Testing the distance duality relation with present and future data

The assumptions that "light propagates along null geodesics of the spacetime metric" and "the number of photons is conserved along the light path" lead to the distance duality relation (DDR), $\eta = D_L(z) (1 + z)^{-2}/D_A(z) = 1$, with $D_L(z)$ and $D_A(z)$ the luminosity and angular diameter distances to a source at redshift $z$. In order to test the DDR, we follow the usual strategy comparing the angular diameter distances of a set of clusters, inferred from X - ray and radio data, with the luminosity distance at the same cluster redshift using the local regression technique to estimate $D_L(z)$ from Type Ia Supernovae (SNeIa) Hubble diagram. In order to both strengthen the constraints on the DDR and get rid of the systematics related to the unknown cluster geometry, we also investigate the possibility to use Baryon Acoustic Oscillations (BAO) to infer $D_A(z)$ from future BAO surveys. As a test case, we consider the proposed Euclid mission investigating the precision can be afforded on $\eta(z)$ from the expected SNeIa and BAO data. We find that the combination of BAO and the local regression coupled allows to reduce the errors on $\eta_a = d\eta/dz|_{z = 0}$ by a factor two if one $\eta_0 = \eta(z = 0) = 1$ is forced and future data are used. On the other hand, although the statistical error on $\eta_0$ is not significantly reduced, the constraints on this quantity will be nevertheless ameliorated thanks to the reduce impact of systematics.Comment: 10 pages, 1 figure, 1 table, accepted for publication on Physical Review

Validation and determination of a reference interval for Canine HbA1c using an immunoturbidimetric assay

Background: Hemoglobin A1c (HbA1c) provides a reliable measure of glycemic control over 2–3 months in human diabetes mellitus. In dogs, presence of HbA1c has been demonstrated, but there are no validated commercial assays. Objective: The purpose of the study was to validate a commercially available automated immunoturbidimetric assay for canine HbA1c and determine an RI in a hospital population. Methods: The specificity of the assay was assessed by inducing glycosylation in vitro using isolated canine hemoglobin, repeatability by measuring canine samples 5 times in succession, long term inter-assay imprecision by measuring supplied control materials, stability using samples stored at 4°C over 5 days and −20°C over 8 weeks, linearity by mixing samples of known HbA1c in differing proportions, and the effect of anticoagulants with paired samples. An RI was determined using EDTA-anticoagulated blood samples from 60 nondiabetic hospitalized animals of various ages and breeds. Hemoglobin A1c was also measured in 10 diabetic dogs. Results: The concentration of HbA1c increased proportionally with glucose concentration in vitro. For repeat measurements, the CV was 4.08% (range 1.16–6.10%). Samples were stable for 5 days at 4°C. The assay was linear within the assessed range. Heparin- and EDTA-anticoagulated blood provided comparable results. The RI for HbA1c was 9–18.5 mmol/mol. There was no apparent effect of age or breed on HbA1c. In diabetic dogs, HbA1c ranged from 14 to 48 mmol/mol. Conclusions: The assay provides a reliable method for canine HbA1c measurement with good analytic performance

On the structure of framed vertex operator algebras and their pointwise frame stabilizers

In this paper, we study the structure of a general framed vertex operator algebra. We show that the structure codes (C,D) of a framed VOA V satisfy certain duality conditions. As a consequence, we prove that every framed VOA is a simple current extension of the associated binary code VOA V_C. This result would give a prospect on the classification of framed vertex operator algebras. In addition, the pointwise frame stabilizer of V is studied. We completely determine all automorphisms in this pointwise stabilizer, which are of order 1, 2 or 4. The 4A-twisted sector and the 4A-twisted orbifold theory of the famous Moonshine VOA are also constructed explicitly. We verify that the top module of this twisted sector is of dimension 1 and of weight 3/4 and the VOA obtained by 4A-twisted orbifold construction of the moonshine VOA is isomorphic to the moonshine VOA itself.Comment: Version 3: 59 pages. Corrected version. 54 pages on my LaTeX system version 2: We add Theorem 5.16 in which we give a necessary and sufficient condtion for a code to be a structure code of a holomorphic framed VOA. "hyperref" style is also introduce

Novel schedule for treatment of inflammatory breast cancer

Inflammatory breast cancer (IBC) is the most aggressive form of this tumor, with the clinical and biological characteristics of a rapidly proliferating disease. This tumor is always diagnosed at advanced stages, atleast stage IIIB (locally advanced), so its management requires an integrated multidisciplinary approach with a systemic therapy followed by surgery and radiation therapy. Patients with IBC usually have a worse prognosis but the achievement of a pathologic complete response after neoadjuvant chemotherapy may have good rates of overall survival. We present the case of a 47 year old women with IBC, luminal B and with high proliferative index; she was successfully treated with a sequential schedule of chemotherapy (anthracyclines dose-dense/carboplatin+ taxane/Cyclophosphamide Methotrexate Fluorouracil), hormone-therapy, complementary radiotherapy and finally surgery until the achievement of a complete clinical and pathological response. Luminal B inflammatory breast cancer with high proliferation index can benefit from sequential schedules of neoadjuvant chemotherapy and hormonal treatment and this can result in pathological complete response

The Power of Negative Reasoning

Semialgebraic proof systems have been studied extensively in proof complexity since the late 1990s to understand the power of Gröbner basis computations, linear and semidefinite programming hierarchies, and other methods. Such proof systems are defined alternately with only the original variables of the problem and with special formal variables for positive and negative literals, but there seems to have been no study how these different definitions affect the power of the proof systems. We show for Nullstellensatz, polynomial calculus, Sherali-Adams, and sums-of-squares that adding formal variables for negative literals makes the proof systems exponentially stronger, with respect to the number of terms in the proofs. These separations are witnessed by CNF formulas that are easy for resolution, which establishes that polynomial calculus, Sherali-Adams, and sums-of-squares cannot efficiently simulate resolution without having access to variables for negative literals