel multinomial-models were used to analyse similarity in alcohol habits in relation to ego-alter similarity in ethnic background, religious beliefs, age, sex, risk-taking, educational level, closure in network, duration, and type of relationship, as well as interactions between ethnicity and central network characteristics. Ego-alter similarity in terms of ethnic origin, age and sex was associated with ego-alter similarity in alcohol use. That both ego and alters were non-religious and were members of closed networks also had an impact on similarity in alcohol habits. It was concluded that network similarity might be an explanation for the co-existence of alcohol use among members of peer networks. People’s social contacts and networks have been found to have an impact on their norms and behaviours. It is for example well known from individual-level studies that alcohol habits are socially patterned, and that family, friends, and other people in the extended network influence people’s drinking behaviours. Although people hold individual norms about behaviours, these are often revised during such interactions. This influence is, furthermore, bimodal since networks can have both positive and negative impact on people’s drinking behaviour  i.e., soLittle is, however, known about what aspects of these relationships that is associated people’s drinking. It has been suggested  that a pDyads are the smallest entity in a network, and these are the most immediate level of peer interaction. It has for example been observed in psychological experimental settings that people in dyads tend to ‘imitate’ the drinking level (non/light/heavy) of the other peer . Most dyHomophily e.g., similarity between peers, is known to be strong in dyads. This has for example been observed regarding demographic characteristics such as ethnicity, social class, and gender ,11. SimiAnother interest of this study is to investigate the role of ethnic background for drinking habits in social networks. The number of people with migrant background is fairly large in Sweden and has furthermore increased during later years (Statistics Sweden). Alcohol habits are known to vary largely by national drinking culture, but also to differ between first- and second-generation immigrants in the destination country ,25. LittWhen people are very similar to each other regarding personal characteristics e.g., if they have similar ethnic background, share similar religious beliefs, have the same gender and age, it is likely that they also share similar attitudes and norms about certain behaviours e.g., alcohol habits.Alcohol habits are known to differ between various drinking cultures, expressed as differences in what situations alcohol is consumed , total volume of alcohol consumed, or volumes consumed on one occasion (binge drinking), but differences in alcohol cultures are at least in part also related to religious beliefs . The traParents are expected to keep some of their traditional norms e.g., alcohol culture, also in the new country ,30. SincStill, also within one drinking culture, there can be variations in norms e.g., by population groups . It is wAlthough wider networks have been suggested to influence a person’s alcohol habits, as is the case when alcohol habits are spread in societies and form collective  drinking cultures , the immTheories of homophily imply that social interactions occur more often between similar people than among dissimilar people . People The intention with this study is to fill a research gap by considering how peer similarity and other network characteristics relate to health behaviours e.g., alcohol use, in relation to disparate ethnic origin. Thus, in this study the homophily concept has a broader definition than what is the common use by not only focusing on socio-demographic similarities but by also considering similarities in behaviours.The objective is to study whether homophily in dyadic relationships—by ethnic background, religious beliefs, gender, age, and social behaviours—and other social network aspects co-exist with peer similarity in alcohol habits.It is hypothesized that 1) peer similarity in alcohol habits is related to other peer similarity i.e., behaviours are norm-based (culture); that 2) alcohol use is more common and consumed in higher quantities (binge drinking) in homogeneous peer dyads representing population groups commonly known to have higher use e.g., men, younger people, risk-takers; and that 3) alcohol use is more similar among friends with greater contact opportunities with their peers e.g., in close or closed peer tiesSocial Capital and Labor Market Integration: A Cohort Study”, a randomly selected representative sample of Swedish residents born in 1990. The strategic sample of respondents  comprised Swedish citizens stratified by the most common ethnic origins in this cohort. Respondents with at least one parent from former Yugoslavia refer to 50% of this subgroup in the total population in Sweden. Those with at least one parent from Iran comprise the entire ethnic subgroup. A simple random sample of descendants of Swedish parents represents 2.5% of the total population group at that age in Sweden. This sample was representative of the groups included in the analyses, of which 49.4% had two Swedish-born parents, 21.5% had Iranian descent , and 29.1% were descendants from former Yugoslavia .The data used in this study was derived from a survey entitled “From the strategic sample of n = 5,695 in the first wave, n = 2,244 was re-interviewed by telephone by Statistics Sweden in 2013. The response rate was 39.4 per cent in this wave. The widespread use of non-registered prepaid phones in this specific age group was the primary reason for non-responses in the study. The three groups with distinct ethnic background also represent different drinking cultures i.e., habits with