Minimality of planes in normed spaces

We prove that a region in a two-dimensional affine subspace of a normed space $V$ has the least 2-dimensional Hausdorff measure among all compact surfaces with the same boundary. Furthermore, the 2-dimensional Hausdorff area density admits a convex extension to $\Lambda^2 V$. The proof is based on a (probably) new inequality for the Euclidean area of a convex centrally-symmetric polygon.Comment: 10 pages, v2: minor changes according to referees' comments, to appear in GAF

The Effect of Axial Compression and Distraction on Cervical Facet Cartilage Apposition During Shear and Bending Motions

During cervical spine trauma, complex intervertebral motions can cause a reduction in facet joint cartilage apposition area (CAA), leading to cervical facet dislocation (CFD). Intervertebral compression and distraction likely alter the magnitude and location of CAA, and may influence the risk of facet fracture. The aim of this study was to investigate facet joint CAA resulting from intervertebral distraction (2.5 mm) or compression (50, 300 N) superimposed on shear and bending motions. Intervertebral and facet joint kinematics were applied to multi rigid-body kinematic models of twelve C6/C7 motion segments (70 ± 13 year, nine male) with specimen-specific cartilage profiles. CAA was qualitatively and quantitatively compared between distraction and compression conditions for each motion; linear mixed-effects models (a = 0.05) were applied. Distraction significantly decreased CAA throughout all motions, compared to the compressed conditions (p<0.001), and shifted the apposition region towards the facet tip. These observations were consistent bilaterally for both asymmetric and symmetric motions. The results indicate that axial neck loads, which are altered by muscle activation and head loading, influences facet apposition. Investigating CAA in longer cervical spine segments subjected to quasistatic or dynamic loading may provide insight into dislocation and fracture mechanisms.Ryan D. Quarrington, Darcy W. Thompson-Bagsshaw and Claire F. Jone

Normal Cones and Thompson Metric

The aim of this paper is to study the basic properties of the Thompson metric $d_T$ in the general case of a real linear space $X$ ordered by a cone $K$. We show that $d_T$ has monotonicity properties which make it compatible with the linear structure. We also prove several convexity properties of $d_T$ and some results concerning the topology of $d_T$, including a brief study of the $d_T$-convergence of monotone sequences. It is shown most of the results are true without any assumption of an Archimedean-type property for $K$. One considers various completeness properties and one studies the relations between them. Since $d_T$ is defined in the context of a generic ordered linear space, with no need of an underlying topological structure, one expects to express its completeness in terms of properties of the ordering, with respect to the linear structure. This is done in this paper and, to the best of our knowledge, this has not been done yet. The Thompson metric $d_T$ and order-unit (semi)norms $|\cdot|_u$ are strongly related and share important properties, as both are defined in terms of the ordered linear structure. Although $d_T$ and $|\cdot|_u$ are only topological (and not metrical) equivalent on $K_u$, we prove that the completeness is a common feature. One proves the completeness of the Thompson metric on a sequentially complete normal cone in a locally convex space. At the end of the paper, it is shown that, in the case of a Banach space, the normality of the cone is also necessary for the completeness of the Thompson metric.Comment: 36 page

The Structural Response of the Human Head to a Vertex Impact.

OnlinePublIn experimental models of cervical spine trauma caused by near-vertex head-first impact, a surrogate headform may be substituted for the cadaveric head. To inform headform design and to verify that such substitution is valid, the force-deformation response of the human head with boundary conditions relevant to cervical spine head-first impact models is required. There are currently no biomechanics data that characterize the force-deformation response of the isolated head supported at the occiput and compressed at the vertex by a flat impactor. The effect of impact velocity (1, 2 or 3 m/s) on the response of human heads (N = 22) subjected to vertex impacts, while supported by a rigid occipital mount, was investigated. 1 and 2 m/s impacts elicited force-deformation responses with two linear regions, while 3 m/s impacts resulted in a single linear region and skull base ring fractures. Peak force and stiffness increased from 1 to 2 and 3 m/s. Deformation at peak force and absorbed energy increased from 1 to 2 m/s, but decreased from 2 to 3 m/s. The data reported herein enhances the limited knowledge on the human head's response to a vertex impact, which may allow for validation of surrogate head models in this loading scenario.Darcy W. Thompson, Bagshaw, Ryan D. Quarrington, Andrew M. Dwyer, Nigel R. Jones, Claire F. Jone

Spin-3/2 Nucleon and Delta Baryons in Lattice QCD

We present first results for masses of spin-3/2 N and Delta baryons in lattice QCD using Fat-Link Irrelevant Clover (FLIC) fermions. Spin-3/2 interpolating fields providing overlap with both spin-3/2 and spin-1/2 states are considered. In the isospin-1/2 sector, we observe, after appropriate spin and parity projection, a strong signal for the J^P=3/2^- state together with a weak but discernible signal for the 3/2^+ state with a mass splitting near that observed experimentally. We also find good agreement between the 1/2^+/- masses and earlier nucleon mass simulations with the standard spin-1/2 interpolating field. For the isospin-3/2 Delta states, clear mass splittings are observed between the various 1/2^+/- and 3/2^+/- channels, with the calculated level orderings in good agreement with those observed empirically.Comment: 17 pages, 8 figures, 2 table

