Tilt Perturbations Research Articles

Assessable and interpretable sensitivity analysis in the pattern graph framework for nonignorable missingness mechanisms.

The pattern graph framework solves a wide range of missing data problems with nonignorable mechanisms. However, it faces two challenges of assessability and interpretability, particularly important in safety-critical problems such as clinical diagnosis: (i) How can one assess the validity of the framework's apriori assumption and make necessary adjustments to accommodate known information about the problem? (ii) How can one interpret the process of exponential tilting used for sensitivity analysis in the pattern graph framework and choose the tilt perturbations based on meaningful real-world quantities? In this paper, we introduce Informed Sensitivity Analysis, an extension of the pattern graph framework that enables us to incorporate substantive knowledge about the missingness mechanism into the pattern graph framework. Our extension allows us to examine the validity of assumptions underlying pattern graphs and interpret sensitivity analysis results in terms of realistic problem characteristics. We apply our method to a prevalent nonignorable missing data scenario in clinical research. We validate and compare our method'sresults of our method with a number of widely-used missing data methods, including Unweighted CCA, KNN Imputer, MICE, and MissForest. The validation is done using both boot-strapped simulated experiments as well as real-world clinical observations in the MIMIC-III public dataset.

A Stability Training Method of Legged Robots Based on Training Platforms and Reinforcement Learning with Its Simulation and Experiment.

This paper continues the proposed idea of stability training for legged robots with any number of legs and any size on a motion platform and introduces the concept of a learning-based controller, the global self-stabilizer, to obtain a self-stabilization capability in robots. The overall structure of the global self-stabilizer is divided into three modules: action selection, adjustment calculation and joint motion mapping, with corresponding learning algorithms proposed for each module. Taking the human-sized biped robot, GoRoBoT-II, as an example, simulations and experiments in three kinds of motions were performed to validate the feasibility of the proposed idea. A well-designed training platform was used to perform composite random amplitude-limited disturbances, such as the sagittal and lateral tilt perturbations (±25°) and impact perturbations (0.47 times the robot gravity). The results show that the proposed global self-stabilizer converges after training and can dynamically combine actions according to the system state. Compared with the controllers used to generate the training data, the trained global self-stabilizer increases the success rate of stability verification simulations and experiments by more than 20% and 15%, respectively.

Projection-Based Local and Global Lipschitz Moduli of the Optimal Value in Linear Programming

In this paper, we use a geometrical approach to sharpen a lower bound given in [5] for the Lipschitz modulus of the optimal value of (finite) linear programs under tilt perturbations of the objective function. The key geometrical idea comes from orthogonally projecting general balls on linear subspaces. Our new lower bound provides a computable expression for the exact modulus (as far as it only depends on the nominal data) in two important cases: when the feasible set has extreme points and when we deal with the Euclidean norm. In these two cases, we are able to compute or estimate the global Lipschitz modulus of the optimal value function in different perturbations frameworks.

Fully stable well-posedness and fully stable minimum with respect to an admissible function

ABSTRACT In this paper, the notions of fully stable well-posedness and fully stable minimum of optimization problems with an extended real-valued objective function in an Asplund space setting are considered, where the objective function undergoes both tilt perturbations and general parameter perturbations. Special cases of the first notion reduce to the stable Hölder minimizers by Zheng and Ng [SIAM J Optim. 2015;25:416–438] and the fully stable Hölder minimizers introduced by Zheng, Zhu and Ng [SIAM J Optim. 2018;28:2601–2624], respectively. By using techniques of variational analysis and generalized differentiation, the results presented in this paper provide insight into necessary or sufficient conditions for tilt-stable minimizers of nonlinear programmes in Asplund spaces and therefore generalize some existing ones in the recent literature.

The Effect of Ankle Bracing on Kinematics in Simulated Sprain and Drop Landings: A Double-Blind, Placebo-Controlled Study

