Papers by Giorgio Ottaviani
Pacific Journal of Mathematics, 1995
Let MIp2n+i(fc) be the moduli space of stable instanton bundles on F 2n+1 with c<ι -k. We prove t... more Let MIp2n+i(fc) be the moduli space of stable instanton bundles on F 2n+1 with c<ι -k. We prove that MI P 2n+i(2) is smooth, irreducible, unirational and has zero Euler-Poincare characteristic, as it happens for F 3 . We find instead that Mips (3) and Mips (4) are singular.
Eprint Arxiv Alg Geom 9502008, Feb 1, 1995
Let ${\cal M}_{I\!\! P^3}(c_1,c_2)$ be the moduli space of stable rank-$2$ vector bundles on $I\!... more Let ${\cal M}_{I\!\! P^3}(c_1,c_2)$ be the moduli space of stable rank-$2$ vector bundles on $I\!\! P^3$ with Chern classes $c_1$, $ c_2$. We prove the following results. 1) Let $0 \le \beta < \gamma $ be two integers, ($\gamma \ge 2)$, such that $2\gamma-3\beta>0$; then ${\cal M}_{I\!\! P^3}(0,2\gamma^2-3\beta^2)$ is singular (the case $\beta =0$ was previously proved by M. Maggesi). 2) Let $0 \le \beta < \gamma $ be two odd integers ($\gamma \ge 5)$, such that $2\gamma-3\beta+1>0$; then ${\cal M}_{I\!\! P^3}(-1,2(\gamma/2)^2-3(\beta/2)^2+1/4)$ is singular. In particular ${\cal M}_{I\!\! P^3}(0,5)$, ${\cal M}_{I\!\! P^3}(-1,6)$ are singular.
Therapy with a Selective Cannabinoid Receptor Type 2 Agonist Limits Albuminuria and Renal Injury in Mice with Type 2 Diabetic Nephropathy
Nephron, 2015
A critical involvement of the endocannabinoid/cannabinoid receptor system in diabetes and its com... more A critical involvement of the endocannabinoid/cannabinoid receptor system in diabetes and its complications has been recognized. Experimental evidence suggested that activation of the cannabinoid receptor type 2 (CB2), which is expressed in the kidney by podocytes and inflammatory cells, had a protective role in early streptozotocin-induced type 1 diabetes in mice. No experimental evidence is so far available on the effects of CB2 agonists in type 2 diabetes. In this study, we investigated the effects of a CB2 agonist given at a phase of overt disease on renal functional and structural changes in BTBR ob/ob mice, a model of type 2 diabetic nephropathy. BTBR ob/ob mice received, from 10 to 21 weeks of age, vehicle, the selective CB2 agonist HU910, or lisinopril used as standard therapy for comparison. BTBR wild-type mice served as controls. Treatment with CB2 agonist reduced progressive albuminuria of BTBR ob/ob mice to a similar extent as ACE inhibitor. The antiproteinuric effect of CB2 agonist was associated with the amelioration of the defective nephrin expression in podocytes of diabetic mice. CB2 agonist limited mesangial matrix expansion, fibronectin accumulation and sclerosis. Glomerular infiltration of Mac-2-positive monocytes/machrophages was attenuated by CB2 agonist, at least in part due to the drug&amp;amp;amp;amp;#39;s ability to reduce MCP-1 chemotactic signals. Renoprotective effects of CB2 were similar to those achieved by ACE inhibitor. These results suggest that CB2 agonism is a potential option to be added to the available therapeutic armamentarium for type 2 diabetic nephropathy.
Siam Journal on Matrix Analysis and Applications, Sep 27, 2012
We introduce an inductive method for the study of the uniqueness of decompositions of tensors, by... more We introduce an inductive method for the study of the uniqueness of decompositions of tensors, by means of tensors of rank 1. The method is based on the geometric notion of weak defectivity. For three-dimensional tensors of type (a, b, c), a ≤ b ≤ c, our method proves that the decomposition is unique (i.e. k-identifiability holds) for general tensors of rank k, as soon as k ≤ (a + 1)(b + 1)/16. This improves considerably the known range for identifiability. The method applies also to tensor of higher dimension. For tensors of small size, we give a complete list of situations where identifiability does not hold. Among them, there are 4 × 4 × 4 tensors of rank 6, an interesting case because of its connection with the study of DNA strings.
