Papers by José Julio Conde Mones
This work implements a stable algorithm in Field-Programmable Gate Arrays (FPGAs) for which two a... more This work implements a stable algorithm in Field-Programmable Gate Arrays (FPGAs) for which two architectures (unrolling the loop) were developed and analyzed. The algorithm recovers sources located at the boundary separating two homogeneous media that make up a two-dimensional non-homogeneous region from measurements on the boundary of such region. The problem of recovering these sources is an ill-posed inverse problem as small errors in the measurement can produce important changes in the source location. Inverse source problems have many applications in different areas, such as engineering and medicine, making the proposed implementation important. The first architecture (mode one) allows considering different operating speeds, which is an advantage depending on whether we work with fast or slow signals. The second one (mode two) reduces resource consumption by exploiting the characteristics of the source identification algorithm, which is an advantage for multichannel problems s...
Objetivo: Presentar un algoritmo estable que determina, a partir de mediciones electroencefalográ... more Objetivo: Presentar un algoritmo estable que determina, a partir de mediciones electroencefalográficas, los parámetros de fuentes de tipo dipolar asociadas a focos epilépticos ubicados sobre la superficie de la corteza cerebral. Metodología: Se utiliza un problema de contorno para establecer correlaciones entre la fuente y la medición. El problema se divide en dos subproblemas lineales y en cada uno de ellos, se utilizan el método de mínimos cuadrados y la regularización de Tikhonov para encontrar soluciones estables. Estos subproblemas son problemas mal planteados en el sentido de Hadamard, debido a la inestabilidad numérica que presentan, es decir, pequeños cambios en las mediciones pueden producir grandes variaciones en la solución de cada problema. El parámetro de regularización de Tikhonov fue elegido usando el método de la curva L. Para hallar la solución del problema de contorno se utiliza el método de las series de Fourier y el Método del Elemento Finito. Resultados: Se propuso un tipo de fuente para representar a los focos epilépticos en la corteza cerebral y un algoritmo estable para el problema de identificación de los parámetros de dichas fuentes. Se desarrollaron ejemplos sintéticos y programas en MATLAB para el caso de geometría simple bidimensional. Originalidad: La separación del problema original en dos subproblemas así como los ejemplos sintéticos son producto de esta investigación. Conclusión general: Se propuso un algoritmo estable que determina a los parámetros de fuentes de corriente dipolar definidas en la corteza cerebral.
Mathematics
In this work, we present a numerical algorithm to solve the inverse problem of volumetric sources... more In this work, we present a numerical algorithm to solve the inverse problem of volumetric sources from measurements on the boundary of a non-homogeneous conductive medium, which is made of conductive layers with constant conductivity in each layer. This inverse problem is ill-posed since there is more than one source that can generate the same measurement. Furthermore, the ill-posedness is due to the fact that small variations (or errors) in the measurement (input data) can produce substantial variations in the identified source location. We propose two steps to solve this inverse problem in some classes of sources: we first recover the harmonic part of the volumetric source, and, in a second step, we compute the non-harmonic part of the source. For the reconstruction of the harmonic part of the source, we follow a variational approach based on the reformulation of the inverse problem as a distributed control problem, for which the cost function incorporates a penalized term with th...
Mathematics, 2021
This paper presents a stable method for the identification of sources located on the separation i... more This paper presents a stable method for the identification of sources located on the separation interface of two homogeneous media (where one of them is contained by the other one), from measurement yielded by those sources on the exterior boundary of the media. This is an ill-posed problem because numerical instability is presented, i.e., minimal errors in the measurement can result in significant changes in the solution. To obtain the proposed stable method the identification problem is categorized into three subproblems, two of which present numerical instability and regularization methods must be applied to obtain their solution in a stable form. To manage the numerical instability due to the ill-posedness of these subproblems, the Tikhonov regularization and sequential smoothing methods are used. We illustrate this methodology in a circular and irregular region to demonstrate the feasibility of the proposed method, which yields convergent and stable solutions for input data wit...
