Multilevel Monte Carlo for Random Degenerate Scalar Convection Diffusion Equation

We consider the numerical solution of scalar, nonlinear degenerate convection-diffusion problems with random diffusion coefficient and with random flux functions. Building on recent results on the existence, uniqueness and continuous dependence of weak solutions on data in the deterministic case, we develop a definition of random entropy solution. We establish existence, uniqueness, measurability and integrability results for these random entropy solutions, generalizing \cite{Mishr478,MishSch10a} to possibly degenerate hyperbolic-parabolic problems with random data. We next address the numerical approximation of random entropy solutions, specifically the approximation of the deterministic first and second order statistics. To this end, we consider explicit and implicit time discretization and Finite Difference methods in space, and single as well as Multi-Level Monte-Carlo methods to sample the statistics. We establish convergence rate estimates with respect to the discretization parameters, as well as with respect to the overall work, indicating substantial gains in efficiency are afforded under realistic regularity assumptions by the use of the Multi-Level Monte-Carlo method. Numerical experiments are presented which confirm the theoretical convergence estimates.Comment: 24 Page

Measurement of energy eigenstates by a slow detector

We propose a method for a weak continuous measurement of the energy eigenstates of a fast quantum system by means of a "slow" detector. Such a detector is only sensitive to slowly-changing variables, e. g. energy, while its back-action can be limited solely to decoherence of the eigenstate superpositions. We apply this scheme to the problem of detection of quantum jumps between energy eigenstates in a harmonic oscillator.Comment: 4 page

Prolonged alterations of cardiomyocyte gene expression following low dose high charge and energy particle radiation--implications for future deep space travel

INTRODUCTION: Space exploration is ultra-hazardous and unpredictably dangerous. One area of significant concern is the exposure of astronauts to deep space radiation and the development of deleterious health effects. Earth's magnetic field and atmosphere both act to deflect the majority of deep space radiation, protecting humans on the surface of earth as well as astronauts in low Earth orbit missions. Because this type of radiation is not encountered terrestrially, very limited evidence exists in regards to the effects on the well-being. Deep space radiation, which consists of high charge and energy (HZE) particles, may be experimentally reproduced for studies using a particle accelerator. The long-term degenerative effects of cosmic irradiation on the cardiovascular system are vastly unknown. Detailing the molecular response within cardiomyocytes after exposure to HZE irradiation will provide needed knowledge for scientists to accurately assess the cardiovascular risks associated with deep space radiation exposure. OBJECTIVE: The primary objective of this study is to characterize the molecular alterations of gene expression within murine cardiomyocytes following exposure to two different types of HZE. METHODS: Wild type C57B1/6NT (Taconic) mice were exposed to either 90 cGy, 1 GeV proton (1H) or 15 cGy, 1 GeV/nucleon iron (56Fe) HZE particle-radiation. Radiation exposure was performed at the NASA Space Radiation Laboratory located at the Brookhaven National Laboratory (Upton, NY). Biological samples were taken and transcriptome profiling was performed at various time points following irradiation (1, 3, 7, 14, and 28 days). RESULTS: Samples exposed to 56Fe-IR displayed significant levels of gene modulation, while proton-irradiation failed to elicit significant alterations in cardiomyocyte gene transcription compared to sham-irradiated samples. Network pathway analysis of iron-irradiated samples identified multiple biological pathways being significantly modulated. These biological pathways included cell death and survival, free radical scavenging, and inflammatory processes. Multiple points of upstream transcription regulation were identified as key nodes for regulating downstream expression. Validation of the signal transduction network by protein analysis showed that particle-IR clearly regulates a long lived signaling mechanism for p38 MAPK signaling and NFATc4 activation. Electrophoresis mobility shift assays supported the role of transcription factors GATA-4, STAT-3 and NF-B as key regulators. CONCLUSIONS: The molecular response to 56Fe-IR is unique and induces long-term modulations of gene expression in cardiomyocytes that last up to at least 28 days following radiation exposure. However, exposure to 1H-IR failed to elicit significantly robust alterations in gene expression in cardiomyocytes. Additionally, proteins involved in signal transduction and transcriptional activation via DNA binding play a significant role in the molecular response following HZE particle radiation. This study may have multiple implications for NASA's efforts to develop cardio-degenerative risk estimates for astronauts participating in future deep space missions. By identifying molecular mechanisms and potential molecular markers, scientists can begin to assess excess relative risks and develop strategies to mitigate risks of developing physiological changes which may compromise future missions. This study may also have major safety implications for the increasing number of patients receiving conventional and particle radiotherapy

Collaborative Lawyering: A Closer Look at an Emerging Practice

A critical analysis of collaborative law (CL) is only now beginning, and should be based on actual, not hypothetical information about the practice and its impact on clients as courts, the bar, and the public begin to digest the idea of CL. This Article intends to present a more comprehensive picture of collaborative practice than is currently available, to better inform the ongoing conversation about what role CL will play in the legal system. Toward that end, the following sketches some basic questions about CL, and provides some preliminary answers. Part I recounts the origin of CL and introduces the process, including a discussion of how the limitations imposed on both lawyers and clients by the collaborative law agreement are designed to affect the quality of negotiations. Part II considers the ethical concerns raised by CL, particularly by the demands made by the collaborative law agreement. The results of a survey of collaborative lawyers and their clients are discussed in Part III, including findings relevant to the claims of both CL\u27s fans and critics, and additional questions raised with indications for further research. Part IV relates the experience of CL with a real couple and their lawyers in the context of divorce. Part V concludes with the reasons that persist for both lawyers\u27 and clients\u27 resistance to CL

