Outer Approximation of the Spectrum of a Fractal Laplacian

We present a new method to approximate the Neumann spectrum of a Laplacian on a fractal K in the plane as a renormalized limit of the Neumann spectra of the standard Laplacian on a sequence of domains that approximate K from the outside. The method allows a numerical approximation of eigenvalues and eigenfunctions for lower portions of the spectrum. We present experimental evidence that the method works by looking at examples where the spectrum of the fractal Laplacian is known (the unit interval and the Sierpinski Gasket (SG)). We also present a speculative description of the spectrum on the standard Sierpinski carpet (SC), where existence of a self-similar Laplacian is known, and also on nonsymmetric and random carpets and the octagasket, where existence of a self-similar Laplacian is not known. At present we have no explanation as to why the method should work. Nevertheless, we are able to prove some new results about the structure of the spectrum involving "miniaturization" of eigenfunctions that we discovered by examining the experimental results obtained using our method.Comment: 61 pages, 24 figures, to appear, Exp. Mat

9-O-Ethyl­berberrubinium iodide monohydrate

In the title compound (systematic name: 9-eth­oxy-10-meth­oxy-5,6-dihydro-1,3-dioxolo[4,5-g]isoquinolino­[3,2-a]isoquin­olin-7-ium iodide monohydrate), 2C21H20NO4 +·2I−·H2O, two independent mol­ecules pack in the unit cell, where interactions between the molecules are stabilized by weak inter­molecular π–π stacking inter­actions [centroid–centroid distances in the range 3.571 (4) to 3.815 (4)Å]. Inter­molecular C—H⋯O inter­actions are also observed. The iodide anions are disordered with occupancy ratios of 0.94 (1):0.06 (1) and 0.91 (1):0.09 (1). The cationic molecule is planar in structure with a small torsion resulting from the dihydropyridine ring

A Uniform Approximation for the Fidelity in Chaotic Systems

In quantum/wave systems with chaotic classical analogs, wavefunctions evolve in highly complex, yet deterministic ways. A slight perturbation of the system, though, will cause the evolution to diverge from its original behavior increasingly with time. This divergence can be measured by the fidelity, which is defined as the squared overlap of the two time evolved states. For chaotic systems, two main decay regimes of either Gaussian or exponential behavior have been identified depending on the strength of the perturbation. For perturbation strengths intermediate between the two regimes, the fidelity displays both forms of decay. By applying a complementary combination of random matrix and semiclassical theory, a uniform approximation can be derived that covers the full range of perturbation strengths. The time dependence is entirely fixed by the density of states and the so-called transition parameter, which can be related to the phase space volume of the system and the classical action diffusion constant, respectively. The accuracy of the approximations are illustrated with the standard map.Comment: 16 pages, 4 figures, accepted in J. Phys. A, special edition on Random Matrix Theor

Risk of Complication and Revision Total Hip Arthroplasty Among Medicare Patients with Different Bearing Surfaces

To address the long-term problems of bearing surface wear and osteolysis associated with conventional metal-polyethylene (M-PE) total hip arthroplasty (THA), metal-metal (M-M), and ceramic-ceramic (C-C) bearings have been introduced. These bearing surfaces are associated with unique risks and benefits and higher costs. However the relative risks of these three bearings in an older population is unknown. We compared the short-term risk of complication and revision THA among Medicare patients having a primary THA with metal-polyethylene (M-PE), metal-metal (M-M), and ceramic-ceramic (C-C) bearings. We used the 2005 to 2007 100% Medicare inpatient claim files to perform a matched cohort analysis in three separate cohorts of THA patients (M-PE, M-M, and C-C) who were matched by age, gender, and US census region. Multivariate Cox proportional-hazards models were constructed to compare complication and revision THA risk among cohorts, adjusting for medical comorbidities, race, socioeconomic status, and hospital factors. After adjusting for patient and hospital factors, M-M bearings were associated with a higher risk of periprosthetic joint infection (hazard ratio, 3.03; confidence interval, 1.02–9.09) when compared with C-C bearings (0.59% versus 0.32%, respectively). There were no other differences among bearing cohorts in the adjusted risk of revision THA or any other complication. The risk of short-term complication (including dislocation) and revision THA were similar among appropriately matched Medicare THA patients regardless of bearing surface. Hard-on-hard THA bearings are of questionable value in Medicare patients, given the higher cost associated with their use and uncertain long-term benefits in older patients. Level II, prognostic study. See Guidelines for Authors for a complete description of levels of evidence

The Epidemiology of Revision Total Knee Arthroplasty in the United States

Understanding the cause of failure and type of revision total knee arthroplasty (TKA) procedures performed in the United States is essential in guiding research, implant design, and clinical decision making in TKA. We assessed the causes of failure and specific types of revision TKA procedures performed in the United States using newly implemented ICD-9-CM diagnosis and procedure codes related to revision TKA data from the Nationwide Inpatient Sample (NIS) database. Clinical, demographic, and economic data were reviewed and analyzed from 60,355 revision TKA procedures performed in the United States between October 1, 2005 and December 31, 2006. The most common causes of revision TKA were infection (25.2%) and implant loosening (16.1%), and the most common type of revision TKA procedure reported was all component revision (35.2%). Revision TKA procedures were most commonly performed in large, urban, nonteaching hospitals in Medicare patients ages 65 to 74. The average length of hospital stay (LOS) for all revision TKA procedures was 5.1 days, and the average total charges were $49,360. However, average LOS, average charges, and procedure frequencies varied considerably by census region, hospital type, and procedure performed