restrictive alcohol use and habits including regular binge drinking. Only data from the second wave of the survey (2013) was considered for the purpose of this study since it contained all variables of interest i.e., information on alcohol habits and ethnic background for individuals and their peers, and information about peer network characteristics; respondents were then around the age of 23. After excluding the non-responses on the variables of interest, 2,071 individuals remained in the analytical sample of the present study . These aFor the purpose of analysing dyads, respondents (egos) were asked to name up to five persons  who they considered to be their closest peers. These nominations covered different types of relationships, and a distinction was made between friends, family members and romantic partners. Egos nominated four peers  on average, which resulted in a total of 7,987 ego-alter pairs (dyads) to be included in this study. Since a friendship is intrinsically dyadic and depends on both peers to persist, these dyads are the basis for the analyses. By using a dyadic design, both features of the ego and alter are used to estimate their association toa behaviour. Estimations of social behaviours, such as use of alcohol, are more reliable if they are based on the social ties through which most alcohol use occurs i.e., not only ego’s characteristics but of their peer’s as well. Data were in long format, including multiple observations (up to five observations) per ego . Composite variables at the dyad level to account for the similarity and dissimilarity in ego-alter ties were constructed; if both ego and alter answered that they had an Iranian parent they were coded as Iranian but if only one of them had an Iranian parent, they were coded as of mixed origin. Thus, all variables refer to similarities in behaviours and attributes in these dyads (pairs) or of characteristics describing the relationship between egos and alters .The dependent variable was constructed from two items on ego’s drinking habits 1) prevalence of alcohol use i.e., egos answered an item on whether they drink alcohol or not, and 2) weekly binge drinking, constructed from an item asking how many times ego had been drinking enough alcohol to feel intoxicated during the last 12 months  was recoded to ‘binge drinking at least weekly’, and corresponding items for alters drinking. The final variable used in these analyses was a composite measure of similarity in prevalence of alcohol use and frequency of weekly binge drinking in the ego-alter dyads (peer ties). It had four categories: 1) disparate drinking habits in dyads (peers reporting congruent habits), 2) both ego and alter non-drinkers, 3) both ego and alter reported any level of drinking but not weekly binge drinking, and 4) both ego and alter at least weekly binge drinkers. It is important to note that the variables on ego-alter similarity in alcohol use measure the co-occurrence of drinking habits, but it does not necessarily mean that egos and alters drink alcohol in the presence of each other.Likewise, the dependent variables were based on egos’ responses and constructed based on similarity at the dyadic level. While the dependent variables regarded similarity in drinking habits, the independent variables indicated ego-alter similarity in relation to sex, age, ethnic background, religious beliefs, educational level and risk-taking. ‘Sex composition’ of the dyad distinguished between dyads of the same sex  and of ‘opposite sex’ . ‘Similar age’ accounted for possible age differences between ego and alter, and denoted whether the age gap was smaller or larger than three years. Ethnic background was categorized as dyads with similar ethnic backgrounds i.e., both peers had at least one parent who had migrated from former Yugoslavia or Iran, or both peers had parents with only Swedish descent, or peers had disparate ethnic backgrounds. Partly overlapping with this measure was the measure for religious beliefs/faith, which distinguished between dyads where both peers belonged to ‘disparate confessions and dyads where both peers were Christians (Protestant/Catholic), Muslims, belonged to another religious group  or where both peers were ‘non-religious’. Similarity in educational level referred to both ego and alter having completed at least secondary school. Another measure of similarity in peer-ties referred to risk-taking. The composite measure of ego-alter similarity in risk-taking was derived from two variables referring to whether ego was prepared to take risks and how strongly ego perceived that each alter in the ego’s network was to take risks. The new variable was coded “1” if ego agreed/strongly agreed to the statement of being a risk taker, and if ego also regarded alters as being risk-seekers. “Conformity” is a composite score reflecting the degree of similarity between ego and alter. The independent variables  were used to create the index and each similarity counted as 1 point, resulting in a score with a range from 0 to 6.Other types of social network characteristics comprised of the structure and content of the studied networks. ‘Type of relationship’ measured whether ego and alter were friends, relatives, or romantic partners, and ‘relationship duration’ referred to how many years ego and alter had known each other. ‘Network closure’, furthermore, referred to both the degree of closeness and the networks’ closure. Closed networks (coded as “1”) referred to all alters listed by ego knowing each other and networks which were more open  (coded as “0”). ‘Discussing important matters’ (coded as “1”) was used as an indicator of a strong relationship ,50,51. IA hierarchical data structure with alters clustered by egos was applied. All components of the analysis refer to the dyad-level, which means that ego-alter ties (dyads) were treated as the smallest