arXiv subjects
Publications and source records attributed to Jorge Cervantes-Ojeda.
In this study, the Rank Genetic Algorithm was adapted to address a problem in the field of Chromatic Graph Theory, namely, on the parameter called the connected-pseudoachromatic index. We successfully improved several previously known bounds of that index of the complete graph.
In 2020 Bang-Jensen et. al. generalized the Hajós join of two graphs to the class of digraphs and generalized several results for vertex colorings in digraphs. Although, as a consequence of these results, a digraph can be obtained by Hajós constructions (directed Hajós join and identifying non-adjacent vertices), determining the Hajós constructions to obtain the digraph is a complex problem. In particular, Bang-Jensen et al. posed the problem of determining the Hajós operations to construct the symmetric 5-cycle from the complete symmetric digraph of order 3 using only Hajós constructions. We successfully adapted a rank-based genetic algorithm to solve this problem by the introduction of innovative recombination and mutation operators from graph theory. The Hajós Join became the recombination operator and the identification of independent vertices became the mutation operator. In this way, we were able to obtain a sequence of only 16 Hajós operations to construct the symmetric cycle of order 5.
The dichromatic number of a digraph $D$ is the minimum number of colors of a vertex coloring of $D$ such that $D$ has no monochromatic cycles. The Hajós join were recently extended to digraphs (using the dichromatic number) by J. Bang-Jensen et. al. and Hajós (directed) operations is a tool to obtain r-(di)chromatic (di)graphs. J. Bang-Jensen et. al. posed in 2020 the problem of how to obtain the symmetric cycle of length 5 from symmetric cycles of length 3. We recently solved this problem by applying a genetic algorithm. In this article, a procedure is presented to construct any odd symmetric cycle by applying directed Hajós operations to symmetric cycles of length 3, thus, generalizing the known construction of the symmetric cycle of length 5. In addition, this procedure is analyzed to determine its computational complexity.
Over the past decade, convolutional neural networks (CNNs) have become the driving force of an ever-increasing set of applications, achieving state-of-the-art performance. Most of the modern CNN architectures are composed of many convolutional and fully connected layers and typically require thousands or millions of parameters to learn. CNNs have also been effective in the detection of Event-Related Potentials from electroencephalogram (EEG) signals, notably the P300 component which is frequently employed in Brain-Computer Interfaces (BCIs). However, for this task, the increase in detection rates compared to approaches based on human-engineered features has not been as impressive as in other areas and might not justify such a large number of parameters. In this paper, we study the performances of existing CNN architectures with diverse complexities for single-trial within-subject and cross-subject P300 detection on four different datasets. We also proposed SepConv1D, a very simple CNN architecture consisting of a single depthwise separable 1D convolutional layer followed by a fully connected Sigmoid classification neuron. We found that with as few as four filters in its convolutional layer and a small overall number of parameters, SepConv1D obtained competitive performances in the four datasets. We believe this may represent an important step towards building simpler, cheaper, faster, and more portable BCIs.