28,564 research outputs found

    Quantum ground state isoperimetric inequalities for the energy spectrum of local Hamiltonians

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    We investigate the relationship between the energy spectrum of a local Hamiltonian and the geometric properties of its ground state. By generalizing a standard framework from the analysis of Markov chains to arbitrary (non-stoquastic) Hamiltonians we are naturally led to see that the spectral gap can always be upper bounded by an isoperimetric ratio that depends only on the ground state probability distribution and the range of the terms in the Hamiltonian, but not on any other details of the interaction couplings. This means that for a given probability distribution the inequality constrains the spectral gap of any local Hamiltonian with this distribution as its ground state probability distribution in some basis (Eldar and Harrow derived a similar result in order to characterize the output of low-depth quantum circuits). Going further, we relate the Hilbert space localization properties of the ground state to higher energy eigenvalues by showing that the presence of k strongly localized ground state modes (i.e. clusters of probability, or subsets with small expansion) in Hilbert space implies the presence of k energy eigenvalues that are close to the ground state energy. Our results suggest that quantum adiabatic optimization using local Hamiltonians will inevitably encounter small spectral gaps when attempting to prepare ground states corresponding to multi-modal probability distributions with strongly localized modes, and this problem cannot necessarily be alleviated with the inclusion of non-stoquastic couplings

    \u27Workshops in healing\u27 for senior medical students: 5 year overview and appraisal

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    We report upon the design, content and feedback from an interactive, experiential series of Workshops in Healing for senior medical students. Fifty-six final year medical students enrolled in 2×3 h workshops designed around the core themes of ‘physician know thyself’ (Workshop 1) and ‘confronting suffering’ (Workshop 2). Of the 56 students who initially enrolled, 48 students completed both workshops and provided a written openended reflection of their learning experience. The study, undertaken over a consecutive 5-year period (2008–2012), employed an emergent, qualitative design using thematic analysis of the reflective comments. We found that the design and content of both workshops promoted transformative learning for these final year medical students. Students identified the following benefits: (1) the opportunity to reaffirm their commitment to their chosen career path; (2) the value of listening to other students share their stories; (3) the importance of the timing of the workshops to occur after exams; (4) the use of various mediums such as art, poetry, music and contemporary/classic literature to present concepts of suffering and healing; and (5) the creation of a safe and confidential space. Students reported that these innovative workshops gave them a renewed sense of drive and enthusiasm for their chosen career. They highlighted the importance of addressing an aspect of medicine (healing) not covered in the traditional medical curriculum. Workshops in Healing helped them to rediscover a deeper meaning to medicine and their roles as future healthcare professionals

    [Review of] Sherman Alexie. The Lone Ranger and Tonto Fistfight in Heaven

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    A member of the Spokane tribe, Alexie writes the heart of a community that is joined through hardship, hope, land, and story. On and off the reservation, from the storytelling of Thomas Builds-the-Fire to Norma\u27s fancydancing, a drumbeat of home follows everyone

    Ranking Risk Inequities

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    Comparing recent data on age-adjusted death rates for blacks and whites, the authors attempt to clarify how ranking risks based on degree of inequity might differ from ranking them according to frequency of health impairments in the overall population. They also identify problems in choosing a method for ranking causes of death that incorporates both frequency and equity and suggest that agreement will be difficult to reach

    Mortgage loan securitization and relative loan performance

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    We compare the ex ante observable risk characteristics and the default rates of securitized mortgage loans and mortgage loans retained by the original lender. We find that privately securitized loans tend to be riskier and to default at a faster rate than loans securitized with the GSEs and lender-retained loans. However, the differences in default rates across investor types are of secondary importance for explaining mortgage defaults compared to more conventional predictors, such as original loan-to-value ratios and the path for house prices. Privately securitized home mortgages have conditionally higher expected returns than retained loans, suggesting the presence of risk factors that are unobservable but nonetheless at least partially acknowledged by the market.Mortgage loans

    Identifying evolutionary trees and substitution parameters for the general Markov model with invariable sites

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    The general Markov plus invariable sites (GM+I) model of biological sequence evolution is a two-class model in which an unknown proportion of sites are not allowed to change, while the remainder undergo substitutions according to a Markov process on a tree. For statistical use it is important to know if the model is identifiable; can both the tree topology and the numerical parameters be determined from a joint distribution describing sequences only at the leaves of the tree? We establish that for generic parameters both the tree and all numerical parameter values can be recovered, up to clearly understood issues of `label swapping.' The method of analysis is algebraic, using phylogenetic invariants to study the variety defined by the model. Simple rational formulas, expressed in terms of determinantal ratios, are found for recovering numerical parameters describing the invariable sites

    Paying for Politics

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    The identifiability of tree topology for phylogenetic models, including covarion and mixture models

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    For a model of molecular evolution to be useful for phylogenetic inference, the topology of evolutionary trees must be identifiable. That is, from a joint distribution the model predicts, it must be possible to recover the tree parameter. We establish tree identifiability for a number of phylogenetic models, including a covarion model and a variety of mixture models with a limited number of classes. The proof is based on the introduction of a more general model, allowing more states at internal nodes of the tree than at leaves, and the study of the algebraic variety formed by the joint distributions to which it gives rise. Tree identifiability is first established for this general model through the use of certain phylogenetic invariants.Comment: 20 pages, 1 figur
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