A comparison of some criteria for states selection in the latent Markov model for longitudinal data

We compare different selection criteria to choose the number of latent states of a multivariate latent Markov model for longitudinal data. This model is based on an underlying Markov chain to represent the evolution of a latent characteristic of a group of individuals over time. Then, the response variables observed at different occasions are assumed to be conditionally independent given this chain. Maximum likelihood estimation of the model is carried out through an Expectation–Maximization algorithm based on forward–backward recursions which are well known in the hidden Markov literature for time series. The selection criteria we consider are based on penalized versions of the maximum log-likelihood or on the posterior probabilities of belonging to each latent state, that is, the conditional probability of the latent state given the observed data. Among the latter criteria, we propose an appropriate entropy measure tailored for the latent Markov models. We show the results of a Monte Carlo simulation study aimed at comparing the performance of the above states selection criteria on the basis of a wide set of model specifications.     

Polymerization (Polycondensation) of Alkanes over Fluosulfonic Acid and Antimony Pentafluoride

Several low molecular weight alkanes have been polymerized (polycondensed) over HSO₃ F-SbF₅ to yield a highly branched oily oligomer with a molecular weight range from the molecular weight of the monomer to around 700. The order of reactivity for butane and lower molecular alkanes is isobutane > n-butane > propane > ethane > methane. The reactivity is explained by the ease of attack of an acid proton derived from the acid on the alkane sigma bonds as well as the relative stability of the resulting cation formed. A cationic mechanism for this reaction is proposed.     

Short-Chain Branching in Polyethylene and Poly(vinyl Chloride) Using Pyrolysis Hydrogenation Gas Chromatography and 13C Nuclear Magnetic Resonance Analysis

This study compares the use of pyrolysis hydrogenation gas chromatography (PHGC) and ¹³C Fourier transform nuclear magnetic resonance (FTNMR) methods for the analysis of reference polyethylene (PE) samples, ethylene-α-olefin copolymers, and specially prepared poly(vinyl chloride) (PVC) samples which were reduced to their PE skeletal structures. The nature and relative quantities of the short branches along the polymer chains were determined using both techniques. Improved high-resolution PHGC data, obtained with a fused silica capillary separation column, gave results which were in satisfactory agreement with the ¹³C FTNMR data. This approach confirms that detailed microstructural information can be obtained with these methods by using carefully controlled experimental conditions and appropriate reference systems.     

Tentative Identification of the Reactive Species in the Reaction of Cp2 TiCl2 with Salts of Diacids

The tentative identification of the reactive species in the condensation of Cp₂ TiCl₂ with salts of diacids to form titanium polysters is made. The reactive species are believed to be the same for both aqueous solution and interfacial systems, i.e., R -CO₂ ^? and Cp₂ Ti²⁺ with reaction occurring in the aqueous phase. The condensation of Cp₂ TiCl₂ with disodium terephthalate in interfacial systems occurs via a pseudo-first-order reaction:

Rate = K[Cp₂ TiCl₂] The rate-determining step (s) is believed to be diffusion of CP₂ TiCl₂ into the aqueous layer and/or hydrolysis of Cp₂ TiCl₂     

Reversed‐phase high‐performance liquid chromatography method with fluorescence detection to screen nitric oxide synthases inhibitors

Nitric oxide synthase (NOS) inhibitors are potential drug candidates due to the critical role of an excessive production of nitric oxide in a range of diseases. At present, the radiometric detection of l ‐[³H]‐citrulline produced from l ‐[³H]‐arginine during the enzymatic reaction is one of the most accepted methods to assess the in vitro activity of NOS inhibitors. Here we report a fast, easy, and cheap reversed‐phase high‐performance liquid chromatography method with fluorescence detection, based on the precolumn derivatization of l ‐citrulline with o‐phthaldialdehyde/N‐acetyl cysteine, for the in vitro screening of NOS inhibitors. To evaluate enzyme inhibition by the developed method, N‐[3‐(aminomethyl)benzyl]acetamidine, a potent and selective inhibitor of inducible NOS, was used as a test compound. The half maximal inhibitory concentration obtained was comparable to that derived by the well‐established radiometric assay.     

Applicability of generic linear scoring mosels in the U.S. credit-union environment

Although credit-scoring models represent a widely used managerialaid for large financial intermediaries, the vast majority ofU.S. credit unions—relatively small cooperatively ownedretail intermediaries, constrained by sample and funding limitations—haveyet to adopt such techniques. Lovie & Lovie (1986) havetheorized that the flat-maximum effect or curve of insensitivityassociated with linear scoring models could be advantageousin areas of applied prediction such as credit scoring. In thiscontext, we reported the relative predictive power of genericcredit-scoring models versus customized models in an earlierpaper (Overstreet et al. 1992). Unfortunately, these findingswere not readily adaptable to the credit-union industry dueto a dated sample with incomplete credit-bureau information.Consequently, from 1988 to 1991, we gathered a refined databasefrom which to further develop and field-test generic scoringmodels in the credit-union environment. The results reportedherein not only confirm, but amplify, the relative predictivepower of such models found earlier. Relative costs and benefitsof generic versus customized models are modelled for a representativecredit union. Future research directions are set forth in theconclusions.     

The standard regulator problem for systems with input delays. An approach through singular control theory

We present a new solution to the quadratic regulator problem for systems with input delays. Our approach makes use of the existing theory of the singular quadratic regulator problem for distributed systems.This paper was written with the financial support of the Italian Ministero della Ricerca Scientifica e Tecnologica within the program of GNAFA-CNR.     

The Controllability of the Gurtin-Pipkin Equation: A Cosine Operator Approach

In this paper we give a semigroup-based definition of the solution of the Gurtin-Pipkin equation with Dirichlet boundary conditions. It turns out that the dominant term of the input-to-state map is the control to displacement operator of the wave equation. This operator is surjective if the time interval is long enough. We use this observation in order to prove exact controllability in finite time of the Gurtin-Pipkin equation.     

Proton-induced grain boundary segregation in stainless steel

Abstract

A technique is developed which addresses the problem of irradiation assisted stress corrosion cracking of stainless steels in light water reactors using high energy protons to induce grain boundary segregation. These results represent the first grain boundary segregation measurements in bulk produced by proton irradiation of stainless steel. The technique allows the study of grain boundary composition with negligible sample activation, short irradiation time, rapid sample turnaround and at minimal cost. Scanning Auger electron microscopy is used to obtain grain boundary composition measurements of irradiated and unirradiated samples of ultra high purity (UHP) type 304L stainless steel and UHP type 304L steels with the additions of phosphorus (UHP + P) and sulphur (UHP + S). Results show that irradiation of all three alloys causes significant Ni segregation to the grain boundary and Cr and Fe away from it. Irradiation of the UHP + P alloy also results in segregation of P at the grain boundary from 5.3 to 8.7 at %, over 80 times the bulk value. No radiation-induced grain boundary segregation of S was measured in the UHP + S alloy. Results also indicate that the presence of P or S may enhance radiation-induced segregation of major alloying elements at the boundary. Comparison of irradiated and unirradiated regions of the UHP + P alloy indicate that while a prior thermal treatment segregates P to the grain boundary to 5.3 at %, the major element concentrations at the grain boundary are completely different from those under irradiation.