On polynomials with given Hilbert function and applications

Using Macaulay's correspondence we study the family of Artinian Gorenstein local algebras with fixed symmetric Hilbert function decomposition. As an application we give a new lower bound for the dimension of cactus varieties of the third Veronese embedding. We discuss the case of cubic surfaces, where interesting phenomena occur.

Convergence Of A Specialized Root Trait In Plants From Nutrient-impoverished Soils: Phosphorus-acquisition Strategy In A Nonmycorrhizal Cactus.

In old, phosphorus (P)-impoverished habitats, root specializations such as cluster roots efficiently mobilize and acquire P by releasing large amounts of carboxylates in the rhizosphere. These specialized roots are rarely mycorrhizal. We investigated whether Discocactus placentiformis (Cactaceae), a common species in nutrient-poor campos rupestres over white sands, operates in the same way as other root specializations. Discocactus placentiformis showed no mycorrhizal colonization, but exhibited a sand-binding root specialization with rhizosheath formation. We first provide circumstantial evidence for carboxylate exudation in field material, based on its very high shoot manganese (Mn) concentrations, and then firm evidence, based on exudate analysis. We identified predominantly oxalic acid, but also malic, citric, lactic, succinic, fumaric, and malonic acids. When grown in nutrient solution with P concentrations ranging from 0 to 100 μM, we observed an increase in total carboxylate exudation with decreasing P supply, showing that P deficiency stimulated carboxylate release. Additionally, we tested P solubilization by citric, malic and oxalic acids, and found that they solubilized P from the strongly P-sorbing soil in its native habitat, when the acids were added in combination and in relatively low concentrations. We conclude that the sand-binding root specialization in this nonmycorrhizal cactus functions similar to that of cluster roots, which efficiently enhance P acquisition in other habitats with very low P availability.

LATENT RANK CHANGE DETECTION FOR ANALYSIS OF SPLICE-JUNCTION MICROARRAYS WITH NONLINEAR EFFECTS

Alternative splicing of gene transcripts greatly expands the functional capacity of the genome, and certain splice isoforms may indicate specific disease states such as cancer. Splice junction microarrays interrogate thousands of splice junctions, but data analysis is difficult and error prone because of the increased complexity compared to differential gene expression analysis. We present Rank Change Detection (RCD) as a method to identify differential splicing events based upon a straightforward probabilistic model comparing the over-or underrepresentation of two or more competing isoforms. RCD has advantages over commonly used methods because it is robust to false positive errors due to nonlinear trends in microarray measurements. Further, RCD does not depend on prior knowledge of splice isoforms, yet it takes advantage of the inherent structure of mutually exclusive junctions, and it is conceptually generalizable to other types of splicing arrays or RNA-Seq. RCD specifically identifies the biologically important cases when a splice junction becomes more or less prevalent compared to other mutually exclusive junctions. The example data is from different cell lines of glioblastoma tumors assayed with Agilent microarrays.

Characterizing QALYs under a general rank dependent utility model

This paper provides a characterization of QALYs, the most important outcome measure in medical decision making, in the context of a general rank dependent utility model. We show that both for chronic and for nonchronic health states the characterization of QALYs depends on intuitive conditions. This facilitates the assessment of the validity of QALYs in rank dependent non-expected utility theories and a comparison with other utility based measures of health.

Cannabidiol decreases bone resorption by inhibiting RANK/RANKL expression and pro-inflammatory cytokines during experimental periodontitis in rats

Cannabidiol (CBD) is a cannabinoid component from Cannabis sativa that does not induce psychotomimetic effects and possess anti-inflammatory properties. In the present study we tested the effects of CBD in a periodontitis experimental model in rats. We also investigated possible mechanisms underlying these effects. Periodontal disease was induced by a ligature placed around the mandible first molars of each animal. Male Wistar rats were divided into 3 groups: control animals; ligature-induced animals treated with vehicle and ligature-induced animals treated with CBD (5 mg/kg, daily). Thirty days after the induction of periodontal disease the animals were sacrificed and mandibles and gingival tissues removed for further analysis. Morphometrical analysis of alveolar bone loss demonstrated that CBD-treated animals presented a decreased alveolar bone loss and a lower expression of the activator of nuclear factor-kappa B ligand RANKL/RANK. Moreover, gingival tissues from the CBD-treated group showed decreased neutrophil migration (MPO assay) associated with lower interleukin (IL)-1 beta and tumor necrosis factor (TNF)-alpha production. These results indicate that CBD may be useful to control bone resorption during progression of experimental periodontitis in rats. Crown Copyright (C) 2008 Published by Elsevier B.V. All rights reserved.

Effects of feeding high levels of cactus (Opuntia ficus-indica Mill) cladodes on urinary output and electrolyte excretion in goats

A study was conducted to determine the effects of feeding spineless cactus cladodes on diuresis and urinary electrolyte excretion in goats. Five bucks were used in a 5 x 5 Latin square experiment with 17-day periods. Experimental diets contained (g/kg dry matter (DM) basis) 370, 470, 570, 670, and 770 spineless cactus cladodes. Water consumption from feed and urine output increased linearly (P<0.05) as the level of cactus cladodes in the diet increased. However, water intake from drinking was low and unaffected by cactus cladode level. Creatinine clearance and urinary Na excretion were similar for all dietary treatments while K excretion decrease linearly (P<0.05) as the level of cactus cladodes in the diet increased. Feeding cactus cladodes caused diuresis and reduced urinary K excretion in goats. Possible reasons for these effects include water over-consumption from cactus cladodes and high dietary K intake. (C) 2007 Elsevier B.V. All rights reserved.

