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3. Quartic Integral Polynomial Pell Equations

Author

Scherr, Zachary and Thompson, Katherine

Subjects
Mathematics - Number Theory, 14H52, 11G05
Abstract

In this paper we classify all monic, quartic, polynomials $d(x)\in\mathbb{Z}[x]$ for which the Pell equation $$f(x)^2-d(x)g(x)^2=1$$ has a non-trivial solution with $f(x),g(x)\in\mathbb{Z}[x]$.

Published
2023

4. Densities of integer sets represented by quadratic forms

Author

Clark, Pete L., Pollack, Paul, Rouse, Jeremy, and Thompson, Katherine

Subjects
Mathematics - Number Theory, Primary 11E12, Secondary 11E20
Abstract

Let $f(t_1,\ldots,t_n)$ be a nondegenerate integral quadratic form. We analyze the asymptotic behavior of the function $D_f(X)$, the number of integers of absolute value up to $X$ represented by $f$. When $f$ is isotropic or $n$ is at least $3$, we show that there is a $\delta(f) \in \mathbb{Q} \cap (0,1)$ such that $D_f(X) \sim \delta(f) X$ and call $\delta(f)$ the density of $f$. We consider the inverse problem of which densities arise. Our main technical tool is a Near Hasse Principle: a quadratic form may fail to represent infinitely many integers that it locally represents, but this set of exceptions has density $0$ within the set of locally represented integers., Comment: 25 pages

Published
2023

6. Palindromic Polynomials over Finite Fields

Author

Price, Geoffrey and Thompson, Katherine

Subjects
Mathematics - Number Theory, Mathematics - Combinatorics, 11T06, 15A06
Abstract

For any finite field $\mathbb{F}$ and any positive integer $n$ we count the number of monic polynomials of degree $n$ over $\mathbb{F}$ with nonzero constant coefficient and a self-reciprocal factor of any specified degree. An application is given for systems of linear equations over $\mathbb{F}$ of index $2$.

Published
2022

7. Elementary Proofs of Representation by Ternary Quadratic Forms

Author

Rainear, Benjamin and Thompson, Katherine

Subjects
Mathematics - Number Theory
Abstract

Mordell in 1958 gave a new proof of the three squares theorem. Those techniques were generalized by Blackwell, et al., in 2016 to characterize the integers represented by the remaining six "Ramanujan-Dickson ternaries". We continue the generalization of these techniques to four additional forms.

Published
2022

8. Quaternary quadratic forms with prime discriminant

Author

Rouse, Jeremy and Thompson, Katherine

Subjects
Mathematics - Number Theory, Primary 11E20, Secondary 11F27, 11F30, 11E12
Abstract

Let $Q$ be a positive-definite quaternary quadratic form with prime discriminant. We give an explicit lower bound on the number of representations of a positive integer $n$ by $Q$. This problem is connected with deriving an upper bound on the Petersson norm $\langle C, C \rangle$ of the cuspidal part of the theta series of $Q$. We derive an upper bound on $\langle C, C \rangle$ that depends on the smallest positive integer not represented by the dual form $Q^{*}$. In addition, we give a non-trivial upper bound on the sum of the integers $n$ excepted by $Q$., Comment: 20 pages

Published
2022

9. Sovereign and Pseudo-Hosts: The Politics of Hospitality for Negotiating Culturally Nourishing Schools

Author

Weuffen, Sara, Lowe, Kevin, Burgess, Cathie, and Thompson, Katherine

Abstract

Since contact, there has been a foundation of inhospitable interactions between the original sovereign peoples of the Australian continent and Eurpoean arrivals. Despite government policies appearing to shift from assimilative practices to reconciliation processes in the latter half of the 20th Century, ongoing interactions continue to be factious, caught up in discourses of power/knowledge, and, perhaps provocatively, couched primarily in misunderstandings. In the Australian schooling space, while there has been increased attention paid to the academic success of Aboriginal and/or Torres Strait Islander students, and greater inclusion of their families, communities, and cultural practices, non-Indigenous led schools continue to be hamstrung by their epistemic inertia -- the cognitive inability to move beyond the fear of getting it wrong, offending, or being labelled racist. In this paper, we argue that the major impediment to ongoing and unresolved discord is concealed in the onto-epistemological foundation of what it means to respect, accept, and work with. To address this, we take up Welcoming to Country practices and Derrida's concept of hospitality to interrogate how more nuanced conceptualisations of reciprocity may be used to move beyond performative acts of reconciliation. The outcome of which may be a reimagining of practices that are relational and responsive for embracing and nourishing Indigenous cultures and languages.

