RUNNING SHOE STIFFNESS:THE EFFECT ON WALKING GAIT

Sports shoes can be grouped into various categories based on their stability, protection capabilities, traction, impact characteristics and stiffness. The majority of shoe tests involve measures of traction and impact. Few studies have examined shoe sole stiffness. Therefore, the purpose of this study was to assess shoe sole stiffness by a materials testing procedure, and then examine the effect of shoe stiffness on walking gait. A damped oscillation technique, previously used on muscle-tendon complexes, was utilised to calculate the stiffness and the damping factor of six types of running shoes. The shoes used different rnidsole components which included air sacs, gel sacs, ethylene vinyl acetate (EVA), and kevlar reinforcing. Two shoes at the extremes of the range were then selected from the materials test results for use in the subsequent gait analysis. Nine males ranging in age from 25 to 45 years (mean =36 years) participated in the experiment. Heights ranged from 186cm to 176cm (mean=182cm) and weights ranged from 72.5kg to 89kg (mean=8lkg). No subjects had any musculoskeletal problems affecting the lower limb. Two dimensional video data were collected on the right leg using an Ariel Video Analysis system sampling at 50 Hz, as subjects walked at 5.1 km/hr on a motor driven treadmill. Markers were placed on the greater trochanter, lateral condyle of the femur, lateral malleolus of the fibular, the heel of the shoe and on the shoe at the level of the fifth metatarsal head. Three stride cycles were collected after the subjects had walked on the treadmill for one minute. Data were digitised and downloaded to FMAP software to calculate kinematic variables such as knee and ankle angle and knee and ankle angular velocity. Data were then normalised to 50 points and averaged across stride cycles and subjects. Although a comparison of the stiff and flexible shoes indicated no differences in the kinematic parameters (p>0.05), it may be that the muscles of the lower limb adjust their activity level for the stiffness of the shoe to maintain an invariant kinematic pattern

Evolution of the pairing pseudogap in the spectral function with interplane anisotropy

We study the pairing pseudogap in the spectral function as a function of interplane coupling. The analytical expressions for the self-energy in the critical regime are obtained for any degree of anisotropy. The frequency dependence of the self-energy is found to be qualitatively different in two and three dimensions, and the crossover from two to three dimensional behavior is discussed. In particular, by considering the anisotropy of the Fermi velocity and gap along the Fermi surface, we can qualitatively explain recent photoemission experiments on high temperature superconductors concerning the temperature dependent Fermi arcs seen in the pseudogap phase.Comment: 20 pages, revtex, 5 encapsulated postscript figures include

Detecting fractions of electrons in the high-TcT_c cuprates

We propose several tests of the idea that the electron is fractionalized in the underdoped and undoped cuprates. These include the ac Josephson effect, and tunneling into small superconducting grains in the Coulomb blockade regime. In both cases, we argue that the results are qualitatively modified from the conventional ones if the insulating tunnel barrier is fractionalized. These experiments directly detect the possible existence of the chargon - a charge $e$ spinless boson - in the insulator. The effects described in this paper provide a means to probing whether the undoped cuprate (despite it's magnetism) is fractionalized. Thus, the experiments discussed here are complementary to the flux-trapping experiment we proposed in our earlier work(cond-mat/0006481).Comment: 7 pages, 5 figure

Generalized Drinfeld-Sokolov Reductions and KdV Type Hierarchies

Generalized Drinfeld-Sokolov (DS) hierarchies are constructed through local reductions of Hamiltonian flows generated by monodromy invariants on the dual of a loop algebra. Following earlier work of De Groot et al, reductions based upon graded regular elements of arbitrary Heisenberg subalgebras are considered. We show that, in the case of the nontwisted loop algebra $\ell(gl_n)$, graded regular elements exist only in those Heisenberg subalgebras which correspond either to the partitions of $n$ into the sum of equal numbers $n=pr$ or to equal numbers plus one $n=pr+1$. We prove that the reduction belonging to the grade $1$ regular elements in the case $n=pr$ yields the $p\times p$ matrix version of the Gelfand-Dickey $r$-KdV hierarchy, generalizing the scalar case $p=1$ considered by DS. The methods of DS are utilized throughout the analysis, but formulating the reduction entirely within the Hamiltonian framework provided by the classical r-matrix approach leads to some simplifications even for $p=1$.Comment: 43 page

