This grating encoder is composed of a stationary reading head and a movable grating reflector. A light beam from the reading head is projected onto the grating, and three diffracted beams  are generated, collimated, and received by three separate quadrant photodetectors (QPDs). The information of θx, θy, θz, and Z is coded into spot positions of these three diffracted beams on the QPDs. Thus, the modeling and decoupling algorithms were investigated, and an independent calculation of these four-DOF absolute positions was theoretically guaranteed. A prototype was then designed, constructed, and evaluated. Experimental results verified that the proposed grating encoder could achieve the absolute measurement of four-DOF θx, θy, θz, and Z with an accuracy of sub-arcseconds and sub-micrometers. To the best of our knowledge, the proposed encoder in this research is the first one to achieve absolute simultaneous measurements of four-DOF position and pose with a large measurement range. The success of this new grating encoder can benefit various multi-DOF positioning applications, especially for large-scale synthetic aperture optics (SAO), including stitching off-axis parabolic mirrors and pulse compression grating.An absolute-type four-degree-of-freedom (four-DOF) grating encoder that can simultaneously measure the three-axis pose ( Large-scale synthetic aperture optics (SAO) systems are highly important in several applications, such as deep space exploration , high-enCurrently, the multi-degree-of-freedom position and pose measurement schemes mainly include optical and electrical schemes. The electrical method can demonstrate a high accuracy but is limited in its applications ,7 becausX- and Y-directions. Furthermore, Shi et al. [X- and Y-direction absolute position measurement, the main research work of the six-DOF absolute measurement can focus on the out-of-plane, i.e., the 4-DOF absolute position and pose measurement of θx, θy, θz, and Z-direction. To address the same problems, some effective measurement schemes were proposed for in-plane position measurement by phase detection . Li et ai et al.  proposedi et al.  and an iθx, θy, θz,) autocollimator by using a grating reflector to replace the flat mirror in the conventional laser autocollimator [Z-direction position measurement. Then, Liu et al. modified the proposal in Ref. [Z-direction [Several related types of research have been proposed for out-of-plane measurement ,29. Gao llimator ,31. Alth in Ref.  and propirection , which wirection . These sIn order to meet the high accuracy and absolute measurement demand of the out-of-plane 4-DOFs of the sub-mirror, three improvement works based on the abovementioned multi-DOF out-of-plane research were carried out in this study. Firstly, an absolute zero-point of the QPD coordinate system was proposed to establish the absolute coordinate of the spot position, and the absolute position and pose of the grating reflector can be decoupled by the absolute coordinates of the three diffracted spots . Secondly, a homogeneous error compensation matrix involving installation posture error and installation distance error was proposed, which can significantly reduce the crosstalk error and improve the measurement accuracy. Finally, a compact prototype system was designed and built in this study. For the first time, a verification experiment of simultaneous input of multiple main motions was used to obtain the optimal homogeneous error compensation matrix, and high-precision independent decoupling of the absolute position and pose of the out-of-plane 4-DOF was realized, fully verifying the excellent performance of the proposed grating encoder.As shown in xA, yA, xB, yB, xC, yC) of the light spot are calculated according to the back-end photocurrent information, and the specific calculation formula can be expressed as formula (1). In this paper, the obtained coordinates are absolute coordinates; thus, the position coordinates on the QPD are all signed, and from the front of the QPD, right and up are positive directions.Iα are the four-way current signal outputs of the QPD, α = A, B, or C.xA, yA) of the coordinate system of the QPD, and xA and yA are very close to 0. The point  is used as the origin of a new QPDA coordinate system in Taking QPDA as an example, due to different light intensity distributions, the coordinate value can be calculated from Formula (1). The coordinate origin of the two-dimensional coordinate system is the symmetric center of the four photodetectors. Due to the mechanical structure, it is difficult to adjust the light spot to be perfectly located at the symmetrical center of the QPD. Therefore, at the beginning of the test, the light spot is located at the position , , and  positions, respectively, which are unique coordinates for calculating the absolute position and pose. First, the initial positions of the spots are set as the zero-point positions, i.e., every spot position is at the origin of the new QPD coordinate system. When the grating moves simultaneously in four degrees of freedom, the three light spots in the QPDA, QPDB, and QPDC assume the  and (3). In addition, z and z also cause the movement of the other spots and can be solved using Formulas (4) and (5).zk, kθx, kθy, and kθz are the parameters measured in the pre-experiment. f is the focal length of the convex lens, and L is the equivalent distance between the photodetectors A and B (or C and B). θxzk1 and θxzk−1 are the impact factors of x on the +1st- and −1st-order spot positions during the movement, and so are θydzk1 and θydzk−1 of y.In these coordinates, the position of the 0th-order light change is only related to O ) and the true value T (shown in Formula (7)) due to the imperfection in grating encoder alignment. This posture error can be viewed as a system error and be predicted by using a compensation matrix. The error compensation matrix is a 4 × 4 matrix (M), which can be obtained using Formula (8) after the pre-experiment. With this error compensation matrix, the original value can be converted into the output of the grating encoder .M can be obtained in the pre-experiment with one main motion.However, in the simultaneous motions of 4-DOF absolute position and pose experiment, there is an unexpected posture error inevitably generated between the grating encoder measured value θx, θz, O composed of θx_Original, θy_Original, θz_Original, and z_Original can be collected, and M = T × O1−.Due to installation errors, the 4-DOF movement is output simultaneously. The three main motions move separately, i.e., θx and θz.The absolute 4-DOF grating encoder test bench was built, and the schematic figure of the experiment is shown in θx, θz) of the grating with a measurement accuracy of 0.1′′. The laser interferometer can measure the absolute displacement of the z-direction with a resolution and measurement accuracy of 0.1 nm and ±160 nm, respectively. The movement element is shown in θx, θz, z, and error motion θy. The z-direction movement is controlled by the high-dynamic Z Nanopositioner (PI) (model: p-733. Z), with a resolution of 0.3 nm and a linearity of 0.03%, and the angles are controlled by a two-axis tilt table driver, with a resolution of 0.02” and a linearity of 0.5%.The actual test bench is shown in θx_True, θz_True, and z_True. Owing to the limitation of the autocollimator, the true value of θy was obtained during another set of repeated experiments by changing the measurement surface. The following single motion, resolution, and multiple motion experiments were carried out in this study.The value measured by the laser interferometer and autocollimator is called the true value, as described below and shown in the following figure as θx(80′′), θz(80′′), and the z-direction (100 μm) as the main motions and obtained all the constant parameters and the error compensation matrix (M) in Formulas (2)–(8). As is evident from Iα1, Iα2, Iα3, and Iα4 on QPDs A, B, and C are 0.1802, 0.2662, and 0.3135, respectively. Upon this, the resolutions of rotation around the x- and z-axes and the displacement along the z-axis are 0.02′′, 0.06′′, and 20 nm, respectively, as shown in The pre-experiment was performed in θx rotation, −0.81 to 0.85 arcsec in 40 arcsec θz rotation, and −0.55 to 0.49 μm in the 100 μm z-direction displacement. This indicates that in the continuous measurement of a single degree of freedom, the encoder has good linearity and stability without a large drift.In In multiple motion experiments, the square wave rotation motions with a frequency of 0.1 Hz and the amplitude of 40′′ and 80′′ around the x- and z-axes and a z-direction motion with 100 μm at a speed of 2 μm/s are simultaneously given by the movement element. Three main movements are input concurrently, and their comparison with the true value is shown in z-axis displacement is different from that of the grating encoder in periodic motion, a moving arm length linearly increases the displacement along the z-axis. Since the error matrix calculation includes the linear relationship based on this structure, the measured value of the laser interferometer represents the true value of the grating displacement herein.Because the measurement point of the θx = 40′′, θz = 40′′, z = 100 μm) shown in x-axis is about −3′′ to 7′′, while the angular measurement error around the z-axis is large, reaching the degree of about ±40′′. Additionally, the angular measurement error first decreases overall and then rises and returns, mainly because the rotation around the z-axis is affected by z-axis displacement. The error of the original value is far from the true value; therefore, the original signal requires compensation by the error matrix.During the period  is applied to the grating, the θz error range is  before compensation and  after compensation. The error range in z-direction position is  before compensation and  after compensation. When the motion period  is applied to the grating after compensation, the θz error range is , and the error range in the z-direction position is reduced to . θx remains a relatively low error range without obvious change in these two periods. During the period  shown in x-axis increased by 2.26%, mainly because the fluctuations of the other three degrees of freedom were superimposed on it after compensation by the error matrix. The RMS of the errors around the z-axis was reduced by 78.99%, and the RMS of the errors of the displacement of the z-axis was reduced by 88.14%, demonstrating the effectiveness of the error matrix compensation method. As shown in θx = 80′′, θz = 80′′, and z = 100 μm, the same compensation matrix is used, and the RMS of the errors of the encoder value is 3.02′′, 3.25′′, and 1.21 μm in θx, θz, and z-direction, respectively. When the measuring range is enlarged, the error does not increase obviously, which proves the effectiveness and reliability of the compensation method.