Mass perturbation of a body segment: 1. Effects on segment dynamics

Investigators often use mass perturbation of body segments as an experimental paradigm to study movement coordination. To analyze the effect of mass perturbation on small-amplitude oscillations, the authors linearize the equation of motion of a single segment moving in a vertical plane and derive the effect of added mass on the undamped eigenfrequency, the relative damping, and the low-frequency control gain of the segment. Mass addition results in a decrease in both the relative damping and the low-frequency control gain; the undamped eigenfrequency increases for mass addition between the pivot point and R0 (where R0 is the length of a point mass pendulum whose undamped eigenfrequency is identical to that of the unperturbed segment), decreases for mass addition beyond R0, and remains unaffected for mass addition at R0. For a typical lower leg + foot segment, R0 is just proximal to the ankle joint. That location may explain the absence of an effect on oscillation frequency in studies in which mass has been added to the ankle. The authors' analysis provides a basis for a more effective application of mass perturbations in future experiments.     

Mass Perturbation of a Body Segment: 2. Effects on Interlimb Coordination

The shifts in relative phase that are observed when rhythmically coordinated limbs are submitted to asymmetric mass perturbations have typically been attributed to the induced eigenfrequency difference ($DL$oM) between the limbs. Modeling the moving limbs as forced linear oscillators, however, reveals that asymmetric mass perturbations may induce a difference not only in eigenfrequency (i.e., $DL$oM $$ 0) but also in the covarying low-frequency control gains (i.e., $DLk $$ 0). Because the inverse of the lowfrequency control gain (k) reflects the level of muscular torque (input) required for a particular displacement from equilibrium (output), asymmetric mass perturbations may result in an imbalance in the muscular torques required for task performance (related to $DLk $$ 0). Thus, it is possible that the effects attributed to $DL$oM were in fact mediated by $DLk. In 2 experiments, the authors manipulated $DLk and $DL$oM separately by applying mass perturbations to the lower legs of 9 participants. The relative phasing between the legs was not affected by $DLk, but manipulation of $DL$oM (while $DLk remained approximately 0) induced systematic relative phase shifts that were more pronounced for antiphase than for in-phase coordination. That indication that the coordination dynamics is indeed influenced by an imbalance in eigenfrequency is discussed vis-à-vis the question of how such a merely peripheral property may affect the underlying coordination process.     

Mass perturbation of a body segment: 2. Effects on interlimb coordination

The shifts in relative phase that are observed when rhythmically coordinated limbs are submitted to asymmetric mass perturbations have typically been attributed to the induced eigenfrequency difference (delta omega) between limbs. Modeling the moving limbs as forced linear oscillators, however, reveals that asymmetric mass perturbations may induce a difference not only in eigenfrequency (i.e., delta omega not equal 0) but also in the covarying low-frequency control gains (i.e., delta k not equal 0). Because the inverse of the low-frequency control gain (k) reflects the level of muscular torque (input) required for a particular displacement from equilibrium (output), asymmetric mass perturbations may result in an imbalance in the muscular torques required for task performance (related to delta k not equal 0). Thus, it is possible that the effects attributed to delta omega were in fact mediated by delta k. In 2 experiments, the authors manipulated delta k and delta omega separately by applying mass perturbations to the lower legs of 9 participants. The relative phasing between the legs was not affected by delta k, but manipulation of delta omega (while delta k remained approximately 0) induced systematic relative phase shifts that were more pronounced for antiphase than for in-phase coordination. That indication that the coordination dynamics is indeed influenced by an imbalance in eigenfrequency is discussed vis-a-vis the question of how such a merely peripheral property may affect the underlying coordination process.     

A model and algorithm for multidimensional scaling with external constraints on the distances

A method for externally constraining certain distances in multidimensional scaling configurations is introduced and illustrated. The approach defines an objective function which is a linear composite of the loss function of the point configurationX relative to the proximity dataP and the loss ofX relative to a pseudo-data matrixR. The matrixR is set up such that the side constraints to be imposed onX's distances are expressed by the relations amongR's numerical elements. One then uses a double-phase procedure with relative penalties on the loss components to generate a constrained solutionX. Various possibilities for constructing actual MDS algorithms are conceivable: the major classes are defined by the specification of metric or nonmetric loss for data and/or constraints, and by the various possibilities for partitioning the matricesP andR. Further generalizations are introduced by substitutingR by a set ofR matrices,R _i ,i=1, ...r, which opens the way for formulating overlapping constraints as, e.g., in patterns that are both row- and column-conditional at the same time.     

