Rocha Clavijo, Daniel M.

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    Towards a rapid estimation system in calcium signaling
    (2023-05-10) Rocha Clavijo, Daniel M.; Isaza Brando, Clara E.; University of Puerto Rico at Mayaguez; College of Engineering; Cabrera Ríos, Mauricio; Latorre Esteves, Magda; Pérez Morales, Jaileene; Other; Bustillo Zárate, Alcibíades
    Plants have receptors on their cell surface capable of recognizing pathogens, triggering an immune response, and activating local or systemic defense. Calcium is one of the primary messengers in this response. The Calcium signature plays a crucial role in encoding and decoding the Calcium signal, enabling changes in cytosolic free Calcium to be maintained at nanomolar amounts. This work is part of the NSF EMBRIO institute and aims to proposes a series of empirical statistical models to represent Calcium signaling in the Arabidopsis plant. The proposed models were applied to a case study analyzing data on Arabidopsis epidermal cell cytosolic calcium levels over time, relating to three neighboring layers of cells: initiator cells (0), standby cell (1), and sub-standby cells (2) response, when the bacterial peptide Flagellin 22 (flg22) is applied. The methodology consists of, i) organizing the elements of the experiment as a system representation (inputs, processes, outputs), ii) fitting empirical statistical models, and iii) evaluating models using the Akaike information criterion (AIC) to select a parsimonious representation. The functional ANOVA with scalar effect as proposed here allows determining the behavior of the average curves of the calcium signal through time for the different neighboring layers of cells and represents a way to explore to model calcium signaling in the Arabidopsis plant. An R Shiny interface was also developed to support this work, as demonstrated here.
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    Análisis de datos de conducción aplicando modelos de regresión funcional
    (2019-05-15) Rocha Clavijo, Daniel M.; Lorenzo González, Edgardo; College of Arts and Sciences - Sciences; Torres Saavedra, Pedro A.; Santana, Dámaris; Department of Mathematics; Rodríguez, Daniel
    Studies in transportation engineering carried out in simulators seek to analyze the behavior of drivers given the characteristics of the driver and different scenarios resulting from the consideration of design elements on the road. These studies collect information at short time intervals (for instance, every 0.016 seconds), which implies that the number of observations is extremely large at the end of the study, compared to traditional ones. Currently, the practices of analyzing these data involve i) dividing the domain of the experiment or route into zones or segments, ii) reducing the data of each segment to a descriptive measure, usually the mean, and iii) applying conventional data analysis techniques to the reduced data, such as generalized linear models or mixed effect models. However, this practice of data analysis is inefficient because it does not consider the nature of the simulator data. Therefore, this work proposes functional regression models with functional response and scalar covariables in order to analyze the data of driving simulators. The proposed models are based on the functional data theory, which assumes that the phenomenon being observed follows a smooth function but is observed discreetly in a fine grid. One of the advantages of the proposed models is that the behavior of the drivers can be completely characterized through time using average curves and the behavior change while driving can be studied using the first derivatives of the curves. Comparisons of driving behavior between groups can also be carried out efficiently using all the information collected. In this work, simulation studies were carried out to determine the adjustment parameters of the models in the application to a set of real data from the driving simulator of the University of Puerto Rico at Mayagüez (UPRM). The simulations indicate that the models present lower estimation error with 10 and 15 bases of P-splines (B-splines penalized) for the functional response and the global functional intercept, respectively. In the analysis of the application using the proposed approach, after a model selection process, it was concluded that a reasonable model to determine variables significantly related to driving speed is a functional linear mixed-effect model with functional random intercept of the driver, smooth effects of day time, lane width and scalar effect of the limit speed.