Schatten p-norm inequalities related to a characterization of inner product spaces

Let $A_1, ... A_n$ be operators acting on a separable complex Hilbert space such that $\sum_{i=1}^n A_i=0$. It is shown that if $A_1, ... A_n$ belong to a Schatten $p$-class, for some $p>0$, then 2^{p/2}n^{p-1} \sum_{i=1}^n \|A_i\|^p_p \leq \sum_{i,j=1}^n\|A_i\pm A_j\|^p_p for $0<p\leq 2$, and the reverse inequality holds for $2\leq p<\infty$. Moreover, \sum_{i,j=1}^n\|A_i\pm A_j\|^2_p \leq 2n^{2/p} \sum_{i=1}^n \|A_i\|^2_p for $0<p\leq 2$, and the reverse inequality holds for $2\leq p<\infty$. These inequalities are related to a characterization of inner product spaces due to E.R. Lorch.Comment: Minor revision, to appear in Math. Inequal. Appl. (MIA

Limitations of quantum computing with Gaussian cluster states

We discuss the potential and limitations of Gaussian cluster states for measurement-based quantum computing. Using a framework of Gaussian projected entangled pair states (GPEPS), we show that no matter what Gaussian local measurements are performed on systems distributed on a general graph, transport and processing of quantum information is not possible beyond a certain influence region, except for exponentially suppressed corrections. We also demonstrate that even under arbitrary non-Gaussian local measurements, slabs of Gaussian cluster states of a finite width cannot carry logical quantum information, even if sophisticated encodings of qubits in continuous-variable (CV) systems are allowed for. This is proven by suitably contracting tensor networks representing infinite-dimensional quantum systems. The result can be seen as sharpening the requirements for quantum error correction and fault tolerance for Gaussian cluster states, and points towards the necessity of non-Gaussian resource states for measurement-based quantum computing. The results can equally be viewed as referring to Gaussian quantum repeater networks.Comment: 13 pages, 7 figures, details of main argument extende

Methods of producing new nutrient data for popularly consumed multi ethnic foods in the UK

Minority ethnic groups in UK disproportionately suffer from nutrition related diseases compared to the mainstream population, contributing to widening health inequalities. However, reliable nutrient composition data of the traditional foods of these ethnic groups, which play an important part in their diets, is lacking. This makes it impossible to provide adequate and culturally acceptable nutrition interventions to reduce prevalent metabolic disorders. This study aimed to identify and analyse popularly consumed African and Caribbean foods in the UK for macro and micronutrients. Various approaches including focus group discussions, individual interviews and 24 hr dietary recalls were used to identify traditional foods. Defined criteria were used to prioritise and prepare 33 composite samples (26 dishes, 4 snacks and 3 beverages) for nutrient analyses in a UK accredited laboratory. This study methodology is novel because it uses various approaches to generate new data of commonly consumed ethnic foods and traditional recipes. In addition, the approach used in preparation of the food samples enhanced their authenticity and representativeness compared to previously published work. This paper describes the procedures undertaken and analytical methods used to develop a multi ethnic nutrient data for inclusion in UK food composition tables

Case-based review and olinical guidance on the use of genomic assays for early-stage breast cancer: Breast Cancer Therapy Expert Group (BCTEG)

In addition to classical clinicopathologic factors, such as hormone receptor positivity, human epidermal growth factor receptor 2 (HER2) status, and tumor size, grade, and lymph node status, a number of commercially available genomic tests may be used to help inform treatment decisions for early breast cancer patients. Although these tests improve our understanding of breast cancer and help to individualize treatment decisions, clinicians face challenges when deciding on the most appropriate test to order, and the advantages, if any, of one test over another. The Breast Cancer Therapy Expert Group (BCTEG) recently convened a roundtable meeting to discuss issues surrounding the use of genomic testing in early breast cancer, with the goal of providing practical guidance on the use of these tests by the community oncologist, for whom breast cancer may be only one of many tumor types they treat. The group recognizes that genomic testing can provide important prognostic (eg, risk for recurrence), and in some cases predictive, information (eg, benefit of chemotherapy, or extended adjuvant endocrine therapy), which can be used to help guide treatment decisions in breast cancer. The available tests differ in the types of information they provide, and in the patient populations and clinical trials that were conducted to validate them. We summarize the discussion of the BCTEG on this topic, and we also consider several patient cases and clinical scenarios in which genomic testing may, or may not, be useful to guide treatment decisions for the practicing community oncologist

Nutrient Composition of Popularly Consumed African and Caribbean Foods in The UK.

(1) Background: Traditional foods are important in the diets of Black Africans and Caribbeans and, more widely, influence UK food culture. However, little is known about the nutritional status of these ethnic groups and the nutrient composition of their traditional foods. The aim was to identify and analyse African and Caribbean dishes, snacks and beverages popularly consumed in the UK for energy, macronutrients and micronutrients. (2) Methods: Various approaches including focus group discussions and 24-h dietary recalls were used to identify traditional dishes, snacks, and beverages. Defined criteria were used to prioritise and prepare 33 composite samples for nutrient analysis in a UK accredited laboratory. Quality assurance procedures and data verification were undertaken to ensure inclusion in the UK nutrient database. (3) Results: Energy content ranged from 60 kcal in Malta drink to 619 kcal in the shito sauce. Sucrose levels did not exceed the UK recommendation for adults and children. Most of the dishes contained negligible levels of trans fatty acid. The most abundant minerals were Na, K, Ca, Cu, Mn and Se whereas Mg, P, Fe and Zn were present in small amounts. (4) Conclusion: There was wide variation in the energy, macro- and micronutrients composition of the foods analysed

Some inequalities on generalized entropies

We give several inequalities on generalized entropies involving Tsallis entropies, using some inequalities obtained by improvements of Young's inequality. We also give a generalized Han's inequality.Comment: 15 page

Use of cyclin-dependent kinase (CDK) 4/6 inhibitors for hormone receptor-positive, human epidermal growth factor receptor 2-negative, metastatic breast cancer: a roundtable discussion by The Breast Cancer Therapy Expert Group (BCTEG)

Purpose: To provide an overview of clinical data supporting the use of cyclin-dependent kinases 4 and 6 (CDK 4/6) inhibitors in the treatment of hormone receptor-positive (HR+), human epidermal growth factor receptor 2-negative (HER2−), metastatic breast cancer (mBC), from the perspective of the practicing oncologist community. Methods: A recent roundtable discussion was convened by The Breast Cancer Therapy Expert Group (BCTEG) to review existing data on this topic and its impact on their current practice. Results: Level 1 evidence now supports use of a CDK 4/6 inhibitor in combination with endocrine therapy for patients with HR+, HER2−, mBC. Currently, there are no biomarkers that reliably define patients who will, or will not, benefit from the addition of a CDK 4/6 inhibitor to their endocrine therapy. Additional research is needed to identify the optimal sequencing of CDK 4/6 inhibitors in relation to other therapies as well as the optimal duration of therapy; at present, evidence suggests that use in the upfront setting is better than waiting for a later line of therapy, or adding after endocrine therapy has started. Conclusions: Thus far, three CDK 4/6 inhibitors—palbociclib, ribociclib, and more recently, abemaciclib—have been approved for use in the setting of HR+, HER2−, mBC. The degrees to which these agents differ in terms of CDK4/6 affinity, side-effect profiles, dosing, degree of central nervous system (CNS) penetration, optimal use in combination with antiestrogen therapy, and across other subsets of breast cancer, remain an active area of investigation