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The Pascal Matrix, Commuting Tridiagonal Operators and Fourier Algebras
We consider the (symmetric) Pascal matrix, in its finite and infinite versions, and prove the existence of symmetric tridiagonal matrices commuting with it by giving explicit expressions for these commuting matrices. This is achieved by studying the associated Fourier algebra, which as a byproduct, allows us to show that all the linear relations of a certain general form for the entries of the Pascal matrix arise from only three basic relations. We also show that pairs of eigenvectors of the tridiagonal matrix define a natural eigenbasis for the binomial transform. Lastly, we show that the commuting tridiagonal matrices provide a numerically stable means of diagonalizing the Pascal matrix.https://doi.org/10.1016/j.laa.2025.09.02
The persistence of very low correlations between NIH research funding and disease burdens
Objectives: The degree to which the allocation of disease-specific research funding by the NIH is proportional to disease burden is an important question. This study examined the historical relationship between NIH funding allocation and disease burden for a variety of medical conditions. Study design: Coefficients of relatedness for the linear relationships between funding and disease burden for 27 medical conditions over a period exceeding twenty years were calculated. Methods: Publicly available data from 2009 to 2019, and previously published data from 1994 to 2004, was obtained to compare disease-specific research funding from the NIH to burden of disease values (mortality, prevalence, incidence, DALYs, and YLLs) for 27 diseases. Results: We identified very weak and declining correlations (e.g., R2 < 0.03) between funding and the five measures of burden for the 27 diseases. The weak relationships persist even when HIV/AIDS is omitted (e.g., R2 < 0.1). A recent decline in the overall strengths of the funding burden relationships is attributable to novel investment in Alzheimer's disease research. Conclusions: The weak correlations reveal long-standing inefficiencies in the NIH disease funding allocation process. The recent increased and focused funding for Alzheimer's disease may not be justified by an objective analysis which considers disease burdens. Increased efficiency of medical research may be realized by improving the poor match between disease burden and funding allocation.https://www.sciencedirect.com/science/article/pii/S2666535224001174https://doi.org/10.1016/j.puhip.2024.1005802666-535
Autonomous Drone Communication Using LoRa and MAVLink for Long-Range Control
This project focuses on extending the range of communication from an autonomous drone control by integrating LoRa technology with MAVlink protocol on an onboard computer (Raspberry Pi). This system will increase the range from traditional communication protocols like Wi-Fi or Bluetooth where range has limitations. Key objectives include establishing LoRa communication where commands can be sent or received between ground stations and the onboard computer. The command received by the onboard computer will be able to translate into a MAVlink message for the pixhawk flight controller. Testing performance in various environments demonstrates significant range improvement making this approach viable and low power for long-range autonomous missions
Advanced Left Atrial Segmentation Using Heart MRI Images for Cardiac Care
This research assesses deep learning models, including U-Net and SegNet, for segmentation of cardiac MRI images for the segmentation of the left atrium. To benchmark, U-Net and SegNet were trained on a dataset of cardiac MRI scans and evaluated based on their accuracy, efficiency and clinical relevance. The comparisons of the models were done based on two scores, which include the Dice coefficient and the training loss. The evaluation results also revealed that the U-Net provided a much higher segmentation accuracy than SegNet achieving a Dice coefficient of up to 0.973 as compared to 0.6789 for SegNet. The outcomes demonstrate how U-Net's architecture outperforms its rivals, especially the encoder-decoder structure with skip connections for detailed and broader anatomical structures necessary for excellent medical imaging. This is important for the future of the clinical application of U-Net in the cardiac care because the more detailed and more precise segmentations are likely to help the doctor in diagnosis and the planning of the treatment process of cardiac patients. The paper also evaluates the existing studies and defines further opportunities for their development: model refinement, combinations of multi-modal imaging data, and innovative machine learning approaches for improving the effectiveness of segmentation instruments in medical practice
Optimizing a Tree Network to Minimize Communication Delayin Synchronized Distributed Machine Learning Process