Revisiting the X:BOT Naltrexone Clinical Trial Using a Comprehensive Survival Analysis

Objectives This paper illustrates survival models for analysis of trials of substance use treatment programs. It uses public release data from a study of extended-release naltrexone (XR-NTX), relative to buprenorphine-naloxone (BUP-NX). Methods We used publicly available data from the X:BOT trial (n = 570), which compared XR-NTX to BUP-NX on 2 efficacy outcomes (opioid relapse, use of nonprescribed opioids; positive opioid urine test) and 1 safety outcome (overdose). Intention-to-treat (ITT) and per-protocol approaches were implemented using survival models that included treatment-by-time interactions. Results Consistent with the original trial findings, 72% of XR-NTX and 94% of BUP-NX subjects initiated treatment; the ITT hazard ratio for XR-NTX relative to BUP-NX was 1.40 (95% confidence interval: 1.13, 1.73; P < 0.01) for opioid relapse and 1.31 (1.07, 1.60; P = 0.01) for positive urine test. Using treatment-by-time interactions, we examined the time-dependent effect of XR-NTX and found an elevated ITT overdose hazard ratio of 2.4 (1.1, 5.3; P = 0.03) overall and 3.8 (1.2, 11.6; P = 0.02) during the study treatment phase. This result (28 overdoses overall; 17 overdoses during the study treatment phase) contrasts with the previous analysis, which reported minimal differences in overdose between XR-NTX and BUP-NX. Conclusions An advantage of using time-dependent Cox models is its ability to isolate effects during specific periods. In general, our survival analyses concur with the conclusions of Lee et al (2018) for the efficacy outcomes, which demonstrated superiority of BUP-NX. In contrast to the original report, our analysis indicates a greater risk of overdose for XR-NTX, predominantly during the study treatment phase. Further investigation of this finding is a pressing research priority

Extensions of the matrix Gelfand-Dickey hierarchy from generalized Drinfeld-Sokolov reduction

The $p\times p$ matrix version of the $r$-KdV hierarchy has been recently treated as the reduced system arising in a Drinfeld-Sokolov type Hamiltonian symmetry reduction applied to a Poisson submanifold in the dual of the Lie algebra $\widehat{gl}_{pr}\otimes {\Complex}[\lambda, \lambda^{-1}]$. Here a series of extensions of this matrix Gelfand-Dickey system is derived by means of a generalized Drinfeld-Sokolov reduction defined for the Lie algebra $\widehat{gl}_{pr+s}\otimes {\Complex}[\lambda,\lambda^{-1}]$ using the natural embedding $gl_{pr}\subset gl_{pr+s}$ for $s$ any positive integer. The hierarchies obtained admit a description in terms of a $p\times p$ matrix pseudo-differential operator comprising an $r$-KdV type positive part and a non-trivial negative part. This system has been investigated previously in the $p=1$ case as a constrained KP system. In this paper the previous results are considerably extended and a systematic study is presented on the basis of the Drinfeld-Sokolov approach that has the advantage that it leads to local Poisson brackets and makes clear the conformal ($\cal W$-algebra) structures related to the KdV type hierarchies. Discrete reductions and modified versions of the extended $r$-KdV hierarchies are also discussed.Comment: 60 pages, plain TE

Microscopic theory of weak pseudogap behavior in the underdoped cuprate superconductors I: General theory and quasiparticle properties

