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# Gaze, visual, myoelectric, and inertial data of grasps for intelligent prosthetics

## Abstract

A hand amputation is a highly disabling event, having severe physical and psychological repercussions on a person’s life. Despite extensive efforts devoted to restoring the missing functionality via dexterous myoelectric hand prostheses, natural and robust control usable in everyday life is still challenging. Novel techniques have been proposed to overcome the current limitations, among them the fusion of surface electromyography with other sources of contextual information. We present a dataset to investigate the inclusion of eye tracking and first person video to provide more stable intent recognition for prosthetic control. This multimodal dataset contains surface electromyography and accelerometry of the forearm, and gaze, first person video, and inertial measurements of the head recorded from 15 transradial amputees and 30 able-bodied subjects performing grasping tasks. Besides the intended application for upper-limb prosthetics, we also foresee uses for this dataset to study eye-hand coordination in the context of psychophysics, neuroscience, and assistive robotics.

 Measurement(s) muscle electrophysiology trait • eye movement measurement • first person video • body movement coordination trait • head movement trait • eye-hand coordination Technology Type(s) electromyography • eye tracking device • Accelerometer • accelerometer and gyroscope • data transformation Factor Type(s) age • sex • handedness • amputation side • amputation cause • years since amputation • residual limb length • prosthesis Sample Characteristic - Organism Homo sapiens

Machine-accessible metadata file describing the reported data: https://doi.org/10.6084/m9.figshare.11672442

## Background & Summary

The human hand has a fundamental role in many aspects of everyday life. Its morphological structure not only makes it one of the distinctive characteristics of the human species, but it also provides us with unique manipulative abilities1,2. We use it to sense and interact with the environment and it has an essential role in social interactions and communication. Losing a hand therefore has severe physical and psychological consequences on a person’s life. Myoelectric hand prostheses have enabled amputees to restore some of the missing functionality. In their conventional form, prostheses use surface electromyography (sEMG) from an antagonist pair of muscles to open and close a simple gripper. A large number of pattern recognition (PR) approaches have been developed over the years aiming to increase the functionality and control of more dexterous prostheses3,4,5. Despite these efforts, PR-based prostheses have not managed to deliver their full potential in practical clinical applications6,7. One of the primary causes is that they are sensitive to the variability of sEMG, limiting the robustness and reliability in long-term practical applications4,8,9,10,11,12,13,14. This limitation is inherent in the use of sEMG as a control modality, since myoelectric signals are known to depend on factors such as electrode displacement, inconsistency of the skin-electrode interface, changes in arm position, and characteristics of the amputation.

Several techniques have been proposed to address this variability and thus improve the stability of the prosthetic control4,11,15,16. One approach relies on fusing sEMG with complementary sources of information, such as gaze and computer vision17,18,19,20. Studies on eye-hand coordination have in fact shown that gaze typically anticipates and guides grasping and manipulation21,22,23. In other words, humans will look at an object they intend to grasp before executing the movement itself. Gaze behavior therefore holds valuable information for recognizing not only the intention to grasp an object, but also to identify which object the person intends to grasp. The set of likely grasps can then be estimated based on the size, shape, and affordances of this object. For large objects, this may be further refined by considering the exact part or side of the object on which the person fixates.

There are two compelling motivations for using gaze behavior in the context of upper limb prosthetics. The first is that gaze behavior is not necessarily affected by the amputation. Any information on muscular activation recorded from the residual limb, such as sEMG, is inherently degraded due to muscular reorganization after the amputation and subsequent atrophy due to reduced use. The second advantage is that integrating some level of autonomy in a prosthesis can lower the physical and psychological burden placed on its user. Fatigue is one of the causes of variability in sEMG data24,25,26, so reducing it can help to stabilize control.

This paper presents the MeganePro dataset 1 (MDS1) acquired during the MeganePro project, which was designed based on the experience gained during the NinaPro project27. The goals of the MeganePro project were to investigate the use of gaze and computer vision to improve the control of myoelectric hand prostheses for transradial amputees, and to better understand the neurocognitive effects of amputation. This dataset was acquired to explore the first goal: it contains multimodal data from 15 transradial amputees and 30 able-bodied subjects while involved in grasping and manipulating objects using 10 common grasps. Throughout the exercise, we acquired sEMG and accelerometry using twelve electrodes on the forearm. Gaze, first person video, and inertial measurements of the head were recorded using eye tracking glasses.

In the following sections, we describe the experimental protocol, the processing procedures, and the resulting data records. Although prosthetic control was our motivation for acquiring this dataset, it is our belief that the data will find broader applications. For instance, scientists working in neuroscience, psychophysics, or rehabilitation robotics may use it to study gaze and manipulation independently as well as via their coordination. In particular, the data allow direct comparison of able-bodied subjects and transradial amputees in an identical experimental setting. As such, it may contribute not only to develop better prostheses but also a better understanding of human behavior and the implications of amputation.

## Methods

The acquisition of the dataset consisted of defining an experimental protocol and determining the requirements in terms of devices and software. A general overview of the setup and protocol is shown in Fig. 1. Once the ethical approval was obtained, we proceeded with subject recruitment. In the following, all these phases are described in detail.

### Ethical Requirements

The experiment was designed and conducted in accordance with the principles expressed in the Declaration of Helsinki. Ethical approval for our study was requested to and approved by the Ethics Commission of the canton of Valais in Switzerland (CCVEM 010/11) and by the Ethics Commission of the Province of Padova in Italy (NRC AOP1010, CESC 4078/AO/17). Prior to the experiment, each subject was given a detailed written and oral explanation of the experimental setup and protocol. They were then required to give informed consent to participate in the research study.

### Subject Recruitment

A total of 15 transradial amputees and 30 able-bodied subjects were recruited for this study. The former group consists of 13 male and 2 female (13.3%) participants with an average age of (47.13 ± 14.16) years. As seen in Table 1, among them are diverse causes for amputation and different preferences with respect to prosthetic use. To remove possible confounding variables, we recruited a control group of able-bodied participants that matched the former group as much as possible in terms of age and gender. This group is composed of 27 male and 3 female (10.0%) subjects, with an average age of (46.63 ± 15.11) years.

### Acquisition Setup

We designed an acquisition setup that allowed us to perform eye tracking and to acquire sEMG from the forearm, while leaving the subjects as free as possible in their movements. Custom developed software interfaced with the acquisition devices and provided stimuli instructing the subjects when to grasp which object.

#### Sensors

The electrical activity of the forearm muscles was recorded with a Delsys Trigno Wireless sEMG System (Delsys Inc., USA, http://www.delsys.com/). This system consists of sEMG electrodes with an inter-sensor latency lower than 500 μs and a signal baseline noise lower than 750 nV Root Mean Square (RMS). In addition, a three-axial accelerometer is embedded in each electrode. Up to 16 electrodes communicate wirelessly with the base station, which is connected through a USB 2.0 cable to the acquisition laptop. The sEMG data are sampled at 1926 Hz and the accelerometer at 148 Hz. The accelerometer range was set at ±1.5 g, for which the device documentation reports a noise of 0.007 g RMS. The corresponding offset error is ±0.201 g for the X and Y axes and (0.201 to −0.343) g for the Z axis28.

The gaze behavior and first person video were recorded with the Tobii Pro Glasses 2 (Tobii AB, Sweden, http://www.tobiipro.com/). The head unit of this device is similar to regular eyeglasses and equipped with four eye cameras recording the eye movement, a camera capturing the scene in front of the subject, an Inertial Measurement Unit (IMU), and a microphone. It weighs only 45 g and corrective lenses can be applied for subjects with visual deficit. The eyes are tracked using corneal reflection and dark pupil methods with automatic parallax and slippage compensation. These eye tracking data are sampled at 100 Hz with a theoretical accuracy and precision of 0.5° and 0.3° RMS29. Video with Full HD resolution (1920 px × 1080 px) is recorded at 25 fps by the scene camera with a horizontal and vertical field of view of approximately 82° and 52°. The head unit is connected via a cable to a portable recording unit that is responsible for transmitting the data wirelessly and storing them on a memory card. A rechargeable and replaceable battery powers both head and recording units and provides a maximum recording time of approximately 120 min. The system can quickly and easily be calibrated with a single point calibration procedure.

#### Acquisition Software

The role of the acquisition software is to simultaneously acquire and store the data from all sensor devices, and to guide the subject through the exercises. To ensure high performance and low latency, the application was developed in C++ and based on the multithreaded producer-consumer pattern, as implemented in CEINMS30. More specifically, for each data source there is a dedicated producer thread responsible for acquiring its data, assigning a high-resolution timestamp, and then storing these in a queue. Per queue there is at least one consumer thread that stores available data to a file. The advantage of this architecture is that it uncouples the data acquisition from I/O latency when saving the data to a persistent storage.

