Sharp comparison and maximum principles via horizontal normal mapping in the Heisenberg group

In this paper we solve a problem raised by Gutiérrez and Montanari about comparison principles for H−convex functions on subdomains of Heisenberg groups. Our approach is based on the notion of the sub-Riemannian horizontal normal mapping and uses degree theory for set-valued maps. The statement of the comparison principle combined with a Harnack inequality is applied to prove the Aleksandrov-type maximum principle, describing the correct boundary behavior of continuous H−convex functions vanishing at the boundary of horizontally bounded subdomains of Heisenberg groups. This result answers a question by Garofalo and Tournier. The sharpness of our results are illustrated by examples.

Numerical assessment on the effective mechanical stimuli for matrix-associated metabolism in chondrocyte-seeded constructs

The self-regeneration capacity of articular cartilage is limited, due to its avascular and aneural nature. Loaded explants and cell cultures demonstrated that chondrocyte metabolism can be regulated via physiologic loading. However, the explicit ranges of mechanical stimuli that correspond to favourable metabolic response associated with extracellular matrix (ECM) synthesis are elusive. Unsystematic protocols lacking this knowledge produce inconsistent results. This study aims to determine the intrinsic ranges of physical stimuli that increase ECM synthesis and simultaneously inhibit nitric oxide (NO) production in chondrocyte-agarose constructs, by numerically re-evaluating the experiments performed by Tsuang et al. (2008). Twelve loading patterns were simulated with poro-elastic finite element models in ABAQUS. Pressure on solid matrix, von Mises stress, maximum principle stress and pore pressure were selected as intrinsic mechanical stimuli. Their development rates and magnitudes at the steady state of cyclic loading were calculated with MATLAB at the construct level. Concurrent increase in glycosaminoglycan and collagen was observed at 2300 Pa pressure and 40 Pa/s pressure rate. Between 0-1500 Pa and 0-40 Pa/s, NO production was consistently positive with respect to controls, whereas ECM synthesis was negative in the same range. A linear correlation was found between pressure rate and NO production (R = 0.77). Stress states identified in this study are generic and could be used to develop predictive algorithms for matrix production in agarose-chondrocyte constructs of arbitrary shape, size and agarose concentration. They could also be helpful to increase the efficacy of loading protocols for avascular tissue engineering. Copyright (c) 2010 John Wiley \& Sons, Ltd.

A total variation discontinuous Galerkin approach for image restoration

The focal point of this paper is to propose and analyze a P 0 discontinuous Galerkin (DG) formulation for image denoising. The scheme is based on a total variation approach which has been applied successfully in previous papers on image processing. The main idea of the new scheme is to model the restoration process in terms of a discrete energy minimization problem and to derive a corresponding DG variational formulation. Furthermore, we will prove that the method exhibits a unique solution and that a natural maximum principle holds. In addition, a number of examples illustrate the effectiveness of the method.

Immunomodulatory therapy to achieve maximum efficacy: doses, monitoring, compliance, and self-infusion at home

The Oxford Programme for Immunomodulatory Immunoglobulin Therapy has been operating since 1992 at Oxford Radcliffe Hospitals in the UK. Initially, this program was set up for patients with multifocal motor neuropathy or chronic inflammatory demyelinating poly-neuropathy to receive reduced doses of intravenous immunoglobulin (IVIG) in clinic on a regular basis (usually every 3 weeks). The program then rapidly expanded to include self-infusion at home, which monitoring showed to be safe and effective. It has been since extended to the treatment of other autoimmune diseases in which IVIG has been shown to be efficacious.

Maximum flight velocity of blood drops in analysing blood traces

When analysing blood spatters, traces often occur which regarding the collision angle, cannot be allocated to any supposed centre of origin. Drops following highly curved (ballistic) trajectories usually form these types of traces. The reconstruction of such trajectories requires knowledge of the mass, the diameter (of which approximations are known) and the velocity of the blood drops. This article provides an upper range of the velocity in relation to the diameter of the blood drops based on physical laws. This is very helpful in analysing ballistic trajectories.

Early last glacial maximum in the southern Central Andes reveals northward shift of the westerlies at similar to 39 ka

The latitudinal position of the southern westerlies has been suggested to be a key parameter for the climate on Earth. According to the general notion, the southern westerlies were shifted equatorward during the global Last Glacial Maximum (LGM: ~24–18 ka), resulting in reduced deep ocean ventilation, accumulation of old dissolved carbon, and low atmospheric CO2 concentrations. In order to test this notion, we applied surface exposure dating on moraines in the southern Central Andes, where glacial mass balances are particularly sensitive to changes in precipitation, i.e. to the latitudinal position of the westerlies. Our results provide robust evidence that the maximum glaciation occurred already at ~39 ka, significantly predating the global LGM. This questions the role of the westerlies for atmospheric CO2, and it highlights our limited understanding of the forcings of atmospheric circulation.

Reconstruction of large supra-eyebrow and forehead defects using the hatchet flap principle and sparing sensory nerve branches

To reconstruct a forehead defect, a plastic surgeon must be knowledgeable about the neural, vascular, and muscular anatomy. The position of fixed structures such as eyebrows and hairline should be respected. For the past 5 years, we have used double hatchet flaps for reconstruction of relatively large supra-eyebrow and forehead defects. Because this flap does not appear to be among the techniques used by young plastic surgeons, we thought that it would be valuable to report our experience.

A randomized comparison of microtip and air-charged catheter for the measurement of maximum urethral closure pressure

Measurements of maximum urethral closure pressure (MUCP) are a part of urodynamic investigations preceding an incontinence surgery and a part of urethral function tests.