A note on the heat kernel method applied to fermions

The spectrum of the fermionic operators depending on external fields is an important object in Quantum Field Theory. In this paper we prove, using transition to the alternative basis for the $\gamma$-matrices, that this spectrum does not depend on the sign of the fermion mass, up to a constant factor. This assumption has been extensively used, but usually without proof. As an illustration, we calculated the coincidence limit of the coefficient $a_2(x,x^\prime)$ on the general metric background, vector and axial vector fields.Comment: 5 pages, LaTeX, no figures. Revised versio

Emergence of robustness against noise: A structural phase transition in evolved models of gene regulatory networks

We investigate the evolution of Boolean networks subject to a selective pressure which favors robustness against noise, as a model of evolved genetic regulatory systems. By mapping the evolutionary process into a statistical ensemble and minimizing its associated free energy, we find the structural properties which emerge as the selective pressure is increased and identify a phase transition from a random topology to a "segregated core" structure, where a smaller and more densely connected subset of the nodes is responsible for most of the regulation in the network. This segregated structure is very similar qualitatively to what is found in gene regulatory networks, where only a much smaller subset of genes --- those responsible for transcription factors --- is responsible for global regulation. We obtain the full phase diagram of the evolutionary process as a function of selective pressure and the average number of inputs per node. We compare the theoretical predictions with Monte Carlo simulations of evolved networks and with empirical data for Saccharomyces cerevisiae and Escherichia coli.Comment: 12 pages, 10 figure

Emotional distress in Angolan patients with several types of tuberculosis

Background: There is growing evidence that emotional distress expressed in terms of anxiety and depression is very high among tuberculosis (TB) patients.Objectives: This study aims to determine levels of anxiety, depression and emotional distress in patients with several types of TB and to determine the association between social-demographic and economical factors, clinical variables and anxiety, depression and emotional distress.Methods: A cross-sectional study was performed in a sample of 81 TB patients. A social-demographic and economical questionnaire was used, followed by the hospital anxiety and depression scale.Results: 38.3% and 49.4% of our sample presented significant levels of anxiety and depression. 44.4% of patients had significant levels of emotional distress.Married subjects, a diagnosis of extra-pulmonary TB and multidrug resistant TB were related to higher risk for anxiety. Gender, extra-pulmonary and multidrug resistant TB were associated to depression. Female gender and cases of extra-pulmonary TB presented a 1.5 times risk for emotional distress.Conclusions: Our study found high rates of anxiety, depression and emotional distress among TB patients. Marital status, gender, type and treatment of TB were related to higher levels of emotional disorder. Mental health services should be an integral part of programs against tuberculosis.Keywords: Anxiety, Depression, Common Mental Disorders, Mycobacterium tuberculosis, Miliary Tuberculosis, Pulmonary Tuberculosis, Pott's Disease, Huambo

Boolean networks with reliable dynamics

We investigated the properties of Boolean networks that follow a given reliable trajectory in state space. A reliable trajectory is defined as a sequence of states which is independent of the order in which the nodes are updated. We explored numerically the topology, the update functions, and the state space structure of these networks, which we constructed using a minimum number of links and the simplest update functions. We found that the clustering coefficient is larger than in random networks, and that the probability distribution of three-node motifs is similar to that found in gene regulation networks. Among the update functions, only a subset of all possible functions occur, and they can be classified according to their probability. More homogeneous functions occur more often, leading to a dominance of canalyzing functions. Finally, we studied the entire state space of the networks. We observed that with increasing systems size, fixed points become more dominant, moving the networks close to the frozen phase.Comment: 11 Pages, 15 figure

SOLUTION OF 1D AND 2D POISSON'S EQUATION BY USING WAVELET SCALING FUNCTIONS

The use of multiresolution techniques and wavelets has become increasingly popular in the development of numerical schemes for the solution of partial differential equations (PDEs). Therefore, the use of wavelet scaling functions as a basis in computational analysis holds some promise due to their compact support, orthogonality and localization properties. Daubechies and Deslauriers-Dubuc functions have been successfully used as basis functions in several schemes like the Wavelet- Galerkin Method (WGM) and the Wavelet Finite Element Method (WFEM). Another possible advantage of their use is the fact that the calculation of integrals of inner products of wavelet scaling functions and their derivatives can be made by solving a linear system of equations, thus avoiding the problem of using approximations by some numerical method. These inner products were defined as connection coefficients and they are employed in the calculation of stiffness matrices and load vectors. In this work, some mathematical foundations regarding wavelet scaling functions, their derivatives and connection coefficients are reviewed. A scheme based on the Galerkin Method is proposed for the direct solution of Poisson's equation (potential problems) in a meshless formulation using interpolating wavelet scaling functions (Interpolets). The applicability of the proposed method and some convergence issues are illustrated by means of a few examples

Beyond spatial scalability limitations with a massively parallel method for linear oscillatory problems

This is the author accepted manuscript. The final version is available from SAGE Publications via the DOI in this record.This paper presents, discusses and analyses a massively parallel-in-time solver for linear oscillatory PDEs, which is a key numerical component for evolving weather, ocean, climate and seismic models. The time parallelization in this solver allows us to significantly exceed the computing resources used by parallelization-in-space methods and results in a correspondingly significantly reduced wall-clock time. One of the major difficulties of achieving Exascale performance for weather prediction is that the strong scaling limit – the parallel performance for a fixed problem size with an increasing number of processors – saturates. A main avenue to circumvent this problem is to introduce new numerical techniques that take advantage of time parallelism. In this paper we use a time-parallel approximation that retains the frequency information of oscillatory problems. This approximation is based on (a) reformulating the original problem into a large set of independent terms and (b) solving each of these terms independently of each other which can now be accomplished on a large number of HPC resources. Our results are conducted on up to 3586 cores for problem sizes with the parallelization-in-space scalability limited already on a single node. We gain significant reductions in the time-to-solution of 118.3 for spectral methods and 1503.0 for finite-difference methods with the parallelizationin-time approach. A developed and calibrated performance model gives the scalability limitations a-priory for this new approach and allows us to extrapolate the performance method towards large-scale system. This work has the potential to contribute as a basic building block of parallelization-in-time approaches, with possible major implications in applied areas modelling oscillatory dominated problems.The authors gratefully acknowledge the Gauss Centre for Supercomputing e.V. (www.gauss-centre.eu) for funding this project by providing computing time on the GCS Supercomputer SuperMUC at Leibniz Supercomputing Centre (LRZ, www.lrz. de). We also acknowledge use of Hartree Centre resources in this work on which the early evaluation of the parallelization concepts were done

Superdiffusion of massive particles induced by multi-scale velocity fields

We study drag-induced diffusion of massive particles in scale-free velocity fields, where superdiffusive behavior emerges due to the scale-free size distribution of the vortices of the underlying velocity field. The results show qualitative resemblance to what is observed in fluid systems, namely the diffusive exponent for the mean square separation of pairs of particles and the preferential concentration of the particles, both as a function of the response time.Comment: 5 pages, 5 figures. Accepted for publication in EP

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

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