unit of analyses. Depending on the number of named alters, each respondent (ego) in the survey data contributed with up to five observations .Multi-level multinomial logistic regression models with random effects (at ego-level) and 95% confidence intervals were used to estimate the relative risk ratios of dyadic alcohol habits by ego-alter (dis)similarity with regards to sex, age, ethnic background, religion, educational level and risk-taking, as well as other social network characteristics i.e., type of relationship, duration, network closure and closeness. A similar method with intra-class correlations to that used by colleagues  was usedTo study interactions between demographic variables and network characteristics in relation to co-evolvement in alcohol habits, a predictive margins approach was used. Interactions between ethnic background and conformity, duration or density are illustrated in figures. Interactions between sex and ethnic origin were also analysed but were found to be non-significant and are therefore not presented further in this article.To illustrate how network characteristics i.e., similarity in peers’ individual characteristics etc., relate to similarities in drinking habits in ego-alter dyads, both abstaining from alcohol, prevalence of drinking and frequency of binge-drinking was considered.The demographic characteristics of the sample illustrated in Most egos (83.3%) had listed friends (not relatives or romantic partners) as their closest peers. These relationships had, on average, prevailed for more than 8 years. The closure in these networks were also strong, given that in 74.2% of the dyads, all alters of the ego were friends with each other. Analyses of the types of subjects’ egos discussed with their peers (proxies for closeness in peer relationships) illustrated that 87.6% talked about important matters . More specifically, 74.3% reported talking about sex life, and 52.6% talked about religion/faith.A strong relationship could be observed between peers in dyads being non-drinkers and similarity in terms of them both being Muslims . In concAmong drinkers (lower level), female peers were less prone to drink alcohol than those in mixed-sex (dissimilar) dyads. Non-religious peer dyads, in contrast, were more likely to be drinkers. Also, peers of Swedish descent and ego-alter pairs with roots in former Yugoslavia, were more likely to be drinkers than peers of dissimilar ethnic origin. Among peers who both had started tertiary education, it was also more common that they both were drinkers. Similarity in age also mattered, since ego-alter pairs of similar age were more likely to both be drinkers. Similarity in risk-taking behaviour among both peers also increased the risk of both peers being drinkers. Additionally, being members of a closed peer group was observed to increase the risk of being a drinker. Talking about sex among peers did also covariate with being a drinker.In line with the results for prevalence of drinking, female and Muslim dyads were less likely to consume larger volumes of alcohol i.e., weekly binge drinking (subjective feeling of being intoxicated) were less common among these peers. Weekly binge drinking was found to be prevalent significantly more often in male and non-religious dyads in comparison to the mixed reference groups. Peers who had a similar ethnic background were additionally more likely to binge drink weekly than peers with dissimilar backgrounds. Similarity in age and educational level were two other demographics which also increased the risk of weekly binge drinking. For this riskier drinking behaviour, similarity in risk-taking behaviour among both peers were also observed to increase the risk. Binge drinking was additionally more common among peers who belonged to closed networks and among those who were close enough to talk about their sex life. Peers discussing important subjects more in general were, however, less likely to binge drink weekly. Type of relationship was also shown to be important, since dyads of romantic partners were significantly less likely to binge drink than dyads of relatives. Note that this was not the case for drinking in general.The predictive margins plots illustrate that the concordance in drinking habits in relation to conformity in peer groups, duration of friendship and network closure differ between groups with different ethnic background. This study analysed how peer similarity in alcohol habits i.e., sobriety, prevalence of alcohol use and frequency of binge-drinking, relates to peer similarity in terms of gender, age, educational level, ethnic origin, religious beliefs and risk-taking. Peer similarity has been observed to be important for other health risk behaviours ,19 and iTwo main incentives were assumed to drive peer clustering processes and the development of common drinking habits: norm-based aspects and contact opportunities. That peers similar to each other cluster partly happens early in life, when families with similar ethnic background, religious beliefs and socio-economic status tend to share more social arenas than families with larger differences –55. ManyNational drinking cultures have had a central role in research aiming to explain differences in alcohol habits between countries. Young people are known to be influenced by their parents drinking ,60, and Peer dyads where both were Muslims were more often observed to abstain from alcohol than dyads with disparate religious beliefs. The Muslim dyads who did drink were much less likely to binge drink than the mixed group. Further in line with expectations was that peer dyads where both considered themselves to be non-religious were more likely to be drinkers and to binge drink than the mixed group. Faith in either part was on the contrary associated with a lower likelihood of peers in these dyads to be drinkers. While