Haloperidol and Ziprasidone for Treatment of Delirium in Critical Illness

BACKGROUND: There are conflicting data on the effects of antipsychotic medications on delirium in patients in the intensive care unit (ICU). METHODS: In a randomized, double-blind, placebo-controlled trial, we assigned patients with acute respiratory failure or shock and hypoactive or hyperactive delirium to receive intravenous boluses of haloperidol (maximum dose, 20 mg daily), ziprasidone (maximum dose, 40 mg daily), or placebo. The volume and dose of a trial drug or placebo was halved or doubled at 12-hour intervals on the basis of the presence or absence of delirium, as detected with the use of the Confusion Assessment Method for the ICU, and of side effects of the intervention. The primary end point was the number of days alive without delirium or coma during the 14-day intervention period. Secondary end points included 30-day and 90-day survival, time to freedom from mechanical ventilation, and time to ICU and hospital discharge. Safety end points included extrapyramidal symptoms and excessive sedation. RESULTS: Written informed consent was obtained from 1183 patients or their authorized representatives. Delirium developed in 566 patients (48%), of whom 89% had hypoactive delirium and 11% had hyperactive delirium. Of the 566 patients, 184 were randomly assigned to receive placebo, 192 to receive haloperidol, and 190 to receive ziprasidone. The median duration of exposure to a trial drug or placebo was 4 days (interquartile range, 3 to 7). The median number of days alive without delirium or coma was 8.5 (95% confidence interval [CI], 5.6 to 9.9) in the placebo group, 7.9 (95% CI, 4.4 to 9.6) in the haloperidol group, and 8.7 (95% CI, 5.9 to 10.0) in the ziprasidone group (P=0.26 for overall effect across trial groups). The use of haloperidol or ziprasidone, as compared with placebo, had no significant effect on the primary end point (odds ratios, 0.88 [95% CI, 0.64 to 1.21] and 1.04 [95% CI, 0.73 to 1.48], respectively). There were no significant between-group differences with respect to the secondary end points or the frequency of extrapyramidal symptoms. CONCLUSIONS: The use of haloperidol or ziprasidone, as compared with placebo, in patients with acute respiratory failure or shock and hypoactive or hyperactive delirium in the ICU did not significantly alter the duration of delirium. (Funded by the National Institutes of Health and the VA Geriatric Research Education and Clinical Center; MIND-USA ClinicalTrials.gov number, NCT01211522 .)

Hadron Masses From Novel Fat-Link Fermion Actions

The hadron mass spectrum is calculated in lattice QCD using a novel fat-link clover fermion action in which only the irrelevant operators in the fermion action are constructed using smeared links. The simulations are performed on a 16^3 x 32 lattice with a lattice spacing of a=0.125 fm. We compare actions with n=4 and 12 smearing sweeps with a smearing fraction of 0.7. The n=4 Fat-Link Irrelevant Clover (FLIC) action provides scaling which is superior to mean-field improvement, and offers advantages over nonperturbative 0(a) improvement, including a reduced exceptional configuration problem.Comment: 12 pages, 4 figures, new simulation with mean-field improved clover, further discussion of actio

Magnetoluminescence

Pulsar Wind Nebulae, Blazars, Gamma Ray Bursts and Magnetars all contain regions where the electromagnetic energy density greatly exceeds the plasma energy density. These sources exhibit dramatic flaring activity where the electromagnetic energy distributed over large volumes, appears to be converted efficiently into high energy particles and gamma-rays. We call this general process magnetoluminescence. Global requirements on the underlying, extreme particle acceleration processes are described and the likely importance of relativistic beaming in enhancing the observed radiation from a flare is emphasized. Recent research on fluid descriptions of unstable electromagnetic configurations are summarized and progress on the associated kinetic simulations that are needed to account for the acceleration and radiation is discussed. Future observational, simulation and experimental opportunities are briefly summarized.Comment: To appear in "Jets and Winds in Pulsar Wind Nebulae, Gamma-ray Bursts and Blazars: Physics of Extreme Energy Release" of the Space Science Reviews serie

Excited Baryons in Lattice QCD

We present first results for the masses of positive and negative parity excited baryons calculated in lattice QCD using an O(a^2)-improved gluon action and a fat-link irrelevant clover (FLIC) fermion action in which only the irrelevant operators are constructed with APE-smeared links. The results are in agreement with earlier calculations of N^* resonances using improved actions and exhibit a clear mass splitting between the nucleon and its chiral partner. An correlation matrix analysis reveals two low-lying J^P=(1/2)^- states with a small mass splitting. The study of different Lambda interpolating fields suggests a similar splitting between the lowest two Lambda1/2^- octet states. However, the empirical mass suppression of the Lambda^*(1405) is not evident in these quenched QCD simulations, suggesting a potentially important role for the meson cloud of the Lambda^*(1405) and/or a need for more exotic interpolating fields.Comment: Correlation matrix analysis performed. Increased to 400 configurations. 22 pages, 13 figures, 15 table