Hopf Algebras in the Representation Theory of Combinatorial//Families of Groups

The main result of this thesis is that there exists a positive, self-adjoint Hopf (PSH) algebra structure in the representation theory of a certain family of groups. This new construction is inspired directly by Andrey Zelevinsky’s discovery of such a structure in the representation theory of the symmetric groups. Zelevinsky’s work Representations of finite classical groups: a Hopf algebra approach gives an account of this. We will walk through Zelevinsky’s work in this field in detail, and then follow up with the construction on the groups in question. We will develop the necessary theory along the way, with the reader assumed to be familiar with the basic properties of groups and rings. The notion of categories, functors, and Grothendieck groups will be useful, but knowledge of these concepts is not necessary for the reading of this thesis

Combinatorial Hopf algebras from representations of families of wreath products

We construct Hopf algebras whose elements are representations of combinatorial automorphism groups, by generalising a theorem of Zelevinsky on Hopf algebras of representations of wreath products. As an application we attach symmetric functions to representations of graph automorphism groups, generalising and refining Stanley's chromatic symmetric function.Comment: 26 page

Mindfulness as a Means to a Better Politics

Most people can recall a discussion or social situation in which their political views conflicted with those of other participants. A recent poll conducted of Ohioans by the Institute for Civics and Public Policy found that two-thirds of respondents reported they had strained personal relationships because of the political environment and nearly 8 in 10 agreed that the current political environment was as toxic as it had ever been in their lifetimes. Participating in society means coexisting with others and self-governance requires that individuals are able to come together to solve collective problems. With people feeling polarized within the current political climate, mindfulness can help remedy our civic engagement

Student Loan Forgiveness

Higher education is a gateway to better employment opportunities, and attending colleges, universities, or trade schools is essential for individuals hoping to pursue a career in specific fields. The cost to attend four-year universities has skyrocketed over the last several decades. Studies indicate that the average cost of tuition, room and board, and fees for an undergraduate degree has nearly tripled from 1980 to 2020. The Federal Reserve estimates that borrowers in the U.S. have accumulated an estimated $1.75 trillion worth of student loan debt. The Biden Administration has sought to address this by canceling billions of dollars in student loan debt

The State of the Union Address

Communication is one of the most important instruments in politics. Frequent and effective communication is a necessary benchmark for a well-functioning government. The State of the Union Address is among the most important dialogues between the executive and legislative branches. It has evolved into an opportunity for a president to tout their accomplishments and set an agenda for the upcoming year. The ability to broadcast the State of the Union Address via television, radio, and other communication forums allows it to function as more than just the president’s address to Congress, giving the president a medium to communicate with the public

Students Completion Rates: Implications for Teaching and Learning Resources in Secondary Schools in Kenya

This study provided a critical appraisal of the effect teaching and learning resources on students’ completion rates in secondary schools in Kenya. The main objective of the study was to investigate the influence of teaching and learning resources on students’ completion rates in secondary in schools in Kenya. The study examined the role played by bench marks on instructional materials in influencing students’ completion rates. The paper also assessed the role played instructional materials in promotion of students’ completion rates. The paper further investigated the availability of teaching and learning resources. Particular attention is given to the availability and utility of teaching and learning resources that affect completion rates of students. This study was guided by the systems and benchmarking theories. Systems theory was advanced by Ludwig von Bertalnffy (1968). He emphasized that systems are open and interact with their environments to acquire qualitatively properties. Systems theory focuses on the arrangement of relations between the parts which connect them into a whole. It focused on teaching and learning resources and how changes can impact on the completion rates of students. Benchmarking theory, as advanced by Watson (1993) is established upon the performance comparisons and gaps realized in performance process. Benchmarking approach performs the same function as performance gap analysis. In this context, benchmarking determines the performance gaps with respect to generation and utilization within the management system. The paper adopted document analysis method. This was drawn from international and local studies on students’ completion rates. The study further adopted the mixed method approach. Descriptive survey design was used to collect data from one set of questionnaires. The reliability was estimated through use of Cranach's Alpha Coefficient using Statistical Package for Social Sciences (SPSS) version 20.0.The target population comprised of head teachers, teachers and students in secondary schools. Using the sampling guide developed by Krejcie and Morgan (1970), a sample size of 24 head teachers and 120 teachers and 240 students was selected. The total sample size for the study was 384. This conformed to the confidence Interval of 0.05, confidence level of 95 percent which is a Z-score of 1.96 and standard of deviation of 0.5. The study findings revealed that teaching and learning resources were crucial for achieving high completion rates in secondary schools in Kenya. It was therefore concluded from the findings that teaching and learning resources contribute to a great extent the students’ completion rates in secondary schools in Kenya. Findings of the study are significant to Kenya in particular and sub Saharan Africa in general, as they would assist to redress challenges of quality education arising from constrained learning and teaching resources. The findings might help the policy formulators formulate education policies and the legal framework which are skewed towards students’ completion rates. The policy implementers would understand and appreciate education policies that contribute to students’ completion rates in secondary schools The study is significant to the field of comparative and International education, since it provides data on what the Kenyan government is doing in promoting the students’ completion rates in secondary schools. The entire education stakeholders would understand how to redress issues of teaching and learning resources. This study is significant to the field of comparative and International education, since it provides data on how teaching and learning resources impact on students’ completion rates in secondary schools in Kenya. Keywords: Completion rates, learning resources, pedagogical practices, Secondary education

Determining the Quantitative Principles of T Cell Response to Antigenic Disparity in Stem Cell Transplantation

