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• Title: Gaps between close factors of an integer
• Mentor: Dr. Tsz Chan, Assistant Professor of Mathematics
• Format: In-person, Marietta Campus

Summary: One major theme in number theory is the study of integers through their factorization. For example, 3950100 = 1881*2100 = 1890*2090 = 1900*2079 has three factorizations which are close to each other. In this project, we will extend the study to numbers with four or more such close factorizations. We will quantify the meaning of closeness, search for better examples, and deduce limitations to such special integers. 
  
Participating students are expected to study and learn relevant materials and research literature through the guidance of the mentor and peer discussions. Thoughtful questions and sharing of ideas are encouraged. There will be up to 4 hours of weekly in-person meeting or group work (with potential online component) at the mentor's office and neighboring classroom in the Math Building of the Marietta campus. 
  
Students will learn how to typeset research articles and slides with LaTeX and grow in their problem-solving and communication skills through discussing and analyzing the research question with computer experimentation and presenting their final results at conferences. The ultimate aim is for students to become more independent and critical thinkers. 

• Project Title: Decoding function of proteins through protein-protein interactions using a yeast two hybrid assay
• Mentor: Dr. Rajnish Singh, Associate Professor of Chemistry
• Format: In-person, Kennesaw Campus

Summary: Proteins are essential macromolecules that play an essential role in biological processes involved in health and disease. Proteins carry out their functions by interacting with other proteins through a complicated network of protein-protein interactions (PPIs) and recently this network of interactions has been named: The Interactome! Disruption of the interactome in tissues can lead to disease and hence protein-protein interactions not only shed light on protein function and its regulation but also have the potential to be valuable drug targets. The Inspire Summer 2025 research project seeks to decode the function of two proteins: a mitogen-activated-kinase -activated protein-kinase 2 (MK2) and the Ecdysone Receptor. A yeast two hybrid assay is used to screen for putative protein-protein interactions and positive hits from the screen will be further analyzed to determine the interactome of the two proteins. Students will conduct hands on experiments in the Science Laboratory Building on the Kennesaw campus. They will gain experience with the yeast two hybrid assay and learn techniques such as PCR, molecular cloning, restriction digestions, bacterial and yeast transformations, SDS-PAGE, western blotting, protein purification, DNA sequencing and the use of common protein databases. Students will work a minimum of 15 hr. per week. Faculty mentor will provide training on all techniques and weekly meetings will be conducted to communicate results, collaborate, plan experiments and troubleshoot. At the end of summer, students will write a report and target regional and national conferences for poster presentations. 

• Project Title: Modeling the Dynamics of Legionnaires’ Disease
• Mentor: Dr. Lihong Zhao, Assistant Professor of Mathematics
• Format: Hybrid (In-person meetings will be on Marietta campus)

Summary: Legionnaires' disease (LD) is an atypical pneumonia caused by bacteria of the genus Legionella. The primary way that individuals contract LD is through the inhalation of bacteria suspended in aerosolized water; it is generally not spread through human-to-human contact but rather through environmental factors, with possible sources of contamination including potable water for showers (especially in hotels and hospitals), decorative fountains, and hot tubs. LD can lead to life-threatening complications including respiratory failure, acute kidney and multi-organ failure, and brain sequelae. The first documented LD outbreak in the United States occurred in Pennsylvania in 1976. The disease burden has steadily increased since, with a mortality rate of 5-15%. The true incidence of the disease is likely higher as LD is often underdiagnosed and underreported. We will develop a mathematical modeling framework to better understand the transmission dynamics of LD and derive possible mitigation strategies.

By participating in this summer research project, students will learn fundamental mathematical modeling techniques, develop hands-on programming skills on how to simulate and visualize solutions to systems of ordinary differential equations, and learn how to interpret mathematical results in the context of a real-world problem. Model simulations will be conducted using MATLAB. Familiarity with MATLAB is recommended but not required to be successful in this project.

• Project title: Characterization and Site-Directed Mutagenesis of Aldehyde Dehydrogenases in the Plant Pathogen Pseudomonas syringae
• Mentor: Dr. Soon Goo Lee, Assistant Professor of Molecular and Cellular Biology
• Format: In-person, Kennesaw Campus

Summary: Indole-3-Acetic Acid (IAA) is a common form of the plant hormone auxin that regulates diverse signal transduction pathways involved in plant development. The plant pathogen Pseudomonas syringae DC3000 synthesizes the phytohormone IAA using indole-3-acetaldehyde dehydrogenase enzymes, manipulating the defense signaling of its host plants. This process influences the production of virulence factors, altering hormone responses and plant hormone synthesis. While the role of pathogen-derived IAA in pathogenesis by leaf-spotting pathogens is well understood, the biosynthetic pathways and regulatory mechanisms of pathogen-derived IAA remain largely unexplored. Our 2025 Inspire Summer Scholars Program research team aims to investigate the structure-function relationships of enzymes and regulatory proteins involved in pathogen-derived IAA metabolism using computational, biochemical, and biophysical research tools, with a particular focus on protein X-ray crystallography. As part of this program, Inspire Summer Scholars fellows will engage in hands-on, in-person experiments, including biochemical and structural analyses of multiple proteins from various Pseudomonas species. Each student will independently conduct molecular biology and biochemical experiments on their assigned samples. For complex experiments, such as X-ray crystallography, undergraduate students will collaborate with graduate students in the Lee Protein Lab (located in the Science Laboratory on Kennesaw Campus) to complete a team-based project. Understanding the three-dimensional (3D) structures of key proteins will provide fundamental insights into active site features essential for catalysis and substrate recognition and will support the development of a structure-based substrate screening algorithm. By the end of the summer semester, students will gain scientific knowledge through a project-based inquiry approach and student-centered active learning. This experience will serve as an important asset for students applying to graduate programs and pursuing future careers in scientific research. 