Expression of bone resorption regulators (RANK, RANKL, and OPG) in odontogenic tumors

Objective. To investigate the expression of bone resorption regulators (receptor activator of nuclear factor kappa B [RANK], RANK ligand [RANKL], and osteoprotegerin [OPG]) in calcifying cystic odontogenic tumor (CCOT), adenomatoid odontogenic tumor (AOT), calcifying epithelial odontogenic tumor (CEOT), odontogenic myxoma (OM), and ameloblastic fibroma (AF). Study design. The expression of these mediators was evaluated by means of immunohistochemistry. Results. All specimens demonstrated positive immunoreactivity to RANK, RANKL, and OPG. The quantification of these mediators in epithelium revealed a similar pattern of expression for RANKL and OPG in CCOT, AOT, CEOT, and AF. With regard to stromal/mesenchymal cells, the majority of AOT and CCOT cases showed a higher content of OPG than RANKL, whereas CEOT, OM, and especially AF had a tendency to present a greater content of RANKL than OPG. Conclusion. Our data indicate that the CCOT, AOT, CEOT, OM, and AF cell constituents express key regulators of bone metabolism that might locally modulate tumor-associated bone resorption. (Oral Surg Oral Med Oral Pathol Oral Radiol Endod 2008;106:548-55)

Enhanced effector and memory CTL responses generated by incorporation of receptor activator of NF-kappa B(RANK)/RANK ligand costimulatory molecules into dendritic cell immunogens expressing a human tumor-specific antigen

The outcome of dendritic cell (DC) presentation of Ag to T cells via the TCR/MHC synapse is determined by second signaling through CD80/86 and, importantly, by ligation of costimulatory ligands and receptors located at the DC and T cell surfaces. Downstream signaling triggered by costimulatory molecule ligation results in reciprocal DC and T cell activation and survival, which predisposes to enhanced T cell-mediated immune responses. In this study, we used adenoviral vectors to express a model tumor Ag (the E7 oncoprotein of human papillomavirus 16) with or without coexpression of receptor activator of NF-kappaB (RANK)/RANK ligand (RANKL) or CD40/CD40L costimulatory molecules, and used these transgenic DCs to immunize mice for the generation of E7-directed CD8(+) T cell responses. We show that coexpression of RANK/RANKL, but not CD40/CD40L, in E7-expressing DCs augmented E7-specific IFN-gamma-secreting effector and memory T cells and E7-specific CTLs. These responses were also augmented by coexpression of T cell costimulatory molecules (RANKL and CD40L) or DC costimulatory molecules (RANK and CD40) in the E7-expressing DC immunogens. Augmentation of CTL responses correlated with up-regulation of CD80 and CD86 expression in DCs transduced with costimulatory molecules, suggesting a mechanism for enhanced T cell activation/survival. These results have generic implications for improved tumor Ag-expressing DC vaccines, and specific implications for a DC-based vaccine approach for human papillomavirus 16-associated cervical carcinoma.

Error bounds for low-rank approximations of the first exponential integral kernel

A hierarchical matrix is an efficient data-sparse representation of a matrix, especially useful for large dimensional problems. It consists of low-rank subblocks leading to low memory requirements as well as inexpensive computational costs. In this work, we discuss the use of the hierarchical matrix technique in the numerical solution of a large scale eigenvalue problem arising from a finite rank discretization of an integral operator. The operator is of convolution type, it is defined through the first exponential-integral function and, hence, it is weakly singular. We develop analytical expressions for the approximate degenerate kernels and deduce error upper bounds for these approximations. Some computational results illustrating the efficiency and robustness of the approach are presented.

Patofisiologia de osteonecrose induzida por bisfosfonatos e inibidores de RANK-L

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Equidistribution for higher-rank Abelian actions on Heisenberg nilmanifolds

2010 Mathematics Subject Classification: Primary: 37C85, 37A17, 37A45; Secondary: 11K36, 11L07.

The automorphism group of a free-by-cyclic group in rank 2

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Stable rank of leavitt path algebra

We characterize the values of the stable rank for Leavitt path algebras, by giving concrete criteria in terms of properties of the underlying graph.

Real rank zero algebras have the corona factorization property

The purpose of this short note is to prove that a stable separable C*-algebra with real rank zero has the so-called corona factorization property, that is, all the full multiplier projections are properly in finite. Enroute to our result, we consider conditions under which a real rank zero C*-algebra admits an injection of the compact operators (a question already considered in [21]).

The Rank Lecture: Has imaging told us anything new about human visual organisation?

The functional architecture of the occipital cortex is being studied with increasing detail. Functional and structural MR based imaging are altering views about the organisation of the human visual system. Recent advances have ranged from comparative studies with non-human primates to predictive scanning. The latter multivariate technique describes with sub-voxel resolution patterns of activity that are characteristic of specific visual experiences. One can deduce what a subject experienced visually from the pattern of cortical activity recorded. The challenge for the future is to understand visual functions in terms of cerebral computations at a mesoscopic level of description and to relate this information to electrophysiology. The principal medical application of this new knowledge has focused to a large extent on plasticity and the capacity for functional reorganisation. Crossmodality visual-sensory interactions and cross-correlations between visual and other cerebral areas in the resting state are areas of considerable current interest. The lecture will review findings over the last two decades and reflect on possible roles for imaging studies in the future.