Electrons and Heavy Quark at PHENIX Detector

Measurement of heavy quark production is one of the tools used to investigate the matter produced in extremely hot and dense conditions in heavy ion collisions at RHIC. The PHENIX experiment has measured mid-rapidity transverse momentum spectra of electrons. After subtracting the photonic background contribution, the electron spectra are mainly due to semileptonic decays of hadrons containing heavy quarks and therefore provide a measurement of heavy quark production and its energy loss in hot and dense matter. This paper will present the technique used by the PHENIX experiment and recent results on heavy quark production in p+p, d+Au and Au+Au collisions at sqrt{s_NN}=200 GeV.Comment: 15 pages, 10 figures. To be present in proceedings of the 22nd Winter Workshop on Nuclear Dynamics (March 11-18, 2006

Constraining the Doublet Left-Right Model

Left-Right Models (LRM) attempt at giving an understanding of the violation of parity (or charge-conjugation) by the weak interactions in the SM through a similar description of left- and right-handed currents at high energies. The spontaneous symmetry breaking of the LRM gauge group is triggered by an enlarged Higgs sector, usually consisting of two triplet fields (left-right symmetry breaking) and a bidoublet (electroweak symmetry breaking). I reconsider an alternative LRM with doublet instead of triplet fields. After explaining some features of this model, I discuss constraints on its parameters using electroweak precision observables (combined using the CKMfitter frequentist statistical framework) and neutral-meson mixing observables.Comment: Proceedings of the workshop "Flavorful Ways to New Physics", 28-31 October 2014, Freudenstadt, German

Local Conformal Rigidity in Codimension ≤\leq 5

In this paper, for an immersion $f$ of an $n$-dimensional Riemannian manifold $M$ into $(n+d)$-Euclidean space we give a sufficient condition on $f$ so that, in case $d\leq 5$, any immersion $g$ of $M$ into $(n+d+1)$-Euclidean space that induces on $M$ a metric that is conformal to the metric induced by $f$ is locally obtained, in a dense subset of $M$, by a composition of $f$ and a conformal immersion from an open subset of $(n+d)$-Euclidean space into an open subset of $(n+d+1)$-Euclidean space. Our result extends a theorem for hypersurfaces due to M. Dajczer and E. Vergasta. The restriction on the codimension is related to a basic lemma in the theory of rigidity obtained by M. do Carmo and M. Dajczer.Comment: 16 page

Cr-invariants for surfaces in 4-space

We establish cross-ratio invariants for surfaces in 4-space in an analogous way to Uribe-Vargas's work for surfaces in 3-space. We study the geometric locii of local and multi-local singularities of ortogonal projections of the surface. The cross-ratio invariants at $P_3(c)$-points are used to recover two moduli in the 4-jet of the projective parametrization of the surface and show the stable configurations of asymptotic curves.Comment: 22 page

Moving frames and the characterization of curves that lie on a surface

In this work we are interested in the characterization of curves that belong to a given surface. To the best of our knowledge, there is no known general solution to this problem. Indeed, a solution is only available for a few examples: planes, spheres, or cylinders. Generally, the characterization of such curves, both in Euclidean ($E^3$) and in Lorentz-Minkowski ($E_1^3$) spaces, involves an ODE relating curvature and torsion. However, by equipping a curve with a relatively parallel moving frame, Bishop was able to characterize spherical curves in $E^3$ through a linear equation relating the coefficients which dictate the frame motion. Here we apply these ideas to surfaces that are implicitly defined by a smooth function, $\Sigma=F^{-1}(c)$, by reinterpreting the problem in the context of the metric given by the Hessian of $F$, which is not always positive definite. So, we are naturally led to the study of curves in $E_1^3$. We develop a systematic approach to the construction of Bishop frames by exploiting the structure of the normal planes induced by the casual character of the curve, present a complete characterization of spherical curves in $E_1^3$, and apply it to characterize curves that belong to a non-degenerate Euclidean quadric. We also interpret the casual character that a curve may assume when we pass from $E^3$ to $E_1^3$ and finally establish a criterion for a curve to lie on a level surface of a smooth function, which reduces to a linear equation when the Hessian is constant.Comment: 22 pages (23 in the published version), 3 figures; this version is essentially the same as the published on

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

Dynamic Difficulty Adjustment on MOBA Games

This paper addresses the dynamic difficulty adjustment on MOBA games as a way to improve the player's entertainment. Although MOBA is currently one of the most played genres around the world, it is known as a game that offer less autonomy, more challenges and consequently more frustration. Due to these characteristics, the use of a mechanism that performs the difficulty balance dynamically seems to be an interesting alternative to minimize and/or avoid that players experience such frustrations. In this sense, this paper presents a dynamic difficulty adjustment mechanism for MOBA games. The main idea is to create a computer controlled opponent that adapts dynamically to the player performance, trying to offer to the player a better game experience. This is done by evaluating the performance of the player using a metric based on some game features and switching the difficulty of the opponent's artificial intelligence behavior accordingly. Quantitative and qualitative experiments were performed and the results showed that the system is capable of adapting dynamically to the opponent's skills. In spite of that, the qualitative experiments with users showed that the player's expertise has a greater influence on the perception of the difficulty level and dynamic adaptation.Comment: 103-12

A Tutor Agent for MOBA Games

Digital games have become a key player in the entertainment industry, attracting millions of new players each year. In spite of that, novice players may have a hard time when playing certain types of games, such as MOBAs and MMORPGs, due to their steep learning curves and not so friendly online communities. In this paper, we present an approach to help novice players in MOBA games overcome these problems. An artificial intelligence agent plays alongside the player analyzing his/her performance and giving tips about the game. Experiments performed with the game {\em League of Legends} show the potential of this approach

On the Development of Intelligent Agents for MOBA Games

Multiplayer Online Battle Arena (MOBA) is one of the most played game genres nowadays. With the increasing growth of this genre, it becomes necessary to develop effective intelligent agents to play alongside or against human players. In this paper we address the problem of agent development for MOBA games. We implement a two-layered architecture agent that handles both navigation and game mechanics. This architecture relies on the use of Influence Maps, a widely used approach for tactical analysis. Several experiments were performed using {\em League of Legends} as a testbed, and show promising results in this highly dynamic real-time context