A Graphical User Interface (GUI) developed in Qt5 (https://www.qt.io/) was added to the application to demonstrate using videos and images how to perform the exercises. In previous studies, such as NinaPro27, the subjects had to mimic a grasp movement that was shown in a video. This approach is not compatible with the present study, since it influences the subject’s gaze behavior. We therefore opted to avoid the need for visual attention and to instruct the subjects via vocal instructions during the real exercise. These instructions were automatically synthesized by a text-to-speech engine, which allowed us to prepare instructions in English, Italian, French, and German. At the start of the exercise subjects could choose the language they were most comfortable with.

#### Grasp Types and Objects

A total of ten grasp types were selected for our exercise from well-known hand taxonomies31,32,33,34 based on their relevance for Activities of Daily Living (ADLs)35. These grasp types were then matched with three household objects each that would regularly be manipulated using a given grasp. An overview of the ten grasp types and eighteen objects is given in Table 2. When possible, these pairings were chosen to obtain a many-to-many relationship between objects and grasp types; that is, a grasp could be used with multiple objects and vice versa. This requirement helped to limit the possibility that the mere presence of an object would be sufficient to unequivocally determine the grasp type.

In the case that an object is not usually found on a table (e.g., a door handle or a door lock), a custom made support was created. To avoid complications during the exercise, the key, bulb, lid of the jar, and the screw used with the screwdriver were modified such that they could not be completely removed from the support. Furthermore, the pull tab of the can was bent to facilitate the execution of the grasp.

During the exercise, at least five objects were simultaneously placed in the scene with a predefined position. The presence of multiple objects in front of the subjects helped to simulate a real environment, while a standardized object arrangement minimized the possibility of an error during the placement of the objects. In addition, these objects were spread throughout the subject’s reachable workspace so that grasps had to be performed while reaching in various directions.

### Acquisition Protocol

After the ethical requirements were fulfilled, the subject’s data, such as age, gender, height, weight, and handedness were collected. The amputees were asked additional information regarding the amputation, such as cause, type, years since amputation, and prosthesis use. A summary of this information is reported in Table 1.

The subjects were asked to sit with the forearm comfortably leaning on a desk and, for amputees, to remove the prosthesis. The skin was cleaned with isopropyl alcohol and twelve sEMG electrodes were placed in two arrays around the right forearm or residual limb. An array of eight electrodes was placed equidistantly around the forearm, starting at the radio-humeral joint and moving in the direction of pronation. A second array was located approximately 45 mm more distally and aligned with the gaps between electrodes one and two, three and four, and so on (see Fig. 1). In addition to the Trigno-specific adhesive strips, a latex-free elastic band was wrapped around the electrodes to assure a good and reliable interface with the skin. As widely done in the field of PR myoelectric control, the sEMG electrodes were placed around the proximal part of the forearm, where most of the extrinsic muscles of the hand lie, following an untargeted approach5. This approach consists of several equidistantly placed electrodes, recording the forearm (intact or residual) musculature’s electrical activity from multiple sEMG sites, without targeting any specific muscles or muscle parts36.

The subject was then asked to wear the Tobii Pro glasses, where we made sure to choose the nose pad that aligned the eye tracking cameras’ appropriately. Once the subject felt ready, the Tobii Pro glasses were calibrated using the built-in one point target calibration procedure and, in case of success, the subject was asked to perform a calibration assessment. This assessment consisted in asking the subject to fixate a black cross against a green background that was displayed on a monitor at a distance of about 1.3 m. This cross remained fixed for 3 s in the same location before alternating to another one out of five positions in total.

The actual exercise consisted of repeatedly executing the grasps on the set of corresponding objects, as described in Table 2. In the first part, which we refer to as static, subjects were requested to grasp the objects without actually moving or lifting them. Prior to executing a grasp, videos in first and third person perspectives demonstrated the grasp and the three corresponding objects. The subjects were however instructed to execute the movements spontaneously, rather than trying to mimic the exact kinematics of the demonstration videos. Amputees were asked to attempt executing the movements as naturally as possible, as they would intuitively perform the grasp with the missing hand. During these videos, the subject was free to decide whether to perform or not the grasps to get confident about the exercise. Once the grasp and objects had been shown, the subject had to repeat each combination four times while seated and then another four times while standing. This change in position was intended to include variability in the limb position in the data. The duration of the movement and rest periods depends on the selected language for the vocal instructions. A grasp interval lasted approximately 5.2 s, 5.7 s, 5.9 s, and 6.0 s for English, Italian, French, and German. A rest period followed for about 4.1 s, 4.7 s, 4.7 s, and 4.7 s for English, Italian, French, and German. The exact order of the objects within each repetition was randomized to avoid learning and habituation effects. A vocal command guided the subject through the exercise, indicating which object to grasp, when to return to the rest position, and when to stand up or sit. These instructions were accompanied by a static image of the current grasp type, which was intended as an undistracting reminder of the stimulus. When finishing a grasp series, an experimenter changed the object scene when necessary before resuming with the next grasp.

The static part of the exercise was followed by a dynamic one. This second part followed the same structure as the first, but in this case the grasp had to be used to perform a functional task with an object. The motivation for this variation was again to introduce variability into the data but this time by means of a dynamic, goal-oriented movement. As can be seen in Table 3, these functional movements reflect common activities with the combination of grasp type and object, such as drinking from a can held with a medium wrap. To limit the total duration of the exercise, the ten grasps were only combined with two objects each and executed either standing or seated. This position was chosen based on how the action would usually be performed in real life, for instance a door is more frequently opened while standing.

After the exercise finished the amputated subjects underwent three more exercises and a comprehensive questionnaire to investigate the neurocognitive effects of the amputation. The data and results of those exercises and the questionnaire will be published separately.

### Post-Processing

Several processing steps were applied to the raw data acquired with the protocol described above. The objective of these steps was to sanitize the data, synchronize all modalities, and remove identifying information from the videos. In the following, we describe all procedures in detail.

#### Timestamp Correction

Due to an unfortunate implementation error, during a number of acquisitions the modalities were assigned timestamps from individual clocks. To unify all timestamps in a shared clock, the offset of all clocks was estimated and corrected with respect to the clock of the sEMG modality using statistics of their relative timing collected during trial acquisitions. Validations on the remaining unaffected acquisitions confirm that the maximum deviation of our estimate from the ground truth is less than 12 ms.

#### sEMG and Accelerometer Data

For computational efficiency, the sEMG and accelerometer streams from the Delsys Trigno device were acquired and timestamped in batches. During post-processing, individual timestamps were assigned to each sample via piecewise linear interpolation. A new piece is created if the linear model results in a deviation of more than 100 ms, which may happen if the fit is skewed due to missing or delayed data.

For the sEMG data, we furthermore filtered outliers by replacing samples that exceeded 30 standard deviations from the mean within a sliding window of 1 s with the preceding sample. The signals were subsequently filtered for power-line interference at 50 Hz (and its harmonics) using a Hampel filter, which interpolates the spectrum in processing windows only when it detects a clear peak37. Contrary to the more common notch filter, this method does not affect the spectrum if there is no interference.

#### Gaze Data

The data from the Tobii Pro glasses were acquired as individually timestamped JavaScript Object Notation (JSON) messages. During post-processing, these messages were decoded and separated based on their type. Messages that arrived out-of-order were filtered and the resulting set of messages was used to determine the skew and offset between the computer clock and the one of the Tobii Pro glasses. This routine removes the constant part of the transmission delay as much as possible, while avoiding the possibility to antedate any events. The messages that relate directly to gaze information, such as gaze points, pupil diameter and so on, were then grouped together based on their timestamps.

#### Stimulus

The text-to-speech engine that was used to give vocal instructions introduced noticeable delays in the corresponding changes of the stimulus. We measured these delays for all sentences and languages, and moved the stimulus changes forward by these amounts during post-processing. Furthermore, small refinements were made to the object column, whereas its more specific object-part counterpart was calculated based on a fixed mapping from the original stimulus information.

#### Synchronization

For the standard data records (see the following section) all modalities were resampled at the original 1926 Hz sampling rate of the sEMG stream. For real-valued signals, this was done using a linear interpolation, while for discrete signals we used a nearest-neighbor interpolation. The signals that indicate the time and index of the MP4 video were handled separately using a custom routine, since they require to identify the exact change-point where one video transitions to the next.

