Uncovering Ramanujan's "Lost" Notebook: An Oral History

Here we weave together interviews conducted by the author with three prominent figures in the world of Ramanujan's mathematics, George Andrews, Bruce Berndt and Ken Ono. The article describes Andrews's discovery of the "lost" notebook, Andrews and Berndt's effort of proving and editing Ramanujan's notes, and recent breakthroughs by Ono and others carrying certain important aspects of the Indian mathematician's work into the future. Also presented are historical details related to Ramanujan and his mathematics, perspectives on the impact of his work in contemporary mathematics, and a number of interesting personal anecdotes from Andrews, Berndt and Ono

Energy-Aware Cloud Management through Progressive SLA Specification

Novel energy-aware cloud management methods dynamically reallocate computation across geographically distributed data centers to leverage regional electricity price and temperature differences. As a result, a managed VM may suffer occasional downtimes. Current cloud providers only offer high availability VMs, without enough flexibility to apply such energy-aware management. In this paper we show how to analyse past traces of dynamic cloud management actions based on electricity prices and temperatures to estimate VM availability and price values. We propose a novel SLA specification approach for offering VMs with different availability and price values guaranteed over multiple SLAs to enable flexible energy-aware cloud management. We determine the optimal number of such SLAs as well as their availability and price guaranteed values. We evaluate our approach in a user SLA selection simulation using Wikipedia and Grid'5000 workloads. The results show higher customer conversion and 39% average energy savings per VM.Comment: 14 pages, conferenc

Decoherence and Entropy Production in Relativistic Nuclear Collisions

Short thermalization times of less than 1 fm/c for quark and gluon matter have been suggested by recent experiments at the Relativistic Heavy Ion Collider (RHIC). It has been difficult to justify this rapid thermalization in first-principle calculations based on perturbation theory or the color glass condensate picture. Here, we address the related question of the decoherence of the gluon field, which is a necessary component of thermalization. We present a simplified leading-order computation of the decoherence time of a gluon ensemble subject to an incoming flux of Weizsacker-Williams gluons. We also discuss the entropy produced during the decoherence process and its relation to the entropy in the final state which has been measured experimentally.Comment: 8 pages, 3 figure

On an Asymptotic Series of Ramanujan

An asymptotic series in Ramanujan's second notebook (Entry 10, Chapter 3) is concerned with the behavior of the expected value of $\phi(X)$ for large $\lambda$ where $X$ is a Poisson random variable with mean $\lambda$ and $\phi$ is a function satisfying certain growth conditions. We generalize this by studying the asymptotics of the expected value of $\phi(X)$ when the distribution of $X$ belongs to a suitable family indexed by a convolution parameter. Examples include the problem of inverse moments for distribution families such as the binomial or the negative binomial.Comment: To appear, Ramanujan

Benefit Plan Design and Prescription Drug Utilization Among Asthmatics: Do Patient Copayments Matter?

Objective: The ratio of controller to reliever medication use has been proposed as a measure of treatment quality for asthma patients. In this study we examine the effects of plan level mean out-of-pocket asthma medication patient copayments and other features of benefit plan design on the use of controller medications alone, controller and reliever medications (combination therapy), and reliever medications alone. Methods: 1995-2000 MarketScan claims data were used to construct plan-level out-of-pocket copayment and physician/practice prescriber preference variables for asthma medications. Separate multinomial logit models were estimated for patients in fee-for-service (FFS) and non-FFS plans relating benefit plan design features, physician/practice prescribing preferences, patient demographics, patient comorbidities and county-level income variables to patient-level asthma treatment patterns. Results: We find that the controller reliever ratio rose steadily over 1995-2000, along with out-of-pocket payments for asthma medications, which rose more for controllers than for relievers. However, after controlling for other variables, plan level mean out-of-pocket copayments were not found to have a statistically significant influence upon patient-level asthma treatment patterns. On the other hand, physician practice prescribing patterns strongly influenced patient level treatment patterns. Conclusions: There is no strong statistical evidence that higher levels of out-of-pocket copayments for prescription drugs influence asthma treatment patterns. However, physician/practice prescribing preferences influence patient treatment.

Price Indexes for Medical Care Goods and Services: An Overview of Measurement Issues

We review in considerable detail the conceptual and measurement issues that underlie construction of medical care price indexes in the U.S., particularly the medical care consumer price indexes (MCPIs) and medical-related producer price indexes (MPPIs). We outline salient features of the medical care marketplace, including the impacts of insurance, moral hazard, principal-agent relationships, technological progress and organizational changes. Since observed data are unlikely to correspond with efficient outcomes, we discuss implications of the failure of transactions data in this market to reveal reliable marginal valuations, and the consequent need to augment traditional transactions data with information based on cost-effectiveness and outcomes studies. We describe procedures currently used by the BLS in constructing MCPIs and MPPIs, including recent revisions, and then consider alternative notions of medical care output pricing that involve the price or cost of an episode of treatment, rather than prices of fixed bundles of inputs. We outline features of a proposed new experimental price index -- a medical care expenditure price index -- that is more suitable for evaluation and analyses of medical care cost changes, than are the current MCPIs and MPPIs. We conclude by suggesting future research and measurement issues that are most likely to be fruitful.

Block circulant matrices with circulant blocks, weil sums and mutually unbiased bases, II. The prime power case

In our previous paper \cite{co1} we have shown that the theory of circulant matrices allows to recover the result that there exists $p+1$ Mutually Unbiased Bases in dimension $p$, $p$ being an arbitrary prime number. Two orthonormal bases $\mathcal B, \mathcal B'$ of $\mathbb C^d$ are said mutually unbiased if $\forall b\in \mathcal B, \forall b' \in \mathcal B'$ one has that $$| b\cdot b'| = \frac{1}{\sqrt d}$$ ($b\cdot b'$ hermitian scalar product in $\mathbb C^d$). In this paper we show that the theory of block-circulant matrices with circulant blocks allows to show very simply the known result that if $d=p^n$ ($p$ a prime number, $n$ any integer) there exists $d+1$ mutually Unbiased Bases in $\mathbb C^d$. Our result relies heavily on an idea of Klimov, Munoz, Romero \cite{klimuro}. As a subproduct we recover properties of quadratic Weil sums for $p\ge 3$, which generalizes the fact that in the prime case the quadratic Gauss sums properties follow from our results

Determination and Monitoring of through Hole Diameters in Thin Plates Using Acoustic Diffraction

In this paper, we describe a method to monitor changes in the diameter of through holes in thin plates. The method has the potential for applications in the industry

Weak helix submanifolds of euclidean spaces

It is shown that there exist nonstrong weak 2-helix surfaces of R