θx and z-direction. Initially, the precision of sub-angular seconds can be reached in θz; however, after a movement of long duration, the average measurement residuals of −1.03′′ and 2.93′′ are generated, respectively. This is because in the calculation of the roll angle of the grating, the rotation movement of the light spot is simplified to a linear movement, and its initial position is not at the QPD center, resulting in the enhancement of nonlinearity and error during the measurement. yθ is not caused by crosstalk but by the motion of the movement element itself due to the installation, which could be detected in the repeated experiments. The data time length in yθ is more stable and shows a similar change of displacement of the z-axis, indicating that the compensation matrix method is correct. It proves that during the simultaneous operation of the four degrees of freedom, although the DOFs affect each other, they share a relatively linear relationship within a certain range. A larger measurement range and accuracy can be achieved by optimizing the nonlinear formula and the design of the optical path onto the QPD center. Since the autocollimator cannot measure 3-DOF angles simultaneously, only the compensation data are shown in θx, θy, θz, and Z) of the grating reflector in space can be decoupled. Secondly, the homogeneous error compensation matrix was proposed to greatly reduce the crosstalk error caused by installation posture error and installation distance error and improve the accuracy. Finally, a compact prototype system was designed, and the effectiveness of the proposed structure and compensation matrix was fully verified by experiments. Experiments demonstrate that this encoder can provide absolute 4-DOF position and pose monitoring with sub-arcsecond and sub-micron accuracy and high stability. This paper proposes an ultra-precision absolute-type multi-degree-of-freedom grating encoder. Three aspects are studied as follows: Firstly, the absolute position matrix was constructed by establishing the zero-points of the diffracted light spots on QPD coordinates, and the absolute 4-DOF position and pose (x and y can be realized at present [z-direction. The current commercial products, such as the TriAngle Products of Trioptics [In terms of absolute measurement, the measurement of  present ,26,27, b present ,31 do norioptics , can onl


We propose a stochastic generative model to represent a directed graph constructed by citations among academic papers, where nodes and directed edges represent papers with discrete publication time and citations respectively. The proposed model assumes that a citation between two papers occurs with a probability based on the type of the citing paper, the importance of cited paper, and the difference between their publication times, like the existing models. We consider the out-degrees of citing paper as its type, because, for example, survey paper cites many papers. We approximate the importance of a cited paper by its in-degrees. In our model, we adopt three functions: a logistic function for illustrating the numbers of papers published in discrete time, an inverse Gaussian probability distribution function to express the aging effect based on the difference between publication times, and an exponential distribution  for describing the out-degree distribution. We consider that our model is a more reasonable and appropriate stochastic model than other existing models and can perform complete simulations without using original data. In this paper, we first use the Web of Science database and see the features used in our model. By using the proposed model, we can generate simulated graphs and demonstrate that they are similar to the original data concerning the in- and out-degree distributions, and node triangle participation. In addition, we analyze two other citation networks derived from physics papers in the arXiv database and verify the effectiveness of the model. Scientific papers are major achievements in the academic field. Recently, the number of academic papers has increased rapidly; hence, it is necessary to evaluate their quality. Impact factor  and h-inSeveral studies have proposed network models to grow a network, which are categorized as random graph generators. The Barabási–Albert model  attempteKrapivsky and Redner  note theIn this study, we consider a stochastic generative model for citation networks generated on discrete time. The proposed model comprises several functions expressing the number of nodes at each time, the aging effects based on the difference in publication times between citing and cited papers, and the out-degree distribution for nodes. These functions are used to grow a network based on PA and TF mechanisms. In the next section, we discuss the data obtained from the Web of Science database. Subsequently, we define our stochastic model, estimate it using data, and demonstrate the performance of the proposed model by comparing the original data with simulated results based on our model and a few previously defined models. In addition, we similarly analyze other citation networks on the arXiv database. Finally, we conclude the paper with a few remarks.WoS-Stat, which is a citation network that comprises the citations between papers published in journals whose subject is associated with “Statistics and Probability.” We construct a citation network utilizing a paper identifier (ID), publication year, and reference list (list of paper IDs) for 36 years, from 1981 to 2016. WoS-Stat consists of 179483 papers and 1106622 citations. Although it includes 6411 books, we have checked that they have little effect on the following analysis. Note that the “Statistics and Probability” journals are also associated with subjects such as “Mathematics”, “Computer Science”, etc. WoS-Stat. We used publication year because the time granularity of the papers varies annually, monthly, and daily. WoS-Stat. It has generally increased and saturated in recent years.Our research was started by analyzing the citation network generated from the Web of Science (WoS), which is a famous large-scale scientific bibliographic database . Each reG = , where a paper i corresponds to a node vi ∈ V, and the citation relationship in which paper i cites paper j is represented by a directed edge ∈E. Each node vi has a publication time τ(vi). We usually assume that the time is normalized as 1, 2, …, T.We denote the citation network using a directed graph vi, vj), τ(vi)≥τ(vj) should be satisfied. However, a few exceptions to this rule exist in the data. Possibly, these exceptions emerge when multiple papers are submitted in a short period of time and have citation relationships, and when there are different periods of reference processes.It is evident that a paper cannot cite future papers, i.e., for an edge (Ain(v) = {u |  ∈ E} and Aout(v) = {u |  ∈ E}, i.e., sets of the adjacent nodes of a node v that connects by in-coming and out-going edges. The in-degree of node v is defined by din(v) = |Ain(v)| and the out-degree of node v is defined by dout(v) = |Aout(v)|, where |⋅| denotes the number of elements. We note that the out-degree of a paper depends on the type of the paper, for example, a survey paper has many citations, and a paper that analyzes data mainly has few citations in WoS-Stat.It is known that the typical features of a paper include the number of papers that cite it (in-degree in graph terminology), the number of citing papers (out-degree in graph terminology). Let v ∈ V is defined byδ(v) is the number of triads  that consists of connected nodes  adjacent to v, ignoring the direction of edge. For example in v has 3 triangles. Although directions of edges have a clear meaning in bibliographic contexts as citing and cited papers, we consider the number of triads for simplicity of analysis. This is called node triangle participation in [We also consider triangle-type citation structures (node triangle participation in graph terminology) , 7, 10. In the citation network, it is known that more triangles are generated than those of the graph that uses only the preferential attachment , becausek. The node triangle participation is defined as k. pin and pout, and the node triangle participation ptri in WoS-Stat. Note that each plot adopts the log-scale axes, and the x-axis is shifted by + 1, i.e, x = 1 corresponds to k = 0. From these figures, we can infer that they follow heavy-tailed distributions. Note that 10.2% of papers have out-degree k = 0; this means that these papers have no citations in “Statistics and Probability” because WoS-Stat includes citations within this field. These papers must have citations to papers in other fields or older papers before 1981, but they are outside the scope of our data.The in- and out-degree distributions are defined as A citation network constructed from bibliographic data has clear characteristics: older papers have fewer out-degrees, while newer papers have fewer in-degrees. If features of the entire network are modeled by considering all nodes equally, biases will appear in the modeling of the generative process. We need some corrections for features depending on time.s by the time difference s = τ(vi) − τ(vj) between a citing paper vi ∈ V and a cited paper vj ∈ Aout(vi). Then the number of citations for age s at time t isc for citing age s and citing time t is c = m/n(t), where n(t) = |{v | v ∈ V, τ(v) = t}| [v to age s isWe define the citation age v) = t}| . Then, ws ≤ τ(v) − 1, and dout(v) is given bys < 0). It is clear that dout(v) depends on τ(v) heavily, for example, dout(v) is near 0 if τ(v) = 1. Therefore, we correct dout(v) under the assumption that c is almost independent with respect to time t. We define k.Note that 0 ≤ c for citing age s for each time t and the time-adjusted out-degree distribution t. They are plotted for citing time t ∈ {10, 13, 16, 19, 22, 25, 28, 31}. It can be observed that both features c and t. The citing age distribution is discussed in [ussed in –14.n(t) published at time t is approximated by the logistic functionfn(t) + ϵn(t)⎣, where ϵn(t) is an independent x⎣ denotes a maximum integer that does not exceed the real number x. We note that [nf = a(1 𒈒 exp(−bt)) for this purpose; however, we assume that it is not satisfactory, at least for WoS-Stat.The proposed model for a citation network comprises several components. We first assume that the expected value of the number of papers ote that  adopted c(s) for citing age (time difference) s is approximated byNext, we assume that the expected value of the citing age distribution κc times the probability density function (PDF) of the inverse Gaussian distribution [WoS-Stat, the citing age distribution c(s) after publication is relatively low, rapidly increases toward the peak, and then gradually decreases. Such shapes are appropriately approximated by the PDF of the inverse Gaussian distribution.This function is ribution . Note thribution , the expSubsequently, we assume that the time-adjusted out-degree distribution ribution , whose Pγo = 0 and μo = 0. Since the estimation for WoS-Stat shows that these are almost zero, we will use the simpler exponential distribution, whose PDF was given byThe generalized Pareto distribution is equivalent to an exponential distribution when WoS-Stat: n(t) for t ∈ {1, 2, …, T} are used to estimate fn(t), c(s) for s ∈ {0, 1, …, T − 1} are used for fc(s), and fo. For fn, We adopt the least squares method to estimate parameters and obtain estimates fc, it is also estimated by the least squares method; accordingly, we obtain estimates v as data, to estimate parameters using the maximum likelihood method, and obtain estimates fo. We estimated parameters of fc and fo using c and t ≥ 10, which are stable and can be seen in n(t), c(s), and WoS-Stat. We infer that these estimated functions fit well to the real network.We estimate these functions for fn, fc, and fo. Nodes at time t are generated according to ⎥fn(t) + ϵn(t)⎦. Each node has out-degree generated from fo. We generate edges according to the combination of PA and TF, where PA and TF are