The AppMaR Laboratory worked in several research projects :
Archeology - In november 2021 the Archeology laboratory of the University of Puerto Rico at Utuado was able to obtain a piece of a Taino canoe that was found in the coast of Añasco Puerto Rico.
This project utilized approximation by ellipses to study the mathematical properties associated to the canoe shape. (Undergraduate Researcher - Meredith A. Ortiz-Rivera - Biology Department)
Coastal Science - Coastal Erosion, which is the wear down or carry away rocks, soils, and/or sands along the coast done by local sea level rise, strong wave action, and coastal flooding is a process that affects all coast lines. But with climate change that lead to rising sea levels and the addition of more frequent and stronger tropical storms such as 2017’s María Puerto Rico’s coast line is changing at a rapid pace.
This project aims at fractal dimension analysis on images of various coast sites in Puerto Rico to determine if there is any relationship between the fractal measure of the coast and the recorded level of erosion. This by analyzing available aerial and/or satellite images to measure fractal dimensions for various coast sites and classify them each location according to both fractal dimension and recorded level of erosion. (Student Researchers - Anna Novoselov and Margaret Basinger - REU: Resilience and Adaptation to Coastal Change Across Communities)
Speleology - This project aims at the characterization of caves in Puerto Rico by means of fractal dimension using various methods.
Using data provided by Prof. Ángel Acosta from the Physics-Chemistry Department we have currently created a MATLAB code that utilizes the box counting method in order to calculate the fractal dimension of the cave. (Undergraduate Researcher - Sebastián Valentín Vega - Computer Science Department)
Speleology - The research project related to Speleology is the digital cave cartography project caveGEOmap designed by Dr. José F. Candelaria Soberal.
Developed by the Department of Mathematics in collaboration with Prof. Ángel Acosta from the Physics-Chemistry Department, caveGEOmap is a MATLAB® written code for research and educational purposes that utilizes cave measurements to create 2D and 3D maps of a cave with minimal user work.
Data is collected using standard digital laser distance measurer, clinometer and a compass and the measurements are treated as data points from a two variable piece-wise function that are then used to interpolate the cave surface. As a user friendly cave mapping software, caveGEOmap evaluates the given measurements using spatial analysis and uses the data itself to estimate the necessary variables to produce the 2-D and 3-D cave maps. (Undergraduate Researchers - various from various departments at UPRA)
Ecology - We utilized monitorR (an R package that is designed for long-term, multi-taxa automated passive acoustic monitoring program for birds) to identify the presence of the Crested Toad (Peltophryne [Bufo] lemur) in audio files from the field. Working in collaboration with Dr. Sondra Vega, the objective of this research is to utilize sound recordings (audio waves) to identify breeding patterns of a metapopulation of the Crested Toad which has been struggling to survive in Puerto Rico’s northen region.
(Undergraduate Researcher - Joemar Pérez Guzmán - Biology Department)
To study the toad one needs to first find it and that has proven not to be an easy task.
With this work utilizing audio waves from Puerto Rico’s northern region crested toad will not only help us identify the whereabouts and use their location to construct a network model but by studying frequency and length of the toad’s song we could determine if other variables such as humidity, temperature, time of the year or time of the day are related to the toad’s behavior and song patterns. Thus making available more data to help the scientific community that is trying to save the toad better understand it once is in the field.
Math Education - The research project related to Math Education is the work of Dr. Yuitza Humarán Martinez. This work studies the effect of the use of manipulatives in the understanding of the concept of the fraction (fraction of natural numbers), specifically the meaning of measurement (fractions in the number line). Data was collected from pre-service elementary school teachers by a quasi-experimental design and it is being analyzed.