Quantum Algorithms for Tree Isomorphism and State Symmetrization

The graph isomorphism problem is theoretically interesting and also has many practical applications. The best known classical algorithms for graph isomorphism all run in time super-polynomial in the size of the graph in the worst case. An interesting open problem is whether quantum computers can solve the graph isomorphism problem in polynomial time. In this paper, an algorithm is shown which can decide if two rooted trees are isomorphic in polynomial time. Although this problem is easy to solve efficiently on a classical computer, the techniques developed may be useful as a basis for quantum algorithms for deciding isomorphism of more interesting types of graphs. The related problem of quantum state symmetrization is also studied. A polynomial time algorithm for the problem of symmetrizing a set of orthonormal states over an arbitrary permutation group is shown

The New Forgotten Half and Research Directions to Support Them

This is one of a series of five papers outlining the particular domains and dimensions of inequality where new research may yield a better understanding of responses to this growing issue.Using data from the nationally representative Educational Longitudinal Survey (ELS), the authors examine the circumstances of youth who drop out of community college before attaining a credential, discuss institutional challenges in the era of increased college access, and outline a research agenda to help youth move beyond "some college" and achieve their potential

Symposium Introduction: The Myth of Moral Justice: Why Our Legal System Fails to Do What\u27s Right

I wrote The Myth ofMoral justice,\u27 primarily, as a moral critique of the legal system. In examining the rituals and practices of the law under moral criteria-its obsessive focus on zero-sum contests, its dedication to cold rules and procedural technicalities over human emotion, its failure to acknowledge the spiritual pain of those who come before it, its inability to create an atmosphere where apologies, reconciliation, and the restoring of moral balance to relationships is possible, its preference for judicial economy over truth, its privileging of secrets and indifference to lies, and its failure to promote an atmosphere of mutual caring and connection by not imposing a duty to rescue-the book is an indictment of the legal system for smugly believing that the correct legal result is necessarily consistent with the right moral outcome

Legal Solutions in Health Reform: Insurance Discrimination on the Basis of Health Status: An Overview of Discrimination Practices, Federal Law, and Federal Reform Options

Provides an overview of the insurance industry's discriminatory practices based on health status in designing and administering health insurance and employee health benefit plans. Discusses current federal law and interim and long-term reform options

Poetic License: Learning Morality from Fiction in light of Imaginative Resistance

Imaginative resistance (IR) is rejecting a claim that is true within a fictional world. Accounts that describe IR hold that readers exit a fiction at points of resistance. But if resistance entails exiting a fiction, then learning morality from fiction doesn’t occur. But moral learning from fiction does occur; some such cases are instances of accepting a norm one first denied. I amend current solutions to IR with poetic license. The more poetic license granted a work, the more flexible one is regarding perceived falsehoods. Instead of exiting the fiction, one has the chance to stay engaged and possibly learn norms she previously denied

An exact adaptive test with superior design sensitivity in an observational study of treatments for ovarian cancer

A sensitivity analysis in an observational study determines the magnitude of bias from nonrandom treatment assignment that would need to be present to alter the qualitative conclusions of a na\"{\i}ve analysis that presumes all biases were removed by matching or by other analytic adjustments. The power of a sensitivity analysis and the design sensitivity anticipate the outcome of a sensitivity analysis under an assumed model for the generation of the data. It is known that the power of a sensitivity analysis is affected by the choice of test statistic, and, in particular, that a statistic with good Pitman efficiency in a randomized experiment, such as Wilcoxon's signed rank statistic, may have low power in a sensitivity analysis and low design sensitivity when compared to other statistics. For instance, for an additive treatment effect and errors that are Normal or logistic or $t$-distributed with 3 degrees of freedom, Brown's combined quantile average test has Pitman efficiency close to that of Wilcoxon's test but has higher power in a sensitivity analysis, while a version of Noether's test has poor Pitman efficiency in a randomized experiment but much higher design sensitivity so it is vastly more powerful than Wilcoxon's statistic in a sensitivity analysis if the sample size is sufficiently large.Comment: Published in at http://dx.doi.org/10.1214/11-AOAS508 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org