Some of the most severe structural loadings come in the form of blast loads, which may be caused by severe accidents or even terrorist activities. Most commonly after exposure to explosive forces, a structure will suffer from different degrees of damage, and even progress towards a state of collapse. Therefore, damage detection of a structure subject to explosive loads is of importance. This paper proposes a new approach to damage detection of a concrete column structure subjected to blast loads using embedded piezoceramic smart aggregates (SAs). Since the sensors are embedded in the structure, the proposed active-sensing based approach is more sensitive to internal or through cracks than surface damage. In the active sensing approach, the embedded SAs act as actuators and sensors, that can respectively generate and detect stress waves. If the stress wave propagates across a crack, the energy of the wave attenuates, and the reduction of the energy compared to the healthy baseline is indicative of a damage. With a damage index matrix constructed by signals obtained from an array of SAs, cracks caused by blast loads can be detected throughout the structure. Conventional sensing methods such as the measurement of dynamic strain and acceleration were included in the experiment. Since columns are critical elements needed to prevent structural collapse, knowledge of their integrity and damage conditions is essential for safety after exposure to blast loads. In this research, a concrete column with embedded SAs was chosen as the specimen, and a series of explosive tests were conducted on the column. Experimental results reveal that surface damages, though appear severe, cause minor changes in the damage index, and through cracks result in significant increase of the damage index, demonstrating the effectiveness of the active sensing, enabled by embedded SAs, in damage monitoring of the column under blast loads, and thus providing a reliable indication of structural integrity in the event of blast loads. Recent years have seen a rise in terrorist activities, and the number of bombing incidents in particular have risen across the globe. Terrorists have been known to indiscriminately target civilian populations, thus exposing civil structures to dangerous blast loads ,2. FurthProgressive collapse is a chain reaction of failures initiated by instantaneous loss of at least one load carrying element . Such a Various non-destructive testing (NDT) techniques are available to detect the condition of critical elements in a structure. Among the most popular NDT techniques used in blast engineering are the ultrasonic velocity method, ground penetrating radar (GRP) techniques, impact-echo (IE) approaches, among others . ŠtollerIn recent years, piezoceramic materials, such as lead zirconate titanate (PZT), have been widely used in structural health monitoring (SHM) ,25,26,27Since columns are critical elements needed to prevent structural collapse, knowledge of their integrity and damage conditions is essential for safety after exposure to blast loads. Without accurate information about column health, any risk evaluations of the entire structure may not be reliable. In this research, a new approach to damage detection of a concrete column structure subject blast loads using embedded piezoceramic-based devices, smart aggregates (SAs), is proposed. Since the sensors are embedded in the structure, the proposed active-sensing based approach is more sensitive to internal or through cracks than the surface damage. To facilitate the proposed research, a concrete column specimen was fabricated and subjected to air-blast loadings in an explosion containment vessel. The column was placed in a horizontal position with no axial load, and one end of the column was fixed into a concrete bed while the other end was supported by a steel roller to simulate the inflection point . Five blasting tests were implemented at different standoff distances above the column. Since the mass of the charges were controlled to a very low level, it is possible to detect the development of the cracks and evaluate the accumulation of damage in the column. Four SAs were installed in the column prior to pouring, two of which were used as actuators to generate probing stress waves, while the other two were used as sensors to detect the stress waves. Blast loads applied on the column caused a damage zone between the actuators and sensors that would directly influence the stress wave attenuation through this area. The stress wave energy attenuated more when travelling through a cracked area. In this paper, the changes of received signal energy were analyzed by wavelet packet analysis, and a damage index was developed to quantify the damage status in the column. For the measurement purpose, dynamic strain gauges and an accelerometer were installed on the column specimen. Experimental results reveal that surface damages, though appear severe, cause minor changes in the damage index, and through cracks result in significant increase of the damage index, demonstrating the effectiveness of the active sensing, enabled by embedded SAs, in damage monitoring of the column under blast loads.Piezoceramic materials are brittle and cannot be directly used without protection, therefore a smart aggregate (SA) is fabricated to protect the PZT disk by sandwiching it between two marble blocks with epoxy, as shown in Essentially, an SA is a kind of protected piezoelectric transducer. It will generate an electric charge when subjected to a stress or strain, which is called the direct piezoelectric effect; conversely, it also can produce stress or strain when an electric field is applied to it, which is called the inverse piezoelectric effect . n-level wavelet packet into 2n signal sets jX can be expressed as:m is the number of the sampled data. Additionally, the energy of the decomposed signal is defined as:i is the time index, and j is the frequency band number (j = 1 … 2n). The proposed blast damaged index at the ith time is defined as:h, jE is the energy of the decomposed sensor signal at the jth frequency band in the healthy status.Wavelet packet analysis enables the inspection of a signal in relatively narrow frequency bands over a relatively short time window. It is an effective signal-processing tool for damage feature extraction. In this paper, wavelet packet-based analysis is applied to offer the corresponding values of the received energy due to different damages. The sensor signal can be decomposed by an 2,⋯,X2n} , where XMr×s [pth row and the qth column, pIq, is the damage index of the pth smart aggregate at the time of the qth test ; r is the total number of smart aggregates and s is the total number of tests. The damage status at different positions of the specimen at different test times can be described by a 3-dimensional damage index matrix plot. The blast damage index represents the loss portion of the transmission energy. When the index is close to zero, the structure is in a healthy status. When the damage index goes up to a certain threshold value, that means the severe damage occurs in the structure. In this case, the higher the index, the severer the damage. To demonstrate the health status at different locations of the concrete structure, a Sensor-History Damage Index Matrix (SHDIM) Mr×s  is definIn this research, a concrete column, as shown in In addition, as shown in In this experimental study, a thick-walled explosion containment vessel (ECV), as shown in The SAs were controlled and monitored through a multifunction data acquisition and control system (DACS). The SAs as sensors are connected to the A/D  convertor of DACS. The SA as an actuator is connected to the D/A  convertor of the DACS through a power amplifier. A laptop PC was used to interface with the system and record the data. During the tests, the pre-amplified excitation voltage is 3V for the D/A convertor. A swept sine wave was employed to excite the SAs repeatedly. The sinusoidal sweep signal increased linearly from 100 Hz to 200 kHz in a one-second cycle, and the sampling frequency was 2 MS/s for the data acquisition and control system. The amplifier provided a fixed gain of 10×, and an operation bandwidth of 0.1–200 kHz.For comparison, a dynamic strain meter was used to record vertical acceleration and the dynamic strain in the axial direction. The sampling frequency of the strain gage was 128 kHz. As shown in Test No. B0 is used to represent the healthy status and B1–B5 represent the five different explosions. Before the first explosion and after each explosion, smart aggregate based active sensing was conducted following the actuator-sensor sequences, as shown in It is clear that the maximum strain grows gradually with the decrease of standoff distances, and the last blast resulted in the most strain since the charge was directly placed on the specimen. This phenomenon is also reflected in the acceleration responses of the specimen, as shown in As clearly shown in The results of the smart aggregate based active sensing of the signal path P2 (SA-2 as an actuator and SA-3 as a sensor) for the five blast are shown in All these indicate that the structure was severely damaged after the last blast, which is verified by the damages to structure graphically . Figure Concrete is a kind of material that possesses initial micro-cracks. These initial cracks will extend and join each other when disturbed by a severe impact load, and the joining of the cracks results in a certain degree of damage to the structure. The merging of the micro-cracks after the first blast (B1) can be indicated with the blast damage index, as shown in The final blast, which exploded directly on the surface of the structure, severely damaged the structure. As shown in In this paper, the damage status of a concrete column under blast loads is monitored by an active sensing method enabled by embedded piezoceramic smart aggregate (SA) transducers. Since the cracks caused by blast loads weaken the stress wave propagation energy across the detection area, the amplitude of the time-domain signal received by embedded PZT sensors decreases when the cracks occur. A wavelet packet-based blast damage index is used to report the initiation and the further evolution of the damage status. Since the sensors are embedded in the structure, the proposed active-sensing based approach is more sensitive to internal or through cracks than surface damages. In addition, the values in damage index matric obtained by distributed PZT sensors not only describe the damage evolution process but also reflect the local severity of damage condition in the concrete structure. Experimental results reveal that surface damages, though appear severe, cause minor changes in the damage index, and through cracks, which dramatically weaken a structure, result in significant increase of the damage index, demonstrating the effectiveness of the proposed active sensing method, enabled by embedded SAs, in damage monitoring of the column under blast loads, and thus providing a reliable indication of structural integrity in the event of blast loads. Future work will include more systematic studies of monitoring of the damages on a concrete structure subject to blast loads using SAs. One of the test will involve investigating the damage index increase when the blast loads are repeated at the same distance from the structure.


