227 research outputs found
Guided growth for correction of knee flexion deformity: a series of four cases
Fixed knee flexion deformity can present as an insidious and significant problem in diverse etiologies, most commonly in cerebral palsy. Traditional surgical intervention has included posterior capsulotomy and supracondylar femoral osteotomy, both of which carry significant associated morbidity and risks. In the skeletally immature patient, guided growth may be used to correct or substantially diminish the deformity. We are presenting our early experience encompassing four subjects who completed instrumented gait analysis both prior to and after distal femoral anterior guided growth (hemiepiphysiodesis). Changes in gait and function resulting from surgery in each individual are reported. Outcomes indicate improved knee range of motion and alleviation of crouch at the knee with secondary improvements in the ankle, hip and pelvis. Three subjects with initially slow gait velocity improved to within normal limits by demonstrating increased stride length. A measure of overall gait kinematics showed improvements in all limbs. Anterior guided growth (hemiepiphysiodesis) of the distal femur resulted in positive quantitative changes in all four patients, though degree and types of changes were variable in this small series. Encouraged by these findings, we now prefer guided growth to extension supracondylar osteotomy for the skeletally immature patient with fixed knee flexion deformity
Simple Quantum Error Correcting Codes
Methods of finding good quantum error correcting codes are discussed, and
many example codes are presented. The recipe C_2^{\perp} \subseteq C_1, where
C_1 and C_2 are classical codes, is used to obtain codes for up to 16
information qubits with correction of small numbers of errors. The results are
tabulated. More efficient codes are obtained by allowing C_1 to have reduced
distance, and introducing sign changes among the code words in a systematic
manner. This systematic approach leads to single-error correcting codes for 3,
4 and 5 information qubits with block lengths of 8, 10 and 11 qubits
respectively.Comment: Submitted to Phys. Rev. A. in May 1996. 21 pages, no figures. Further
information at http://eve.physics.ox.ac.uk/ASGhome.htm
Quantum Error Correcting Codes Using Qudit Graph States
Graph states are generalized from qubits to collections of qudits of
arbitrary dimension , and simple graphical methods are used to construct
both additive and nonadditive quantum error correcting codes. Codes of distance
2 saturating the quantum Singleton bound for arbitrarily large and are
constructed using simple graphs, except when is odd and is even.
Computer searches have produced a number of codes with distances 3 and 4, some
previously known and some new. The concept of a stabilizer is extended to
general , and shown to provide a dual representation of an additive graph
code.Comment: Version 4 is almost exactly the same as the published version in
Phys. Rev.
Facial structures for various notions of positivity and applications to the theory of entanglement
In this expository note, we explain facial structures for the convex cones
consisting of positive linear maps, completely positive linear maps,
decomposable positive linear maps between matrix algebras, respectively. These
will be applied to study the notions of entangled edge states with positive
partial transposes and optimality of entanglement witnesses.Comment: An expository note. Section 7 and Section 8 have been enlarge
Nonbinary Codeword Stabilized Quantum Codes
The codeword stabilized (CWS) quantum codes formalism presents a unifying
approach to both additive and nonadditive quantum error-correcting codes
(arXiv:0708.1021 [quant-ph]), but only for binary states. Here we generalize
the CWS framework to the nonbinary case (of both prime and nonprime dimension)
and map the search for nonbinary quantum codes to a corresponding search
problem for classical nonbinary codes with specific error patterns. We show
that while the additivity properties of nonbinary CWS codes are similar to the
binary case, the structural properties of the nonbinary codes differ
substantially from the binary case, even for prime dimensions. In particular,
we identify specific structure patterns of stabilizer groups, based on which
efficient constructions might be possible for codes that encode more dimensions
than any stabilizer codes of the same length and distance; similar methods
cannot be applied in the binary case. Understanding of these structural
properties can help prune the search space and facilitate the identification of
good nonbinary CWS codes.Comment: 7 pages, no figur
Morphodynamics of a width-variable gravel bed stream: new insights on pool-riffle formation from physical experiments
