On the rate of convergence to stationarity of the M/M/N queue in the Halfin-Whitt regime

We prove several results about the rate of convergence to stationarity, that is, the spectral gap, for the M/M/n queue in the Halfin-Whitt regime. We identify the limiting rate of convergence to steady-state, and discover an asymptotic phase transition that occurs w.r.t. this rate. In particular, we demonstrate the existence of a constant $B^*\approx1.85772$ s.t. when a certain excess parameter $B\in(0,B^*]$, the error in the steady-state approximation converges exponentially fast to zero at rate $\frac{B^2}{4}$. For $B>B^*$, the error in the steady-state approximation converges exponentially fast to zero at a different rate, which is the solution to an explicit equation given in terms of special functions. This result may be interpreted as an asymptotic version of a phase transition proven to occur for any fixed n by van Doorn [Stochastic Monotonicity and Queueing Applications of Birth-death Processes (1981) Springer]. We also prove explicit bounds on the distance to stationarity for the M/M/n queue in the Halfin-Whitt regime, when $B<B^*$. Our bounds scale independently of $n$ in the Halfin-Whitt regime, and do not follow from the weak-convergence theory.Comment: Published in at http://dx.doi.org/10.1214/12-AAP889 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Complex zero strip decreasing operators

In this paper we study the effect of linear differential operators coming from the Laguerre-Polya class that act on functions in the extended Laguerre-Polya class with zeros in a horizontal strip in the complex plane. These operator decrease the size of the strip containing the zeros.Comment: 17 pages, corrected several typos, added a citation. appears in Math. Anal. Appl. (2015

A Mixed-Methods Study of the Variables that Influence Southern Baptists’ Affirmation of the Inerrancy of the Bible

The Southern Baptist Convention (SBC) had discovered by the late 1970s that belief in the inerrancy of the Bible was not consistently affirmed by their leadership. After a twenty year battle, the SBC attempted to clarify the doctrine of inerrancy through the Baptist Faith and Message 2000. A mixed-method analysis was conducted by surveying 502 Florida Southern Baptist (FSB) church members with a 68-question survey instrument to determine the degree to which they affirmed the doctrine of inerrancy. The study revealed that a large percentage of FSB church members affirmed the doctrine, but the underlining beliefs were not always consistently acknowledged

The Massachusetts Health Plan: The Good, the Bad, and the Ugly

In spring 2006, Massachusetts enacted legislation to ensure universal health insurance coverage to all residents. The legislation was a hybrid of ideas from across the political spectrum, promoted by a moderately conservative Republican governor with national political aspirations, and passed by a liberal Democratic state House and Senate. Groups from across the political spectrum supported the plan, from the Heritage Foundation on the right to Families USA on the left, although the plan had detractors from across the political spectrum as well. This study briefly describes the basic structure of the Massachusetts plan and identifies the good, the bad, and the ugly. Although the legislation, as Stuart Altman put it, "is not a typical Massachusetts -- Taxachusetts, oh -- just -- crazy -- liberal plan," there is enough "bad" and "ugly" in the mix to raise serious concerns, particularly when the desire to overregulate the health insurance market appears to be hard -- wired into Massachusetts policymakers' DNA. If we want to make health insurance more affordable and avoid the "bad" and the "ugly" of the Massachusetts plan, Congress -- or, barring that, individual states -- should consider a "regulatory federalism" approach. Under such an approach, insurers and insurance purchasers would be required to subject themselves to the laws and regulations of a single state but allowed to select the state. As with corporate charters, this system would allow employers and insurers to select the regulatory regime that most efficiently and cost -- effectively matches the needs of their risk pools. The ability of purchasers and insurers to exit from the state's regulatory oversight (taking their premium taxes with them) would temper opportunistic behavior by legislators and regulators, including the temptation to impose inefficient mandates and otherwise overregulate

The Jurisprudence of Non-Proliferation: Taking International Law Seriously

This essay is about the power of the international law of nonproliferation- its mounting power in the world today and its properly augmented power in an enlightened future. The article focuses on three primary areas in which international law may play a greater role than is commonly appreciated in affecting the behavior of potential proliferators, their suppliers, and their resolute opponents. The three topics-areas in which the essay pleads for law to be taken even more seriously, and by a wider audience of governments and the international public-are: (a) treaties (especially the provisions of those treaties that commit the parties to pursue further incremental measures of disarmament); (b) customary international law (especially those aspects of behaviorbased jurisprudence which provide unwritten, but nevertheless binding, constraints upon the preparation for and conduct of state violence); and (c) disarmament institutions (especially those novel multilateral organizations that have recently sprung up to play a variety of fact-finding, confidence-building, and dispute-resolution functions). In all of this, the core notion is the suggestion that international law works, and that it would work even better if more people would notice it and come to understand how lawfulness advances their own self-interest

Effect of Strong Electron Correlation on the Efficiency of Photosynthetic Light Harvesting

Research into the efficiency of photosynthetic light harvesting has focused on two factors: (1) entanglement of chromophores, and (2) environmental noise. While chromophores are conjugated $\pi$-bonding molecules with strongly correlated electrons, previous models have treated this correlation implicitly without a mathematical variable to gauge correlation-enhanced efficiency. Here we generalize the single-electron/exciton models to a multi-electron/exciton model that explicitly shows the effects of enhanced electron correlation within chromophores on the efficiency of energy transfer. The model provides more detailed insight into the interplay of electron correlation within chromophores and electron entanglement between chromophores. Exploiting this interplay is assisting in the design of new energy-efficient materials, which are just beginning to emerge