not all results were significant, peer clustering related to cultural norms in network dyads, and more specifically those related to drinking culture, were observed to be related to differences in alcohol habits.As mentioned earlier, differences in drinking culture are not limited to national borders but can be observed also within a country , by sub-Drinking was also hypothesized to occur in peer groups of similar (young) age. To assume a causal relationship to similarity and age would, however, be problematic since egos were 23 years old and peers of similar age here means that peers were between 20 and 26 years old. This result could instead be interpreted in the light of drinking being more common among younger people. Young people tend to spend time with other young people, due to similar lifestyles. This is increasing the contact opportunities with others part of this population group who is known to drink more alcohol than older people. This is likely to have impact on the common norms in the group and for peers to self-select to other groups with similar characteristics and behaviours. Given that they are likely to share these characteristics, drinking is more likely to occur, and binge-drinking is furthermore more likely to take place in party settings, assumed to be more frequent in this age group. As people grow older, lifestyles can change, resulting in changes of opportunities to drink as well as changes in norms, with the consequence that people tend to drink less alcohol. A dyad of two older people of similar age would therefore be expected to drink less alcohol than the group of young people in this study.Education level was partly associated to age since many in this group of young people have not yet finished their studies. Although, the dyads where both peers had started some tertiary education were more likely to be drinkers as well as more often binge drink weekly compared to other dyads. Campus environments are known to encourage alcohol use , thus coBoth ego and alter being identified as risk-takers furthermore increased the risk for dyads to binge drink at least weekly, which was also what we would expect from other studies on risk-taking and alcohol .Based on the joint findings of similarity in peer dyads, similarity as an explanation of similar alcohol habits seems to be fairly strong. Dyads of peers being members of population groups known to more often be drinkers in individual-level studies were also found to be drinkers more often, and to drink larger amounts at single occasions (binge drink). This suggests that people who are similar in other aspects also tend to share similar norms and behaviours about whether to use alcohol at all or specifically to encourage binge drinking.Other general social network characteristics i.e., relationship type, network closure, friendship duration and closeness in ties could have an impact on similarity and contact opportunities. With greater contact opportunities, peers are also more likely to share similar norms and behaviours regarding use of alcohol. The intensity in the relationship was for example expected to increase the number of contact opportunities, which was assumed to make peers more likely to share similar norms regarding drinking. In their early twenties, people tend to spend more time with other peers than with relatives and given that alcohol use is a social activity, alcohol use is likely to take place during some of these occasions and contributing to more drinking opportunities. Drinking among friends were not found to differ significantly from that among relatives but drinking among romantic partners did. Dyads of romantic partners were less likely to binge drink weekly than dyads of family members. Partners have been observed to have a central role in pressuring their partners to drink less . This isClose friendships also seemed to be important when explaining differences in drinking habits, since binge drinking were less common in peer dyads where important matters were usually discussed. Studies have shown that close friends influence drinking and have additionally suggested that ties are closer among peers sharing similar habits –70. ConsAdditionally, if peers were part of a closed network, they were more likely to be drinkers and to binge drink at least weekly. Other health behaviours, positive or negative, have also been explained by stronger joint norms being upheld in closed networks, and what more that the norms in closed networks, once developed between peers, are harder to change . Any polA limitation of this study is the focus on dyads and that the information about the extended network is limited. It is possible that ‘dyadic effects’ and ‘group effects’ work simultaneously to influence drinking in peers. Although, as stated in the introduction, the closest dyads are expected to have the strongest impact on behaviours. Still, in order to study the effects of the complete network, information about all peers and how they are connected would be needed. Another limitation with the analyses is that data was ego-based and thus only providing second-hand information from egos (secondary source) regarding peers’ drinking. Several studies have stated that there is a tendency that people overestimate peers’ drinking, although the accuracy of this conclusion has also been questioned . Such miIn conclusion, the results in this study suggest that network similarity i.e., homophily, and other network characteristics are important when explaining co-existence of both prevalence of alcohol use and drinking patterns i.e., frequency of binge drinking, in dyads of peer networks. Knowing that people are connected through social network ties has bearing on policy development since interventions are more successful if there is similarity in the intervention group and if they also target spouses or peers . Policie