• Project Title: Designing Magnetic Material for Sustainable Technology
• Mentor: Dr. Madalynn Marshall, Assistant Professor of Chemistry
• Format: In-person, Kennesaw Campus

Summary: Here we will explore the geometrically frustrated kagome lattice and it’s 3D analogue, named after a traditional Japanese basket-weaving pattern, for various sustainable applications where the control of magnetic properties is crucial. By distorting the kagome lattice and through tuning the degree of distortion, new magnetic and electrical properties can be realized. To understand how the magnetic behavior of these materials can be controlled, we will employ various internal and external stimuli such as temperature and chemical pressure by elemental doping. High temperature solid state crystal growth techniques will be utilized to grow single crystalline or powder samples. Structural characterization will be performed using both powder and single crystal X-ray diffraction instrumentation and the magnetic and electrical properties will be analyzed. This research training will teach students solid-state chemistry techniques from synthesis methods to various characterization methods as well as help students develop their critical thinking and scientific mindset. Through this research training students will take part in interdisciplinary research, collect and analyze experimental data, and gain experience writing and presenting results and publishing manuscripts. This research experience will help students pursue a PhD or MS in areas such as solid-state chemistry, condensed matter physics and materials science and provide students with the opportunity to explore a broad range of career paths including positions at national laboratories, in advanced materials industry and in academia. Depending at what stage the students are in the research process, the weekly duties will range from 1) reading scientific literature and completing assignments 2) synthesis and crystal growth 3) characterizing and interpreting chemical structures and physical properties 4) drafting manuscripts, posters, and presentations. This project will take place in person on the Kennesaw campus.

• Title: Applying Combinatorial Proofs to Examine Properties of Generalized Delannoy Numbers
• Mentor: Dr. William Griffiths, Associate Professor of Mathematics
• Format: In-person, Marietta Campus

Summary: Students begin the project learning the art of the combinatorial proof or mentoring other students, depending on their level of expertise. As students gain experience, they will be examine and study what is known about Generalized Delannoy Numbers, and finally will work together on actual discovery of interesting properties and attempt to prove them in partnership with the team lead.

More specifically, students will utilize the Online Encyclopedia of Integer Sequences (OEIS). We will examine a number of such sequences and their enumerations in the Encyclopedia, and students will practice proving properties of a number of known sequences, gaining knowledge in how researchers utilize OEIS in discovery and application. Activities will include independent study of these sequences and presenting findings to the group, resulting in students’ improvement in communicating mathematical ideas effectively.

The format of this project is in person and takes place on the Marietta campus. Student participants will work closely with the team lead as well as other members of the team, respecting each other’s differing skill levels and experiences. Working together, the project will move from education and studying interesting historical results to the recent work of the team lead on Generalized Delannoy Numbers. At this stage, the students will receive lectures from the team lead and essentially be taught the recent history of this project. Over the final four weeks of the project, the students will work together independently to apply all that they have learned to the actual discovery and proof of new properties of these numbers. There is an expectation of the students to be available in person on Tuesdays and Thursdays from 12:00 PM to approximately 7 PM, and to do two hours of independent work on Mondays, Wednesdays, and Fridays. Finally, the students will collaborate with the team lead in the dissemination of their results, which will minimally include a reflective report, a digital poster, and a presentation that will be made at a local and/or regional conference over the following academic year. 

• Title: From Benford’s Phenomenon to Scientific Explanation
• Mentor: Irina Pashchenko, Lecturer of Mathematics
• Format: Hybrid (In-person meetings will be on the Kennesaw Campus)

Summary: In this project, the students will first do online research about Benford's phenomenon, and then about any group of functions related to the students area of expertise. Any natural processes can be chosen for the research. Then the data will be compared to those of basic algebraic functions, and the closest one will be chosen for a further comparison. All the data related to the previously mentioned functions can be found in the article First Digit Probability and Benford's Law written by Irina Pashchenko. As a result, a conclusion about the nature of a particular process will be made in terms of the probability of its first digits.

The student will do online research and prepare a report for me. Then, the student will meet with me to discuss what was done and future plans. My office is located at the Kennesaw campus. However, we can meet online as well. Thus, the project will have a mixed format. 
Upon completing this project, students will be able to:

1. Use online resources for collecting data.
2. Organize collected data using an Excel file.
3. Perform data analysis using graphing software.
4. Apply Math to their area of expertise.