Artigos - Matemática e Computação - FCT

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  • ItemTrabalho apresentado em evento
    Analyzing Accessibility Reviews Associated with Visual Disabilities or Eye Conditions
    (2023-04-19) Oliveira, Alberto Dumont Alves; Dos Santos, Paulo Sérgio Henrique; Marcílio, Wilson Estécio [UNESP]; Aljedaani, Wajdi M.; Eler, Danilo Medeiros [UNESP]; Eler, Marcelo Medeiros; Universidade de São Paulo (USP); Universidade Estadual Paulista (UNESP); University of North Texas
    Accessibility reviews collected from app stores may contain valuable information for improving apps accessibility. Recent studies have presented insightful information on accessibility reviews, but they were based on small datasets and focused on general accessibility concerns. In this paper, we analyzed accessibility reviews that report issues affecting users with visual disabilities or conditions. Such reviews were identified based on selection criteria applied over 179,519,598 reviews of popular apps on the Google Play Store. Our results show that only 0,003% of user reviews mention visual disabilities or conditions; accessibility reviews are associated with 36 visual disabilities or eye conditions; many users do not give precise feedback and refer to their disability using generic terms; accessibility reviews can be grouped into general topics of concerns related to different types of disabilities; and positive reviews are generally associated with high scores and negative feedback with lower scores.
  • ItemArtigo
    A Cubic Memristive System with Two Twin Rössler-Type Chaotic Attractors Symmetrical About an Invariant Plane
    (2022-10-01) Messias, Marcelo [UNESP]; Meneguette, Messias [UNESP]; De Carvalho Reinol, Alisson; Gokyildirim, Abdullah; Akgül, Akif; Universidade Estadual Paulista (UNESP); Federal University of Technology - Paraná (UTFPR); Bandirma Onyedi Eylul University; Hitit University
    Memristive circuits and systems have been widely studied in the last years due to their potential applications in several technological areas. They are capable of producing nonlinear periodic and chaotic oscillations, due to their locally-active characteristics. In this paper, we consider a cubic four-parameter differential system which models a memristive circuit consisting of three elements: a passive linear inductor, a passive linear capacitor and a locally-active current-controlled generic memristor. This system has a saddle-focus equilibrium point at the origin, whose global stable and unstable manifolds are, respectively, the x-axis and the plane x = 0, which are invariant sets where the dynamic is linear. We show that this structure can generate two twin Rössler-type chaotic attractors symmetrical with respect to the plane x = 0. We describe the mechanism of creation of these chaotic attractors, showing that, although being similar to the Rössler attractor, the twin attractors presented here have simpler structural mechanism of formation, since the system has no homoclinic or heteroclinic orbits to the saddle-focus, as presented by the Rössler system. The studied memristive system has the rare property of having chaotic dynamics and an invariant plane with linear dynamic, which is quite different from other chaotic systems presented in the literature that have invariant surfaces filled by equilibrium points. We also present and discuss the electronic circuit implementation of the considered system and study its dynamics at infinity, via the Poincaré compactification, showing that all the solutions, except the ones contained in the plane x = 0, are bounded and cannot escape to infinity.
  • ItemArtigo
    Mathematical modeling for drug delivery and inflammation process: An application in macular edema
    (2023-09-01) Gonçalves, M. B.; Gudiño, E.; Maia, M.; Oishi, C. M. [UNESP]; Universidade Federal do Paraná (UFPR); Universidade Federal de São Paulo (UNIFESP); Universidade Estadual Paulista (UNESP)
    In this paper, we introduce a mathematical model for the drug release from an intravitreal implant and the subsequent effect of the drug on the inflammation process of macular edema. Coupling the drug transport problem with the growth of the edema, we compare the numerical simulations with patient-specific medical images. We fit the model with respect to one parameter and match the retinal thickness observed in the patient. After the validation of the proposed model, we perform numerical experiments regarding patient-specific treatments. In particular, we analyze the drug concentration in the different sub-domains (e.g., the implant and the retina) and simulate the scenario of edema recurrence and implant re-injection. The proposed mathematical model has the potential to provide important insights into the use of intravitreal dexamethasone implants and the treatment of macular edema.
