Invariantes de planaridade

Orientador: Candido Ferreira Xavier de Mendonça NetoDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de ComputaçãoResumo: O splitting number de um grafo G consiste no número mínimo de operações de quebra de vértice que devem ser realizadas em G para produzir um grafo planar, onde uma operação de quebra de vértice em um determinado vértice u significa substituir algumas das arestas ( u, v) por arestas (u', v), onde u' é um novo vértice. O skewness de G é o número mínimo de arestas que devem ser removidas de G para torná-Io planar. O vertex deletion number de G é o menor inteiro k tal que existe um subgrafo induzido planar de G obtido através da remoção de k vértices de G.Neste trabalho, apr~sentamos valores exatos para o splitting number, o skewness e o vertex deletion number dos grafos Cn x Cm, onde Cn é o circuito simples com n vértices, e para o splitting number e o vertex deletion number de uma triangulação dos grafos Cn x CmAbstract: The splíttíng number of a graph G is the minimum number of splitting steps needed to turn G into a planar graph; where each step replaces some of the edges (u, v) incident to a selected vertex u by edges (u', v), where u' is a new vertex. The skewness of G is the minimum number of edges that need to be deleted from G to produce a planar graph. The vertex deletíon number of G is the smallest integer k such that there is a planar induced subgraph of G obtained by the removal of k vertices of G. In this work, we show exact values for the splíttíng number, skewness and vertex deletíon number of the graphs Cn x Cm, where Cn is the simple circuit on n vertices, and for the splíttíng number and vertex deletíon number of a triangulation of Cn x CmMestradoMestre em Ciência da Computaçã

Intrinsic vs. extrinsic anomalous Hall effect in ferromagnets

A unified theory of the anomalous Hall effect (AHE) is presented for multi-band ferromagnetic metallic systems with dilute impurities. In the clean limit, the AHE is mostly due to the extrinsic skew-scattering. When the Fermi level is located around anti-crossing of band dispersions split by spin-orbit interaction, the intrinsic AHE to be calculated ab initio is resonantly enhanced by its non-perturbative nature, revealing the extrinsic-to-intrinsic crossover which occurs when the relaxation rate is comparable to the spin-orbit interaction energy.Comment: 5 pages including 4 figures, RevTex; minor changes, to appaer in Phys. Rev. Let

Non-Bessel-Gaussianity and Flow Harmonic Fine-Splitting

Both collision geometry and event-by-event fluctuations are encoded in the experimentally observed flow harmonic distribution $p(v_n)$ and $2k$-particle cumulants $c_n\{2k\}$. In the present study, we systematically connect these observables to each other by employing Gram-Charlier A series. We quantify the deviation of $p(v_n)$ from Bessel-Gaussianity in terms of flow harmonic fine-splitting. Subsequently, we show that the corrected Bessel-Gaussian distribution can fit the simulated data better than the Bessel-Gaussian distribution in the more peripheral collisions. Inspired by Gram-Charlier A series, we introduce a new set of cumulants $q_n\{2k\}$ that are more natural to study distributions near Bessel-Gaussian. These new cumulants are obtained from $c_n\{2k\}$ where the collision geometry effect is extracted from it. By exploiting $q_2\{2k\}$, we introduce a new set of estimators for averaged ellipticity $\bar{v}_2$ which are more accurate compared to $v_2\{2k\}$ for $k>1$. As another application of $q_2\{2k\}$, we show we are able to restrict the phase space of $v_2\{4\}$, $v_2\{6\}$ and $v_2\{8\}$ by demanding the consistency of $\bar{v}_2$ and $v_2\{2k\}$ with $q_2\{2k\}$ equation. The allowed phase space is a region such that $v_2\{4\}-v_2\{6\}\gtrsim 0$ and $12 v_2\{6\}-11v_2\{8\}-v_2\{4\}\gtrsim 0$, which is compatible with the experimental observations.Comment: 24 pages; 9 figures; v2: published version; minor revision of the tex

Higher-order moments of the elliptic flow distribution in lead-lead collisions at √sNN=5.02 TeV

The collective anisotropic hydrodynamic behavior of charge hadrons is studied using the multiparticle correlation method. The elliptic anisotropy harmonic from different orders of multiparticle cumulants, v2{2k} , are measured up to the tenth order (k=5 ) as functions of the collision centrality in lead-lead collisions at an energy of sNN−−−√= 5.02 TeV. The data were obtained by the CMS experiment at the LHC, with an integrated luminosity of 0.58 nb−1 . A fine splitting v2{2} > v2{4}≳v2{6}≳v2{8}≳v2{10} is observed. The subtle differences in the higher-order cumulants allow for a precise determination of the underlying hydrodynamics. Based on these results, centrality-dependent moments for the fluctuation-driven event-by-event v2 distribution are determined, including the skewness, the kurtosis and, for the first time, the superskewness. Assuming a hydrodynamic expansion of the produced medium, these moments probe the initial-state geometry in high-energy nucleus-nucleus collisions.BPU11 : 11th International Conference of the Balkan Physical Union : Proceedings book; Aug 11 - Sep 1, 2022S05-HEP High Energy Physics (Particles and Fields)Jovan Milosevic on behalf of the CMS Collaboratio