#### Concatenation

The static and dynamic parts of the protocol were acquired independently and therefore produced separate sets of raw acquisition files. Furthermore, our acquisition protocol and software allowed to interrupt and resume the acquisition, either at request of the subject or to handle technical problems. After applying the previous processing steps to the individual acquisition segments, they were concatenated to obtain the standard data record. During this merging, we incremented the timestamps and video counter to ensure that they are monotonically increasing. Furthermore, if part of the protocol was repeated when resuming the acquisition, we took care to insert the novel segment at exactly the right place to avoid duplicate data.

#### Relabeling

The response of the subject and therefore the sEMG activation may not be aligned perfectly with the stimulus. As a consequence, the stimulus labels around the on- or offset of a grasp movement may be incorrect, resulting in an undue reduction in recognition performance. We addressed this shortcoming by realigning the stimulus boundaries with the procedure described by Kuzborskij et al.38. In short, this method optimizes the log-likelihood of a rest-grasp-rest sequence on the whitened sEMG data within a feasible window that spans from 1 s before until 2 s after the original grasp stimulus. As opposed to the uniform prior used in the earlier method, we adopted a smoothed variant of the original stimulus label as prior. The advantage is that for trials without a clear difference in muscular activity during rest and the movement (i.e., the “evidence”), we recover the original label boundaries. Based on visual inspection of the updated movement boundaries, we assigned a certainty of $$p=0.6$$ to this prior and selected a Gaussian filter with $$\sigma =0.5\,{\rm{s}}$$ as smoothing operator. The recalculated stimulus boundaries were saved in addition to the original ones.

#### Removing Identifying Information

All videos were checked manually for identifying information of anyone other than the experimenters. The segments of video that were marked as privacy-sensitive were subsequently anonymized with a Gaussian blur. In this procedure, we took care to re-encode only the private segments and to preserve the exact number and timestamps of all frames. In addition, the audio stream was removed from all videos for privacy reasons.

## Data Records

The data that were acquired and processed with the described methodology are stored in the Harvard Dataverse repository39. For each subject, this repository contains two data files in Matlab format (http://www.mathworks.com) and a series of corresponding videos encoded with MPEG-4 AVC in an MP4 container. The dataset39 is provided with the DatasetContentCRC.sfv file, which contains a description of the dataset structure together with the Cyclic Redundancy Check (CRC) value for each file. This document can therefore be used to investigate how the dataset is structured as well as to verify the correctness of the downloaded data. The primary data file contains the concatenated sEMG data at their original sampling rate, to which all other modalities were resampled. An exhaustive listing of all the fields in these files together with a description is provided in Table 4. Further information regarding the content of the fields are described below:

• The fields (re)grasp, (re)object, and (re)objectpart contain the grasp, object, and objectpart IDs as described in Tables 2 and 3.

• The emg field typically (see the Usage Notes section) contains 12 columns: columns 1–8 refer to the signals of the electrodes forming the proximal array while columns 9–12 the signals of the electrodes forming the distal array.

• The same structure is maintained for the acceleration data in the acc field, in which groups of 3 columns are used to report the acceleration in the X, Y and Z axes for each electrode. In all the electrodes, the X axis is parallel to the forearm, the Z axis is orthogonal to the forearm surface, and the Y axis obeys the right-hand rule28.

• The gazepoint field contains the position of the gaze point relative to the video frame expressed in $$(x,y)$$ coordinates, having the origin of the coordinate system in the top left corner40.

• The fields gazepoint3D, pupilcenterleft, pupilcenterright, gazedirectionleft, and gazedirectionright are expressed in $$(x,y,z)$$ coordinates relative to the scene camera reference system, which has origin in the center of the camera, X axis pointing to the subject’s left, Y axis pointing upwards, and the Z axis obeying the right-hand rule40. The gazedirectionleft and gazedirectionright fields are unit vectors, with the respective left and right pupil centers as origin.

• The angular velocity and the acceleration of the Tobii Glasses in the X, Y, and Z axes are contained in the tobiigyr and tobiiacc fields40.

Since resampling may not always be desirable due to its impact on the the signal spectrum, we also provide an auxiliary data file with all non-sEMG modalities at their original sampling rate. Each of these includes a timestamp column, which can be used to synchronize them with each other or with the sEMG data in the primary data file. The fields and their detailed specification is shown in Table 5.

## Technical Validation

Our intended purpose for the dataset is to investigate the fusion of sEMG with gaze behavior. In this section we therefore concentrate on validating these two modalities. Some of these analyses are low-level to ensure the quality of the recorded signals, while others are meant to verify that the data can in fact be used for the motivations and objectives for which they were created.

### Gaze Data

#### Error Validation

The quality of gaze data primarily depends on the correctness of the initial calibration phase of the Tobii Pro glasses. Validating the effectiveness of this calibration consists of acquiring gaze data while the user is focused on a known target and subsequently comparing the measured gaze location with this ground truth41,42. We used the data recorded during the calibration assessment described in the Acquisition Protocol section to evaluate the effectiveness of the calibration as well as possible quality degradation. These data were typically collected at the beginning and end of an exercise. If the exercise was interrupted, the procedure was shown again before resuming it. We determined the ground truth by manually locating the cross position in pixels at intervals of 0.2 s using custom software. Since we also included calibration data for the other exercises done jointly as part the MeganePro project, a total of 498 acquisitions were processed in this manner.

The quality of eye tracking is often quantified in terms of accuracy and precision41,43. For each axis, the former measures the systematic error, that is, the mean offset between the actual and expected gaze locations. Precision, on the other hand, measures the dispersion around the gaze position and thus the random error of the gaze point. In Fig. 2 these values are visualized with respect to the location within the video frame. This separation is intentional, as the eye tracking appears to be more accurate and precise in the center of the frame, namely (−3.5 ± 19.4) px and (−1.5 ± 29.6) px on the x and y axes. Moving away from the center, the gaze results systematically shift towards the borders of the frame and its random error increases. We only visualize regions where we acquired at least 40 validation samples. Pooling all data, the overall accuracy and precision is (−0.8 ± 25.8) px and (−9.9 ± 33.6) px on the horizontal and vertical axes. At a typical manipulation distance of 0.8 m, this corresponds to a real-world precision and accuracy of approximately (−0.4 ± 11.5) mm and (−4.4 ± 14.9) mm. This is deemed sufficiently accurate considering the size of the household objects used in our experimental protocol.

To establish whether the calibration deteriorated over time, we compared the accuracy and precision collected at the beginning of an acquisition with those taken at the end. In total, we considered 210 uninterrupted acquisitions in which there was a calibration validation routine both at the beginning and the end. We found no statistically significant difference in accuracy (sign test, $$p=0.95$$ and $$p=1.0$$ in the horizontal and vertical axes) or precision (sign test, $$p=0.24$$ and $$p=0.37$$) indicating that drift does not pose an issue for the gaze data.

#### Statistical Parameters

To statistically describe a user’s gaze behavior during the exercises and validate it against related literature, we first identified fixations and saccades in our eye tracking data using the Identification Velocity Threshold (IVT) method44. To ensure that we could calculate the angular velocity of both eyes for a maximum number of samples, we linearly interpolated gaps of missing pupil data when shorter than 0.075 s45. We used a threshold of 70°/s to discriminate between fixations and saccades46. When the Tobii Pro glasses failed to produce a valid eye-gaze point, even after interpolating small gaps, the corresponding sample was marked as invalid. Excluding one subject who had strabismus, the percentage of such invalid samples ranged between (1.7 to 21.0)% and (4.3 to 30.7)% for able-bodied and amputated subjects. Sequences of events of the same type were then merged into segments identified by a time range and processed following the approach described by Komogortsev et al.46. First, to filter noise or other disturbances, fixations separated by a short saccadic period of less than 0.075 s and 0.5° amplitude are merged. Second, fixations shorter than 0.1 s are marked as invalid and are excluded from the analysis.

In the resulting sequence of gaze events, the majority of invalid data are located between two periods of saccades, namely (92.2 ± 2.7)% and (92.6 ± 3.9)% for able-bodied and amputated subjects. This indicates that the Tobii Pro glasses fail predominantly to register high velocity data. Devices with sampling frequency lower than 250 Hz have indeed been categorized as “fixation pickers”47 and often do not provide reliable results for all saccades. For this reason, in the following analysis we concentrate on fixation events.

