Holomorphic families of nonequivalent embeddings and of holomorphic group actions on affine space

We construct holomorphic families of proper holomorphic embeddings of \mathbb {C}^{k} into \mathbb {C}^{n} (0\textless k\textless n-1), so that for any two different parameters in the family, no holomorphic automorphism of \mathbb {C}^{n} can map the image of the corresponding two embeddings onto each other. As an application to the study of the group of holomorphic automorphisms of \mathbb {C}^{n}, we derive the existence of families of holomorphic \mathbb {C}^{*}-actions on \mathbb {C}^{n} (n\ge5) so that different actions in the family are not conjugate. This result is surprising in view of the long-standing holomorphic linearization problem, which, in particular, asked whether there would be more than one conjugacy class of \mathbb {C}^{*}-actions on \mathbb {C}^{n} (with prescribed linear part at a fixed point).

Therapeutic drug monitoring of once daily aminoglycoside dosing: comparison of two methods and investigation of the optimal blood sampling strategy.

PURPOSE Therapeutic drug monitoring of patients receiving once daily aminoglycoside therapy can be performed using pharmacokinetic (PK) formulas or Bayesian calculations. While these methods produced comparable results, their performance has never been checked against full PK profiles. We performed a PK study in order to compare both methods and to determine the best time-points to estimate AUC0-24 and peak concentrations (C max). METHODS We obtained full PK profiles in 14 patients receiving a once daily aminoglycoside therapy. PK parameters were calculated with PKSolver using non-compartmental methods. The calculated PK parameters were then compared with parameters estimated using an algorithm based on two serum concentrations (two-point method) or the software TCIWorks (Bayesian method). RESULTS For tobramycin and gentamicin, AUC0-24 and C max could be reliably estimated using a first serum concentration obtained at 1 h and a second one between 8 and 10 h after start of the infusion. The two-point and the Bayesian method produced similar results. For amikacin, AUC0-24 could reliably be estimated by both methods. C max was underestimated by 10-20% by the two-point method and by up to 30% with a large variation by the Bayesian method. CONCLUSIONS The ideal time-points for therapeutic drug monitoring of once daily administered aminoglycosides are 1 h after start of a 30-min infusion for the first time-point and 8-10 h after start of the infusion for the second time-point. Duration of the infusion and accurate registration of the time-points of blood drawing are essential for obtaining precise predictions.

Full and hat inductive definitions are equivalent in NBG

A new research project has, quite recently, been launched to clarify how different, from systems in second order number theory extending ACA 0, those in second order set theory extending NBG (as well as those in n + 3-th order number theory extending the so-called Bernays−Gödel expansion of full n + 2-order number theory etc.) are. In this article, we establish the equivalence between Δ10\bf-LFP and Δ10\bf-FP, which assert the existence of a least and of a (not necessarily least) fixed point, respectively, for positive elementary operators (or between Δn+20\bf-LFP and Δn+20\bf-FP). Our proof also shows the equivalence between ID 1 and ^ID1, both of which are defined in the standard way but with the starting theory PA replaced by ZFC (or full n + 2-th order number theory with global well-ordering).

Do individual directors matter?

Paper 1: Pilot study of Swiss firms Abstract Using a fixed effects approach, we investigate whether the presence of specific individuals on Swiss firms’ boards affects firm performance and the policy choices they make. We find evidence for a substantial impact of these directors’ presence on their firms. Moreover, the director effects are correlated across policies and performance measures but uncorrelated to the directors’ background. We find these results interesting but conclude that they should to be substantiated on a dataset that is larger and better understood by researchers. Also, further tests are required to rule out methodological concerns. Paper 2: Evidence from the S&P 1,500 Abstract We ask whether directors on corporate boards contribute to firm performance as individuals. From the universe of the S&P 1,500 firms since 1996 we track 2,062 directors who serve on multiple boards over extended periods of time. Our initial findings suggest that the presence of these directors is associated with substantial performance shifts (director fixed effects). Closer examination shows that these effects are statistical artifacts and we conclude that directors are largely fungible. Moreover, we contribute to the discussion of the fixed effects method. In particular, we highlight that the selection of the randomization method is pivotal when generating placebo benchmarks. Paper 3: Robustness, statistical power, and important directors Abstract This article provides a better understanding of Senn’s (2014) findings: The outcome that individual directors are unrelated to firm performance proves robust against different estimation models and testing strategies. By looking at CEOs, the statistical power of the placebo benchmarking test is evaluated. We find that only the stronger tests are able to detect CEO fixed effects. However, these tests are not suitable to analyze directors. The suitable tests would detect director effects if the inter quartile range of the true effects amounted to 3 percentage points ROA. As Senn (2014) finds no such effects for outside directors in general, we focus on groups of particularly important directors (e.g., COBs, non-busy directors, successful directors). Overall, our evidence suggests that the members of these groups are not individually associated with firm performance either. Thus, we confirm that individual directors are largely fungible. If the individual has an effect on performance, it is of small magnitude.