This report explores the development of an efficient network design for distributed machine learning. It is specifically for the Distributed Dual Coordinate Ascent (DDCA) on a tree network. Traditional algorithms, such as the Minimum Spanning Tree (MST), focus on minimizing the sum of edge weights but are not optimal with respect to communication delay for distributed machine learning models. This project introduces the Optimal Minimum Worst Distance Tree (OMWDT) algorithm, a novel approach aimed at reducing the length of the longest communication path between leaf nodes in a network with a given depth. By structuring connections to reduce the maximum distance across the network, OMWDT provides a marked improvement in communication efficiency. This leads to accelerated convergence in distributed machine-learning processes. Experimental results show that OMWDT not only reduces the worst-case communication delays compared to MST but also leads to significant improvements in the practical efficiency of the DDCA algorithm. These results demonstrate the potential of OMWDT as a foundational structure for data driven application optimization on general tree networks
The Granola Revolution: Crafting a Health-Conscious Snack for the Modern Consumer
[ABSTRACT ONLY; NO FULL TEXT] This report was developed as part of a consulting project for Sweet Debbie's, a granola company. Sweet Debbie's currently follows a direct-to-consumer (DTC) model, having originated during the early 2000s when demand for healthier sweet alternatives was on the rise. Initially focused on vegan and sugar-free cupcakes, the company quickly gained popularity due to the owner's belief that healthy food could be both delicious and nourishing. With an eye on long-term growth, the owner envisions transforming Sweet Debbie's into a national brand. Our research highlighted the deep passion and expertise of the owner in promoting the health benefits of granola and incorporating high-quality superfood ingredients that set Sweet Debbie's apart as a premium brand. Key strategies for successfully scaling the business include enhancing brand awareness, optimizing revenue, and expanding distribution channels. Distribution should be expanded to multi-channel outlets such as Amazon, farmer's markets, coffee shops and health-conscious platforms
Thesis - Granola Revolution. Crafting a Health Conscious Snack for Modern Consumers
[ABSTRACT ONLY; NO FULL TEXT] We produced this report as a consulting project for Sweet Debbie's granola company. Sweet Debbie's is a company that operates in a direct-to-consumer (DTC) model. The company's inception began with the increased public demand for healthier alternatives to sweets, and thus, Sweet Debbie's was born. Given the public's interest in this "healthier" sector, Sweet Debbie's experienced growth, predicated on the hypothesis that you can bring healthy food to consumers that is pleasing to the palate and positive for the body. Our client is interested in a long-term growth plan for the Sweet Debbie's brand. Our research revealed a passionate owner and operator of the company who has expertise in the health benefits of granola and superfood ingredients that differentiate the product as a premium and high quality brand. Our research also revealed a business that does not have a scalable supply chain. This was revealed through company financials in which we analyzed specific financial ratios and indicators. We also uncovered competitors in the space with substantially more brand recognition who pose a threat to Sweet Debbies. Interventions needed for the scaling of the company include increasing brand awareness, revenue optimization, and the widening of distribution channels. Refining current marketing efforts and developing online reels leveraging the client's expertise will be vital. The company's supply chain will require more cost-effective ingredients, packaging and shipping solutions. Lastly, Sweet Debbie's will need to widen distribution channels through multi-channel distribution and fulfillment. I have contributed to this project in numerous ways, including administrative items, contributions to analysis, drafting of interview questions and overall guidance on a business-oriented approach. I drafted the team contract and created the shared calendar. I also created many of the questions we used to guide our initial conversation with the client as well as synthesized the client's answers into categorical areas for our group to further explore and utilize for analysis. My contribution to the analysis was specifically around product line expansion and wholesale and retail partnerships. Lastly, I contributed by sharing context with our committee members and will have participated in the final presentation to faculty and our client
The Effects Of Attire On Athlete's Perception Of Health Care Professionals
