Using a matrix in life transition research

Life transitions can be planned or can occur unexpectedly. They can cause a major change to a person's life patterns and well-being. Older adulthood is a time for many life transitions as a result of changes in life roles and health status. In this exploratory study, the authors investigate the transition involved in driving cessation for older people. In analyzing and organizing the data, they develop a matrix that incorporated descriptive and temporal factors associated with the transition. This matrix is useful in organizing and communicating the findings as a whole and could be used in describing individual experiences. It might be of use for the organization of qualitative data about other life transitions such as illness, retirement, and the development and adoption of new behaviors.

A numerical study of large sparse matrix exponentials arising in Markov chains

Krylov subspace techniques have been shown to yield robust methods for the numerical computation of large sparse matrix exponentials and especially the transient solutions of Markov Chains. The attractiveness of these methods results from the fact that they allow us to compute the action of a matrix exponential operator on an operand vector without having to compute, explicitly, the matrix exponential in isolation. In this paper we compare a Krylov-based method with some of the current approaches used for computing transient solutions of Markov chains. After a brief synthesis of the features of the methods used, wide-ranging numerical comparisons are performed on a power challenge array supercomputer on three different models. (C) 1999 Elsevier Science B.V. All rights reserved.AMS Classification: 65F99; 65L05; 65U05.

Career versus motherhood? A case study describing a cognitive-existential approach to the dilemma

The present paper reports a case study concerning a professional woman in her 30s, who presented to the Occupational Health department of a metropolitan hospital with work stress stemming from accelerating work demands and marital problems related to the decision about whether to start a family or continue her career. No clinical diagnosis was warranted; however, Maslach Burnout Inventory Scores indicated a high degree of emotional exhaustion and moderate levels of depersonalisation, offset by a high sense of personal accomplishment in her work role. The client also demonstrated severe stress and moderate depression on the Depression-Anxiety-Stress Scale (DASS-21). The case was conceptualised from a combined cognitive-existential perspective. The woman's cognitions about her work, relationship, and prospective motherhood roles were identified, as well as underlying existential issues such as finding a meaning in life and a fear of being alone and unloved. Eight sessions of therapy incorporated components of cognitive and existential therapies, aimed at managing stress and improving marital adjustment. Posttreatment results showed substantial reductions in all the measures of distress, while personal accomplishment remained high. The woman and her husband decided to defer starting a family until other issues had been addressed.

Quantum dynamics of two coupled qubits

We investigate the difference between classical and quantum dynamics of coupled magnetic dipoles. We prove that in general the dynamics of the classical interaction Hamiltonian differs from the corresponding quantum model, regardless of the initial state. The difference appears as nonpositive-definite diffusion terms in the quantum evolution equation of an appropriate positive phase-space probability density. Thus, it is not possible to express the dynamics in terms of a convolution of a positive transition probability function and the initial condition as can be done in the classical case. It is this feature that enables the quantum system to evolve to an entangled state. We conclude that the dynamics are a quantum element of nuclear magnetic resonance quantum-information processing. There are two limits where our quantum evolution coincides with the classical one: the short-time limit before spin-spin interaction sets in and the long-time limit when phase diffusion is incorporated.

A new method for analysing the equilibrium and time-dependent behaviour of Markovian models

Many large-scale stochastic systems, such as telecommunications networks, can be modelled using a continuous-time Markov chain. However, it is frequently the case that a satisfactory analysis of their time-dependent, or even equilibrium, behaviour is impossible. In this paper, we propose a new method of analyzing Markovian models, whereby the existing transition structure is replaced by a more amenable one. Using rates of transition given by the equilibrium expected rates of the corresponding transitions of the original chain, we are able to approximate its behaviour. We present two formulations of the idea of expected rates. The first provides a method for analysing time-dependent behaviour, while the second provides a highly accurate means of analysing equilibrium behaviour. We shall illustrate our approach with reference to a variety of models, giving particular attention to queueing and loss networks. (C) 2003 Elsevier Ltd. All rights reserved.

Attachment insecurity, depression, and the transition to parenthood

In a longitudinal study of adult attachment and depression during the transition to parenthood, 76 couples completed questionnaires on three occasions: during the second trimester of pregnancy, and six weeks and six months postbirth. On the first and second occasions, the couples were also interviewed about their experiences of pregnancy and parenthood, respectively. Measures were also completed at similar time intervals by a comparison group of 74 childless couples. Attachment security was assessed in terms of the dimensions of discomfort with closeness and relationship anxiety. Relationship anxiety was less stable for transition wives than for other participants. Relationship anxiety also predicted increases in new mothers' depressive symptoms, after controlling for a broad range of other risk factors. However, the association between relationship anxiety and maternal depression was moderated by husbands' caregiving style. Maternal depression was linked to increases in husbands' and wives' attachment insecurity and marital dissatisfaction. Results are discussed in terms of the impact of depression and negative working models of attachment on couple interaction.

