An Interesting Class of Operators with unusual Schatten-von Neumann behavior

We consider the class of integral operators Q_\f on $L^2(\R_+)$ of the form (Q_\f f)(x)=\int_0^\be\f (\max\{x,y\})f(y)dy. We discuss necessary and sufficient conditions on $\phi$ to insure that $Q_{\phi}$ is bounded, compact, or in the Schatten-von Neumann class \bS_p, $1<p<\infty$. We also give necessary and sufficient conditions for $Q_{\phi}$ to be a finite rank operator. However, there is a kind of cut-off at $p=1$, and for membership in \bS_{p}, $0<p\leq1$, the situation is more complicated. Although we give various necessary conditions and sufficient conditions relating to Q_{\phi}\in\bS_{p} in that range, we do not have necessary and sufficient conditions. In the most important case $p=1$, we have a necessary condition and a sufficient condition, using $L^1$ and $L^2$ modulus of continuity, respectively, with a rather small gap in between. A second cut-off occurs at $p=1/2$: if \f is sufficiently smooth and decays reasonably fast, then \qf belongs to the weak Schatten-von Neumann class \wS{1/2}, but never to \bS_{1/2} unless \f=0. We also obtain results for related families of operators acting on $L^2(\R)$ and $\ell^2(\Z)$. We further study operations acting on bounded linear operators on $L^{2}(\R^{+})$ related to the class of operators Q_\f. In particular we study Schur multipliers given by functions of the form $\phi(\max\{x,y\})$ and we study properties of the averaging projection (Hilbert-Schmidt projection) onto the operators of the form Q_\f.Comment: 87 page

Optimal solutions to matrix-valued Nehari problems and related limit theorems

In a 1990 paper Helton and Young showed that under certain conditions the optimal solution of the Nehari problem corresponding to a finite rank Hankel operator with scalar entries can be efficiently approximated by certain functions defined in terms of finite dimensional restrictions of the Hankel operator. In this paper it is shown that these approximants appear as optimal solutions to restricted Nehari problems. The latter problems can be solved using relaxed commutant lifting theory. This observation is used to extent the Helton and Young approximation result to a matrix-valued setting. As in the Helton and Young paper the rate of convergence depends on the choice of the initial space in the approximation scheme.Comment: 22 page

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

Taylor approximations of operator functions

This survey on approximations of perturbed operator functions addresses recent advances and some of the successful methods.Comment: 12 page

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

Bacillus cereus Biovar Anthracis Causing Anthrax in Sub-Saharan Africa—Chromosomal Monophyly and Broad Geographic Distribution

Through full genome analyses of four atypical Bacillus cereus isolates, designated B. cereus biovar anthracis, we describe a distinct clade within the B. cereus group that presents with anthrax-like disease, carrying virulence plasmids similar to those of classic Bacillus anthracis. We have isolated members of this clade from different mammals (wild chimpanzees, gorillas, an elephant and goats) in West and Central Africa (Côte d’Ivoire, Cameroon, Central African Republic and Democratic Republic of Congo). The isolates shared several phenotypic features of both B. anthracis and B. cereus, but differed amongst each other in motility and their resistance or sensitivity to penicillin. They all possessed the same mutation in the regulator gene plcR, different from the one found in B. anthracis, and in addition, carry genes which enable them to produce a second capsule composed of hyaluronic acid. Our findings show the existence of a discrete clade of the B. cereus group capable of causing anthrax-like disease, found in areas of high biodiversity, which are possibly also the origin of the worldwide distributed B. anthracis. Establishing the impact of these pathogenic bacteria on threatened wildlife species will require systematic investigation. Furthermore, the consumption of wildlife found dead by the local population and presence in a domestic animal reveal potential sources of exposure to humans