[ABSTRACT ONLY; NO FULL TEXT] Athletic Trainers (ATs) play a vital role in the prevention, treatment, and rehabilitation of injuries, working closely with other allied healthcare professionals. Despite the importance of their work, limited research has been conducted on the impact of attire within the athletic training career field. Studies in other allied healthcare fields suggest that attire can significantly influence perceptions of professionalism, knowledge, competence, and approachability. To address this gap, this study aims to investigate the effects of attire on student athletes' perceptions of ATs regarding their healthcare competencies. A comprehensive search of literature from 2004 to 2023 was conducted, focusing on systematic reviews, quantitative research, and case studies. As well as studies related to athletes' and patients' perception on attire in athletic training and other allied healthcare professions. While limited evidence exists regarding the direct impact of athletic trainers' attire on professionalism and perception, existing literature underscores the importance of attire in shaping first impressions. First impressions based on appearance and attire can significantly influence perceptions of competence and health status, not only among athletes but also within the broader healthcare community. Healthcare professionals across various disciplines, including nurses, physicians, dieticians, and psychologists, emphasize the critical role of first impressions in building rapport with patients. Attire is recognized as a key factor in shaping these initial perceptions. Continued research is necessary to better understand the effects of attire on perception within the athletic training profession. By enhancing professional identity and aligning with standards observed in other allied healthcare professions, athletic trainers can elevate their status and presence within the healthcare field. Understanding the nuances of attire and its impact on perception can contribute to more effective interactions and relationships between ATs and their patient
Addressing Substance Use Disparities
[ABSTRACT ONLY; NO FULL TEXT] The Division of Adolescent and Young Adult Medicine at Children's Hospital Los Angeles provides comprehensive healthcare to adolescents and young adults by addressing their physical, emotional, and social wellbeing. Among its wide range of programs and services is a state-certified Substance Use Prevention and Treatment Program that offers outpatient services and community programming. An innovative strategy is being proposed to adapt the Collective of Youth Leaders program, which focuses on preventing opioid overdoses among youth of color. This adaptation of the program will target LGBTQ youth and will be guided by the PRECEDE PROCEED program planning model. LGBTQ youth experience disproportionately higher rates of opioid misuse and poorer health outcomes compared to their peers. The conceptual framework for the adaptation of the program is rooted in the constructs of the Health Belief Model and Social Cognitive Theory, aiming to enhance self-efficacy and address health related behaviors among LGBTQ youth. The goal of the program is to reduce opioid overdose rates among LGBTQ youth. The program is structured around four key objectives that serve as the foundation for the program. The adapted program will be piloted over a 12-month period, and evaluation methods have been carefully developed to assess and measure the effectiveness of the innovative strategy
Distribution of Naloxone to prevent opioid overdose in Indiana
[ABSTRACT ONLY; NO FULL TEXT] The Indiana Department of Health plays a crucial role in public health by emphasizing disease prevention, health education, and access to healthcare services for all the residents of Indiana. The organization ensures the overall well-being of the community through different programs like naloxone distribution to Local Health Departments to prevent opioid overdose in Indiana. The distribution of the naloxone program was recently started by the Division of Trauma and Injury Prevention of the Indiana Department of Health. The organization provides vital education and training on naloxone by working closely with the Local Health Departments, stakeholders, the general public, and prevention organizations. The program planning model that best fits based on the services provided by the organization is the Precede-Proceed model. Approximately 108,000 people died in the year 2022 due to drug overdose, of which 76 percent of deaths were due to opioids. The proposed strategy focuses on reducing the prevalence of opioid overdose in Indiana. To achieve the goal, four objectives will be used based on the constructs of the Theory of Planned Behavior and the Health Belief Model. To measure and evaluate the impact of the intervention, appropriate evaluation techniques will be used. The proposed strategy will be piloted for a year and will provide a deeper understanding of the strengths and areas for improvement in the naloxone distribution program of the Indiana Department of Health