The Emerging Role of Group Medicare Private Fee-for-Service Plans

Examines the legislative and regulatory changes contributing to the rapid growth of enrollment in group Medicare Advantage plans in private fee-for-service plans. Considers projected trends and implications for retirees, employers, and policy makers

Estimation under group actions: recovering orbits from invariants

Motivated by geometric problems in signal processing, computer vision, and structural biology, we study a class of orbit recovery problems where we observe very noisy copies of an unknown signal, each acted upon by a random element of some group (such as Z/p or SO(3)). The goal is to recover the orbit of the signal under the group action in the high-noise regime. This generalizes problems of interest such as multi-reference alignment (MRA) and the reconstruction problem in cryo-electron microscopy (cryo-EM). We obtain matching lower and upper bounds on the sample complexity of these problems in high generality, showing that the statistical difficulty is intricately determined by the invariant theory of the underlying symmetry group. In particular, we determine that for cryo-EM with noise variance $\sigma^2$ and uniform viewing directions, the number of samples required scales as $\sigma^6$. We match this bound with a novel algorithm for ab initio reconstruction in cryo-EM, based on invariant features of degree at most 3. We further discuss how to recover multiple molecular structures from heterogeneous cryo-EM samples.Comment: 54 pages. This version contains a number of new result

Security of Quantum Bit-String Generation

We consider the cryptographic task of bit-string generation. This is a generalisation of coin tossing in which two mistrustful parties wish to generate a string of random bits such that an honest party can be sure that the other cannot have biased the string too much. We consider a quantum protocol for this task, originally introduced in Phys. Rev. A {\bf 69}, 022322 (2004), that is feasible with present day technology. We introduce security conditions based on the average bias of the bits and the Shannon entropy of the string. For each, we prove rigorous security bounds for this protocol in both noiseless and noisy conditions under the most general attacks allowed by quantum mechanics. Roughly speaking, in the absence of noise, a cheater can only bias significantly a vanishing fraction of the bits, whereas in the presence of noise, a cheater can bias a constant fraction, with this fraction depending quantitatively on the level of noise. We also discuss classical protocols for the same task, deriving upper bounds on how well a classical protocol can perform. This enables the determination of how much noise the quantum protocol can tolerate while still outperforming classical protocols. We raise several conjectures concerning both quantum and classical possibilities for large n cryptography. An experiment corresponding to the scheme analysed in this paper has been performed and is reported elsewhere.Comment: 16 pages. No figures. Accepted for publication in Phys. Rev. A. A corresponding experiment is reported in quant-ph/040812

Dust Evolution in Protoplanetary Disks

(abridged) In the core accretion scenario for the formation of planetary rocky cores, the first step toward planet formation is the growth of dust grains into larger and larger aggregates and eventually planetesimals. Although dust grains are thought to grow from the submicron sizes typical of interstellar dust to micron size particles in the dense regions of molecular clouds and cores, the growth from micron size particles to pebbles and kilometre size bodies must occur in protoplanetary disks. This step in the formation of planetary systems is the last stage of solids evolution that can be observed directly in young extrasolar systems. In this chapter we review the constraints on the physics of grain-grain collisions as they have emerged from laboratory experiments and numerical computations. We then review the current theoretical understanding of the global processes governing the evolution of solids in protoplanetary disks, including dust settling, growth, and radial transport. The predicted observational signatures are summarized. We discuss recent developments in the study of grain growth in molecular cloud cores and in collapsing envelopes of protostars as these provide the initial conditions for the dust in disks. We discuss the observational evidence for the growth of grains in young disks from mm surveys, as well as the recent evidence of radial variations of the dust properties in disks. We include a brief discussion of the constraints on the small end of the grain size distribution and on dust settling as derived from optical and IR observations. The observations are discussed in the context of global dust evolution models, in particular we focus on the emerging evidence for a very efficient early growth of grains and the radial distribution of grain sizes in disks. We also highlight the limits of current models, including the need to slow the radial drift of grains.Comment: Accepted for publication as a chapter in Protostars and Planets VI, University of Arizona Press (2014), eds. H. Beuther, R. Klessen, C. Dullemond, Th. Hennin

Renal Epithelioid Angiomyolipoma: Genomic Characterization and Malignant Potential

Introduction: Renal angiomyolipoma (AML) is one of the most common benign kidney tumors diagnosed. Epithelioid angiomyolipoma (eAML) is a rare variant of these kind of masses that have been classified by the World Health Organization as a potentially malignant mesenchymal neoplasm that metastasizes in one-third of cases. However, conflicting reports have brought in to question the true malignant potential of eAML. Due to eAMLs overall rarity, few studies have characterized this entity. In this study, we further define eAML by describing its genomic alterations and malignant potential by comparing it to a cohort of AML patients at a large-volume cancer center. Methods: After IRB approval, a prospectively maintained kidney cancer database was queried for all patients with eAML and AML who underwent nephrectomy between 1994 and 2008 at the Memorial Sloan Kettering Cancer Center. Patients were separated into two histologic groups, those with eAML and those with AML. Clinicopathologic features and genomic alterations were analyzed and then compared between the two cohorts. Descriptive statistics were performed using Mann-Whitney U test, and Chi-squared test, where appropriate, and reported as either median with interquartile range (IQR) or number with percentage. Genomic data was available in 6 eAML and 10 AML patients with mutational burden described as a proportion. Overall survival (OS) and recurrence-free survival (RFS) data were analyzed using Kaplan-Meier method with significance determined by log-rank tests. All statistical analyses were performed using R 3.5.2 with significance set at \u3c0.05. Results: Out of 103 patients, 44 had eAML and 59 had AML. Females in their fifth and sixth decade were more commonly diagnosed than males, Table 1. Patients with eAML had larger tumors (p\u3c0.001) and underwent radical nephrectomy more often (p=0.014). Twelve (27.3%) eAML patients metastasized, while no metastases were observed in AML patients. Median RFS for eAML patients was 131 months, and median RFS was not reached in AML patients (p\u3c0.0001), Figure 1. The most frequently mutated gene across both groups expectedly was TSC2, a mutation commonly found in AMLs. The mutational burden in eAMLs was heterogeneous compared to AMLs, with more mutations observed within TP53(43%), RB1 (14%), APC (14%), TERT (14%), ATRX (14%), TSC1 (14%), PIK3CA (14%), GNA11 (14%), and FGFR3 (14%), Figure 2. Conclusion: Patients with eAML were observed to have larger tumors and metastasized at a higher rate than patients with AML. A greater frequency of eAML patients underwent radical nephrectomy. The mutational burden across eAML was notable for a more heterogeneity, with largest mutations in TSC2 and TP53 genes. Further investigation into the impact of mutational burden on metastatic potential is warranted

The War on Terror

Presents comments (from the EPIIC Symposium at Tufts University, February 2004) concerning the war on terror; concern on the problem about terrorism; elaboration on the claim that the world is not in a global war on terror; and problems of the use and abuse of the word terrorism