Discrete concavity and the half-plane property

Murota et al. have recently developed a theory of discrete convex analysis which concerns M-convex functions on jump systems. We introduce here a family of M-concave functions arising naturally from polynomials (over a field of generalized Puiseux series) with prescribed non-vanishing properties. This family contains several of the most studied M-concave functions in the literature. In the language of tropical geometry we study the tropicalization of the space of polynomials with the half-plane property, and show that it is strictly contained in the space of M-concave functions. We also provide a short proof of Speyer's hive theorem which he used to give a new proof of Horn's conjecture on eigenvalues of sums of Hermitian matrices.Comment: 14 pages. The proof of Theorem 4 is corrected

Quantum Pieri rules for isotropic Grassmannians

We study the three point genus zero Gromov-Witten invariants on the Grassmannians which parametrize non-maximal isotropic subspaces in a vector space equipped with a nondegenerate symmetric or skew-symmetric form. We establish Pieri rules for the classical cohomology and the small quantum cohomology ring of these varieties, which give a combinatorial formula for the product of any Schubert class with certain special Schubert classes. We also give presentations of these rings, with integer coefficients, in terms of special Schubert class generators and relations.Comment: 59 pages, LaTeX, 6 figure

Stable Grothendieck polynomials and K-theoretic factor sequences

We formulate a nonrecursive combinatorial rule for the expansion of the stable Grothendieck polynomials of [Fomin-Kirillov '94] in the basis of stable Grothendieck polynomials for partitions. This gives a common generalization, as well as new proofs of the rule of [Fomin-Greene '98] for the expansion of the stable Schubert polynomials into Schur polynomials, and the K-theoretic Grassmannian Littlewood-Richardson rule of [Buch '02]. The proof is based on a generalization of the Robinson-Schensted and Edelman-Greene insertion algorithms. Our results are applied to prove a number of new formulas and properties for K-theoretic quiver polynomials, and the Grothendieck polynomials of [Lascoux-Schutzenberger '82]. In particular, we provide the first $K$-theoretic analogue of the factor sequence formula of [Buch-Fulton '99] for the cohomological quiver polynomials

Cardiac magnetic resonance imaging for the detection of myocardial involvement in granulomatosis with polyangiitis

The prevalence of undiagnosed cardiac involvement in granulomatosis with polyangiitis (GPA) is unknown. In this prospective study we investigated the utility of cardiovascular magnetic resonance (CMR) to identify myocardial abnormalities in GPA and their correlation with disease phenotype. Twenty-six patients with GPA and no cardiovascular disease or diabetes mellitus underwent contrast-enhanced CMR, including late gadolinium-enhancement (LGE), T1-mapping for native T1 and extra-cellular volume (ECV) quantification for assessment of myocardial fibrosis, cine imaging and tissue tagging for assessment of left ventricular (LV) function. Twenty-five healthy volunteers (HV) with comparable age, sex, BMI and arterial blood pressure served as controls. Patients with GPA had similar cardiovascular risk profile to HV. A focal, non-ischaemic LGE pattern of fibrosis was detected in 24% of patients and no controls (p = 0.010). Patients with myocardial LGE were less frequently PR3 ANCA (7% vs 93%, p = 0.007), and had involvement of the lower respiratory tract and skin. LGE scar mass was higher in patients presenting with renal involvement. Native T1 and ECV were higher in patients with GPA than HV; ECV was higher in those with relapsing disease, and native T1 was inversely associated with PR3 ANCA (β = − 0.664, p = 0.001). Peak systolic strain was slightly reduced in GPA compared to controls; LV ejection function was inversely correlated with disease duration (β = − 0.454, p = 0.026). Patients with GPA have significant myocardial abnormalities on CMR. ANCA, systemic involvement and disease severity were associated with myocardial fibrosis. CMR could be a useful tool for risk stratification of myocardial involvement in GPA

Quantum cohomology via vicious and osculating walkers

We relate the counting of rational curves intersecting Schubert varieties of the Grassmannian to the counting of certain non-intersecting lattice paths on the cylinder, so-called vicious and osculating walkers. These lattice paths form exactly solvable statistical mechanics models and are obtained from solutions to the Yang–Baxter equation. The eigenvectors of the transfer matrices of these models yield the idempotents of the Verlinde algebra of the gauged u^(n)k -WZNW model. The latter is known to be closely related to the small quantum cohomology ring of the Grassmannian. We establish further that the partition functions of the vicious and osculating walker model are given in terms of Postnikov’s toric Schur functions and can be interpreted as generating functions for Gromov–Witten invariants. We reveal an underlying quantum group structure in terms of Yang–Baxter algebras and use it to give a generating formula for toric Schur functions in terms of divided difference operators which appear in known representations of the nil-Hecke algebra

Long-term outcome with the automatic implantable cardioverter-defibrillator

AbstractThe automatic implantable cardioverter-defibrillator was implanted in 270 patients because of life-threatening arrhythmias over a 7 year period. There was a history of sustained ventricular tachycardia or fibrillation, or both, in 96% of these patients, 80% had one or more prior cardiac arrests and 78% had coronary artery disease as their underlying diagnosis. The average ejection fraction was 34%, and 96% of these patients had had an average of 3.4 antiarrhythmic drug failures per patient before defibrillator implantation. There were four perioperative deaths and eight patients had generator infection or generator erosion, or both, during the perioperative period or during long-term follow-up. Concomitant antiarrhythmic drug therapy was given to 69% of patients.Shocks from the device were given to 58% of patients, and 20% received “problematic” shocks. The device was removed from 16 patients during long-term follow-up for a variety of reasons. There were 7 sudden cardiac deaths and 30 nonsudden cardiac deaths, 18 of which were secondary to congestive heart failure. The actuarial incidence of sudden death, total cardiac death and total mortality from all causes was 1%, 7% and 8%, respectively, at 1 year, and 4%, 24% and 26% at 5 years.The automatic implantable cardioverter-defibrillator nearly eliminates sudden death over a long-term follow-up period in a high risk group of patients. It has an acceptable rate of complications or problems, or both, and most late deaths in these patients are nonsudden and of cardiovascular origin

Exosome-mediated shuttling of microRNA-29 regulates HIV Tat and morphine-mediated neuronal dysfunction.

Neuronal damage is a hallmark feature of HIV-associated neurological disorders (HANDs). Opiate drug abuse accelerates the incidence and progression of HAND; however, the mechanisms underlying the potentiation of neuropathogenesis by these drugs remain elusive. Opiates such as morphine have been shown to enhance HIV transactivation protein Tat-mediated toxicity in both human neurons and neuroblastoma cells. In the present study, we demonstrate reduced expression of the tropic factor platelet-derived growth factor (PDGF)-B with a concomitant increase in miR-29b in the basal ganglia region of the brains of morphine-dependent simian immunodeficiency virus (SIV)-infected macaques compared with the SIV-infected controls. In vitro relevance of these findings was corroborated in cultures of astrocytes exposed to morphine and HIV Tat that led to increased release of miR-29b in exosomes. Subsequent treatment of neuronal SH-SY5Y cell line with exosomes from treated astrocytes resulted in decreased expression of PDGF-B, with a concomitant decrease in viability of neurons. Furthermore, it was shown that PDGF-B was a target for miR-29b as evidenced by the fact that binding of miR-29 to the 3\u27-untranslated region of PDGF-B mRNA resulted in its translational repression in SH-SY5Y cells. Understanding the regulation of PDGF-B expression may provide insights into the development of potential therapeutic targets for neuronal loss in HIV-1-infected opiate abusers