On the non-availability of Dawson-modeling into certain relevance alethic modal logics

This paper shows that the Dawson technique of modelling deontic logics into alethic modal logics to gain insight into deontic formulas is not available for modelling a normal (in the spirit of Anderson) relevance deontic modal logic into either of the normal relevance alethic modal logics R _S4or R _M. The technique is to construct an extension of the well known entailment matrix set M ₀and show that the model of the deontic formula P (A v B). PA v PB is excluded.     

A fixed interval schedule in which the interval is initiated by a response

The fixed interval schedule described requires the animal to initiate every time interval by making a response on a bar other than the one on which it is reinforced. This response, R_A, demarcates the postreinforcement pause (S^R-R_A interval) from the fixed interval pause (R_A-R_B interval) so that these pauses may be measured separately. Twelve rats and three monkeys, working in two-bar Skinner boxes, were trained and stabilized on this schedule. The resulting performances, presented for individual animals, are analyzed in terms of (1) the relative frequencies with which the animal waits various lengths of time between consecutive responses, (2) the relative frequencies with which various rates of responding appear, (3) the change in response rate throughout the fixed interval, (4) the average length of the postreinforcement pause, (5) the relative frequencies with which the animal waits different lengths of time between the R_A and the first R_B, and (6) the average inter-response time as a function of the rank order in the fixed interval of the inter-response time. The joint interpretation of the several measures taken leads to the following conclusions: 1. The probability of an R_B increases throughout the fixed interval. 2. The increase is discontinuous at the first R_B, at which point the probability increases sharply. 3. The frequency distributions of R_A-R_B pauses exhibit three discrete types of behavior with no intermediate cases. 4. The (main) mode of R_A-R_B interval length usually occurs just below the fixed interval requirement.     

Note on a rank test of cronholm and revusky

A rank testR _n has been proposed by Cronholm and Revusky which in effect increases the number of observations per subject by the device of randomly assigning a subject to a treated group in each of a series of sub-experiments. In this note further results on the asymptotic normality of theR _n test are discussed both under the null hypothesisH ₀ of randomness and under a class of alternatives toH ₀. The limiting power of the test is also discussed.     

Local Dynamic Stability of the Locomotion of Lower Extremity Joints and Trunk During Backward Upslope Walking

Backward slope walking was considered as a practical rehabilitation and training skill. However, its gait stability has been hardly studied, resulting in its limited application as a rehabilitation tool. In this study, the effect of walking direction and slope grade were investigated on the local dynamic stability of the motion of lower extremity joints and trunk segment during backward and forward upslope walking (BUW/FUW). The local divergence exponents (λ_S) of 16 adults were calculated during their BUW and FUW at grades of 0%, 5%, 10%, and 15%. Mean standard deviation over strides (MeanSD) was analyzed as their gait variability. Backward walking showed larger λ_S for the abduction-adduction and rotational angles of knee and ankle on inclined surface than forward walking, while λ_S for hip flexion-extension angle at steeper grades was opposite. No grade effect for any joint existed during BUW, while λ_S increased with the increasing grade during FUW. As to the trunk, walking direction did little impact on λ_S. Still, significant larger λ_S for its medial-lateral and vertical motion were found at the steeper grades during both FUW and BUW. Results indicate that during BUW, the backward direction may influence the stability of joint motions, while the trunk stability was challenged by the increasing grades. Therefore, BUW may be a training tool for the stability of both upper and lower body motion during gait.     

Local muscle oxygen consumption related to external and joint specific power

The purpose of the present study was to examine the effects of external work rate on joint specific power and the relationship between knee extension power and vastus lateralis muscle oxygen consumption (mVO₂). We measured kinematics and pedal forces and used inverse dynamics to calculate joint power for the hip, knee and ankle joints during an incremental cycling protocol performed by 21 recreational cyclists. Vastus lateralis mVO₂ was estimated using near-infrared spectroscopy with an arterial occlusion. The main finding was a non-linear relationship between vastus lateralis mVO₂ and external work rate that was characterised by an increase followed by a tendency for a levelling off (R² = 0.99 and 0.94 for the quadratic and linear models respectively, p < 0.05). When comparing 100 W and 225 W, there was a ∼43 W increase in knee extension but still a ∼9% decrease in relative contribution of knee extension to external work rate resulting from a ∼47 W increase in hip extension. When vastus lateralis mVO₂ was related to knee extension power, the relationship was still non-linear (R² = 0.99 and 0.97 for the quadratic and linear models respectively, p < 0.05). These results demonstrate a non-linear response in mVO₂ relative to a change in external work rate. Relating vastus lateralis mVO₂ to knee extension power showed a better fit to a linear equation compared to external work rate, but it is not a straight line.     

