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Implementation of an algorithm to compute the strong apparent distance of bivariate codes

Published in Journal of Physics: Conference Series, 2019

Abstract

The BCH bound is the oldest lower bound for the minimum distance of a cyclic code. The study of this bound and its generalizations are classical topics, which includes the study of the very well-known family of BCH codes. In 1970, P. Camion extended the notion of BCH bound to the family of abelian codes by introducing the apparent distance of polynomials. Camion showed that the minimum value of the apparent distance of certain polynomials associated to codewords is less than or equal to the minimum distance of the code. The mentioned minimum value is known as the apparent distance of an abelian code. In 2016, Bernal-Bueno-Simón introduced the notion of strong apparent distance of polynomials and hypermatrices and developed an algorithm to compute the minimum strong apparent distance of a hypermatrix based on g-orbits manipulations. In this work, we will present the implementation of an algorithm to compute the strong apparent distance of bivariate codes.

Recommended citation: Bueno-Carreño, D. H., & López, J. M. (2019, January). Implementation of an algorithm to compute the strong apparent distance of bivariate codes. In Journal of Physics: Conference Series (Vol. 1160, No. 1, p. 012012). IOP Publishing. https://iopscience.iop.org/article/10.1088/1742-6596/1160/1/012012/meta

Estimating Formation Mechanisms and Degree Distributions in Mixed Attachment Networks

Published in Journal of Physics A: Mathematical and Theoretical, 2019

Abstract

Our work introduces an approach for estimating the contribution of attachment mechanisms to the formation of growing networks. We present a generic model in which growth is driven by the continuous attachment of new nodes according to random and preferential linkage with a fixed probability. Past approaches apply likelihood analysis to estimate the probability of occurrence of each mechanism at a particular network instance, exploiting the concavity of the likelihood function at each point in time. However, the probability of connecting to existing nodes, and consequently the likelihood function itself, varies as networks grow. We establish conditions under which applying likelihood analysis guarantees the existence of a local maximum of the time-varying likelihood function and prove that an expectation maximization algorithm provides a convergent estimate. Furthermore, the in-degree distributions of the nodes in the growing networks are analytically characterized. Simulations show that, under the proposed conditions, expectation maximization and maximum-likelihood accurately estimate the actual contribution of each mechanism, and in-degree distributions converge to stationary distributions.

Recommended citation: Medina, J. A., Finke, J., & Rocha, C. (2019). Estimating formation mechanisms and degree distributions in mixed attachment networks. Journal of Physics A: Mathematical and Theoretical, 52(9), 095001. https://iopscience.iop.org/article/10.1088/1751-8121/aaffeb

Use of Arabidopsis thaliana as a model to understand specific carcinogenic events: Comparison of the molecular machinery associated with cancer-hallmarks in plants and humans

Published in Heliyon, 2023

Abstract

Model organisms are fundamental in cancer research given that they rise the possibility to characterize in a quantitative-objective fashion the organisms as a whole in ways that are infeasible in humans. From this perspective, model organisms with short generation times and established protocols for genetic manipulation allow the understanding of basic biology principles that might guide carcinogenic onset. The cancer-hallmarks (CHs) approach, a modular perspective for cancer understanding, stands that underlying the variability among different cancer types, critical events support the carcinogenic origin and progression. Thus, CHs as interconnected genetic circuitry, have a causal effect over cancer biogenesis and might represent a comparison scaffold among model organisms to identify and characterize evolutionarily conserved modules to understand cancer. Nevertheless, the identification of novel cancer regulators by comparative genomics approaches relies on selecting specific biological processes or related signaling cascades that limit the type of detected regulators, even more, holistic analysis from a systemic perspective is absent. Similarly, although the plant Arabidopsis thaliana has been used as a model organism to dissect specific disease-associated mechanisms, given the evolutionary distance between plants and humans, a general concern about the utility of using A. thaliana as a cancer model persists. In the present research, we take advantage of the CHs paradigm as a framework to establish a functional systemic comparison between plants and humans, that allowed the identification not only of specific novel key genetic regulators, but also, biological processes, metabolic systems, and genetic modules that might contribute to the neoplastic transformation. We propose five cancer-hallmarks that overlapped in conserved mechanisms and processes between Arabidopsis and human and thus, represent mechanisms which study can be prioritized in A. thaliana as an alternative model for cancer research. Additionally, derived from network analyses and machine learning strategies, a new set of potential candidate genes that might contribute to neoplastic transformation is described. These findings postulate A. thaliana as a suitable model to dissect, not all, but specific cancer properties, highlighting the importance of using alternative complementary models to understand carcinogenesis.

Recommended citation: Clavijo-Buriticá, D. C., Sosa, C. C., Heredia, R. C., Mosquera, A. J., Álvarez, A., Medina, J., & Quimbaya, M. (2023). Use of Arabidopsis thaliana as a model to understand specific carcinogenic events: Comparison of the molecular machinery associated with cancer-hallmarks in plants and humans. Heliyon, 9(4). https://doi.org/10.1016/j.heliyon.2023.e15367

Differential Calculus (Calculus I - Mat102)

Adjunct, School of Natural Sciences, Exact and Education - Universidad del Cauca, 2015

Differential Calculus (Calculus I - Mat102)

Adjunct, School of Natural Sciences, Exact and Education - Universidad del Cauca, 2016