Inverse Problems for multiple invariant curves

Planar polynomial vector fields which admit invariant algebraic curves, Darboux integrating factors or Darboux first integrals are of special interest. In the present paper we solve the inverse problem for invariant algebraic curves with a given multiplicity and for integrating factors, under generic assumptions regarding the (multiple) invariant algebraic curves involved. In particular we prove, in this generic scenario, that the existence of a Darboux integrating factor implies Darboux integrability. Furthermore we construct examples where the genericity assumption does not hold and indicate that the situation is different for these.

The retained capacity of Lutzomya longipalpis (Lutz & Neiva) to transmit Leishmania chagasi (Cunha & Chagas) after eight years (64 generations in a closed laboratory colony

A closed Lutzomyia longipalpis colony, from Ceará has been used to transmit Leishmania chagasi isolated from a fox in Pará state. The last time this colony was successfully used in similar transmission experiments was eight years (64 generations) ago indicating that this colony of Lu. longipalpis has fully maintained its vectorial capacity in spite of such a long period of maintainance in the laboratory.

Inverse problems for invariant algebraic curves: explicit computations

Given an algebraic curve in the complex affine plane, we describe how to determine all planar polynomial vector fields which leave this curve invariant. If all (finite) singular points of the curve are nondegenerate, we give an explicit expression for these vector fields. In the general setting we provide an algorithmic approach, and as an alternative we discuss sigma processes.

On the growth rate of minor-closed classes of graphs

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Estimating Phillips Curves in Turbulent Times using the ECB’s Survey of Professional Forecasters

This paper uses forecasts from the European Central Bank's Survey of Professional Forecasters to investigate the relationship between inflation and inflation expectations in the euro area. We use theoretical structures based on the New Keynesian and Neoclassical Phillips curves to inform our empirical work. Given the relatively short data span of the Survey of Professional Forecasters and the need to control for many explanatory variables, we use dynamic model averaging in order to ensure a parsimonious econometric speci cation. We use both regression-based and VAR-based methods. We find no support for the backward looking behavior embedded in the Neo-classical Phillips curve. Much more support is found for the forward looking behavior of the New Keynesian Phillips curve, but most of this support is found after the beginning of the financial crisis.

Estimating United States Phillips Curves With Expectations Consistent With The Statistical Process Of Inflation

‘Modern’ Phillips curve theories predict inflation is an integrated, or near integrated, process. However, inflation appears bounded above and below in developed economies and so cannot be ‘truly’ integrated and more likely stationary around a shifting mean. If agents believe inflation is integrated as in the ‘modern’ theories then they are making systematic errors concerning the statistical process of inflation. An alternative theory of the Phillips curve is developed that is consistent with the ‘true’ statistical process of inflation. It is demonstrated that United States inflation data is consistent with the alternative theory but not with the existing ‘modern’ theories.

Environmental Kuznets Curves for Carbon Emissions: A Critical Survey

The empirical finding of an inverse U-shaped relationship between per capita income and pollution, the so-called Environmental Kuznets Curve (EKC), suggests that as countries experience economic growth, environmental deterioration decelerates and thus becomes less of an issue. Focusing on the prime example of carbon emissions, the present article provides a critical review of the new econometric techniques that have questioned the baseline polynomial specification in the EKC literature. We discuss issues related to the functional form, heterogeneity, “spurious” regressions and spatial dependence to address whether and to what extent the EKC can be observed. Despite these new approaches, there is still no clear-cut evidence supporting the existence of the EKC for carbon emissions. JEL classifications: C20; Q32; Q50; O13 Keywords: Environmental Kuznets Curve; Carbon emissions; Functional form; Heterogeneity; “Spurious” regressions; Spatial dependence.Residential satisfaction is often used as a barometer to assess the performance of public policy and programmes designed to raise individuals' well-being. However, the fact that responses elicited from residents might be biased by subjective, non-observable factors casts doubt on whether these responses can be taken as trustable indicators of the individuals' housing situation. Emotional factors such as aspirations or expectations might affect individuals' cognitions of their true residential situation. To disentangle this puzzle, we investigated whether identical residential attributes can be perceived differently depending on tenure status. Our results indicate that tenure status is crucial not only in determining the level of housing satisfaction, but also regarding how dwellers perceive their housing characteristics. Keywords: Housing satisfaction, subjective well-being, homeownership. JEL classification: D1, R2.

A computational and geometric approach to phase resetting curves and surfaces

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On hyperbolic once-punctured-torus bundles IV: automata for lightning curves

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Syntaxin1a variants lacking an N-peptide or bearing the LE mutation bind to Munc18a in a closed conformation.

