Super-optimal approximation by meromorphic functions.

Let G be a matrix function of type m × n and suppose that G is expressible as the sum of an H∞ function and a continuous function on the unit circle. Suppose also that the (k – 1)th singular value of the Hankel operator with symbol G is greater than the kth singular value. Then there is a unique superoptimal approximant to G in : that is, there is a unique matrix function Q having at most k poles in the open unit disc which minimizes s∞(G – Q) or, in other words, which minimizes the sequence with respect to the lexicographic ordering, where and Sj(·) denotes the jth singular value of a matrix. This result is due to the present authors [PY1] in the case k = 0 (when the hypothesis on the Hankel singular values is vacuous) and to S. Treil[T2] in general. In this paper we give a proof of uniqueness by a diagonalization argument, a high level algorithm for the computation of the superoptimal approximant and a recursive parametrization of the set of all optimal solutions of a matrix Nehari—Takagi problem

The New Public Law Movement: Moderation as a Postmodern Cultural Form

The past twenty years have witnessed an explosion of public law scholarship, as legal scholars reconceptualized themes of administrative law, legislation, and constitutional law; created almost from scratch whole new areas of public law scholarship, including discrimination, environmental, and consumer protection theory; and enlivened discourse with concepts drawn from microeconomics, public choice theory, civic republicanism, practical philosophy, and hermeneutics. This intellectually intense activity has suggested the possibility that public law discourse has entered a critical stage and stimulated the Michigan Law Review to hold a conference in October 1990 on whether there is something that might be called New Public Law. At first we thought there certainly was. We still do, but on further reflection we think that the more interesting inquiry is how these new developments in public law relate to the recent politicization of jurisprudence. This inquiry was a daunting project for us, in part· because the complexity of the historical analysis and our tendency toward abstraction continually threatened to blur the focus of the inquiry, namely, to identify and analyze a movement within legal scholarship. Also~ we approached the topic from very different perspectives. One of us viewed the New Public Law as an exciting positive development, the other viewed it with skepticism. What we needed was a method for concretizing the discussion and for presenting its historical complexity and for allowing us to explore our own differences of perspective. Based upon these concerns, we have chosen to focus on two state court cases, one involving nuclear protesters and the other involving a Catholic university\u27s refusal to recognize a gay and lesbian student group. We use these cases as a grounding to present three accounts of twentieth-century American legal thought, each of which illuminates new developments in public law in a different but perhaps complementary way

The New Public Law Movement: Moderation as a Postmodern Cultural Form

The past twenty years have witnessed an explosion of public law scholarship, as legal scholars reconceptualized themes of administrative law, legislation, and constitutional law; created almost from scratch whole new areas of public law scholarship, including discrimination, environmental, and consumer protection theory; and enlivened discourse with concepts drawn from microeconomics, public choice theory, civic republicanism, practical philosophy, and hermeneutics. This intellectually intense activity has suggested the possibility that public law discourse has entered a critical stage and stimulated the Michigan Law Review to hold a conference in October 1990 on whether there is something that might be called New Public Law. At first we thought there certainly was. We still do, but on further reflection we think that the more interesting inquiry is how these new developments in public law relate to the recent politicization of jurisprudence. This inquiry was a daunting project for us, in part· because the complexity of the historical analysis and our tendency toward abstraction continually threatened to blur the focus of the inquiry, namely, to identify and analyze a movement within legal scholarship. Also~ we approached the topic from very different perspectives. One of us viewed the New Public Law as an exciting positive development, the other viewed it with skepticism. What we needed was a method for concretizing the discussion and for presenting its historical complexity and for allowing us to explore our own differences of perspective. Based upon these concerns, we have chosen to focus on two state court cases, one involving nuclear protesters and the other involving a Catholic university\u27s refusal to recognize a gay and lesbian student group. We use these cases as a grounding to present three accounts of twentieth-century American legal thought, each of which illuminates new developments in public law in a different but perhaps complementary way

Quantifying and Analyzing Synthetic Microfiber Pollution in Great Lakes Sediment near Cladophora Mats

Microfiber pollution is ubiquitous in aquatic environments. Synthetic microfibers, a major class of microplastics, such as polyester, rayon, acrylic, and nylon, are present in clothing and other textile items, and are now viewed as contaminants of emerging concern. Routine laundering of synthetic fabrics has contributed to massive microfiber contamination in surface waters. In addition to its presence in water and sediment, previous microfiber research by our group showed that Great Lakes Cladophora, a common macroalgae, entangles and adsorbs microfibers in much greater amounts. This research aims to assess the role of the lake sediment below and near Cladophora mats in the fate of these microplastics. To determine if this sediment traps synthetic microfibers, research was conducted with sediment samples collected by the United States Geological Survey (USGS). Samples were cleaned using a ZnCl2 solution for density separation, which suspends most microfibers from the heavier sediment. All samples were then subjected to an advanced oxidation technique, which generates hydroxyl radicals that decompose most natural organic materials, including natural fibers. Microscopic analysis was implemented to quantify synthetic microfibers. The early analyses indicate that the lake sediment does not have entanglement or adsorbent properties. Due to the ubiquitousness of microfibers, method blanks were implemented to determine the amount of microfiber contamination introduced in the lab and suggest some work is still needed to reduce external contamination. A range of 0 to 12 microfibers (Av = 7) have been found in the samples per average dry weight of 32.152 g

