APPLICATIONS OF THE MATHIEU GROUPS AND INFORMATION THEORY IN DNA ENCODING FUNCTIONS

A foundational idea in mathematics lies in breaking down existing components into their bare fundamentals. As evidenced by prime numbers and composites, we learn this idea at an early age. Categorizing these broken-down components into their simplest form allows mathematicians to construct proofs from emergent patterns. John Conway’s Atlas of Finite Groups in the 1990s was particularly concerned with the categorization of structures known as groups. There are certain axioms a group must adhere to, which amount to the retention of symmetry; ultimately a group helps us to better understand symmetric actions performed on a set with a binary operation. The Jordan-H¨older Theorem states that a finite group, that is, a binary operation coupled with a set, which contains a finite amount of symmetries, will break down into a simpler group; these are known as follows: cyclic groups, alternating groups, groups of Lie type, or a sporadic group (of which there are 26 varieties). This classification of finite groups breaking down into simple finite groups is considered a milestone in modern mathematics. The goal of this research is to search for applications of sporadic groups. It is our hope that we will yield applications for sporadic groups, in particular Mathieu groups in other fields of mathematics and sciences. Deoxyribonucleic acid (DNA) sequencing is one potential application for the use of these sporadic groups. Mathieu groups have existing applications in error correction because they are automorphisms of a linear code. Error correction ensures that the transmission of data is consistently possible and that noise in a system cannot corrupt the information in it; the goal is to discover if a similar approach might allow for error correction in mutations. It is assumed that by treating the set of DNA sequences as a linear code, we may iv be able to apply error correcting algorithms to preserve intended sequences of DNA and prevent harmful mutations. A set of codewords that form a vector subspace of a finite vector space over a finite field is called a linear code; treating DNA as such is one assumption made in the research. We will also discover if perhaps DNA may already come equipped with such properties. The study of certain open problems in mathematics allows us to sometimes put to the test existing theorems and discover new applications. It is our aim that through the work we may discover a sequence, encoding function or group isomorphism that can emulate DNA sequencing, for the medical technology to flourish. Throughout the course of the research, we have shown encodings and decodings of both DNA sequences applied through Hamming and Golay codes, but discovered that a group acting as an automorphism to these codes does not necessarily act as an automorphism on the DNA code. We consider the need for other functions to accommodate for the intricacies imposed by the geometry of nucleotides and enzymes

Voices in the Borderlands: Reimagining Identity, Cultural Belonging, and Dystopian Spaces in Anzaldúa’s Borderlands and Viramontes’s “The Cariboo Café”

This thesis explores how Gloria Anzaldúa’s Borderlands/La Frontera (1987) and Helena María Viramontes’ short story “The Cariboo Café” (1985) portray marginalized individuals navigating liminal spaces of identity, oppression, and survival. Borderlands/La Frontera and “The Cariboo Café” show how systematic violence and displacement shatter the self, pushing characters to navigate trauma in a dystopian space. Sonya, Macky, the café owner, and the grieving mother represent Anzaldúa’s concepts of borderland subjectivity, betrayal, and spectral haunting. Sonya and Macky, two undocumented children, represent Anzaldúa’s borderlands subjects and reside in a state of nepantla, an in-between space of cultural dislocation. The café owner represents an authoritative distortion of Anzaldúa’s La Llorona and La Malinche, both of whom are symbols of betrayal and loss. Anzaldúa’s critique of internalized oppression correlates with his responsibility in the children’s suffering, where “[the] dual of oppressor and oppressed; locked in mortal combat, like the cop and the criminal, both are reduced to a common denominator of violence” (Borderlands 84). His café, which was meant to be a refuge, devolved into a dystopian trap that fostered systemic violence. The grieving mother whose child was abducted by state forces appears as a spectral borderland figure, combining La Llorona’s wailing with the political horror of the desaparecidos. Anzaldúa’s claim that borders cause people to live “entre dos mundos” emphasizes the narrow line between sanity and insanity (83). The grieving mother’s fragmented mind reflects the collective trauma of oppressed individuals. This thesis argues that through their writing, both writers show the brutal reality of liminal existence, where survival necessitates resistance to erasure. By combining Anzaldúa’s Borderlands theory with Viramontes’ short story, this thesis will show how dystopian spaces like the Cariboo café embody the violence of borders, both physical and ideological, while also emphasizing the resilience of individuals who live there

Three Essays on Green Innovation

This study examines the strategic role of green innovation in addressing escalating environmental challenges. Comprising of three interrelated essays, the study integrates computational, theoretical, and empirical approaches to provide a comprehensive understanding of the antecedents, mechanisms, and outcomes of green innovation at the firm level. The first essay conducts a systematic literature review employing advanced computation tools, including topic modeling (LDA and BERTopic) and scientometric analysis to elucidate the intellectual framework, thematic evolution, and central knowledge areas and flows within the green innovation research field. The second essay empirically investigates how internal firm resources- research & development (R&D) intensity, acquisition intensity, and absorbed slack- influence green innovation and, in turn, financial and market performance, grounded in the Natural Resources-Based View (NRBV). Drawing on the Behavioral Theory of the Firm (BTOF), the third essay examines how performance feedback relative to historical and social aspiration levels, both environmental and financial, shapes green innovation engagement under diverse levels of industry dynamism. Collectively, these essays bridge theoretical gaps by extending theoretical frameworks, NRBV and BTOF, employ advanced analytical methods, and offer multidimensional insights into how green innovation contributes to organizational sustainability, legitimacy, and resilience in a dynamic corporate landscape