Published
2023
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10. Nearest neighbor ratio imputation with incomplete multi-nomial outcome in survey sampling

Author

Gao, Chenyin, Thompson, Katherine Jenny, Yang, Shu, and Kim, Jae Kwang

Subjects
Statistics - Methodology, Statistics - Applications
Abstract

Nonresponse is a common problem in survey sampling. Appropriate treatment can be challenging, especially when dealing with detailed breakdowns of totals. Often, the nearest neighbor imputation method is used to handle such incomplete multinomial data. In this article, we investigate the nearest neighbor ratio imputation estimator, in which auxiliary variables are used to identify the closest donor and the vector of proportions from the donor is applied to the total of the recipient to implement ratio imputation. To estimate the asymptotic variance, we first treat the nearest neighbor ratio imputation as a special case of predictive matching imputation and apply the linearization method of \cite{yang2020asymptotic}. To account for the non-negligible sampling fractions, parametric and generalized additive models are employed to incorporate the smoothness of the imputation estimator, which results in a valid variance estimator. We apply the proposed method to estimate expenditures detail items based on empirical data from the 2018 collection of the Service Annual Survey, conducted by the United States Census Bureau. Our simulation results demonstrate the validity of our proposed estimators and also confirm that the derived variance estimators have good performance even when the sampling fraction is non-negligible., Comment: Accepted for publication in JRSS(A)

Published
2022
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12. Outcome assessment of a complex mental health intervention in the workplace. Results from the MENTUPP pilot study

Author

Tsantila, Fotini, Coppens, Evelien, De Witte, Hans, Arensman, Ella, Amann, Benedikt, Cerga-Pashoja, Arlinda, Corcoran, Paul, Creswell-Smith, Johanna, Cully, Grace, Toth, Monika Ditta, Greiner, Birgit, Griffin, Eve, Hegerl, Ulrich, Holland, Carolyn, Leduc, Caleb, Leduc, Mallorie, Ni Dhalaigh, Doireann, O’Brien, Cliodhna, Paterson, Charlotte, Purebl, György, Reich, Hanna, Ross, Victoria, Rugulies, Reiner, Sanches, Sarita, Thompson, Katherine, and Van Audenhove, Chantal

Published
2023
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16. Trajectories of childhood social isolation in a nationally representative cohort: Associations with antecedents and early adulthood outcomes.

Author

Thompson, Katherine, Bryan, Bridget, Danese, Andrea, Milne, Barry, Strange, Lily, Matthews, Timothy, Arseneault, Louise, and Odgers, Candice

Subjects
developmental trajectories, growth mixture modelling, longitudinal research, mental health, social isolation
Abstract

BACKGROUND: This study examined early life antecedents of childhood social isolation, whether these factors accounted for poor outcomes of isolated children, and how these associations varied according to patterns of stability and change in childhood isolation. METHODS: Participants included 2232 children from the Environmental Risk (E-Risk) Longitudinal Twin Study. We conducted growth mixture modelling (GMM) on combined parent and teacher reports of childrens social isolation when children were 5, 7, 10 and 12 years, and we assessed associations with age-5 antecedents and age-18 outcomes using regression analyses. RESULTS: We identified three linear developmental trajectories of increasing (4.75%), decreasing (5.25%) and low stable (90.00%) social isolation. Age-5 attention deficit hyperactivity disorder (ADHD) symptoms, emotional problems, prosocial behaviours, maternal personality (openness) and size of school were associated with the decreasing trajectory of social isolation. When controlling for these antecedents, increasingly isolated children were still more likely to experience ADHD symptoms, loneliness, lower job optimism and lower physical activity at age 18. CONCLUSIONS: Isolated children follow distinct patterns of change over childhood and isolation seems most detrimental to health at the time it is experienced. Social isolation can be a valuable indicator of co-occurring problems and provide targets for mental health intervention in young people.

