On the number of support points of maximin and Bayesian D-optimal designs in nonlinear regression models

We consider maximin and Bayesian D-optimal designs for nonlinear regression models. The maximin criterion requires the specification of a region for the nonlinear parameters in the model, while the Bayesian optimality criterion assumes that a prior distribution for these parameters is available. It was observed empirically by many authors that an increase of uncertainty in the prior information (i.e. a larger range for the parameter space in the maximin criterion or a larger variance of the prior distribution in the Bayesian criterion) yields a larger number of support points of the corresponding optimal designs. In this paper we present a rigorous proof of this phenomenon and show that in many nonlinear regression models the number of support points of Bayesian- and maximin D-optimal designs can become arbitrarily large if less prior information is available. Our results also explain why maximin D-optimal designs are usually supported at more different points than Bayesian D-optimal designs. --Bayesian optimal design,maximin optimal design,nonlinear regression

The asymptotic minimax risk for the estimation of constrained binomial and multinomial probabilities

In this note we present a direct and simple approach to obtain bounds on the asymptotic minimax risk for the estimation of restrained binominal and multinominal proportions. Quadratic, normalized quadratic and entropy loss are considered and it is demonstrated that in all cases linear estimators are asymptotically minimax optimal. For the quadratic loss function the asymptotic minimax rsik does not change unless a neighborhood of the point 1/2 is excluded by the restrictions on the parameter space. For the two other loss functions the asymptotic minimax risks remain unchanged if additional knowledge about the location of the unknown probability of success is imposed. The results are also extended to the problem of minimax estimation of a vector of contrained multinominal propabilities. --binominal distribution,multinominal distribution,entropy loss,quadratic loss,constrained parameter space,least favourable distribution

Electronic Structure of Cesium-based Photocathode Materials from Density Functional Theory: Performance of PBE, SCAN, and HSE06 functionals

The development of novel materials for vacuum electron sources in particle accelerators is an active field of research that can greatly benefit from the results of \textit{ab initio} calculations for the characterization of the electronic structure of target systems. As state-of-the-art many-body perturbation theory calculations are too expensive for large-scale material screening, density functional theory offers the best compromise between accuracy and computational feasibility. The quality of the obtained results, however, crucially depends on the choice of the exchange-correlation potential, $v_{xc}$. To address this essential point, we systematically analyze the performance of three popular approximations of $v_{xc}$ (PBE, SCAN, and HSE06) on the structural and electronic properties of bulk Cs$_3$Sb and Cs$_2$Te, two representative materials of Cs-based semiconductors employed in photocathode applications. Among the adopted approximations, PBE shows expectedly the largest discrepancies from the target: the unit cell volume is overestimated compared to the experimental value, while the band gap is severely underestimated. On the other hand, both SCAN and HSE06 perform remarkably well in reproducing both structural and electronic properties. Spin-orbit coupling, which mainly impacts the valence region of both materials inducing a band splitting and, consequently, a band-gap reduction of the order of 0.2 eV, is equally captured by all functionals. Our results indicate SCAN as the best trade-off between accuracy and computational costs, outperforming the considerably more expensive HSE06

Small scale distribution patterns and vertical migration of North Sea erring larvae (Clupea harengus, Teleostei: Clupeidae) in relation to abiotic and biotic factors

