Sorting Permutations with Finite-Depth Stacks

Sorting organizes information for optimal usage and is desirable in many different fields. Noted computer scientist Donald Knuth first considered using stacks of infinite depth as a powerful means to sort data. We extend this work to consider stack-sortable permutations using stacks of specified finite depths. We characterize patterns that sortable permutations must avoid and derive a handy enumeration formula. Further generalizations include the introduction of multiple stacks and the analysis of the resulting counting sequences

ESTIMATION OF MULTI-DIRECTIONAL ANKLE IMPEDANCE AS A FUNCTION OF LOWER EXTREMITY MUSCLE ACTIVATION

The purpose of this research is to investigate the relationship between the mechanical impedance of the human ankle and the corresponding lower extremity muscle activity. Three experimental studies were performed to measure the ankle impedance about multiple degrees of freedom (DOF), while the ankle was subjected to different loading conditions and different levels of muscle activity. The first study determined the non-loaded ankle impedance in the sagittal, frontal, and transverse anatomical planes while the ankle was suspended above the ground. The subjects actively co-contracted their agonist and antagonistic muscles to various levels, measured using electromyography (EMG). An Artificial Neural Network (ANN) was implemented to characterize the relationship between the EMG and non-loaded ankle impedance in 3-DOF. The next two studies determined the ankle impedance and muscle activity during standing, while the foot and ankle were subjected to ground perturbations in the sagittal and frontal planes. These studies investigate the performance of subject-dependent models, aggregated models, and the feasibility of a generic, subject-independent model to predict ankle impedance based on the muscle activity of any person. Several regression models, including Least Square, Support Vector Machine, Gaussian Process Regression, and ANN, and EMG feature extraction techniques were explored. The resulting subject-dependent and aggregated models were able to predict ankle impedance with reasonable accuracy. Furthermore, preliminary efforts toward a subject-independent model showed promising results for the design of an EMG-impedance model that can predict ankle impedance using new subjects. This work contributes to understanding the relationship between the lower extremity muscles and the mechanical impedance of the ankle in multiple DOF. Applications of this work could be used to improve user intent recognition for the control of active ankle-foot prostheses

Using Lower Extremity Muscle Activations to Estimate Human Ankle Impedance in the External-Internal Direction

For millions of people, mobility has been afflicted by lower limb amputation. Lower extremity prostheses have been used to improve the mobility of an amputee; however, they often require additional compensation from other joints and do not allow for natural maneuverability. To improve upon the functionality of ankle-foot prostheses, it is necessary to understand the role of different muscle activations in the modulation of mechanical impedance of a healthy human ankle. This report presents the results of using artificial neural networks (ANN) to determine the functional relationship between lower extremity electromyography (EMG) signals and ankle impedance in the transverse plane. The Anklebot was used to apply pseudo-random perturbations to the human ankle in the transverse plane, while motion of the ankle in the sagittal and frontal planes was constrained. Using a stochastic system identification method, the mechanical impedance of the ankle in external-internal (EI) direction was determined as a function of the applied torque and corresponding ankle motion. The impedance of the ankle and muscle EMG signals were determined for three muscle activation levels, including with relaxed muscles, and with muscles activated and 10% and 20% of the subject’s maximum voluntary contraction (MVC). This information was used as the input and target matrices to train an ANN for each subject. The resulting ankle impedance from the proposed ANN was effectively predicted within 85% accuracy for nine out of ten subjects, and was within ±5 Nm/rad of the target impedance for all subjects. This work provides more understanding of the neuromuscular characteristics of the ankle and provides insight toward future design and control of ankle-foot prostheses

Deep Drilling in the Time Domain with DECam: Survey Characterization

This paper presents a new optical imaging survey of four deep drilling fields (DDFs), two Galactic and two extragalactic, with the Dark Energy Camera (DECam) on the 4 meter Blanco telescope at the Cerro Tololo Inter-American Observatory (CTIO). During the first year of observations in 2021, $>$4000 images covering 21 square degrees (7 DECam pointings), with $\sim$40 epochs (nights) per field and 5 to 6 images per night per filter in $g$, $r$, $i$, and/or $z$, have become publicly available (the proprietary period for this program is waived). We describe the real-time difference-image pipeline and how alerts are distributed to brokers via the same distribution system as the Zwicky Transient Facility (ZTF). In this paper, we focus on the two extragalactic deep fields (COSMOS and ELAIS-S1), characterizing the detected sources and demonstrating that the survey design is effective for probing the discovery space of faint and fast variable and transient sources. We describe and make publicly available 4413 calibrated light curves based on difference-image detection photometry of transients and variables in the extragalactic fields. We also present preliminary scientific analysis regarding Solar System small bodies, stellar flares and variables, Galactic anomaly detection, fast-rising transients and variables, supernovae, and active galactic nuclei.Comment: 22 pages, 17 figures, 2 tables. Accepted to MNRA

