QUANTIZATION OF A CLASS OF PIECEWISE AFFINE TRANSFORMATIONS ON THE TORUS

We present a unified framework for the quantization of a family of discrete dynamical systems of varying degrees of "chaoticity". The systems to be quantized are piecewise affine maps on the two-torus, viewed as phase space, and include the automorphisms, translations and skew translations. We then treat some discontinuous transformations such as the Baker map and the sawtooth-like maps. Our approach extends some ideas from geometric quantization and it is both conceptually and calculationally simple.Comment: no. 28 pages in AMSTE

Spending by commercial insurers on chemotherapy based on site of care, 2004-2014

The impact of price variation because of the site of care—receiving treatment in a physician office vs a hospital outpatient department (HOPD)—is an important driver of health care spending. While patients may receive the same treatment in either setting, insurers typically reimburse payments to HOPDs at a higher rate than to physician offices.Hospitals justify this payment difference because they incur higher overhead costs and treat more medically complex patient populations

Out-of-pocket and health care spending changes for patients using orally administered anticancer therapy after adoption of state parity laws

IMPORTANCE Oral anticancer medications are increasingly important but costly treatment options for patients with cancer. By early 2017, 43 states andWashington, DC, had passed laws to ensure patients with private insurance enrolled in fully insured health plans pay no more for anticancer medications administered by mouth than anticancer medications administered by infusion. Federal legislation regarding this issue is currently pending. Despite their rapid acceptance, the changes associated with state adoption of oral chemotherapy parity laws have not been described. OBJECTIVE To estimate changes in oral anticancer medication use, out-of-pocket spending, and health plan spending associated with oral chemotherapy parity law adoption. DESIGN, SETTING, AND PARTICIPANTS Analysis of administrative health plan claims data from 2008-2012 for 3 large nationwide insurers aggregated by the Health Care Cost Institute. Data analysis was first completed in 2015 and updated in 2017. The study population included 63 780 adults living in 1 of 16 states that passed parity laws during the study period and who received anticancer drug treatment for which orally administered treatment options were available. Study analysis used a difference-in-differences approach. EXPOSURES Time period before and after adoption of state parity laws, controlling for whether the patient was enrolled in a plan subject to parity (fully insured) or not (self-funded, exempt via the Employee Retirement Income Security Act). MAIN OUTCOMES AND MEASURES Oral anticancer medication use, out-of-pocket spending, and total health care spending. RESULTS Of the 63 780 adults aged 18 through 64 years, 51.4%participated in fully insured plans and 48.6%in self-funded plans (57.2%were women; 76.8%were aged 45 to 64 years). The use of oral anticancer medication treatment as a proportion of all anticancer treatment increased from 18%to 22%(adjusted difference-in-differences risk ratio [aDDRR], 1.04; 95%CI, 0.96-1.13; P = .34) comparing months before vs after parity. In plans subject to parity laws, the proportion of prescription fills for orally administered therapy without copayment increased from 15.0%to 53.0%, more than double the increase (12.3%-18.0%) in plans not subject to parity (P < .001). The proportion of patients with out-of-pocket spending of more than $100 per month increased from 8.4$19.44 at the 25th percentile, by $32.13 at the 50th percentile, and by$10.83 at the 75th percentile but increased at the 90th ($37.19) and 95th ($143.25) percentiles after parity (all P < .001, controlling for changes in plans not subject to parity). Parity laws did not increase 6-month total spending for users of any anticancer therapy or for users of oral anticancer therapy alone. CONCLUSIONS AND RELEVANCE While oral chemotherapy parity laws modestly improved financial protection for many patients without increasing total health care spending, these laws alone may be insufficient to ensure that patients are protected from high out-of-pocket medication costs

Oral oncology parity laws, medication use, and out-of-pocket spending for patients with blood cancers

Background: In this study, we sought to estimate the association between oral oncology parity law adoption and anticancer medication use for patients with chronic myeloid leukemia or multiple myeloma. Methods: This was an observational study of administrative claims from 2008 to 2017. Among individuals initiating tyrosine kinase inhibitors (TKIs) for chronic myeloid leukemia or immunomodulatory drugs for multiple myeloma, we compared out-of-pocket spending, adherence, and discontinuation before and after parity among individuals in fully insured plans (subject to parity) vs self-funded plans (exempt from parity) using propensity-score weighted difference-in-differences regression models. Results: Among patients initiating TKIs (N = 2082) or immunomodulatory drugs (N = 3326) there were no statistically significant differences in adherence or discontinuation associated with parity. The proportion of patients with initial out-of-pocket payments of $0 increased in fully insured plans after parity from 5.7$100 decreased from 30.3% to 24.7% for TKIs and 30.6% to 27.5% for immunomodulatory drugs in fully insured plans after parity. Relative to changes in self-funded plans, those in fully insured plans were 0.74 (95% CI = 0.54 to 1.01) times as likely to pay more than $100 for TKIs and 0.85 (95$100 for immunomodulatory drugs after parity. Conclusions: Among patients initiating TKIs or immunomodulatory drugs, parity was not associated with better adherence or less discontinuation of therapy but yielded decreased patient out-of-pocket payments for some patients

Quantum Iterated Function Systems

Iterated functions system (IFS) is defined by specifying a set of functions in a classical phase space, which act randomly on an initial point. In an analogous way, we define a quantum iterated functions system (QIFS), where functions act randomly with prescribed probabilities in the Hilbert space. In a more general setting a QIFS consists of completely positive maps acting in the space of density operators. We present exemplary classical IFSs, the invariant measure of which exhibits fractal structure, and study properties of the corresponding QIFSs and their invariant states.Comment: 12 pages, 1 figure include

First sagittarius A* Event Horizon Telescope results. VI. Testing the black hole metric

Galaxie

Resolving the inner parsec of the blazar J1924-2914 with the event horizon telescope

Galaxie

First sagittarius A* Event Horizon Telescope results. IV. Variability, morphology, and black hole mass

Galaxie

First Sagittarius A* Event Horizon Telescope results. I. The shadow of the supermassive black hole in the center of the Milky Way

Galaxie

First Sagittarius A* event horizon telescope results. II. EHT and multiwavelength observations, data processing, and calibration

Instrumentatio