Digital dental models provide a more accurate and comprehensive assessment of orthodontic cases. Although this technique is quite promising, there are few three-dimensional measurements methods described in the literature.  The aim of this study was to propose a method for assessing the degree of mandibular anterior dental crowding in the three planes of space, using digital dental models. t-test. Thirty dental casts were selected and scanned by Maestro 3D Dental Scanner and imported by Geomagic Qualify 2013 software. The degree of crowding was calculated by two examiners, based on the Little’s Irregularity Index, by means of the definition of axial, coronal and sagittal planes for each model. Intraexaminer analysis was performed with Dahlberg’s Formula (DF) and Intraclass Correlation Coefficients (ICC), and interexaminer analysis was performed with ICC and paired p < 0.05) for all measurements, except for the intraexaminer and interexaminer in the Z-axis, in which it was found a moderate agreement. The DF showed a satisfactory accuracy with all measurements showing less than 1 mm difference. The paired t-test showed statistical difference between the examiners in two measurements, although it was clinical irrelevant. The ICC showed an excellent agreement (When comparing the three planes of space, the Z-axis showed the greatest variation in landmarks placement; however, overall, the present method seems precise and reproducible. Dental casts are widely used in dental practice as well as on research projects. In Orthodontics, it is considered to be of extreme value for diagnosis and the clinical decision making process. With the introduction of three-dimensional scanners, it has become possible to obtain digital dental models aiming the study of dental arches. These models feature precision and can be manipulated through specific software, enabling the completion of its analysis, which is an important step for orthodontic treatment planning.--Among the many advantages attributed to the digital dental models, it can be cited the easy manipulation and the fact that they do not require physical space to be stored. They are saved on the computer, producing durable images without loss or damage to the original models.,,,-Digital dental models acquisition by computed tomography,-,-,,,,,,,,,,-,,,Some studies have analyzed the reliability of the digital dental models compared to conventional exams, by comparing linear measurements in both digital and plaster dental casts.Although an extensive literature proving digital dental models can substitute plaster dental casts with satisfactory degrees of accuracy and reproducibility of linear measurements,-Mandibular anterior crowding often leads patients to seek for dental alignment; being so, this malocclusion should be investigated, in order to obtain an appropriate treatment plan. Many methods have been proposed to evaluate this malocclusionThe goal of this study was to propose a method to assess the degree of mandibular anterior dental crowding in the three planes of space, using Cartesian coordinates on digital dental models.Universidade do Estado do Rio de Janeiro .After approval by the Institution Ethical Committee, thirty lower plaster dental casts were selected from the diagnostic records of patients that were receiving orthodontic treatment at the Orthodontic Clinic of the The inclusion criteria were lower dental casts with complete permanent dentition, with or without the second and third molars. The first molars should have their five cusps relatively equidistant in relation to the occlusal plane. Models with tipped first molars and/or lacking structural integrity could compromise the measurements and thus were excluded from this study.The dental casts were digitized by using the Maestro 3D Dental Scanner, MDS300 Model , which uses the structured light for its image acquisition method. The images were automatically processed by the Maestro Easy Dental Scan software (4.018.086.4295), generating files with the .STL (stereolithography) extension for each dental model. Three-dimensional images were analyzed by Geomagic Qualify 2013 software .An individual coordinate system was created for each digital dental model in order to permit a customized assessment of them in the three planes of space, as proposed in this study. The whole process was made by two examiners, who were previously calibrated before performing the landmark placement and measurements.It was established that the axial plane should be coincident with the patients’ occlusal plane. Three points defined it: mesiobuccal cusp tip of both lower first molars and the contact point between lower central incisors. If the patient had a diastema in this region, the third point was marked where it should be the contact point in the lower right central incisor. This plane was related to the X and Y-axes .Three points also defined the coronal plane: mass center (centroid) of the dental crowns of both lower first molars and center of the mesiodistal groove of the right lower first molar. This plan was related to the X and Z-axes .Sagittal plane was defined as being perpendicular to the two plans previously described, passing through the contact point between lower central incisors. If the patient had a diastema in this region, the third point was marked where it should be the contact point in the lower right central incisor. This plan was related to the Y and Z-axes .For the custom-made coordinate system described above, changes in the X-axis reflected transversal displacements in the anterior region of the digital dental models A, while Usually, while creating a digital dental model, it is placed in a standard coordinate system according to the spatial position of the dental model in the scanner at the time of acquisition. Aiming proper measurements as planned, it was mandatory to set the software to use the newly defined coordinate system instead of the standard one. From this time-point on, all markings and measurements made were related to the customized coordinate system .In order to quantify the degree of crowding in the mandibular anterior region of each dental model, it was necessary to mark the contact points of the incisors and its adjacent teeth. Thus, the anatomic points from the mesial of the right canine to the mesial of the left canine were marked, as proposed by the Irregularity Index.The next step was to measure the linear displacement of the contact points in this region. As proposed by this study, it was evaluated not only the real distance (RD), defined as the linear distance between two points without projecting its localization in the three planes of space , but the measurements of the projections of the RD on the three axes , separately . So, it All data was recorded and compiled in a spreadsheet, followed by the statistical analysis. All of the values found for the RD, DX, DY and DZ were added, in an analogous way to that described by Little,t-test. Ten randomly selected digital dental models had all measurements repeated after fifteen days by both examiners, in order to evaluate the reproducibility and the intraexaminer precision, which were evaluated with Intraclass Correlation Coefficient (ICC) and with Dahlberg’s Formula (DF).Statistical analysis was done with the IBM SPSS Statistics 22 software. The sample size calculation was carried out using an expected difference of 0.5mm, with 90% power and an 5% alpha level. The Shapiro-Wilk test found normal distribution and the Levene test verified the equality of variances. Two examiners made the whole process of landmark placement and measurements, in order to assess the reproducibility and the interexaminer precision of the proposed method, which was performed with Intraclass Correlation Coefficient (ICC) and with paired The Shapiro-Wilk test indicated a normal distribution for the sample, and the sample’s descriptive analysis is shown in The DF showed a satisfactory precision of all measurements  showing less than 1 mm difference . The lest-test showed statistical differences between both examiners for real distance (RD) and for the X-axis (DX). The results were considered significant at p< 0.05 . The greatest difference observed in the RD is because it represents the projections of the axes , so small differences in each axis are summed in the RD.The paired Although the digital dental models are well known and recently widely studied, it can still be considered a new diagnostic approach, not being used very often by most orthodontists worldwide, since there are additional costs that could limit the accessibility and the diffusion of this three-dimensional method. Moreover, as any other technique, there is a learning curve for the clinician to be proficient in the use of digital dental models.The goal of this study was to propose a diagnostic tool that allows a comprehensive assessment of the mandibular anterior crowding through the three-dimensional analysis that is available on the Geomagic Qualify software. More studies should be carried out using a true three-dimensional analysis of digital dental models, through a customized coordinated system, in order to corroborate and/or reject the findings of the present study aiming to supply clinicians the best and accurate tools possible to support diagnosis, treatment planning at the same time it provides a more effective assessment of treatment results.The results of this study indicated that:» The proposed method of assessing the degree of mandibular anterior dental crowding in the three planes of space, using Cartesian coordinates in digital dental models, is precise and reproducible, although the accuracy of the method was not tested.» When comparing the three planes separately, it was concluded that the Z-axis showed the greatest variation in landmarks placement, indicating that it is necessary a special attention in vertical direction when evaluating mandibular anterior dental crowding using the method proposed by this study.