International Journal of Mathematics
Let M I P 3 (c 1 , c 2 ) be the moduli space of stable rank-2 vector bundles on IP 3 with Chern c... more Let M I P 3 (c 1 , c 2 ) be the moduli space of stable rank-2 vector bundles on IP 3 with Chern classes c 1 , c 2 . We prove the following results. 1) Let 0 ≤ β < γ be two integers, (γ ≥ 2), such that 2γ − 3β > 0; then M I P 3 (0, 2γ 2 − 3β 2 ) is singular (the case β = 0 was previously proved by M. Maggesi).
Transactions of the American Mathematical Society
We prove that the special instanton bundles of rank 2« on P2n+1(C) with a symplectic structure st... more We prove that the special instanton bundles of rank 2« on P2n+1(C) with a symplectic structure studied by Spindler and Trautmann are stable in the sense of Mumford-Takemoto. This implies that the generic special instanton bundle is stable. Moreover all instanton bundles on P5 are stable. We get also the stability of other related vector bundles.
Discovery of 4-Aryl-5,6,7,8-tetrahydroisoquinolines as Potent, Selective, and Orally Active Aldosterone Synthase (CYP11B2) Inhibitors: In Vivo Evaluation in Rodents and Cynomolgus Monkeys
Journal of medicinal chemistry, Jan 2, 2015
Inappropriately high levels of aldosterone are associated with many serious medical conditions, i... more Inappropriately high levels of aldosterone are associated with many serious medical conditions, including renal and cardiac failure. A focused screen hit has been optimized into a potent and selective aldosterone synthase (CYP11B2) inhibitor with in vitro activity against rat, mouse, human, and cynomolgus monkey enzymes, showing a selectivity factor of 160 against cytochrome CYP11B1 in the last species. The novel tetrahydroisoquinoline compound (+)-(R)-6 selectively reduced aldosterone plasma levels in vivo in a dose-dependent manner in db/db mice and cynomolgus monkeys. The selectivity against CYP11B1 as predicted by cellular inhibition data and free plasma fraction translated well to Synacthen challenged cynomolgus monkeys up to a dose of 0.1 mg kg(-1). This compound, displaying good in vivo potency and selectivity in mice and monkeys, is ideally suited to perform mechanistic studies in relevant rodent models and to provide the information necessary for translation to non-human pr...
We study some properties of the natural action of $SL(V_0) \times...\times SL(V_p)$ on nondegener... more We study some properties of the natural action of $SL(V_0) \times...\times SL(V_p)$ on nondegenerate multidimensional complex matrices $A\in\P (V_0\otimes...\otimes V_p)$ of boundary format(in the sense of Gelfand, Kapranov and Zelevinsky); in particular we characterize the non stable ones,as the matrices which are in the orbit of a "triangular" matrix, and the matrices with a stabilizer containing $\C^*$, as those which
Annali di Matematica Pura ed Applicata, 2011
New classes of modules of equations for secant varieties of Veronese varieties are defined using ... more New classes of modules of equations for secant varieties of Veronese varieties are defined using representation theory and geometry. Some old modules of equations (catalecticant minors) are revisited to determine when they are sufficient to give scheme-theoretic defining equations. An algorithm to decompose a general ternary quintic as the sum of seven fifth powers is given as an illustration of our methods. Our new equations and results about them are put into a larger context by introducing vector bundle techniques for finding equations of secant varieties in general. We include a few homogeneous examples of this method.