  • ItemArtigo
    Effects of anisotropy on the stability of Giesekus fluid flow
    (2022-12-01) Furlan, L. J.S.; Araujo, M. T.; Mendonca, M. T.; Brandi, A. C. [UNESP]; Souza, L. F.; Universidade de São Paulo (USP); National Institute for Space Research; Universidade Estadual Paulista (UNESP)
    In the present work, the stability of a viscoelastic fluid flow is studied by linear stability theory, and some results are verified by direct numerical simulation. The investigation considers the fluid flow between two parallel plates, modeled by the Giesekus constitutive equation. The results show the influence of the anisotropic tensorial correction parameter αG on this model, showing a stabilizing influence for two-dimensional disturbances for small values of αG. However, as αG increases, a reduction in the critical Reynolds number values is observed, possibly hastening the transition to turbulence. Low values for αG for three-dimensional disturbances cause more significant variations for the critical Reynolds number. This variation decreases as the value of this parameter increases. The results also show that low values of αG increase the instability of three-dimensional disturbances and confirm that Squire's theorem is not valid for this model. As for the two-dimensional disturbances, the anisotropic term on the Giesekus model lowers the critical Reynolds number for higher quantities of polymer viscosity in the mixture and high values for the Weissenberg number.
  • ItemArtigo
    Numerical verification of sharp corner behavior for Giesekus and Phan-Thien-Tanner fluids
    (2022-11-01) Evans, J. D.; Palhares Junior, I. L.; Oishi, C. M. [UNESP]; Ruano Neto, F.; University of Bath; Universidade Federal Do Rio Grande Do Norte; Universidade Estadual Paulista (UNESP); Universidade de São Paulo (USP)
    We verify numerically the theoretical stress singularities for two viscoelastic models that occur at sharp corners. The models considered are the Giesekus and Phan-Thien-Tanner (PTT), both of which are shear thinning and are able to capture realistic polymer behaviors. The theoretical asymptotic behavior of these two models at sharp corners has previously been found to involve an integrable solvent and polymer elastic stress singularity, along with narrow elastic stress boundary layers at the walls of the corner. We demonstrate here the validity of these theoretical results through numerical simulation of the classical contraction flow and analyzing the 270 ° corner. Numerical results are presented, verifying both the solvent and polymer stress singularities, as well as the dominant terms in the constitutive equations supporting the elastic boundary layer structures. For comparison at Weissenberg order one, we consider both the Cartesian stress formulation and the alternative natural stress formulation of the viscoelastic constitutive equations. Numerically, it is shown that the natural stress formulation gives increased accuracy and convergence behavior at the stress singularity and, moreover, encounters no upper Weissenberg number limitation in the global flow simulation for sufficiently large solvent viscosity fraction. The numerical simulations with the Cartesian stress formulation cannot reach such high Weissenberg numbers and run into convergence failure associated with the so-called high Weissenberg number problem.
  • ItemArtigo
    On a quasilinear elliptic problem involving the 1-Laplacian operator and a discontinuous nonlinearity
    (Cambridge Univ Press, 2022-12-28) Pimenta, Marcos T. O. [UNESP]; Santos, Gelson Conceicao G. dos; Santos Junior, Joao R.; Universidade Estadual Paulista (UNESP); Univ Fed Para
    In this work, we study a quasilinear elliptic problem involving the 1-Laplacian operator, with a discontinuous, superlinear and subcritical nonlinearity involving the Heaviside function H(middot - beta). Our approach is based on an analysis of the associated p-Laplacian problem, followed by a thorough analysis of the asymptotic behaviour or such solutions as p -> 1(+). We study also the asymptotic behaviour of the solutions, as beta -> 0(+) and we prove that it converges to a solution of the original problem, without the discontinuity in the nonlinearity.
