An octonion algebra originating in combinatorics

C.H. Yang discovered a polynomial version of the classical Lagrange identity expressing the product of two sums of four squares as another sum of four squares. He used it to give short proofs of some important theorems on composition of delta-codes (now known as T-sequences). We investigate the possible new versions of his polynomial Lagrange identity. Our main result shows that all such identities are equivalent to each other.Comment: 11 pages, A simpler proof of the main theorem, due to Alberto Elduque, is inserted. The paper will appear in the Proc. Amer. Math. So

Symmetric Hadamard matrices of orders 268, 412, 436 and 604

We construct many symmetric Hadamard matrices of small order by using the so called propus construction. The necessary difference families are constructed by restricting the search to the families which admit a nontrivial multiplier. Our main result is that we have constructed, for the first time, symmetric Hadamard matrices of order 268, 412, 436 and 604.Comment: 12 page

Ralstonia pickettii bacteremia in a cardiac surgery patient in Belgrade, Serbia

Ralstonia pickettii is an opportunistic bacterium found in the water environment with an increasing incidence as a nosocomial pathogen. The objectives of this study were to describe R. pickettii bacteremia in a cardiac surgery patient and to evaluate its ability to grow in a saline solution and to form biofilm. The patient in this study underwent mitral and aortic valve replacement surgery with two aortocoronary bypasses. She developed signs of respiratory and renal failure, therefore hemodialysis was started. After 25 days in an intensive care unit, the patient had recurrent episodes of fever with signs of bacteremia. R. pickettii was identified from blood cultures by MALDI-TOF MS. Antimicrobial susceptibility testing was performed using disc diffusion and broth microdilution methods in accordance with EUCAST methodology and results were interpreted following clinical breakpoints for Pseudomonas spp. The isolate was susceptible to all tested antimicrobial agents except aminoglycosides and colistin. Survival of R. pickettii was analyzed in saline solution with four different starting concentrations at 25 degrees C and 37 degrees C for six days. Biofilm capacity was tested using the microtiter plate method. R. pickettii showed substantial growth in saline solution, with starting concentration of 2 CFU ml(-1) reaching 107 CFU ml(-1) after six days. There was no significant difference between growth at 25 degrees C and 37 degrees C. This indicates that storage of contaminated solutions at room temperature can enhance the count of R. pickettii. Our strain did not show the capacity to form biofilm. The patient responded well to adequate treatment with ceftazidime, and after 48 days in ICU she was discharged to convalesce

Geometric approach to entanglement quantification with polynomial measures

We show that the quantification of entanglement of any rank-2 state with any polynomial entanglement measure can be recast as a geometric problem on the corresponding Bloch sphere. This approach provides insight into the properties of entanglement and allows us to relate different polynomial measures to each other, simplifying their quantification. In particular, unveiling and exploiting the geometric structure of the concurrence for two qubits, we show that the convex roof of any polynomial measure of entanglement can be quantified exactly for all rank-2 states of an arbitrary number of qubits which have only one or two unentangled states in their range. We give explicit examples by quantifying the three-tangle exactly for several representative classes of three-qubit states. We further show how our methods can be used to obtain analytical results for entanglement of more complex states if one can exploit symmetries in their geometric representation

PEGylation Potentiates the Effectiveness of an Antagonistic Peptide That Targets the EphB4 Receptor with Nanomolar Affinity

The EphB4 receptor tyrosine kinase together with its preferred ligand, ephrin-B2, regulates a variety of physiological and pathological processes, including tumor progression, pathological forms of angiogenesis, cardiomyocyte differentiation and bone remodeling. We previously reported the identification of TNYL-RAW, a 15 amino acid-long peptide that binds to the ephrin-binding pocked of EphB4 with low nanomolar affinity and inhibits ephrin-B2 binding. Although ephrin-B2 interacts promiscuously with all the EphB receptors, the TNYL-RAW peptide is remarkably selective and only binds to EphB4. Therefore, this peptide is a useful tool for studying the biological functions of EphB4 and for imaging EphB4-expressing tumors. Furthermore, TNYL-RAW could be useful for treating pathologies involving EphB4-ephrin-B2 interaction. However, the peptide has a very short half-life in cell culture and in the mouse blood circulation due to proteolytic degradation and clearance by the kidneys and reticuloendothelial system. To overcome these limitations, we have modified TNYL-RAW by fusion with the Fc portion of human IgG1, complexation with streptavidin or covalent coupling to a 40 KDa branched polyethylene glycol (PEG) polymer. These modified forms of TNYL-RAW all have greatly increased stability in cell culture, while retaining high binding affinity for EphB4. Furthermore, PEGylation most effectively increases peptide half-life in vivo. Consistent with increased stability, submicromolar concentrations of PEGylated TNYL-RAW effectively impair EphB4 activation by ephrin-B2 in cultured B16 melanoma cells as well as capillary-like tube formation and capillary sprouting in co-cultures of endothelial and epicardial mesothelial cells. Therefore, PEGylated TNYL-RAW may be useful for inhibiting pathological forms of angiogenesis through a novel mechanism involving disruption of EphB4-ephrin-B2 interactions between endothelial cells and supporting perivascular mesenchymal cells. Furthermore, the PEGylated peptide is suitable for other cell culture and in vivo applications requiring prolonged EphB4 receptor targeting

HIBISCUS: Hydroxychloroquine for the secondary prevention of thrombotic and obstetrical events in primary antiphospholipid syndrome

The relapse rate in antiphospholipid syndrome (APS) remains high, i.e. around 20%-21% at 5 years in thrombotic APS and 20-28% in obstetrical APS [2, 3]. Hydroxychloroquine (HCQ) appears as an additional therapy, as it possesses immunomodulatory and anti-thrombotic various effects [4-16]. Our group recently obtained the orphan designation of HCQ in antiphospholipid syndrome by the European Medicine Agency. Furthermore, the leaders of the project made the proposal of an international project, HIBISCUS, about the use of Hydroxychloroquine in secondary prevention of obstetrical and thrombotic events in primary APS. This study has been launched in several countries and at now, 53 centers from 16 countries participate to this international trial. This trial consists in two parts: a retrospective and a prospective study. The French part of the trial in thrombosis has been granted by the French Minister of Health in December 2015 (the academic trial independent of the pharmaceutical industry PHRC N PAPIRUS) and is coordinated by one of the members of the leading consortium of HIBISCUS