The distribution of herring larvae in relation to environmental conditions and the occurrence of possible prey and predator organisms was studied during a 4-day period on a permanent station in the northern North Sea in September 1999. The vertical distribution of herring larvae was sampled in 20-m intervals by means of a multiple-closing net. To resolve the small-scale patchiness of herring larvae and planktonic prey and predator organisms, a towed in-situ video system was used, the Ichthyoplankton Recorder. A diel vertical migration of herring larvae was observed with different intensities depending on their body length. Small larvae (16 mm) showed the highest abundances in the upper water layers during the day and were concentrated in deeper water layers during the night. The presented results appear to be relevant for individual-based modelling of the fate of larval herring populations. La distribución a pequeña escala y la migración vertical de larvas de arenque del Mar del Norte (Clupea harengus, Teleostei: Clupeidea) en relación con factores abióticos y bióticos. – Se han estudiado la distribución de las larvas de arenque en relación a las condiciones ambientales y la incidencia de posibles presas y organismos depredadores a lo largo de un periodo de 4 días en una estación permanente situada en el Mar del Norte en septiembre de 1999. La distribución vertical de las larvas de arenque fue muestreada en intervalos de 20 m mediante una red de apertura múltiple (multiple opening/closing net). Para determinar a pequeña escala la heterogeneidad en la distribución de las larvas de arenque, así como de las presas y depredadores planctónicos, se utilizó un sistema de vídeo in-situ (The Ichthyoplankton Recorder). Se observó una migración vertical nictimeral con diferentes intensidades dependiendo de la longitud corporal de las larvas. Las larvas pequeñas (16 mm) mostraban su mayor abundancia en las capas superiores de la columna de agua durante el día y se concentraban en capas de agua más profundas durante la noche. Los resultados presentados en este trabajo pueden ser relevantes para la modelización (individual based modeling) del destino de las poblaciones de larvas del arenque

Non-Surgical Periodontal Therapy with Adjunctive Amoxicillin/Metronidazole or Metronidazole When No Aggregatibacter actinomycetemcomitans Is Detected-A Randomized Clinical Trial.

BACKGROUND The aim was to compare two different systemic antibiotics regimens adjunctive to non-surgical periodontal therapy when Aggregatibacter actinomycetemcomitans was not detected in the subgingival biofilm. METHODS A total of 58 patients with periodontitis and with no A. actinomycetemcomitans in the subgingival biofilm were treated with full-mouth subgingival instrumentation and either metronidazole (MET; n = 29) or amoxicillin/metronidazole (AMX/MET; n = 29). Probing depth (PD), clinical attachment level (CAL) and bleeding on probing (BOP) were recorded at baseline, as well as after three and six months. Subgingival biofilm and gingival crevicular fluid were collected and analyzed for major periodontopathogens and biomarkers. RESULTS PD, CAL and BOP improved at 3 and 6 months (each p < 0.001 vs. baseline) with no difference between the groups. Sites with initial PD ≥ 6 mm also improved in both groups after 3 and 6 months (p < 0.001) with a higher reduction of PD in the AMX/MET group (p < 0.05). T. forsythia was lower in the AMX/MET group after 3 months (p < 0.05). MMP-8 and IL-1β were without significant changes and differences between the groups. CONCLUSION When A. actinomycetemcomitans was not detected in the subgingival biofilm, the adjunctive systemic use of amoxicillin/metronidazole results in better clinical and microbiological outcomes of non-surgical periodontal therapy when the application of systemic antibiotics is scheduled

Ramsey numbers for sets of small graphs

AbstractThe Ramsey number r=r(G1-G2-⋯-Gm,H1-H2-⋯-Hn) denotes the smallest r such that every 2-coloring of the edges of the complete graph Kr contains a subgraph Gi with all edges of one color, of a subgraph Hi with all edges of a second color. These Ramsey numbers are determined for all sets of graphs with at most four vertices, and in the diagonal case (m=n,Gi=Hi) for all pairs of graphs, one with at most four and the other with five vertices, so as for all sets of graphs with five vertices

Aerosol properties over Southeastern China from multi-wavelength Raman and depolarization lidar measurements

A dataset of particle optical properties of highly polluted urban aerosol over the Pearl River Delta, Guangzhou, China is presented. The data were derived from multi-wavelengths Raman and depolarization lidar PollyXT and AERONET sun photometer measurements. The measurement campaign was conducted from Nov 2011 to June 2012. High aerosol optical depth was observed in the polluted atmosphere over this megacity, with a mean value of 0.54 ± 0.33 and a peak value of even 1.9. For the particle characterization the lidar ratio and the linear particle depolarization ratio, both at 532 nm, were used. The mean values of these properties are 48.0 sr ± 10.7 sr for the lidar ratio and 4%+-4% for the particle depolarization ratio, which means most depolarization measurements stayed below 10%. So far, most of these results indicate urban pollution particles mixed with particles arisen from biomass and industrial burning