Property closures are envelopes representing the complete set of theoretically feasible macroscopic property combinations for a given material system. In this paper, we present a computational procedure based on fast Fourier transforms (FFTs) for delineation of elastic property closures for hexagonal close packed (HCP) metals. The procedure consists of building a database of non-zero Fourier transforms for each component of the elastic stiffness tensor, calculating the Fourier transforms of orientation distribution functions (ODFs), and calculating the ODF-to-elastic property bounds in the Fourier space. In earlier studies, HCP closures were computed using the generalized spherical harmonics (GSH) representation and an assumption of orthotropic sample symmetry; here, the FFT approach allowed us to successfully calculate the closures for a range of HCP metals without invoking any sample symmetry assumption. The methodology presented here facilitates for the first time computation of property closures involving normal-shear coupling stiffness coefficients. We found that the representation of these property linkages using FFTs need more terms compared to GSH representations. However, the use of FFT representations reduces the computational time involved in producing the property closures due to the use of fast FFT algorithms. Moreover, FFT algorithms are readily available as opposed to GSH codes. Property closures are defined as the complete set of the single-crystal and polycrystalline homogenized anisotropic property combinations for a given material. These constructs are important for microstructure based material design. Within the applied mathematics community, the property closures are referred to as the G-closures. In the past, the G-closures have been calculated for properties such as effective conductivity and elastic stiffness for a limited set of two-dimensional microstructures comprised of isotropic phases ,2,3,4. MIn prior work, the spectral representation necessary for MSD was implemented most commonly with generalized spherical harmonics (GSH) basis functions . The GSHSeveral examples exist in the current literature on using property closures to theoretically design and optimize microstructure to improve performances of components. These examples identified microstructures and associated properties maximizing the deflection in a compliant beam , the eneIn crystal plasticity ,46,47,48In this paper, we have successfully formulated a new approach using FFTs to compute elastic property closures for HCP polycrystals. To this end, we have built a database of the orientation invariant Fourier transforms for components of the elastic stiffness and developed an optimization scheme for finding the boundary points of the convex property envelopes. This new approach is introduced in this paper and demonstrated with examples. The selected materials for this study were titanium, zinc, zirconium, beryllium, magnesium, and cobalt. These materials were chosen to validate the FFT based closures against reported property closures based on the GSH representation for orthotropic HCP metals . It was g, in the sample of a polycrystalline material. An ODF can be mathematically expressed in its continuous or discrete form. While the former is required for the GSH representation, the latter is necessary for the FFT representation. In its discrete form, an ODF is expressed as [N is the total number of orientations in the sample; g. FZ and b will be defined shortly. The orientation, g, can be described using an ordered set of three Bunge-Euler rotation angles i.e., several locations in this space may correspond to a single crystal orientation) and the inherent distortion caused by the fact that the invariant measure in this space is proportional to The Orientation Distribution Function (ODF), essed as :(1)fbΔgΔϕ1ΔΦΔϕ2 . In spitb, and k, while i.e., *, denotes the complex conjugate transforms.Knowing the function values on a uniform grid, FFTs can be computed ,63,64,65For simplicity of notation, Equation (2) will be expressed in a shortened notation as:B, the FFTs are:The shortened notation will be used hereafter. For given values of the ODF on the grid over Computing the ODF transforms using the FFT methods was over two orders of magnitude faster compared to that obtained using the GSH methods. Benefits of the FFT method over the GSH method increase with the number of ODFs considered in the calculations of property closures because the computational time involved in ODF-to-elastic property calculations scales linearly with the number of ODFs.B. FZ is the fundamental zone within B containing the complete set of all physically distinct orientations that can occur in the sample. These redundancies within B can be exploited in the computations. To this end, we calculate function values in FZ and translate these throughout the rest of the space B while preserving the uniform grid. The translations are done as follows. For crystals of any symmetry, the definitions of the Bunge-Euler angles require that locations Due to hexagonal crystal symmetry, there are 24 physically indistinctive orientations over the discretized Bunge-Euler space defined above, FZ space for HCP is FZ and subsequently extended over the entire periodic space using the above defined equivalencies preserving the uniform grid over B.As a result of all of the considerations described above, the FZ3 [FZ for cubic crystals. The reason for using FZ3 instead of FZ is that a uniform grid is only possible in FZ3. FZ upon being subjected to three-fold <111> symmetry operation, does not result in a uniform grid that can be used to fill out the remainder of the B space [FZ3 space for cubic crystals while they conveniently span the FZ domain for HCP crystals.It should be noted that the smallest space defined earlier for cubic metals was defined as FZ3 , which i B space . TherefoFZ, which are computed using Equation (4). Let N enumerate the single crystals that are distributed over in FZ. It is then possible to define a convex and compact texture hull [The FFT representation allows defining the texture hull for HCP crystals. Let ure hull  as:(5)MM represents the complete set of all theoretically feasible ODFs including all of their linear combinations. M is defined in n-dimensional FFT space, where the number of dimensions in this space is equal to the discretization B. Selected projections of M are presented in As mentioned earlier, In previous work , it was The components of the stiffness tensor for an HCP single crystal as a function of the local crystal orientation and the five fundamental elastic constants We use bold letters to denote tensors. It is convenient to separate the orientation dependence of the tensor  as:(8a)Equation (6) then becomes:B and represented using FFTs as:Orientation dependent functions B. The grid was refined to capture all of the non-zero frequencies present in the functions. A grid with one degree grid point spacing placed over B was found to satisfy this requirement, meaning that all of the important frequencies were captured by the transform. The non-zero Fourier transforms for elastic stiffness components are presented in To evaluate the property transforms, we had to evaluate the functions (Equation (8)) on a regular grid over ented in  for the The FFT representations in Equation (10) permit the efficient computation of the property bounds for any given ODF from the HCP texture hull. The first-order upper and lower bounds of effective elastic stiffness for the diagonal components are expressed as ,18,19,20In Equations (11) and (12), no implicit summation on repeated indices is used . The bars on top of a field quantity denote the volume averaged value over constituent crystals in a polycrystal: V is the physical volume of a sample and x is a location in the sample. Alternatively, the volume average functions A, B and D can be calculated by multiplication of the precomputed kF and their summation as: A, B and D by the As mentioned in the previous section, the first-order homogenization theory requires calculations of the volume average quantities. As an example, the upper bound for the components of the homogenized elastic stiffness tensor can be expressed as the following (no implicit summation on repeated indices):FZ for HCP metals calculated using Equations (6) and (13). The single crystal elastic constants of Zn were used. It can be clearly seen that the results are identical, which validates the FFT representation of the ODF-to-elastic stiffness relationship. The same checks were conducted for all components of the local elastic stiffness tensor.Equation (13) can be used to calculate the volume average elastic stiffness as well as the elastic stiffness of a single crystal. It should be noted that the number of calculations (multiplications and summations) for stiffness components is the same for a single crystal and a polycrystal comprised of any number of crystals in this spectral representation. The number of calculations is determined by the number of non-zero transforms . Figure i.e., from  pair to  pair, which resulted with nine weighted combinations. As expected, these computations involving combinations of textures expand the property closures. Next, a new set of textures corresponding to the new boundary of the expanded closure were selected (this time these were a mixture of eigen textures and non-eigen textures) and the property combinations corresponding to the weighted combinations of these were evaluated. This process was repeated until the closure expansion saturated. The method of delineation of closures follows the main ideas underlying genetic algorithms, where good solutions are pre-selected and used in further calculations. This approach was applied successfully to delineate closures of plastic properties involving uniform ductility and ultimate tensile strength in cubic metals in [The methodology used here for building first-order elastic stiffness closures starts with a consideration of a set of points in the texture hull that correspond to “eigen textures” . The setetals in .i.e., the texture hull). The shaded areas inside the closures represent the possible property combinations of the selected elastic stiffness components that can be obtained according to the first-order bounding theories for the particular material as a function of ODFs. We provide three examples of atlases of property closures corresponding to selection of different pairs of effective elastic properties. The FFT representation of the ODF-to-elastic stiffness bounds is used in this study to obtain the first-order property closures, which identify the complete set of theoretically realizable combinations of selected macroscale properties in a given material system through a consideration of the complete set of textures (As a final comment, we note that the FFT framework developed here for the efficient calculation of elastic properties can also be used to accelerate the calculations of the elasto-viscoplastic response of polycrystalline HCP metals that is under development. This framework has been recently reported for cubic metals in . The impIn this paper, we have extended the recently developed first-order ODF-to-elastic stiffness linkages using FFTs for cubic metals to more computationally challenging HCP polycrystals. The benefit of using FFTs to represent these linkages is the substantial reduction in the computational time involved in the property calculations due to the use of fast and readily available FFT algorithms. First, we have shown that it is possible to construct texture hulls using FFTs for HCP polycrystals, as was done earlier for cubic polycrystals. Next, we have calculated elastic stiffness FFTs and presented the actual values in


