7,408 research outputs found
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
Duality and ontology
A âdualityâ is a formal mapping between the spaces of solutions of two empirically equivalent theories. In recent times, dualities have been found to be pervasive in string theory and quantum field theory. NaĂŻvely interpreted, duality-related theories appear to make very different ontological claims about the worldâdiffering in e.g. space-time structure, fundamental ontology, and mereological structure. In light of this, duality-related theories raise questions familiar from discussions of underdetermination in the philosophy of science: in the presence of dual theories, what is one to say about the ontology of the world? In this paper, we undertake a comprehensive and non-technical survey of the landscape of possible ontological interpretations of duality-related theories. We provide a significantly enriched and clarified taxonomy of optionsâseveral of which are novel to the literature
Sticky prices in the euro area: a summary of new micro evidence
This paper presents original evidence on price setting in the euro area at the individual level. We use micro data on consumer (CPI) and producer (PPI) prices, as well as survey information. Our main findings are: (i) prices in the euro area are sticky and more so than in the US; (ii) there is evidence of heterogeneity and of asymmetries in price setting behaviour; (iii) downward price rigidity is only slightly more marked than upward price rigidity and (iv) implicit or explicit contracts and coordination failure theories are important, whereas menu or information costs are judged much less relevant by firms. JEL Classification: C25, D40, E31consumer prices, price setting, Price stickiness, producer prices, survey data
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 on
the space of ternary forms of even degree . 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 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
-equivariance properties. Our explicit construction of these
bases should be relevant well beyond the scope of this paper. The expression of
the -invariants can then be given in a compact form as the
composition of two equivariant maps. Instead of providing (cumbersome) explicit
expressions for the -invariants, we provide efficient algorithms
for their evaluation and rewriting. We also use the constructed
-invariants to determine the -orbit locus and
provide an algorithm for the inverse problem of finding an element in
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
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
Estimation of Fiber Orientations Using Neighborhood Information
Data from diffusion magnetic resonance imaging (dMRI) can be used to
reconstruct fiber tracts, for example, in muscle and white matter. Estimation
of fiber orientations (FOs) is a crucial step in the reconstruction process and
these estimates can be corrupted by noise. In this paper, a new method called
Fiber Orientation Reconstruction using Neighborhood Information (FORNI) is
described and shown to reduce the effects of noise and improve FO estimation
performance by incorporating spatial consistency. FORNI uses a fixed tensor
basis to model the diffusion weighted signals, which has the advantage of
providing an explicit relationship between the basis vectors and the FOs. FO
spatial coherence is encouraged using weighted l1-norm regularization terms,
which contain the interaction of directional information between neighbor
voxels. Data fidelity is encouraged using a squared error between the observed
and reconstructed diffusion weighted signals. After appropriate weighting of
these competing objectives, the resulting objective function is minimized using
a block coordinate descent algorithm, and a straightforward parallelization
strategy is used to speed up processing. Experiments were performed on a
digital crossing phantom, ex vivo tongue dMRI data, and in vivo brain dMRI data
for both qualitative and quantitative evaluation. The results demonstrate that
FORNI improves the quality of FO estimation over other state of the art
algorithms.Comment: Journal paper accepted in Medical Image Analysis. 35 pages and 16
figure
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
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, SĂŁo Paulo, BrazilUniversidade Federal de SĂŁo Paulo, Escola Paulista Med, SĂŁo Paulo, BrazilDisciplina Cardiol, BR-04024002 SĂŁo Paulo, BrazilUniversidade Federal de SĂŁo Paulo, Escola Paulista Med, SĂŁo Paulo, BrazilWeb of Scienc
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'
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