Examining the Dampening Effects of Varying Shoe Architecture During Gait

Studies have shown that running shoe architecture may play a major role in lower extremity injury prevention (Wiegerinck, et al). It has been hypothesized that shoes with added support are more effective at preventing injury, due to the greater force dampening effect that the increased stability provides. Initial studies tested this hypothesis by measuring the in-shoe force data in the heel region of two running shoe types from two different companies. The two running shoe types were classified as flexible and stability where the flexible shoes provided a lower level of support than the stability shoes. The recorded walking trials yielded consistent results supporting the hypothesis; increased stability acts as a dampener in the heel region. This current study expands upon the previous work by gathering data from additional subjects and including the effects of impact forces on the mid-foot region during the gait cycle. Ten subjects walked in the two shoe types from each of the two companies using a treadmill to dictate a constant walking speed across all of the subjects. Impact forces were recording utilizing a Tekscan Fscan in-shoe pressure mapping system. The data was filtered and grouped to isolate the heel and midfoot regions throughout 25 gait cycles per shoe per subject. Of the ten subjects recorded, eight subjects displayed a statistically significant reduction in peak forces from the flexible shoes to the stability shoes across both regions

Estimation of the two degreesof- freedom time-varying impedance of the human ankle

© 2018 by ASME. An understanding of the time-varying mechanical impedance of the ankle during walking is fundamental in the design of active ankle-foot prostheses and lower extremity rehabilitation devices. This paper describes the estimation of the time-varying mechanical impedance of the human ankle in both dorsiflexion-plantarflexion (DP) and inversion-eversion (IE) during walking in a straight line. The impedance was estimated using a two degreesof- freedom (DOF) vibrating platform and instrumented walkway. The perturbations were applied at eight different axes of rotation combining different amounts of DP and IE rotations of four male subjects. The observed stiffness and damping were low at heel strike, increased during the mid-stance, and decreases at push-off. At heel strike, it was observed that both the damping and stiffness were larger in IE than in DP. The maximum average ankle stiffness was 5.43 N˙m/rad/kg at 31% of the stance length (SL) when combining plantarflexion and inversion and the minimum average was 1.14 N˙m/rad/kg at 7% of the SL when combining dorsiflexion and eversion. The maximum average ankle damping was 0.080 Nms/rad/kg at 38% of the SL when combining plantarflexion and inversion, and the minimum average was 0.016 Nms/rad/kg at 7% of the SL when combining plantarflexion and eversion. From 23% to 93% of the SL, the largest ankle stiffness and damping occurred during the combination of plantarflexion and inversion or dorsiflexion and eversion. These rotations are the resulting motion of the ankle\u27s subtalar joint, suggesting that the role of this joint and the muscles involved in the ankle rotation are significant in the impedance modulation in both DP and IE during gait

Towards a generalized model of multivariable ankle impedance during standing based on the lower extremity muscle EMG

The ankle mechanical impedance of healthy subjects was estimated during the standing pose while they co-contracted their lower-leg muscles. Subsequently, the impedance parameters were modeled as a function of the level of co-contraction using machine learning regression methods. From the experimental results, the average ankle stiffness coefficients in dorsi-plantar flexion (DP) showed more dependence to the muscle contraction than stiffness in inversion-eversion (IE): 4.6 Nm/rad per %MVC (percent of the maximum voluntary contraction) and 1.1 Nm/rad per %MVC, respectively. To accurately estimate the ankle impedance parameters as a function of the electromyography (EMG) signals, multiple EMG feature selection methods, regression models, and types of models were evaluated. Using a 1-vs-All model validation approach, the best regression model to fit the stiffness and damping in DP was the Least Square method with Regularization, and the best IE stiffness was the Gaussian Process Regression. No model was able to estimate the IE damping well, possibly because this parameter is not modulated with a changing co-contraction of the lower-leg muscles

Estimating the multivariable human ankle impedance in dorsi-plantarflexion and inversion-eversion directions using EMG signals and artificial neural networks

© 2017, Springer Singapore. The use of a suitably designed ankle-foot prosthesis is essential for transtibial amputees to regain lost mobility. A desired ankle–foot prosthesis must be able to replicate the function of a healthy human ankle by transferring the ground reaction forces to the body, absorbing shock during contact, and providing propulsion. During the swing phase of walking, the human ankle is soft and relaxed; however, it hardens as it bears the body weight and provides force for push-off. The stiffness is one of the components of the mechanical impedance, and it varies with muscle activation (Stochastic estimation of human ankle mechanical impedance in medial-lateral direction, 2014, Stochastic estimation of the multivariable mechanical impedance of the human ankle with active muscles, 2010). This study defines the relationship between ankle impedance and the lower extremity muscle activations using artificial neural networks (ANN). We used the Anklebot, a highly backdrivable, safe, and therapeutic robot to apply stochastic position perturbations to the human ankle in the sagittal and frontal planes. A previously proposed system identification method was used to estimate the target ankle impedance to train the ANN. The ankle impedance was estimated with relaxed muscles and with lower leg muscle activations at 10 and 20% of the maximum voluntary contraction (MVC) of each individual subject. Given the root mean squared (rms) of the electromyography (EMG) signals, the proposed ANN effectively predicted the ankle impedance with mean accuracy of 89.8 ± 6.1% in DP and mean accuracy of 88.3 ± 5.7% in IE, averaged across three muscle activation levels and all subjects