performed with probability 1 − β and β, respectively. Consider that a node vi is introduced to the network. In PA, vi selects vj ∈ V with probabilityIm(vj) represents the importance of vj and fc(τ(vi) − τ(vj)) denotes the aging effect for the time difference τ(vi) − τ(vj). In TF, vi selects vk ∈ A(vj) with probabilityvj is selected in the last PA and A(vj) denotes the adjacent nodes of vj. Subsequently, we repeat PA or TA specified times using the out-degree of vi. It is difficult to determine the importance of a paper. Hence, we decide to adopt the value din(v) + 1 as Im(v). The verification of the proposed model will be provided by simulations in the next section.The last component of the model is the generating mechanism of edges. We adopt the PA and TF mechanisms considering functions Our edge generation mechanism combines the PA proposed by   + ϵn(t)⎦ nodes to V′ at each time t. For t ≥ 1, each node vi generates k edges using PA or TF. Here k = ⎥x⎦ and x were generated from fo(x). PA was first executed, and then PA or TF was executed with probabilities 1 − β and β, respectively. In our simulation based on s ∈ {0, 1, …, T − 1} with a probability proportional to fc(s), then vj was selected from the subset of nodes {v | v ∈ V′, τ(iv) − τ(v) = s} with a probability proportional to din(vj) + 1. In TF based on W = { v | v ∈ A(jv), τ(iv) − τ(v) = s} \ {iv} of the node vj selected at the preceding PA, for each time difference s. Then, we selected a time difference s that has a nonempty W with a probability proportional to fc(s), and chose a node vk ∈ W with a probability proportional to din(vk) + 1. When all W were empty, PA was executed instead of TF. We skipped the edge generation when t was in past, i.e., t ≤ 0. Finally, we deleted the out-of-range nodes and edges: V = {v | v ∈ V′, 1 ≤ τ(v) ≤ T} and E = { | iv, jv ∈ V,  ∈ E′}, respectively.We first set nodes β parameter; hence, we adopted simulations to determine it. We executed simulations for values of β from 0.85 to 0.99, with an increment of 0.01. Then we compared the Kullback–Leibler (K–L) divergence [WoS-Stat for the in- and out-degree distributions, and node triangle participation. More precisely, we compared appropriate histograms of given data to calculate K–L divergence. β values, and the node triangle participation takes its minimum around β = 0.92. So we decided to adopt β = 0.92. Note that β = 0.92 does not necessarily imply that TF is executed with a probability of 0.92 in the simulations because PA is executed at the first edge generation process.It is difficult to estimate the value of the vergence  between n(t), c(s) and WoS-Stat. Each figure presents the mean with the approximately 95% confidence interval obtained via ten times simulations. It can be inferred that all features fit well together. Note that this simulation checks the total model appropriateness, and is different from WoS-Stat) for each node on Barabási–Albert and Holme–Kim, which assume a constant out-degree. Holme–Kim, Wu–Holme and our models used β = 0.92. The Wu–Holme model requires the order of publication of papers. We adopted the sorted order by considering the paper ID and publication year in WoS-Stat. We applied the NetworkX implementations [We diagnosed the model fitting by visualizing network features suitable for elucidating a citation network: in- and out-degree distributions, node triangle participation, and scree plot. The scree plot shows the singular values of the graph adjacency matrix, versus their rank, using the logarithmic scale . These pntations  of the Bntations  and the ntations . We adopntations  to compuWoS-Stat. All models succeeded in imitating the in-degrees. This may indicate that PA works well for all models. Regarding the out-degree, there are severe problems in the data generated by the Barabási–Albert and Holme–Kim models because these models assume the out-degree is a constant. The Wu–Holme model seems to fit well; however, it is natural because it uses the out-degree of the original data directly in simulations. Compared with the Wu–Holme model, the proposed model does not require the original out-degrees but adopts the estimated out-degree distribution. For the node triangle participation, the proposed model has similar results to those of the Wu–Holme model and exhibits better results than the Holme–Kim model, which does not consider the aging effect. Although scree-plot has a similar pattern among models, our model has larger differences from the data than other models.Note that our model can produce a legitimate simulation results for considered network features.arXiv-HepTh and arXiv-HepPh. These citation networks are generated from papers and citations of the high-energy physics fields, hep-ph and hep-th, in the bibliographic data of arXiv [arXiv-HepTh has publication dates. Because almost all papers did not have the publication date in arXiv-HepPh, we assumed their publication months from their paper IDs. Note that arXiv-HepTh was analyzed in [arXiv-HepPh in [arXiv-HepTh and arXiv-HepPh.This section shows that the proposed model also works well for two other citation networks: of arXiv . We usedof arXiv . The arXlyzed in , 10, 12 fc and fo with t ≥ 10 and compare fitted functions in arXiv-HepTh in arXiv-HepPh in arXiv-HepTh and arXiv-HepPh are presented in Figs β = 0.99 in both arXiv-HepTh and arXiv-HepPh, which are obtained by performing simulations similar to WoS-Stat. This result for β is consistent with the existing model [WoS-Stat case, the proposed model visually fits well for in- and out-degree distributions and node triangle participation. For the scree plot, the proposed model is confirmed to fit the same or more, compared with other models for arXiv-HepTh and arXiv-HepPh. The proposed model fits better than the Wu–Holme model, especially from the scree plot for arXiv-HepPh.We estimated parameters of ng model . SimilarWoS-Stat generated from the statistics and probability field in the bibliographic data from the Web of Science. We obtained the models on this network for the number of papers on publication time, the citing age distribution, and the time-adjusted out-degree distribution. In other words, we assume that their structures do not change for all publication times in the data. These assumptions are supported by the data to some extent and are required to estimate parameters accurately. However, today, situations in the academic society are changing rapidly. So the citation structure may change in the future.We proposed a stochastic generative model for a graph representing a citation network. Our research motivation first came from the citation network We adopted three functions to define the model: a logistic function, an exponential distribution, and an inverse Gaussian probability density function. These functions were selected to approximate the data. However, it is difficult to interpret or theoretically verify their meaning. Our objective is to ensure that they are beneficial in generating similar data to the original data. Accordingly, we adopted PA and TF mechanisms. PA is employed to approximate the importance of the paper by the in-degree. We understand that the true importance of a paper is a latent variable and needs to be estimated by a significantly more complex model. We considered that the out-degree approximates the type of a paper; for example, a small out-degree indicates that the paper focuses on other fields. Because cited papers of old papers are not included in the data, they usually exhibit a small out-degree. Therefore, we considered papers focusing on other fields and old papers are in the same type. It may be problematic. In-degree and out-degree consider relationships between two nodes. Triangle considers relationships among three nodes. Hence, it is clear that our model explicitly considers the relationships among up to three nodes. We demonstrated that our model is a simple but satisfactory approximation of the graph generating process in this constraint. This constraint may explain that the scree plots of the simulated graphs tend to be relatively apart from that of original data because the scree-plot can exhibit the relationships among more than three nodes.arXiv-HepTh and arXiv-HepPh. Consequently, we can expect that the proposed model provides a good approximation of general citation networks.The important feature of the model is that the discrete-time is considered explicitly, and the discrete-time information is easy to interpret the graph structure. In addition, it enables the data generation outside of the data period, especially in past time. We can generate edges in the past and execute simulations similar to the real situation. The outside nodes and edges are discarded in the final phase of the generative algorithm, similar to the real data. This differs from other existing models , 6, and


N = 130, 102 women, 28 men) read a gendered (feminine or masculine) text and a gender-neutral text with passive voice. Most gave a masculine name to the person in the neutral text, but addressed them in a gender-neutral way when asked to react to them in presented scenarios. The gender-neutral text was evaluated as being less comprehensible than the gendered texts, and the non-binary person was rated less competent and colder than a man or a woman and was less socially accepted. Furthermore, the negative evaluation of non-binary people seemed to be attributable to unfamiliarity with gender-neutral language and its lower comprehensibility. More research is needed to understand these perceptions better and to be able to prevent their potential negative consequences.People can express their identity in different ways, one of which is through language. Non-binary individuals often speak in a gender-neutral way and use specific language forms. Language use not only reveals their identity but also can shape how others perceive them. The present study’s purpose was to analyze how non-binary people are perceived through the language they use. The research was conducted in Polish, a language that is especially challenging for non-binary individuals because it has many gender markers. To avoid using gendered forms, they often use a specific form of passive voice. In an experiment, participants (The online version contains supplementary material available at 10.1007/s10508-021-02234-y. One important way to express one’s gender identity is through language. Within the LGBTQ+ community: non-binary people. The term non-binary can be described as an umbrella term for individuals who do not identify as male or female Barker, , encompacoming out and are at risk of being misunderstood or rejected. An example of this can be found in what Respondent 89 said in a study by Hord  and an invented (onu) neutral version of on (he) and ona (she) that can be considered equivalents of the singular they , a non-binary person may say jestem osobą psychologa (I am a psychologist person) or jestem osobą profesji psychologicznej . To avoid this, one can use an adverb (jest mi wesoło).When it comes to personal pronouns, some Polish non-binary people use or ask others to refer to them with ild Bąk, . Onu is ć Dukaj, . It thenć Dukaj, . Some noć Dukaj, . Generalem for masculine forms and –am for feminine ones. Some non-binary people use –um or –om endings as an alternative  or czytałem książkę (I was readingmas a book), they say czytało mi się książkę. This is not a standard passive voice, like the book was read by me (książka była czytana przeze mnie), but