Background: The efficacy of external ankle braces to protect against sudden inversion sprain has yet to be determined while taking into account the possible placebo effect of brace application. Purpose: To assess the protective effect of an external ankle brace on ankle kinematics during simulated inversion sprain and single-legged drop landings among individuals with a history of unilateral lateral ankle sprain. Hypothesis: The primary hypothesis was that active and placebo external braces would reduce inversion angle during simulated inversion sprain. Study Design: Controlled laboratory study. Methods: Sixteen participants with ankle instability and previous sprain performed single-legged drop landings and sudden inversion tilt perturbations. Kinematics of the affected limb were assessed in 3 conditions (active bracing, passive placebo bracing, and unbraced) across 2 measurement days. Participators and investigators were blinded to the brace type tested. The effect of bracing on kinematics was assessed with repeated measures analysis of variance with statistical parametric mapping, with post hoc tests performed for significant interactions. Results: Only active bracing reduced inversion angles during a sudden ankle inversion when compared with the unbraced condition. This reduction was apparent between 65 and 140 milliseconds after the initial fall. No significant differences in inversion angle were found between the passive placebo brace and unbraced conditions during sudden ankle inversion. Furthermore, no significant differences were found among all tested conditions in the sagittal plane kinematics at the knee and ankle. Conclusion: During an inversion sprain, only the actively protecting ankle brace limited inversion angles among participants. These results do not indicate a placebo effect of external bracing for patients with ankle instability and a history of unilateral ankle sprain. Furthermore, sagittal plane knee kinematics appear to remain unaffected by bracing during single-legged landing, owing to the limited effects of bracing on sagittal ankle kinematics. These results highlight the role of brace design on biomechanical function during sports-related and injury-prone movements. Clinical Relevance: Athletes prone to reinjury after lateral ankle sprain may benefit from brace designs that allow for full sagittal range of motion but restrict only frontal plane motion.

Stable well-posedness and tilt stability with respect to admissible functions

Note that the well-posedness of a proper lower semicontinuous function f can be equivalently described using an admissible function. In the case when the objective function f undergoes the tilt perturbations in the sense of Poliquin and Rockafellar, adopting admissible functions ϕ and ψ , this paper introduces and studies the stable well-posedness of f with respect to ϕ (in brief, ϕ -SLWP) and tilt-stable local minimum of f with respect to ψ (in brief, ψ -TSLM). In the special case when ϕ ( t ) = t 2 and ψ ( t ) = t , the corresponding ϕ -SLWP and ψ -TSLM reduce to the stable second order local minimizer and tilt stable local minimum respectively, which have been extensively studied in recent years. We discover an interesting relationship between two admissible functions ϕ and ψ : ψ ( t ) = ( ϕ ′) -1 ( t ), which implies that a proper lower semicontinuous function f on a Banach space has ϕ -SLWP if and only if f has ψ -TSLM. Using the techniques of variational analysis and conjugate analysis, we also prove that the strong metric ϕ ′-regularity of ∂f is a sufficient condition for f to have ϕ -SLWP and that the strong metric ϕ ′-regularity of ∂ [co( f + δ B X [ x,r ] ) ] for some r > 0 is a necessary condition for f to have ϕ -SLWP. In the special case when ϕ ( t ) = t 2 , our results cover some existing main results on the tilt stability.

Ground tilt changes in Japan caused by the 2010 Maule, Chile, earthquake tsunami

Oscillating ground tilt perturbations accompanied by the 2010 Maule, Chile, earthquake tsunami were observed over a broad inland area facing the Pacific Ocean coast in Japan by a high‐density tiltmeter network. Through an analysis of ground tilt data observed at more than 500 stations, we were able to obtain a detailed spatiotemporal distribution of the tsunami‐induced tilt changes and reveal a relationship between the tilt amplitude and the distance from the coast. At distances of 1 km or less, the peak tilt amplitudes were ~5 × 10–2 µrad and were almost constant with respect to the distance. At distances greater than 3 km, amplitudes were inversely proportional to the distance and reached ~5 × 10–3 µrad approximately 50 km away from the coast. The dominant ground tilting directions were almost the same as the direction orthogonal to the coastline. These observed ground tilt changes and their characteristics were successfully modeled with a loading deformation caused by sea level variations accompanied by the tsunami. Applying a two‐dimensional boxcar tsunami model to the observed data, we estimated the water volume per unit length of coast for the Maule earthquake tsunami to be 2–7 × 103 m3/m within the distance of 14–20 km seaward of the coastline.

Platform Tilt Perturbation as an Intervention for People With Chronic Vestibular Dysfunction

Training to improve responses to perturbations may be beneficial for individuals with unilateral vestibular dysfunction. We evaluated the effects of an incrementally increasing surface tilt perturbation intervention for individuals with chronic vestibular pathology on gait, activities of daily living, and dizziness. Participants (n = 29) were randomly assigned to 1 of 3 groups. The first group received random surface tilt perturbations of increasing angles and speed, half of the trials with vision-occluding goggles, 3 times weekly for 3 weeks (P group). The second group received tilt perturbation intervention (as above) plus a home program of vestibular rehabilitation exercises (P+EX group). The third group performed only the vestibular rehabilitation exercises (EX group). Outcome measures included temporospatial gait measures, Dynamic Gait Index (DGI), Dizziness Handicap Inventory (DHI), Patient Specific Functional Scale (PSFS), and a Perceived Outcomes Scale (POS). The P and P+EX groups showed greater improvement on the PSFS and the POS compared to the EX group. DGI scores indicated decreased fall risk in 8 of 9 individuals who participated in P or P+EX training and who initially scored below the 19-point cutoff score. Both the P and P+EX groups showed significant within-group changes on some gait characteristics, DGI, DHI, PSFS, and POS measures. The EX group showed within-group change only on the DHI. Surface tilt perturbation training appears to be more effective for improving abilities at the activities and participation levels than vestibular exercises alone. In addition, tilt perturbation training reduced fall risk as measured by the DGI.