Tactile estimation of sub-second time is essential for correct recognition of sensory inputs and dexterous manipulation of objects. Despite our intuitive understanding that time is robustly estimated in any situation, tactile sub-second time is altered by, for example, body movement, similar to how visual time is modulated by eye movement. The effects of simpler factors, such as stimulus location, intensity, and frequency, have also been reported in temporal tasks in other modalities, but their effects on tactile sub-second interval estimation remain obscure. Here, we were interested in whether a perceived short interval presented by tactile stimuli is altered only by changing stimulus features. The perceived interval between a pair of stimuli presented on the same finger apparently became short relative to that on different fingers; that of a weak-intensity pair relative to that of a pair with stronger intensity was decreased; and that of a pair with the same frequency relative to one with different frequencies was underestimated. These findings can be ascribed to errors in encoding temporal relationships: nearby-space/weak-intensity/similar-frequency stimuli presented within a short time difference are likely to be integrated into a single event and lead to relative time compression. Accurate estimation of sub-second time is a critical challenge for the brain. Vision research on perception of this time range has repeatedly demonstrated plasticity and a lack of robustness by introducing temporal illusions . The appFor tactile brief-interval estimation, body movement can alter the perceived interval . When a Our first concern was the effect of stimulus location, in particular, the inter-stimulus distance, on brief-interval estimation. Tactile input is encoded by peripheral mechanoreceptors, which are distributed over the entire surface of the body. Thus, it takes inputs at different locations on the skin different amounts of time to reach the brain. Previous studies revealed that a single input at different locations induces different perceived timings , and, imOur second concern was the effect of intensity. One visual study has shown that reducing the visibility of presented stimuli (two flashes) could cause apparent underestimation of their temporal interval . AlthougFinally, we were interested in the effect of frequency differences between paired stimuli on the perceived interval. In the auditory modality, the frequency/pitch of the stimuli and their perceived duration are not perceptually independent . FurtherOne of the authors (SK) and seven volunteers  participated in the main experiments. Five volunteers who did not participate in the main experiments and one of the authors  participated in a subsidiary experiment. The volunteers had no specialized knowledge about psychophysical experiments and were unaware of the purpose of the experiments. They gave written informed consent before the start of the experiment. Recruitment of participants and experimental procedures were approved by the NTT Communication Science Laboratory Research Ethics Committee and were conducted in accordance with the Declaration of Helsinki.Figure 1A. The diameters of the actuator and the hole were 12.0 and 14.0 mm, respectively. The rigid surround localized the strain energy of the vibration by preventing the spread of skin surface waves  on the actuator(s). The actuator was in contact with the finger throughout the experiment. Participants made responses by clicking a mouse with their right hand. They performed experiments with their eyes open to maintain their arousal level, but they could not see the vibration of the stimulator because their hand and the resting box worked as an occluder. They wore earplugs and headphones, through which white noise was continuously presented throughout the experiment to mask any subtle sound made by the tactile stimulation. Auditory cues were also presented through the headphones.We used 30-μm 30-Hz sinusoidal vibrations as low-frequency stimuli and 4-μm 300-Hz vibrations as high-frequency stimuli. The amplitude of low-frequency stimuli was 10 times above the detection threshold , and thaFigure 1B). At the beginning of each trial, a beep was sounded. The first pair of vibrations was presented 1000 ms after the beep, and the second one was presented after another 1000 ms. As a standard pair, we presented two vibrations with the stimulus onset asynchrony (SOA) of 150 ms. As a comparison pair, we presented two vibrations whose SOA was chosen from seven different levels between 75 and 300 ms on the basis of preliminary experiments performed individually before the main experiment. The presentation order of the standard and comparison pairs was randomized. The participant made a binary response  about the perceived interval (SOA) between vibrations.Participants made a two-alternative forced choice of the longer interval between the two vibrations pairs . The finger receiving the first vibration of the standard pair, the one receiving the comparison pair, and the pair presented first were all randomized across trials. The stimulus intensity and frequency of the standard pair and comparison pair were the same and fixed during a block. In the intensity-effect experiment (experiment 2), the intensity of the comparison pair was the same as in experiment 1, but that of the standard pair was halved . The stimulus site of the standard and comparison pairs was the left-hand index finger. The frequency of both pairs was the same and fixed during a block. In the frequency-effect experiment (experiment 3), the standard pair was composed of low- and high-frequency stimuli. Two kinds of standard pairs were tested: A low-high pair composed of a 30-Hz vibration followed by 300-Hz vibration and a high-low pair composed of a 300-Hz vibration followed by 30-Hz vibration. Only one of these standard pairs was presented during a block. The frequency of the comparison pair was fixed at 300 Hz because previous findings suggested that high-frequency stimuli play a dominant role in tactile temporal judgments (In the distance-effect experiment (experiment 1), each vibration of the standard pair was presented on the index and middle finger of the left hand, while both vibrations of the comparison pair were presented either on the index or the middle finger of the left hand  except that an auditory tone pair was used for as the comparison pair. For the standard pair, each vibration was presented on the index and middle finger in the two-finger condition, and both vibrations were presented on the index or middle finger of the left hand in the one-finger condition. The comparison pair comprised two tones , and the SOA was chosen from seven different levels between 75 and 300 ms. Each participant performed 2 fingers × 2 base frequency × 7 SOAs × 20 repetitions. One block consisted of 35 trials, and there were 16 blocks in total.N = 1000 bootstrap estimates . We calculated 95% confidence intervals (CIs) of PSEs from stimates  to see wFigure 1A). Eight participants made a two-alternative forced choice of which interval between the pair of vibrations was longer, the first or the second. The results showed that the apparent interval  of the pair presented over different fingers was substantially overestimated compared to the pair on the same finger with the 150-ms interval  . This PSE shift was observed when the frequencies of the stimuli were 30 Hz  and 300 Hz .We first measured the perceived interval between paired vibrations presented on different fingers  relative to that on the same finger  . The results showed that the apparent interval in the weak standard pair was substantially underestimated , regardless of the stimulus frequency range  .We next examined the perceived interval of the weak-intensity pair relative to that of the base-intensity pair. The amplitude of the weak pair was half that of the base-intensity pair, and both pairs were presented on the index finger of participants’ left hand . The results showed that the apparent interval of the vibrations with the different frequency range was substantially overestimated  . In addition, we found no significant difference due to the presented frequency order of the standard pair, 30 Hz first or 300 Hz first .The final experiment was conducted to examine the perceived interval between paired vibrations with a different frequency range compared to those with the same frequency. In this experiment, the standard pair was a combination of 30- and 300-Hz vibrations, while the comparison pair consisted of 300-Hz vibrations (Tactile behavior studies have investigated the temporal perception of nearly simultaneous tactile stimuli using simultaneity or temporal order judgments and revealed that these judgments change depending on the stimulus attributes, such as the number and length of the stimuli and where on the body they are presented . HoweverThe stimulus location effect, or somatotopic distance effect, on tactile temporal tasks has been reported for simultaneity judgments , temporaThe intensity effect on duration perception has been reported in visual and auditory studies . AlthougThe frequency effect on interval judgment tasks has been examined in auditory studies. One study  used a pThe temporal illusion in this study presumably engaged the attention mechanism. Many studies have found that stimuli grabbing more transient attention or less predictable events are relatively overestimated, while those that engage less attention or predictable events are relatively underestimated . In addiAlthough the main focus of this study was to assess behavioral changes associated with tactile binding/separation, there is a possible link between our results and intracortical interaction of neural activity. When two stimuli are presented within a brief interval, the first stimulus inhibits the amplitude level of somatosensory evoked activation for the second stimulus, and the effectiveness of this inhibition depends on the stimulus location, intensity, and frequency . AccordiIn summary, we examined whether stimulus saliency can change perceived brief time, presented as an interval between vibrations, and found the following temporal illusions: separating the stimulus location caused apparent overestimation of the temporal interval of the two vibrations; reducing the stimulus intensity caused apparent underestimation; and separating the stimulus frequency/channel of the two vibrations caused apparent overestimation. These results suggest that two tactile events with low-saliency tend to be bound/grouped, which results in apparent compression of the perceived interval between events. Misperceptions of time are often ascribed to time differences in neural transmission or cortical processing, but can sometimes be ascribed to errors in encoding temporal relationships . Though SK and JW contributed to conception and design of the experiments. SK collected and analyzed the data. SK drafted the paper, and TY and JW provided critical revisions.The authors SK, TY, and JW are employees of NTT Communication Science Laboratories, which is a basic-science research section of Nippon Telegraph and Telephone Corporation. There are no patents, products in development or marketed products to declare.