Solution of the relativistic Schrödinger equation for the δ ′ -Function potential in one dimension using cutoff regularization

We study the relativistic version of the Schrödinger equation for a point particle in one dimension with the potential of the first derivative of the delta function. The momentum cutoff regularization is used to study the bound state and scattering states. The initial calculations show that the reciprocal of the bare coupling constant is ultraviolet divergent, and the resultant expression cannot be renormalized in the usual sense, where the divergent terms can just be omitted. Therefore, a general procedure has been developed to derive different physical properties of the system. The procedure is used first in the nonrelativistic case for the purpose of clarification and comparisons. For the relativistic case, the results show that this system behaves exactly like the delta function potential, which means that this system also shares features with quantum filed theories, like being asymptotically free. In addition, in the massless limit, it undergoes dimensional transmutation, and it possesses an infrared conformal fixed point. The comparison of the solution with the relativistic delta function potential solution shows evidence of universality.

New Algorithms for M-Estimation of Multivariate Scatter and Location

We present new algorithms for M-estimators of multivariate scatter and location and for symmetrized M-estimators of multivariate scatter. The new algorithms are considerably faster than currently used fixed-point and related algorithms. The main idea is to utilize a second order Taylor expansion of the target functional and to devise a partial Newton-Raphson procedure. In connection with symmetrized M-estimators we work with incomplete U-statistics to accelerate our procedures initially.

On the CFT operator spectrum at large global charge

We calculate the anomalous dimensions of operators with large global charge J in certain strongly coupled conformal field theories in three dimensions, such as the O(2) model and the supersymmetric fixed point with a single chiral superfield and a W = Φ3 superpotential. Working in a 1/J expansion, we find that the large-J sector of both examples is controlled by a conformally invariant effective Lagrangian for a Goldstone boson of the global symmetry. For both these theories, we find that the lowest state with charge J is always a scalar operator whose dimension ΔJ satisfies the sum rule J2ΔJ−(J22+J4+316)ΔJ−1−(J22+J4+316)ΔJ+1=0.04067 up to corrections that vanish at large J . The spectrum of low-lying excited states is also calculable explcitly: for example, the second-lowest primary operator has spin two and dimension ΔJ+3√. In the supersymmetric case, the dimensions of all half-integer-spin operators lie above the dimensions of the integer-spin operators by a gap of order J+12. The propagation speeds of the Goldstone waves and heavy fermions are 12√ and ±12 times the speed of light, respectively. These values, including the negative one, are necessary for the consistent realization of the superconformal symmetry at large J.

A Proof-Theoretic Analysis of Theories for Stratified Inductive Definitions

In this article we study subsystems SIDᵥ of the theory ID₁ in which fixed point induction is restricted to properly stratified formulas.

Gibbs point process approximation: Total variation bounds using Stein's method

We obtain upper bounds for the total variation distance between the distributions of two Gibbs point processes in a very general setting. Applications are provided to various well-known processes and settings from spatial statistics and statistical physics, including the comparison of two Lennard-Jones processes, hard core approximation of an area interaction process and the approximation of lattice processes by a continuous Gibbs process. Our proof of the main results is based on Stein's method. We construct an explicit coupling between two spatial birth-death processes to obtain Stein factors, and employ the Georgii-Nguyen-Zessin equation for the total bound.

