Principal Rings and their Invariant Factors

In this article we put forward a new look at the theory of principal and Invariant-Factor rings, with a view toward facilitating the formalization, automation, and archiving of results and their proofs. We take an elementary and constructive approach: standard techniques such as prime ideals and factorization of elements are avoided, and determinant constructions are minimized. Using such computationally friendly methods, the main existence and uniqueness results on invariant factors for a f.g. torsion module are derived, and several new algebraic constructions and results are found. The lattice of principal integral ideals for any commutative Bézoutian ring is explicitly constructed based on a first-order proof overlooked in the literature, together with a proof that this lattice is distributive. A Lagrange quotient theorem for finitely generated modules over any principal ring is stated for the first time. A very constructive new proof is given that a principal ring has the Hermite property, so is also an Invariant-Factor ring. A calculus that is needed in the ideal lattice, naturally yields a number of formulas valid for a function lattice.     

Microwave Initiated Self-Propagating High-Temperature Synthesis of SiC

The use of microwave energy to initiate self-propagating, high-temperature synthesis (SHS) of Si + graphite mixtures has been investigated. The results indicate that, unlike with conventional ignition techniques, green densities in excess of 80% of theoretical can be ignited and the combustion wavefront can be crudely controlled. It was found that the induction time for ignition increased with increasing green density and that a higher microwave power level was required with the denser green pellets to achieve the same ignition time. Combustion front velocity increased with green density. The degree of densification was found to decrease with increasing green density. For a given green density, the degree of densification increased with increasing microwave power. The product contained a significant proportion of ultrafine (36–72 nm diameter) SiC whiskers; despite this, final densities as high as 83.6% of theoretical could be obtained without the use of applied pressure. This compares with the 50% densities obtained via conventional ignition techniques.     

In situ column generation for a cutting-stock problem

Working with an integer bilinear programming formulation of a one-dimensional cutting-stock problem, we develop an ILP-based local-search heuristic. The ILPs holistically integrate the master and subproblem of the usual price driven pattern-generation paradigm, resulting in a unified model that generates new patterns in situ. We work harder to generate new columns, but we are guaranteed that new columns give us an integer linear-programming improvement (rather then the continuous linear-programming improvement sought by the usual price driven column generation). The method is well suited to practical restrictions such as when a limited number of cutting patterns should be employed, and our goal is to generate a profile of solutions trading off trim loss against the number of patterns utilized. We describe our implementation and results of computational experiments on instances from a chemical-fiber company.     

A randomized controlled trial of goal choice interventions for alcohol use disorders among men who have sex with men.

This study tested the efficacy of behavioral treatments for alcohol use disorders (AUD) among men who have sex with men (MSM) and who are at risk for HIV transmission. HIV-negative MSM with current AUD (N = 198) were recruited, offered treatment focused on reducing drinking and HIV risk, and followed during treatment and 12 months posttreatment. Participants (n = 89) accepted treatment and were randomized to either 4 sessions of motivational interviewing (MI) or 12 sessions of combined MI and coping skills training (MI + CBT). Other participants (n = 109) declined treatment but were followed, forming a non-help-seeking group (NHS). MI yielded significantly better drinking outcomes during the 12-week treatment period than MI + CBT, but posttreatment outcomes were equivalent. NHS participants significantly reduced their drinking as well. Service delivery and treatment research implications are discussed. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Coping style use predicts posttraumatic stress and complicated grief symptom severity among college students reporting a traumatic loss.

Problem-focused coping, and active and avoidant emotional coping were examined as correlates of grief and posttraumatic stress disorder (PTSD) severity among 123 college students reporting the unexpected death of an immediate family member, romantic partner, or very close friend. The authors administered to participants, via the Internet, 5 survey instruments that measured demographic characteristics, traumatic event exposure (Stressful Life Events Screening Questionnaire; L. Goodman, C. Corcoran, K. Turner, N. Yuan, & B. L. Green, 1998), complicated grief (CG) severity (Inventory of Complicated Grief--Revised--Short Form; A. E. Latham & H. G. Prigerson, 2004; H. G. Prigerson & S. C. Jacobs, 2001), PTSD severity (PTSD Checklist; F. W. Weathers, B. T. Litz, D. S. Herman, J. A. Huska, & T. M. Keane, 1993), and coping style use (Brief COPE; C. S. Carver, 1997). Results demonstrated that CG and PTSD severity were both significantly positively correlated with problem-focused, and active and avoidant emotional coping styles. The authors used path analysis to control for time since the loss and trauma frequency and found that only avoidant emotional coping remained significant in predicting CG and PTSD severity. Results are discussed in terms of their clinical implications for treating individuals with traumatic losses. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

The effect of nicotine and attention allocation on physiological and self-report measures of induced anxiety in PTSD: A double-blind placebo-controlled trial.