Figure 3 shows the distribution of the duration of fixations for both types of subjects. The characteristics of these distributions, summarized in Table 6, coincide with those described in analogous studies21,48,49. For instance, the mean values are similar to the mean duration of around 0.5 s reported by Hessels et al.50. Moreover, both the median duration and the range between the 25th and 75th percentile are comparable with the results of Johansson et al.21, who report 0.286 s as median duration and (0.197 to 0.536) s as range between the same percentiles. These similarities confirm the quality of the eye tracking data and highlight that the subjects maintained a natural gaze behavior throughout the exercise.

Since one of the intended uses of these data is to investigate gaze behavior in anticipation of object manipulation, we also verified that subjects indeed looked at the object when asked to manipulate it. With the help of an automated approach to detect objects, we determined for each grasp trial whether the distance between the gaze point and the boundary of the object of interest was at least once lower than 20 px. On average, this was the case in 95.9% of the subject’s trials. Manual examination of the remaining 4.1% indicated that the fixation exceeded the distance 20 px not because of lack of subject engagement, but due to a low accuracy calibration of the Tobii Pro glasses. Regardless of this, in the vast majority of the trials the subjects visually located and fixated the object prior to its manipulation. For purely illustrative purposes, an example of gaze behavior of an able-bodied subject while grasping a door handle and a bottle is given in Fig. 4.

### Myoelectric signals

#### Spectral Analysis

To assure the soundness of the recorded sEMG, we first analyzed the spectral properties and compared these with known results from the literature. For each subject and for each channel, we calculated the power spectral density via Welch’s method with a Hann window of length 1024 (approximately 530 ms) and 50% overlap. Figure 5a shows the distribution over these densities via its median and the range between the 10th and 90th percentiles. The first observation is that nearly all of the energy of the signals is contained within (0 to 400) Hz, as is typical for sEMG51. Furthermore, there is no sign of powerline interference at 50 Hz or its harmonics, confirming the efficacy of the filtering approach detailed in the previous section.

We do however observe a rather large variability of densities among subjects and electrodes. The reason is that the spectrum and amplitude of sEMG depend on the exact position of an electrode over a muscle24. In our protocol, none of the electrodes was positioned precisely on a muscle belly, thus causing a wide variety in the spectrum. In some cases, the signal may even be almost absent (e.g., an electrode over the radial bone).

The same variability is also noticeable in Fig. 5b, which reports the distribution of the median frequency over all subjects and electrodes throughout the entire exercise. The median frequencies we find are close to the approximately (120 to 130) Hz typically reported for the flexor digitorum superficialis52,53, which is one of the muscles we primarily recorded from with our electrode positioning. Finally, we note that the distribution of the median frequency remains relatively stable over time, indicating that there are no persistent down- or upward shifts in the spectrum.

#### Grasp Classification

As a more high-level validation of the sEMG signals, we verify that these can indeed be used to discriminate the grasp a subject was performing, which is one of the anticipated applications of this dataset. We employ the standard window-based classification approach described by Englehart and Hudgins54 with a window length of 400 samples (approximately 208 ms) and 95% overlap between successive windows. As feature-classifier combinations we consider:

• a (balanced) Linear Discriminant Analysis (LDA) classifier used with the popular four time-domain features54;

• k-Nearest Neighbors (KNN) applied on RMS features55; and

• Kernel Regularized Least Squares (KRLS) with a nonlinear exponential $${\chi }^{2}$$ kernel and marginal Discrete Wavelet Transform (mDWT) features55,56.

As commonly done in the field, a within-subject classification was performed. In contrast to prior work where we employed a single train-test split55,56, the classification accuracy is defined here as the average accuracy of 4-fold cross validation. In each of these folds, one of the four repetitions per grasp-object-position combination was used as held-out test data, while the remaining three repetitions formed the training data. Similarly, any hyperparameters were optimized via nested 3-fold cross validation on the train repetitions. For all methods, the training data were downsampled with a factor of 10 for computational reasons, while the data used for hyperparameter optimization were downsampled with an additional factor of 4.

The results in Fig. 6 show a median classification accuracy between 63 and 82% for either able-bodied or amputated subjects, depending on the classification method. This is significantly higher than the approximately 50% accuracy a baseline classifier would achieve by simply predicting the most frequent rest class, confirming the discriminative power of the sEMG signals for the grasp type. Although a quantitative comparison with related work is of limited value due to discrepancies in experimental setup and protocol, the current results are a few percentage points higher than those presented by Atzori et al.55. The most likely explanation is the lower number of grasps (i.e., only 10 rather than 40), which inevitably boosts performance. For amputees, the fact that we are considering subjects with different clinical parameters from previous studies may contribute to influence the performance difference, since it has been shown that remaining forearm length, phantom limb sensation intensity, and years passed since the amputation can influence the classification outcome57.

## Usage Notes

### Relabeling

The data records come with both the original stimulus as well as a variant that has been aligned to actual sEMG activation (see the Post-Processing section). The latter variant is preferable when the stimulus is used as ground-truth of the grasp type, such as grasp recognition, since it reduces the number of incorrect labels due to response times. In other studies one may actually be interested in these response times, such as when investigating the psychophysical response to the vocal instruction. In these cases we advise users to use the original stimulus.

### Trial Repetitions

In the experimental protocol, each new grasp started with two videos in first and third person perspective per object to introduce the subject to the grasp and the objects. Although subjects were encouraged to practice the grasps during this phase, some of them did not do this and focused on the video on the computer screen. For this reason, the hand and gaze behavior are unreliable and users of the dataset are advised to remove movements where the (re)objectrepetition column has a value of −3 or −2.

### sEMG & Accelerometer Data

A problem with sEMG and accelerometer data concerned electrode number 8 (the 8th column of the emg field and the 22nd, 23rd, and 24th columns of the acc field). Unfortunately, the data from this electrode seem unreliable. Myoelectric and accelerometer data recorded by this electrode sometimes have a substantially lower amplitude than the others, indicating a probable hardware issue. We therefore recommend to carefully consider this aspect when using the data.

Accelerometer data are known to be affected by systematic errors and noise. Therefore, we applied the method described in Tedaldi et al.58 to estimate the calibration parameters for the accelerometers embedded in the Delsys Trigno electrodes as well as for the IMU of the Tobii glasses. The parameters and the original data are provided in the archive accelerometer_calibration.tgz.

#### S024

Due to the difficulties reported in the previous subsection, no myoelectric data were received from electrode number 8 during this acquisition. Therefore, the sEMG and accelerometer data for this subject were recorded from eleven electrodes instead of twelve.

#### S115 & S039

The small circumference of these participants’ residual limb and forearm prevented the placement of 8 electrodes in the proximal array. For these two subjects only, the proximal array was composed of 7 electrodes and the distal one with the usual 4 electrodes. The corresponding emg field has therefore 11 columns instead of 12 as well as the acc field, which is composed of 33 columns and not 36 as for the other subjects.

#### S108

The high amputation level of S108 prevented the placement of the second array of electrodes. Therefore, only the first array consisting of eight electrodes was placed on the residual limb of this subject.

### Gaze

It is known that various factors, such as physical characteristics of the test participant, recording environment, eye tracker features, and quality of calibration affect the gaze data quality41. The experiment was intentionally relatively unconstrained (e.g., the head was not fixed and subjects could move their torso) to encourage natural behavior. In the following cases we have identified potential problems with gaze data that may require consideration.

#### S111

A high percentage (~30%) of invalid gaze data were obtained for this subject. This is probably due to this participant’s specific eye physiology, which is known to influence the tracking performance42,59. The gaze data are included in the dataset for completeness.

#### S114

For this subject, calibration could not be performed due to strabismus. In such cases, the Tobii Pro glasses use a built-in default calibration. This allowed us to continue the experiment, but the quality of eye tracking is significantly worse40. The difficulty in tracking the subject’s eye in this particular condition is highlighted by the high proportion of invalid gaze samples (~50%). Although included in the dataset, the use of the gaze data for this subject should be carefully evaluated.

#### S115

A specific physical condition of this subject prevented a stable placement of the Tobii Pro glasses. The slippage compensation of the device may have helped to limit the consequences, as the proportion of invalid gaze samples (~10%) indicates a proper tracking of the eye. This condition should nonetheless be taken into account when analyzing the gaze and Tobii Pro glasses’ IMU data for this subject.

### Video

MPEG transport stream (MPEG-TS) videos were recorded wirelessly via the Tobii Pro glasses Application Programming Interface (API). The fields pts, tspipelineidx, and tsvideoidx of the data records serve to synchronize the data with these videos. We however release only the MP4 videos, this for two main reasons: to limit the size of the dataset and to ensure a high quality of the scene camera videos, since the MP4 videos were immune to packet loss problems.

