Closed forms for asymptotic bias and variance in autoregressive models with unit roots

AbstractFor a first-order autoregressive AR(1) model with zero initial value, xt = αxt−1 + εt, we provide closed-form analytical expressions for the asymptotic bias and variance of the maximum likelihood (ML) estimator α = ∑1n xtxt−1∑1n−1 xt2 when ¦α¦ = 1. For the bias, numerical accuracy of up to six significant digits is achieved for sample sizes n > 100

Numerical Evidence that the Perturbation Expansion for a Non-Hermitian PT\mathcal{PT}-Symmetric Hamiltonian is Stieltjes

Recently, several studies of non-Hermitian Hamiltonians having $\mathcal{PT}$ symmetry have been conducted. Most striking about these complex Hamiltonians is how closely their properties resemble those of conventional Hermitian Hamiltonians. This paper presents further evidence of the similarity of these Hamiltonians to Hermitian Hamiltonians by examining the summation of the divergent weak-coupling perturbation series for the ground-state energy of the $\mathcal{PT}$-symmetric Hamiltonian $H=p^2+{1/4}x^2+i\lambda x^3$ recently studied by Bender and Dunne. For this purpose the first 193 (nonzero) coefficients of the Rayleigh-Schr\"odinger perturbation series in powers of $\lambda^2$ for the ground-state energy were calculated. Pad\'e-summation and Pad\'e-prediction techniques recently described by Weniger are applied to this perturbation series. The qualitative features of the results obtained in this way are indistinguishable from those obtained in the case of the perturbation series for the quartic anharmonic oscillator, which is known to be a Stieltjes series.Comment: 20 pages, 0 figure

Numerical methods for self-validating computations of probabilities and percentiles in selected distributions using interval analysis

Most scientific computations are carried out on computers which employ fixed-precision floating-point number systems. Therefore, the accuracy of the values produced by an scalar algorithm without given associated error estimators still pose a problem in today\u27s software. Self-validating numerical methods which not only produce an answer but also produce a guaranteed error bound would be of interest, especially for the following situations: (1) an essentially true answer is required for an accuracy comparison study among several competing algorithms or an accuracy study of a newly developed algorithm, and (2) the computed result has to satisfy given accuracy requirements because it is to be used in subsequent computations;In this study, we use four different numerical tools--interval arithmetic, automatic differentiation, continued fraction, and Taylor series expansion--to develop self-validating numerical integration methods. Then we apply these methods to the computations of probabilities and percentiles in selected distributions;Our software was developed in IBM compatible personal computers equipped with INTEL 80287 NPX. This software includes a support library and several algorithms which compute the probabilities and percentiles of selected distributions. The support library includes basic rounded interval arithmetic operations and some utility routines such as interval complete gamma function and interval tan[superscript]-1 function. These software are available upon request from the authors

Discrete Pearson distributions

These distributions are generated by a first order recursive scheme which equates the ratio of successive probabilities to the ratio of two corresponding quadratics. The use of a linearized form of this model will produce equations in the unknowns matched by an appropriate set of moments (assumed to exist). Given the moments we may find valid solutions. These are two cases; (1) distributions defined on the non-negative integers (finite or infinite) and (2) distributions defined on negative integers as well. For (1), given the first four moments, it is possible to set this up as equations of finite or infinite degree in the probability of a zero occurrence, the sth component being a product of s ratios of linear forms in this probability in general. For (2) the equation for the zero probability is purely linear but may involve slowly converging series; here a particular case is the discrete normal. Regions of validity are being studied. 11 refs

Blood transfusion and colorectal cancer

Blood transfusion enhances graft survival in renal transplant recipients. The mechanisms involved are unclear, but suppression of cell- mediated immunity plays a central role. This has led to the suggestion that blood transfusion may cause immunosuppression in cancer patients and this could have a detrimental effect on their survival.A retrospective study of 314 patients who had bowel resection for colorectal cancer was performed. Transfused patients had a poorer five year survival rate, but this was probably related to the fact that over 90% of patients with low rectal carcinoma who had an abdomino -perineal resection were transfused. Subsequently, the patients who had abdomino -perineal resections were excluded to limit analysis to the 159 patients who had abdominal resections. The 5 -year survival was 34% in those transfused, compared with 47% in those who were not, but this was not a significant difference.In the experimental research the aim was to establish a model of colonic cancer in which blood transfusion caused immunosuppression. Analysis of peripheral T cell subsets has been used to assess suppression of cell -mediated immunity. Subsets were counted using flow cytometry and monoclonal antibodies to T lymphocytes. There were no significant changes in subsets after transfusion with blood in normal rats. However, in older rats, transfusion with blood caused a significant increase in suppressor cells.Blood transfusion enhances growth of transplanted tumours in animals and recent evidence implicated macrophage prostaglandin E2 as a mediator of transfusion- mediated immunosuppression. The next objective was to study the influence of blood transfusion on the course of colonic carcinogeneis and the possible abrogating effects of indomethacin. This study confirmed that blood transfusion enhanced dimethylhydrazine carcinogenesis and suggested that treated rats with indomethacin, a prostaglandin synthetase inhibitor, at the time of transfusion may abrogate this effect.Using a rat peritoneal macrophage model, it was shown that blood transfusion increased prostaglandin E2 production by these cells in vitro. Allogeneic serum caused the greatest increase, while transfusion with stored allogeneic and syngeneic blood both caused an increase in prostaglandin E2 production. This suggests immunomodulation by factors associated with storage of blood in addition to a genetic effect.In conclusion, there is evidence that blood transfusion is associated with reduced survival of colorectal cancer patients, but this may be due to more advanced malignancy in transfused patients. Blood transfusion enhances colonic carcinogenesis in rats and this may be abrogated by indomethacin. Blood transfusion increased prostaglandin E2 production by macrophages and this supports the theory that transfusion associated immunosuppression may be mediated by this effect