rather reflects the English I’ve got my hair cut, or in this case, I’ve got my book read. In Polish, it emphasizes the activity, rather than the person, and is gender neutral. Another example is the sentence Szłam ulicą  or Szedłem ulicą . Instead of using the gendered forms, a non-binary person could say Szło mi się ulicą, which is gender neutral.Past-tense verbs also are gendered and often end with – Helena, . An inteyou instead of the more common and polite, but gender marked, Sir/Madam by Pan/i coś do picia? (Wouldmas/fem you Sir/Madam like something to drink?), one can say Czy chcesz coś do picia? (Would you like something to drink?).Non-binary people choose the language that they, themselves, want to use, but how should others address them? In Polish, some non-binary individuals prefer that strangers address them directly using The present study’s focus was on how others perceive non-binary individuals through the language they use. While gender-fair language focuses on personal pronouns and nouns, especially professional names, we focused on omnipresent verbs , and in the second version, they were in a store and answered a phone (Text B). Therefore, there were four possible versions of the questionnaire. If the participant was assigned randomly to a condition with a masculine/feminine Text A, they were automatically assigned to receive a gender-neutral Text B. In the case of being assigned to a masculine/feminine Text B, the second text was a gender-neutral Text A. After each of the texts, participants answered questions regarding the text and its narrator.N = 130 .Mage = 26.80, SD = 10.03), with most studying at a university (41%) or holding a higher education degree (39%). Most lived in a city of more than 500,000 residents (37%), but there were also many from medium-size cities (18%), smaller cities (21%), towns (11%), or villages (13%).The sample was collected using a snowball method. The questionnaire was posted on a private social media profile with a request to share it with others. Altogether, 222 participants clicked the study link, and 133 filled out the entire questionnaire. We excluded one trans-man and two non-binary people from the analyses. Thus, the maximum final sample was Participants were informed that the questionnaire comprises three parts and takes approximately 10 min to complete.n = 61) after a masculine text and part of them (n = 75) after a feminine text. Thus, on the crucial comparison between gendered and neutral texts, the study had a within-participant design, and on a secondary comparison between male and female texts, a between-participants design.3There were three versions of the text, depending on the narrator’s language: masculine, feminine, and gender neutral. Participants randomly received two texts: a masculine and a gender-neutral text or a feminine and a gender-neutral text. The two texts varied in content, and participants were assigned randomly to version A or B of the text. The texts described everyday activities and short interactions with others (family members or friends). We used everyday activities to ensure that the texts’ protagonists would not be special in any way other than their gender identity, allowing the reader to relate to the texts easily. All participants evaluated gender-neutral texts, part of them (strongly disagree) to 5 (strongly agree). The Text Comprehensibility scale comprised the items understandable, sounds good, and is reliable . The Person Evaluation scale comprised a set of four questions asking whether the person from the text seems competent, credible, nice, and whether the participant would like to go out for coffee with this person . As a separate question, we included an item from the social distance scale that measures acceptance of a minority member in different spheres that are closer to or more distant from the participant. We chose the most intimate item, asking whether participants would accept a relationship between a person from their family and the person from the text  to 5 (I definitely would accept it).For each text, participants were asked whether they were familiar with this kind of language . The main dependent variables were then assessed with a few questions measuring text comprehensibility and person evaluation using Likert-type scales, from 1 .hard to say , 0 people = 2, 1–2 people = 3, a few = 4, many = 5, and very many = 6. As all six items showed high reliability of the scale (α = 0.83), the mean of all items  was taken. Finally, participants answered demographic questions about their gender identification with an open-ended question, age, education, and place of residence.After text and person evaluation, we measured contact with non-heteronormative individuals.The study’s purpose then was explained to the participants, who were informed that the questionnaire measured reactions to gender-neutral language used by non-binary individuals. There was also a request to share the questionnaire with others but without revealing the study’s purpose. The participants also were invited to leave comments about the study.Most participants (89%) declared that they were familiar with the language used in the gendered texts. However, the opposite was the case with the gender-neutral texts, in which 81% answered that they were not familiar with this kind of language.Alex).When asked to provide a name for the narrator of the text, for the masculine text, most participants gave a masculine name, and for the feminine text, most gave a feminine name Fig. , left. Wyou or plural and passive forms that avoid gender , we explored the potential influence of the text version and the participants’ gender, age, education, and place of residence on the dependent variables of text comprehensibility, person evaluation, and social acceptance.Fs <  .58, ps > .45, s < .004) nor were there any interactions . Therefore, we combined the data from both versions.Three 2  × 2 (Gendered Text: Masculine vs. Feminine) × 2 (Text Version: A vs. B) mixed ANOVAs showed that reading version A or B of the text did not exert significant influence on any of the dependent variables: text comprehensibility, person evaluation, or social acceptance. There were no significant main effects of the text version  than women did . There was no such effect on person evaluation . To sum up, in the current sample, there were very few gender effects that did not replicate on different variables and did not involve the study’s main comparison between gendered and neutral texts.To explore gender differences, we conducted three 2  × 2 (Gendered Text: Masculine vs. Feminine) × 2 (Participant’s Gender: Woman vs. Man) ANOVAs. The results showed that there was a weak main effect of gender on comprehensibility .Correlations showed no significant relationships concerning age, education, and place of residence with comprehensibility, person evaluation, and social acceptance  = 165.51, p < .001, d = 1.08, which showed that the participants rated gendered texts as being much more comprehensible  than the neutral texts  = 0.003, p = .96, To compare the effect of a gendered (masculine/feminine) vs. neutral version of the text on text comprehensibility, we conducted a 2  × 2 (Gendered Text: Masculine vs. Feminine) ANOVA. There was a main effect of gendered vs. neutral text, F = 121.28, p < .001, d = 0.95. The participants rated men and women more favorably on the person evaluation scale  than non-binary individuals from the neutral texts  = 0.29, p = .59, A similar ANOVA for person evaluation showed, again, a large main effect of gendered vs. neutral text, F = 86.45, p < .001, d = 0.81.M = 3.88, SD = 0.85) than a non-binary individual as a new member of their family  = 0.004, p = .95, The last ANOVA was for social acceptance, and it showed, yet again, a large main effect of gendered vs. neutral text, entclass1pt{minimaIn terms of contact with non-heteronormative people, our sample had more such contact than an average Pole. Most participants (69%) knew at least one non-heteronormative person, with relatively many knowing a few (36%), and also relatively many (21%) stating that it is hard to say. Most participants (94%) personally knew gays and/or lesbians, with almost half (46%) knowing a few and 4% indicating that it is hard to say.To explore relationships between the amount of contact with non-heteronormative people and the main dependent measures, correlations were computed  = 0.15, p = .19, nor was the influence of the text on person evaluation, b = 0.04, SE(boot) = 0.10, p = .66.The mediation analysis showed that, as in the earlier ANOVA, people from gender-neutral texts were evaluated much less favorably than people from gendered texts. However, when including comprehensibility, the effect disappeared Fig. . The modyou.The current research shows that non-binary language forms, such as passive voice, are unfamiliar to most listeners or readers and are perceived as less comprehensible than gendered and active language. Furthermore, non-binary people using such language are evaluated more negatively and are socially less accepted than women and men. The negative evaluation could be due to the lower comprehensibility of the language that some non-binary people use. When study participants were asked to give a name to a non-binary person on the basis of their speech, they more often chose a masculine over a feminine name, but when given more freedom on how to address a non-binary person, they often chose gender-neutral language forms, such as There may be different reasons for the negative evaluation of non-binary people and their language. First, gender-neutral language can indicate the speaker’s non-normative gender identity. Second, it also may be that participants evaluated non-binary people negatively partly because passive voice is used more frequently to talk about negative emotions and events, so these people may expect more negativity from a person using it Kałkus, . Third, If negative evaluation of non-binary people was indeed largely due to the incomprehensibility of their language, familiarizing people with non-binary language could help the social perception of non-binary individuals. Extant research on gender-fair language shows that more exposure to, and preferably usage of, gender-fair language makes people more tolerant not only to such language, but also to the people it describes  and would, thus, choose a gendered form. It could also be that if the people in the scenarios were described as much older than an average participant, even younger participants might tend to use Sir/Madam.As expected, most people gave the non-binary person a masculine name, which is, regrettably, in line with the male-as-the-norm phenomenon and vast research showing that people assume that the protagonist or the narrator of a text is male even when described using gender-neutral language , a question about readiness to help would tell us something about the potential discrimination.As in all research with non-representative samples, the current results should not be generalized to all languages, cultures, or to the whole Polish population. Our participants were more likely than an average Pole to be female, live in bigger cities, and were relatively young. Most also had contact with non-heteronormative individuals, which does not reflect the low amount of contact in the whole Polish population Supplementary file2 (SAV 826 kb)Supplementary file3 (DOCX 29 kb)Below is the link to the electronic supplementary material.