Published
2022

17. Trends on 3d Transition Metal Coordination on Monolayer MoS$_2$

Author

Liu, He, Silva, Walner Costa, de Souza, Leonardo Santana Gonçalves, Veiga, Amanda Garcez, Seixas, Leandro, Fujisawa, Kazunori, Kahn, Ethan, Zhang, Tianyi, Zhang, Fu, Yu, Zhuohang, Thompson, Katherine, Lei, Yu, de Matos, Christiano J. S., Rocco, Maria Luiza M., Terrones, Mauricio, and Grasseschi, Daniel

Subjects
Condensed Matter - Materials Science, Physics - Applied Physics
Abstract

Two-dimensional materials (2DM) have attracted much interest due to their distinct optical, electronic, and catalytic properties. These properties can be by tuned a range of methods including substitutional doping or, as recently demonstrated, by surface functionalization with single atoms, increasing even further 2DM portfolio. Here we theoretically and experimentally describe the coordination reaction between MoS$_2$ monolayers with 3d transition metals (TMs), exploring the nature and the trend of MoS$_2$-TMs interaction. Density Functional Theory calculations, X-Ray Photoelectron Spectroscopy (XPS), and Photoluminescence (PL) point to the formation of MoS$_2$-TM coordination complexes, where the adsorption energy trend for 3d TM resembles the crystal-field (CF) stabilization energy for weak-field complexes. Pearson's theory for hard-soft acid-base and Ligand-field theory were applied to discuss the periodic trends on 3d TM coordination on the MoS$_2$ surface. We found that softer acids with higher ligand field stabilization energy, such as Ni$^{2+}$, tend to form bonds with more covalent character with MoS$_2$, which can be considered a soft base. On the other hand, harder acids, such as Cr$^{3+}$, tend to form bonds with more ionic character. Additionally, we studied the trends in charge transfer and doping observed in the XPS and PL results, where metals such as Ni led to an n-type of doping, while Cu functionalization results in p-type doping. Therefore, the formation of coordination complexes on TMD's surface is demonstrated to be a promising and effective way to control and to understand the nature of the single-atom functionalization of TMD., Comment: 27 pages, 8 figures, Support Information after references section

Published
2021

18. Effect of the Communities that HEAL intervention on receipt of behavioral therapies for opioid use disorder: A cluster randomized wait-list controlled trial

Author

Glasgow, LaShawn, Douglas, Christian, Sprunger, Joel G., Campbell, Aimee N.C., Chandler, Redonna, Dasgupta, Anindita, Holloway, JaNae, Marks, Katherine R., Roberts, Sara M., Martinez, Linda Sprague, Thompson, Katherine, Weiss, Roger D., Aldridge, Arnie, Asman, Kat, Barbosa, Carolina, Blevins, Derek, Chassler, Deborah, Cogan, Lindsay, Fanucchi, Laura, Hall, Megan E., Hunt, Timothy, Jadovich, Elizabeth, Levin, Frances R., Lincourt, Patricia, Lofwall, Michelle R., Loukas, Vanessa, McAlearney, Ann Scheck, Nunes, Edward, Oga, Emmanuel, Oller, Devin, Rudorf, Maria, Sullivan, Ann Marie, Talbert, Jeffery, Taylor, Angela, Teater, Julie, Vandergrift, Nathan, Woodlock, Kristin, Zarkin, Gary A., Freisthler, Bridget, Samet, Jeffrey H., Walsh, Sharon L., and El-Bassel, Nabila

Published
2024
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21. CommunityRx, a social care assistance intervention for family and friend caregivers delivered at the point of care: two concurrent blinded randomized controlled trials

Author

Abramsohn, Emily M., De Ornelas, MariaDelSol, Borson, Soo, Frazier, Cristianne R. M., Fuller, Charles M., Grana, Mellissa, Huang, Elbert S., Jagai, Jyotsna S., Makelarski, Jennifer A., Miller, Doriane, Schulman-Green, Dena, Shiu, Eva, Thompson, Katherine, Winslow, Victoria, Wroblewski, Kristen, and Lindau, Stacy Tessler

Published
2023
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22. Sociodemographic, mental health, and physical health factors associated with participation within re-contactable mental health cohorts: an investigation of the GLAD Study

Author

Bright, Steven J., Hübel, Christopher, Young, Katherine S., Bristow, Shannon, Peel, Alicia J., Rayner, Christopher, Mundy, Jessica, Palmos, Alish B., Purves, Kirstin L., Kalsi, Gursharan, Armour, Cherie, Jones, Ian R., Hotopf, Matthew, McIntosh, Andrew M., Smith, Daniel J., Walters, James T. R., Rogers, Henry C., Thompson, Katherine N., Adey, Brett N., Monssen, Dina, Kakar, Saakshi, Malouf, Chelsea M., Hirsch, Colette, Glen, Kiran, Kelly, Emily J., Veale, David, Eley, Thalia C., Breen, Gerome, and Davies, Molly R.