‘GOOD OLD JOHN DECKER’: CONFRONTING ENTREPRENEURIAL CHALLENGES IN THE MID-NINETEENTH CENTURY RIO GRANDE BORDERLANDS

ABSTRACT \u27Good Old John Decker\u27: Confronting Entrepreneurial Challenges In The Mid-Nineteenth Century Rio Grande Borderlands (May 2025) Grace C. Maciel, M.A., Texas A&M International University Chair of Committee: Dr. Jerry Thompson This thesis presents the first scholarly study of John Decker, a French-born immigrant whose rise as a merchant and civic figure in the 19th-century U.S.–Mexico borderlands offers a compelling case of adaptability, resilience, and immigrant success. Settling in Rio Grande City and Camargo, Tamaulipas, Decker built a lasting presence during a period marked by regional volatility, navigating war, revolution, and economic transformation. His story is explored across five chapters, tracing his journey from arrival to lasting influence. The study analyzes the key factors behind Decker’s success and his strategies to adapt to the borderlands\u27 unpredictable political and economic conditions. Drawing from a range of primary sources, including archival collections at the Dolph Briscoe Center for American History at the University of Texas at Austin, as well as regional newspapers and correspondence, this thesis reconstructs Decker’s rise in the merchant trade, with special attention to his partnership with José San Román, a leading figure in cross-border commerce. Decker’s cultural adaptability, political engagement, and strategic mindset are central to overcoming linguistic and social barriers, ultimately securing a prominent role in Civil War-era transnational trade. This study also highlights Decker’s entry into the global transatlantic market. Decker’s experience challenges dominant historical narratives that often overlook the contributions of European immigrants to the Texas frontier. His ability to persist, thrive, and remain anchored in the region for nearly four decades, while most French immigrants were unable to do so, highlights his significance to the region\u27s development and the history of South Texas. This study not only recovers the legacy of an unknown historical figure but also contributes to a broader understanding of immigrant agency in shaping the economic and cultural landscape of South Texas. Ultimately, it argues that the development of the borderlands was shaped not only by dominant Anglo-American colonizers or aristocratic Mexican elites but also by immigrant pioneers who made the frontier their own

Capturing the Realities of Space and Culture: An Exploration of Landscape in The House on Mango Street and Woman Hollering Creek

ABSTRACT Capturing the Realities of Space and Culture: An Exploration of Landscape in The House on Mango Street and Woman Hollering Creek (May 2025) Leanna Carmela Mendiola, B.A., Texas A&M International University; Chair of Committee: Dr. Zachary Hernandez This thesis explores Sandra Cisneros’s The House on Mango Street and Woman Hollering Creek. Cisneros’s books explore the landscape and culture around her characters as readers piece together the experiences of women. The two novels use architectural elements to examine each book’s protagonists’ community and culture. The thesis argues that Cisneros employs space and place to underscore empowerment and the characters’ journeys toward self-discovery. Chapter one, “Bird’s Eye View of Mango Street’s Architecture and Identity,” analyzes how architectural structures embedded within the landscapes and historical context reveal the cultural identity of community through generational stories. This chapter further examine how man-made landscape directly mirror women’s domestic lives. Chapter two, “Cultural Identity in Woman Hollering Creek,” underscores the strength and resilience required for women in Mexican American communities to overcome patriarchal culture norms. Specifically, the chapter’s analysis will explore how Cisneros uses water in Woman Hollering Creek to symbolize women’s struggles and triumphs, revealing the significant role of water within the landscape and character’s lives

A PRELIMINARY STUDY OF HILBERT–KUNZ FUNCTIONS: COEFFICIENT BEHAVIOR IN A NORMAL AFFINE SEMIGROUP RING

In 1890, David Hilbert published a set of notes on what now constitutes one of the bases of Commutative Algebra; his work would eventually influence the efforts of mathematicians like Ernst Kunz. In 1969, Ernst Kunz introduced a particular mapping regarding modules of regular local rings. His goal was to characterize Noetherian local rings of prime characteristic by computing the length of the composition series under Frobenius power transformations. In this thesis, the focus will be on stating the initial steps on finding the coefficients of the Hilbert-Kunz function of the normal affine semigroup ring of the form R = k[u, su, s^2 u, ..., s^a u, lu, slu, s^2 lu, ..., s^b l^h u] with characteristic p = 2 which is associated with the affine semigroup ring generated by A(0, 0, 1), B(0, a, 1), C(2a, a, 1), and D(a, 0, 1) in Z^3 . The Hilbert-Kunz function will determine the length of the module of such a Noetherian ring when under frobenious power transformations. Finding such length offers a measure on the severity of the singularity of the ring as well as growth behavior insights. The initial geometric approach will require the use of Pick’s theorem, Ehrhart theory, and software like Macaulay2 and GeoGebra to compute the number of lattice points enclosed by the convex hull that corresponds to aforementioned normal affine semigroup ring

