Lattice point inequalities and face numbers of polytopes in view of central symmetry

Magdeburg, Univ., Fak. für Mathematik, Diss., 2012

Limit cycles for cubic systems with a symmetry of order 4 and without in nite critical points

"Vegeu el resum a l'inici del document del fitxer adjunt."

Symmetry for a Dirichlet-Neumann problem arising in water waves

"Vegeu el resum a l'inici del document del fitxer adjunt."

Bilateral symmetry of radial pulse in high-level tennis players: implications for the validity of central aortic pulse wave analysis.

BACKGROUND: Reconstruction of the central aortic pressure wave from the noninvasive recording of the radial pulse with applanation tonometry has become a standard tool in the field of hypertension. It is not presently known whether recording the radial pulse on the dominant or the nondominant side has any effect on such reconstruction. METHOD: We carried out radial applanation tonometry on both forearms in young, healthy, male volunteers, who were either sedentary (n = 11) or high-level tennis players (n = 10). The purpose of including tennis players was to investigate individuals with extreme asymmetry between the dominant and nondominant upper limb. RESULTS: In the sedentary individuals, forearm circumference and handgrip strength were slightly larger on the dominant (mean +/- SD respectively 27.9 +/- 1.5 cm and 53.8 +/- 10 kg) than on nondominant side (27.3 +/- 1.6 cm, P < 0.001 vs. dominant, and 52.1 +/- 11 kg, P = NS). In the tennis players, differences between sides were more conspicuous (forearm circumference: dominant 28.0 +/- 1.7 cm nondominant 26.4 +/- 1.5 cm, P < 0.001; handgrip strength 61.4 +/- 10.8 vs. 53.4 +/- 9.7 kg, P < 0.001). We found that in both sedentary individuals and tennis players, the radial pulse had identical shape on both sides and, consequently, the reconstructed central aortic pressure waveforms, as well as derived indices of central pulsatility, were not dependent on the side where applanation tonometry was carried out. CONCLUSION: Evidence from individuals with maximal asymmetry of dominant vs. nondominant upper limb indicates that laterality of measurement is not a methodological issue for central pulse wave analysis carried out with radial applanation tonometry.

Broken symmetry.

Review of the book : Lucifer's legacy, the meaning of asymmetry, by F. Close, Oxford University Press, Oxford, UK

Evaluation of the 3D symmetry of the knees when walking using na ambulatory inertia system: results 14 months after ACL Plasty.

Purpose of the study: Reconstruction of the anterior cruciate ligament (ACL) controls laxity but does not enable restoration of strictly normal 3D kinematics. The purpose of this study was to compare the kinematics of the pathological knee with that of the healthy knee after ACL plasty. This study applied a new ambulatory system using miniature captors. Material and method: Five patients with an isolated injury of the ACL participated in this study. The patients were assessed after injury (T1), at five months (T2), and at 14 months (T3) after surgery. The assessment included laxity (KT-1000), the IKDC score and the Lysholm score. The 3D angles of the knees were measured when walking 30 m on flat ground using a system composed of to small inertia units (3D accelerometer and 3D gyroscope) and a portable recorder. Functional settings were optimised and validating to ensure easy precise measurement of the 3D angles. Symmetry of the two knees was quantified using a symmetry index (SI) (difference in amplitude normalised in relation to mean amplitude) and the correlation coefficient CC. Results: Clinical indicators improved during the follow-up (IKDC T1: 3C, 2C; T2: 5B; T3: 2A, 3B; subjective IKD: 53-95; Lysholm 67-96). Mean laxity improved from 8.6m to 2.5 mm. The gait analysis showed increased symmetry in terms of amplitude for flexion-extension (SI: −17% at T1, −1% at T2, 1% at T3), and an increase in symmetry in terms of the rotation signature (CC: 0.16 at T1, 0.99 at T2, 0.99 at T3). There was no trend to varus-valgus. Discussion: This study demonstrates the clinical application of the new ambulatory system for measuring 3D angles of the knee joint. Joint symmetry increased after ACL plasty but still showed some perturbation at 14 months. The results observed here are in agreement with the literature. Other patients and other types of gait are being analysed. Conclusion: This portable system allows gait analysis outside the laboratory, before and after ACL injury. It is very useful for follow-up after surgery.