  • ItemTrabalho apresentado em evento
    Fireasy: a tool to aid security policy modeling, translation and understanding firewall configuration
    (Ieee, 2022-01-01) Marinho Queiroz, Leandro Meira [UNESP]; Garcia, Rogerio Eduardo [UNESP]; Eler, Danilo Medeiros [UNESP]; Messias Correia, Ronaldo Celso [UNESP]; Rocha, A.; Bordel, B.; Penalvo, F. G.; Goncalves, R.; Universidade Estadual Paulista (UNESP)
    Companies store increasing amounts of data, requiring the implementation of mechanisms to protect them from malicious people. There are techniques and procedures that aim to increase the security of computer systems, such as network protection services, firewalls. They are intended to filter packets that enter and leave a network. Its settings depend on security policies, which consist of documents that describe what is allowed to travel on the network and what is prohibited. The transcription of security policies into rules, written in native firewall language, that represent them, is the main source of errors in firewall configurations. In this work, concepts related to security between networks and firewalls are presented. Related works on security policies and their translations into firewall rules are also referenced. Furthermore, the developed tool, named Fireasy, is presented, which allows the modeling of security policies through graphic elements, and the maintenance of rules written in native firewall language, also representing them in graphic elements. Finally, a controlled experiment was conducted to validate the approach, which indicated, in addition to the correct functioning of the tool, an improvement in the translation of security policies into firewall rules using the tool. In the task of understanding firewall rules, there was a homogenization of the participants' performance when they used the tool.
  • ItemArtigo
    A Memetic Framework for Solving the Lot Sizing and Scheduling Problem in Soft Drink Plants
    (Springer, 2012-01-01) Toledo, Claudio F. M.; Arantes, Marcio S.; Franca, Paulo M. [UNESP]; Morabito, Reinaldo; Chiong, R.; Weise, T.; Michalewicz, Z.; Universidade de São Paulo (USP); Univ Lavras; Universidade Estadual Paulista (UNESP); Universidade Federal de São Carlos (UFSCar)
    This chapter presents a memetic framework for solving the Synchronized and Integrated Two-level Lot Sizing and Scheduling Problem (SITLSP). A set of algorithms from this framework is thoroughly evaluated. The SITLSP is a real-world problem typically found in soft drink plants, but its presence can also be seen in many other multi-level production processes. The SITLSP involves a two-level production process where lot sizing and scheduling decisions have to be made for raw material storage in tanks and soft drink bottling in various production lines. The work presented here extends a previously proposed memetic computing approach that combines a multi-population genetic algorithm with a threshold accepting heuristic. The novelty and its main contribution is the use of tabu search combined with the multi-population genetic algorithm as a method to solve the SITLSP. Two real-world problem sets, both provided by a leading market soft drink company, have been used for the computational experiments. The results show that the memetic algorithms proposed significantly outperform the previously reported solutions used for comparison.
  • ItemArtigo
    Heuristics and meta-heuristics for lot sizing and scheduling in the soft drinks industry: a comparison study
    (Springer, 2008-01-01) Ferreira, D.; Franca, P. M. [UNESP]; Kimms, A.; Morabito, R.; Rangel, S. [UNESP]; Toledo, C. F. M.; Xhafa, F; Abraham, A; Universidade Federal de São Carlos (UFSCar); Universidade Estadual Paulista (UNESP); Univ Duisburg Essen; Universidade Federal de Lavras (UFLA)
    This chapter studies a two-level production planning problem where, on each level, a lot sizing and scheduling problem with parallel machines, capacity constraints and sequence-dependent setup costs and times must be solved. The problem can be found in soft drink companies where the production process involves two interdependent levels with decisions concerning raw material storage and soft drink bottling. Models and solution approaches proposed so far are surveyed and conceptually compared. Two different approaches have been selected to perform a series of computational comparisons: an evolutionary technique comprising a genetic algorithm and its memetic version, and a decomposition and relaxation approach.
  • ItemArtigo
    Periodic Orbits in the Muthuswamy-Chua Simplest Chaotic Circuit
    (2022-01-01) Messias, Marcelo [UNESP]; Reinol, Alisson C.; Universidade Estadual Paulista (UNESP); Federal University of Technology - Paraná (UTFPR)
    In 2010, Muthuswamy and Chua presented an autonomous chaotic circuit using only three elements in series: an inductor, a capacitor and a memristor. This circuit is known as the simplest chaotic circuit and it is determined by a three-dimensional differential system, which depends on the real parameters C, L, α and β. Although the Muthuswamy-Chua system is simpler in formulation than other chaotic systems, its dynamics has proven to be complicated. Here we analytically prove the existence of periodic orbits in this system for suitable choice of the parameter values α and β leading to interesting phenomena as multistability and formation of chaotic attractors. In order to do that, we consider the existence of first integrals, invariant algebraic surfaces and a result from averaging theory. In addition, we relate the obtained results to the memristance and to the physical characteristics of the memristor.