Field observations, experiments, and numerical simulations suggest that pool-riffles along gravel bed mountain streams develop due to downstream variations of channel width. Where channels narrow, pools are observed, and at locations of widening, riffles occur. Based on previous work, we hypothesize that the bed profile is coupled to downstream width variations through momentum fluxes imparted to the channel surface, which scale with downstream changes of flow velocity. We address this hypothesis with flume experiments understood through scaling theory. Our experiments produce pool-riffle like structures across average Shields stresses t* that are a factor 1.5–2 above the threshold mobility condition of the experimental grain size distribution. Local topographic responses are coupled to channel width changes, which drive flows to accelerate or decelerate on average, for narrowing and widening, respectively. We develop theory which explains the topography-width-velocity coupling as a ratio of two reinforcing timescales. The first timescale captures the time necessary to do work to the channel bed. The second timescale characterizes the relative time magnitude of momentum transfer from the flowing fluid to the channel bed surface. Riffle-like structures develop where the work and momentum timescales are relatively large, and pools form where the two timescales are relatively small. We show that this result helps to explain local channel bed slopes along pool-riffles for five data sets representing experimental, numerical, and natural cases, which span 2 orders of magnitude of reach-averaged slope. Additional model testing is warranted.Peer ReviewedPostprint (published version
Finite covers of random 3-manifolds
A 3-manifold is Haken if it contains a topologically essential surface. The
Virtual Haken Conjecture posits that every irreducible 3-manifold with infinite
fundamental group has a finite cover which is Haken. In this paper, we study
random 3-manifolds and their finite covers in an attempt to shed light on this
difficult question. In particular, we consider random Heegaard splittings by
gluing two handlebodies by the result of a random walk in the mapping class
group of a surface. For this model of random 3-manifold, we are able to compute
the probabilities that the resulting manifolds have finite covers of particular
kinds. Our results contrast with the analogous probabilities for groups coming
from random balanced presentations, giving quantitative theorems to the effect
that 3-manifold groups have many more finite quotients than random groups. The
next natural question is whether these covers have positive betti number. For
abelian covers of a fixed type over 3-manifolds of Heegaard genus 2, we show
that the probability of positive betti number is 0.
In fact, many of these questions boil down to questions about the mapping
class group. We are lead to consider the action of mapping class group of a
surface S on the set of quotients pi_1(S) -> Q. If Q is a simple group, we show
that if the genus of S is large, then this action is very mixing. In
particular, the action factors through the alternating group of each orbit.
This is analogous to Goldman's theorem that the action of the mapping class
group on the SU(2) character variety is ergodic.Comment: 60 pages; v2: minor changes. v3: minor changes; final versio
Efficient implementation of selective recoupling in heteronuclear spin systems using Hadamard matrices
We present an efficient scheme which couples any designated pair of spins in
heteronuclear spin systems. The scheme is based on the existence of Hadamard
matrices. For a system of spins with pairwise coupling, the scheme
concatenates intervals of system evolution and uses at most pulses
where . Our results demonstrate that, in many systems, selective
recoupling is possible with linear overhead, contrary to common speculation
that exponential effort is always required.Comment: 7 pages, 4 figures, mypsfig2, revtex, submitted April 27, 199
The Glasgow-Maastricht foot model, evaluation of a 26 segment kinematic model of the foot
BACKGROUND: Accurately measuring of intrinsic foot kinematics using skin mounted markers is difficult, limited in part by the physical dimensions of the foot. Existing kinematic foot models solve this problem by combining multiple bones into idealized rigid segments. This study presents a novel foot model that allows the motion of the 26 bones to be individually estimated via a combination of partial joint constraints and coupling the motion of separate joints using kinematic rhythms. METHODS: Segmented CT data from one healthy subject was used to create a template Glasgow-Maastricht foot model (GM-model). Following this, the template was scaled to produce subject-specific models for five additional healthy participants using a surface scan of the foot and ankle. Forty-three skin mounted markers, mainly positioned around the foot and ankle, were used to capture the stance phase of the right foot of the six healthy participants during walking. The GM-model was then applied to calculate the intrinsic foot kinematics. RESULTS: Distinct motion patterns where found for all joints. The variability in outcome depended on the location of the joint, with reasonable results for sagittal plane motions and poor results for transverse plane motions. CONCLUSIONS: The results of the GM-model were comparable with existing literature, including bone pin studies, with respect to the range of motion, motion pattern and timing of the motion in the studied joints. This novel model is the most complete kinematic model to date. Further evaluation of the model is warranted
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