Effects of a DRL contingency added to a fixed-interval reinforcement schedule

Following 30 days of reinforcement for the bar press response of two white rats on 30-sec fixed-interval (FI), a DRL component was added so that a minimal interresponse time (IRT) for the reinforced response, in addition to the FI variable, was necessary for reinforcement. Marked control over response rate by the superimposed DRL requirement was demonstrated by an inverse hyperbolic function as the DRL component was increased from 1 to 24 sec within the constant 30-sec FI interval. Interresponse time and post-reinforcement (post-S^R) “break” distributions taken at one experimental point (DRL = 24 sec) suggested that a more precise temporal discrimination was initiated by an S^R than by a response, since the relative frequency of a sequence of two reinforced responses appeared greater than that of a sequence of a non-reinforced response followed by a reinforced one. This latter finding was confirmed with new animals in a follow-up experiment employing a conventional 24-sec DRL schedule.     

Constructing a covariance matrix that yields a specified minimizer and a specified minimum discrepancy function value

A method is presented for constructing a covariance matrix Σ*₀ that is the sum of a matrix Σ(γ₀) that satisfies a specified model and a perturbation matrix,E, such that Σ*₀=Σ(γ0) +E. The perturbation matrix is chosen in such a manner that a class of discrepancy functionsF(Σ*₀, Σ(γ₀)), which includes normal theory maximum likelihood as a special case, has the prespecified parameter value γ₀ as minimizer and a prespecified minimum δ A matrix constructed in this way seems particularly valuable for Monte Carlo experiments as the covariance matrix for a population in which the model does not hold exactly. This may be a more realistic conceptualization in many instances. An example is presented in which this procedure is employed to generate a covariance matrix among nonnormal, ordered categorical variables which is then used to study the performance of a factor analysis estimator. We are grateful to Alexander Shapiro for suggesting the proof of the solution in section 2.     

Myelin breakdown mediates age-related slowing in cognitive processing speed in healthy elderly men

Background

To assess the hypothesis that in a sample of very healthy elderly men selected to minimize risk for Alzheimer’s disease (AD) and cerebrovascular disease, myelin breakdown in late-myelinating regions mediates age-related slowing in cognitive processing speed (CPS).

Materials and methods

The prefrontal lobe white matter and the genu of the corpus callosum myelinate later in brain development (late-myelinating white matter; LMWM) and are more vulnerable to breakdown due to the effects of normal aging. An in vivo MRI biomarker of myelin integrity (transverse relaxation rates; R₂) of LMWM was obtained for 38 very healthy elderly adult men (mean age = 66.3 years; SD = 6.0; range = 55–76). To evaluate regional specificity, we also assessed a contrasting early-myelinating region (splenium of the corpus callosum; SWM), which primarily contains axons involved in visual processing. CPS was assessed using the Trail Making Test.

Results

LMWM R₂ and CPS measures were significantly correlated (r = .515, p = .0009), but no significant association between R₂ and CPS was detected in the splenium (p = .409). LMWM R₂, but not SWM R₂, was a significant mediator of the relationship between age and CPS (p = .037).

Conclusions

In this very healthy elderly sample, age-related slowing in CPS is mediated by myelin breakdown in highly vulnerable late-myelinating regions but not in the splenium.     

On sensitive rank tests for comparing the effects of two treatments on a single group

The rank testR _n of Cronholm and Revusky [1965] in effect doubles the number of comparisons carried out in the Mann-Whitney test between Treated and Control subjects chosen from a single group ofn and triples the asymptotic Pitman efficiency against shift alternatives by using a series ofn — 1 subexperiments. However, the full series can be too costly or time-consuming. It is shown thatj appropriately chosen subexperiments will permit one to make at leastj/(j+1) of the number of comparisons possible underR _n, with large sample efficiency ofj/(j+2) relative toR _n against shift alternatives and small sample efficiency greater than that,j=2, 3, ...,n — 2. The resulting test criterion is a sum ofj independent Mann-Whitney test statistics. Its null distribution is tabulated forn10 and small sample efficiency comparisons are carried out forn=10.     

