Effect of different jump distributions on the dynamics of jump processes

The paper investigates stochastic processes forced by independent and identically distributed jumps occurring according to a Poisson process. The impact of different distributions of the jump amplitudes are analyzed for processes with linear drift. Exact expressions of the probability density functions are derived when jump amplitudes are distributed as exponential, gamma, and mixture of exponential distributions for both natural and reflecting boundary conditions. The mean level-crossing properties are studied in relation to the different jump amplitudes. As an example of application of the previous theoretical derivations, the role of different rainfall-depth distributions on an existing stochastic soil water balance model is analyzed. It is shown how the shape of distribution of daily rainfall depths plays a more relevant role on the soil moisture probability distribution as the rainfall frequency decreases, as predicted by future climatic scenarios. © 2010 The American Physical Society.

Changes in landing mechanics in patients following anterior cruciate ligament reconstruction when wearing an extension constraint knee brace.

BACKGROUND: Anterior cruciate ligament (ACL) reconstruction is associated with a high incidence of second tears (graft tears and contralateral ACL tears). These secondary tears have been attributed to asymmetrical lower extremity mechanics. Knee bracing is one potential intervention that can be used during rehabilitation that has the potential to normalize lower extremity asymmetry; however, little is known about the effect of bracing on movement asymmetry in patients following ACL reconstruction. HYPOTHESIS: Wearing a knee brace would increase knee joint flexion and joint symmetry. It was also expected that the joint mechanics would become more symmetrical in the braced condition. OBJECTIVE: To examine how knee bracing affects knee joint function and symmetry over the course of rehabilitation in patients 6 months following ACL reconstruction. STUDY DESIGN: Controlled laboratory study. LEVEL OF EVIDENCE: Level 3. METHODS: Twenty-three adolescent patients rehabilitating from ACL reconstruction surgery were recruited for the study. The subjects all underwent a motion analysis assessment during a stop-jump activity with and without a functional knee brace on the surgical side that resisted extension for 6 months following the ACL reconstruction surgery. Statistical analysis utilized a 2 × 2 (limb × brace) analysis of variance with a significant alpha level of 0.05. RESULTS: Subjects had increased knee flexion on the surgical side when they were braced. The brace condition increased knee flexion velocity, decreased the initial knee flexion angle, and increased the ground reaction force and knee extension moment on both limbs. Side-to-side asymmetry was present across conditions for the vertical ground reaction force and knee extension moment. CONCLUSION: Wearing a knee brace appears to increase lower extremity compliance and promotes normalized loading on the surgical side. CLINICAL RELEVANCE: Knee extension constraint bracing in postoperative ACL patients may improve symmetry of lower extremity mechanics, which is potentially beneficial in progressing rehabilitation and reducing the incidence of second ACL tears.

Using ground reaction force to predict knee kinetic asymmetry following anterior cruciate ligament reconstruction.

Asymmetries in sagittal plane knee kinetics have been identified as a risk factor for anterior cruciate ligament (ACL) re-injury. Clinical tools are needed to identify the asymmetries. This study examined the relationships between knee kinetic asymmetries and ground reaction force (GRF) asymmetries during athletic tasks in adolescent patients following ACL reconstruction (ACL-R). Kinematic and GRF data were collected during a stop-jump task and a side-cutting task for 23 patients. Asymmetry indices between the surgical and non-surgical limbs were calculated for GRF and knee kinetic variables. For the stop-jump task, knee kinetics asymmetry indices were correlated with all GRF asymmetry indices (P < 0.05), except for loading rate. Vertical GRF impulse asymmetry index predicted peak knee moment, average knee moment, and knee work (R(2)  ≥ 0.78, P < 0.01) asymmetry indices. For the side-cutting tasks, knee kinetic asymmetry indices were correlated with the peak propulsion vertical GRF and vertical GRF impulse asymmetry indices (P < 0.05). Vertical GRF impulse asymmetry index predicted peak knee moment, average knee moment, and knee work (R(2)  ≥ 0.55, P < 0.01) asymmetry indices. The vertical GRF asymmetries may be a viable surrogate for knee kinetic asymmetries and therefore may assist in optimizing rehabilitation outcomes and minimizing re-injury rates.

Risk of dislocation using large- vs. small-diameter femoral heads in total hip arthroplasty.

BACKGROUND: Dislocation remains a difficult problem in total hip arthroplasty. Large-diameter femoral heads may lower the incidence of dislocation by enhancing the jump distance and decreasing impingement, but their performance against small-diameter heads has not been assessed. This study compared the mid-term radiographic and functional outcomes of two matched cohorts of patients undergoing total hip arthroplasty who had a high pre-operative risk for dislocation and who received either small-diameter (26- or 28-millimeters) or large-diameter (≥36-millimeters) femoral heads. METHODS: All patients who received large-diameter heads (≥36-millimeter) between 2002 and 2005, and who had pre-operative risk factors for dislocation, were identified in the institution's joint registry. Forty-one patients (52 hips) who received large-diameter heads were identified, and these patients were matched to 48 patients (52 hips) in the registry who received small-diameter femoral heads. RESULTS: At mean final follow-up of 62 months (range, 49 to 101 months), both groups achieved excellent functional outcomes as measured by Harris Hip scores, with slightly better final scores in the large-diameter group (90 vs. 83 points). No patient showed any radiographic signs of loosening. No patient dislocated in the large-diameter femoral head group; the smaller-diameter group had a greater rate of dislocation (3.8%, 2 out of 52). CONCLUSIONS: Large-diameter femoral head articulations may reduce dislocation rates in patients who have a high pre-operative risk for dislocation while providing the same functional improvements and safety as small-diameter bearings.

Measuring Tail Risks at High Frequency

I develop a new methodology for measuring tail risks using the cross section of bid-ask spreads. Market makers embed tail risk information into spreads because (1) they lose to arbitrageurs when changes to asset values exceed the cost of liquidity and (2) underlying price movements and potential costs are linear in factor loadings. Using this insight, simple cross-sectional regressions relating spreads and trading volume to factor betas can recover tail risks in real time for priced or non-priced return factors. The methodology disentangles financial and aggregate market risks during the 2007-2008 Financial Crisis; anticipates jump risks associated with Federal Open Market Committee announcements; and quantifies a sharp, temporary increase in market tail risk before and throughout the 2010 Flash Crash. The recovered time series of implied market risks also aligns closely with both realized market jumps and the VIX.