Analytic approximation of matrix functions in LpL^p

We consider the problem of approximation of matrix functions of class $L^p$ on the unit circle by matrix functions analytic in the unit disk in the norm of $L^p$, 2\le p<\be. For an $m\times n$ matrix function $\Phi$ in $L^p$, we consider the Hankel operator $H_\Phi:H^q(C^n)\to H^2_-(C^m)$, $1/p+1/q=1/2$. It turns out that the space of $m\times n$ matrix functions in $L^p$ splits into two subclasses: the set of respectable matrix functions and the set of weird matrix functions. If $\Phi$ is respectable, then its distance to the set of analytic matrix functions is equal to the norm of $H_\Phi$. For weird matrix functions, to obtain the distance formula, we consider Hankel operators defined on spaces of matrix functions. We also describe the set of $p$-badly approximable matrix functions in terms of special factorizations and give a parametrization formula for all best analytic approximants in the norm of $L^p$. Finally, we introduce the notion of $p$-superoptimal approximation and prove the uniqueness of a $p$-superoptimal approximant for rational matrix functions.Comment: 43 page

Analytic approximation of matrix functions in Lp

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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

Compactness properties of operator multipliers

We continue the study of multidimensional operator multipliers initiated in [arXiv:math/0701645]. We introduce the notion of the symbol of an operator multiplier. We characterise completely compact operator multipliers in terms of their symbol as well as in terms of approximation by finite rank multipliers. We give sufficient conditions for the sets of compact and completely compact multipliers to coincide and characterise the cases where an operator multiplier in the minimal tensor product of two C*-algebras is automatically compact. We give a description of multilinear modular completely compact completely bounded maps defined on the direct product of finitely many copies of the C*-algebra of compact operators in terms of tensor products, generalising results of Saar

The interdependence of behavioral and somatic health: implications for conceptualizing health and measuring treatment outcomes

<b>Purpose:</b> The interdependence of behavioral and somatic aspects of various health conditions warrants greater emphasis on an integrated care approach.<br><br> <b>Theory:</b> We propose that integrated approaches to health and wellness require comprehensive and empirically-valid outcome measures to assess quality of care.<br><br> <b>Method:</b> We discuss the transition from independent to integrated treatment approaches and provide examples of new systems for integrated assessment of treatment outcome.<br><br> <b>Results:</b> Evidence suggests that support for an independent treatment approach is waning and momentum is building towards more integrated care. In addition, research evidence suggests integrated care improves health outcomes, and both physicians and patients have favorable impressions of integrated care.<br><br> <b>Conclusions:</b> As treatment goals in the integrated perspective expand to take into account the intimate relationships among mental illness, overall health, and quality of life, clinicians need to develop outcome measures that are similarly comprehensive. Discussion: Increased recognition, by researchers, providers, and insurers, of the interdependence between behavioral and physical health holds great promise for innovative treatments that could significantly improve patients' lives

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

Hyperthermia and Thermosensitive Liposomes for Improved Delivery of Chemotherapeutic Drugs to Solid Tumors

Lipid-based nanocarriers or liposomes have been proven successful in the delivery of chemotherapeutic agents and are currently applied clinically in the treatment of various types of cancer. Liposomes offer the advantage of a high drug payload, decreased drug toxicity and enhanced drug accumulation at tumor sites. Increased accumulation is due to the relatively leaky tumor vasculature that allows liposome extravasation. Between different types of tumors and even within one tumor, vascular permeability and thus liposome extravasation may differ greatly. Furthermore, upon accumulation of liposomes in the tumor area, drug bioavailability is not guaranteed. At present, these are the major issues for clinically used liposomal drugs

A Heat‐Activated Drug‐Delivery Platform Based on Phosphatidyl‐(oligo)‐glycerol Nanocarrier for Effective Cancer Treatment

The potential of cancer drugs is not fully exploited due to low tumor uptake and occurrence of systemic side effects, limiting maximum tolerated dose. Actively targeted nanocarriers improve efficacy while minimizing off‐target toxicity. Herein, it is the first time a drug‐delivery platform for heat‐triggered intravascular drug release is described, based on synthetic phosphatidyl‐(oligo)‐glycerols from organic synthesis to preclinical investigation in feline patients. For the nanocarrier formulated doxorubicin (DOX), superior tumor drug delivery and antitumor activity compared with free DOX, conventional liposomal DOX (Caelyx), and temperature‐sensitive lysolipid‐containing DOX‐liposomes in rat sarcoma are demonstrated. In a comparative oncological study with neoadjuvant treatment of feline sarcoma, a metabolic response determined with 18 F‐FDG‐positron emission tomography/magnetic resonance imaging (PET/MRI) and histopathological response after tumor resection are significantly better compared with free DOX, potentially by overcoming drug resistance based on improved intratumoral drug distribution. This novel drug‐delivery platform has great potential for the treatment of locally advanced tumors in humans

NOXA as critical mediator for drug combinations in polychemotherapy

During polychemotherapy, cytotoxic drugs are given in combinations to enhance their anti-tumor effectiveness. For most drug combinations, underlying signaling mechanisms responsible for positive drug–drug interactions remain elusive. Here, we prove a decisive role for the Bcl-2 family member NOXA to mediate cell death by certain drug combinations, even if drugs were combined which acted independently from NOXA, when given alone. In proof-of-principle studies, betulinic acid, doxorubicin and vincristine induced cell death in a p53- and NOXA-independent pathway involving mitochondrial pore formation, release of cytochrome c and caspase activation. In contrast, when betulinic acid was combined with either doxorubicine or vincristine, cell death signaling changed considerably; the drug combinations clearly depended on both p53 and NOXA. Similarly and of high clinical relevance, in patient-derived childhood acute leukemia samples the drug combinations, but not the single drugs depended on p53 and NOXA, as shown by RNA interference studies in patient-derived cells. Our data emphasize that NOXA represents an important target molecule for combinations of drugs that alone do not target NOXA. NOXA might have a special role in regulating apoptosis sensitivity in the complex interplay of polychemotherapy. Deciphering the differences in signaling of single drugs and drug combinations might enable designing highly effective novel polychemotherapy regimens