Entanglement in a simple quantum phase transition

What entanglement is present in naturally occurring physical systems at thermal equilibrium? Most such systems are intractable and it is desirable to study simple but realistic systems that can be solved. An example of such a system is the one-dimensional infinite-lattice anisotropic XY model. This model is exactly solvable using the Jordan-Wigner transform, and it is possible to calculate the two-site reduced density matrix for all pairs of sites. Using the two-site density matrix, the entanglement of formation between any two sites is calculated for all parameter values and temperatures. We also study the entanglement in the transverse Ising model, a special case of the XY model, which exhibits a quantum phase transition. It is found that the next-nearest-neighbor entanglement (though not the nearest-neighbor entanglement) is a maximum at the critical point. Furthermore, we show that the critical point in the transverse Ising model corresponds to a transition in the behavior of the entanglement between a single site and the remainder of the lattice.

Spectral properties of the tandem Jackson network, seen as a quasi-birth-and-death process

Quasi-birth-and-death (QBD) processes with infinite “phase spaces” can exhibit unusual and interesting behavior. One of the simplest examples of such a process is the two-node tandem Jackson network, with the “phase” giving the state of the first queue and the “level” giving the state of the second queue. In this paper, we undertake an extensive analysis of the properties of this QBD. In particular, we investigate the spectral properties of Neuts’s R-matrix and show that the decay rate of the stationary distribution of the “level” process is not always equal to the convergence norm of R. In fact, we show that we can obtain any decay rate from a certain range by controlling only the transition structure at level zero, which is independent of R. We also consider the sequence of tandem queues that is constructed by restricting the waiting room of the first queue to some finite capacity, and then allowing this capacity to increase to infinity. We show that the decay rates for the finite truncations converge to a value, which is not necessarily the decay rate in the infinite waiting room case. Finally, we show that the probability that the process hits level n before level 0 given that it starts in level 1 decays at a rate which is not necessarily the same as the decay rate for the stationary distribution.

Inhibition of transmitter release and long-term depression in the avian hippocampus

Long-term depression has recently been shown to occur at glutamatergic synapses in the avian hippocampus and requires activation of calcium/calmodulin-dependent protein kinase II in the nerve terminal. Here using whole cell and intracellular recordings from brain slices, we show that the N-type calcium channel contributes significantly to glutamate release in the avian hippocampus. Activation of the metabotrobic gamma-aminobutyric acid (GABA)(B) receptor by the specific agonist baclofen blocks synaptic transmission. The action of baclofen was associated with a change in paired pulse facilitation indicating that it resulted from a reduction in the probability of transmitter release, In contrast, no change in paired pulse facilitation was observed following the induction of long-term depression. These results show that activation of GABA(B) receptors and long-term depression reduce transmitter release by distinct mechanisms. (C) 2000 Elsevier Science Ireland Ltd. All rights reserved.

High-breakdown linear discriminant analysis

The classification rules of linear discriminant analysis are defined by the true mean vectors and the common covariance matrix of the populations from which the data come. Because these true parameters are generally unknown, they are commonly estimated by the sample mean vector and covariance matrix of the data in a training sample randomly drawn from each population. However, these sample statistics are notoriously susceptible to contamination by outliers, a problem compounded by the fact that the outliers may be invisible to conventional diagnostics. High-breakdown estimation is a procedure designed to remove this cause for concern by producing estimates that are immune to serious distortion by a minority of outliers, regardless of their severity. In this article we motivate and develop a high-breakdown criterion for linear discriminant analysis and give an algorithm for its implementation. The procedure is intended to supplement rather than replace the usual sample-moment methodology of discriminant analysis either by providing indications that the dataset is not seriously affected by outliers (supporting the usual analysis) or by identifying apparently aberrant points and giving resistant estimators that are not affected by them.

