Is every toric variety an M-variety?

A complex algebraic variety X defined over the real numbers is called an M-variety if the sum of its Betti numbers (for homology with closed supports and coefficients in Z/2) coincides with the corresponding sum for the real part of X. It has been known for a long time that any nonsingular complete toric variety is an M-variety. In this paper we consider whether this remains true for toric varieties that are singular or not complete, and we give a positive answer when the dimension of X is less than or equal to 3.Comment: 13 page

Asymptotically maximal families of hypersurfaces in toric varieties

A real algebraic variety is maximal (with respect to the Smith-Thom inequality) if the sum of the Betti numbers (with $\mathbb{Z}_2$ coefficients) of the real part of the variety is equal to the sum of Betti numbers of its complex part. We prove that there exist polytopes that are not Newton polytopes of any maximal hypersurface in the corresponding toric variety. On the other hand we show that for any polytope $\Delta$ there are families of hypersurfaces with the Newton polytopes $(\lambda\Delta)_{\lambda \in \mathbb{N}}$ that are asymptotically maximal when $\lambda$ tends to infinity. We also show that these results generalize to complete intersections.Comment: 18 pages, 1 figur

Rational invariants of even ternary forms under the orthogonal group

In this article we determine a generating set of rational invariants of minimal cardinality for the action of the orthogonal group $\mathrm{O}_3$ on the space $\mathbb{R}[x,y,z]_{2d}$ of ternary forms of even degree $2d$. The construction relies on two key ingredients: On one hand, the Slice Lemma allows us to reduce the problem to dermining the invariants for the action on a subspace of the finite subgroup $\mathrm{B}_3$ of signed permutations. On the other hand, our construction relies in a fundamental way on specific bases of harmonic polynomials. These bases provide maps with prescribed $\mathrm{B}_3$-equivariance properties. Our explicit construction of these bases should be relevant well beyond the scope of this paper. The expression of the $\mathrm{B}_3$-invariants can then be given in a compact form as the composition of two equivariant maps. Instead of providing (cumbersome) explicit expressions for the $\mathrm{O}_3$-invariants, we provide efficient algorithms for their evaluation and rewriting. We also use the constructed $\mathrm{B}_3$-invariants to determine the $\mathrm{O}_3$-orbit locus and provide an algorithm for the inverse problem of finding an element in $\mathbb{R}[x,y,z]_{2d}$ with prescribed values for its invariants. These are the computational issues relevant in brain imaging.Comment: v3 Changes: Reworked presentation of Neuroimaging application, refinement of Definition 3.1. To appear in "Foundations of Computational Mathematics

Microstructural damage of the posterior corpus callosum contributes to the clinical severity of neglect

One theory to account for neglect symptoms in patients with right focal damage invokes a release of inhibition of the right parietal cortex over the left parieto-frontal circuits, by disconnection mechanism. This theory is supported by transcranial magnetic stimulation studies showing the existence of asymmetric inhibitory interactions between the left and right posterior parietal cortex, with a right hemispheric advantage. These inhibitory mechanisms are mediated by direct transcallosal projections located in the posterior portions of the corpus callosum. The current study, using diffusion imaging and tract-based spatial statistics (TBSS), aims at assessing, in a data-driven fashion, the contribution of structural disconnection between hemispheres in determining the presence and severity of neglect. Eleven patients with right acute stroke and 11 healthy matched controls underwent MRI at 3T, including diffusion imaging, and T1-weighted volumes. TBSS was modified to account for the presence of the lesion and used to assess the presence and extension of changes in diffusion indices of microscopic white matter integrity in the left hemisphere of patients compared to controls, and to investigate, by correlation analysis, whether this damage might account for the presence and severity of patients' neglect, as assessed by the Behavioural Inattention Test (BIT). None of the patients had any macroscopic abnormality in the left hemisphere; however, 3 cases were discarded due to image artefacts in the MRI data. Conversely, TBSS analysis revealed widespread changes in diffusion indices in most of their left hemisphere tracts, with a predominant involvement of the corpus callosum and its projections on the parietal white matter. A region of association between patients' scores at BIT and brain FA values was found in the posterior part of the corpus callosum. This study strongly supports the hypothesis of a major role of structural disconnection between the right and left parietal cortex in determining 'neglect'

The functions of the A1A2A3 domains in von Willebrand factor include multimerin 1 binding.

Multimerin 1 (MMRN1) is a massive, homopolymeric protein that is stored in platelets and endothelial cells for activation-induced release. In vitro, MMRN1 binds to the outer surfaces of activated platelets and endothelial cells, the extracellular matrix (including collagen) and von Willebrand factor (VWF) to support platelet adhesive functions. VWF associates with MMRN1 at high shear, not static conditions, suggesting that shear exposes cryptic sites within VWF that support MMRN1 binding. Modified ELISA and surface plasmon resonance were used to study the structural features of VWF that support MMRN1 binding, and determine the affinities for VWF-MMRN1 binding. High shear microfluidic platelet adhesion assays determined the functional consequences for VWF-MMRN1 binding. VWF binding to MMRN1 was enhanced by shear exposure and ristocetin, and required VWF A1A2A3 region, specifically the A1 and A3 domains. VWF A1A2A3 bound to MMRN1 with a physiologically relevant binding affinity (KD: 2.0 ± 0.4 nM), whereas the individual VWF A1 (KD: 39.3 ± 7.7 nM) and A3 domains (KD: 229 ± 114 nM) bound to MMRN1 with lower affinities. VWF A1A2A3 was also sufficient to support the adhesion of resting platelets to MMRN1 at high shear, by a mechanism dependent on VWF-GPIbα binding. Our study provides new information on the molecular basis of MMRN1 binding to VWF, and its role in supporting platelet adhesion at high shear. We propose that at sites of vessel injury, MMRN1 that is released following activation of platelets and endothelial cells, binds to VWF A1A2A3 region to support platelet adhesion at arterial shear rates.This study was supported by the Heart and Stroke Foundation (CPMH), the Canadian Institutes of Health Research (CPMH), the British Heart Foundation (RWF), The Wellcome Trust (RWF), and the National Institutes of Health (JES).This is the author accepted manuscript. The final version is available from Schattauer Publishers via http://dx.doi.org/10.1160/TH15-09-070

Hydroxyproline Ring Pucker Causes Frustration of Helix Parameters in the Collagen Triple Helix.