Rates of smoking among populations with psychiatric disorders are more than twice as high as among the general population, yet there are few controlled studies of the mechanisms of this relationship. This trial examined the effect of nicotine by way of cigarette smoking on both self-report and autonomic parameters of anxiety among individuals with PTSD who were also heavy smokers. Half of the participants were randomized to an anxiety-eliciting condition, whereas the other half were assigned to a condition of neutral emotional content. Within each of these conditions, participants were randomized into a nicotine condition (high-yield nicotine cigarette) or a placebo condition (denicotinized cigarette). The final layer of randomization involved assigning participants to either an attention-demanding task or a no task condition. We examined the interactive effects of nicotine and attentional demand on parameters of anxious responding. Nicotine exerted an anxiolytic effect relative to placebo on self-report measures; however, nicotine did not interact with attentional demand in producing this effect. In contrast to the findings on the self-report measures of distress, nicotine enhanced autonomic reactivity to trauma cues, thereby suggesting a decoupling of self-reported anxiety and autonomic arousal associated with responding to trauma-relevant cues. The implications for understanding smoking and psychiatric comorbidity are discussed. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

DNA double-strand break repair: a theoretical framework and its application

DNA double-strand breaks (DSBs) are formed as a result of genotoxic insults, such as exogenous ionizing radiation, and are among the most serious types of DNA damage. One of the earliest molecular responses following DSB formation is the phosphorylation of the histone H2AX, giving rise to γH2AX. Many copies of γH2AX are generated at DSBs and can be detected in vitro as foci using well-established immuno-histochemical methods. It has previously been shown that anti-γH2AX antibodies, modified by the addition of the cell-penetrating peptide TAT and a fluorescent or radionuclide label, can be used to visualize and quantify DSBs in vivo. Moreover, when labelled with a high amount of the short-range, Auger electron-emitting radioisotope, ¹¹¹In, the amount of DNA damage within a cell can be increased, leading to cell death. In this report, we develop a mathematical model that describes how molecular processes at individual sites of DNA damage give rise to quantifiable foci. Equations that describe stochastic mean behaviours at individual DSB sites are derived and parametrized using population-scale, time-series measurements from two different cancer cell lines. The model is used to examine two case studies in which the introduction of an antibody (anti-γH2AX-TAT) that targets a key component in the DSB repair pathway influences system behaviour. We investigate: (i) how the interaction between anti-γH2AX-TAT and γH2AX effects the kinetics of H2AX phosphorylation and DSB repair and (ii) model behaviour when the anti-γH2AX antibody is labelled with Auger electron-emitting ¹¹¹In and can thus instigate additional DNA damage. This work supports the conclusion that DSB kinetics are largely unaffected by the introduction of the anti-γH2AX antibody, a result that has been validated experimentally, and hence the hypothesis that the use of anti-γH2AX antibody to quantify DSBs does not violate the image tracer principle. Moreover, it provides a novel model of DNA damage accumulation in the presence of Auger electron-emitting ¹¹¹In that is supported qualitatively by the available experimental data.     

Representation of analysis results involving aleatory and epistemic uncertainty

Procedures are described for the representation of results in analyses that involve both aleatory uncertainty and epistemic uncertainty, with aleatory uncertainty deriving from an inherent randomness in the behaviour of the system under study and epistemic uncertainty deriving from a lack of knowledge about the appropriate values to use for quantities that are assumed to have fixed but poorly known values in the context of a specific study. Aleatory uncertainty is usually represented with probability and leads to cumulative distribution functions (CDFs) or complementary CDFs (CCDFs) for analysis results of interest. Several mathematical structures are available for the representation of epistemic uncertainty, including interval analysis, possibility theory, evidence theory and probability theory. In the presence of epistemic uncertainty, there is not a single CDF or CCDF for a given analysis result. Rather, there is a family of CDFs and a corresponding family of CCDFs that derive from epistemic uncertainty and have an uncertainty structure that derives from the particular uncertainty structure (e.g. interval analysis, possibility theory, evidence theory or probability theory) used to represent epistemic uncertainty. Graphical formats for the representation of epistemic uncertainty in families of CDFs and CCDFs are investigated and presented for the indicated characterisations of epistemic uncertainty.