A formula for the trace of symmetric powers of matrices

We present a formula for the trace of any symmetric power of a $n\times n$ matrix (with coefficients in a field) in terms of the ordinary powers of the matrix, an arbitrarily chosen linear function which vanishes on the identity matrix, and $n-2$ polynomial functions defined recursively

Um olhar sobre a Cooperação Sul-Sul em Saúde

O artigo apresenta uma breve revisão sobre o significado da cooperação técnica no seio da ONU, ressaltando a dimensão política, isto é, das relações entre os Estados. Destaca a importância da saúde nesse contexto, tomando como referências a situação das Américas e do Brasil. Analisa uma experiência, na área da saúde, ilustrativa do novo paradigma denominado de Cooperação Sul-Sul, ressaltando a triangulação de uma agência intergovernamental. Conclui resumindo os argumentos que situam um determinado processo de cooperação internacional no marco desse paradigma

Construct by Contract: Construct by Contract: An Approach for Developing Reliable Software

This research introduces “Construct by Contract” as a proposal for a general methodology to develop dependable software systems. It describes an ideal process to construct systems by propagating requirements as contracts from the client’s desires to the correctness proof in verification stage, especially in everyday-used software like web applications, mobile applications and desktop application. Such methodology can be converted in a single integrated workspace as standalone tool to develop software. To achieve the already mentioned goal, this methodology puts together a collection of software engineering tools and techniques used throughout the software’s lifecycle, from requirements gathering to the testing phase, in order to ensure a contract-based flow. Construct by Contract is inclusive, regarding the roles of the people involved in the software construction process, including for instance customers, users, project managers, designers, developers and testers, all of them interacting in one common software development environment, sharing information in an understandable presentation according to each stage. It is worth to mention that we focus on the verification phase, as the key to achieve the reliability sought. Although at this point, we only completed the definition and the specification of this methodology, we evaluate the implementation by analysing, measuring and comparing different existing tools that could fit at any of the stages of software’s lifecycle, and that could be applied into a piece of commercial software. These insights are provided in a proof of concept case study, involving a productive Java Web application using struts framework

Propiedades ópticas y eléctricas de nanopartículas de sulfuro de cobre estabilizadas con ditiocarbamatos de cadena larga

En el documento se presentan los resultados de la preparación de nanoparticulas de sulfuro de cobre estabilizadas con DTC, su estudio de obtención, asi como caracterizaciones espectroscopicas y por microscopia para su identificacion. Se presenta tambien su estudio de las porpiedades opticas y termicas.In the present project copper sulfide nanoparticles were prepared by a chemical reaction between copper (II) complexes of long chained n-alkyldithiocarbamate (6, 12 and 18 carbon atoms) and sodium borohydride. The nanoparticles were characterized by infrared spectroscopy, X-ray powder diffraction, scanning electron microscopy, transmission electron microscopy, termogravimetric analysis and differential scanning calorimetry. In addition, the samples were characterized by diffuse reflectance spectroscopy in order to calculate the optical band gap energy of every case using the Kubelka-Munk theory. The results obtained demonstrate that the nanoparticles size average is around 10.0 nm distributed throughout the dithiocarbamate matrix. These particles present three different copper sulfide phases (covellite, digenite and chalcocite). Finally, the optical band gap energy is 3.4 eV in average

When and How to Fool Explainable Models (and Humans) with Adversarial Examples

Reliable deployment of machine learning models such as neural networks continues to be challenging due to several limitations. Some of the main shortcomings are the lack of interpretability and the lack of robustness against adversarial examples or out-of-distribution inputs. In this paper, we explore the possibilities and limits of adversarial attacks for explainable machine learning models. First, we extend the notion of adversarial examples to fit in explainable machine learning scenarios, in which the inputs, the output classifications and the explanations of the model's decisions are assessed by humans. Next, we propose a comprehensive framework to study whether (and how) adversarial examples can be generated for explainable models under human assessment, introducing novel attack paradigms. In particular, our framework considers a wide range of relevant (yet often ignored) factors such as the type of problem, the user expertise or the objective of the explanations in order to identify the attack strategies that should be adopted in each scenario to successfully deceive the model (and the human). These contributions intend to serve as a basis for a more rigorous and realistic study of adversarial examples in the field of explainable machine learning.Comment: 12 pages, 1 figur

Extending Adversarial Attacks to Produce Adversarial Class Probability Distributions

Despite the remarkable performance and generalization levels of deep learning models in a wide range of artificial intelligence tasks, it has been demonstrated that these models can be easily fooled by the addition of imperceptible but malicious perturbations to natural inputs. These altered inputs are known in the literature as adversarial examples. In this paper we propose a novel probabilistic framework to generalize and extend adversarial attacks in order to produce a desired probability distribution for the classes when we apply the attack method to a large number of inputs. This novel attack strategy provides the attacker with greater control over the target model, and increases the complexity of detecting that the model is being attacked. We introduce three different strategies to efficiently generate such attacks, and illustrate our approach extending DeepFool, a state-of-the-art attack algorithm to generate adversarial examples. We also experimentally validate our approach for the spoken command classification task, an exemplary machine learning problem in the audio domain. Our results demonstrate that we can closely approximate any probability distribution for the classes while maintaining a high fooling rate and by injecting imperceptible perturbations to the inputs.Comment: 13 pages, 7 figures, 2 tables, 2 algorithm