Strong Asymptotics of the Orthogonal Polynomials with Respect to a Measure Supported on the Plane

We consider the orthogonal polynomials with respect to the measure over the whole complex plane. We obtain the strong asymptotic of the orthogonal polynomials in the complex plane and the location of their zeros in a scaling limit where n grows to infinity with N . The asymptotics are described in terms of three (probability) measures associated with the problem. The first measure is the limit of the counting measure of zeros of the polynomials, which is captured by the g‐function much in the spirit of ordinary orthogonal polynomials on the real line. The second measure is the equilibrium measure that minimizes a certain logarithmic potential energy, supported on a region K of the complex plane. The third measure is the harmonic measure of K ^c with a pole at ∞ . This appears as the limit of the probability measure given (up to the normalization constant) by the squared modulus of the n^th orthogonal polynomial times the orthogonality measure, i.e., The compact region K that is the support of the second measure undergoes a topological transition under the variation of the parameter in a double scaling limit near the critical point given by we observe the Hastings‐McLeod solution to Painlevé II in the asymptotics of the orthogonal polynomials. © 2014 Wiley Periodicals, Inc.     

Optimum step-stress accelerated degradation test for Wiener degradation process under constraints

To assess a product's reliability for subsequent managerial decisions such as designing an extended warranty policy and developing a maintenance schedule, Accelerated Degradation Test (ADT) has been used to obtain reliability information in a timely manner. In particular, Step-Stress ADT (SSADT) is one of the most commonly used stress loadings for shortening test duration and reducing the required sample size. Although it was demonstrated in many previous studies that the optimum SSADT plan is actually a simple SSADT plan using only two stress levels, most of these results were obtained numerically on a case-by-case basis. In this paper, we formally prove that, under the Wiener degradation model with a drift parameter being a linear function of the (transformed) stress level, a multi-level SSADT plan will degenerate to a simple SSADT plan under many commonly used optimization criteria and some practical constraints. We also show that, under our model assumptions, any SSADT plan with more than two distinct stress levels cannot be optimal. These results are useful for searching for an optimum SSADT plan, since one needs to focus only on simple SSADTs. A numerical example is presented to compare the efficiency of the proposed optimum simple SSADT plans and a SSADT plan proposed by a previous study. In addition, a simulation study is conducted for investigating the efficiency of the proposed SSADT plans when the sample size is small.     

A Brief Review of the Anticancer Activity of α-Aminophosphonic Acid Derivatives and a Report on the in Vitro Activity of Some Dialkyl α-aryl- (or Heteroaryl)-α-(Diphenylmethylamino)Methanephosphonates

Abstract

Reports on the anticancer activity of representative α-aminophosphonic acid derivatives are briefly reviewed, with comments where possible on modes of action. Preliminary in vitro screening results are also presented for selected dialkyl α-aryl (or heteroaryl)-α-(diphenylmethylamino)methanephosphonates against the National Cancer Institute (NCI) 60-cell line panel of human tumor cells, which showed average response parameters for active compounds of GI₅₀ between 4.81 × 10^?6 and 2.40 × 10^?5 M, TGI between 1.88 and 6.28 × 10^?5 M, and LC₅₀ between 5.71 and 9.37 × 10^?5 M. The highest activity was shown by the α-phenyl compound for which GI₅₀ 10^?7 M was recorded against leukemia cell line MOLT-4.     

Quantification of Intact and Truncated Stromal Cell-Derived Factor-1α in Circulation by Immunoaffinity Enrichment and Tandem Mass Spectrometry

Stromal cell-derived factor 1α (SDF-1α) or CXCL12 is a small pro-inflammatory chemoattractant cytokine and a substrate of dipeptidyl peptidase IV (DPP-IV). Proteolytic cleavage by DPP-IV inactivates SDF-1α and attenuates its interaction with CXCR4, its cell surface receptor. To enable investigation of suppression of such inactivation with pharmacologic inhibition of DPP-IV, we developed quantitative mass spectrometric methods that differentiate intact SDF-1α from its inactive form. Using top-down strategy in quantification, we demonstrated the unique advantage of keeping SDF-1α’s two disulfide bridges intact in the analysis. To achieve the optimal sensitivity required for quantification of intact and truncated SDF-1α at endogenous levels in blood, we coupled nano-flow tandem mass spectrometry with antibody-based affinity enrichment. The assay has a quantitative range of 20 pmol/L to 20 nmol/L in human plasma as well as in rhesus monkey plasma. With only slight modification, the same assay can be used to quantify SDF-1α in mice. Using two in vivo animal studies as examples, we demonstrated that it was critical to differentiate intact SDF-1α from its truncated form in the analysis of biomarkers for pharmacologic inhibition of DPP-IV activity. These novel methods enable translational research on suppression of SDF-1 inactivation with DPP-IV inhibition and can be applied to relevant clinical samples in the future to yield new insights on change of SDF-1α levels in disease settings and in response to therapeutic interventions.