  • ItemCapítulo de livro
    New solutions and methodologies for data acquisition and management in small municipalities
    (2021-04-09) Juliao, Rui Pedro; Amorim, Amilton [UNESP]; Hespanha, João Paulo; de Souza, Guilherme Henrique Barros [UNESP]; Correia, Ronaldo Celso Messias [UNESP]; Destro, Rafael Delli Colli [UNESP]; Universidade NOVA de Lisboa; Universidade Estadual Paulista (UNESP); Universidade de Aveiro
    Promoting and managing sustainable territorial development require adequate tools that enable territorial managers to formulate appropriate choices. Technological solutions have emerged, and the paradigm has shifted from isolated GIS to a more collaborative production and dissemination of geographic data using spatial data infrastructures (SDI). A critical dataset for municipal land administration is cadastre. ISO 19152 standard of the Land Administration Domain Model (LADM) was published in 2012. Also, technology evolution, namely unmanned aerial vehicles (UAV), has changed data acquisition for cadastre. These are three pillars of modern territorial management: openness, co-production, and data sharing (SDI); models (LADM); affordable technology (UAV). This chapter presents how municipalities can develop an SDI project, incorporating LADM guidelines and UAV data acquisition. The case study is based on a group of 32 small municipalities from São Paulo state, in Brazil, known as UNIPONTAL.
  • ItemTrabalho apresentado em evento
    Fireasy: a tool to aid security policy modeling, translation and understanding firewall configuration
    (2022-01-01) Marinho Queiróz, Leandro Meira [UNESP]; Garcia, Rogério Eduardo [UNESP]; Eler, Danilo Medeiros [UNESP]; Messias Correia, Ronaldo Celso [UNESP]; Universidade Estadual Paulista (UNESP)
    Companies store increasing amounts of data, requiring the implementation of mechanisms to protect them from malicious people. There are techniques and procedures that aim to increase the security of computer systems, such as network protection services, firewalls. They are intended to filter packets that enter and leave a network. Its settings depend on security policies, which consist of documents that describe what is allowed to travel on the network and what is prohibited. The transcription of security policies into rules, written in native firewall language, that represent them, is the main source of errors in firewall configurations. In this work, concepts related to security between networks and firewalls are presented. Related works on security policies and their translations into firewall rules are also referenced. Furthermore, the developed tool, named Fireasy, is presented, which allows the modeling of security policies through graphic elements, and the maintenance of rules written in native firewall language, also representing them in graphic elements. Finally, a controlled experiment was conducted to validate the approach, which indicated, in addition to the correct functioning of the tool, an improvement in the translation of security policies into firewall rules using the tool. In the task of understanding firewall rules, there was a homogenization of the participants' performance when they used the tool.
  • ItemArtigo
    Nonchaotic Behavior and Transition to Chaos in Lorenz-like Systems Having Invariant Algebraic Surfaces
    (2022-03-01) Messias, Marcelo [UNESP]; Silva, Rafael Paulino [UNESP]; Universidade Estadual Paulista (UNESP)
    The famous and well-studied Lorenz system is considered a paradigm for chaotic behavior in three-dimensional continuous differential systems. After the appearance of such a system in 1963, several Lorenz-like chaotic systems have been proposed and studied in the related literature, as Rossler system, Chen- Ueta system, Rabinovich system, Rikitake system, among others. However, these systems are parameter dependent and are chaotic only for suitable combinations of parameter values. This raises the question of when such systems are not chaotic, which can be seen as a dual problem regarding chaotic systems. In this paper, we give sufficient algebraic conditions for a generalized class of Lorenz-like systems to be nonchaotic. Using the general results obtained, we give some examples of nonchaotic behavior of some classical chaotic Lorenz-like systems, including the Lorenz system itself. The nonchaotic differential systems presented here have invariant algebraic surfaces, which contain the stable (or unstable) invariant manifolds of their equilibrium points. We show that, in some cases, the deformation of these invariant manifolds through the destruction of the invariant algebraic surfaces, by perturbing the parameter values, can reorganize the global structure of the phase space, leading to a transition from nonchaotic to chaotic behavior of such differential systems.
