Learning From Strategically Controlled Information

In the first chapter, ``Promoting a Reputation for Quality,\u27\u27 I model a firm that manages its reputation for selling high quality products by investing in the quality of the product and by controlling the information consumers observe. As in \citet{BMTV}, quality is persistent, and evolves stochastically over time. Consumers do not observe product quality or the firm\u27s actions directly, instead they form beliefs about the quality of the firm\u27s product based on the information they observe. I focus on two cases, the good news case, where the firm can promote its product by releasing positive information, and the bad news case, where the firm can choose to censor negative information, and characterize Markov perfect equilibria. In the good news case, promotion and investment are complements. The firm has incentives to invest because it can then promote its product. the firm does not invest in quality or promote at high reputation, invests and promotes at low reputations, and promotes but does not invest at intermediate reputations. This intermediate region reduces the firm’s incentives to invest in quality, relative to what would happen if information was exogenous. But reputation effects are persistent. The firm will always eventually have incentives to invest in quality and renew its reputation. In contrast, in the bad news case censorship and investment are substitutes. The firm can either invest to hide negative information about its product or censor this bad news. Unless censorship is sufficiently expensive, reputation effects break down and the firm never invests in the quality of its product. In the second chapter, ``Bounded Rationality and Learning: A Framework and A Robustness Result\u27\u27 (joint with Aislinn Bohren), we investigate how consumers learn from the actions of others. We consider what happens in a social learning environment when agents have potentially misspecified models of the world. Agents may misinterpret information they see about the world, and may also misinterpret how others view the world. We develop a set of tools that allow us to analyze asymptotic learning outcomes in the presence of model misspecification. This framework allows us to consider agents with a variety of biases, including the level-k models, confirmation bias, partisan bias, and models where agents over or under-weight the information contained in their private signals

A non-perturbative method of calculation of Green functions

A new method for non-perturbative calculation of Green functions in quantum mechanics and quantum field theory is proposed. The method is based on an approximation of Schwinger-Dyson equation for the generating functional by exactly soluble equation in functional derivatives. Equations of the leading approximation and the first step are solved for $\phi^4_d$-model. At $d=1$ (anharmonic oscillator) the ground state energy is calculated. The renormalization program is performed for the field theory at $d=2,3$. At $d=4$ the renormalization of the coupling involves a trivialization of the theory.Comment: 13 pages, Plain LaTex, no figures, some discussion of results for anharmonic oscillator and a number of references are added, final version published in Journal of Physics

Improving the reliability of model-based decision-making estimates in the two-stage decision task with reaction-times and drift-diffusion modeling

A well-established notion in cognitive neuroscience proposes that multiple brain systems contribute to choice behaviour. These include: (1) a model-free system that uses values cached from the outcome history of alternative actions, and (2) a model-based system that considers action outcomes and the transition structure of the environment. The widespread use of this distinction, across a range of applications, renders it important to index their distinct influences with high reliability. Here we consider the two-stage task, widely considered as a gold standard measure for the contribution of model-based and model-free systems to human choice. We tested the internal/temporal stability of measures from this task, including those estimated via an established computational model, as well as an extended model using drift-diffusion. Drift-diffusion modeling suggested that both choice in the first stage, and RTs in the second stage, are directly affected by a model-based/free trade-off parameter. Both parameter recovery and the stability of model-based estimates were poor but improved substantially when both choice and RT were used (compared to choice only), and when more trials (than conventionally used in research practice) were included in our analysis. The findings have implications for interpretation of past and future studies based on the use of the two-stage task, as well as for characterising the contribution of model-based processes to choice behaviour

Antenatal Depression: Prevalence and Determinants in a High-Risk Sample of Women in Saskatoon

Pregnancy is often portrayed as a happy time for the woman and her family. In reality, many women struggle with negative emotions and moods that can have deleterious effects on the mother, the fetus, and the growing family. Depression is an increasing, worldwide problem, with women in their childbearing years and those of low socioeconomic status the most vulnerable. This study explores depression, as determined by the Edinburgh Postnatal Depression Scale (EPDS), in a high-risk sample of pregnant women enrolled in two prenatal programs in Saskatoon, Saskatchewan, Canada. A prevention and population health approach has been used to identify potential determinants and implications of antenatal depression. The data analyzed in this study were from the first cross-sectional portion of a longitudinal, epidemiological study of depression in pregnancy into the postpartum. Women were invited to participate in the study at their first prenatal visit. Data were collected by program staff. The prevalence of depression in this sample of 402 high-risk women was 29.5%, which is similar to other studies of inner-city, low income, and minority women elsewhere in the world. In the final model, antenatal depression was associated with a history of depression, moods going up and down, current smoking status, high levels of stressors, and social support.Factor analysis of the EPDS revealed three underlying factors: Anxiety, Depression, and Self-harm thoughts. The anxiety factor explained most of the variance in the overall EPDS scores in this sample of women. A history of problems with mood fluctuations was significantly associated with anxiety and depression subscales and self-harm. Significantly more women aged 21 and under experienced anxiety, and more Aboriginal women experienced depressive symptoms and self-harm thoughts. Twenty percent of women reported self-harm thoughts in the preceding seven days. Depressed, Aboriginal, and single women, and women who use alcohol were most at risk for self-harm thoughts. The level of depressive symptoms in this sample of women represents a significant public and mental health problem in women already challenged by inequities in their life circumstances. We need to develop public health policy that will support screening and identification of women with depression. Interventions at the primary, secondary, and tertiary levels of prevention can help to improve the health of women struggling with antenatal depression, promote the optimal intrauterine environment for their unborn children, and reduce the intergenerational transmission of depression

