Vanishing largest Lyapunov exponent and Tsallis entropy

We present a geometric argument that explains why some systems having vanishing largest Lyapunov exponent have underlying dynamics aspects of which can be effectively described by the Tsallis entropy. We rely on a comparison of the generalised additivity of the Tsallis entropy versus the ordinary additivity of the BGS entropy. We translate this comparison in metric terms by using an effective hyperbolic metric on the configuration/phase space for the Tsallis entropy versus the Euclidean one in the case of the BGS entropy. Solving the Jacobi equation for such hyperbolic metrics effectively sets the largest Lyapunov exponent computed with respect to the corresponding Euclidean metric to zero. This conclusion is in agreement with all currently known results about systems that have a simple asymptotic behaviour and are described by the Tsallis entropy.Comment: 15 pages, No figures. LaTex2e. Some overlap with arXiv:1104.4869 Additional references and clarifications in this version. To be published in QScience Connec

Sodium pentosan polysulfate resulted in cartilage improvement in knee osteoarthritis - An open clinical trial-

BACKGROUND: Pentosan polysulfate sodium (pentosan) is a semi-synthetic drug manufactured from beech-wood hemicellulose by sulfate esterification of the xylopyranose hydroxyl groups. From in vitro and animal model studies, pentosan has been proposed as a disease modifying osteoarthritis drug (DMOAD). The objective of this study was to assess the efficacy, safety, and patient satisfaction in patients with mild radiographic knee osteoarthritis (OA) findings and OA-associated symptoms and signs. METHODS: Twenty patients were assessed clinically at Nagasaki University Hospital. The radiographic indications of OA were grade 1 to 3 using the Kellgren-Lawrence Grading System (K/L grade). Pentosan used in this study was manufactured and supplied in sterile injectable vials (100 mg/ml) by bene GmbH, Munich, Germany. The study was a single-center, open-label trial. Treatment consisted of 6 weekly subcutaneous injections (sc) of pentosan (2 mg/kg). Patients were clinically assessed at entry and 1 to 8, 11, 15, 24 & 52 weeks post treatment. The results were analyzed using one way ANOVA and Dunnett's method. RESULTS: Hydrarthroses were reduced quickly in all cases. The clinical assessments, i.e., knee flexion, pain while walking, pain after climbing up and down stairs, etc, were improved significantly and these clinical improvements continued for almost one year. The dose used in this study affected the blood coagulation test, but was within safe levels. Slightly abnormal findings were noted in serum triglycerides. CONCLUSIONS: Pentosan treatment in twenty patients with mild knee OA seemed to provide improvements in clinical assessments and C2C level of cartilage metabolism

Multicenter study of peroneal mononeuropathy: clinical, neurophysiologic, and quality of life assessment

This is a multicenter study on peroneal mononeuropathy (PM), in which a multidimensional protocol was performed to evaluate (1) the predisposing factors and their occurrence; (2) the relationships between the etiological, clinical, and neurophysiologic findings; and (3) disability and quality of life (QoL) in a wide sample with PM. Clinical and neurophysiologic evaluation was performed in all patients; moreover, the group adopted validated disability and QoL measurements to obtain more comprehensive and reliable data on PM. From November 2002 to January 2004, 69 patients were enrolled consecutively in 11 Italian centers. Our data showed that PM involves men more frequently than women (male : female = 4.11). PM was idiopathic (16%) or due to prolonged posture (23.1%), surgery (20.3%), weight loss (14.5%), trauma (11.6%), bedridden condition (7.3%), external compression from cast (5.8%), and arthrogenic cyst at the fibula (1.4%). Unexpectedly, peroneal nerve lesions were not only due to surgical operation close to the peroneal region but were also associated with thoracic-abdominal surgery. We observed conduction block in about 50-70% of postural and weight loss PM; in perioperative and idiopathic PM, conduction block or mixed damage was equally present; in PM due to trauma, we observed an exclusive axonal damage in about 60% of cases. Only in three cases (one postural PM, one idiopathic PM, and one weight loss PM), we observed a slowing of conduction velocity in the popliteal fossa-fibular head segment without conduction block. The comparison between QoL in patients with PM and in healthy subjects showed a significant involvement of physical and mental aspects. With regard to disability, 68% of patients walked with difficulty. Our data show that (1) most of the cases of PM are due to an identifiable predisposing factor; (2) there is a good correlation between predisposing factors and clinical-neurophysiologic findings; and (3) PM causes disability and deterioration of the physical and emotional aspects of QoL