### Communication

Being able to select among four languages allowed the subjects to choose the one they were most comfortable with and, in most cases, it corresponded to their native language. For S111 only, none of the languages available in the acquisition software were appropriate. We were however able to communicate in Italian and, in case of difficulties, communication was facilitated by a relative of the subject translating from Italian to the subject’s native language.

## Code availability

The post-processing procedure described above was implemented in Matlab and executed in compiled form with Matlab 2016b. The relabeling procedure was implemented in Python and interpreted with Python 3.6. Censoring of the videos was done using a custom Bash script that interfaced with the FFmpeg 4.1.3 video manipulation tool. The GNU Parallel tool was used to run jobs in parallel60. A copy of the code that was used to create the data records from the raw recordings is publicly available in the megane_postprocess.tgz archive within the MDSScript61. This archive also contains a README file that lists and describes the main processing steps. Although the original data files cannot be released for privacy reasons, the code is made available to allow the user to thoroughly investigate and comprehend the procedure we used to process the data as well as to provide the community with a tool that can be re-used and re-adapted for similar tasks.

## Change history

• ### 17 February 2020

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

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## Acknowledgements

This work was supported by the Swiss National Science Foundation Sinergia project #160837 “MeganePro” and by the Hasler Foundation in the project ELGAR PRO. We thank the subjects for their participation in the Myo-Electricity, Gaze And Artificial-intelligence for Neurocognitive Examination & Prosthetics (MeganePro) project. We thank Prof. G. Pajardi, Dr. E. Rosanda, and the team of the hand surgery and rehabilitation department of the Ospedale San Giuseppe MultiMedica Group in Milan, Italy for their help in recruiting subjects for this study. Furthermore, we thank Mara Graziani, Francesca Giordaniello, and Francesca Palermo for their help in developing a preliminary version of the acquisition protocol and testing the acquisition software.

## Author information

Authors

### Contributions

M.C. created the acquisition protocol, developed the acquisition software, performed data acquisition, and wrote the paper. A.G. created the acquisition protocol, developed the post-processing procedure and software, performed data analysis, and wrote the paper. V.G. created the acquisition protocol, performed data analysis, and wrote the paper. G.S. helped with the creation of the acquisition protocol and with the data acquisition, obtained ethical approval, and reviewed the paper. K.G. recruited the participants, helped with the data acquisition, checked the videos for private data, and reviewed the paper. A.-G.M.H., C.T. and F.B. recruited the participants and reviewed the paper. A.G. helped with the post-processing software, performed data analysis, and reviewed the paper. D.F. recruited the participants, helped with the data acquisition and reviewed the paper. B.C., P.B. and H.M. ideated the project and reviewed the paper. M.A. ideated the project, created the acquisition protocol, obtained ethical approval, helped with the data acquisition, and reviewed the paper.

### Corresponding authors

Correspondence to Matteo Cognolato or Manfredo Atzori or Henning Müller.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Rights and permissions

The Creative Commons Public Domain Dedication waiver http://creativecommons.org/publicdomain/zero/1.0/ applies to the metadata files associated with this article.

Reprints and Permissions

Cognolato, M., Gijsberts, A., Gregori, V. et al. Gaze, visual, myoelectric, and inertial data of grasps for intelligent prosthetics. Sci Data 7, 43 (2020). https://doi.org/10.1038/s41597-020-0380-3

• Accepted:

• Published:

• ### Gaze, behavioral, and clinical data for phantom limbs after hand amputation from 15 amputees and 29 controls

• Gianluca Saetta
• , Matteo Cognolato
• , Manfredo Atzori
• , Diego Faccio
• , Katia Giacomino
• , Anne-Gabrielle Mittaz Hager
• , Cesare Tiengo
• , Franco Bassetto
• , Henning Müller
•  & Peter Brugger

Scientific Data (2020)


text:
# zbMATH — the first resource for mathematics

Smoothness of solenoidal attractors. (English) Zbl 1106.37015
The authors deal with dynamical systems generated by skew products of affine contractions on the real line over angle-multiplying maps on the circle $$S^1= \mathbb{R}/\mathbb{Z}$$: $T: S^1\times\mathbb{R}\to S^1\times\mathbb{R},\quad T(x,y)= (\ell x,\lambda y+ f(x)),$ where $$\ell\geq 2$$ is an integer, $$\lambda\in (0,1)$$ and $$f\in C^r(S^1)$$, $$r> 3$$. The authors study the smoothness of the density of the SBR measure in more detail, and the mixing properties of $$T$$.

##### MSC:
 37C70 Attractors and repellers of smooth dynamical systems and their topological structure 37C40 Smooth ergodic theory, invariant measures for smooth dynamical systems 37C30 Functional analytic techniques in dynamical systems; zeta functions, (Ruelle-Frobenius) transfer operators, etc. 37A25 Ergodicity, mixing, rates of mixing 37E10 Dynamical systems involving maps of the circle
##### Keywords:
skew-product; mixing property; SBR measure; maps on the circle
Full Text:

format: plain


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# Instantaneous Velocity and Speed

#### description

• Speed and Velocity

## Instantaneous velocity and Instantaneous Speed

Instantaneous velocity
The rate of change of displacement of an object in a particular direction is its velocity. Its S.I unit is meter per second.

The direction of instantaneous velocity at any time gives the direction of motion of a particle at that point in time. The magnitude of instantaneous velocity equals the instantaneous speed. This happens because, for an infinitesimally small time interval, the motion of a particle can be approximated to be uniform.
v=lim_(Δt→0) (Δx)/(Δt)

We can use the above equation for obtaining the value of velocity at an instant either graphically or numerically. Suppose that we want to obtain graphically the value of velocity at time t = 4 s (point P) for the motion of the car.

• The figure has been redrawn in the above Fig. choosing different scales to facilitate the calculation. Let us take ∆t = 2 s centred at t = 4 s.

• Then, by the definition of the average velocity, the slope of line P1P2 (Fig. 3.6) gives the value of average velocity over the interval 3 s to 5 s. Now, we decrease the value of ∆t from 2 s to 1 s. Then line P1P2 becomes Q1Q2 and its slope gives the value of the average velocity over the interval 3.5 s to 4.5 s.

• In the limit ∆t → 0, the line P1P2 becomes tangent to the position time curve at the point P and the velocity at t = 4 s is given by the slope of the tangent at that point. It is difficult to show this process graphically. But if we use numerical method to obtain the value of the velocity, the meaning of the limiting process becomes clear.

It is difficult to show this process graphically. But if we use numerical method to obtain the value of the velocity, the meaning of the limiting process becomes clear.

For the graph shown above, x = 0.08 t^3. Table given below gives the value of ∆x/∆t calculated for ∆t equal to 2.0 s, 1.0 s, 0.5 s, 0.1 s and 0.01 s centred at t = 4.0 s. The second and third columns give the value of

(t-(∆t)/2) and t_2=(t+(∆t)/2)

and the fourth and the fifth columns give the corresponding values of x, i.e. x (t1) = 0.08 t1 3 and x (t2) = 0.08 t2 3. The sixth column lists the difference ∆x = x (t2) – x (t1) and the last column gives the ratio of ∆x and ∆t, i.e. the average velocity corresponding to the value of ∆t listed in the first column. We see from Table that as we decrease the value of ∆t from 2.0 s to 0.010 s, the value of the average velocity approaches the limiting value 3.84 m s–1 which is the value of velocity at
t = 4.0 s, i.e. the value of (dx)/dt at t = 4.0s.

In this manner, we can calculate velocity at each instant for motion of the car. For this case, the variation of velocity with time is found to be as shown in Fig. below.

 ∆t(s) t_1(s) t_2(s) x(t_1)(m) x(t_2)(m) ∆x(m) (∆x)/(∆t)(ms^-1) 2.0 3.0 5.0 2.16 10.0 7.84 3.92 1.0 3.5 4.5 3.43 7.29 3.86 3.86 0.5 3.75 4.25 4.21875 6.14125 1.9225 3.845 0.1 3.95 4.05 4.93039 5.31441 0.38402 3.8402 0.01 3.995 4.005 5.100824 5.139224 0.0384 3.8400

Instantaneous Speed

• The average velocity tells us how fast an object has been moving over a given time interval but does not tell us how fast it moves at different instants of time during that interval. For this, we define instantaneous speed. It is the rate of change of distance with respect to time.
v = (ds)/dt

• Instantaneous speed is always greater than or equal to zero and is a scalar quantity. For uniform motion, instantaneous speed is constant. To understand it in simple words we can say that instantaneous speed at any given time is the magnitude of instantaneous velocity at that time. It is a limit of the average speed as the time interval become very small.