Published
2023
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29. Correction: Outcome assessment of a complex mental health intervention in the workplace. Results from the MENTUPP pilot study

Author

Tsantila, Fotini, Coppens, Evelien, De Witte, Hans, Arensman, Ella, Amann, Benedikt, Cerga-Pashoja, Arlinda, Corcoran, Paul, Creswell-Smith, Johanna, Cully, Grace, Toth, Monika Ditta, Greiner, Birgit, Griffin, Eve, Hegerl, Ulrich, Holland, Carolyn, Leduc, Caleb, Leduc, Mallorie, Ni Dhalaigh, Doireann, O’Brien, Cliodhna, Paterson, Charlotte, Purebl, György, Reich, Hanna, Ross, Victoria, Rugulies, Reiner, Sanches, Sarita, Thompson, Katherine, and Van Audenhove, Chantal

Published
2023
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34. The e-scooter pandemic at a UK Major Trauma Centre: A cost-based cohort analysis of injury presentation and treatment

Author

Babalola, Folasade, Barker, Matthew, Smyth, Delia, Kingham, Matthew, Dua, Radihka, Almousa, O., Pepper, Tom, Thompson, Katherine, Alltimes, Gary, Hothi, Harinder, Al Soogun, Al-Farhane, Walter, Lorna, Dandeniya, Gulchan, Bently, Robert, Ahluwalia, Raju, Grainger, Charlotte, Coffey, Duncan, Malhotra, Prabhjot-Singh, Sommerville, Charlotte, Tan, P Sze, Johal, Kavan, Sivaprakasam, Manju, Almousa, Omar, Janakan, Gnananandan, Din, Asmat, Reichert, Ines, and Fan, Kathy

Published
2023
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35. Loss of control eating in relation to blood pressure among adolescent girls with elevated anxiety at-risk for excess weight gain

Author

Bauman, Viviana, Sanchez, Natalia, Repke, Hannah E., Spinner, Holly, Thorstad, Isabel, Gulley, Lauren D., Mains, Autumn M., Lavender, Jason M., Thompson, Katherine A., Emerick, Jill E., Thomas, Victoria, Arnold, Thomas B., Heroy, Andrew, Gutierrez-Colina, Ana M., Haigney, Mark C., Shomaker, Lauren B., and Tanofsky-Kraff, Marian

Published
2023
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46. Decolonising Schooling Practices through Relationality and Reciprocity: Embedding Local Aboriginal Perspectives in the Classroom

Author

Bishop, Michelle, Vass, Greg, and Thompson, Katherine

Abstract

Indigenous communities share concerns related to power, tokenism, and the reproduction of patterns of privilege and discrimination within formal schooling systems. These are issues that were central to ambitions of the "Culture, Community and Curriculum Project" (CCCP), the focus of this paper. The CCCP was a three-year 'pilot' study that accepted from the outset that Aboriginal parents and community members should have a genuine and meaningful role in education-related decision making and practices. We report on the processes and experiences of community members and teachers as they drew on local expertise to embed contextually responsive perspectives, knowledges, and ways of teaching that met national curriculum requirements, while concurrently fostering learners' critical social consciousness. We hope to illustrate how and why the embedding of local Aboriginal perspectives has enriched the learning experiences for all involved, whilst highlighting some of the challenges of such an approach being genuinely taken up more widely.

Published
2021
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47. Looking Closely at Clinical Practice: A Clear-Eyed Vision for the Future of Teacher Education

Author

Dresden, Janna and Thompson, Katherine F.

Abstract

Clinical practice has long been an integral component of teacher education. In the past two decades, however, the call has intensified for more purposeful, inclusive, integrated, and reflective clinical experiences for teacher candidates learning how to teach and, more broadly, what it means to be a teacher. This article aims to offer a conceptual understanding of clinical practice, the challenges to its viability, and recommendations for its future in teacher-education programs. The authors lay out defining characteristics of clinical practice; describe structural features that provide for extended time in the field, meaningful dialogue between stakeholders in clinical settings, and alignment between university coursework and field-based experiences; and cite the benefits of teacher candidates learning to teach in clinically rich settings. The authors also identify significant threats to establishing and maintaining a clinically based model of teacher education--specifically, the perception that theory and practice exist in distinct and disparate spaces in teacher preparation, the complex nature of school-university partnerships, and an entrenched neoliberal reform perspective. The essay concludes with recommendations for the sustainability of clinically rich teacher education, including the articulation of clinical-practice components and structures; a comprehensive research agenda derived from diverse purposes, methods, frameworks, and perspectives; inclusive and boundary-spanning collaborations between and among P-12 and university partners; and patience to work through the inevitable deliberations, challenges, and complexities of implementing and maintaining an effective clinical-practice model.

