The Conformal Anomaly in General Rank 1 Symmetric Spaces and Associated Operator Product

We compute the one-loop effective action and the conformal anomaly associated with the product $\bigotimes_p{\cal L}_p$ of the Laplace type operators ${\cal L}_p, p=1,2$, acting in irreducible rank 1 symmetric spaces of non-compact type. The explicit form of the zeta functions and the conformal anomaly of the stress-energy momentum tensor is derived.Comment: 10 pages, LaTe

Constraints on the duality relation from ACT cluster data

The cosmic distance-duality relation (CDDR), $d_L(z) (1 + z)^{2}/d_{A}(z) = \eta$, where $\eta = 1$ and $d_L(z)$ and $d_A(z)$ are, respectively, the luminosity and the angular diameter distances, holds as long as the number of photons is conserved and gravity is described by a metric theory. Testing such hypotheses is, therefore, an important task for both cosmology and fundamental physics. In this paper we use 91 measurements of the gas mass fraction of galaxy clusters recently reported by the Atacama Cosmology Telescope (ACT) survey along with type Ia supernovae observations of the Union2.1 compilation to probe a possible deviation from the value $\eta = 1$. Although in agreement with the standard hyphothesis, we find that this combination of data tends to favor negative values of $\eta$ which might be associated with some physical processes increasing the number of photons and modifying the above relation to $d_L < (1+z)^2d_A$.Comment: 4 pages, 2 figures, 2 table

Forms on Vector Bundles Over Compact Real Hyperbolic Manifolds

We study gauge theories based on abelian $p-$ forms on real compact hyperbolic manifolds. The tensor kernel trace formula and the spectral functions associated with free generalized gauge fields are analyzed.Comment: Int. Journ. Modern Physics A, vol. 18 (2003), 2041-205

On Useful Conformal Tranformations In General Relativity

Local conformal transformations are known as a useful tool in various applications of the gravitational theory, especially in cosmology. We describe some new aspects of these transformations, in particular using them for derivation of Einstein equations for the cosmological and Schwarzschild metrics. Furthermore, the conformal transformation is applied for the dimensional reduction of the Gauss-Bonnet topological invariant in $d=4$ to the spaces of lower dimensions.Comment: 17 pages, LaTeX. The paper is intended mainly for pedagogical purposes and represents a collection of exercises concerning local conformal transformations and dimensional reduction. To be published in "Gravitation and Cosmology

The anisotropic XY model on the inhomogeneous periodic chain

The static and dynamic properties of the anisotropic XY-model $(s=1/2)$ on the inhomogeneous periodic chain, composed of $N$ cells with $n$ different exchange interactions and magnetic moments, in a transverse field $h,$ are determined exactly at arbitrary temperatures. The properties are obtained by introducing the Jordan-Wigner fermionization and by reducing the problem to a diagonalization of a finite matrix of $nth$ order. The quantum transitions are determined exactly by analyzing, as a function of the field, the induced magnetization 1/n\sum_{m=1}^{n}\mu_{m}\left ($j$ denotes the cell, $m$ the site within the cell, $\mu_{m}$ the magnetic moment at site $m$ within the cell) and the spontaneous magnetization $1/n\sum_{m=1}^{n}\left< S_{j,m}^{x},\right>$ which is obtained from the correlations $\left< S_{j,m}^{x}S_{j+r,m}^{x}\right>$ for large spin separations. These results, which are obtained for infinite chains, correspond to an extension of the ones obtained by Tong and Zhong(\textit{Physica B} \textbf{304,}91 (2001)). The dynamic correlations, $\left< S_{j,m}^{z}(t)S_{j^{\prime},m^{\prime}}^{z}(0)\right>$, and the dynamic susceptibility, $\chi_{q}^{zz}(\omega),$ are also obtained at arbitrary temperatures. Explicit results are presented in the limit T=0, where the critical behaviour occurs, for the static susceptibility $\chi_{q}^{zz}(0)$ as a function of the transverse field $h$, and for the frequency dependency of dynamic susceptibility $\chi_{q}^{zz}(\omega)$.Comment: 33 pages, 13 figures, 01 table. Revised version (minor corrections) accepted for publiction in Phys. Rev.

Femtocell deployment in LTE-A networks: A sustainability, economical and capacity analysis

Increasingly mobile data traffic and high quality service demand has driven standard developments and new mobile technologies deployment at an unprecedented level. Long Term Evolution (LTE) standard and its improved version LTE-Advanced (LTE-A) are two technology standards developed to cope with high levels of mobile data traffic demand. However, traffic and revenue disparity still is a reality, suggesting that traditional network deployment methods - based mainly on macro cellular sites - might prove to be cost ineffective in the long term. From another perspective, and increasingly important for mobile network operators, revenue is also a function of each mobile network deployment's sustainability. This work aims to comprehensively elaborate on those matters by presenting four specific scenarios with a comparative analysis of both macro and femtocell deployments (single and both technology networks). For each scenario, capacity, cost effectiveness and expected carbon emissions are the evaluated key indicators. This kind of analysis provides mobile networks operators with relevant information, enabling them to sustainably adapt business and provisioning models as well as network deployment strategies to current and future technological standards, while minimizing capital and operational expenditure (CAPEX/OPEX). The main contribution is that in short term, mixed macro and femtocell deployment scenarios are the most cost effective and sustainable option, while in mid to long term, as data traffic demand rises, femtocell deployments become the most sustainable, not only from economical and environmental points of view, but also from network coverage stand point.info:eu-repo/semantics/acceptedVersio

Economic and environmental comparative analysis on macro-femtocell deployments in LTE-A

This paper describes the economic and environmental comparative analysis performed on macro and femtocell deployments and most prevalent results obtained. Four specific scenarios are studied and, for each one, an evaluation is made in terms of capacity, cost effectiveness and expected carbon emissions. It provides mobile networks operators (MNO) with relevant information, enabling them to adapt business models and deployment approaches to current and future trends in a sustainable way, while minimizing capital (CAPEX) and operation expenses (OPEX).info:eu-repo/semantics/acceptedVersio

Hybrid Model For Word Prediction Using Naive Bayes and Latent Information

Historically, the Natural Language Processing area has been given too much attention by many researchers. One of the main motivation beyond this interest is related to the word prediction problem, which states that given a set words in a sentence, one can recommend the next word. In literature, this problem is solved by methods based on syntactic or semantic analysis. Solely, each of these analysis cannot achieve practical results for end-user applications. For instance, the Latent Semantic Analysis can handle semantic features of text, but cannot suggest words considering syntactical rules. On the other hand, there are models that treat both methods together and achieve state-of-the-art results, e.g. Deep Learning. These models can demand high computational effort, which can make the model infeasible for certain types of applications. With the advance of the technology and mathematical models, it is possible to develop faster systems with more accuracy. This work proposes a hybrid word suggestion model, based on Naive Bayes and Latent Semantic Analysis, considering neighbouring words around unfilled gaps. Results show that this model could achieve 44.2% of accuracy in the MSR Sentence Completion Challenge