Bone-anchored limb prostheses allow for the direct transfer of external loads from the prosthesis to the skeleton, eliminating the need for a socket and the associated problems of poor fit, discomfort, and limited range of movement. A percutaneous implant system for direct skeletal attachment of an external limb must provide a long-term, mechanically stable interface to the bone, along with an infection barrier to the external environment. In addition, the mechanical integrity of the implant system and bone must be preserved despite constant stresses induced by the limb prosthesis. Three different percutaneous implant systems for direct skeletal attachment of external limb prostheses are currently clinically available and a few others are under investigation in human subjects. These systems employ different strategies and have undergone design changes with a view to fulfilling the aforementioned requirements. This review summarises such strategies and design changes, providing an overview of the biomechanical characteristics of current percutaneous implant systems for direct skeletal attachment of amputation limb prostheses. However, the socket-stump interface often causes such complications as poor fit, discomfort, skin problems, sweating, and pressure sores.In the early 1960s, P.-I. Brånemark discovered the ability of bone tissue to closely adhere and form a strong mechanical bond to titanium. He introduced the term osseointegration as direct anchorage to bone tissue to describe this close contact.18Previous reviews have focused on clinicalScopus, Web of Science, and PubMed. Article title, key words, and abstracts were searched using the following search condition:  AND (limb OR prosthes*) AND (amput*) AND (implant*). The inclusion criteria for the articles required them to contain a description of an implant system that allows for direct skeletal attachment of a load-bearing artificial limb. Load-bearing limbs were defined as upper or lower legs and arms. Journal articles published prior to 1 April 2017 were considered. Conference proceedings, book chapters, editorial letters, non-English, and non-Spanish articles were excluded. The screening procedure is presented in detail in Fig. Derwent Innovations Index and Espacenet was performed to obtain further information about these implant systems. Only patents describing the components of the previously identified implant systems were considered. The peer-reviewed research articles and patents were studied to determine the characteristics of each of the implant systems presented here.A systematic literature review was performed using the three databases: The eight identified implant systems are shown in Figs. In 1998, the Swedish implant system, surgical technique, and postoperative rehabilitation protocol was standardized for transfemoral amputees by the introduction of the OPRA treatment protocol. Similar standardisation has also been done for transhumeral and thumb/finger amputations. Apart from the standardised implant versions, custom-made implants are available for the aforementioned levels, as well as for transtibial and transradial amputations. The OPRA implant system mainly consists of three components: (1) an externally threaded, cylinder-like, fully implanted component known as a “fixture”, where osseointegration takes place; 2) a percutaneous component called “abutment”, which is press-fit into the distal end of the fixture and to which the limb prosthesis is attached; and (3) an “abutment screw”, which extends through the hollow centre of the abutment to clamp the abutment and the fixture together by the proximal thread engagement to the fixture and the abutment screw head on the distal end of the abutment ,64Three different anchoring strategies were found in the studied systems: (1) a threaded connection, which is utilised in the OPRA and the original AEAHBM system; (2) a press-fit interface, which is present in the ILP, OPL, ITAP, POP, Keep Walking Advanced, and the redesigned AEAHBM system; and (3) a bone anchor with transverse intraosseous pins in combination with a compressive force and bone-ingrowth at the bone-collar interface, as is used in the COMPRESS system. A threaded connection inherently has good mechanical stability in the longitudinal direction. Initial rotational stability is achieved by friction and long-term stability is achieved by a combination of friction and mechanical interlocking, where the bone tissue grows into macro, micro, and nano “irregularities” on the implant surface. The press-fit interface has a lower longitudinal axial stability, initially relying solely on friction and in the long term relying on both friction and bone ingrowth for longitudinal and rotational stability. A bone anchor with transverse intraosseous pins, in combination with a compressive bone collar with bone ingrowth promoting surface properties, naturally creates a high mechanical stability, both in the longitudinal and the rotational directions. In order to create a more stable interface between the implant and the bone, additional features have been added to some of these systems. These include longitudinal splines or fluted regions for improved rotational stability as in OPRA, OPL, ITAP, POP, Keep Walking Advanced and the AEAHBM systems; a curvature along the longitudinal axis, as is utilized in the ILP and the OPL systems; and a flared, or collared interface at the distal bone interface, as used in all systems except OPRA. Geometrical fit between the implant and the bone appears to be crucial for a successful outcome as observed by loosening and failure of undersized implants,In the OPRA system, the abutment is connected to the fixture by a smooth surface press-fit. The abutment is also clamped to the fixture by a preload from the abutment screw with a thread engagement with the fixture proximal to the abutment.The ILP and OPL systems have a press-fit Morse taper connection between the implant and the percutaneous part, called the dual-cone adapter. A safety screw inserted longitudinally from the dual-cone adapter to the implant provides additional locking of the components.In the POP system used in the ongoing human trial, the implant is connected to the exterior of the body by a ceramic-coated percutaneous post, which is clamped to the implant with a locking screw.12The porous coated collar in the COMPRESS system is connected to the bone anchor by a traction rod and a compression nut, which, in combination with a number of Belleville washers, apply a compressive force at the distal bone end.In the Keep Walking Advanced system, the implant is attached to the percutaneous extension by a tapered interface and a locking screw, which has a proximal thread engagement with the implant.26The percutaneous component of the OPRA system is the abutment, which has a smooth polished surface to minimise contact and friction at the skin interface. In the ILP and the OPL systems, the percutaneous interface consists of the dual-cone adapter and, in some designs, also the distal end of the implant. The percutaneous surfaces of the implant are smooth-polished and have a niobium-oxide coating aimed to minimise soft tissue adhesion at the percutaneous interface.23In the ITAP system, the percutaneous interface is stabilised by the subdermal porous flange, allowing for soft tissue ingrowth and suture of the thinned skin flap to minimise relative movement.66The COMPRESS and the AEAHBM systems both have a porous subdermal surface distal to the bone to promote soft tissue integration and to provide a soft tissue seal to the implant. In the COMPRESS system, the porous coating consists of titanium, while the AEAHBM system uses tantalum.Safety precautions have been taken to protect the bone and the implant from direct exposure to high loads, especially in the event of a fall. The OPRA implant system has different safety devices for different amputation levels. They are separate components, which are connected between the abutment and the external prosthesis and automatically release the connection between the implant and the prosthesis if they are exposed to a load exceeding a pre-set limit. All OPRA safety systems protect against excessive torque around the longitudinal axis, while the transfemoral system also protects from excessive bending moments in the normal plane of the longitudinal axis. Release limits for the systems are set to be high enough to avoid release during normal use, but low enough to ensure that the bone or the implant system is not damaged. The limits are set to 15 Nm torque and 70 Nm bending moment. In case of release, the safety system can be restored to normal operation by the patient without the need to meet a prosthetist. The ILP and OPL safety systems are protecting from high torques being transferred to the implant by a connection adapter50Several systems have been developed for bone-anchored limb prostheses and different approaches have been employed to achieve a stable attachment between the implant and the bone. Comparing the ILP and OPL implant systems with the OPRA implant system reveals that the latter follows a slower rehabilitation protocol for lower limb amputations. This could indicate that a longer time is needed to achieve a mechanically stable interface for a threaded implant than for a press-fit implant. However, the historical development of the implants must also be considered. The threaded implant design used in the OPRA system was developed using experience gained from the dental industry as the first and longest user of osseointegration, whereas the press-fit implant design originates from intramedullary hip implants, which have a tradition of fixation to the bone by press-fit in combination with bone cement.The OPRA system follows a conservative approach, with a healing period before any load is applied to the implant. This is based on experimental results from animal studies, which have shown that the mechanical capacity of the bone-implant interface for threaded implants is improved by healing under unloaded conditions in both torsion and pull-out load.Another difference between the clinically available implant systems is the intramedullary length of the implant . This indicates that press-fit implants require a longer intramedullary length to achieve a stable connection in the longitudinal direction than a threaded implant. A shorter implant length is advantageous, as it imposes fewer eligibility constraints on the residual stump length. Furthermore, in the event of a catastrophic failure, with the worst-case scenario requiring re-amputation above the implant, a shorter intramedullary length leads to a longer residual length of the stump after the re-amputation surgery.To achieve bone ingrowth, the trend is to use the titanium alloy Ti6Al4 V as the bulk material in combination with porous surface on the implant. The degree of porosity varies between systems, but inevitably comes with a trade-off by having reduced mechanical strength and fatigue properties in these regions. Most of the systems used in humans are modular, which limits the mechanical capacity but simplifies the surgical intervention in case a revision surgery is needed. To avoid irritation and superficial infections, which could potentially lead to more severe deep infections, two approaches are employed at the percutaneous interface in the different implant systems. The first approach is to try to prevent skin and soft tissue adhesion by having a polished surface on the percutaneous component as in the OPRA, OPL, POP, Keep Walking Advanced and later designs of the ILP system. In the OPRA system, this approach is combined with suture of the skin directly to the distal end of the bone at the percutaneous interface in order to minimize relative movement and to create an infection barrier. The other approach is to create an infection barrier by promoting soft-tissue ingrowth to the percutaneous component. This approach is used in the ITAP, COMPRESS, AEAHBM, and earlier designs of the ILP systems, by having a porous surface on the percutaneous component.The scientific literature contains limited information about the mechanical features of bone-anchoring implant systems. Reporting the performance of such systems under mechanical stress in bench tests, or activities of the daily living, has been given a low priority by the development teams in favor of clinical outcomes. The available literature refers to osseointegration as the responsible mechanism that allows direct skeletal attachment of limb prostheses; however, insufficient evidence has been provided for most of the implant systems on the degree of osseointegration achieved with the different designs.It is difficult to compare the available systems because they have undergone several changes over time, and clinical trials continue to be limited. The three design principles known at present are fundamentally different and pose particular advantages and disadvantages, which might in the future serve as the basis to determine which approach is most suitable for particular subjects.Current systems for bone anchoring of limp prostheses use intramedullary implants. Primary stability between bone and implant is achieved by one of three strategies: a threaded connection, a press-fit connection, or axial compression. Secondary stability is achieved by bone ingrowth into porous surfaces of the implant. Although there are large differences between current implant systems, the three clinically available systems  have shown functional improvements for patients with socket-related issues. Recent developments of implant systems, surgical protocols, and safety devices have reduced the rate of mechanical failure and infectious complications. Moreover, further improvements are likely to continue based on field data and information from the ongoing human trials. Future developments are likely to address several factors, such as the perceived long rehabilitation time before loading, the need for two separate surgeries, the incidence of superficial infection at the percutaneous interface, mechanical failures in highly demanding activities, and the possibility of additionally providing closed-loop, neuro-muscular control of the limb prostheses.