Desenvolupament de codis numèrics per a la resolució de fluxos turbulents en ordinadors paral·lels emprant discretitzacions tipus symmetry-preserving

Projecte de recerca elaborat a partir d’una estada a la University of Groningen, Holanda, entre 2007 i 2009. La simulació directa de la turbulència (DNS) és una eina clau dins de la mecànica de fluids computacional. Per una banda permet conèixer millor la física de la turbulència i per l'altra els resultats obtinguts són claus per el desenvolupament dels models de turbulència. No obstant, el DNS no és una tècnica vàlida per a la gran majoria d'aplicacions industrials degut al elevats costos computacionals. Per tant, és necessari cert grau de modelització de la turbulència. En aquest context, s'han introduïts importants millores basades en la modelització del terme convectiu (no lineal) emprant symmetry-preserving regularizations. En tracta de modificar adequadament el terme convectiu a fi de reduir la producció d'escales més i més petites (vortex-stretching) tot mantenint tots els invariants de les equacions originals. Fins ara, aquest models s'han emprat amb èxit per nombres de Rayleigh (Ra) relativament elevats. En aquest punt, disposar de resultats DNS per a configuracions més complexes i nombres de Ra més elevats és clau. En aquest contexte, s'han dut a terme simulacions DNS en el supercomputador MareNostrum d'una Differentially Heated Cavity amb Ra=1e11 i Pr=0.71 durant el primer any dels dos que consta el projecte. A més a més, s'ha adaptat el codi a fi de poder simular el fluxe al voltant d'un cub sobre una pared amb Re=10000. Aquestes simulacions DNS són les més grans fetes fins ara per aquestes configuracions i la seva correcta modelització és un gran repte degut la complexitat dels fluxes. Aquestes noves simulacions DNS estan aportant nous coneixements a la física de la turbulència i aportant resultats indispensables per al progrés de les modelitzacións tipus symmetry-preserving regularization.

Symmetry-breaking in cumulative measures of shapes of polymer models.

Using numerical simulations we investigate shapes of random equilateral open and closed chains, one of the simplest models of freely fluctuating polymers in a solution. We are interested in the 3D density distribution of the modeled polymers where the polymers have been aligned with respect to their three principal axes of inertia. This type of approach was pioneered by Theodorou and Suter in 1985. While individual configurations of the modeled polymers are almost always nonsymmetric, the approach of Theodorou and Suter results in cumulative shapes that are highly symmetric. By taking advantage of asymmetries within the individual configurations, we modify the procedure of aligning independent configurations in a way that shows their asymmetry. This approach reveals, for example, that the 3D density distribution for linear polymers has a bean shape predicted theoretically by Kuhn. The symmetry-breaking approach reveals complementary information to the traditional, symmetrical, 3D density distributions originally introduced by Theodorou and Suter.

Reduction of symmetry in grandite solid solution

The results of a crystal structure refinement of an anisotropic grandite garnet specimen with composition Gro36-4 And63-6 are given. The structure obtained has orthorrombic symmetry (space group Fddd) and is compared with similar results obtained by other authors. In all cases the reduction of symmetry is due to the ordering of Fe3+ and Al in octahedral sites. Non cubic structures of grandites are discussed in connection with optical, morphological an grou-th features of these minerals.

Density dependence of the symmetry free energy of hot nuclei

The density and excitation energy dependence of symmetry energy and symmetry free energy for finite nuclei are calculated microscopically in a microcanonical framework, taking into account thermal and expansion effects. A finite-range momentum and density-dependent two-body effective interaction is employed for this purpose. The role of mass, isospin, and equation of state (EOS) on these quantities is also investigated; our calculated results are in consonance with the available experimental data.

D-String on near horizon geometries and infinite conformal symmetry

We show that the symmetries of effective D-string actions in constant dilaton backgrounds are directly related to homothetic motions of the background metric. In the presence of such motions, there are infinitely many nonlinearly realized rigid symmetries forming a loop (or looplike) algebra. Near horizon (antideSitter) D3 and D1+D5 backgrounds are discussed in detail and shown to provide 2D interacting field theories with infinite conformal symmetry.

Prescription footwear for severe injuries of foot and ankle: effect on regularity and symmetry of the gait assessed by trunk accelerometry.

After foot and/or ankle fracture, the restoration of optimal gait symmetry is one of the criteria of recovery. Orthotic insoles and orthopaedic shoes improve gait symmetry and regularity by controlling joint motion and improving alignment. The aim of the present study was to assess the effect of prescription footwear on gait quality by using accelerometers attached to the lower back. Sixteen adult patients with persistent disability after ankle and/or foot fractures performed two 30-s walking trials with and without prescription footwear (insoles and stabilizing shoes). Sixteen control subjects were also tested for comparison. The autocorrelation function was computed from the acceleration signal and the first two dominant periods were assessed (d1 and d2). Two parameters were used: (1) Stride Regularity (SR) which expresses the similarity between strides over time (d2), and (2) Stride Symmetry (SS) a ratio (d1/d2) which expresses the left/right similarity of gait independently of repeatability in the successive movements of each limb. In control subjects, SR and SS were 0.86+/-0.05 (correlation coefficient) and 81+/-10%, respectively. In the patient group, the effect of footwear was significant (SR: 0.88+/-0.06 vs. 0.90+/-0.05, SS: 38+/-23% vs. 46+/-27%). Pain was also significantly reduced (-34%). By using a rapid and low-cost method, we objectively quantified gait quality improvement after footwear intervention, concomitant to pain reduction. Substantial inter-patient variability in the footwear outcome was observed. In conclusion, we believe that trunk accelerometry can be a useful tool in the field of gait rehabilitation.