Analysis of Postural Adjustment Responses to Perturbation Stimulus by Surface Tilts in the Feet-together Position

Base of support (BOS) influences the postural control of upright standing in humans. Since a narrowed BOS in the upright position makes postural control difficult, it is important to evaluate and practice balance with a narrowed BOS. We performed an experimental study to clarify the postural control mechanism in a feet-together position in response to dynamic perturbations. Subjects were 10 healthy young adults. Using an electrically operated platform, tilting perturbation was applied to subjects standing in feet-together position. Perturbation was in four directions: backward, forward, right, and left. Using a motion analysis system and electromyography (EMG), we simultaneously measured the three-dimensional postural change and EMG of seven muscles of the trunk and legs. We obtained joint angular change from the motion analysis and the integrated values of muscle activity and latency of the lower extremities from the EMG. In terms of pitch tilt, the ankle strategy was observed: this involved simultaneous contraction of the ankle muscles as usual in the upright position. In contrast, in terms of roll tilt, ”counterweighting” was observed. We also observed a change in postural control to respond to the narrowed BOS. We found that, unlike the feet-apart position, the feet-together position, narrowing the BOS in the left-right direction causes a prominent change and makes postural control strategy difficult only in response to roll tilt perturbations. In the future, we need to investigate the effectiveness of balance training including roll tilting in the feet-together position in improving balance ability in the left-right direction.

Development of a three-degrees-of-freedom moveable platform for providing postural perturbations

The purpose of this study was to design and develop a three-degrees-of-freedom moveable platform to provide postural perturbations for balance assessment and training. The platform consists of three motion mechanisms, which can provide forward-backward translation, upward-downward tilt, and clockwise-counterclockwise rotation. This platform can move in any of its degrees of freedom separately or simultaneously. The precision and accuracy of the platform movement were examined by calculating the standard deviations in repeated trials and comparing the real amplitude and velocity of the movement with the preset values. All the standard deviations in repeated trials were small in that the variation coefficients were less than 2 per cent, except that in the highest-velocity test, and all the mean differences were less than 1 mm for translational and 1 degree for tilt or rotational perturbations. The results demonstrated that the platform is a reliable and valid instrument for providing postural perturbations. The preliminary investigation of the kinematic postural responses to translational and tilt perturbation showed that this platform is a useful apparatus for balance research. Potential applications of this platform include investigation of the postural responses to yaw rotation or any combination of its degrees of freedom and studying the effects of perturbation-based balance-training programmes provided by this platform.

Triggering of balance corrections and compensatory strategies in a patient with total leg proprioceptive loss

