arXiv subjects

Daniel A. Cruz

Publications and source records attributed to Daniel A. Cruz.

3 recordsLinked to original sources

arXiv2025

Defunding Sexual Healthcare: A Topological Investigation of Resource Accessibility

Government actions, such as the Medina v. Planned Parenthood South Atlantic Supreme Court ruling and the passage of the Big Beautiful Bill Act, have aimed to restrict or prohibit Medicaid funding for Planned Parenthood Healthcare Centers (PPHCs) at both the state and national levels. These funding cuts are particularly harmful in states like California, which has a large population of Medicaid users. This analysis focuses on the distribution of Planned Parenthood clinics and Federally Qualified Health Centers (FQHCs), which offer essential reproductive healthcare services including, but not limited to, abortions, birth control, HIV services, pregnancy testing and planning, STD testing and treatment, and cancer screenings. While expanded funding for FQHCs has been proposed as a solution, it fails to address the locational accessibility of Medicaid-funded health centers that provide sexual and reproductive care. To assess this issue, we analyze the proximity of data points representing California's PPHC and FQHC locations. Topological Data Analysis (TDA)-an approach that examines the shape and structure of data -- is used to detect disparities in reproductive and sexual healthcare coverage. To conduct data collection and visualization, we utilize R and Python. We apply an n-closest neighbor algorithm to examine distances between facilities and assess changes in travel time required to reach healthcare sites. We apply persistent homology to analyze current gaps across multiple scales in healthcare coverage and compare them to potential future gaps. Our findings aim to identify areas where access to care is most vulnerable and demonstrate how TDA can be used to analyze spatial inequalities in public health.

cs.SI↗

arXiv2022

Estimating the Long-term Behavior of Biologically Inspired Agent-based Models

An agent-based model (ABM) is a computational model in which the local interactions of autonomous agents with each other and with their environment give rise to global properties within a given domain. As the detail and complexity of these models has grown, so too has the computational expense of running several simulations to perform sensitivity analysis and evaluate long-term model behavior. Here, we generalize a framework for mathematically formalizing ABMs to explicitly incorporate features commonly found in biological systems: appearance of agents (birth), removal of agents (death), and locally dependent state changes. We then use our broader framework to extend an approach for estimating long-term behavior without simulations, specifically changes in population densities over time. The approach is probabilistic and relies on treating the discrete, incremental update of an ABM via "time steps" as a Markov process to generate expected values for agents at each time step. As case studies, we apply our extensions to both a simple ABM based on the Game of Life and a published ABM of rib development in vertebrates.

math.DS↗

arXiv2019

Insertions Yielding Equivalent Double Occurrence Words

A double occurrence word (DOW) is a word in which every symbol appears exactly twice; two DOWs are equivalent if one is a symbol-to-symbol image of the other. We consider the so called repeat pattern ($αα$) and the return pattern ($αα^R$), with gaps allowed between the $α$'s. These patterns generalize square and palindromic factors of DOWs, respectively. We introduce a notion of inserting repeat/return words into DOWs and study how two distinct insertions into the same word can produce equivalent DOWs. Given a DOW $w$, we characterize the structure of $w$ which allows two distinct insertions to yield equivalent DOWs. This characterization depends on the locations of the insertions and on the length of the inserted repeat/return words and implies that when one inserted word is a repeat word and the other is a return word, then both words must be trivial (i.e., have only one symbol). The characterization also introduces a method to generate families of words recursively.

math.CO↗