• A moving object does not have the same speed during its travel. Sometimes it speeds up and sometimes slows down. At a given instant time what we read from the speedometer is instantaneous speed. When a cop pulls you over for speeding, he clocked your car’s instantaneous speed or speed at a specific point in time as your car sped down the road.

If you would like to contribute notes or other learning material, please submit them using the button below.

### Shaalaa.com

Straight line motion Part 3 (Speed and velocity) [00:06:22]
S
0%


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# Baryons and Baryonic Matter in Holographic QCD from Superstring - High Energy Physics - Theory

Baryons and Baryonic Matter in Holographic QCD from Superstring - High Energy Physics - Theory - Download this document for free, or read online. Document in PDF available to download.

Abstract: We study baryons and baryonic matter in holographic QCD using aD4-D8-$\bar{ m D8}$ multi-D-brane system in the superstring theory. We obtainthe chiral soliton solution for baryons in the four-dimensional meson theoryderived from the multi-D-brane system. For the analysis of finitebaryon-density matter, we investigate the chiral soliton on $S^3$ inholographic QCD, and find the delocalization of the soliton, i.e., the swellingof baryons in dense matter.

Author: Hideo Suganuma Kyoto U., Kanabu Nawa RCNP, Osaka U., Toru Kojo RIKEN-BNL

Source: https://arxiv.org/


text:
# Raptor Composite Aircraft

Discussion in 'Aircraft Design / Aerodynamics / New Technology' started by Dexacare, Mar 28, 2016.

### Help Support HomeBuiltAirplanes Forum by donating:

1. Jun 13, 2019

### rv6ejguy

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Very well said Bob.

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### Tom Nalevanko

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First of all, I never thought much of this design from the beginning. But I’m a guy who likes my wings on top! I do however admire the effort, speed and transparency of the build.

Agree on the comment that CFIs seem to know little about aircraft. Had a CFI friend who killed himself in a Questair after adding a turbonormalizer and not considering the CG implications with minimum fuel. He was also a medical professional and they seem to have problems with hard limits.

However I don’t accept the arguments that Peter had to pay his dues before designing a successful aircraft. Well, all Elon Musk did to design a rocket was read a couple of books. So he should not have founded SpaceX? There are first principle people who can do good designs. The difference may be that once they get a grounded mental model, they talk to LOTS of experts and have a good filter to take good advice.

So the saga continues, Peter won’t give up and we’ll see what happens. As for the believers who lost , think of it as cheap education.

Blue skies,

Tom

3. Jun 13, 2019

### BBerson

#### Well-Known MemberHBA Supporter

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Yeah, the CEO and owners call the shots, not the designers or engineers usually.
The Klapmeier's had to learn the "shaft" lessons with the first design before switching to aircraft engines. No doubt some concerns of experts were ignored. But they eventually had a product.

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4. Jun 14, 2019

### Andy_RR

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Haha! A cheap education! Today that's unfortunately very accurate, even at \$20k and probably better value!

5. Jun 14, 2019

### akwrencher

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Some life lessons you can't learn in school. 19 years ago I bought a wood fishing boat on the word of my neighbor that it was in good shape. It looked good too. Turned out to be rotten wood faired nicely with cement and epoxy. Paid off the 15k it cost and gave it away. Those lessons you remember. I survived, feeding three kids. I'm sure these guys will too. And they won't forget very quickly. Probably take a much closer look at their next investment.

6. Jun 14, 2019

### dcarr

#### Well-Known Member

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Here's what Peter has to say about the flexible coupling:
(https://www.youtube.com/channel/UCyEqCPjfEG1Cwt8-YEAOxbg/community)

A replacement for the broken Elpex has been found and ordered. It's a different product produced by Lord. Should be twice as strong and will slip instead of break if the torque max is exceeded. Shouldn't take too much effort to fit into our existing setup. Will show it in the next vid. We're back in the game!
...
Mat Helm the Elpex has 4 separate torque numbers, rated, max, fatigue and overload. They are 400nm, 800, 200 and 1000 respectively. My estimate is that the engine puts out max 700nm. The Elpex we chose was the one with the highest ratings. Obviously it was not enough. As with everything we needed to test it and now we have and it failed.
...
David Hanson no that's not the case. If it slips because of max exceeded torque it will stop slipping when the torque is reduced. Likewise the max torque of this one is 2260nm. Our engine probably maxes out at 750nm. I think that's enough margin.
...
[Question asking about coupling being limited to 3500rpm]
Martin Renschler actually the one I saw today is set up on a Dyno that has run to over 5000 rpm without a problem. However, it's easy enough to limit our engine to 3500rpm if necessary.
---
Looks to me like he's chosen a Lord LCD-0600 (edited---thanks BoKu) which has a "nominal RPM" of 2000. Lord says "Operation up to 3500 rpm is permitted with reduced misalignment."
(https://www.lord.com/sites/default/files/Dynaflex_LCD_Series_Couplings.pdf)

Last edited: Jun 14, 2019
7. Jun 14, 2019

### BoKu

#### Well-Known MemberHBA Supporter

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8. Jun 14, 2019

### BJC

#### Well-Known Member

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No problem: just add a little depleted uranium in the nose ….

BJC

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9. Jun 14, 2019

### BoKu

#### Well-Known MemberHBA Supporter

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To be fair, we don't know what the Elpex connector weighs. So it could go either way.

Edit add--Whatever connector they get, they should probably get two of them. My bet is that this rig is gonna eat them like popcorn. Near as I can tell they've done no TV analysis on this driveline (and little rigorous analysis of any type on it), so at this point they're just throwing stuff at the wall to see what sticks. I wish they'd get Ross in there with some accelerometers to see what they're actually up against.

Last edited: Jun 14, 2019
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10. Jun 14, 2019

### rv6ejguy

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If the system is in resonance, peak engine torque is meaningless since we've seen stuff go 30X over this value. Secondly, as discussed previously, you should never mount the drive to an external structure not directly bolted to the engine as has been done in this case. There will be serious misalignment between the crankshaft and PSRU when the engine is developing high torque and the rubber engine mounts distort due to that reaction. Using the coupler at or above its max RPM rating is also a bad idea, especially with the high misalignment likely to be present here. There are several other problems with the drive design discussed previously too.

Anyone who thinks using a 60 lb. drive coupler on an aircraft is a good idea needs a slap in the head. The entire 300 hp PSRU on my RV weighs 54 lbs., including the flywheel and weights.

If this powerplant and drive is really going to used for production, get a professional vibe engineer involved and instrument the thing to do a proper analysis. IMO you're asking for trouble proceeding down the present path with a blindfold on and fingers crossed. This is serious stuff.

Last edited: Jun 14, 2019
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11. Jun 14, 2019

### dcarr

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That coupler weighs more than my entire 80" aluminum propeller!

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12. Jun 14, 2019

### BoKu

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Okay, I just looked the Elpex up in the catalog. Based on Peter's description in the video comments, it's a ELPEX-S size 220 with SN rubber element and SAE #8 drive flange. The Elpex catalog shows it weighing in at 6.4 kg (14.1 lbs). So unless they can shave some more weight off of the Lord than they did by trimming the flange of the Elpex, they're in for about a 48 lb weight gain.

13. Jun 14, 2019

### rv6ejguy

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The empty weight for the plane will soon exceed the original gross weight projection once they add the required ballast to the nose. Time for a total rethink.

Last edited: Jun 15, 2019
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14. Jun 15, 2019

### pictsidhe

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Hmmm, has he reinforced the structure, reduced the g ratings, or changed the safety factor?
My dollar is on the last option, because it was so well designed that it can take the extra weight.

Bob, is that weight gain with the nose ballast that will be needed?

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15. Jun 15, 2019

### BoKu

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Nope, that is just the pure delta between the catalog mass for the Lord coupling (62 lbs) minus the catalog mass for the Elpex (14 lbs). However, the engine is closer to the CG than the nose compartment, so the trim mass is probably less than 10% of the delta.

16. Jun 15, 2019

### rv7charlie

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Haven't followed this thread very closely, but the video of the coupler failure mode was...surprising. Are there any other couplers on flying a/c that are totally dependent on the 'rubber' to couple the engine to output? Everything else I've ever seen have the 'hard' parts of the drive & driven ends overlapping, so that if the soft stuff fails, there's at least some chance that the prop will keep turning as long as the system stays away from resonance while in flight.