We derive in detail a novel solution of the spin fermion model which is valid in the quasi-static limit pi T<<omega_sf, found in the intermediate (pseudoscaling) regime of the magnetic phase diagram of cuprate superconductors, and use it to obtain results for the temperature and doping dependence of the single particle spectral density, the electron-spin fluctuation vertex function, and the low frequency dynamical spin susceptibility. The resulting strong anisotropy of the spectral density and the vertex function lead to the qualitatively different behavior of_hot_ (around k=(pi,0)) and_cold_ (around k=(pi/2,pi/2)) quasiparticles seen in ARPES experiments. We find that the broad high energy features found in ARPES measurements of the spectral density of the underdoped cuprate superconductors are determined by strong antiferromagnetic (AF) correlations and incoherent precursor effects of an SDW state, with reduced renormalized effective coupling constant. The electron spin-fluctuation vertex function, i.e. the effective interaction of low energy quasiparticles and spin degrees of freedom, is found to be strongly anisotropic and enhanced for hot quasiparticles; the corresponding charge-fluctuation vertex is considerably diminished. We thus demonstrate that, once established, strong AF correlations act to reduce substantially the effective electron-phonon coupling constant in cuprate superconductors.Comment: REVTEX with EPS figures, uses multicol.sty, epsfig,sty, psfig.st

Pinned Balseiro-Falicov Model of Tunneling and Photoemission in the Cuprates

The smooth evolution of the tunneling gap of Bi_2Sr_2CaCu_2O_8 with doping from a pseudogap state in the underdoped cuprates to a superconducting state at optimal and overdoping, has been interpreted as evidence that the pseudogap must be due to precursor pairing. We suggest an alternative explanation, that the smoothness reflects a hidden SO(N) symmetry near the (pi,0) points of the Brillouin zone (with N = 3, 4, 5, or 6). Because of this symmetry, the pseudogap could actually be due to any of a number of nesting instabilities, including charge or spin density waves or more exotic phases. We present a detailed analysis of this competition for one particular model: the pinned Balseiro-Falicov model of competing charge density wave and (s-wave) superconductivity. We show that most of the anomalous features of both tunneling and photoemission follow naturally from the model, including the smooth crossover, the general shape of the pseudogap phase diagram, the shrinking Fermi surface of the pseudogap phase, and the asymmetry of the tunneling gap away from optimal doping. Below T_c, the sharp peak at Delta_1 and the dip seen in the tunneling and photoemission near 2Delta_1 cannot be described in detail by this model, but we suggest a simple generalization to account for inhomogeneity, which does provide an adequate description. We show that it should be possible, with a combination of photoemission and tunneling, to demonstrate the extent of pinning of the Fermi level to the Van Hove singularity. A preliminary analysis of the data suggests pinning in the underdoped, but not in the overdoped regime.Comment: 18 pages LaTeX, 26 ps. figure

Stripes, Pseudogaps, and Van Hove Nesting in the Three-band tJ Model

Slave boson calculations have been carried out in the three-band tJ model for the high-T_c cuprates, with the inclusion of coupling to oxygen breathing mode phonons. Phonon-induced Van Hove nesting leads to a phase separation between a hole-doped domain and a (magnetic) domain near half filling, with long-range Coulomb forces limiting the separation to a nanoscopic scale. Strong correlation effects pin the Fermi level close to, but not precisely at the Van Hove singularity (VHS), which can enhance the tendency to phase separation. The resulting dispersions have been calculated, both in the uniform phases and in the phase separated regime. In the latter case, distinctly different dispersions are found for large, random domains and for regular (static) striped arrays, and a hypothetical form is presented for dynamic striped arrays. The doping dependence of the latter is found to provide an excellent description of photoemission and thermodynamic experiments on pseudogap formation in underdoped cuprates. In particular, the multiplicity of observed gaps is explained as a combination of flux phase plus charge density wave (CDW) gaps along with a superconducting gap. The largest gap is associated with VHS nesting. The apparent smooth evolution of this gap with doping masks a crossover from CDW-like effects near optimal doping to magnetic effects (flux phase) near half filling. A crossover from large Fermi surface to hole pockets with increased underdoping is found. In the weakly overdoped regime, the CDW undergoes a quantum phase transition ($T_{CDW}\to 0$), which could be obscured by phase separation.Comment: 15 pages, Latex, 18 PS figures Corrects a sign error: major changes, esp. in Sect. 3, Figs 1-4,6 replace