Modern Pathology 10.1038/s41379-022-01147-y, published online 10 September 2022Correction to: The “Competing interests” section was erroneously not transferred from the manuscript to the originally published version of the article. The “Competing interests” section should read: F.Z. is a shareholder of asgen GmbH. P.S. is a member of the supervisory board of asgen GmbH. All other authors declare that they have no conflict of interest. The original article has been corrected accordingly.


Correction: Journal of NeuroEngineering and Rehabilitation (2020) 17:86 https://doi.org/10.1186/s12984-020-00713-2Following publication of the original article , there iThen the values under the Methods and Results has been changed. So, the Methods and Results will read as follows:Methods: We assessed participants twice within 15 days on all tasks presently available in KST. We determined the 5–95% confidence intervals for each task parameter, and derived thresholds for significant change. We tested for learning effects and corrected for the false discovery rate (FDR) to identify task parameters with significant learning effects. Finally, we calculated intraclass correlation of type ICC  (ICC-C) to quantify consistency across assessments.Results: We recruited an average of 56 participants per task. Confidence intervals for Z-Task Scores ranged between 0.84 and 1.41, and the threshold for significant change ranged between 1.19 and 2.00. We determined that 6/11 tasks displayed learning effects that were significant after FDR correction; these 6 tasks primarily tested cognition or cognitive-motor integration. ICC-C values for Z-Task Scores ranged from 0.29 to 0.70.Also, a text “running Dexterit-E version 3.7 software” needs to be inserted under the section “Robotic assessment”. So, the line has been changed.from:Robotic assessment for the study was conducted on the Kinarm exoskeleton robotic platform .to:Robotic assessment for the study was conducted on the Kinarm exoskeleton robotic platform running Dexterit-E version 3.7 software .An equation number under the section “Intraclass correlation” has been changed.from:For the purpose of this study, the consistency ICC metric ) was used, which we refer to as ICC-C throughout. ICC-C is calculated as follows:to:For the purpose of this study, the consistency ICC metric ) was used, which we refer to as ICC-C throughout. ICC-C is calculated as follows:The values under the section “Significant change across assessments and assessment confidence interval” has been changed. So, the paragraph will read as follows:diff.Significant change thresholds (SC) and confidence intervals (CI) were estimated by first computing the difference in performance between the first and second assessments and determining the variability of these difference scores. A parameter Z-score difference (i.e. the difference between first and second assessments) exceeding ± 3.2 was considered an outlier, reflecting the fact that such a large difference should only be observed 1 in 1000 data samples. These outliers were not included in any further calculations; however, we quantified the number of difference scores removed in this way. We then computed the standard deviation (SD) of the remaining difference scores, referred to as SDdiff allowed the determination of both the CI and the SC. CIs were simply represented as CI = ± 1.64 * SDdiff. The choice of 1.64 as the width of the CI signifies that only 5% of healthy subjects should display such a large increase or a large decrease in performance across repeat testing. This can also be considered as approximately the 90% one-tailed confidence interval, to reflect that the most common question under consideration will be whether or not a participant had improved or deteriorated specifically . The CI then led to the threshold for significant change (SC) in the following ways [31–35]:Determination of the SDdiff may be replaced with sqrt(2) * SDpre * sqrt(1 − ICC) .Note that in situations in which only the pre- or posttest SD is known, and the SD of difference scores is not, the SDThere is a text change under the section “Simulations: CI, SC, and effect of task score transform on CI”. So, the text will change.from:We performed three simulations of (1) the probability that a participant is “truly impaired”, (2) that their score had “significantly changed” using the example of the Reaction Time (RT) parameter of VGR, and (3) of the effects on the CI of the conversion of the Task Score from a two-sided metric (the “Z-Task Score”) to a one-sided metric (the “Task Score”).to:We performed three simulations of (1) the probability that a participant is “truly impaired”, (2) that their score had “significantly changed” using a simulated parameter score with a CI of 0.95, and (3) of the effects on the CI of the conversion of the Task Score from a two-sided metric (the “Z-Task Score”) to a one-sided metric (the “Task Score”).Also, there is value change under the section “Accounting for intra-individual variability”. So, the text will change.from:diff, so we calculated the final IS error by multiplying SEM by √2 * 1.64 so that it would be comparable to the SC .The SEM is in the same units as SDto:diff, so we calculated the final IS error by multiplying SEM by 1.64 so that it would be comparable to the SC .The SEM is in the same units as SDThere is value and text change under the sections “Significant change and confidence intervals”, “Learning effects”, “ICC”, “Probabilistic interpretation of impairment and change”. So, the passage will read as follows:Significant change and confidence intervalsTable Significant change and confidence intervals for all task parameters are presented in Fig. We additionally calculated IS error to understand the contribution of the variability across trials within the same assessment to the overall SC. We identified that IS values were typically on the order of 20–30% of the SC value , with the RVGR-D reaction time parameters being the highest and VGR-ND speed maxima count being the lowest. We report all of these values in the Additional file as an additional column for each of the tables for RVGR-D and RVGR-ND , and for VGR-D and VGR-ND .Learning effectsLearning effects ranged from 0.12 to − 0.76 for Z-Task Scores and the average learning effect was − 0.30 ; ICC-C); see Table , 1; ICC-The cumulative sum plots of ICC-C for all parameters are presented in Fig. Probabilistic interpretation of impairment and changeWe performed simulations of parameter values to depict the probabilistic interpretation of our CI and SC results in terms of identifying impairments and quantifying significant change see Fig. . There iThere is also, a value change under the section “Discussion”. So, the value in the text will change.from:We determined that the confidence intervals averaged approximately 1.12 across Z-Task Scores and 1.07 across all parameters.to:We determined that the confidence intervals averaged approximately 1.08 across Z-Task Scores and 1.12 across all parameters.Also, there is a text change under the section “Discussion”. So, the text will change.from:We observed the highest IS errors relative to SC in VGR reaction time at ~ 20%.to:We observed the highest IS errors relative to SC in RVGR reaction time at ~ 35%.Also, there is a the text change under the section “Discussion” and the text will change.from:Importantly, we observed learning effects in some parameters and in some Z-Task Scores. In particular, RVGR had a preponderance of significant learning effects, with 18 parameters out of 24 (across both arms) demonstrating learning effects that were significant after correction for FDR.to:Importantly, we observed learning effects in some parameters and in some Z-Task Scores. In particular, RVGR had a preponderance of significant learning effects, with 22 parameters out of 28 (across both arms) demonstrating learning effects that were significant after correction for FDR.Also, there is a percentage change under the section “Limitation”, so the text needs to change.from:The IS error was typically < 10% of the absolute value of the SC, suggesting that the dominant source of variability is change over repeated assessments, and not change within a single session.to:The IS error was typically < 30% of the absolute value of the SC, suggesting that the dominant source of variability is change over repeated assessments, and not change within a single session.The values in Table There is a change in the x-axis for the Fig. There is a small change in the label for Fig. The original article has been corrected.