The effects of obesity on balance recovery using an ankle strategy

Obesity is associated with an increased risk of falls. The purpose of this study was to investigate the effects of obesity on balance recovery using an ankle strategy. In addition, computer simulations to understand how increased inertia and weight associated with obesity independently influence balance recovery. Ten normal weight (BMI: 22.7 ± 0.6 kg/m²) and ten obese (BMI: 32.2 ± 2.2 kg/m²) adult male subjects participated in the study. Subjects recovered balance using an ankle strategy after three types of postural perturbations: an initial angular displacement, an initial angular velocity from the natural stance, and an initial angular velocity from a prescribed position. Balance recovery was quantified by the largest initial angular displacement or angular velocity from which balance could be recovered. Obesity impaired balance recovery from perturbations involving an initial angular velocity, but not from an initial angular displacement. Similarly, computer simulations determined that increased inertia is beneficial to balance recovery when there is little to no initial angular velocity. These findings indicate that the effects of obesity on balance recovery are dependent on the type of perturbation, and that increased inertia associated with obesity can be beneficial for perturbations that involve little to no initial angular velocity.     

Relative damping improves linear mass-spring models of goal-directed movements

A limitation of a simple linear mass-spring model in describing goal directed movements is that it generates rather slow movements when the parameters are kept within a realistic range. Does this imply that the control of fast movements cannot be approximated by a linear system? In servo-control theory, it has been proposed that an optimal controller should control movement velocity in addition to position. Instead of explicitly controlling the velocity, we propose to modify a simple linear mass-spring model. We replaced the damping relative to the environment (absolute damping) with damping with respect to the velocity of the equilibrium point (relative damping). This gives the limb a tendency to move as fast as the equilibrium point. We show that such extremely simple models can generate rapid single-joint movements. The resulting maximal movement velocities were almost equal to those of the equilibrium point, which provides a simple mechanism for the control of movement speed. We further show that peculiar experimental results, such as an 'N-shaped' equilibrium trajectory and the difficulties to measure damping in dynamic conditions, may result from fitting a model with absolute damping where one with relative damping would be more appropriate. Finally, we show that the model with relative damping can be used to model subtle differences between multi-joint interceptions. The model with relative damping fits the data much better than a version of the model with absolute damping.     

Restricted ranking

This paper is a study of certain aspects of restricted ranking, a method intended for use by a panel ofm judges evaluating the relative merits ofN subjects, candidates for scholarships, awards, etc. Each judge divides theN subjects intoR classes so thatn _i individuals receive a gradei (i = 1, 2, ...,R; Σn _i =N) where theR numbersn _i are close toN/R (n _i =N/R whenN is divisible byR) and are preassigned and the same for all judges. This method is superior in several respects to other likely alternatives. Under the null hypothesis that allnR =N subjects are of equal merit, four tests of significance are developed. The effectiveness of the method is investigated both theoretically by means of the asymptotic relative efficiency and more generally by simulation studies. When the numbersn _i are not restricted to values close to or equal toN/R but instead are given values conforming to a normally distributed pattern, the resulting method is known as theQ-sort, so designated by certain investigators in psychotherapy. The simulation studies reveal that restricted ranking is only slightly inferior to complete ranking and generally superior in the cases considered to theQ-sort, although there are likely to be other situations when the latter is superior. The authors are indebted to Dr. Clyde Kramer of Virginia Polytechnic Institute for bringing theQ-sort ranking technique of psychotherapy to their attention.     

