Lp-norms of polynomials with positive real part

AbstractWe derive an estimate for Δn, 1 = sup{(2π)−1 ∝02π¦p(eit)¦dt: p(z) = 1 + a1z + · · · + anzn, Re(p(z)) > 0 for ¦z¦ < 1}. In particular it is shown that Δn, 1 ⩽ 1 + log(C1(n + 1) + 1), where C1 = 0.686981293…, It is also shown that 2π ⩽ lim infn → ∞ Δn, 1log n. Finally, upper bounds are found for the Lp-norms of polynomials with positive real part on the unit disk

Additive factors and stages of mental processes in task networks.

To perform a task a subject executes mental processes. An experimental manipulation, such as a change in stimulus intensity, is said to selectively influence a process if it changes the duration of that process leaving other process durations unchanged. For random process durations a definition of a factor selectively influencing a process by increments is given in terms of stochastic dominance (also called “the usual stochastic order”. A technique for analyzing reaction times, Sternberg\u27s Additive Factor Method, assumes all the processes are in series. When all processes are in series, each process is called a stage. With the Additive Factor Method, if two experimental factors selectively influence two different stages by increments, the factors will have additive effects on reaction time. An assumption of the Additive Factor Method is that if two experimental factors interact, then they influence the same stage. We consider sets of processes in which some pairs of processes are sequential and some are concurrent (i. e., the processes are partially ordered). We propose a natural definition of a stage for such sets of processes. For partially ordered processes, with our definition of a stage, if two experimental factors selectively influence two different processes by increments, each within a different stage, then the factors have additive effects. If each process selectively influenced by increments is in the same stage, then an interaction is possible, although not inevitable

A BPS Interpretation of Shape Invariance

We show that shape invariance appears when a quantum mechanical model is invariant under a centrally extended superalgebra endowed with an additional symmetry generator, which we dub the shift operator. The familiar mathematical and physical results of shape invariance then arise from the BPS structure associated with this shift operator. The shift operator also ensures that there is a one-to-one correspondence between the energy levels of such a model and the energies of the BPS-saturating states. These findings thus provide a more comprehensive algebraic setting for understanding shape invariance.Comment: 15 pages, 2 figures, LaTe

Stochastic PERT networks as models of cognition: Derivation of the mean, variance, and distribution of reaction time using Order-of-Processing (OP) diagrams

It is frequently assumed that the mental activity which leads to a given response is made up of separable components or processes. One or more of the processes are assumed to contribute to the time required to respond. Computation of the mean, variance, and distribution of the reaction time is relatively straightforward when all processes are arranged in series or parallel. However, such is not the case when the processes have complex arrangements. A solution to a useful special case of the above problem is proposed. Specifically, it is shown that simple computations yield closed form expressions for the mean, variance, and distribution of reaction time when the processes can be arranged in a stochastic PERT network and when the durations of individual processes are sums of mutually independent, exponentially distributed random variables. The method of solution relies on the construction of an Order-of-Processing (OP) diagram from the original PERT network representation of behavior.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/25195/1/0000634.pd

Tobacco Use Treatment at the U.S. National Cancer Institute's Designated Cancer Centers

Tobacco use is a leading cause of cancer, and continued use after cancer diagnosis puts patients at greater risk for adverse health outcomes, including increased risk for cancer recurrence. This study surveyed National Cancer Institute (NCI)–designated Cancer Centers to assess the availability of tobacco use treatment (TUT) services

Diabetic microcirculatory disturbances and pathologic erythropoiesis are provoked by deposition of amyloid-forming amylin in red blood cells and capillaries.

In the setting of type-2 diabetes, there are declines of structural stability and functionality of blood capillaries and red blood cells (RBCs), increasing the risk for microcirculatory disturbances. Correcting hyperglycemia is not entirely effective at reestablishing normal cellular metabolism and function. Therefore, identification of pathological changes occurring before the development of overt hyperglycemia may lead to novel therapeutic targets for reducing the risk of microvascular dysfunction. Here we determine whether RBC-capillary interactions are altered by prediabetic hypersecretion of amylin, an amyloid forming hormone co-synthesized with insulin, and is reversed by endothelial cell-secreted epoxyeicosatrienoic acids. In patients, we found amylin deposition in RBCs in association with type-2 diabetes, heart failure, cancer and stroke. Amylin-coated RBCs have altered shape and reduced functional (non-glycated) hemoglobin. Amylin-coated RBCs administered intravenously in control rats upregulated erythropoietin and renal arginase expression and activity. We also found that diabetic rats expressing amyloid-forming human amylin in the pancreas (the HIP rat model) have increased tissue levels of hypoxia-inducible transcription factors, compared to diabetic rats that express non-amyloid forming rat amylin (the UCD rat model). Upregulation of erythropoietin correlated with lower hematocrit in the HIP model indicating pathologic erythropoiesis. In the HIP model, pharmacological upregulation of endogenous epoxyeicosatrienoic acids protected the renal microvasculature against amylin deposition and also reduced renal accumulation of HIFs. Thus, prediabetes induces dysregulation of amylin homeostasis and promotes amylin deposition in RBCs and the microvasculature altering RBC-capillary interaction leading to activation of hypoxia signaling pathways and pathologic erythropoiesis. Hence, dysregulation of amylin homeostasis could be a therapeutic target for ameliorating diabetic vascular complications

