Eisenstein Series and String Thresholds

We investigate the relevance of Eisenstein series for representing certain $G(Z)$-invariant string theory amplitudes which receive corrections from BPS states only. $G(Z)$ may stand for any of the mapping class, T-duality and U-duality groups $Sl(d,Z)$, $SO(d,d,Z)$ or $E_{d+1(d+1)}(Z)$ respectively. Using $G(Z)$-invariant mass formulae, we construct invariant modular functions on the symmetric space $K\backslash G(R)$ of non-compact type, with $K$ the maximal compact subgroup of $G(R)$, that generalize the standard non-holomorphic Eisenstein series arising in harmonic analysis on the fundamental domain of the Poincar\'e upper half-plane. Comparing the asymptotics and eigenvalues of the Eisenstein series under second order differential operators with quantities arising in one- and $g$-loop string amplitudes, we obtain a manifestly T-duality invariant representation of the latter, conjecture their non-perturbative U-duality invariant extension, and analyze the resulting non-perturbative effects. This includes the $R^4$ and $R^4 H^{4g-4}$ couplings in toroidal compactifications of M-theory to any dimension $D\geq 4$ and $D\geq 6$ respectively.Comment: Latex2e, 60 pages; v2: Appendix A.4 extended, 2 refs added, thms renumbered, plus minor corrections; v3: relation (1.7) to math Eis series clarified, eq (3.3) and minor typos corrected, final version to appear in Comm. Math. Phys; v4: misprints and Eq C.13,C.24 corrected, see note adde

The Network of Epicenters of the Olami-Feder-Christensen Model of Earthquakes

We study the dynamics of the Olami-Feder-Christensen (OFC) model of earthquakes, focusing on the behavior of sequences of epicenters regarded as a growing complex network. Besides making a detailed and quantitative study of the effects of the borders (the occurrence of epicenters is dominated by a strong border effect which does not scale with system size), we examine the degree distribution and the degree correlation of the graph. We detect sharp differences between the conservative and nonconservative regimes of the model. Removing border effects, the conservative regime exhibits a Poisson-like degree statistics and is uncorrelated, while the nonconservative has a broad power-law-like distribution of degrees (if the smallest events are ignored), which reproduces the observed behavior of real earthquakes. In this regime the graph has also a unusually strong degree correlation among the vertices with higher degree, which is the result of the existence of temporary attractors for the dynamics: as the system evolves, the epicenters concentrate increasingly on fewer sites, exhibiting strong synchronization, but eventually spread again over the lattice after a series of sufficiently large earthquakes. We propose an analytical description of the dynamics of this growing network, considering a Markov process network with hidden variables, which is able to account for the mentioned properties.Comment: 9 pages, 10 figures. Smaller number of figures, and minor text corrections and modifications. For version with full resolution images see http://fig.if.usp.br/~tpeixoto/cond-mat-0602244.pd

Disease Localization in Multilayer Networks

We present a continuous formulation of epidemic spreading on multilayer networks using a tensorial representation, extending the models of monoplex networks to this context. We derive analytical expressions for the epidemic threshold of the SIS and SIR dynamics, as well as upper and lower bounds for the disease prevalence in the steady state for the SIS scenario. Using the quasi-stationary state method we numerically show the existence of disease localization and the emergence of two or more susceptibility peaks, which are characterized analytically and numerically through the inverse participation ratio. Furthermore, when mapping the critical dynamics to an eigenvalue problem, we observe a characteristic transition in the eigenvalue spectra of the supra-contact tensor as a function of the ratio of two spreading rates: if the rate at which the disease spreads within a layer is comparable to the spreading rate across layers, the individual spectra of each layer merge with the coupling between layers. Finally, we verified the barrier effect, i.e., for three-layer configuration, when the layer with the largest eigenvalue is located at the center of the line, it can effectively act as a barrier to the disease. The formalism introduced here provides a unifying mathematical approach to disease contagion in multiplex systems opening new possibilities for the study of spreading processes.Comment: Revised version. 25 pages and 18 figure

A new approach to implement a customized anatomic insole in orthopaedic footwear of lower limb orthosis

This paper concerns the development of a new approach for orthopaedic footwear to apply in KAFO orthosis (acronym for Knee Ankle Foot Orthosis). This procedure starts with full characterization of the problem with the purpose to characterize a plantar of a patient’s foot with polio. A 3D Scanner was used to collect their feet's data to produce an anatomic insole. After this step, the patient performs a study of his gait using a static and dynamic study with the aim of characterizing the parameters to improve quality in the footwear. The insole was produced using a 3D printing technology. It was essential to optimize manufacturing processes and it was developed a footwear prototype with innovative characteristics, which is 25% lighter, allowing the user to consume less energy in daily routines.This work is supported by FEDER funding on the COMPETE program and by national funds through FCT-Foundation for Science and Technology within the scope of the project POCI-01-0145-FEDER- 007136 and UID/CTM/00264.info:eu-repo/semantics/publishedVersio

Caracterização de abóboras quanto aos teores carotenóides totais, alfa e beta-caroteno.

Esse trabalho teve como objetivo caracterizar variedades locais de abóboras de diferentes origens para os teores de carotenóides totais, alfa e beta caroteno.bitstream/item/57215/1/BPD-78.pd

The effect of different remineralizing agents on caries-like lesions – a pilot study

Poster apresentado no XXV Congresso da Ordem dos Médicos Dentistas, 10-12 Novembro 2016, Porto, PortugalSob uma licença CC-BY-NC - http://creativecommons.org/licenses/by-nc/4.0/Aim: To quantify the surface microhardness of enamel when using different remineralizing agents, after the induction of artificial dental caries.N/