Doctor of Philosophy

dissertationMost proteins assemble into oligomeric complexes. These supramolecular associations may confer many advantages to the substituents. Polyhedral capsids represent a common, highly symmetric nanoscale architecture in which multiple subunits self-assemble to form a hollow three-dimensional surface which often serve as molecular containers or platforms for multivalent display of ligands. Capsids can be tailored to serve in applications such as drug delivery, biocatalysis, and materials synthesis. In this dissertation, I present a body of work undertaken on the Aquifex aeolicus lumazine synthase (AaLS) capsid to expand our knowledge of supramolecular protein associations and to generate capsids with novel functions. First, the construction and characterization of a novel nanoreactor is described. Using a previously established tagging system, an esterase was encapsulated in a laboratory-evolved variant of AaLS. Characterization of the purified complex shows an average loading of two esterases per capsid and an approximately 20-fold decrease in efficiency compared to the free esterase. This decrease is larger than most of the previously reported capsid-based nanoreactor systems which suggests that both the confinement molarity and the electrostatic environment of the capsid interior may significantly influence the kinetic parameters of guest enzymes. Second, I utilize charge complementarity to decorate the exterior of an AaLS capsid variant with green fluorescent protein (GFP). A new interface was engineered by negatively supercharging the five-fold symmetric capsid pores and appending a deca-arginine tag to the C-terminus of GFP. This interaction requires the engineered features of both binding partners and shows steep dependence on the buffer ionic strength, although it retains high affinity at physiological ionic strength. Thus, charge complementarity can provide a simple, powerful, and general method for designing protein associations de novo. Finally, I expand upon previous work in which a redox switch was developed to control capsid assembly. The original switch relies on the formation of a disulfide-bonded adduct between a pentameric variant of AaLS and thiophenol. I explore alterations to the prosthetic group structure which reveal that the three-fold symmetric interface of the assembled capsid is highly plastic and can tolerate a range of different adduct sizes and shapes. These studies also identified two new disassembly switches, providing greater control over the supramolecular chemistry of the AaLS capsid

Diagenetic and Mineralogical Effects in Clumped Isotope Thermometry and Application to Last Interglacial Climate.

This dissertation focuses on how mineralogical differences affect original clumped isotope (Δ47) values and how they are changed through diagenesis. A primary motivation for this work was to understand the geologic conditions under which the clumped isotope thermometer can be applied with confidence to paleoclimatic problems. To place empirical constraints on the conditions under which Δ47 alteration can occur, samples from a ~4500 m long drill core from Andros Island, Bahamas were analyzed. These limestones and dolomites formed under near-surface temperature conditions, but for samples below ~1.3 km in depth, calculated Δ47 temperatures increase by ~10° C. This indicates a shift from preserved near-surface temperatures to diagenetically modified values. Importantly, this shift is not accompanied by changes in common diagenetic indicators, and thus raises the possibility of solid-state clumped isotope alteration occurring at much lower temperatures than previously thought. Similar Δ47 temperatures recorded by each carbonate phase suggest that fine-grained dolomites and calcites are equally viable materials for recording surface temperature conditions, but both are also equally susceptible to alteration of their primary clumped isotope abundances when buried. A challenge remaining in clumped isotope thermometry was the lack of an empirical calibration for dolomite, which had been theoretically predicted to differ from established calibrations. Here, analysis of a set of synthetic and natural dolomites formed at known temperatures results in a calibration line statistically indistinguishable from calcite clumped isotope calibrations. This supports the idea of a universal calibration for carbonate clumped isotope thermometry and enables new investigations into conditions of dolomite formation. Finally, the clumped isotope thermometer can be applied to key intervals for investigating paleoclimate and testing paleoclimate questions. To determine sea surface temperatures and water composition in Bermuda during the onset of Last Interglacial sea level rise, conventional and clumped isotope measurements of fossil shells were conducted. These results suggest meltwater influence and temperatures as much as 10° C colder than modern, requiring explanations that allow for major changes in North Atlantic surface ocean circulation. They also illustrate extreme sensitivity of Bermudian climate to broad-scale climate and ocean circulation changes.PhDEarth and Environmental SciencesUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/120655/1/ianzw_1.pd