Collagens, the most abundant proteins in mammals, are defined by their triple-helical structures and distinctive Gly-Xaa-Yaa repeating sequence, where Xaa is often proline and Yaa, hydroxyproline (Hyp/O). It is known that hydroxyproline in the Yaa position stabilises the triple helix, and that lack of proline hydroxylation in vivo leads to dysfunctional collagen extracellular matrix assembly, due to a range of factors such as a change in hydration properties. In addition, we note that in model peptides, when Yaa is unmodified proline, the Xaa proline has a strong propensity to adopt an endo ring conformation, whilst when Yaa is hydroxyproline, the Xaa proline adopts a range of endo and exo conformations. Here we use a combination of solid-state NMR spectroscopy and potential energy landscape modelling of synthetic triple-helical collagen peptides to understand this effect. We show that hydroxylation of the Yaa proline causes the Xaa proline ring conformation to become metastable, which in turn confers flexibility on the triple helix.The authors acknowledge BBSRC grant number BB/G021392/1 (MJD, DGR), EPSRC DTA studentship and Doctoral Prize (WYC), British Heart Foundation RG/09/003/27122 and PG/08/011/24416 (RWF, DB, DAS), Wellcome Trust 094470/Z/10/Z (RWF, DB, DAS), ERC and EPSRC (DJW).This is the final version of the article. It first appeared from NPG via http://dx.doi.org/10.1038/srep1255

Price Setting in the Euro Area: Some Stylized Facts from Individual Consumer Price Data.

This paper documents patterns of price setting at the retail level in the euro area. A set of stylized facts on the frequency and size of price changes is presented along with an econometric investigation of their main determinants. Price adjustment in the euro area can be summarized in six stylized facts. First, prices of most products change rarely. The average monthly frequency of price adjustment is 15 p.c., compared to about 25 p.c. in the US. Second, the frequency of price changes is characterized by substantial cross-product heterogeneity and pronounced sectoral patterns: prices of (oil-related) energy and unprocessed food products change very often, while price adjustments are less frequent for processed food products, non-energy industrial goods and services. Third, cross-country heterogeneity exists but is less pronounced. Fourth, price decreases are not uncommon. Fifth, price increases and decreases are sizeable compared to aggregate and sectoral inflation rates. Sixth, price changes are not highly synchronized across price-setters. Moreover, the frequency of price changes in the euro area is related to a number of factors, in particular seasonality, outlet type, indirect taxation, use of attractive prices as well as aggregate or product-specific inflation.Price-setting ; consumer price ; frequency of price change.

Markov models for fMRI correlation structure: is brain functional connectivity small world, or decomposable into networks?

Correlations in the signal observed via functional Magnetic Resonance Imaging (fMRI), are expected to reveal the interactions in the underlying neural populations through hemodynamic response. In particular, they highlight distributed set of mutually correlated regions that correspond to brain networks related to different cognitive functions. Yet graph-theoretical studies of neural connections give a different picture: that of a highly integrated system with small-world properties: local clustering but with short pathways across the complete structure. We examine the conditional independence properties of the fMRI signal, i.e. its Markov structure, to find realistic assumptions on the connectivity structure that are required to explain the observed functional connectivity. In particular we seek a decomposition of the Markov structure into segregated functional networks using decomposable graphs: a set of strongly-connected and partially overlapping cliques. We introduce a new method to efficiently extract such cliques on a large, strongly-connected graph. We compare methods learning different graph structures from functional connectivity by testing the goodness of fit of the model they learn on new data. We find that summarizing the structure as strongly-connected networks can give a good description only for very large and overlapping networks. These results highlight that Markov models are good tools to identify the structure of brain connectivity from fMRI signals, but for this purpose they must reflect the small-world properties of the underlying neural systems

Associations between mothers’ perceptions of the cost of fruit and vegetables and children’s diets : Will children pay the price?

Background/Objectives: Perceptions that fruit and vegetables are expensive are more common among the socio-economically disadvantaged groups and are linked to poor dietary outcomes. Such perceptions may be exacerbated in countries recently affected by natural disasters, where devastation of fruit and vegetable crops has resulted in increase in prices of fruit and vegetables. Examining the associations of perceptions of fruit and vegetable affordability and children\u27s diets can offer insights into how the high prices of fruit and vegetables might have an impact on the diets of children.Subjects/Methods: We analysed the data from 546 socio-economically disadvantaged mother&ndash;child pairs to assess the relationship between maternal perceptions of fruit and vegetable affordability and the diets of their children.Results: Fruit consumption was lower among children whose mothers felt the cost of fruit was too high. Maternal perceptions of fruit and vegetable affordability were not associated with any other aspect of child\u27s diet.Conclusions: Our results suggest a possible role for maternal perceptions of fruit affordability in children\u27s diet, though further research is warranted.<br /

Design and synthesis of imidazoline derivatives active on glucose homeostasis in a rat model of type II diabetes.2. Syntheses and biological activities of 1,4-dialkyl-,1,4-dibenzyl and 1-benzyl-4-alkyl-2-(4',5'-dihydro-1' H-imidazol-2'yl)piperazines and isosteric analogues of imidazoline

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