Numerical Differentiation of Approximated Functions with Limited Order-of-Accuracy Deterioration

We consider the problem of numerical differentiation of a function f from approximate or noisy values of f on a discrete set of points; such discrete approximate data may result from a numerical calculation (such as a finite element or finite difference solution of a partial differential equation), from experimental measurements, or, generally, from an estimate of some sort. In some such cases it is useful to guarantee that orders of accuracy are not degraded: assuming the approximating values of the function are known with an accuracy of order O(h^r), where h is the mesh size, an accuracy of O(h^r) is desired in the value of the derivatives of f. Differentiation of interpolating polynomials does not achieve this goal since, as shown in this text, n-fold differentiation of an interpolating polynomial of any degree ≥ (r − 1) obtained from function values containing errors of order O(h^r) generally gives rise to derivative errors of order O(h^(r−n)); other existing differentiation algorithms suffer from similar degradations in the order of accuracy. In this paper we present a new algorithm, the LDC method (low degree Chebyshev), which, using noisy function values of a function f on a (possibly irregular) grid, produces approximate values of derivatives f^((n)) (n = 1, 2 . . .) with limited loss in the order of accuracy. For example, for (possibly nonsmooth) O(h^r) errors in the values of an underlying infinitely differentiable function, the LDC loss in the order of accuracy is “vanishingly small”: derivatives of smooth functions are approximated by the LDC algorithm with an accuracy of order O(h^r) for all r' < r. The algorithm is very fast and simple; a variety of numerical results we present illustrate the theory and demonstrate the efficiency of the proposed methodology

Folic Acid Supplementation Improves Vascular Function in Professional Dancers With Endothelial Dysfunction

Objective To determine if folic acid supplementation improves vascular function (brachial artery flow-mediated dilation [FMD]) in professional dancers with known endothelial dysfunction. Design Prospective cross-sectional study. Setting Academic institution in the Midwestern United States. Subjects Twenty-two professional ballet dancers volunteered for this study. Main Outcome Measures Subjects completed a 3-day food record to determine caloric and micronutrient intake. Menstrual status was determined by interview and questionnaire. Endothelial function was determined as flow-induced vasodilation measured by high-frequency ultrasound of the brachial artery. A change in brachial diameter of Results Sixty-four percent of dancers (n = 14) had abnormal brachial artery FMD (P\u3c .0001). Conclusions This study reveals that vascular endothelial function improves in dancers after supplementation with folic acid (10 mg/day) for at least 4 weeks. This finding may have clinically important implications for future cardiovascular disease risk prevention

Association Between the Female Athlete Triad and Endothelial Dysfunction in Dancers

Objective: To determine the prevalence of the 3 components of the female athlete triad [disordered eating, menstrual dysfunction, low bone mineral density (BMD)] and their relationships with brachial artery flow-mediated dilation in professional dancers. Design: Prospective study. Setting: Academic institution in the Midwest. Participants: Twenty-two professional ballet dancers volunteered for this study. Interventions: The prevalence of the female athlete triad and its relationship to endothelial dysfunction. Main Outcome Measures: Subjects completed questionnaires to assess disordered eating and menstrual status/history. They also completed a 3-day food record and wore an accelerometer for 3 days to determine energy availability. Serum baseline thyrotropin, prolactin, and hormonal concentrations were obtained. Bone mineral density and body composition were measured with a GE Lunar Prodigy dual-energy X-ray absorptiometry. Endothelial function was determined as flow-mediated vasodilation measured by high-frequency ultrasound in the brachial artery. An increase in brachial diameter Results: Seventeen dancers (77%) had evidence of low/negative energy availability. Thirty-two percent had disordered eating (EDE-Q score). Thirty-six percent had menstrual dysfunction and 14% were currently using hormone contraception. Twenty-three percent had evidence of low bone density (Z-score \u3c -1.0). Sixty-four percent had abnormal brachial artery flow-mediated dilation ( Conclusions: Endothelial dysfunction was correlated with reduced BMD, menstrual dysfunction, and low serum estrogen. These findings may have profound implications for cardiovascular and bone health in professional women dancers