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17. Jun 15, 2019

### rv6ejguy

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I've seen a couple of drives using rubber couplers with no fail safe but it's not a good idea. I'd say from his comments, Peter doesn't appreciate the possible destructive effects of TV at all nor does he think there is anything fundamentally wrong with his PSRU design.

The more I look at the fin/ rudder area on Raptor, it seems like they have far less area than something like a Velocity and more fuselage area forward. I wonder if directional stability will be adequate?

18. Jun 15, 2019

### Kyle Boatright

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I had the same concern when I saw the Commuter Craft prototype with extended endplates on the canard.

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19. Jun 15, 2019

### BBerson

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Are you saying more fuselage area forward because it is longer or because it is wider? (or both)
I think the RC model had some problems and he had mentioned "Dutch roll".
I don't remember what Dutch roll is actually, the term isn't mentioned in Perkins and Hage stability book.
What I know is uncontrolled free flight models have larger dihedral and smaller vertical tails. Pilot controlled RC models and full size airplanes have less or no dihedral and bigger vertical tails.

20. Jun 16, 2019

### Marc Zeitlin

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I obviously don't spend a great deal of time and effort defending Peter's design skills, but I'll throw this in for consideration.

When the first Long-EZ was built, it was basically an enlarged Varieze, per Burt's design, with slightly larger wings and strakes. The winglets weren't enlarged. I have it on good authority that it was very happy to fly in one direction and point in another. Apparently, the current winglet size was arrived at by adding foam and glass in small increments by Mike and Dick, until it was interested in pointing where it was going. Hence, the current size of the winglets. The rudders, which were the absurd small square ones to start with, were soon changed to the longer, skinny ones that you see on almost all EZ's now. Having flown both kinds, I can attest to the efficacy of the higher A/R rudders . And with respect to area forward of the CG, having recently flown a Long-EZ with a VERY large extended nose, as well as minimal lower winglets, the directional stability at low speeds was not as good as the stock Long-EZ. Not dangerous, by any means, but definitely less directionally stable.

Getting this stuff right isn't trivial, and is many times a matter of tuning in flight test on a new design. Even SS2, with all the CFD and analysis done prior to flight (and there was a LOT), needed tweaking of the tail sizes and surfaces.

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text:
### 计算机代写|C++作业代写C++代考|Terminology: Data Parallelism

C++ 是一种高级语言，它是由Bjarne Stroustrup 于1979 年在贝尔实验室开始设计开发的。 C++ 进一步扩充和完善了C 语言，是一种面向对象的程序设计语言。 C++ 可运行于多种平台上，如Windows、MAC 操作系统以及UNIX 的各种版本。

statistics-lab™ 为您的留学生涯保驾护航 在代写C++方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写C++代写方面经验极为丰富，各种代写C++相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 计算机代写|C++作业代写C++代考|Terminology: Data Parallelism

Data parallelism (Figure $\mathrm{P}-3$ ) is easy to picture: take lots of data and apply the same transformation to each piece of the data. In Figure P-3, each letter in the data set is capitalized and becomes the corresponding uppercase letter. This simple example shows that given a data set and an operation that can be applied element by element, we can apply the same task in parallel to each element. Programmers writing code for supercomputers love this sort of problem and consider it so easy to do in parallel that it has been called embarrassingly parallel. A word of advice: if you have lots of data parallelism, do not be embarrassed – take advantage of it and be very happy. Consider i happy parallelism.

When comparing the effort to find work to do in parallel, an approach that focuses on data parallelism is limited by the amount of data we can grab to process. Approaches based on task parallelism alone are limited by the different task types we program. Whil both methods are valid and important, it is critical to find parallelism in the data that we process in order to have a truly scalable parallel program. Scalability means that our application can increase in performance as we add hardware (e.g., more processor cores) provided we have enough data. In the age of big data, it turns out that big data and parallel programming are made for each other. It seems that growth in data sizes is a reliable source of additional work. We will revisit this observation, a little later in this Preface, when we discuss Amdahl’s Law.

## 计算机代写|C++作业代写C++代考|Terminology: Pipelining

While task parallelism is harder to find than data parallelism, a specific type of task parallelism is worth highlighting: pipelining. In this kind of algorithm, many independent tasks need to be applied to a stream of data. Each item is processed by each stage, as shown by the letter A in (Figure P-4). A stream of data can be processed more quickly when we use a pipeline, because different items can pass through different stages at the same time, as shown in Figure P-5. In these examples, the time to get a result may not be faster (referred to as the latency measured as the time from input to output) but the throughput is greater because it is measured in terms of completions (output) per unit of time. Pipelines enable parallelism to increase throughput when compared with a sequential (serial) processing. A pipeline can also be more sophisticated: it can reroute data or skip steps for chosen items. TBB has specific support for simple pipelines (Chapter 2) and very complex pipelines (Chapter 3). Of course, each step in the pipeline can use data or task parallelism as well. The composability of TBB supports this seamlessly.

## 计算机代写|C++作业代写C++代考|Example of Exploiting Mixed Parallelism

Consider the task of folding, stuffing, sealing, addressing, stamping, and mailing letters. If we assemble a group of six people for the task of stuffing many envelopes, we can arrange each person to specialize in and perform their assigned task in a pipeline fashion (Figure P-6). This contrasts with data parallelism, where we divide up the supplies and give a batch of everything to each person (Figure P-7). Each person then does all the steps on their collection of materials.
Figure P- 7 is clearly the right choice if every person has to work in a different location far from each other. That is called coarse-grained parallelism because the interactions between the tasks are infrequent (they only come together to collect envelopes, then leave and do their task, including mailing). The other choice shown in Figure P-6 approximates what we call fine-grained parallelism because of the frequent interactions (every envelope is passed along to every worker in various steps of the operation).
Neither extreme tends to fit reality, although sometimes they may be close enough to be useful. In our example, it may turn out that addressing an envelope takes enough time to keep three people busy, whereas the first two steps and the last two steps require only one person on each pair of steps to keep up. Figure P-8 illustrates the steps with the corresponding size of the work to be done. We can conclude that if we assigned only one person to each step as we see done in Figure P-6, that we would be “starving” some people in this pipeline of work for things to do – they would be idle. You might say it would be hidden “underemployment.” Our solution, to achieve a reasonable balance in our pipeline (Figure P-9) is really a hybrid of data and task parallelism.

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## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。


text:
# Recent content by guest1234

1. ### I About Lie group product ($U(1)\times U(1)$ ex.)

I recently got confused about Lie group products. Say, I have a group U(1)\times U(1)'. Is this group reducible into two U(1)'s, i.e. possible to resepent with a matrix \rho(U(1)\times U(1)')=\rho_{1}(U(1))\oplus\rho_{1}(U(1)')=e^{i\theta_{1}}\oplus e^{i\theta_{2}}=\begin{pmatrix}e^{i\theta_{1}}...
2. ### What function I'm looking at?

For some reason your response led me to think that the answer is obvious... :biggrin: So I plotted 1-e^{-x} and it turns out that it's the answer I'm looking for. Never seen an (inverse or whatever it's called) exponential decay plot in log-log scale before .. As for the irrelevant 'where did...
3. ### What function I'm looking at?

Hey all What's could the function be on the plot (see the attachment)?
4. ### Mass dimension of coupling constant -- always an integer?

Well I was thinking whether it'd be pseudoscalar (that shouldn't be any big problem -- if we really want a parity violating theory). I just thought about gauge transformations, and yup, you were right -- the term wouldn't transform as a (pseudo)scalar but as a spinor. Adding scalar and spinor...
5. ### Mass dimension of coupling constant -- always an integer?

Thinking beyond SM, what are the physical consequences if the Lagrangian contains an interaction term with an odd number (i.e. only one) of fermions?
6. ### Mass dimension of coupling constant -- always an integer?

Just a simple question -- can the dimension of coupling constant be a rational number or should it always be an integer? The question arose when I was trying to construct a Lagrangian with an interaction term involving two spin-1 particles and a fermion. The dimensions add up to 7/2, which...
7. ### Momentum space measure -- change of variables

I'm working through an article called "Cosmic abundances of stable particles -- improved analysis" (link -- viewable only in Firefox afaik), the result of which, equation (3.8), is cited quite a lot. I'm more interested in how they arrived there. Particularly, how come momentum space measure...
8. ### Feynman rules - where do the imaginary numbers come from?