Imbalanced outcome is one of common characteristics of oncology datasets. Current machine learning approaches have limitation in learning from such datasets. Here, we propose to resolve this problem by utilizing a human-in-the-loop (HITL) approach, which we hypothesize will also lead to more accurate and explainable outcome prediction models.A total of 119 HCC patients with 163 tumors were used in the study. 81 patients with 104 tumors from the University of Michigan Hospital treated with SBRT were considered as a discovery dataset for radiation outcomes model building. The external testing dataset included 59 tumors from 38 patients with SBRT from Princess Margaret Hospital. In the discovery dataset, 100 tumors from 77 patients had local control (LC) (96% of 104 tumors) and 23 patients had at least one grade increment of ALBI (I-ALBI) during six-month follow up (28% of 81 patients). Each patient had a total of 110 features, where 15 or 20 features were identified by physicians as expert knowledge features (EKFs) for LC or I-ALBI prediction. We proposed a HITL based Bayesian network (HITL-BN) approach to enhance the capability of selecting important features from imbalanced data in terms of accuracy and explainability through humans’ participation by integrating feature importance ranking and Markov blanket algorithms. A pure data-driven Bayesian network (PD-BN) method was applied to the same discovery dataset of HCC patients as a benchmark.In the training and testing phases, the areas under receiver operating characteristic curves of the HITL-BN models for LC or I-ALBI prediction during SBRT are 0.85  or 0.89 (0.81-0.95) and 0.77 or 0.78, respectively. They significantly outperformed the during-treatment PD-BN model in predicting LC or I-ALBI based on the discovery cross-validation and testing datasets from the Delong tests.By allowing the human expert to be part of the model building process, the HITL-BN approach yielded significantly improved accuracy as well as better explainability when dealing with imbalanced outcomes in the prediction of post-SBRT treatment response of HCC patients when compared to the PD-BN method. Hepatocellular cancer (HCC) is the third leading cause of cancer death worldwide. In 2020, the American Society of Clinical Oncology (ASCO) estimated that 830,180 people around the world died from the disease. While radiotherapy is designed to achieve tumor local control (LC) in HCC patients, it may also lead to radiation-induced toxicities (RITs). As a relatively newer radiation treatment technique, stereotactic body radiation therapy (SBRT) uses focused beams of radiation aimed at the tumor from many different angles given in one to five treatment fractions. Thus, the aim of SBRT is to cure tumors in the meanwhile decreasing the radiation to nearby healthy tissues. While it is more effective for tumor LC and RITs reduction compared to conventional approaches, stringent dose volume constraints of SBRT require the treatment planning to be highly personalized to meet its intended goals  into ML frameworks to overcome issues related to model bias and uncertainty  approval from University of Michigan Hospital (Michigan Medicine). Since each patient may have one or more tumors, there are totally 104 tumors in our discovery dataset. In this study, two or more tumors in an HCC patient are assumed to be independent from each other for the sake of simplicity. There are 23 patients with I-ALBI during six-month follow up, and 100 tumors from 77 patients achieved LC. Each patient has 97 features, including dosimetric information, clinical factors, pre- and during-treatment labs and cytokines as summarized in LIVER_GTV_Mean_Dose”, “pre_ICGR15”, “D_ICGR15”, “Child_Pugh”, “Cirrhosis”, “Liver_GTV_Volume”, “pre_HGF”, “D_HGF”, “Age”, “Sex”, “pre_CD40_L”, “D_CD40_L”. The EKFs for LC prediction include “Child_Pugh”, “GTV”, “Total_BED”, “LIVER_GTV_Mean_Dose”, “Prior_Liver_Occurrences”, “pre_MELD”, “pre_Bilirubin”, “pre_Albumin”, “Tumor_Size”, “GTV_Mean_Dose_LQ”, “pre_ICGR15”, “pre_HGF”, and “pre_TGF_Beta”. Except the above EKFs related to two different outcomes, the rest of features in Physicians’ acquired knowledge and experience from treating HCC SBRT patients were collected and treated as expert knowledge (EK) for SBRT outcomes prediction in this study. The EK features (EKFs) related to I-ALBI prediction comprise “Gained from many years of experience, reading articles, training, peers’ interaction, EK has a potential of bypassing otherwise complex systems and providing parsimonious solutions that focus on key aspects of a given situation. By incorporating EKFs into the feature selection of the PD-BN approach, we previously developed a situational awareness BN (SA-BN) method to predict the radiation outcomes of lung cancer patients . With thSelecting an ML approach for outcome prediction often involves a trade-off between prediction accuracy and explainability . While scomputational agent to improve the prediction model’s explainability by exploring EKFs and non-EKFs that have strong relevance to an outcome, the integrated feature ranking list was treated as another computational agent to enhance the prediction model’s accuracy by investigating each feature’s importance in terms of outcome prediction. Then, the HITL-BN approach can improve its capability of learning from the imbalanced HCC SBRT data by allowing human agents to interact these two computational agents during the process of feature selection.The selected features from the EML and UML approaches are generally different, even though they are evaluated from one single dataset. The former and latter have the potential of improving an outcome prediction model’s explainability and accuracy respectively. While the MB algorithm and network structure learning were considered as a K be the total kinds of these UML approaches, k be the index of these approaches , Lk be a feature ranking list obtained from UML approach k  with the most important feature for outcome prediction at the top of the list, and AUCk be the performance of an outcome prediction model developed from UML approach k based on cross validation in the discovery dataset . Let J be the total number of features in the discovery dataset, j be the index randomly assigned to them , Nj(Lk) be the rank of feature j in ranking list Lk . The rankings Nj(Lk) of the feature in different lists Lk may not be the same, and the performance AUCk of UML approaches for outcome prediction could be different. It is assumed that a robust feature ranking list can be developed by integrating all these ranking lists based on their corresponding UML approaches’ prediction performance. Let L* be an integrated feature ranking list based on K UML approaches, be the weighted ranking score (WRS) of feature j to determine its ranking in list L* , and its value can be evaluated from the following equation by integrating its ranks Nj(Lk) in different ranking lists LkAs stated previously, the UML approaches include RF, SVM, GBM, DL, etc., and each of them can generate a feature ranking list in terms of importance in outcome prediction from all features including EKFs and non-EKFs in a dataset. Let L* in terms of features’ importance in outcome prediction can be obtained from sorting all the features based on their WRSj , where the feature with the minimal score value is ranked at the top of the list.Then, the ranking list I be the total number of EKFs in list L* with I<J , i represent the order of an EKF within all EKFs . An initial HITL-BN is developed from the top n percent of features in the list. The value of n depends on the total number N of features in a dataset and appropriate feature dimension D to satisfy the MB algorithms’ faithfulness assumption, and we assumed n = 100* n percent of features in list includes i EKFs (i≤D ), an initial HITL-BN based outcome prediction model can be denoted as HITL-BN(i). Since some EKFs in the top rank of list L* may be redundant or less relevance to an outcome compared to other ones, the most relevant EKFs can be identified from the outcome’s MB. Given the selected EKFs, important non-EKFs in the top rank of the list to improve the outcome prediction should also be strongly related to these EKFs, which can be identified from each of their MBs. Thus, important EKFs and non-EKFs can be selected from the top rank of the list with balanced accuracy and explainability for HITL-BN(i) development. Note that the structure learning of HITL-BN(i) is the same as that of PD-BNs, where less important EKFs and non-EKFs are eliminated from the network to maximize its prediction performance. The rest of our HITL-BN approach is to repeatedly evaluate whether a next EKF and additional non-EKFs before it in list L* can improve the accuracy of previous outcome prediction models or not.Including feature selection and BN structure learning processes, HITL-BN based outcome prediction models are mainly developed based on the integrated ranking list. Let ri be the rank of i-th EKF in list L* . As the evaluation moves from i-th EKF to i+1-th EKF in the integrated feature ranking list, the set of additional indices between them is denoted as ri, i+1 . Let S represents the set of non-EKFs associated with