Clinical and microbiological findings at sites treated with orthodontic fixed appliances in adolescents

INTRODUCTION: Fixed orthodontic appliances can alter the subgingival microbiota. Our aim was to compare the subgingival microbiota and clinical parameters in adolescent subjects at sites of teeth treated with orthodontic bands with margins at (OBM) or below the gingival margin (OBSM), or with brackets (OBR). METHODS: Microbial samples were collected from 33 subjects (ages, 12-18 years) in treatment more than 6 months. The microbiota was assessed by the DNA-DNA checkerboard hybridization method. RESULTS: Bacterial samples were taken from 83 OBR,103 OBSM, and 54 OBM sites. Probing pocket depths differed by orthodontic type (P <0.001) with mean values of 2.9 mm (SD, 0.6) at OBSM sites, 2.5 mm (SD, 0.6) at OBM sites, and 2.3 mm (SD, 0.5) at OBR sites. Only Actinomyces israelii (P <0.001) and Actinomyces naeslundii (P <0.001) had higher levels at OBR sites, whereas Neisseria mucosa had higher levels at sites treated with OBSM or OBM (P <0.001). Aggregatibacter actinomycetemcomitans was found in 25% of sites independent of the appliance. CONCLUSIONS: Different types of orthodontic appliances cause minor differences in the subgingival microbiota (A israelii and A naeslundii) and higher levels at sites treated with orthodontic brackets. More sites with bleeding on probing and deeper pockets were found around orthodontic bands.

[Microbiological point of care tests]

It is well known that the early initiation of a specific antiinfective therapy is crucial to reduce the mortality in severe infection. Procedures culturing pathogens are the diagnostic gold standard in such diseases. However, these methods yield results earliest between 24 to 48 hours. Therefore, severe infections such as sepsis need to be treated with an empirical antimicrobial therapy, which is ineffective in an unknown fraction of these patients. Today's microbiological point of care tests are pathogen specific and therefore not appropriate for an infection with a variety of possible pathogens. Molecular nucleic acid diagnostics such as polymerase chain reaction (PCR) allow the identification of pathogens and resistances. These methods are used routinely to speed up the analysis of positive blood cultures. The newest PCR based system allows the identification of the 25 most frequent sepsis pathogens by PCR in parallel without previous culture in less than 6 hours. Thereby, these systems might shorten the time of possibly insufficient antiinfective therapy. However, these extensive tools are not suitable as point of care diagnostics. Miniaturization and automating of the nucleic acid based method is pending, as well as an increase of detectable pathogens and resistance genes by these methods. It is assumed that molecular PCR techniques will have an increasing impact on microbiological diagnostics in the future.

Gunshot energy transfer profile in ballistic gelatine, determined with computed tomography using the total crack length method

By measuring the total crack lengths (TCL) along a gunshot wound channel simulated in ordnance gelatine, one can calculate the energy transferred by a projectile to the surrounding tissue along its course. Visual quantitative TCL analysis of cut slices in ordnance gelatine blocks is unreliable due to the poor visibility of cracks and the likely introduction of secondary cracks resulting from slicing. Furthermore, gelatine TCL patterns are difficult to preserve because of the deterioration of the internal structures of gelatine with age and the tendency of gelatine to decompose. By contrast, using computed tomography (CT) software for TCL analysis in gelatine, cracks on 1-cm thick slices can be easily detected, measured and preserved. In this, experiment CT TCL analyses were applied to gunshots fired into gelatine blocks by three different ammunition types (9-mm Luger full metal jacket, .44 Remington Magnum semi-jacketed hollow point and 7.62 × 51 RWS Cone-Point). The resulting TCL curves reflected the three projectiles' capacity to transfer energy to the surrounding tissue very accurately and showed clearly the typical energy transfer differences. We believe that CT is a useful tool in evaluating gunshot wound profiles using the TCL method and is indeed superior to conventional methods applying physical slicing of the gelatine.

Kernel density correlation based non-rigid point set matching for statistical model-based 2D/3D reconstruction

This paper presents a kernel density correlation based nonrigid point set matching method and shows its application in statistical model based 2D/3D reconstruction of a scaled, patient-specific model from an un-calibrated x-ray radiograph. In this method, both the reference point set and the floating point set are first represented using kernel density estimates. A correlation measure between these two kernel density estimates is then optimized to find a displacement field such that the floating point set is moved to the reference point set. Regularizations based on the overall deformation energy and the motion smoothness energy are used to constraint the displacement field for a robust point set matching. Incorporating this non-rigid point set matching method into a statistical model based 2D/3D reconstruction framework, we can reconstruct a scaled, patient-specific model from noisy edge points that are extracted directly from the x-ray radiograph by an edge detector. Our experiment conducted on datasets of two patients and six cadavers demonstrates a mean reconstruction error of 1.9 mm