Characterization of curves that lie on a geodesic sphere or on a totally geodesic hypersurface in a hyperbolic space or in a sphere

The consideration of the so-called rotation minimizing frames allows for a simple and elegant characterization of plane and spherical curves in Euclidean space via a linear equation relating the coefficients that dictate the frame motion. In this work, we extend these investigations to characterize curves that lie on a geodesic sphere or totally geodesic hypersurface in a Riemannian manifold of constant curvature. Using that geodesic spherical curves are normal curves, i.e., they are the image of an Euclidean spherical curve under the exponential map, we are able to characterize geodesic spherical curves in hyperbolic spaces and spheres through a non-homogeneous linear equation. Finally, we also show that curves on totally geodesic hypersurfaces, which play the role of hyperplanes in Riemannian geometry, should be characterized by a homogeneous linear equation. In short, our results give interesting and significant similarities between hyperbolic, spherical, and Euclidean geometries.Comment: 15 pages, 3 figures; comments are welcom

Characterization of manifolds of constant curvature by spherical curves

It is known that the so-called rotation minimizing (RM) frames allow for a simple and elegant characterization of geodesic spherical curves in Euclidean, hyperbolic, and spherical spaces through a certain linear equation involving the coefficients that dictate the RM frame motion (da Silva, da Silva in Mediterr J Math 15:70, 2018). Here, we shall prove the converse, i.e., we show that if all geodesic spherical curves on a Riemannian manifold are characterized by a certain linear equation, then all the geodesic spheres with a sufficiently small radius are totally umbilical and, consequently, the given manifold has constant sectional curvature. We also furnish two other characterizations in terms of (i) an inequality involving the mean curvature of a geodesic sphere and the curvature function of their curves and (ii) the vanishing of the total torsion of closed spherical curves in the case of three-dimensional manifolds. Finally, we also show that the same results are valid for semi-Riemannian manifolds of constant sectional curvature.Comment: To appear in Annali di Matematica Pura ed Applicat

Are Voters Rationally Ignorant? An Empirical Study for Portuguese Local Elections

The application of the rational choice postulate to a political context invariably leads to the conclusion that most voters are ill informed when making the decision for whom to vote. In this paper, the authors do an empirical evaluation of the rational ignorance theory, based on the results of the 1997 Portuguese Local Elections. The results only partially sustain the hypothesis of rational ignorance, although it is also possible to identify several limitations that prevent the establishment of definite conclusions in this specific field.JEL Classification: H7 Key words: Voter’s Behaviour; Local Elections; Local Governments; Portugal.

Integral Representation of Generalized Grey Brownian Motion

In this paper we investigate the representation of a class of non Gaussian processes, namely generalized grey Brownian motion, in terms of a weighted integral of a stochastic process which is a solution of a certain stochastic differential equation. In particular the underlying process can be seen as a non Gaussian extension of the Ornstein-Uhlenbeck process, hence generalizing the representation results of Muravlev as well as Harms and Stefanovits to the non Gaussian case.Comment: arXiv admin note: text overlap with arXiv:1708.06784, arXiv:1807.0786

To Be or Not To Be in Office Again: Political Business Cycles with Local Governments

Most opportunistic-type models of political business cycles tend to posit a given objective for incumbents: maximisation of re-election chances. Though taking an opportunistic view too, we suggest a new explanation for a fiscal policy cycle: the incumbent’s concern with her own welfare in cases of victory and defeat. This rationale addresses local policy-making in particular. An equilibrium perfect-foresight model is designed which totally dispenses with any form of irrationality (namely, on the part of voters) or the common objective functions (re- election chances). Being well grounded in basic microeconomic theory (welfare maximisation by the individual agent), our model provides another foundation for the emergence of political business cycles at the local level. The empirical plausibility of theoretical predictions is then tested on Portuguese municipal data. The estimation of an error- components econometric framework finds evidence in favour of the proposed explanation during the period 1986 to 1993, and enlightens the role played by several politico-economic determinants of local governments’ investment outlays, such as electoral calendar, re- candidacy decisions, political cohesion and intergovernmental capital transfers.local public finance; public choice; political business cycle; elections; Portugal

Neural Networks Architecture Evaluation in a Quantum Computer

In this work, we propose a quantum algorithm to evaluate neural networks architectures named Quantum Neural Network Architecture Evaluation (QNNAE). The proposed algorithm is based on a quantum associative memory and the learning algorithm for artificial neural networks. Unlike conventional algorithms for evaluating neural network architectures, QNNAE does not depend on initialization of weights. The proposed algorithm has a binary output and results in 0 with probability proportional to the performance of the network. And its computational cost is equal to the computational cost to train a neural network