Triggering of balance corrections may depend on both leg and trunk proprioceptive inputs. To study this issue and to determine how a total proprioceptive loss in the legs (ToLPL) would affect postural reactions in different directions, we investigated the postural control of a patient with a long-standing dorsal root ganglionopathy. This patient had absent stretch reflexes at the ankle and knee joints, delayed reflexes at the hips, but normal muscle strength. Postural control was probed with support-surface movements driven by two different experimental protocols. The first protocol concentrated on leg muscle responses by varying ankle inputs during pitch plane perturbations. The second protocol focussed on the directional sensitivity of upper body responses using combined roll and pitch tilt perturbations. For both protocols, identical techniques were used to record ankle torques, angular velocities of the upper legs and trunk, and surface EMG from leg, hip and trunk muscles. For the first protocol, pitch plane stance perturbations with three different ankle inputs were imposed by a movable support surface. A simultaneous 4-cm rearward translation and 4-deg toe-up rotation produced an 80-deg/s "enhanced ankle input", a simple toe-up rotation gave a 40-deg/s "normal" ankle input and a simultaneous 4-cm rearward translation and 4-deg "toe-down" rotation yielding a 0-deg/s "nulled ankle input". Responses in the ToLPL patient were compared to those of healthy controls and those of patients with lower-leg proprioceptive loss (LLPL). Following normal and enhanced ankle input perturbations, stretch reflexes were absent in ankle and knee joint muscles of the ToLPL patient. Balance correcting responses in the lower legs were diminished and delayed by some 45 ms. In quadriceps, balance-correcting responses were larger than normal, peaked earlier and were not delayed. During the nulled ankle input condition, the ankle muscle responses in the ToLPL patient were again diminished and delayed by 40 ms with respect to both normal subjects and LLPL patients. However, the ToLPL patient again generated an earlier, larger, balance correcting response in quadriceps. For the second protocol, combinations of roll and pitch perturbations were also delivered by a moving support surface. The amplitude was 7.5 deg at 50 deg/s. Eight different directions were applied randomly (pure "toes down", pure "toes up" and directions at 45-deg intervals of roll). As with the first protocol pre-stimulus background muscle activity was excessive in all trunk and most leg muscles. Responses to roll tilt produced several striking changes from normal in the ToLPL patient. First reflexes in gluteus medius were delayed. Second, the trunk roll which commences around 30 ms in normals was in the opposite direction. This roll was accompanied by oppositely directed stretch reflexes in paraspinal muscles. Third, directional sensitivity of balance corrections was far more roll oriented in leg and trunk muscles. Fourth, some tilt directions caused a deactivation response of background activity. This "deactivation strategy" strongly contrasted with the strategy of controls who had low pre-stimulus background activity and activated responses around 100 ms to correct postural instability. These findings provide new insights into the generation of pitch and roll plane directed balance corrections based on the interaction of proprioceptive trigger signals from the ankles, knees and hips. Without proprioceptive input from the ankle and knee, ankle muscle responses are delayed but not absent. Upper leg and trunk responses are not delayed. This suggests that most, if not all, lower leg balance correcting responses are triggered by hip and, possibly, trunk proprioceptive inputs. When leg proprioceptive input is absent, balance correcting responses lose pitch plane sensitivity. The solution used by the patient to overcome these deficits was to markedly raise background muscle activity levels, presumably to provide a stiffer body structure. The lack of trunk flexibility and lateral instability this produced for roll tilts was offset by the ability to compensate by using a hitherto not described "deactivation response" strategy. The patient had a clinical picture usually described as "deafferented"; yet our roll tilt perturbations revealed delayed reflex responses in hip muscles. With vestibulospinal and neck-proprioceptive inputs, these responses may have helped with the development of compensation processes for the total leg proprioceptive deficit.

Tilt Stability of a Local Minimum

The behavior of a minimizing point when an objective function is tilted by adding a small linear term is studied from the perspective of second-order conditions for local optimality. The classical condition of a positive-definite Hessian in smooth problems without constraints is found to have an exact counterpart much more broadly in the positivity of a certain generalized Hessian mapping. This fully characterizes the case where tilt perturbations cause the minimizing point to shift in a Lipschitzian manner.

Maturation of set-modulation of lower extremity EMG responses to postural perturbations.

To analyse the influence of different "postural sets" on stance stabilizing EMG responses in children, EMG responses to toe-up tilt perturbations were recorded in 70 children between the age of 9 months and 10 years, as well as in a control group of 10 adults under different postural set conditions, using either bilateral destabilization with eyes opened, eyes closed, or introducing additional minute upper extremity support. Recordings were also made with the children seated in front of the platform with the ankle joint angle being identical to that in the standing condition. Also recordings were made after unilateral destabilization in bilateral lower leg muscles, to determine if there is a generalization of EMG response patterns to the mechanically not disturbed side. Across all age-groups the principal modulation of EMG response changes according to postural conditions was identical. Long latency (LL) EMG responses were down-regulated when additional upper extremity support was provided. LL-responses were abolished in the sitting condition. With unilateral destabilizations throughout all age-groups short latency responses were restricted to the perturbed side, whereas long latency responses could be obtained symmetrically. The proximal to distal gradient of recruitment of muscle groups, remained identical across all age-groups. The data indicate that the basic organizational principle of stance stabilizing EMG responses and their modification by postural sets remains invariant across development. This indicates that the involved organizational principles are present as soon as a child is able to stand upright and are not subject to further shaping by motor learning.