Aspects of Mathematics, 1991
The border rank of the matrix multiplication operator for n by n matrices is a standard measure o... more The border rank of the matrix multiplication operator for n by n matrices is a standard measure of its complexity. Using techniques from algebraic geometry and representation theory, we show the border rank is at least 2n^2-n. Our bounds are better than the previous lower bound (due to Lickteig in 1985) of 3/2 n^2+ n/2 -1 for all n>2. The bounds are obtained by finding new equations that bilinear maps of small border rank must satisfy, i.e., new equations for secant varieties of triple Segre products, that matrix multiplication fails to satisfy.
Journal of Algebraic Statistics, 2014
We prove that a general tensor of rank 8 in C 3 ⊗ C 6 ⊗ C 6 has at least 6 decompositions as sum ... more We prove that a general tensor of rank 8 in C 3 ⊗ C 6 ⊗ C 6 has at least 6 decompositions as sum of simple tensors. This is the highest known example of balanced tensors of dimension 3, which are not k-identifiable, when k is smaller than the generic rank.
Transactions of the American Mathematical Society, 2015
We prove that the general symmetric tensor in S d C n+1 of rank r is identifiable, provided that ... more We prove that the general symmetric tensor in S d C n+1 of rank r is identifiable, provided that r is smaller than the generic rank. That is, its Waring decomposition as a sum of r powers of linear forms is unique. Only three exceptional cases arise, all of which were known in the literature. Our original contribution regards the case of cubics (d = 3), while for d ≥ 4 we rely on known results on weak defectivity by Ballico, Ciliberto, Chiantini, and Mella. 7 12 12 7 19 15 28 50 18 28 ⋆ 21 84 ⋆ 24 7 8 16 14 8 25 18 36 72 21 36 ⋆ 25
Novel Triazolopyrimidine-Derived Cannabinoid Receptor 2 Agonists As Potential Treatment for Inflammatory Kidney Diseases
ChemMedChem, 2015
The cannabinoid receptor 2 (CB2) system is described to modulate various pathological conditions,... more The cannabinoid receptor 2 (CB2) system is described to modulate various pathological conditions, including inflammation and fibrosis. A series of new heterocyclic small-molecule CB2 receptor agonists were identified from a high-throughput screen. Lead optimization gave access to novel, highly potent, and selective (over CB1) triazolopyrimidine derivatives. A preliminary structure-activity relationship was established, and physicochemical properties in this compound class were significantly improved toward better solubility, lipophilicity, and microsomal stability. An optimized triazolopyrimidine derivative, (3S)-1-[5-tert-butyl-3-[(1-cyclopropyltetrazol-5-yl)methyl]triazolo[4,5-d]pyrimidin-7-yl]pyrrolidin-3-ol (39), was tested in a kidney ischemia-reperfusion model, in which it showed efficacy at a dose of 10 mg kg(-1) (p.o.). A significant depletion of the three measured kidney markers indicated a protective role of CB2 receptor activation toward inflammatory kidney damage. Compound 39 was also protective in a model of renal fibrosis. Oral treatment with 39 at 3 mg kg(-1) per day significantly decreased the amount of fibrosis by ∼40 % which was induced by unilateral ureter obstruction.
Boundedness for Nongeneral-Type 3-Folds in ℙ5
Complex Analysis and Geometry, 1993
Simultaneous determination of cotinine and trans-3'-hydroxycotinine in human serum by high-performance liquid chromatography
Journal of chromatography, Jan 10, 1992
A high-performance liquid chromatographic method with ultraviolet photometric detection has been ... more A high-performance liquid chromatographic method with ultraviolet photometric detection has been developed for the quantitation of cotinine and trans-3'-hydroxycotinine in human serum. A solid-phase extraction procedure was performed for the analytes and the internal standard, N-ethylnorcotinine, before chromatography. The use of a 30-cm reversed-phase column and a mobile phase of water-methanol-0.1 M sodium acetate-acetonitrile (67:24.5:6.5:2, v/v), pH 4.3, prevented the co-elution of caffeine with cotinine. The limit of quantitation observed with this method was 5 ng/ml for both cotinine and trans-3'-hydroxycotinine. The present method proved useful for the determination of serum levels of these metabolites, correlating with nicotine daily intake.
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Papers by Giorgio Ottaviani