Two-week joint mobilization intervention improves self-reported function, range of motion, and dynamic balance in those with chronic ankle instability

We examined the effect of a 2-week anterior-to-posterior ankle joint mobilization intervention on weight-bearing dorsiflexion range of motion (ROM), dynamic balance, and self-reported function in subjects with chronic ankle instability (CAI). In this prospective cohort study, subjects received six Maitland Grade III anterior-to-posterior joint mobilization treatments over 2 weeks. Weightbearing dorsiflexion ROM, the anterior, posteromedial, and posterolateral reach directions of the Star Excursion Balance Test (SEBT), and self-reported function on the Foot and Ankle Ability Measure (FAAM) were assessed 1 week before the intervention (baseline), prior to the first treatment (pre-intervention), 24–48 h following the final treatment (post-intervention), and 1 week later (1-week follow-up) in 12 adults (6 males and 6 females) with CAI. The results indicate that dorsiflexion ROM, reach distance in all directions of the SEBT, and the FAAM improved (p < 0.05 for all) in all measures following the intervention compared to those prior to the intervention. No differences were observed in any assessments between the baseline and pre-intervention measures or between the postintervention and 1-week follow-up measures (p > 0.05). These results indicate that the joint mobilization intervention that targeted posterior talar glide was able to improve measures of function in adults with CAI for at least 1 week

Plantar Vibrotactile Detection Deficits in Adults with Chronic Ankle Instability

Purpose: The purpose of this study was to investigate the vibrotactile detection thresholds of the plantar cutaneous afferents in subjects with chronic ankle instability compared with healthy control subjects. Methods: Eight adults with chronic ankle instability and eight adults with no ankle sprain history participated. Vibrotactile detection thresholds were assessed using a mechanical stimulus generator system, mounted onto an articulated microscope arm, which delivered sinusoidal vibrotactile inputs to the foot sole at three different sites: head of the first metatarsal, base of the fifth metatarsal, and the heel. Vibrotactile stimulation was delivered at a range of test frequencies that corresponded to the known responsiveness of cutaneous mechanoreceptors in the glabrous skin of the foot sole (10, 25, and 50 Hz). Probe displacement measures (dB) from the last eight displacement trials that contained 50% positive detection responses were averaged to obtain a single threshold estimate for each test frequency and site combination. Results: The results of this study indicate that no significant group-by-site interactions were found for any test frequencies (P \u3e 0.29). However, group main effects were present at the 10-Hz (P \u3c 0.0001), 25-Hz (P = 0.03), and 50-Hz (P = 0.04) test frequencies, indicating that subjects with chronic ankle instability had significantly higher detection thresholds or less sensitivity when stimulation sites were pooled. Conclusions: The results of this study indicate that subjects with chronic ankle instability may demonstrate decreased sensitivity on the plantar surface of the foot. These alterations in plantar cutaneous somatosensation may help explain the underlying mechanisms associated with the prolonged sensorimotor system impairments in postural control and gait commonly exhibited by people with chronic ankle instability

Twitching motility among pathogenic Xylella fastidiosa isolates and the influence of bovine serum albumin on twitching-dependent colony fringe morphology

Fourteen Xylella fastidiosa isolates from grapevines exhibiting Pierce's disease symptoms in California, Texas, and South Carolina were examined for type IV pilus-mediated twitching motility, a phenotype previously observed in a Temecula isolate from California. All isolates except one from South Carolina (SC 19A97) exhibited colonies with a peripheral fringe on PW agar, a feature indicative of twitching motility; however, when individual cells of SC 19A97 were examined at higher magnifications twitching motility was observed. The presence and width of colony peripheral fringes were related to the amount of bovine serum albumin (BSA) present in the medium; no or low levels of BSA (0-1.8 g L−1) permitted development of the widest fringe, whereas higher levels (3.5-6.0 g L−1) severely limited, and in many instances prevented, peripheral fringe development. The growth rate of the wild-type Temecula isolate in PW broth with different concentrations of BSA was similar for all tested concentrations of BSA; however, growth was significantly reduced in medium without BS