Construction of coarse-grained order-parameters in non-equilibrium systems

We develop a renormalization group (RG) procedure that includes important system-specific features. The key ingredient is to systematize the coarse graining procedure that generates the RG flow. The coarse graining technology comes from control and operator theoretic model reduction. The resulting "generalized" RG is a consistent generalization of the Wilsonian RG. We derive the form of the projection operator from the dynamics of a nonlinear wave equation and renormalize the distribution of initial conditions. The probability density of the initial conditions is chosen to be the Boltzmann weight for a standard $\phi^4$-theory. In our calculation, we find that in contrast to conventional implementations of the RG, na\"ive power counting breaks down. The RG-equations that we derive are different from those derived from the conventional RG.Comment: 13 pages, 0 figure

Meromorphic Approximants to Complex Cauchy Transforms with Polar Singularities

We study AAK-type meromorphic approximants to functions $F$, where $F$ is a sum of a rational function $R$ and a Cauchy transform of a complex measure $\lambda$ with compact regular support included in $(-1,1)$, whose argument has bounded variation on the support. The approximation is understood in $L^p$-norm of the unit circle, $p\geq2$. We obtain that the counting measures of poles of the approximants converge to the Green equilibrium distribution on the support of $\lambda$ relative to the unit disk, that the approximants themselves converge in capacity to $F$, and that the poles of $R$ attract at least as many poles of the approximants as their multiplicity and not much more.Comment: 39 pages, 4 figure

The relationship between structural game characteristics and gambling behavior: a population-level study

The aim of this study was to examine the relationship between the structural characteristics and gambling behavior among video lottery terminal (VLT) gamblers. The study was ecological valid, because the data consisted of actual gambling behavior registered in the participants natural gambling environment without intrusion by researchers. Online behavioral tracking data from Multix, an eight game video lottery terminal, were supplied by Norsk-Tipping (the state owned gambling company in Norway). The sample comprised the entire population of Multix gamblers (N = 31,109) who had gambled in January 2010. The individual number of bets made across games was defined as the dependent variable, reward characteristics of a game (i.e., payback percentage, hit frequency, size of winnings and size of jackpot) and bet characteristics of a game (i.e., range of betting options and availability of advanced betting options) served as the independent variables. Control variables were age and gender. Two separate cross-classified multilevel random intercepts models were used to analyze the relationship between bets made, reward characteristics and bet characteristics, where the number of bets was nested within both individuals and within games. The results show that the number of bets is positively associated with payback percentage, hit frequency, being female and age, and negatively associated with size of wins and range of available betting options. In summary, the results show that the reward characteristics and betting options explained 27 % and 15 % of the variance in the number of bets made, respectively. It is concluded that structural game characteristics affect gambling behavior. Implications of responsible gambling are discussed

Chronic lymphocytic leukaemia: the role of T cells in a B cell disease

Chronic lymphocytic leukaemia (CLL) has long been thought to be an immunosuppressive disease and abnormalities in T‐cell subset distribution and function have been observed in many studies. However, the role of T cells (if any) in disease progression remains unclear and has not been directly studied. This has changed with the advent of new therapies, such as chimeric antigen receptor‐T cells, which actively use retargeted patient‐derived T cells as “living drugs” for CLL. However complete responses are relatively low (~26%) and recent studies have suggested the differentiation status of patient T cells before therapy may influence efficacy. Non‐chemotherapeutic drugs, such as idelalisib and ibrutinib, also have an impact on T cell populations in CLL patients. This review will highlight what is known about T cells in CLL during disease progression and after treatment, and discuss the prospects of using T cells as predictive biomarkers for immune status and response to therapy

Quantitative, Multi-institutional Evaluation of MR Thermometry Accuracy for Deep-Pelvic MR-Hyperthermia Systems Operating in Multi-vendor MR-systems Using a New Anthropomorphic Phantom

Clinical outcome of hyperthermia depends on the achieved target temperature, therefore target conformal heating is essential. Currently, invasive temperature probe measurements are the gold standard for temperature monitoring, however, they only provide limited sparse data. In contrast, magnetic resonance thermometry (MRT) provides unique capabilities to non-invasively measure the 3D-temperature. This study investigates MRT accuracy for MR-hyperthermia hybrid systems located at five European institutions while heating a centric or eccentric target in anthropomorphic phantoms with pelvic and spine structures. Scatter plots, root mean square error (RMSE) and Bland–Altman analysis were used to quantify accuracy of MRT compared to high resistance thermistor probe measurements. For all institutions, a linear relation between MRT and thermistor probes measurements was found with R 2 (mean ± standard deviation) of 0.97 ± 0.03 and 0.97 ± 0.02, respectively for centric and eccentric heating targets. The RMSE was found to be 0.52 ± 0.31 ◦C and 0.30 ± 0.20 ◦C, respectively. The Bland-Altman evaluation showed a mean difference of 0.46 ± 0.20 ◦C and 0.13 ± 0.08 ◦C, respectively. This first multi-institutional evaluation of MR-hyperthermia hybrid systems indicates comparable device performance and good agreement between MRT and thermistor probes measurements. This forms the basis to standardize treatments in multi-institution studies of MR-guided hyperthermia and to elucidate thermal dose-effect relations