Fatal anaphylactic sting reaction in a patient with mastocytosis

We report on a 33-year-old female patient with indolent systemic mastocytosis and urticaria pigmentosa who died of an anaphylactic reaction after a yellow jacket sting. As she had no history of previous anaphylactic sting reaction, there was no testing performed in order to detect hymenoptera venom sensitization. But even if a sensitization had been diagnosed, no venom immunotherapy (VIT) would have been recommended. It is almost certain that VIT would have saved her life and it is most likely that VIT is indicated in some patients with mastocytosis with no history of anaphylactic sting reaction. However, no criteria have been established in order to allow a selection of mastocytosis patients eligible for such a `prophylactic' VIT. Copyright (C) 2008 S. Karger AG, Basel

Monodromy-data parameterization of spaces of local solutions of integrable reductions of Einstein's field equations

For the fields depending on two of the four space-time coordinates only, the spaces of local solutions of various integrable reductions of Einstein's field equations are shown to be the subspaces of the spaces of local solutions of the ``null-curvature'' equations constricted by a requirement of a universal (i.e. solution independent) structures of the canonical Jordan forms of the unknown matrix variables. These spaces of solutions of the ``null-curvature'' equations can be parametrized by a finite sets of free functional parameters -- arbitrary holomorphic (in some local domains) functions of the spectral parameter which can be interpreted as the monodromy data on the spectral plane of the fundamental solutions of associated linear systems. Direct and inverse problems of such mapping (``monodromy transform''), i.e. the problem of finding of the monodromy data for any local solution of the ``null-curvature'' equations with given canonical forms, as well as the existence and uniqueness of such solution for arbitrarily chosen monodromy data are shown to be solvable unambiguously. The linear singular integral equations solving the inverse problems and the explicit forms of the monodromy data corresponding to the spaces of solutions of the symmetry reduced Einstein's field equations are derived.Comment: LaTeX, 33 pages, 1 figure. Typos, language and reference correction

Computational and behavioral markers of model-based decision making in childhood

Human decision-making is underpinned by distinct systems that differ in flexibility and associated cognitive cost. A widely accepted dichotomy distinguishes between a cheap but rigid model-free system and a flexible but costly model-based system. Typically, humans use a hybrid of both types of decision-making depending on environmental demands. However, children's use of a model-based system during decision-making has not yet been shown. While prior developmental work has identified simple building blocks of model-based reasoning in young children (1–4 years old), there has been little evidence of this complex cognitive system influencing behavior before adolescence. Here, by using a modified task to make engagement in cognitively costly strategies more rewarding, we show that children aged 5–11-years (N = 85), including the youngest children, displayed multiple indicators of model-based decision making, and that the degree of its use increased throughout childhood. Unlike adults (N = 24), however, children did not display adaptive arbitration between model-free and model-based decision-making. Our results demonstrate that throughout childhood, children can engage in highly sophisticated and costly decision-making strategies. However, the flexible arbitration between decision-making strategies might be a critically late-developing component in human development

Follow-up examination of linkage and association to chromosome 1q43 in multiple sclerosis.

Multiple sclerosis (MS) is a debilitating neuroimmunological and neurodegenerative disease affecting >4,00,000 individuals in the United States. Population and family-based studies have suggested that there is a strong genetic component. Numerous genomic linkage screens have identified regions of interest for MS loci. Our own second-generation genome-wide linkage study identified a handful of non-major histocompatibility complex regions with suggestive linkage. Several of these regions were further examined using single-nucleotide polymorphisms (SNPs) with average spacing between SNPs of approximately 1.0 Mb in a dataset of 173 multiplex families. The results of that study provided further evidence for the involvement of the chromosome 1q43 region. This region is of particular interest given linkage evidence in studies of other autoimmune and inflammatory diseases including rheumatoid arthritis and systemic lupus erythematosus. In this follow-up study, we saturated the region with approximately 700 SNPs (average spacing of 10 kb per SNP) in search of disease-associated variation within this region. We found preliminary evidence to suggest that common variation within the RGS7 locus may be involved in disease susceptibility

Einstein's equations and the chiral model

The vacuum Einstein equations for spacetimes with two commuting spacelike Killing field symmetries are studied using the Ashtekar variables. The case of compact spacelike hypersurfaces which are three-tori is considered, and the determinant of the Killing two-torus metric is chosen as the time gauge. The Hamiltonian evolution equations in this gauge may be rewritten as those of a modified SL(2) principal chiral model with a time dependent `coupling constant', or equivalently, with time dependent SL(2) structure constants. The evolution equations have a generalized zero-curvature formulation. Using this form, the explicit time dependence of an infinite number of spatial-diffeomorphism invariant phase space functionals is extracted, and it is shown that these are observables in the sense that they Poisson commute with the reduced Hamiltonian. An infinite set of observables that have SL(2) indices are also found. This determination of the explicit time dependence of an infinite set of spatial-diffeomorphism invariant observables amounts to the solutions of the Hamiltonian Einstein equations for these observables.Comment: 22 pages, RevTeX, to appear in Phys. Rev.

Agrammatic but numerate

A central question in cognitive neuroscience concerns the extent to which language enables other higher cognitive functions. In the case of mathematics, the resources of the language faculty, both lexical and syntactic, have been claimed to be important for exact calculation, and some functional brain imaging studies have shown that calculation is associated with activation of a network of left-hemisphere language regions, such as the angular gyrus and the banks of the intraparietal sulcus. We investigate the integrity of mathematical calculations in three men with large left-hemisphere perisylvian lesions. Despite severe grammatical impairment and some difficulty in processing phonological and orthographic number words, all basic computational procedures were intact across patients. All three patients solved mathematical problems involving recursiveness and structure-dependent operations (for example, in generating solutions to bracket equations). To our knowledge, these results demonstrate for the first time the remarkable independence of mathematical calculations from language grammar in the mature cognitive system