PLOS ONE, 2020
Several areas, such as physical and health sciences, require the use of matrices as fundamental t... more Several areas, such as physical and health sciences, require the use of matrices as fundamental tools for solving various problems. Matrices are used in real-life contexts, such as control, automation, and optimization, wherein results are expected to improve with increase of computational precision. However, special attention should be paid to ill-conditioned matrices, which can produce unstable systems; an inadequate handling of precision might worsen results since the solution found for data with errors might be too far from the one for data without errors besides increasing other costs in hardware resources and critical paths. In this paper, we make a wake-up call, using 2 × 2 matrices to show how ill-conditioning and precision can affect system design (resources, cost, etc.). We first demonstrate some examples of real-life problems where ill-conditioning is present in matrices obtained from the discretization of the operational equations (ill-posed in the sense of Hadamard) that model these problems. If these matrices are not handled appropriately (i.e., if ill-conditioning is not considered), large errors can result in the computed solutions to the systems of equations in the presence of errors. Furthermore, we illustrate the generated effect in the calculation of the inverse of an ill-conditioned matrix when its elements are approximated by truncation. We present two case studies to illustrate the effects on calculation errors caused by increasing or reducing precision to s digits. To illustrate the costs, we implemented the adjoint matrix inversion algorithm on different field-programmable gate arrays (FPGAs), namely, Spartan-7, Artix-7, Kintex-7, and Virtex-7, using the full-unrolling hardware technique. The implemented architecture is useful for analyzing trade-offs when precision is increased; this also helps analyze performance, efficiency, and energy consumption. By means of a detailed description of the trade-offs among these metrics, concerning precision and ill-conditioning, we conclude that the need for resources seems to grow not linearly when precision is increased. We also conclude that, if error is to be reduced below a certain threshold, it is necessary to determine an optimal precision point. Otherwise, the system becomes more sensitive to measurement errors and a better alternative would be to choose precision
Numerical Methods for Partial Differential Equations, 2017
This article is mainly concerned with the numerical study of the Cauchy problem for the Laplace e... more This article is mainly concerned with the numerical study of the Cauchy problem for the Laplace equation in a bounded annular region. To solve this ill-posed problem we follow a variational approach based on its reformulation as a boundary control problem, for which the cost function incorporates a penalized term with the input data. The cost function is minimized by a conjugate gradient method in combination with a finite element discretization. In the case where the input data is noisy, some preliminary error estimates, show that the penalization parameter may be chosen like the inverse of the level of noise. Numerical solutions in simple and complex domains show that this methodology produces stable and accurate solutions.
Applied Mathematical Modelling, 2015
Abstract In this study, we consider the inverse problem of determining a source term in an ellipt... more Abstract In this study, we consider the inverse problem of determining a source term in an elliptic problem based on boundary measurements. The boundary measurements allow the unique determination of the harmonic component of the source, and thus a priori information is required for its complete identification. Using this a priori information, we determine the compactness of the class of sources and a uniqueness theorem for its identification from Cauchy data, thereby allowing us to propose a stable algorithm for finding “approximate solutions” of the inverse problem. The proposed procedure is demonstrated by individual cases, where we know the “geometry” of the inner region and the source takes a constant value.
Advances in Differential Equations and Control Processes, 2019
The Mamuju area has recorded a higher than average natural radiation dose compared to other regio... more The Mamuju area has recorded a higher than average natural radiation dose compared to other regions in Indonesia. It is possible that inhabitants of Mamuju developed the radioadaptive response (RAR). To prove that the RAR was developed in Mamuju inhabitants, evaluation of lymphocytic radiosensitivity using the G0 micronucleus (MN) assay was conducted herein. The MN frequencies in peripheral blood lymphocytes before and after exposed to 1.5 Gy radiation at a dose rate of 0.38 Gy/min were assessed from 11 samples of Botteng Village, Mamuju inhabitants and control groups. These treated cells were then cultured and exposed to cytochalasin-B to arrest cells during the cytokinesis stage. The mean number of MN induced by radiation per 1000 binucleated cells (BNC) was evaluated for both Mamuju inhabitants and control groups. The lymphocytic radiosensitivity was calculated using standard deviation (SD) of the mean value (MV) of the number of MN induced by radiation found in the control group. Based on the SD and MV values, individual lymphocytes were classified as ''resistant'', ''sensitive'', or ''normal'' if the mean of MN induced by radiation was ≤ MV-(2×SD), ≥ MV + (2×SD) or in between, respectively. The results showed that lymphocytes from six samples in Botteng Village inhabitants were categorized as resistant and five samples were normal. In contrast, all samples in the control group were demonstrated to have normal sensitivities. The study results also revealed that lymphocytic radiosensitivity was not correlated with age and gender, which was probably because of the small sample size used in this study. Further investigation with a larger sample number and higher radiation dose should be conducted to validate our findings.
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Papers by José Julio Conde Mones