The Right To Gender-Affirming Care

As of recent, twenty-four states have enacted bans on gender-affirming care, restricting minors from accessing medically necessary treatment. Existing scholarship has begun to explore the profound impact of these bans on transgender youth, their parents or guardians, and the medical professionals who support them. However, the body of literature on this rapidly evolving issue remains limited. This thesis aims to fill that gap by offering a legal defense of gender-affirming care, grounded in judicial precedent. It argues that parental rights to make medical decisions for their children—recognized in constitutional jurisprudence—extend to decisions involving gender-affirming treatment. Additionally, it draws on anti-discrimination precedents in which courts have interpreted existing laws to protect transgender individuals. Ultimately, this thesis contends that both the right to gender-affirming care for minors and the right of parents to make such decisions constitute fundamental rights. Moreover, it asserts that these state-imposed bans constitute unlawful discrimination

EXAMINING THE CONNECTIONS BETWEEN GENDER, IDENTITY, AND LAND IN LESLIE MARMON SILKO’S CEREMONY AND RUDOLFO ANAYA’S BLESS ME, ULTIMA

This thesis explores the representation of gender, identity, and land in the novels Ceremony by Leslie Marmon Silko and Bless Me, Ultima by Rudolfo Anaya. To understand the role of gender in the novels, women are analyzed as sources of salvation and refuge for men. The male protagonists seek a “cure” or an understanding of themselves, and they are only able to achieve this through the nurturing of the women in their lives. This thesis also examines how the male protagonists develop their masculinity through the formation of a bond with the Earth, their homeland, and nature. In Ceremony and Bless Me, Ultima, the relationship between gender, identity, and land illustrates how a feminine approach to healing allows the male characters to discover and redefine their true selves. The novels present female characters as saviors and healers. Through their feminine intercession, the male protagonists can reconnect to the land and reconstruct their fractured identities

Cultural Identity and Economic Challenges : The Socio-Economic Impact of the Texas Kickapoo Reservation in the South Texas Borderlands

The Kickapoo Traditional Tribe of Texas holds a significant place in Texas history. Facing conflicts with other tribes and experiencing broken treaties with the United States government, the Kickapoo slowly migrated from the Great Lakes region in the 16th century to the Midwest, then to the South, and into northern Mexico. Along the way, the Kickapoo encountered the French, British, Spanish, Americans, Texans, and Mexicans. They became involved in historical events such as the French and Indian War, the Battle of Tippecanoe, the War of 1812, the Battle Creek Massacre of 1838, and the Battle of Dove Creek of 1865. The Mexican government granted the Kickapoos sanctuary in El Nacimiento, near Musquiz, Coahuila, Mexico. However, in the 1940s, Mexico’s modernization campaign, which included the establishment of mining and smelting companies that negatively impacted their farming environment, led the Mexican government to force the Kickapoo back into the United States. Consequently, they migrated to their ancestral lands in South Texas. For forty years, the Kickapoo lived in abject poverty as migrant workers under the International Bridge between Eagle Pass, Texas, and Piedras Negras, Coahuila, Mexico. In 1983, Congress passed the Texas Band of Kickapoo Act, which granted the Kickapoo a reservation, recognized them as a Native American tribe, and entitled them to social and medical benefits. This thesis examines the resilience and determination of the Texas Kickapoo throughout their migrations into the South Texas borderlands and Mexico. It investigates how the Texas Kickapoo preserved their cultural identity while establishing themselves on their reservation and how the development of the casino industry contributed to overcoming poverty

The Mindful Way: A Mindfulness Psychoeducational Group for Latinx College Students

Researchers have extensively studied mindfulness as a promising intervention that can aid college students in managing stressors. Unfortunately, researchers have underrepresented minority populations like Latinx college students in mindfulness literature. The Mindful Way (TMW) is a culturally responsive psychoeducational group program that aims to close the gap in the literature. The pre-test and post-test of TMW program measures student’s tendency to practice mindfulness, their personal and academic resilience, degree of self-compassion, emotion regulation skills, problematic alcohol consumption, and symptoms of anxiety, depression and post-traumatic stress disorder, before and after participating in the program. The hypothesis of the present study is that students will display a significant difference in the aforementioned variables before and after participating in TMW program. TMW program consisted of seven weekly sessions with groups of 7-8 members led by two group facilitators. The sample consisted of 42 Latinx undergraduate students between the ages of 18-25 enrolled in a Hispanic Serving Institution (HSI) in the U.S.-Mexico Border. The results suggested a statistically significant difference in participant’s ability to regulate their emotions, self-compassion, coping abilities, level of resilience and a decrease in their problematic alcohol consumption as well as symptoms of anxiety and depression. This study presents the effects that a culturally responsive intervention has towards Latinx students’ abilities to cope with stressors