The distribution of metabolites across the percolation layers showed correlations between the metabolic integration hierarchy and the network topology. We show that metabolites concentrated in the internal network (maximum kcore) only comprise molecules of the primary basal metabolism. Moreover, we found a high proportion of a set of common metabolites, among the 17 plants, centered at the inner kcore layers. Meanwhile, the metabolites recognized as participants in the secondary metabolism of plants are concentrated in the outermost layers of the network. This data suggests that the metabolites in the central layer form a basic molecular module in which the whole plant metabolism is anchored. The elements from this central core participate in almost all plant metabolic reactions, which suggests that plant metabolic networks follows a centralized topology.Modeling the basic structure of metabolic machinery is a challenge for modern biology. Some models based on complex networks have provided important information regarding this machinery. In this paper, we constructed metabolic networks of 17 plants covering unicellular organisms to more complex dicotyledonous plants. The metabolic networks were built based on the substrate-product model and a topological percolation was performed using the  It is believed that the general architecture of living systems is based on the structure and function of modules . HoweverThe metabolism is perhaps the best network of interactions ever characterized in biology because a large number of studies has defined metabolic pathways , 5. For Data extracted from plant genomes make it possible to investigate correlations of the molecular backbone of living beings that are related to their adaptations to the environment –8. ComplHowever, it is not known exactly how a general design on the distribution of matter in metabolism can be developed based on the observation of the topology from metabolic networks. Consequently, in order to reveal functional, hierarchical and even phylogenetic information hidden in the network structure, new models need to be investigated. The content of plant metabolic networks reflects the species phylogeny, thus groups of plants that are evolutionary closer share a larger proportion of common metabolites. In this case, the specialized metabolism is responsible for the greatest differences; gene coding for specialized metabolic functions have proliferated to a much greater degree and by different mechanisms and display lineage-specific patterns of physical clustering within the genome . Thus, uAlthough some studies have shown that the hierarchical organization and modularity inside the metabolic network is related to the chemical classes of metabolites , these skcore decomposition [kcore percolation, a network is pealed as a set of successively kcores (layers (k)) until a maximum core is achieved. Thus, small values of k define the periphery of the network and the innermost network core corresponds to a large k. This algorithm has been proposed to understand the network hierarchical organization by extracting highly interconnected parts and thus providing ways to find relationships within these substructures [kcores can provide useful insights into the global network topology and also establish a hierarchy of connections from each network node [For instance, some attempts have been made to find fully-connected parts of the metabolic networks . Completposition , 12. It position . Throughructures . Therefoork node .kcore decomposition of plant metabolic networks modeled according to the plant metabolic reaction dataset from 17 plants selected from the PlantCyc database [Brachypodium distachyon (BD), Hordeum vulgare (HV), Oryza sativa japonica (OSJ), Panicum virgatum (PV), Setaria italica (SI), Sorghum bicolor (SB), Zea mays (ZM); Arabidopsis thaliana (AT), Brassica rapa pekinensis (BRP), Carica papaya (CP), Glycine max (GM), Manihot esculenta (ME), Populus trichocarpa (PT), Vitis vinifera (VV); Selaginella moellendorffii (SM); Physcomitrella patens (PP) and Chlamydomonas reinhardtii (CR) were considered.In this study, we present a percolation analysis based on the database . The metkcore decomposition of plant metabolic networks reveals information about the metabolic centralization and functional hierarchy of certain metabolite groups distributed across its layers.Our main objective is to demonstrate that a percolation through the kcore layers of the networks in an opposite way relative to the secondary and non-common metabolism between plants. The common metabolism between plants is completely centralized in the layers with greater connectivity and the metabolism secondary and uncommon between the plants is peripheral along the layers. Together these data show that the decomposition by a layering tool is useful for building hierarchical models of the metabolism organization and brings information that can be used in studies about the evolution of the metabolism.This functional analysis shows that a high proportion of the metabolites from central layers of the networks contain the basic components from basal metabolism. In addition, we show that the metabolites found in the more centralized level of the networks integrate all plant metabolisms because they participate in the absolute majority of their metabolic reactions. As confirmed by previous studies that show that metabolic networks are very modularized , we alsokcore percolation algorithm to 17 plant metabolic networks whose set of metabolic reactions were obtained from the PlantCyc database [We applied the database . The setdatabase .kcore decomposition is applied successively, as shown in The kcore percolation from the metabolic network of Arabidopsis thaliana shows that the last full connected level (maximum kcore) contains 21 metabolites, while the outermost layer contains 3,546 metabolites, from which 149 belong exclusively to k1. As expected, there is a decrease in the number of metabolites in each layer until the central core. It can be observed that the maximum number of layers kmax for all the studied plants varies between 16 and 18. Thus, these plants were grouped into three sets: BD, HV, OSJ, SI and SB with 16 layers; PV, ZM, BRP, CP, GM, ME, VV, SM and CR with 17 layers; AT and PP with 18 layers.The kmax is not related to the number of metabolites (N). For instance, networks with relatively small sizes such as moss Physicomitrela patens (N = 2651) reached the highest number of cores (k = 18), while networks with larger sizes such as the dicotyledonous Manihot esculenta (N = 2991) reached fewer cores (k = 16). The detailed network properties, such as the number of layers and network size for the 17 plant metabolic networks studied here, can be found in We found that the number of layers kcore from all plants studied here namely: ADP, ammonia, AMP, ATP, CO2, coenzyme A, diphosphate, H+, H2O, L-glutamate, NAD+, NADH, NADPH, and phosphate. These 14 metabolites extracted from the central core, found in the 17 studied plants, represent a very connected dataset.We also analyzed the chemical composition of the central core in order to obtain the contents of the innermost network for the 17 plants, which is shown in We observed that the metabolites extracted from the central core of the metabolic networks participate in almost all the sets of the metabolic reactions from plants studied here. This is shown in kcore to the metabolic network from Arabidopsis thaliana  with the maximum kcore of the network. It can be seen for example in kcore).The graphs in kcore class contains only 21 metabolites while the lipids contain around 500. This is almost 20 times higher than the content of the metabolites from the maximum kcore, while the number of the links at the maximum kcore is almost the same as the lipids.There are differences in the number of the metabolites in each class shown in klayer. These metabolites were extracted from the intersection dataset between the 17 plants studied in this work. The klayers for plants belonging to five major clades, namely: the algae Chlamydomonas reinhardtii, the bryophyta moss Physicomitrela patens, the lycophyte Selaginella moelendorffi and two angiosperms, the monocotyledon Zea mays and the dicotyledon Arabidopsis thaliana. The analysis of the proportion from common metabolites in the kcore layers reveals that its content is centered in the innermost kcore, where these metabolites reach to almost the total content of the layers. The distribution of the metabolites per each kcore layer for plants that were not shown in kcore layers, as it is a complementary set of the common metabolites, as shown in klayers as that shown to non-common metabolites between the plants , amino acids (L-glutamate) and the most primary photosynthesis product, the oxygen (O2)  see . This faThe metabolite distribution across the plant’s metabolic reactions showed that at least one element of the set of metabolites belonging to the most central layer of the networks is present in more than 90% of the metabolic reactions from all plants studied here see . It is sArabidopsis thaliana are highly connected within themselves, as the number of connections inside each metabolic class  is higher than with other classes. Interestingly all classes are very connected with metabolites present at the maximum kcore layer. This shows that in addition to being very modularized, the network is also very centralized in the metabolites found in the last level of the network percolation. Earlier studies have demonstrated that the metabolic networks have a modular and hierarchical structure [The analysis of the cross connection between metabolic classes showed that the metabolic classes in the tructure .kcores. Moreover, it is known that the basal metabolism arose early in the evolution of species, therefore it is not unreasonable to assume that the percolation by kcores provides a tool for studying molecular evolution metabolism, which is supposed to occur with the direction of the center to the periphery of the network percolation layers.It is also interesting to note that the common metabolism, represented by common metabolites between all plants studied here, is centralized in the kcore layers also corroborates the hypothesis that the kcore percolation algorithm may reveal evolutionary hierarchies in the metabolism and it is appropriate to demonstrate connectivity hierarchies in plant metabolic networks and their correlation with the metabolic functionality.The peripheral location of the secondary and non-common metabolites between plants along the It should be noted that the secondary metabolism provides alternative ways of molecular interactions between the plant and its environment and for this reason it appeared later in the evolution of species. This metabolism has a differential evolution in relation to the basal metabolism and genes related to it proliferate and diverge more rapidly throughout the evolution .kcore percolation. We observed that the distribution of these metabolites is very similar to that of the secondary metabolites  along the topology of the networks, as the vast majority of the reactions contain at least one element of the central layer and therefore, appear to be embedded in the central module. This suggests that transport of matter at the metabolic pathways does not have an occasional structure and it can be centered in terms of routes. Moreover, it can be assumed that transport is performed by a chemical network, which although is not spatially defined, has logical connections that distribute material components (molecules). Therefore, theoretical correlations about the genesis and dynamics of pathways can be drawn from the knowledge of key metabolic nodes, which could be shown by metabolomic and transcriptomic data, for example. Therefore the kcore analysis can reveal the hierarchy and emergence of these nodes in various topological states of the metabolic network.The kcore also participate in almost all chemical reactions of the secondary metabolism. This observation leads to proposing a model in which the kcore central layer is a kind of network processing unit, which is responsible for anchoring the plant metabolic reactions.All elements of the central core are considered hubs in plant metabolic networks. These metabolites are the basic bricks of which all metabolic pathways are built. Meanwhile, we observed that the metabolites at the maximum kcore percolation layers. It suggests that studies on the modularization of metabolism could be performed with kcore percolation to reveals hierarchies of modularity in metabolism.Hierarchical network models show that their assembly hierarchy is possibly associated with the specialization of metabolism . At the Finally, some questions remain: Can we assume that the molecular evolution of metabolism, i.e. adding and integrating new components can be simulated by the percolation proposed in this study? Is this addition anchored to the metabolites of the central layers?The plant metabolic networks studied here were constructed from the metabolic reactions of 17 plants available at PlantCyc database (Version 9.5) , furtherCommon metabolites This dataset is composed by the intersection among all metabolites of plants analyzed here. The dataset is available in Non-common metabolites This dataset is complementary to the one described above, i.e. it is composed by those elements that do not belong to the intersection of metabolites among all the plants studied.Secondary metabolites This dataset was obtained by discriminating the complete dataset of metabolites of each plant. The secondary metabolites were identified using well-established literature regarding secondary metabolism [tabolism . The numtabolism  and the tabolism  were useMetabolic classes This data set was obtained from the attribution of metabolites belonging to the classes: amino acids, nucleotides, lipids, carbohydrates and those metabolites found in the maximum kcore of the metabolic network of the plant Arabidopsis thaliana -core. A kshell Gk is composed by all the nodes whose shell index is k [k in a given Gk is denoted by kmax [The ures see . A kcoreual to k , 12. As ual to k . Fig 1b dex is k . The max by kmax .kcore were discriminated by identifying metabolites from each respective class present within the full content of metabolites from Arabidopsis thaliana.Metabolites belonging to the classes amino acids, nucleotides, lipids, carbohydrates and maximum The quantification of the cross connection of metabolites was performed by counting the number of links between metabolites belonging to a specific module with metabolites from other modules.S1 File(PDF)Click here for additional data file.S2 File(XLSX)Click here for additional data file.S3 File(XLSX)Click here for additional data file.S4 File(XLSX)Click here for additional data file.S5 File(XLSX)Click here for additional data file.S6 File(ZIP)Click here for additional data file.S7 Filekcore decomposition for Arabidopsis thaliana metabolic network (A video corresponding to the  network . The vid(MOV)Click here for additional data file.