  • ItemArtigo
    Symmetry and symmetry breaking for Hénon-type problems involving the 1-Laplacian operator
    (2022-01-01) Pimenta, Marcos T. O. [UNESP]; Gonzaga, Anderson dos Santos [UNESP]; Universidade Estadual Paulista (UNESP)
    In this work, we study a class of Hénon-type equations which involve the 1-Laplacian operator in the unit ball. Under mild assumptions on the nonlinearity, the existence of radial solutions is proved and, for a parameter in a certain range, the existence of symmetry breaking is proved, through the presence of non-radial solutions. The approach is based on an approximation scheme, where a thorough analysis of the solutions of the associated p-Laplacian problems is necessary.
  • ItemArtigo
    A Machine Learning Strategy Based on Kittler’s Taxonomy to Detect Anomalies and Recognize Contexts Applied to Monitor Water Bodies in Environments
    (2022-05-01) Dias, Maurício Araújo [UNESP]; Marinho, Giovanna Carreira [UNESP]; Negri, Rogério Galante [UNESP]; Casaca, Wallace [UNESP]; Muñoz, Ignácio Bravo; Eler, Danilo Medeiros [UNESP]; Universidade Estadual Paulista (UNESP); University of Alcalá (UAH)
    Environmental monitoring, such as analyses of water bodies to detect anomalies, is recog-nized worldwide as a task necessary to reduce the impacts arising from pollution. However, the large number of data available to be analyzed in different contexts, such as in an image time series acquired by satellites, still pose challenges for the detection of anomalies, even when using comput-ers. This study describes a machine learning strategy based on Kittler’s taxonomy to detect anomalies related to water pollution in an image time series. We propose this strategy to monitor environ-ments, detecting unexpected conditions that may occur (i.e., detecting outliers), and identifying those outliers in accordance with Kittler’s taxonomy (i.e., detecting anomalies). According to our strategy, contextual and non-contextual image classifications were semi-automatically compared to find any divergence that indicates the presence of one type of anomaly defined by the taxonomy. In our strategy, models built to classify a single image were used to classify an image time series due to domain adaptation. The results 99.07%, 99.99%, 99.07%, and 99.53% were achieved by our strat-egy, respectively, for accuracy, precision, recall, and F-measure. These results suggest that our strategy allows computers to recognize contexts and enhances their capabilities to solve contextualized problems. Therefore, our strategy can be used to guide computational systems to make different decisions to solve a problem in response to each context. The proposed strategy is relevant for im-proving machine learning, as its use allows computers to have a more organized learning process. Our strategy is presented with respect to its applicability to help monitor environmental disasters. A minor limitation was found in the results caused by the use of domain adaptation. This type of limitation is fairly common when using domain adaptation, and therefore has no significance. Even so, future work should investigate other techniques for transfer learning.
  • ItemArtigo
    Mid-reversibility properties of semigroup actions on homogeneous spaces
    (2022-06-01) Reis, Ronan A. [UNESP]; Martin, Luiz A. B. San; Rocha, Victor H. L. [UNESP]; Universidade Estadual Paulista (UNESP); Universidade Estadual de Campinas (UNICAMP)
    In this paper we study mid-reversibility of subsemigroups acting on homogeneous spaces. The mid-reversor set of a subsemigroup is defined and it is described in terms of the invariant control sets for semigroups acting on certain homogeneous spaces. Let G be a connected noncompact semi-simple Lie group and L a subgroup of G. Assume that S is a subsemigroup of G with nonempty interior. We characterize the mid-reversibility of the S-action on G/L in terms of the actions of S and L on the flag manifolds of G. We show that the mid-reversibility of S in G/L is related to the reversibility of S in G/L. We also present sufficient conditions for S to generate G if S is mid-reversible in G/L.
  • ItemArtigo
    Nodal Solutions to Quasilinear Elliptic Problems Involving the 1-Laplacian Operator via Variational and Approximation Methods
    (Indiana Univ Math Journal, 2022-01-01) Figueiredo, Giovany M.; Pimenta, Marcos T. O. [UNESP]; Universidade de Brasília (UnB); Universidade Estadual Paulista (UNESP)
    In this work we use two different methods to get nodal solutions to quasilinear elliptic problems involving the 1-Laplacian operator. In the first one, we develop an approach based on a minimization of the energy functional associated with a problem involving the 1-Laplacian operator in R-N, on a subset of the Nehari set which contains just sign-changing functions. In the second part we obtain a nodal solution to a quasilinear elliptic problem involving the 1-Laplacian operator in a bounded domain, through a thorough analysis of the sequence of solutions of the p-Laplacian problem associated with it, as p -> 1(+). In both cases, several technical difficulties appear in comparison with the related results involving signed solutions.