ri, i+1 , and the number of non-EKFs in the set could be zero when two EKFs are consecutive in the list. If set S is not empty, the importance of these non-EKFs for the outcome prediction depends on whether they have strong relevance with selected EKFs, including the EKFs in HITL-BN(i) and i+1-th EKF. Let MBs  ) be these EKFs’ MBs based on non-EKFs in S , and the set of selected non-EKFs from these MBs is indicated as i+1) can be developed based on i+1-th EKF, non-EKFs in i) by employing PD-BN’s structure learning process. The process continues along list until the performance of prediction model cannot be improved or meet a target prediction performance. The details of the HITL-BN approach to generate an accurate and explainable outcome prediction model are described in Let pre_Bilirubin”, “pre_Cirrhosis”, “Portal_Vein_Thrombosis”, “pre_Creatinie”, “pre_CD40_L”, “pre_HGF”, and “Liver_GTV_DC_LQ_EQD2” for pre-treatment I-ALBI prediction, additional variables “D_Protime_INR”, “D_Bilirubin”, and “D_ICGR15” were chosen for during-treatment I-ALBI prediction. The prediction performances of the former and the latter based on the discovery dataset are 0.78 (95%CI: 0.67-0.83) and 0.82 (95%CI: 0.74-0.88) as described in As a comparison of the HITL-BN approach, PD-BN models for I-ALBI or LC prediction were developed based on our HCC SBRT patients as shown in pre_Albumin”, “Active_Liver_Lesions”, “Portal_Vein_Thrombosis”, “pre_ECOG_PS”, “pre_TGF_Beta”, “pre_HGF”, and “GTV_gEUD_N20_LQL_10” for pre-treatment LC prediction, additional variables “pre_Cirrhosis”, “Adapted”, “D_CD40_L”, and “D_TGF_Beta” were chosen for during-treatment LC prediction. The prediction performances of the former and the latter based on the discovery dataset are 0.75 (95%CI: 0.60-0.86) and 0.79 (95%CI: 0.69-0.89) as shown in K=2), were employed in this study to generate an integrated feature ranking list for a HITL-BN based outcome prediction model development before or during treatment. RF and GBM share similar tree/graph structure learning to BN. Packages ‘randomForestSRC’ and ‘gbm’ were used to identify feature ranking lists from the former and latter approaches based on the discovery dataset respectively. After evaluating the two UML approaches’ prediction performances, each feature’s WRS was computed based on its ranks in two different ranking lists and the corresponding UML approaches’ prediction performances from Equation (1). Then, an integrated feature ranking list to rank all the features in the discovery dataset for I-ALBI or LC prediction before or during SBRT can be generated from their WRSs.We conducted numerical experiments to develop or test HITL-BN models for I-ALBI or LC prediction based on the discovery and testing datasets in the same R environment as that of developing or testing the PD-BN models. Two UML approaches, the RF and GBM  and 0.89 (95%CI: 0.81-0.95) as shown in Prior_Liver_Occurences”, “GTV”, “MELD_baseline”, “pre_TGF_Beta”, “pre_HGF”, “GTV_gEUD_LQ”, and “LIVER_GTV_Mean_Dose” for pre-treatment LC prediction, additional variables “MELD_Na_baseline”, “pre_Billirubin”, “pre_ICGR15”, “GTV_Mean_Dose_LQ”, “D_Protime_INR”, and “D_TGF_Beta” were chosen for during-treatment LC prediction. italic font in these tables, and the features from the HITL-BNs are emphasized with bold font in them. Especially, the features marked with italic and bold fonts come from both the PD-BN and HITL-BN.p-value=0.0367. For the testing dataset, the performance of pre- or during-treatment HITL-BN for LC prediction is 0.71 or 0.77 as illustrated by p-value=0.0406. The results of our numerical experiments are summarized in The performances of pre- and during-treatment HITL-BNs for LC prediction based on the discovery dataset are 0.82 (95%CI: 0.67-0.93) and 0.85 (95%CI: 0.75-0.95) as shown in Developed from our previous PD-BN method, the HITL-BN approach also includes feature selection and BN structure learning. To handle imbalanced data, the HITL-BN approach allows human agents to integrate the EML-based and UML-based feature selections in identifying important EKFs and non-EKFs in terms of outcome prediction. The reasons for the improvement of accuracy and explainability of HITL-BN based outcome prediction models in handling the imbalanced proportion of tumors with and without LC or I-ALBI in our HCC SBRT patient dataset could be twofold. First, since traditional ML approaches for crowdsourcing labeled training examples are not effective at locating the scarce minority class examples , they haAs some EKFs may be missing or not available in clinical practice, the HITL-BN approach can skip these EKFs or investigate the EKFs that physicians are most interested in along the integrated ranking list for the outcome prediction model development. The purpose of this study is to verify whether the HITL-BN approach can significantly improve the performance of HCC SBRT patients’ outcome prediction models or not based on imbalanced data compared to the PD-BN method. The HITL-BN approach based on two UML approaches with RF and GBM had been implemented in our numerical experiments to test the hypophysis. Our choices of these two because they resemble BN in terms of graph/tree structures. However, if the number of UML algorithms increases, whether the predictive power of the HITL-BN based outcome prediction models could be improved or not and how much it can be improved are interesting research topics that beyond our current scope and we would like to explore in the next step.via the HITL-BN approach to conduct prospective personalized SBRT trials for improving HCC patients’ radiation treatment outcomes.Our numerical experiments on developing the HITL-BN based outcome prediction models for HCC SBRT patients have shown that human intelligence can positively augment machine intelligence, and the assistance of human agents involved in the learning phase can enhance the capability of learning from imbalanced data. However, our study still has limitations in terms of small sample size and the assumption of two or more independent lesions in an HCC patient. In the next steps, in addition to developing more robust HITL-BN approaches by removing the within patient tumor independence assumption and conducting further external independent validations, we plan to explore an interactive human-computer interface change in albumin–bilirubin score (ALBI) score at three months after SBRT were used in many studies to capture acute toxicity occurring <90 days after SBRT  of at least 5-fold and/or that of bilirubin of at least 3-fold compared to either the upper normal limit or the pretreatment level corresponding to grade 3 or higher hepatic toxicity without disease progression within 3 months after SBRT is one of the conditions to define radiation-induced liver disease  in HCC patients complicating with liver cirrhosis, and lower serum sodium concentration is a useful predictor for these patients  is the most important score when determining the incidence of radiation-induced liver disease during SBRT in patients with CP-A score 6 (INR) is derived from Protime which is calculated as a ratio of the patient’s Protime to a control Protime standardized for the potency of the thromboplastin reagent developed by the World Health Organization. The MELD is used to prioritize patients for liver transplantation and includes results for creatinine, bilirubin, and Protime expressed as international normalized ratio (Protime-INR) . La. Latreatof death . While iof death , study sn cancer  52). In. Intreatsurvival . Prolong score 6 . Internaime-INR) . Evidencime-INR) . While lime-INR) , a mathearcinoma . It turnIn this study, we have developed a new HITL-BN approach for HCC patients’ I-ALBI or LC prediction before and during SBRT based on previous PD-BN method. In addition to incorporating EK into its feature selection process, the HITL-BN approach allows humans to participate in an outcome prediction model building process for better handling of imbalanced HCC SBRT data. Especially, we created a novel feature selection mechanism for the HITL-BN approach by integrating the prediction strength of multiple UML methods and the explainable capability of the theoretically sound MB algorithms. Numerical experiments show that the HITL-BN based outcome prediction models significantly outperform the PD-BN based models during SBRT in terms of accuracy and explainability. In addition to gaining physicians’ trust in clinical decision making, the HITL-BN approach has the potential of becoming an important component of future human-computer interface to bridge physicians and advanced ML techniques in improving HCC patients’ treatment outcomes. Our approach can be applied to the outcome prediction of treating other types of cancer, but it still needs to be validated in external further independent datasets.The raw data supporting the conclusions of this article will be made available upon request from authors and per institutional guidelines.KC, TL, MM, RT, IE, and YL conceived of the presented idea. YL developed the theory and performed the computations. IE and DN verified the analytical methods. LD provided the testing dataset. All authors discussed the results and contributed to the final manuscript.