RELIABILITY OF OPTIONS MARKETS FOR CROP REVENUE INSURANCE RATING

Revenue insurance, only recently introduced for major crops in the U.S., has captured a considerable share of the multiple-peril insurance market. This study evaluates the predictive reliability of using price distributions inferred from options markets to rate revenue insurance products. We find for periods early in the crop growing season that price distributions inferred from options trades offer greater reliability than distributions based on historical futures trades. Options-based price distributions should receive further consideration in crop revenue insurance rating, but current administrative constraints must be considered.Risk and Uncertainty,

Energy dependence and fluctuations of anisotropic fow in Pb-Pb collisions at root s(NN)=5:02 and 2:76 TeV

Measurements of anisotropic flow coefficients with two-and multi-particle cumulants for inclusive charged particles in Pb{Pb collisions at root s(NN) = 5 : 02 and 2.76TeV are reported in the pseudorapidity range vertical bar eta vertical bar <0 : 8 and transverse momentum 0 : 2 <p(T) <50 GeV/c. The full data sample collected by the ALICE detector in 2015 (2010), corresponding to an integrated luminosity of 12.7 (2.0) mu b(-1) in the centrality range 0{80%, is analysed. Flow coefficients up to the sixth flow harmonic (v6) are reported and a detailed comparison among results at the two energies is carried out. The pT dependence of anisotropic flow coefficients and its evolution with respect to centrality and harmonic number n are investigated. An approximate power-law scaling of the form v(n) (p(T)) similar to p(T)(n/3) is observed for all flow harmonics at low p(T) (0.2 <p(T) <3 GeV/c). At the same time, the ratios v(n)/v(m)(n/m) are observed to be essentially independent of pT for most centralities up to about pT = 10 GeV/c. Analysing the di ff erences among higher-order cumulants of elliptic flow (v(2)), which have di ff erent sensitivities to flow fluctuations, a measurement of the standardised skewness of the event-by-event v(2) distribution P (v(2)) is reported and constraints on its higher moments are provided. The Elliptic Power distribution is used to parametrise P (v(2)), extracting its parameters from fi ts to cumulants. The measurements are compared to di ff erent model predictions in order to discriminate among initial-state models and to constrain the temperature dependence of the shear viscosity to entropy-density ratio.Peer reviewe

A Pedagogical Intrinsic Approach to Relative Entropies as Potential Functions of Quantum Metrics: the qq-zz Family

The so-called $q$-z-\textit{R\'enyi Relative Entropies} provide a huge two-parameter family of relative entropies which includes almost all well-known examples of quantum relative entropies for suitable values of the parameters. In this paper we consider a log-regularized version of this family and use it as a family of potential functions to generate covariant $(0,2)$ symmetric tensors on the space of invertible quantum states in finite dimensions. The geometric formalism developed here allows us to obtain the explicit expressions of such tensor fields in terms of a basis of globally defined differential forms on a suitable unfolding space without the need to introduce a specific set of coordinates. To make the reader acquainted with the intrinsic formalism introduced, we first perform the computation for the qubit case, and then, we extend the computation of the metric-like tensors to a generic $n$-level system. By suitably varying the parameters $q$ and $z$, we are able to recover well-known examples of quantum metric tensors that, in our treatment, appear written in terms of globally defined geometrical objects that do not depend on the coordinates system used. In particular, we obtain a coordinate-free expression for the von Neumann-Umegaki metric, for the Bures metric and for the Wigner-Yanase metric in the arbitrary $n$-level case.Comment: 50 pages, 1 figur

Nonparametric maximum likelihood approach to multiple change-point problems

In multiple change-point problems, different data segments often follow different distributions, for which the changes may occur in the mean, scale or the entire distribution from one segment to another. Without the need to know the number of change-points in advance, we propose a nonparametric maximum likelihood approach to detecting multiple change-points. Our method does not impose any parametric assumption on the underlying distributions of the data sequence, which is thus suitable for detection of any changes in the distributions. The number of change-points is determined by the Bayesian information criterion and the locations of the change-points can be estimated via the dynamic programming algorithm and the use of the intrinsic order structure of the likelihood function. Under some mild conditions, we show that the new method provides consistent estimation with an optimal rate. We also suggest a prescreening procedure to exclude most of the irrelevant points prior to the implementation of the nonparametric likelihood method. Simulation studies show that the proposed method has satisfactory performance of identifying multiple change-points in terms of estimation accuracy and computation time.Comment: Published in at http://dx.doi.org/10.1214/14-AOS1210 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org