Comparative analyses of rider position according to skill levels during walk and trot in Jeju horse

The purpose of this study was to evaluate the rider position at walk and trot as a function of rider skill level by analyzing joint angles. Participants included three advanced riders and six beginners, and training was conducted for one hour, twice a week for 24 weeks. In the walk stage of the beginners’ group, the elbows and shoulders sustained postures comparable to those of the advanced riders group; the trunk tilted forwards at first, but later it tilted slightly behind the vertical. The knee, ankle, and left–right angle kept stable postures after 12 weeks of training (p < .05). The front-rear (FR) angle of the beginners group improved during training, but it was still lower than the advanced riders group after 24 weeks of training (p < .05). At trot, while the knee angle measurement of the beginners’ group was similar to the advanced riders, the ankle joint sustained a forward point posture. The ankle joint maintained dorsiflexion posture with 83.9° ± 5.3 in the advanced riders group, while the beginners group had plantar flexion posture with 98.7° ± 6.0. This study suggested that the correlation between the joint and body segment angles could be an important indicator in the evaluation of rider proficiency.     

Stereoscopic acuity for photometrically matched background wavelengths at scotopic and photopic levels

Two Ss made equidistance settings in a two-rod apparatus using white and four chromatic (red, yellow, Feen, and blue) backgrounds, photometrically matched at each of eight or nine teat levels within a total retinal-illuminance range of 4 log units. The binocular depth setting were analyzed in terms of the angular magnitude of both the Yariable error, η_AD, and the constant error, η_ΔR When η_AD is plotted as a function of retinal illuminance, the curves for each of the four chromatic IIIId white backlfound coditions show that at low retinal illuminances, η_AD, is initially large, and with increasing background illumination, η_AD progressively decreases to approach a final low asymptotic value. As predicted by the duplicity theory of vision, each experimental curve shows a dircontinulty at about ?1.0 lot td (corresponding to a background luminance value of about 0.0069 fL with the 2.5-mm artificial pupil used) reflecting the transition from rod to cone functioning. The curves representing the different wavelengths essentially overlap throughout the total illumination range, indicating that, for both rod and cone vision, wavelength has no differential effect on the variability of depth settings. The data for η_ΔR are less regular than those for η_AD and the rod-cone discontinuities appear less pronounced. The data are analyzed in terms of the relative contribution of the rod and cone mechanisms to performance level.     

The effects of initial movement dynamics on human responses to postural perturbations

Falls are a major cause of injury, and often occur while turning, reaching, or bending. Yet, we have little understanding of how an ongoing feet-in place activity at the onset of imbalance, and its associated cognitive and biomechanical demands, influence our ability to recover balance. In the current study, we used an ankle-rocking paradigm to determine how the nature of the baseline task influences the balance recovery response to a backward support surface translation. Fourteen participants were instructed to “recover balance without stepping” and were perturbed at vertical while standing quietly (“S”), while ankle rocking and moving forward (“A_f”), or while ankle rocking and moving backward (“A_b”). The results showed that changes in rocking velocity at the time of the perturbation elicited changes in the incidence of stepping, magnitude of trunk angular displacements (p < .01), and the onset latencies of distal muscles (gastrocnemius and soleus, both p < .01) used to recover balance. In addition, plots of onset latencies across all muscles showed that onset latencies appeared to occur earlier in many muscles when participants held a static position compared to when they performed a dynamic task at the onset of the perturbation. The results suggest that muscle activities used to recover balance are tailored to the nature of the perturbation and the ongoing task, and that onset latencies are later when participants are performing a dynamic as opposed to static task at the time of a perturbation. These findings support previous research suggesting that automatic postural responses are highly adaptable to environmental, situational, and task demands.     

The pendular mechanism does not determine the optimal speed of loaded walking on gradients

The pendular mechanism does not act as a primary mechanism in uphill walking due to the monotonic behavior of the mechanical energies of the center of mass. Nevertheless, recent evidence shows that there is an important minimization of energy expenditure by the pendular mechanism during walking on uphill gradients. In this study, we analyzed the optimum speed (OPT) of loaded human walking and the pendulum-like determining variables (Recovery R, Instantaneous pendular re-conversion R_int, and Congruity percentage %Cong). Ten young men walked on a treadmill at five different speeds and at three different treadmill incline gradients (0, +7 and +15%), with and without a load carried in their backpacks. We used indirect calorimetry and 3D motion analysis, and all of the data were analyzed by computational algorithms. R_int increased at higher speeds and decreased with increasing gradient. R and %Cong decreased with increasing gradient and increased with speed, independent of load. Thus, energy conversion by the pendular mechanism during walking on a 15% gradient is supported, and although this mechanism can explain the maintenance of OPT at low walking speeds, the pendular mechanism does not fully explain the energy minimization at higher speeds.