I'm trying to learn how to derive Feynman rules (what else to do during xmas, lol). The book I'm using is QFT 2nd ed by Mandl&Shaw. On p 428 they're trying to show how to derive a Feynman rule for W W^\dagger Z^2 interaction term g^2 \cos^2\theta_W\left[W_\alpha W_\beta^\dagger Z^\alpha Z^\beta...
9. ### Relative velocity of beams

doh... natural units... thx
10. ### Relative velocity of beams

How come relative velocity of the beams can be expressed by v_{12} = \left| \vec{v}_1 - \vec{v}_2 \right| = \left|\frac{\vec{p}_1}{E_1} - \frac{\vec{p}_2}{E_2}\right| where \vec{p}_{1,2} and E_{1,2} is the momenta and energies of incoming particles, respectively? Similar equation is in Peskin &...
11. ### Plane wave expansion of massive vector boson

So... I think I'll go with two sets of ladder operators as usual in complex scalar field/fermions. It seems that the thesis uses them implicitly -- in Wick contraction the other operator is neglected because of the normal ordering requirement. About path integral.. thanks but I'll skip it for...
12. ### Plane wave expansion of massive vector boson

I'm trying to derive Feynman rules for massive vector boson and its antiparticle. It all boils down to plane wave expansion of the bosons which atm is a little bit confusing. Should I account for two different set of ladder operators (as in the case of complex KG or spinors, cf Peskin&Schröder...
13. ### UDP multiclient server in C

Hi all I'm trying to create a server that uses UDP and is capable of handling multiple clients. The server should 'stream' content to the clients only on the initial request (i.e. when starting the client). The general idea is to test how many clients is the server able to 'serve' before the...
14. ### Dual tensors in Lagrangian

Yeah, I forgot to mention I'm interested in U(1) theory. Thanks for the link, will read it.
15. ### Dual tensors in Lagrangian

Thanks, Bill_K, I didn't know that before. A quick proof for the eager: \begin{align*}\widetilde{F}^{\mu\nu}\widetilde{F}_{\mu\nu} &= \frac{1}{4}\epsilon^{\mu\nu\rho\sigma}\epsilon_{\mu\nu\alpha\beta}F_{ \rho \sigma}F^{\alpha\beta} = \frac{1}{2}\delta_{\alpha...


text:
# Simple line with dots, known coordinates

Are there any easy way to make something similar to this image in tikz, asympote or similar?

I know the coordinates, to each of the points =)

Ofcourse I know how to solve this, but to do it in tikz or simmilar is new to me.

-

There is an easy way to do this in TikZ, with the \foreach statement. Like this:

\documentclass{article}
\usepackage{tikz}
\begin{document}
\noindent
\begin{tikzpicture}
\path[draw, thick, ->] (-.3,0) -- (6.3,0);
\foreach \x in {0,...,6}{
\path[draw, thick] (\x,0) -- ++(0,-.15) node [below] {\x};
}
\foreach \x/\name in {0/A,.6/B,1/C,1.5/D,2/E,2.3/F,3/G,3.3/H,4/I,4.6/J,5/K,5.5/L}{
\path[draw, fill=blue] (\x,0) circle[radius=2pt] node [above=2 mm, blue] {\name};
}
\end{tikzpicture}
\end{document}

You could automate the labeling and make the drawing of the line automated dependent on the coordinates that you enter. This is the basic method though, the result looks like this:

-

Here an example with pstricks (needs xelatex or dvips)

\documentclass{article}
\usepackage{pst-plot}
\begin{document}
\begin{pspicture}(0,-1)(6,1)
\psline{->}(0,0)(6,0)
\def\dotatline#1#2{%
\uput[-90](!#1 ){$#2$}
\psdot(!#1)
}

\dotatline{8 1 3 div exp 0}{8^{\frac{1}{3}}}

\dotatline{5.5 0 exp 0}{5,5^{0}}

\dotatline{21 sqrt 0}{\sqrt{21}}

\dotatline{6 2 1 neg exp mul 0}{6\cdot 2^{-1}}

\end{pspicture}
\end{document}

-

Instead of providing decimal values for the locations, you can use pgfmathsetmacro to compute the location of where the node to be placed is. The first parameter is a general math expression, and the second parameter is the label to be placed.

Instead of just letters you can also provide math expression to label the points. Also the \PlaceNode macro below accepts an optional first parameter that get applied to the label in case you wish to tweak it slightly as I have for the tab(30) label.

\documentclass[border=5pt,tightpage]{standalone}
\usepackage{tikz}

\newcommand*{\PlaceNode}[3][]{%
\pgfmathsetmacro{\result}{#2}%
\node at (\result,0) [fill=red,circle, inner sep=1.5pt] {}; \node at (\result,0) [above, #1] {\scriptsize#3};%
}%
\newcommand*{\PlaceTick}[3][]{%
\pgfmathsetmacro{\result}{#2}%
\draw [blue,thick] (\result,0) -- (\result,-0.1) node [below,#1] {#3};
}%

\begin{document}
\begin{tikzpicture}
\draw [thick, blue] (0,0) -- (10,0);

\foreach \x in {0,...,10} {
\PlaceTick[below]{\x}{$\x$}
}

\PlaceNode{8^(1/3)}{A}
\PlaceNode{5^0}{B}
\PlaceNode{sqrt(21)}{C}
\PlaceNode{tan(30)}{D}
\PlaceNode{15*(2^(-1))}{E}
\PlaceNode{(3/2)^3}{F}
\end{tikzpicture}

\bigskip
\begin{tikzpicture}
\draw [thick, blue] (0,0) -- (10,0);

\foreach \x in {0,...,10} {
\PlaceTick[below]{\x}{$\x$}
}

\PlaceNode{8^(1/3)}{$8^{\frac{1}{3}}$}
\PlaceNode{5^0}{$5^0$}
\PlaceNode{sqrt(21)}{$\sqrt{21}$}
\PlaceNode[yshift=0.3cm]{tan(30)}{$\tan{30^\circ}$}
\PlaceNode{15*(2^(-1))}{$15 \cdot 2^{-1}$}
\PlaceNode{(3/2)^3}{$\left(\frac{3}{2}\right)^3$}
\end{tikzpicture}
\end{document}

-

Here is another stab at it, using many of the pstricks bundle packages. As such, it requires either an xelatex or latex->dvips->ps2pdf compilation sequence:

\documentclass{article}
\usepackage{pst-node}% http://ctan.org/pkg/pst-node
\usepackage[nomessages]{fp}% http://ctan.org/pkg/fp
\usepackage{xcolor}% http://ctan.org/pkg/xcolor
\begin{document}

\begin{pspicture}(7,3)
\SpecialCoor
\psset{xunit=2cm}% Default x-unit

% ========== AXIS ==========
\pcline{->}(-0.5,0)(6.5,0)% Horizontal line

% ========== NODE DEFINITIONS ==========
\pnode(0,0){A}% A
\FPeval{\result}{tan(30*pi/180)}% tan 30 degrees ~ 0.57735026918962576450914878050196
\pnode(\result,0){B}% B
\pnode(1,0){C}% C 5.5^0 = 1
\pnode(1.5,0){D}% D (dummy node)
\pnode(2,0){E}% E 8^(1/3) = 2
\pnode(2.3,0){F}% F (dummy node)
\pnode(3,0){G}% G 6 x 2^{-1} = 3
\FPeval{\result}{pow(3,3/2)}% (3/2)^3 = 3.375
\pnode(\result,0){H}% H
\pnode(4,0){I}% I
\FPeval{\result}{root(2,21)}% sqrt(21) ~ 4.582575694955840006588047193728
\pnode(\result,0){J}% J
\pnode(5,0){K}% K
\pnode(5.55,0){L}% L (dummy node)

% ========== NODE PRESENTATION ==========
\psset{linestyle=solid,linewidth=0.5pt,linecolor=black,fillcolor=blue!60,fillstyle=solid}
\psforeach{\node}{A,C,E,G,I,K,{6,0}}{\uput{10pt}[d]{0}(\node){\the\psLoopIndex}}% Print index
\psforeach{\nNode}{0,1,2,3,4,5,6}{\psline(\nNode,0)(\nNode,-5pt)}% Print index line
\psforeach{\node}{A,B,C,D,E,F,G,H,I,J,K,L}{%
\pscircle(\node){2.5pt}% Print nodes
\uput{10pt}[u]{0}(\node){\color{blue!60}\node}% Print label
}
\end{pspicture}

\end{document}

In the above code, you can modify the xunit to whatever you like, which will stretch out the image horizontally. As-is the horizontal unit distance (from A to C, etc) is 2cm.

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