Maturation of lower extremity EMG responses to postural perturbations: relationship of response-latencies to development of fastest central and peripheral efferents

EMG responses to toe-up tilt perturbations on a movable platform system were analysed in 86 children between the age of 12 months and 13 years. To assess the relative contribution of peripheral and central nerve conduction properties, a concomitant recording of the fastest efferent pathways in the central and peripheral motor system was made using non-invasive transcranial magnetic stimulation of motor cortex and peripheral nerve roots. This allowed the determination of the fastest downstream efferent connection times from motor cortex to lumbar motor neuron pools and to measure the fastest efferent conduction from these motor neuron pools to effector muscles in the lower leg. The sequence observed for stance stabilizing EMG responses was similar to that obtained in earlier studies with short latency (SL) and middle latency (ML) companents occurring in the stretched triceps surae muscle and long latency (LL) responses occurring in the non-stretched tibialis anterior muscle. Homologous responses were also obtained in upper leg muscles, being recruited consistently later than those in lower leg muscles across all age groups. In the short latency range two different SL1- and SL2-responses were obtained in children of all age groups as well as in adult controls. Both the SL1- and the SL2-responses showed a flat developmental profile, reaching adult values between 20 and 30 months of age which correlated with that of the fastest efferents from lumbar motor neuron pools to leg muscles, i.e. the final motor path. ML-responses showed a steeper developmental profile.(ABSTRACT TRUNCATED AT 250 WORDS)

Fault failure with moderate earthquakes

High resolution strain and tilt recordings were made in the near-field of, and prior to, the May 1983 Coalinga earthquake ( M L = 6.7, Δ = 51 km), the August 4, 1985, Kettleman Hills earthquake ( M L = 5.5, Δ = 34 km), the April 1984 Morgan Hill earthquake ( M L = 6.1, Δ = 55 km), the November 1984 Round Valley earthquake ( M L = 5.8, Δ = 54 km), the January 14, 1978, Izu, Japan earthquake ( M L = 7.0, Δ = 28 km), and several other smaller magnitude earthquakes. These recordings were made with near-surface instruments (resolution 10 −8), with borehole dilatometers (resolution 10 −10) and a 3-component borehole strainmeter (resolution 10 −9). While observed coseismic offsets are generally in good agreement with expectations from elastic dislocation theory, and while post-seismic deformation continued, in some cases, with a moment comparable to that of the main shock, preseismic strain or tilt perturbations from hours to seconds (or less) before the main shock are not apparent above the present resolution. Precursory slip for these events, if any occurred, must have had a moment less than a few percent of that of the main event. To the extent that these records reflect general fault behavior, the strong constraint on the size and amount of slip triggering major rupture makes prediction of the onset times and final magnitudes of the rupture zones a difficult task unless the instruments are fortuitously installed near the rupture initiation point. These data are best explained by an inhomogeneous failure model for which various areas of the fault plane have either different stress-slip constitutive laws or spatially varying constitutive parameters. Other work on seismic waveform analysis and synthetic waveforms indicates that the rupturing process is inhomogeneous and controlled by points of higher strength. These models indicate that rupture initiation occurs at smaller regions of higher strength which, when broken, allow runaway catastrophic failure.

Short-period nonseismic tilt perturbations and their relation to episodic slip on the San Andreas Fault in central California

Data from four tilt meters and several creep meters along the San Andreas fault in central California 30 km south of Hollister were selected to investigate nonseismic short-period tilt perturbations of minutes to hours duration. The group of short-period tilt amplitude changes with residual deflections was chosen because many nonseismic creep events have similar durations. Although each of the four tilt meters recorded many short-period events, the distribution in space and time suggests that most of these events are due to causes other than slip on the San Andreas fault, such as local strain release. Only at one station used in this investigation (MEL) were creep-related tilt changes observed. A quasi-static dislocation model was constructed to predict the tilt changes associated with propagating slip. Comparing predicted to observed tilt wave forms and amplitudes and comparing the tilt event data to creep event data suggest that (I) a tilt amplitude change of 10 -8-10 -8 rad associated with nonseismic creep events will be observed only if the tilt meter is less than 0.5-1.0 km from the fault, (2) the vertical extent of the slip zone associated with these creep events is greater than about 0.5 km but perhaps not more than a couple of kilometers, (3) nonseismic episodic slip on this part of the San Andreas fault does not appear to propagate uniformly over more than a couple of kilometers, and (4) the model presented in this paper requires 0.5-1.0 mm of dip-slip displacement to reproduce the residual deflection in the creep-related tilt wave forms observed.

Anomalous tilt preceding the Hollister earthquake of November 28, 1974

The occurrence of a magnitude 5.2 earthquake on November 28, 1974, near Hollister in central California, provided an excellent opportunity to test the potential of a prototype tiltmeter array as a predictive tool. Tilt perturbations on instruments near the epicenter were evident about 36 days before the earthquake and coincided with a magnetic field anomaly reported in a companion paper. The anomalous tilts systematically changed with time, reaching values as great as 7 μrad. These data are interpreted in terms of a preseismic and postseismic slip mechanism involving interaction between the San Andreas and other faults in the region, where slip on one results in a sympathetic slip on others.