Alloreactivity compromising clinical outcomes in stem cell transplantation is observed despite HLA matching of donors and recipients. This has its origin in the variation between the exomes of the two, which provides the basis for minor histocompatibility antigens (mHA). The mHA presented on the HLA class I and II molecules and the ensuing T cell response to these antigens results in graft vs. host disease. In this paper, results of a whole exome sequencing study are presented, with resulting alloreactive polymorphic peptides and their HLA class I and HLA class II (DRB1) binding affinity quantified. Large libraries of potentially alloreactive recipient peptides binding both sets of molecules were identified, with HLA-DRB1 generally presenting a greater number of peptides. These results are used to develop a quantitative framework to understand the immunobiology of transplantation. A tensor-based approach is used to derive the equations needed to determine the alloreactive donor T cell response from the mHA-HLA binding affinity and protein expression data. This approach may be used in future studies to simulate the magnitude of expected donor T cell response and determine the risk for alloreactive complications in HLA matched or mismatched hematopoietic cell and solid organ transplantation

Next-generation carrier screening

Purpose: Carrier screening for recessive Mendelian disorders traditionally employs focused genotyping to interrogate limited sets of mutations most prevalent in specific ethnic groups. We sought to develop a next-generation DNA sequencing–based workflow to enable analysis of a more comprehensive set of disease-causing mutations. Methods: We utilized molecular inversion probes to capture the protein-coding regions of 15 genes from genomic DNA isolated from whole blood and sequenced those regions using the Illumina HiSeq 2000 (Illumina, San Diego, CA). To assess the quality of the resulting data, we measured both the fraction of the targeted region yielding high-quality genotype calls, and the sensitivity and specificity of those calls by comparison with conventional Sanger sequencing across hundreds of samples. Finally, to improve the overall accuracy for detecting insertions and deletions, we introduce a novel assembly-based approach that substantially increases sensitivity without reducing specificity. Results: We generated high-quality sequence for at least 99.8% of targeted base pairs in samples derived from blood and achieved high concordance with Sanger sequencing (sensitivity >99.9%, specificity >99.999%). Our novel algorithm is capable of detecting insertions and deletions inaccessible by current methods. Conclusion: Our next-generation DNA sequencing–based approach yields the accuracy and completeness necessary for a carrier screening test

Progress in adolescent health and wellbeing: tracking 12 headline indicators for 195 countries and territories, 1990–2016

Background: Rapid demographic, epidemiological, and nutritional transitons have brought a pressing need to track progress in adolescent health. Here, we present country-level estimates of 12 headline indicators from the Lancet Commission on adolescent health and wellbeing, from 1990 to 2016. Methods: Indicators included those of health outcomes (disability-adjusted life-years [DALYs] due to communicable, maternal, and nutritional diseases; injuries; and non-communicable diseases); health risks (tobacco smoking, binge drinking, overweight, and anaemia); and social determinants of health (adolescent fertility; completion of secondary education; not in education, employment, or training [NEET]; child marriage; and demand for contraception satisfied with modern methods). We drew data from the Global Burden of Diseases, Injuries, and Risk Factors Study (GBD) 2016, International Labour Organisation, household surveys, and the Barro-Lee education dataset. Findings: From 1990 to 2016, remarkable shifts in adolescent health occurred. A decrease in disease burden in many countries has been offset by population growth in countries with the poorest adolescent health profiles. Compared with 1990, an additional 250 million adolescents were living in multi-burden countries in 2016, where they face a heavy and complex burden of disease. The rapidity of nutritional transition is evident from the 324·1 million (18%) of 1·8 billion adolescents globally who were overweight or obese in 2016, an increase of 176·9 million compared with 1990, and the 430·7 million (24%) who had anaemia in 2016, an increase of 74·2 million compared with 1990. Child marriage remains common, with an estimated 66 million women aged 20–24 years married before age 18 years. Although gender-parity in secondary school completion exists globally, prevalence of NEET remains high for young women in multi-burden countries, suggesting few opportunities to enter the workforce in these settings. Interpretation: Although disease burden has fallen in many settings, demographic shifts have heightened global inequalities. Global disease burden has changed little since 1990 and the prevalence of many adolescent health risks have increased. Health, education, and legal systems have not kept pace with shifting adolescent needs and demographic changes. Gender inequity remains a powerful driver of poor adolescent health in many countries. Funding: Australian National Health and Medical Research Council, and the Bill & Melinda Gates Foundatio

Determining the Quantitative Principles of T Cell Response to Antigenic Disparity in Stem Cell Transplantation

Alloreactivity compromising clinical outcomes in stem cell transplantation is observed despite HLA matching of donors and recipients. This has its origin in the variation between the exomes of the two, which provides the basis for minor histocompatibility antigens (mHA). The mHA presented on the HLA class I and II molecules and the ensuing T cell response to these antigens results in graft vs. host disease. In this paper, results of a whole exome sequencing study are presented, with resulting alloreactive polymorphic peptides and their HLA class I and HLA class II (DRB1) binding affinity quantified. Large libraries of potentially alloreactive recipient peptides binding both sets of molecules were identified, with HLA-DRB1 generally presenting a greater number of peptides. These results are used to develop a quantitative framework to understand the immunobiology of transplantation. A tensor-based approach is used to derive the equations needed to determine the alloreactive donor T cell response from the mHA-HLA binding affinity and protein expression data. This approach may be used in future studies to simulate the magnitude of expected donor T cell response and determine the risk for alloreactive complications in HLA matched or mismatched hematopoietic cell and solid organ transplantation