Managing depression and anxiety in people with epilepsy: A survey of epilepsy health professionals by the ILAE Psychology Task Force

Objectives The Psychology Task Force of the Medical Therapies Commission of the International League Against Epilepsy (ILAE) has been charged with taking steps to improve global mental health care for people with epilepsy. This study aimed to inform the direction and priorities of the Task Force by examining epilepsy healthcare providers’ current practical experiences, barriers, and unmet needs around addressing depression and anxiety in their patients. Methods A voluntary 27‐item online survey was distributed via ILAE chapters and networks. It assessed practices in the areas of screening, referral, management, and psychological care for depression and anxiety. A total of 445 participants, from 67 countries (68% high income), commenced the survey, with 87% completing all components. Most respondents (80%) were either neurologists or epileptologists. Results Less than half of respondents felt adequately resourced to manage depression and anxiety. There was a lack of consensus about which health professionals were responsible for screening and management of these comorbidities. About a third only assessed for depression and anxiety following spontaneous report and lack of time was a common barrier (>50%). Routine referrals to psychiatrists (>55%) and psychologists (>41%) were common, but approximately one third relied on watchful waiting. A lack of both trained mental health specialists (>55%) and standardized procedures (>38%) was common barriers to referral practices. The majority (>75%) of respondents’ patients identified with depression or anxiety had previously accessed psychotropic medications or psychological treatments. However, multiple barriers to psychological treatments were endorsed, including accessibility difficulties (52%). Significance The findings suggest that while the importance of managing depression and anxiety in patients with epilepsy is being recognized, there are ongoing barriers to effective mental health care. Key future directions include the need for updated protocols in this area and the integration of mental health professionals within epilepsy settings

Double-Blind Phase III Trial of Adjuvant Chemotherapy With and Without Bevacizumab in Patients With Lymph Node-Positive and High-Risk Lymph Node-Negative Breast Cancer (E5103)

Purpose Bevacizumab improves progression-free survival but not overall survival in patients with metastatic breast cancer. E5103 tested the effect of bevacizumab in the adjuvant setting in patients with human epidermal growth factor receptor 2-negative disease. Patients and Methods Patients were assigned 1:2:2 to receive placebo with doxorubicin and cyclophosphamide (AC) followed by weekly paclitaxel (arm A), bevacizumab only during AC and paclitaxel (arm B), or bevacizumab during AC and paclitaxel followed by bevacizumab monotherapy for 10 cycles (arm C). Random assignment was stratified and bevacizumab dose adjusted for choice of AC schedule. Radiation and hormonal therapy were administered concurrently with bevacizumab in arm C. The primary end point was invasive disease-free survival (IDFS). Results Four thousand nine hundred ninety-four patients were enrolled. Median age was 52 years; 64% of patients were estrogen receptor positive, 27% were lymph node negative, and 78% received dose-dense AC. Chemotherapy-associated adverse events including myelosuppression and neuropathy were similar across all arms. Grade ≥ 3 hypertension was more common in bevacizumab-treated patients, but thrombosis, proteinuria, and hemorrhage were not. The cumulative incidence of clinical congestive heart failure at 15 months was 1.0%, 1.9%, and 3.0% in arms A, B, and C, respectively. Bevacizumab exposure was less than anticipated, with approximately 24% of patients in arm B and approximately 55% of patients in arm C discontinuing bevacizumab before completing planned therapy. Five-year IDFS was 77% (95% CI, 71% to 81%) in arm A, 76% (95% CI, 72% to 80%) in arm B, and 80% (95% CI, 77% to 83%) in arm C. Conclusion Incorporation of bevacizumab into sequential anthracycline- and taxane-containing adjuvant therapy does not improve IDFS or overall survival in patients with high-risk human epidermal growth factor receptor 2-negative breast cancer. Longer duration bevacizumab therapy is unlikely to be feasible given the high rate of early discontinuation