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

Preoperative left ventricular ejection fraction and left atrium reverse remodeling after mitral regurgitation surgery

Background: Left atrium enlargement has been associated with cardiac events in patients with mitral regurgitation (MR). Left atrium reverse remodeling (LARR) occur after surgical correction of MR, but the preoperative predictors of this phenomenon are not well known. It is therefore important to identify preoperative predictors for postoperative LARR.Methods: We enrolled 62 patients with chronic severe MR (prolapse or flail leaflet) who underwent successful mitral valve surgery (repair or replacement); all with pre-and postoperative echocardiography. LARR was defined as a reduction in left atrium volume index (LAVI) of >= 25%. Stepwise multiple regression analysis was used to identify independent predictors of LARR.Results: LARR occurred in 46 patients (74.2%), with the mean LAVI decreasing from 85.5 mL/m(2) to 49.7 mL/m(2) (p = 25% with a sensitivity of 71.7% and a specificity of 56.3%.Conclusions: LARR occurs frequently after mitral valve surgery and is associated with preoperative LVEF higher than 63.5%.Inst Dante Pazzanese Cardiol, São Paulo, BrazilUniversidade Federal de São Paulo, Escola Paulista Med, São Paulo, BrazilDisciplina Cardiol, BR-04024002 São Paulo, BrazilUniversidade Federal de São Paulo, Escola Paulista Med, São Paulo, BrazilWeb of Scienc

Analytic Metaphysics versus Naturalized Metaphysics: The Relevance of Applied Ontology

The relevance of analytic metaphysics has come under criticism: Ladyman & Ross, for instance, have suggested do discontinue the field. French & McKenzie have argued in defense of analytic metaphysics that it develops tools that could turn out to be useful for philosophy of physics. In this article, we show first that this heuristic defense of metaphysics can be extended to the scientific field of applied ontology, which uses constructs from analytic metaphysics. Second, we elaborate on a parallel by French & McKenzie between mathematics and metaphysics to show that the whole field of analytic metaphysics, being useful not only for philosophy but also for science, should continue to exist as a largely autonomous field

The recognition of collagen and triple-helical toolkit peptides by MMP-13: sequence specificity for binding and cleavage.

Remodeling of collagen by matrix metalloproteinases (MMPs) is crucial to tissue homeostasis and repair. MMP-13 is a collagenase with a substrate preference for collagen II over collagens I and III. It recognizes a specific, well-known site in the tropocollagen molecule where its binding locally perturbs the triple helix, allowing the catalytic domain of the active enzyme to cleave the collagen α chains sequentially, at Gly(775)-Leu(776) in collagen II. However, the specific residues upon which collagen recognition depends within and surrounding this locus have not been systematically mapped. Using our triple-helical peptide Collagen Toolkit libraries in solid-phase binding assays, we found that MMP-13 shows little affinity for Collagen Toolkit III, but binds selectively to two triple-helical peptides of Toolkit II. We have identified the residues required for the adhesion of both proMMP-13 and MMP-13 to one of these, Toolkit peptide II-44, which contains the canonical collagenase cleavage site. MMP-13 was unable to bind to a linear peptide of the same sequence as II-44. We also discovered a second binding site near the N terminus of collagen II (starting at helix residue 127) in Toolkit peptide II-8. The pattern of binding of the free hemopexin domain of MMP-13 was similar to that of the full-length enzyme, but the free catalytic subunit bound none of our peptides. The susceptibility of Toolkit peptides to proteolysis in solution was independent of the very specific recognition of immobilized peptides by MMP-13; the enzyme proved able to cleave a range of dissolved collagen peptides.This work was supported by a British Heart Foundation programme grant, RG/009/003/27122, and peptide synthesis, by grants from Medical Research Council and Wellcome Trust.This is the author accepted manuscript. The final version can be found on the publisher's website at: http://www.jbc.org/content/early/2014/07/09/jbc.M114.58344

Design of high-magnetic field gradient sources for controlling magnetically induced flow of ferrofluids in microfluidic systems

The use of miniature electromagnets for ferrofluid-actuated liquid dispensing into microfluidic channels has been investigated by numerical simulations using the finite element method and measurements of fluid displacement and flow rate. The simulations illustrate the effect of structural and geometrical parameters of single and paired solenoid coils on the magnetic force experienced by the ferrofluid. Dual solenoids were used for extended fluid displacement. Ferrofluid positioning and flow rates were controlled also by using a solenoid with an iron core. The experimental measurements of fluidflow in capillaries were used to validate the modeling calculations. The results can be used as a basis for the development of on-chip ferrofluid-based devices integrated with microfluidic architectures

Nanoscale temperature measurements using non-equilibrium Brownian dynamics of a levitated nanosphere

Einstein realised that the fluctuations of a Brownian particle can be used to ascertain properties of its environment. A large number of experiments have since exploited the Brownian motion of colloidal particles for studies of dissipative processes, providing insight into soft matter physics, and leading to applications from energy harvesting to medical imaging. Here we use optically levitated nanospheres that are heated to investigate the non-equilibrium properties of the gas surrounding them. Analysing the sphere's Brownian motion allows us to determine the temperature of the centre-of-mass motion of the sphere, its surface temperature and the heated gas temperature in two spatial dimensions. We observe asymmetric heating of the sphere and gas, with temperatures reaching the melting point of the material. This method offers new opportunities for accurate temperature measurements with spatial resolution on the nanoscale, and a new means for testing non-equilibrium thermodynamicsComment: 5 pages, 4 figures, supplementary material available upon reques

Polynomial-Time Amoeba Neighborhood Membership and Faster Localized Solving

We derive efficient algorithms for coarse approximation of algebraic hypersurfaces, useful for estimating the distance between an input polynomial zero set and a given query point. Our methods work best on sparse polynomials of high degree (in any number of variables) but are nevertheless completely general. The underlying ideas, which we take the time to describe in an elementary way, come from tropical geometry. We thus reduce a hard algebraic problem to high-precision linear optimization, proving new upper and lower complexity estimates along the way.Comment: 15 pages, 9 figures. Submitted to a conference proceeding

Rapid measurement of intravoxel incoherent motion (IVIM) derived perfusion fraction for clinical magnetic resonance imaging

Objective This study aimed to investigate the reliability of intravoxel incoherent motion (IVIM) model derived parameters D and f and their dependence on b value distributions with a rapid three b value acquisition protocol. Materials and methods Diffusion models for brain, kidney, and liver were assessed for bias, error, and reproducibility for the estimated IVIM parameters using b values 0 and 1000, and a b value between 200 and 900, at signal-to-noise ratios (SNR) 40, 55, and 80. Relative errors were used to estimate optimal b value distributions for each tissue scenario. Sixteen volunteers underwent brain DW-MRI, for which bias and coefficient of variation were determined in the grey matter. Results Bias had a large influence in the estimation of D and f for the low-perfused brain model, particularly at lower b values, with the same trends being confirmed by in vivo imaging. Significant differences were demonstrated in vivo for estimation of D (P = 0.029) and f (P < 0.001) with [300,1000] and [500,1000] distributions. The effect of bias was considerably lower for the high-perfused models. The optimal b value distributions were estimated to be brain500,1000, kidney300,1000, and liver200,1000. Conclusion IVIM parameters can be estimated using a rapid DW-MRI protocol, where the optimal b value distribution depends on tissue characteristics and compromise between bias and variability