Derivation of the probability distribution function for the local density of states of a disordered quantum wire via the replica trick and supersymmetry

We consider the statistical properties of the local density of states of a one-dimensional Dirac equation in the presence of various types of disorder with Gaussian white-noise distribution. It is shown how either the replica trick or supersymmetry can be used to calculate exactly all the moments of the local density of states.' Careful attention is paid to how the results change if the local density of states is averaged over atomic length scales. For both the replica trick and supersymmetry the problem is reduced to finding the ground state of a zero-dimensional Hamiltonian which is written solely in terms of a pair of coupled spins which are elements of u(1, 1). This ground state is explicitly found for the particular case of the Dirac equation corresponding to an infinite metallic quantum wire with a single conduction channel. The calculated moments of the local density of states agree with those found previously by Al'tshuler and Prigodin [Sov. Phys. JETP 68 (1989) 198] using a technique based on recursion relations for Feynman diagrams. (C) 2001 Elsevier Science B.V. All rights reserved.

Brief note on the variation of constants formula for fuzzy differential equations

This note gives a theory of state transition matrices for linear systems of fuzzy differential equations. This is used to give a fuzzy version of the classical variation of constants formula. A simple example of a time-independent control system is used to illustrate the methods. While similar problems to the crisp case arise for time-dependent systems, in time-independent cases the calculations are elementary solutions of eigenvalue-eigenvector problems. In particular, for nonnegative or nonpositive matrices, the problems at each level set, can easily be solved in MATLAB to give the level sets of the fuzzy solution. (C) 2002 Elsevier Science B.V. All rights reserved.

Drug use patterns and mental health of regular amphetamine users during a reported 'heroin drought'

Aims The present study extends the findings of a pilot study conducted among regular amphetamine users in Newcastle, NSW, in 1998. It compares key features between current participants in a state capital city (Brisbane) and a regional city (Newcastle) and between the 1998 and current Newcastle sample. Design Cross-sectional survey. Setting Brisbane and Newcastle, Australia. Participants The survey was conducted among 214 regular amphetamine users within the context of a randomized controlled trial of brief interventions for amphetamine use. Measurements Demographic characteristics, past and present alcohol and other drug use and mental health, treatment, amphetamine-related harms and severity of dependence. Findings The main findings were as follows: (i) the rate of mental health problems was high among regular amphetamine users and these problems commonly emerged after commencement of regular amphetamine use; (ii) there were regional differences in drug use with greater accessibility to a wider range of drugs in a state capital city and greater levels of injecting risk-taking behaviour outside the capital city environment; and (iii) there was a significant increase in level of amphetamine use and percentage of alcohol users, a trend for a higher level of amphetamine dependence and a significant reduction in the percentage of people using heroin and benzodiazepines among the 2002 Newcastle cohort compared to the 1998 cohort. Conclusions Further longitudinal research is needed to elucidate transitions from one drug type to another and from recreational to injecting and regular use and the relationship between drug use and mental health in prospective studies among users. Implications Intervention research should evaluate the effectiveness of interventions aimed at: preventing transition to injecting and regular use of amphetamines; toward reducing levels of depression among amphetamine users and interventions among people with severe psychopathology and personality disorders; and toward reducing the prevalence of tobacco dependence among amphetamine users.

WHOQOL-BREF as a measure of quality of life in older patients with depression

Objective: To assess the reliability and validity of a brief measure of quality of life recently developed by the World Health Organization, the WHOQOL-BREF, and to examine its association with a variety of clinical and sociodemographic factors in older depressed patients. Design: Cross-sectional study. Methods: Older depressed patients (N=41) underwent diagnostic assessment using the Composite International Diagnostic Interview (CIDI) and were independently assessed on a variety of measures including the WHOQOL-BREF (a 26-item self-report questionnaire generating four domain scores), Hamilton Depression Rating Scale (HAM-D); Geriatric Depression Scale (GDS); Mini-mental State Examination (MMSE); Modified Barthel Index (MBI); Instrumental activities of daily living (IADL), and measures of physical health status and social relationships. Estimates of inter-rater and test-retest reliability, and concurrent validity were made. Results: 39 subjects completed the study. The majority of subjects (94.9%) received a diagnosis of DSM-IV Major Depressive Disorder. Levels of comorbidity were high. Three of the four domains of the WHOQOL-BREF (Physical, Psychological and Environment domains) demonstrated satisfactory reliability and validity. However, the Social Relationships domain exhibited poor validity. Quality of life scores were strongly correlated with severity of depression, number of self-reported physical symptoms and self-assessed general health status. There was no relationship between diagnostic comorbidity and quality of life scores. Conclusions: The WHOQOL-BREF was successfully administered to older depressed patients although the concurrent validity of one of its four domains was poor. Quality of life scores were strongly correlated with severity of depression, raising the issue of measurement redundancy.