Managing uncertainty in call centres using Poisson mixtures

We model a call centre as a queueing model with Poisson arrivals having an unknown varying arrival rate. We show how to compute prediction intervals for the arrival rate, and use the Erlang formula for the waiting time to compute the consequences for the occupancy level of the call centre. We compare it to the current practice of using a point estimate of the arrival rate (assumed constant) as forecast. Copyright © 2001 John Wiley & Sons, Ltd.     

Raman Spectroscopy and Fluorescence Photon Migration for Breast Cancer Diagnosis and Imaging

We are developing optical methods based on near infra-red Raman spectroscopy and fluorescence photon migration for diagnosis and localization of breast cancer. We demonstrate the ability of Raman spectroscopy to classify accurately normal, benign and malignant breast tissues, an important step in developing Raman spectroscopic needle probes as a tool for improving the accuracy of needle biopsy. We also show that photon migration imaging can be used to localize accurately small fluorescent objects imbedded in a thick turbid medium with realistic optical properties, thus demonstrating the potential of this technique for optical imaging.     

General framework for testing Poisson‐Voronoi assumption for real microstructures

Modeling microstructures is an interesting problem not just in materials science, but also in mathematics and statistics. The most basic model for steel microstructure is the Poisson‐Voronoi diagram. It has mathematically attractive properties and it has been used in the approximation of single‐phase steel microstructures. The aim of this article is to develop methods that can be used to test whether a real steel microstructure can be approximated by such a model. Therefore, a general framework for testing the Poisson‐Voronoi assumption based on images of two‐dimension sections of real metals is set out. Following two different approaches, according to the use or not of periodic boundary conditions, three different model tests are proposed. The first two are based on the coefficient of variation and the cumulative distribution function of the cells area. The third exploits tools from to topological data analysis, such as persistence landscapes.     

Modelling the process of incoming problem reports on released software products

For big software developing companies, it is important to know the amount of problems of a new software product that are expected to be reported in a period after the date of release, on a weekly basis. For each of a number of past releases, weekly data are present on the number of such reports. Based on the type of data that is present, we construct a stochastic model for the weekly number of problems to be reported. The (non‐parametric) maximum likelihood estimator for the crucial model parameter, the intensity of an inhomogeneous Poisson process, is defined. Moreover, the expectation maximization algorithm is described, which can be used to compute this estimate. The method is illustrated using simulated data. Copyright © 2004 John Wiley & Sons, Ltd.     

Vibrational Analysis of a Molecular Heme-Copper Assembly with a Nearly Linear Fe(III)-CN-Cu(II) Bridge: Insight into Cyanide Binding to Fully Oxidized Cytochrome c Oxidase

The complete vibrational analysis of [(1-MeIm)Fe(OEP)-CN-Cu(Me(6)tren)](2+) (1), which has been constructed as a model for the cyanide-ligated binuclear center in the respiratory protein cytochrome c oxidase, has been carried out. The resonance Raman spectra (lambda(exc) = 647 nm) and the mid-infrared spectra display three cyanide isotope-dependent vibrational modes. Two vibrations showed monotonic decreases with increasing mass of the cyanide ligand (2182-2137-2146-2101 cm(-)(1) and 535-526-526-520 cm(-)(1), respectively, for the (12)C(14)N-(13)C(14)N-(12)C(15)N-(13)C(15)N isotopomers), and could thus be assigned to the C&tbd1;N and Fe-CN-Cu stretching vibrations, respectively. The third vibration, detected with resonance Raman, showed a zigzag-type behavior (495-487-493-485 cm(-)(1) with the set of isotopomers above) with the frequency being more sensitive to (13)C labeling of the cyanide ligand than with (15)N labeling. This pattern of isotopic dependence is characteristic of a bending vibration. Additionally, with the same laser excitation frequency, the C&tbd1;N stretching mode was observed, which is the first time that this vibration has been detected in the resonance Raman spectrum of a synthetic heme-cyanide complex. The normal coordinate analysis showed marked differences between bridged and unbridged heme-cyanide complexes. Internal coordinates that are orthogonal in unbridged systems are significantly mixed in the bridged model, despite the overall linearity of the Fe-CN-Cu moiety. These measurements strengthen the proposal that cyanide bridges the two metal atoms in the cyanide-ligated, oxidized binuclear center of cytochrome c oxidase. A quantitative consideration of the vibrational characteristics of cyanide bound to the resting enzyme, in light of our model compound results, strongly suggests that the binuclear center is flexible and can undergo structural rearrangement to accommodate exogenous ligands. This is likely to be of mechanistic importance in both dioxygen reduction and proton translocation.     

Facile Synthesis and Versatile Reactivity of an Unusual Cyclometalated Rhodium(I) Pincer Complex

The synthesis of the reactive PN(C^H) ligand 2‐di(tert‐butylphosphanomethyl)‐6‐phenylpyridine ( 1^H ) and its versatile coordination to a Rh^I center is described. Facile C?H activation occurs in the presence of a (internal) base, thus resulting in the new cyclometalated complex [Rh^I(CO)(κ³‐P,N,C‐ 1 )] ( 3 ), which has been structurally characterized. The resulting tridentate ligand framework was experimentally and computationally shown to display dual‐site proton‐responsive reactivity, including reversible cyclometalation. This feature was probed by selective H/D exchange with [D₁]formic acid. The addition of HBF₄ to 3 leads to rapid net protonolysis of the Rh?C bond to produce [Rh^I(CO)(κ³‐P,N,(C?H)‐ 1 )] ( 4 ). This species features a rare aryl C?H agostic interaction in the solid state, as shown by X‐ray diffraction studies. The nature of this interaction was also studied computationally. Reaction of 3 with methyl iodide results in rapid and selective ortho‐methylation of the phenyl ring, thus generating [Rh^I(CO)(κ²‐P,N‐ 1^Me )] ( 5 ). Variable‐temperature NMR spectroscopy indicates the involvement of a Rh^III intermediate through formal oxidative addition to give trans‐[Rh^III(CH₃)(CO)(I)(κ³‐P,N,C‐ 1 )] prior to C?C reductive elimination. The Rh^III–trans‐diiodide complex [Rh^I(CO)(I)₂(κ³‐P,N,C‐ 1 )] ( 6 ) has been structurally characterized as a model compound for this elusive intermediate.     

The Iterative Convex Minorant Algorithm for Nonparametric Estimation

Abstract

The problem of minimizing a smooth convex function over a specific cone in IRⁿ is frequently encountered in nonparametric statistics. For that type of problem we suggest an algorithm and show that this algorithm converges to the solution of the minimization problem. Moreover, a simulation study is presented, showing the superiority of our algorithm compared to the EM algorithm in the interval censoring case 2 setting.