Filtered Noise Can Mimic Low-Dimensional Chaotic Attractors

This contribution presents four results. First, calculations indicate that when examined by the Grassberger-Procaccia algorithm alone, filtered noise can mimic low-dimensional chaotic attractors. Given the ubiquity Of signal filtering in experimental investigations, this is potentially important. Second, a criterion is derived which provides an estimate of the minimum data accuracy needed to resolve the dimension of an attractor. Third, it is shown that a criterion derived by Eckmann and Ruelle [Physica D 56, 185 (1992)] to estimate the minimum number of data points required in a Grassberger-Procaccia calculation can be used to provide a further check on these dimension estimates. Fourth, it is shown that surrogate data techniques recently published by Theiler and his colleagues [in Nonlinear Modeling and Forecasting, edited by M. Casdagli and S. Eubanks (Addison Wesley, Reading, MA, 1992)] can successfully distinguish between linearly correlated noise and nonlinear structure. These results, and most particularly the first, indicate that Grassberger-Procaccia results must be interpreted with far greater circumspection than has previously been the case, and that the algorithm should be used in combination with additional procedures such as calculations with surrogate data. When filtered signals are examined by this algorithm alone, a finite noninteger value of D2 is consistent with low-dimensional chaotic behavior, but it is certainly not a definitive diagnostic of chaos

Filtered Noise Can Mimic Low-Dimensional Chaotic Attractors

This contribution presents four results. First, calculations indicate that when examined by the Grassberger-Procaccia algorithm alone, filtered noise can mimic low-dimensional chaotic attractors. Given the ubiquity Of signal filtering in experimental investigations, this is potentially important. Second, a criterion is derived which provides an estimate of the minimum data accuracy needed to resolve the dimension of an attractor. Third, it is shown that a criterion derived by Eckmann and Ruelle [Physica D 56, 185 (1992)] to estimate the minimum number of data points required in a Grassberger-Procaccia calculation can be used to provide a further check on these dimension estimates. Fourth, it is shown that surrogate data techniques recently published by Theiler and his colleagues [in Nonlinear Modeling and Forecasting, edited by M. Casdagli and S. Eubanks (Addison Wesley, Reading, MA, 1992)] can successfully distinguish between linearly correlated noise and nonlinear structure. These results, and most particularly the first, indicate that Grassberger-Procaccia results must be interpreted with far greater circumspection than has previously been the case, and that the algorithm should be used in combination with additional procedures such as calculations with surrogate data. When filtered signals are examined by this algorithm alone, a finite noninteger value of D2 is consistent with low-dimensional chaotic behavior, but it is certainly not a definitive diagnostic of chaos

Filtered Noise Can Mimic Low-Dimensional Chaotic Attractors

This contribution presents four results. First, calculations indicate that when examined by the Grassberger-Procaccia algorithm alone, filtered noise can mimic low-dimensional chaotic attractors. Given the ubiquity Of signal filtering in experimental investigations, this is potentially important. Second, a criterion is derived which provides an estimate of the minimum data accuracy needed to resolve the dimension of an attractor. Third, it is shown that a criterion derived by Eckmann and Ruelle [Physica D 56, 185 (1992)] to estimate the minimum number of data points required in a Grassberger-Procaccia calculation can be used to provide a further check on these dimension estimates. Fourth, it is shown that surrogate data techniques recently published by Theiler and his colleagues [in Nonlinear Modeling and Forecasting, edited by M. Casdagli and S. Eubanks (Addison Wesley, Reading, MA, 1992)] can successfully distinguish between linearly correlated noise and nonlinear structure. These results, and most particularly the first, indicate that Grassberger-Procaccia results must be interpreted with far greater circumspection than has previously been the case, and that the algorithm should be used in combination with additional procedures such as calculations with surrogate data. When filtered signals are examined by this algorithm alone, a finite noninteger value of D2 is consistent with low-dimensional chaotic behavior, but it is certainly not a definitive diagnostic of chaos

The Complex Toda Chains and the Simple Lie Algebras - Solutions and Large Time Asymptotics

The asymptotic regimes of the N-site complex Toda chain (CTC) with fixed ends related to the classical series of simple Lie algebras are classified. It is shown that the CTC models have much richer variety of asymptotic regimes than the real Toda chain (RTC). Besides asymptotically free propagation (the only possible regime for the RTC), CTC allow bound state regimes, various intermediate regimes when one (or several) group(s) of particles form bound state(s), singular and degenerate solutions. These results can be used e.g., in describing the soliton interactions of the nonlinear Schroedinger equation. Explicit expressions for the solutions in terms of minimal sets of scattering data are proposed for all classical series B_r - D_r.Comment: LaTeX, article style, 16 pages; corrections of formulas and text improvement