  • ItemTrabalho apresentado em evento
    Semi-automatic CNN Architectural Pruning using the Bayesian Case Model and Dimensionality Reduction Visualization
    (Scitepress, 2022-01-01) Marcilio-Jr, Wilson E. [UNESP]; Eler, Danilo [UNESP]; Guilherme, Ivan [UNESP]; Hurter, C.; Purchase, H.; Bouatouch, K.; Universidade Estadual Paulista (UNESP)
    Visualization techniques have been applied to reasoning about complex machine learning models. These visual approaches aim to enhance the understanding of black-box models' decisions or guide in hyperparameters configuration, such as the number of layers and neurons/filters in deep neural networks. While several works address the architectural tuning of convolutional neural networks (CNNs), only a few works face the problem from a semi-automatic perspective. This work presents a novel application of the Bayesian Case Model that uses visualization strategies to convey the most important filters of convolutional layers for image classification. A heatmap coordinated with a scatterplot visualization emphasizes the filters with the most contribution to the CNN prediction. Our methodology is evaluated on a case study using the MNIST dataset.
  • ItemTrabalho apresentado em evento
    Software Quality as a Subsidy for Teaching Programming
    (2021-01-01) Gomes, Pedro Henrique [UNESP]; Garcia, Rogerio Eduardo [UNESP]; Eler, Danilo Medeiros [UNESP]; Correia, Ronaldo Celso [UNESP]; Junior, Celso Olivete [UNESP]; Universidade Estadual Paulista (UNESP)
    Well-written code (which meets standards, conventions, and quality specifications) is often associated with the programmer's experience, which is why companies have been looking for increasingly qualified professionals. Codes at odds with these standards tend to be complex and poorly written and are generally difficult to understand. Consequently, the activities inherent to it become costly. Although well defined and consolidated in the industry, the concepts of code quality taught in the academy are insufficient to enable students to meet market expectations. Research indicates that graduates do not feel prepared to enter the labor market, facing difficulties when competing for the best job opportunities. This difficulty highlights a gap between industry and academia. Researchers have identified the gap and have proposed improvements to the teaching-learning process based on using the concepts and tools widely used in the software industry in an academic environment. When analyzing educational institutions' programming disciplines, it is possible to notice a mismatch between programming disciplines and code quality disciplines. In this scenario, this project aims to propose improvements on how knowledge of programming and quality is evolved, proposing an approach that uses software quality as a subsidy for teaching programming, providing the teacher with guidelines for teaching programming focusing on internal quality source code. We idealized an innovative practice that brought programming, usually focused on the execution of algorithms, within the teaching of code quality, focused on software engineering principles. The use of code inspection tools allowed direct teaching according to the class's needs, introducing a guided content-based internal quality teaching in programming disciplines without generating extra work for the teacher. In addition to the improvements for the teacher, we are convinced that from the student's perspective, we were able to motivate them to learn to program not only concerned with the execution results but also how the solution is developed.
  • ItemArtigo
    Toward prioritization of self-admitted technical debt: an approach to support decision to payment
    (2022-01-01) de Lima, Bruno Santos [UNESP]; Garcia, Rogerio Eduardo [UNESP]; Eler, Danilo Medeiros [UNESP]; Universidade Estadual Paulista (UNESP)
    Technical Debt (TD) is a metaphor that describes the cost–benefit relationship between postponing technical development activities and the consequences of this long-term postponement. The lack of TD Management compromises the Software’s internal quality. It makes its maintenance complex and costly. TD instances are called Self-Admitted Technical Debt (SATD) when intentionally committed and documented through comments in the source code. Several studies explore the identification of SATD, but approaches to support the payment stage are lacking, particularly approaches to indicate which SATD priority for payment. This paper presents an approach to support the prioritization activity in SATD payment. The Prioritization Approach focuses on creating associations between SATD associations and problems found in the source code, identified by Automatic Static Analysis. The results demonstrate that using the issues found on source code and SATD description (found in comments) has greater precision to establish the priority among the SATD compared to the SATD description on comments. We applied the approach proposed to different software projects, and the results support developers’ prioritization.