Flavor Changing Neutral Current Effects and CP Violation in the Minimal 3-3-1 Model

We investigate in detail the flavor structure of the minimal 331 model and its implications for several flavor changing neutral current (FCNC) processes. In this model, where the weak SU(2)_L gauge group of the Standard Model is extended to a SU(3)_L, the by far dominant new contributions come from an additional neutral Z' gauge boson, that can transmit FCNCs at tree-level. At the same time, electroweak precision observables receive new contributions only at the loop level and do not constrain the model very strongly. In our analysis, we take into account new CP violating effects that have been neglected in earlier analyses, and account for a general flavor structure without reference to a certain parameterization of the new mixing matrix. We begin by studying the bounds obtained from quantities such as Delta M_K, epsilon_K, Delta M_{d/s} as well as sin 2 beta|_{J/psi K_S}, and go on to explore the implications for several clean rare decay channels, namely the decays K+->pi+ nu nu, K_L -> pi0 nu nu, B_{d/s} -> mu+ mu- and K_L -> pi0 l+l-. We find sizeable effects in all these decays, but the most interesting quantity turns out to be the B_s - bar B_s mixing phase beta_s, as measured in the mixing induced CP asymmetry of B_s -> J/psi phi, which can be large. In general, we find effects in purely hadronic channels to be larger than in (semi-)leptonic ones, due to a suppression of the Z'-lepton couplings.Comment: 29 pages, 11 figures, Some Comments and References added, version to appear in Phys Rev

The Costs of Wrongful-Discharge Laws

We estimate the effects on employment and wages of wrongful-discharge protections in the United States. Over the last three decades, most U.S. state courts have adopted one or more common law wrongful discharge doctrines that limit employers' discretion to terminate workers at-will. Using this cross-state variation with a difference-in-difference framework, we find robust evidence of a modest negative impact ( 0.8 to 1.6 percentage points) of one wrongful-discharge doctrine, the implied-contract exception, on employment to population rates in state labor markets. The short-term impact is most pronounced for female, younger, and less-skilled workers, while the longer term costs appear to be borne by older and more-educated workers those most likely to litigate under this doctrine. We find no robust employment or wage effects of two other widely recognized wrongful-discharge laws: the public -policy and good-faith exceptions. Published findings in the literature range from no effect to very large negative effects. We reanalyze the two leading studies and find the discrepancies can be explained by methodological shortcomings in the one case and limitations in the coding of key court decisions in the other.

Multilevel Quasi-Monte Carlo Methods for Lognormal Diffusion Problems

In this paper we present a rigorous cost and error analysis of a multilevel estimator based on randomly shifted Quasi-Monte Carlo (QMC) lattice rules for lognormal diffusion problems. These problems are motivated by uncertainty quantification problems in subsurface flow. We extend the convergence analysis in [Graham et al., Numer. Math. 2014] to multilevel Quasi-Monte Carlo finite element discretizations and give a constructive proof of the dimension-independent convergence of the QMC rules. More precisely, we provide suitable parameters for the construction of such rules that yield the required variance reduction for the multilevel scheme to achieve an $\varepsilon$-error with a cost of $\mathcal{O}(\varepsilon^{-\theta})$ with $\theta < 2$, and in practice even $\theta \approx 1$, for sufficiently fast decaying covariance kernels of the underlying Gaussian random field inputs. This confirms that the computational gains due to the application of multilevel sampling methods and the gains due to the application of QMC methods, both demonstrated in earlier works for the same model problem, are complementary. A series of numerical experiments confirms these gains. The results show that in practice the multilevel QMC method consistently outperforms both the multilevel MC method and the single-level variants even for non-smooth problems.Comment: 32 page

FDG-PET Lacks Sufficient Sensitivity to Detect Myxoid Liposarcoma Spinal Metastases Detected by MRI

Purpose. To document a case of myxoid liposarcoma in which PET scan was less sensitive than MRI in detecting spinal metastasis. Materials and Methods. The case of a 65-year-old female with a history of myxoid liposarcoma (MLS) of the thigh resected 5 years previously and now presenting with low back pain is presented. Her medical oncologist ordered an FDG-PET scan to evaluate distant recurrence. Subsequently, an MRI of her spine was obtained by her surgeon. Results. The FDG-PET scan was obtained 1 week prior to the MRI, and it did not show increased glucose uptake in the spine. Her MRI did show increased signal intensity in her lumbar spine. CT needle biopsy confirmed the lesion to be metastatic MLS. Conclusion. FDG-PET scans are utilized to detect distant recurrence of cancerous lesions. Myxoid liposarcoma has a unique propensity to metastasize to the spine. Previous reports have documented the unreliability of bone scintigraphy to diagnose these metastases. Our report demonstrates that FDG-PET may also lack the sensitivity needed to detect these lesions. We advocate total spine MRI when screening for metastases in this population when they present with back pain