Atomistic subsemirings of the lattice of subspaces of an algebra

Let A be an associative algebra with identity over a field k. An atomistic subsemiring R of the lattice of subspaces of A, endowed with the natural product, is a subsemiring which is a closed atomistic sublattice. When R has no zero divisors, the set of atoms of R is endowed with a multivalued product. We introduce an equivalence relation on the set of atoms such that the quotient set with the induced product is a monoid, called the condensation monoid. Under suitable hypotheses on R, we show that this monoid is a group and the class of k1_A is the set of atoms of a subalgebra of A called the focal subalgebra. This construction can be iterated to obtain higher condensation groups and focal subalgebras. We apply these results to G-algebras for G a group; in particular, we use them to define new invariants for finite-dimensional irreducible projective representations.Comment: 14 page

Dances With Elephants: Administrative Resolution of Medical Injury Claims by Medicare Beneficiaries

In our judgment, Hoffmann and Rowthorn\u27s research clearly demonstrates that the QIO-based complaint review process does not provide genuine relief to beneficiaries. People who complain typically want an explanation of their bad experience, compensation for harm they may have suffered, and assurance that future experiences will be better for themselves and for others. Medicare beneficiaries, however, receive minimal information about the resolution of their complaints and no substantive relief whatsoever. As Hoffmann and Rowthorn point out, several reform proposals are now before Congress, including moving the beneficiary complaint function from QIOs to new Medicare Provider Review Organizations. It is not clear from the authors\u27 analysis what is motivating bipartisan interest in reform, but it seems to involve potentially conflicting concerns about lack of consumer responsiveness, on one hand, and wasteful bureaucracy, on the other

Resolving Medical Malpractice Claims in the Medicare Program: Can It Be Done?

There is increasing interest in an integrated approach to patient safety and medical liability among policymakers. We have proposed Medicareled malpractice reform that would provide Medicare beneficiaries with better safety, improved communication in the event of error, preservation of therapeutic relationships, timely settlement, and fair compensation at a lower administrative cost. Disputes in the reformed system would be adjudicated by Medicare\u27s existing administrative appeals system that would work together with Medicare\u27s quality improvement regulation and payment policy to reduce errors and compensate injured patients. Despite the laudable rationale for Medicare-led malpractice reform, important issues attend the constitutional and statutory authority for such reform. The first issue, assuming legal authority exists, is the feasibility of Medicare-led malpractice reform. Quite simply, does the Medicare program, with the primary purpose of providing acute care services to the elderly, severely disabled, and people with end stage renal disease, have the requisite infrastructure to launch such reform without compromising its central functions? Second, does the federal Congress and/or the Executive Branch, in our constitutional scheme, have the requisite authority to establish Medicare-led malpractice reform especially when states have and always have had the authority to adjudicate medical malpractice in the common law tort system? This article explores these critical issues for Medicare-led malpractice reform. First, this article explores the infrastructure of the Medicare program and how it could accommodate Medicare-led malpractice reform without compromising its central mission. Second, the article briefly describes the elements of a Medicare malpractice adjudication and compensation system for Medicare beneficiaries. Third, the article explores the legal authority for a federal benefits program to supplant a function performed by state common law of torts in the civil judiciary and generally with jury trials. Finally, the article concludes with an assessment of the legal and practical feasibility of Medicare-led malpractice reform

Loading of a surface-electrode ion trap from a remote, precooled source

We demonstrate loading of ions into a surface-electrode trap (SET) from a remote, laser-cooled source of neutral atoms. We first cool and load $\sim$ $10^6$ neutral $^{88}$Sr atoms into a magneto-optical trap from an oven that has no line of sight with the SET. The cold atoms are then pushed with a resonant laser into the trap region where they are subsequently photoionized and trapped in an SET operated at a cryogenic temperature of 4.6 K. We present studies of the loading process and show that our technique achieves ion loading into a shallow (15 meV depth) trap at rates as high as 125 ions/s while drastically reducing the amount of metal deposition on the trap surface as compared with direct loading from a hot vapor. Furthermore, we note that due to multiple stages of isotopic filtering in our loading process, this technique has the potential for enhanced isotopic selectivity over other loading methods. Rapid loading from a clean, isotopically pure, and precooled source may enable scalable quantum information processing with trapped ions in large, low-depth surface trap arrays that are not amenable to loading from a hot atomic beam

Inelastic collisions of ultra-cold heteronuclear molecules in an optical trap

Ultra-cold RbCs molecules in high-lying vibrational levels of the a$^3\Sigma^+$ ground electronic state are confined in an optical trap. Inelastic collision rates of these molecules with both Rb and Cs atoms are determined for individual vibrational levels, across an order of magnitude of binding energies. A simple model for the collision process is shown to accurately reproduce the observed scattering rates