In neurons, soluble N-ethylmaleimide-sensitive factor attachment receptor (SNARE) proteins drive the fusion of synaptic vesicles to the plasma membrane through the formation of a four-helix SNARE complex. Members of the Sec1/Munc18 protein family regulate membrane fusion through interactions with the syntaxin family of SNARE proteins. The neuronal protein Munc18a interacts with a closed conformation of the SNARE protein syntaxin1a (Syx1a) and with an assembled SNARE complex containing Syx1a in an open conformation. The N-peptide of Syx1a (amino acids 1-24) has been implicated in the transition of Munc18a-bound Syx1a to Munc18a-bound SNARE complex, but the underlying mechanism is not understood. Here we report the X-ray crystal structures of Munc18a bound to Syx1a with and without its native N-peptide (Syx1aΔN), along with small-angle X-ray scattering (SAXS) data for Munc18a bound to Syx1a, Syx1aΔN, and Syx1a L165A/E166A (LE), a mutation thought to render Syx1a in a constitutively open conformation. We show that all three complexes adopt the same global structure, in which Munc18a binds a closed conformation of Syx1a. We also identify a possible structural connection between the Syx1a N-peptide and SNARE domain that might be important for the transition of closed-to-open Syx1a in SNARE complex assembly. Although the role of the N-peptide in Munc18a-mediated SNARE complex assembly remains unclear, our results demonstrate that the N-peptide and LE mutation have no effect on the global conformation of the Munc18a-Syx1a complex.

A Multiple Break Panel Approach to Estimating United States Phillips Curves

Phillips curves are often estimated without due attention being paid to the underlying time series properties of the data. In particular, the consequences of inflation having discrete breaks in mean have not been studied adequately. We show by means of simulations and a detailed empirical example based on United States data that not taking account of breaks may lead to biased, and therefore spurious, estimates of Phillips curves. We suggest a method to account for the breaks in mean inflation and obtain meaningful and unbiased estimates of the short- and long-run Phillips curves in the United States.

'Modern' Phillips Curves and the Implications For The Statistical Process of Inflation

'Modern' theories of the Phillips curve imply that inflation is an integrated, or near integrated process. This paper explains this implication and why these 'modern' theories are logically inconsistent with what is commonly known about the statistical process of inflation.

A Modulated Closed Form solution for Quantitative Susceptibility Mapping - A thorough evaluation and comparison to iterative methods based on edge prior knowledge.

The aim of this study is to perform a thorough comparison of quantitative susceptibility mapping (QSM) techniques and their dependence on the assumptions made. The compared methodologies were: two iterative single orientation methodologies minimizing the l2, l1TV norm of the prior knowledge of the edges of the object, one over-determined multiple orientation method (COSMOS) and anewly proposed modulated closed-form solution (MCF). The performance of these methods was compared using a numerical phantom and in-vivo high resolution (0.65mm isotropic) brain data acquired at 7T using a new coil combination method. For all QSM methods, the relevant regularization and prior-knowledge parameters were systematically changed in order to evaluate the optimal reconstruction in the presence and absence of a ground truth. Additionally, the QSM contrast was compared to conventional gradient recalled echo (GRE) magnitude and R2* maps obtained from the same dataset. The QSM reconstruction results of the single orientation methods show comparable performance. The MCF method has the highest correlation (corrMCF=0.95, r(2)MCF =0.97) with the state of the art method (COSMOS) with additional advantage of extreme fast computation time. The l-curve method gave the visually most satisfactory balance between reduction of streaking artifacts and over-regularization with the latter being overemphasized when the using the COSMOS susceptibility maps as ground-truth. R2* and susceptibility maps, when calculated from the same datasets, although based on distinct features of the data, have a comparable ability to distinguish deep gray matter structures.

Destruction of invariant curves in the restricted circular planar three body problem using comparison of action

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Singular Bott-Chern classes and the arithmetic Grothendieck-Riemann-Roch theorem for closed immersions

We study the singular Bott-Chern classes introduced by Bismut, Gillet and Soulé. Singular Bott-Chern classes are the main ingredient to define direct images for closed immersions in arithmetic K-theory. In this paper we give an axiomatic definition of a theory of singular Bott-Chern classes, study their properties, and classify all possible theories of this kind. We identify the theory defined by Bismut, Gillet and Soulé as the only one that satisfies the additional condition of being homogeneous. We include a proof of the arithmetic Grothendieck-Riemann-Roch theorem for closed immersions that generalizes a result of Bismut, Gillet and Soulé and was already proved by Zha. This result can be combined with the arithmetic Grothendieck-Riemann-Roch theorem for submersions to extend this theorem to arbitrary projective morphisms. As a byproduct of this study we obtain two results of independent interest. First, we prove a Poincaré lemma for the complex of currents with fixed wave front set, and second we prove that certain direct images of Bott-Chern classes are closed.