Motivated by a recent model for elasto-plastic evolutions that are driven by the flow of dislocations, this work develops a theory of space-time integral currents with bounded variation in time, which enables a natural variational approach to the analysis of rate-independent geometric evolutions. Based on this, we further introduce the notion of Lipschitz deformation distance between integral currents, which arises physically as a (simplified) dissipation distance. Several results are obtained: A Helly-type compactness theorem, a deformation theorem, an isoperimetric inequality, and the equivalence of the convergence in deformation distance with the classical notion of weak* (or flat) convergence. Finally, we prove that the Lipschitz deformation distance agrees with the  homogeneous Whitney flat metric for boundaryless currents. Physically, this means that two seemingly different ways to measure the dissipation actually coincide. The recent work  introducb  along the dislocation movement. Also, The 2-current in space given asently in .b) move from time s to time t, is derived in )≤C by  and so tH was assumed to possess T into In this section we consider progressive-in-time deformations of (boundaryless) integral currents. To see how one could generalize currents deformed via Then, by  we have\S itself.Unfortunately, the class of We first consider the case of Lipschitz homotopies in more detail. The following lemma also provides a further motivation for our definitions , 3.2) o o3.2) ofLet k-rectifiable carrier set R such that k-dimensional Jacobian of t, x) with respect to Z. It follows, see, e.g., [k-covector field k-covector field Let kby  and the sumption  now implThen, by , there eis shows ; the bouis shows  follows R being the carrier set of T), instead of  t t\documeo obtain   Let P, S satisfy the conclusion of the theorem for our P, T and S(t)  also follows from the estimates of Lemmas We have As a corollary, we obtain the following version of the isoperimetric inequality: Let P, S as in the deformation theorem withThe proof is similar to the one for the classical isoperimetric inequality and follows immediately from the deformation theorem: Assuming that k-currents via progressive-in-time deformations, namely Lip-integral currents. In all of the following, We now define a metric measuring the distance between two boundaryless integral (Lipschitz) deformation distance between k-currents.For With regard to the notion of convergence induced by the (Lipschitz) deformation distance, we have the following result:j from a subsequence of the j’s, there are  For every N depend only on the dimensions and the domain P that can possibly satisfy the conclusion of the deformation theorem for a For the first direction, assume T)→0. By  we have its, cf. . Thus,\dN sufficiently large , we may find a diagonal subsequence, still denoted by m bounded by Returning to our sequence T. Hence, also We now pass to the limit ur claim .Finally, taking the upper limit of the mass estimate,integral homogeneous Whitney flat norm in the bounded Lipschitz domain Finally, we investigate the relationship of the deformation distance to the (i)(ii)(iii)(iv)For every The equivalence of (i) and (ii) was proved in Theorem global Whitney flat norms For the We can now prove the main result of this section, namely that the integral homogeneous Whitney flat distance is equal to the deformation distance. For S yields the above inequality.First, the inequalityQ) as in . Taking k-face For the other inequality, let Q exists, the result holds trivially since in this case Q.Next, take any Q. According to this result, there is a polyhedral chain We now apply the approximation result of Proposition k-polytope V as required.We claim that there exists For Q with d-current in global boundary operator). Hence, by the constancy theorem (see, e.g., [R is a fixed multiple of Q with globally finite mass, which we denote as Note that in codimension 1, i.e.,


Scientific Reports 10.1038/srep28840, published online 29 June 2016Correction to: This Article contains errors in the Methods section, subheading ‘Mathematical Backgrounds’.Formulation of Lemma 1 is incorrect:n, if n”.“Given a genome should read:“Given a genome The corresponding proof:k such that all k-mers are hapaxes of “The minimum value of should read:k-mers in k are hapaxes too. But, if “For The proof of Lemma 2 is incorrect for the lack of an explicit characterization of “random genomes”. Here a correct proof is given:n is obtained by a random process of generation where, at each step, one of four possible genome symbols is generated with probability 1/4. Let k-mers in a circular sequence k-mer occurs exactly once. Of course, any contiguous portion long n of k-mers and corresponds to a random genome of length n . In fact, all symbols of k-mers, then, maximum statistical homogeneity (required by randomness) is reached when k-mer has of occurring in one of the disjoint n-genomes of k-mer positions of a n-genome . This condition is expressed by equation (14) of the paper, from which equation First at all, a random genome of length Consequently, proposition 3’s opening sentence:“In the class of genomes of length n, for every should read:“In the class of genomes of length n, for every Finally, in Results, subheading ‘Information genomics laws’ Eq. 7 should be removed, because it follows from (8), being


Secondly, we define a new connectivity, which can be referred to as divided connectivity, which differs from traditional connectivity, and present an equivalence relationship between traditional connectivity and our divided connectivity. Afterwards, we explore the structures of graphs based on the vertex-divided connectivity. Then, as an application of our divided operations, we show some necessary and sufficient conditions for a graph to be an Euler’s graph. Finally, we propose some valuable and meaningful problems for further research.The graph connectivity is a fundamental concept in graph theory. In particular, it plays a vital role in applications related to the modern interconnection graphs, e.g., it can be used to measure the vulnerability of the corresponding graph, and is an important metric for reliability and fault tolerance of the graph. Here, firstly, we introduce two types of divided operations, named  Graph connectivity is one of the most basic concepts used in the application of graph theory, both in the combinatorial sense and in the algorithmic sense. Especially, it plays an important role in applications related to graph embedding. The connectivity can serve to assess the vulnerability of the corresponding graph and measure the capability of connection for a set of vertices in the graph. To better understand the characteristics of graph connectivity, a wide range of technical methods were developed and then used to analyze various problems.v of degree s, say s of even degree in a graph G with n vertices and m edges, namely, This classical issue has attracted attention to understanding and utilizing various operations regarding graphs. By consulting the literature, we found that the splitting operations on graphs can be divided two classes: one is the vertex-splitting operation and another is the edge-splitting operation. id graph . Mertzioned an On algorith a graph , O graphs, graphs just organically combine them into a whole, which is also the most natural and reasonable technique.By splitting and refining the network, the minimal structural features are obtained. Similar to how matter is made up of molecules, ions and atoms, the minimal structural features of networks can help us to understand the structure and topological properties of graphs. Battaglia et al., in , points The remaining sections of our article are organized as follows. We present a preliminary introductionin x in a simple graph, and we call neighbor set, so the cardinality x. We present two types of divided operations ..X⊂V(G) tX of a connected graph G below.Thus, we obtain the structure of a connected graph having the most components of a disconnected graph Theorem  4.A connected graph G holds G is 2-connected. In fact, H can produce two or more graphs Q such that Q is 2-connected. The inverse of Theorem 4 is shown below.We show an example in Theorem 5.Let each connected graph G, if H has no two nonadjacent vertices H an overlapping kernel graph of G. Evidently, there are two or more such overlapping kernel graphs of G. What characteristics does H have? First of all, H is connected obviously. An Euler’s graph is one without odd-degree vertex, and such graphs were obtained first by the famous mathematician Euler. We present new characters for Euler’s graphs here.Coinciding two nonadjacent vertices Theorem 6.A simple graph G of n edges is a connected Euler’s graph if and only if(E-1) It can be divided into a cycle (E-2) Its overlapping kernel graph H holds diameter Proof. We prove (E-1) first.Necessary. Let G be a connected Euler’s graph, not being a cycle. A 2-degree 2-connected v-divided operation is defined as follows: Take a vertex x. We divide the vertex 2-degree 2-connected v-divided operation. Thereby, we can perform such operation on Sufficiency. We can coincide a pair of vertices, G by performing a series of v-coinciding operations, because each We come to show (E-2) in the following.The proof of “if”. We perform a so-called non-neighbor coincident operation on a connected graph overlapping kernel graph of the original graph The proof of “only if”. Suppose that the overlapping kernel graph H of the connected graph G has its own diameter H. If H is a complete graph, and has no vertex having two neighbors of odd degrees. Thereby, H is a connected Euler’s graph. Performing a series of 2-degree 2-connected v-divided operations on H produces the original graph G. Clearly, G is a connected Euler’s graph. If H holds H is a connected Euler’s graph since H has no odd-degree vertex. Obviously, the original graph G is the result of v-dividing H after performing a series of 2-degree 2-connected v-divided operations.The proof of the theorem is complete. □t, where t.Notice that each Sierpinski model k-connectivity for each maximal planar graph of order k-connectivity of an Euler’s graph are not easy.To investigate an open question proposed by Battaglia et al. in , we defitivity κ . HoweverX of X controls the topological structure of scale-free deterministic network control the topological structure of the network?We consider that finding connected-perfect subsets of a connected graph (respective networks) may be interesting and important for investigating topological structures of GNs. As known, the Sierpinski model G with its k-connectivity, our v-divided graph (respective networks) G easily, but it is very difficult to rebuild G from the disconnected vertex-deleting graph (respective networks) X of the vertex set G, in which For a connected simple graph (respective networks) We emphasize that our v-divided operation can dilute a connected Euler’s graph into a cycle; conversely, our e-coincident operation can concentrate a cycle to an Euler’s graph. Moreover, each connected simple graph can be obtained by deleting some edges from some Euler’s graph. We ask the following: How many different Euler’s graphs made by a given cycle are there?