A quantum algorithm providing exponential speed increase for finding eigenvalues and eigenvectors

We describe a new polynomial time quantum algorithm that uses the quantum fast fourier transform to find eigenvalues and eigenvectors of a Hamiltonian operator, and that can be applied in cases (commonly found in ab initio physics and chemistry problems) for which all known classical algorithms require exponential time. Applications of the algorithm to specific problems are considered, and we find that classically intractable and interesting problems from atomic physics may be solved with between 50 and 100 quantum bits.Comment: 10 page

Expressiveness and Robustness of First-Price Position Auctions

Since economic mechanisms are often applied to very different instances of the same problem, it is desirable to identify mechanisms that work well in a wide range of circumstances. We pursue this goal for a position auction setting and specifically seek mechanisms that guarantee good outcomes under both complete and incomplete information. A variant of the generalized first-price mechanism with multi-dimensional bids turns out to be the only standard mechanism able to achieve this goal, even when types are one-dimensional. The fact that expressiveness beyond the type space is both necessary and sufficient for this kind of robustness provides an interesting counterpoint to previous work on position auctions that has highlighted the benefits of simplicity. From a technical perspective our results are interesting because they establish equilibrium existence for a multi-dimensional bid space, where standard techniques break down. The structure of the equilibrium bids moreover provides an intuitive explanation for why first-price payments may be able to support equilibria in a wider range of circumstances than second-price payments

Why Underfiling by States Can and Should be Used to Enforce Environmental Regulations

“Overfiling” occurs when the federal government files an environmental enforcement action in situations where the state environmental enforcement agency has not sufficiently prosecuted a violator of a federal environmental statute. A recent case from the Tenth Circuit appears to support the idea of overfiling under the Resource Conservation and Recovery Act, and other courts have upheld overfiling actions under the Clean Water Act and the Clean Air Act. This Note argues that the practice of “underfiling,” a process in which states file environmental enforcement actions even after the federal government has already overfiled, is also supported by these federal court decisions. This Note also suggests that states may intervene under Rule 24 of the Federal Rules of Civil Procedure in federal environmental enforcement actions in order to seek additional relief from violators of environmental statutes

Commutator Leavitt path algebras

For any field K and directed graph E, we completely describe the elements of the Leavitt path algebra L_K(E) which lie in the commutator subspace [L_K(E),L_K(E)]. We then use this result to classify all Leavitt path algebras L_K(E) that satisfy L_K(E)=[L_K(E),L_K(E)]. We also show that these Leavitt path algebras have the additional (unusual) property that all their Lie ideals are (ring-theoretic) ideals, and construct examples of such rings with various ideal structures.Comment: 24 page

Intellectual Growth For Undergraduate Students: Evaluation Results From An Undergraduate Research Conference

We describe the development and evaluation of the university-wide, weeklong undergraduate research conference at the University of New Hampshire. Despite increases nationally in the number of undergraduate research conferences (URC), there has been little research examining the social and educational impact of these events on student presenters. We describe the development and evaluation of the university-wide, weeklong URC at the University of New Hampshire. A survey administered to URC participants over a four year period revealed that research culminating in a presentation at the URC was one of the more influential events students experienced during their undergraduate years and students realized a high level of satisfaction from presenting at the URC

Modelling the cost effectiveness of interferon beta and glatiramer acetate in the management of multiple sclerosis

OBJECTIVE: To evaluate the cost effectiveness of four disease modifying treatments (interferon betas and glatiramer acetate) for relapsing remitting and secondary progressive multiple sclerosis in the United Kingdom. DESIGN: Modelling cost effectiveness. SETTING: UK NHS. PARTICIPANTS: Patients with relapsing remitting multiple sclerosis and secondary progressive multiple sclerosis. MAIN OUTCOME MEASURES: Cost per quality adjusted life year gained. RESULTS: The base case cost per quality adjusted life year gained by using any of the four treatments ranged from £42 000 ($66 469; 61 630) to £98 000 based on efficacy information in the public domain. Uncertainty analysis suggests that the probability of any of these treatments having a cost effectiveness better than £20 000 at 20 years is below 20%. The key determinants of cost effectiveness were the time horizon, the progression of patients after stopping treatment, differential discount rates, and the price of the treatments. CONCLUSIONS: Cost effectiveness varied markedly between the interventions. Uncertainty around point estimates was substantial. This uncertainty could be reduced by conducting research on the true magnitude of the effect of these drugs, the progression of patients after stopping treatment, the costs of care, and the quality of life of the patients. Price was the key modifiable determinant of the cost effectiveness of these treatments