Automated segmentation of planar and linear features of point clouds acquired from construction sites is essential for the automatic extraction of building construction elements such as columns, beams and slabs. However, many planar and linear segmentation methods use scene-dependent similarity thresholds that may not provide generalizable solutions for all environments. In addition, outliers exist in construction site point clouds due to data artefacts caused by moving objects, occlusions and dust. To address these concerns, a novel method for robust classification and segmentation of planar and linear features is proposed. First, coplanar and collinear points are classified through a robust principal components analysis procedure. The classified points are then grouped using a new robust clustering method, the robust complete linkage method. A robust method is also proposed to extract the points of flat-slab floors and/or ceilings independent of the aforementioned stages to improve computational efficiency. The applicability of the proposed method is evaluated in eight datasets acquired from a complex laboratory environment and two construction sites at the University of Calgary. The precision, recall, and accuracy of the segmentation at both construction sites were 96.8%, 97.7% and 95%, respectively. These results demonstrate the suitability of the proposed method for robust segmentation of planar and linear features of contaminated datasets, such as those collected from construction sites. Construction project progress monitoring and dimensional compliance control are essential to allow decision makers to identify discrepancies between the planned and the as-built states of a project and take timely measures where required. In practice, monitoring is performed manually, which is a time consuming, error-prone and labour-intensive task, particularly for large scale projects . Hence, In addition, the reliable determination of a project’s performance is highly dependent on the accuracy of the data collected during the monitoring process. Currently, site supervisory personnel spend 30–50% of their time manually inspecting and controlling the quality of the manually-collected data . ReductiOutliers exist in construction site point clouds due to data artefacts, occlusions and dust.Many object-based recognition models depend on the 3D/4D planned building information model (BIM), which is neither readily available nor accurate, and the as-built is not necessarily constructed to plan. The compliance of the as-built to the planned specifications, must in fact be checked through the monitoring and control process; hence, a monitoring and control process solely reliant on the details of the planned is not desirable.Most planar and linear classification and segmentation algorithms use inconsistent and subjectively-defined thresholds see , which cTo help overcome the limitations associated with current manual monitoring practices, the application of terrestrial laser scanning (TLS) to acquire 3D point clouds of construction site environments has been growing markedly. Since the most generic building elements are constructed from planar  and linear (reinforcement bar) features , the autTo address these limitations, this manuscript reports on the development of a novel robust point cloud processing method with particular emphasis on planar and linear feature classification and segmentation using only the geometric primitives.Key Performance Indicators (KPIs) include onsite data collected to measure the performance of a project. To measure the schedule performance of a project, up-to-date knowledge of the percentage of activities completed is required . To measTo evaluate dimensional conformity, surface flatness/levelness and the length of structural elements are the most commonly collected KPIs . DependiTLS provides 3D point clouds of surrounding surfaces, and hence can be used as a means of automatically measuring the aforementioned KPIs. However, due to the many objects present on construction sites, the manual interpretation of the KPIs from dense point clouds is tedious and impractical ,10. TherCurrent research in construction management is devoted to the automatic extraction of the “scope of the work performed” for each activity from the acquired TLS point clouds. To this end, many research studies propose the superimposition of the planned 4D BIM and the 3D points clouds captured from TLS . This meThe initial step to automatically extract features from point clouds is labelling and grouping of points with similar geometrical attributes, commonly referred to as the classification and segmentation processes, respectively . As mentPlanar (linear) classification: The process of extracting points that locally follow a planar (linear) pattern within a point cloud dataset. In other words, points that locally follow a planar (linear) pattern are classified as planar (linear) regardless of their specific parametric equation.Planar (linear) segmentation: The process of grouping the classified planar (linear) points that follow a similar planar (linear) parametric equation. In other words, points that are globally on the same plane (line).To avoid confusion, from this point on, the following notions are used throughout this manuscript:Local behaviour of points is one of the most widely utilized methods to classify planar and linear points in a point cloud dataset. There are three commonly-used methods for local planar or linear parameter estimation, namely the 3D Hough transform, random sample consensus (RANSAC), and principal components analysis (PCA). Vosselman et al. used 3D Hough transform to assign planar attributes to every point in Cartesian, which allows the determination of planar surfaces without the initial estimation of the local normal vectors . HoweverData artefacts caused by occlusions, moving objects, and dust cause outliers in construction site datasets. Most available planar/linear classification methods are only suited for datasets with no data contamination . In addition, the classification of a dataset affected by outliers using classical statistical methods is highly influenced by the presence of outlier points ,21. SomeClassical PCA is the eigenvalue decomposition of the covariance matrix of a multivariate dataset. It is used to summarize the variation of the dataset into independent  axes. In the case of a three-dimensional point cloud, three orthogonal axes can be determined. Many researchers have used PCA for the classification of planar surfaces ,35,36,37h data points out of a set of n observations. The (n-h) points left are the outliers of the dataset. The MCD selects h points out of n for which the covariance matrix has the smallest determinant. Compared to MVE, MCD is asymptotically normal [Since classical estimates of location and dispersion such as the sample mean and covariance matrix are adversely influenced by even a single outlying observation, they are not able to deal with contaminated datasets . In thisy normal , has a hy normal  and is my normal . TherefoTwo well-known MCD estimators exist: the fast-MCD ; and theTwo methods are generally used to segment the classified planar/linear points, namely region growing  and attribute clustering (parameter domain). Region growing methods are widely implemented ,31,32,44The result of the region growing segmentation may depend on seed point choice, i.e., the results are not permutation invariant and, hence, it is not considered as a robust method ,46. To sThe second method for planar/linear segmentation is attribute clustering. For attribute clustering, an n-dimensional array of feature attributes is first defined. Points sharing similar attributes are grouped into the same cluster following some similarity criteria. Using attribute space clustering, it is possible to group together spatially discontinuous points. Thus, a connected components method is required, typically through a nearest neighbour search or boundary detection , to remoMany methods for clustering points in attribute space exist for planar and linear feature segmentation. In ,50, poinClustering methods are generally more robust than region growing since the result of the segmentation is permutation invariant. However, segmentation quality depends on the accuracy of the estimated attributes. In this manuscript, the latter problem is solved by utilizing robust PCA for the robust estimation of the desired attributes. Since the attributes in this study are accurately estimated during the classification process, compact clusters (clusters with low dispersion) are expected. In the research carried out by ,53,54,55The subjective definition of similarity thresholds is in fact common in both clustering and region growing methods. For instance, in , two locThe correct selection of the aforementioned thresholds is especially important for distinguishing planar (or linear) from non-planar (or non-linear) surfaces. If the selected angular similarity threshold is large, points on non-planar (non-linear) surfaces, such as a cylinder with a large radius, may be grouped together as a plane. Another example is two linear components with different orientations that are attached via a smooth connection that may be merged into one segment . This phIn summary, the choice of threshold used to examine similarity is mostly subjectively defined and may result in over- or under-segmentation depending on the dataset. In this manuscript, a new iterative and robust complete linkage clustering algorithm is presented to reduce the dependency of the segmentation results on the choice of threshold and to minimize the chaining effect to only identify globally planar and linear segments (low curvature segments).As mentioned, the focus of this study was to develop a generic planar and linear segmentation framework whose performance is not a function of subjectively defined attribute similarity criteria, and hence can be used in different construction site environments. The proposed framework is summarized in As described in The Det-MCD estimator is used in this study for multivariate, non-parametric outlier detection due to its efficiency, accuracy and practicality. In this study, the Det-MCD estimator was independently implement; however, this estimator is available as a Matlab function through the LIBRA robust statistical toolbox . The covRobust PCA is performed on the neighbourhood of each point to determine the local pattern/variation. Although robust PCA minimizes the influence of outliers on the eigenvalue estimation, the variations of the eigenvalues due to random measurement errors must also be quantified. This impact can theoretically be derived by variance propagation from the functional TLS positioning model and the stochastic properties of the instrumental random errors. Some research has aimed to determine the impact of point measurement errors on the principal components ,61. HoweThe next step is to group together the classified points with similar attributes, also referred to as segmentation. To segment coplanar and collinear points, a set of attributes are selected from the results of the robust PCA classification process. These attributes must uniquely define planar and linear features.U and V, with the highest degree of attribute similarity are identified and merged together to form cluster UV. The attribute similarity between cluster UV and any cluster W is then calculated as:i and j. The cluster with the highest degree of similarity, say point W, to cluster UV is merged to form cluster UVW. The process is then continued for cluster UVW. The grouping is finalized when the distance measured by Equation (4) is greater than a predefined similarity threshold. The process is repeated for the remaining clusters until every cluster is visited at least once.According to the complete linkage algorithm, one cluster is initially assigned to each point. The “attribute similarity” of two clusters is defined as the distance between the attributes of those clusters. Any acceptable distance