Is the Riemann zeta function in a short interval a 1-RSB spin glass ?

Fyodorov, Hiary & Keating established an intriguing connection between the maxima of log-correlated processes and the ones of the Riemann zeta function on a short interval of the critical line. In particular, they suggest that the analogue of the free energy of the Riemann zeta function is identical to the one of the Random Energy Model in spin glasses. In this paper, the connection between spin glasses and the Riemann zeta function is explored further. We study a random model of the Riemann zeta function and show that its two-overlap distribution corresponds to the one of a one-step replica symmetry breaking (1-RSB) spin glass. This provides evidence that the local maxima of the zeta function are strongly clustered.Comment: 20 pages, 1 figure, Minor corrections, References update

On landmark selection and sampling in high-dimensional data analysis

In recent years, the spectral analysis of appropriately defined kernel matrices has emerged as a principled way to extract the low-dimensional structure often prevalent in high-dimensional data. Here we provide an introduction to spectral methods for linear and nonlinear dimension reduction, emphasizing ways to overcome the computational limitations currently faced by practitioners with massive datasets. In particular, a data subsampling or landmark selection process is often employed to construct a kernel based on partial information, followed by an approximate spectral analysis termed the Nystrom extension. We provide a quantitative framework to analyse this procedure, and use it to demonstrate algorithmic performance bounds on a range of practical approaches designed to optimize the landmark selection process. We compare the practical implications of these bounds by way of real-world examples drawn from the field of computer vision, whereby low-dimensional manifold structure is shown to emerge from high-dimensional video data streams.Comment: 18 pages, 6 figures, submitted for publicatio

Locally Delivered Salicylic Acid From a Poly(anhydride-ester): Impact on Diabetic Bone Regeneration

Diabetes mellitus (DM) involves metabolic changes that can impair bone repair, including a prolonged inflammatory response. A salicylic acid-based poly(anhydride-ester) (SA-PAE) provides controlled and sustained release of salicylic acid (SA) that locally resolves inflammation. This study investigates the effect of polymer-controlled SA release on bone regeneration in diabetic rats where enhanced inflammation is expected. Fifty-six Sprague–Dawley rats were randomly assigned to two groups: diabetic group induced by streptozotocin (STZ) injection or normoglycemic controls injected with citrate buffer alone. Three weeks after hyperglycemia development or vehicle injection, 5 mm critical sized defects were created at the rat mandibular angle and treated with SA-PAE/bone graft mixture or bone graft alone. Rats were euthanized 4 and 12 weeks after surgery, then bone fill percentage in the defect region was assessed by micro-computed tomography (CT) and histomorphometry. It was observed that bone fill increased significantly at 4 and 12 weeks in SA-PAE/bone graft-treated diabetic rats compared to diabetic rats receiving bone graft alone. Accelerated bone formation in normoglycemic rats caused by SA-PAE/bone graft treatment was observed at 4 weeks but not at 12 weeks. This study shows that treatment with SA-PAE enhances bone regeneration in diabetic rats and accelerates bone regeneration in normoglycemic animals

Long distance regularization in chiral perturbation theory with decuplet

We investigate the use of long distance regularization in SU(3) baryon chiral perturbation theory with decuplet fields. The one-loop decuplet contributions to the octet baryon masses, axial couplings, S-wave nonleptonic hyperon decays and magnetic moments are evaluated in a chirally consistent fashion by employing a cutoff to implement long distance regularization. The convergence of the chiral expansions of these quantities is improved compared to the dimensionally regularized version which indicates that the propagation of Goldstone bosons over distances smaller than a typical hadronic size, which is beyond the regime of chiral perturbation theory but included by dimensional regularization, is removed by use of a cutoff.Comment: 31 page

Inter-laboratory Variation in the Chemical Analysis of Acidic Forest Soil Reference Samples from Eastern North America

Long-term forest soil monitoring and research often requires a comparison of laboratory data generated at different times and in different laboratories. Quantifying the uncertainty associated with these analyses is necessary to assess temporal changes in soil properties. Forest soil chemical properties, and methods to measure these properties, often differ from agronomic and horticultural soils. Soil proficiency programs do not generally include forest soil samples that are highly acidic, high in extractable Al, low in extractable Ca and often high in carbon. To determine the uncertainty associated with specific analytical methods for forest soils, we collected and distributed samples from two soil horizons (Oa and Bs) to 15 laboratories in the eastern United States and Canada. Soil properties measured included total organic carbon and nitrogen, pH and exchangeable cations. Overall, results were consistent despite some differences in methodology. We calculated the median absolute deviation (MAD) for each measurement and considered the acceptable range to be the median 6 2.5 3 MAD. Variability among laboratories was usually as low as the typical variability within a laboratory. A few areas of concern include a lack of consistency in the measurement and expression of results on a dry weight basis, relatively high variability in the C/N ratio in the Bs horizon, challenges associated with determining exchangeable cations at concentrations near the lower reporting range of some laboratories and the operationally defined nature of aluminum extractability. Recommendations include a continuation of reference forest soil exchange programs to quantify the uncertainty associated with these analyses in conjunction with ongoing efforts to review and standardize laboratory methods