Physics in Riemann's mathematical papers

Riemann's mathematical papers contain many ideas that arise from physics, and some of them are motivated by problems from physics. In fact, it is not easy to separate Riemann's ideas in mathematics from those in physics. Furthermore, Riemann's philosophical ideas are often in the background of his work on science. The aim of this chapter is to give an overview of Riemann's mathematical results based on physical reasoning or motivated by physics. We also elaborate on the relation with philosophy. While we discuss some of Riemann's philosophical points of view, we review some ideas on the same subjects emitted by Riemann's predecessors, and in particular Greek philosophers, mainly the pre-socratics and Aristotle. The final version of this paper will appear in the book: From Riemann to differential geometry and relativity (L. Ji, A. Papadopoulos and S. Yamada, ed.) Berlin: Springer, 2017

Paget's disease of bone in two medieval skeletons from Poulton Chapel, Cheshire, UK

Paget's disease of bone (PDB) is a chronic, metabolic disease disrupting normal bone turnover and is reported as one of the most common bone diseases after osteoporosis. PDB is characterised by excessive bone remodelling resulting in bone enlargement, fragility, deformity and additional complications. Typically, PDB affects one or a few bones of the axial skeleton and is commonly recorded in older individuals (over 55 years of age) affecting more males than females. Although PDB has been reported worldwide, there is a high concentration of reported cases in the UK, with a regional hotspot in the northwest of England. This study reviews an adult male (SK463) and female (SK750) with skeletal lesions of PDB from Poulton Chapel, Cheshire. Full macroscopic and radiographic analysis has identified the skeletal distribution of PDB, with up to 75% of both skeletons affected. SK463 presents noticeable anterior bowing to both tibiae, likely the result of PDB. AMS radiocarbon dating and stable isotope analysis performed on teeth samples confirmed that both individuals' dates were medieval, had a mixed/varied diet and were local to the northwest of England. This research adds to the emerging paleopathological literature on PDB, while providing additional support for the identification of a geographical hotspot observed in contemporary populations

A fatal case of recurrent amiodarone-induced thyrotoxicosis after percutaneous tracheotomy: a case report

<p>Abstract</p> <p>Background</p> <p>Amiodarone is a widely used antiarrythmic drug, which may produce secondary effects on the thyroid. In 14–18% of amiodarone-treated patients, there is overt thyroid dysfunction, usually in the form of amiodarone-induced thyrotoxicosis, which can be difficult to manage with standard medical treatment.</p> <p>Case presentation</p> <p>Presented is the case of a 65-year-old man, under chronic treatment of atrial fibrillation with amiodarone, who was admitted to the Intensive Care Unit with acute cardio-respiratory failure and fever. He was recently hospitalized with respiratory distress, attributed to amiodarone-induced pulmonary fibrosis. Clinical and laboratory investigation revealed thyrotoxicosis due to amiodarone treatment. He was begun on thionamide, prednisone and beta-blockers. After a short term improvement of his clinical status the patient underwent percutaneous tracheotomy due to weaning failure from mechanical ventilation, which led to the development of recurrent thyrotoxicosis, unresponsive to medical treatment. Finally, the patient developed multiple organ failure and died, seven days later.</p> <p>Conclusion</p> <p>We suggest that percutaneous tracheotomy could precipitate a thyrotoxic crisis, particularly in non-euthyroid patients suffering from concurrent severe illness and should be performed only in parallel with emergency thyroid surgery, when indicated.</p

MSMEG_2731, an Uncharacterized Nucleic Acid Binding Protein from Mycobacterium smegmatis, Physically Interacts with RPS1

While the M. smegmatis genome has been sequenced, only a small portion of the genes have been characterized experimentally. Here, we purify and characterize MSMEG_2731, a conserved hypothetical alanine and arginine rich M. smegmatis protein. Using ultracentrifugation, we show that MSMEG_2731 is a monomer in vitro. MSMEG_2731 exists at a steady level throughout the M. smegmatis life-cycle. Combining results from pull-down techniques and LS-MS/MS, we show that MSMEG_2731 interacts with ribosomal protein S1. The existence of this interaction was confirmed by co-immunoprecipitation. We also show that MSMEG_2731 can bind ssDNA, dsDNA and RNA in vitro. Based on the interactions of MSMEG_2731 with RPS1 and RNA, we propose that MSMEG_2731 is involved in the transcription-translation process in vivo