metric such as Euclidian, and Mahalanobis may be used. Consequently, a pair-wise distance may be utilized for each dimension of the attribute space in case the scale or the similarity threshold for each dimension is different , which are expected to form due to the robust attribute estimation, adopted in this manuscript. However, it may result in over-segmentation when the similarity threshold used for segmentation is not correctly defined. To overcome this shortcoming, an initial similarity threshold is so chosen to prevent under-segmentation of the compact clusters. In other words, the similarity threshold is chosen small enough to reduce Type II errors during the segmentation process. The choice of similarity threshold is reported in iterative complete linkage” process is proposed. According to this new method, the complete linkage is first performed on the estimated robust parameters to group points with similar attributes using the pre-defined similarity threshold. New attributes for the newly-merged clusters are then estimated using robust PCA  caused by random measurement errors are used to systematically quantify the initial similarity thresholds. To do so, Monte Carlo simulation is used. First, 1000 random plane (and line) orientations with 50 different distances from the origin (0.5–25 m) were selected. The point cloud of these 50,000 planes and 50,000 lines containing random instrumental measurement errors were simulated.Point clouds were simulated by projecting rays in angular increments according to the angular resolution of the TLS instrument used in this study. These rays are then intersected with each simulated plane (or line) to identify the range of the noise-free observations. Random measurement errors were incorporated for both angular and range measurements. The random measurement errors were assumed to be normally distributed, σ) of the percentage of relative error for each plane/line attribute versus the distance of the plane/line to the origin. The directional vector components  is consU and V are merged if and only if more than 50% of the points from cluster U are identified as inliers. In other words, the cluster is rejected when the majority of the outliers are from that cluster. The aforementioned steps are then applied to the merged cluster UV until no other cluster can be merged. The robust complete linkage procedure is then repeated for the remaining clusters. The algorithm continues until every cluster is visited at least once. To improve the computational efficiency, clusters with attribute similarity larger than 20% of the attributes of the base cluster (cluster containing more points) are not examined. robust complete linkage” algorithm in 2D. iterative complete linkage” and “robust complete linkage” algorithms together.The two clusters Using the proposed segmentation method, it is possible to group together spatially discontinuous surfaces since spatial connection has not yet been considered. To enforce surface continuity and connectivity of clusters, the inner (openings/windows) and outer boundary points for each linear and planar segment are determined using α-shapes ,65. FirsFlat slab floors and columns are common structural elements on building construction sites. Here, a new method is proposed to identify and extract points of flat slab floors and ceilings using the histogram of point height prior to the application of the proposed robust PCA. This is particularly beneficial to reduce the number of points to be segmented and consequently helps decrease the calculation time of the proposed segmentation procedure. A similar idea was also introduced in  to extraA typical histogram of point height for a room or a construction site with flat slab ceiling and floor is schematically shown in posed in  was adopThe value of this threshold is defined with respect to the measurement errors of points on flat slab ceiling (or floor) using the law of variance propagation and the TLS instrument specifications. ided by  comprise the locus of points in space with the same height from the origin; therefore, ectively . TherefoThe n :(12)MADAfter the significant modes are detected, points within ±3σh/max ,72 from ceilings . After tTo assess the quality of the segmentation, and classification, the precision, recall and accuracy are estimated using the convention presented in :(14)Precmilar to ,32, the milar to . RabbaniThree sets of experiments were designed to demonstrate the effectiveness of the proposed robust planar and linear segmentation. The results from eight datasets collected using a Leica HDS6100 TLS are presented. The first experiment was the as-built modelling of the Mechanics of Materials Laboratory (MML) at the University of Calgary to assess the applicability of the proposed algorithms in a small but complex environment before field data on construction sites were collected. The second experiment was construction progress monitoring of the Graduate Student Hall of Residence (GSHR) building, which mainly consists of reinforced concrete structural elements with flat slab floors, and rectangular cross-section columns. The third experiment was the dimensional compliance control for the Taylor Institute of Teaching and Learning (TITL) building, which features a unique skeletal steel structure composed of rectangular/square Hollow Structural Sections (HSS).To register TLS point clouds acquired at different points in time, signalized targets over pre-surveyed control points were used. At least four non-collinear targets were within the line-of-sight (LOS) of every instrument location. The registration precision, estimated through the Mean Radial Spherical Error (MRSE), for the eight datasets presented in this manuscript is provided in The methods proposed in this manuscript were implemented in Matlab programming language using the Parallel Processing Toolbox, and analysed through a computer with Intel Core i7-4930K @ 3.40 GHz CPU, 32 GB of DDR4 RAM, 500 GB of SSD, and 2 GB of dedicated graphics card.One composite point cloud comprising the data captured from three scan stations was collected from the MML a. As illThe GSHR construction site shown in The third experiment was the monitoring of the TITL construction site c. The obMADN in the vicinity of the detected mode.The histogram of point height is shown in Approximately 18 million points were identified and extracted as belonging to the floor and the ceiling, which accounted for more than half of the total points. The computation time of the robust PCA classification is nearly four times that of the proposed floor extraction method for the same number of points. This is attributed to the higher computational complexity of the nearest neighbour search in 3D as well as the Det-MCD estimation of 3D data during the robust PCA classification compared to the 1D nearest neighbour search and the univariate median-shift algorithm for the proposed floor extraction. Therefore, the use of this method can help improve the computational complexity of the proposed planar classification algorithm. The precision, recall and accuracy of the extracted points were 95.2%, 100.0% and 96.4% for the floor and 94.6%, 100.0% and 95.3% for the ceiling, respectively. These outcomes demonstrate the robustness of the proposed method, especially to Type II errors. Therefore, the proposed method reduces the computational time while providing robust floor extraction results.The reduction of Type II errors in the planar classification also improves computational efficiency since fewer non-planar points are considered during the segmentation process. The robust complete linkage was applied on the classified planar points shown in As indicated in The ability of the robust complete linkage algorithm to cluster planar segments was briefly discussed in our previous work , where oTo further demonstrate, the point cloud of one of the columns from Epoch 1 was selected a, and thThe segmentation results using our method and the region growing method of Rabbani are presented in As indicated in The 100.0% recall rate for all datasets demonstrates that the method is robust to Type II errors. After the flat slab point extraction, the remaining points (including the 5.3% of points on the flat slab ceiling and floors that were not identified as points on floor or ceiling) were classified into planes and lines, and then merged together using the proposed robust segmentation algorithm. Among the points that were not correctly identified as points on floors or ceilings within our initial flat slab identification method (Type I errors), approximately 38.3% were correctly merged to the initially extracted points using the proposed robust complete linkage algorithm.The registered point cloud acquired from the TITL construction site, consisting of six scan stations with overall registration precision of 1.7 mm , is showAs shown in The internal trusses, shown in To show the effectiveness of our proposed method in distinguishing the planes of the web of H-section elements, the point cloud of a subset of an H-section column is used a. The plThe angular threshold and neighbourhood sizes for the region growing were set to 10° and 10 mm , respectively. The neighbourhood size was purposely chosen to be smaller than the thickness of the web to minimize over-segmentation. The results of the planar segmentation using our method and Rabbani’s region growing method are presented in The use of TLS for construction site progress monitoring and structural dimension compliance control is evolving markedly. However, point clouds collected in complex and dynamic environments such as a construction site are contaminated with outliers. A comprehensive review of current planar and linear segmentation methods suggested that most methods rely on subjective predefined thresholds to group together points with similar attributes, which may result in over- or under-segmentation of the point cloud depending on the data and threshold used. This led to the development of the robust complete linkage segmentation algorithm to introduce a point cloud segmentation method that provides robust results independent from a subjectively predefined and scene-dependent similarity threshold.The applicability of the newly developed robust complete linkage planar and linear segmentation method was investigated in eight datasets, seven of which were acquired from actual construction site environments. It was demonstrated that the proposed method achieved an overall accuracy of better than 92.5% for all presented datasets, indicating its generic applicability for processing contaminated point clouds acquired from environments such as construction sites.The segmentation results of two sample subsets of the point clouds were also compared to the region growing method proposed by Rabbani et al. . It was It is important to mention that the size of neighbourhood and the point sampling density may affect the robust classification and consequently the segmentation results. The impact of large registration errors was also not investigated (partly due to the high registration precision of the acquired data), which might adversely affect the segmentation results. In such circumstances, it might be attractive to perform the presented algorithms for robust planar and linear segmentation on a single scan basis, and merge the results while incorporating registration inaccuracies. Furthermore, in the developed system, the impact of random measurement errors on the principal components  were estimated based on Monte Carlo simulation of point clouds from a significant number of randomly oriented planes/lines subjected to random instrumental measurement errors. Monte Carlo simulation was adopted since currently an analytical solution to the impact of correlated random measurement errors on the principal components does not exist. Therefore, the development of a closed-form solution to the problem is an interesting topic for future research. Currently, a new method is under development to address the aforementioned limitations.