Published
2021
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49. Evaluating Eosinophilic Colitis as a Unique Disease Using Colonic Molecular Profiles: A Multi-Site Study

Author

Pablo Abonia, J., Aceves, Seema, Almonte, Samuel, Andrews, Rachel, Anvari, Sara, Arrington, Ashley, Arva, Nicoleta, Atkins, Fred, Bailey, Dominique, Berry, Alexis, Besl, Bridget, Bolton, Scott, Bonis, Peter, Book, Wendy, Bray, Kimberly, Brown, Teresa, Burger, Cassandra, Burke, Deirdre, Cahoon, Jonathon, Capocelli, Kelley, Chehade, Mirna, Chiou, Eric, Collins, Margaret, Davis, Carla, Dellon, Evan, DeMarshall, Maureen, DiTommaso, Lauren, Dohil, Ranjan, Eby, Michael, Falk, Gary, Fleischer, David, Foote, Heather, Foss, Kelci, Friedlander, Joel, Fulkerson, Patricia, Furuta, Glenn, Geno, Debra, Gonsalves, Nirmala, Greuter, Thomas, Gupta, Sandeep, Hamilton, Frank, Harris, Kirk, Harris, Jennifer, Hirano, Ikuo, Hiremath, Girish, Holland-Thomas, Nicole, Jacinto, Lea, Kagalwalla, Amir, Kaseta, Timothy, Katzka, David, Keeley, Kaitlin, Khosh-Hemmat, Emad, Khoury, Paneez, King, Eileen, Kliewer, Kara, Klion, Amy, Knowles, Jennifer, Kocher, Kendra, Kodroff, Ellyn, Krischer, Jeffrey, Kyle, Shay, Leung, John, Levy, Meredith, Liacouras, Chris, Mack, Denise, Martin, Lisa, Martin, Ellen, McCright-Gill, Talaya, Menard-Katcher, Paul, Menard-Katcher, Calies, Mendoza, Gabriela, Mingler, Melissa, Minnicozzi, Mike, Muir, Amanda, Mukkada, Vincent, Murray-Petzold, Cristin, Newbury, Robert, Nhu, Quan, Olive, Anthony, Oyibo, Oghenekpaobor (Joel), Paliana, Allisa, Pan, Zhaoxing, Pesek, Robbie, Peterson, Kathryn, Poppendeck, Heidi, Putnam, Philip, Rivera, Fabian, Rothenberg, Marc, Spergel, Amanda Rudman, Sable, Kathleen, Schoepfer, Alain, Scott, Melissa, Sheridan, Rachel, Sinanovic, Selma, Spergel, Jonathan, Strobel, Mary Jo, Sun, Kiki, Tasco, Amy, Tholen, Crystal, Thompson, Katherine, Tomkinson, Tiffany, Tran, Daisy, Tylicki, Alexandra, Urv, Tiina, Wang, Mei-Lun, Wechsler, Joshua, Wershil, Barry, Wheatley, Lisa, Wilkey, Leah, Yang, Guang-Yu, Zalewski, Angelika, Zicarelli, Amy, Shoda, Tetsuo, Collins, Margaret H., Rochman, Mark, Wen, Ting, Caldwell, Julie M., Mack, Lydia E., Osswald, Garrett A., Besse, John A., Haberman, Yael, Aceves, Seema S., Arva, Nicoleta C., Capocelli, Kelley E., Davis, Carla M., Dellon, Evan S., Falk, Gary W., Gupta, Sandeep K., Mukkada, Vincent A., Putnam, Philip E., Spergel, Jonathan M., Wechsler, Joshua B., Furuta, Glenn T., Denson, Lee A., and Rothenberg, Marc E.

Published
2022
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50. Patient characteristics associated with retrospectively self-reported treatment outcomes following psychological therapy for anxiety or depressive disorders - a cohort of GLAD study participants

Author

Rayner, Christopher, Coleman, Jonathan R.I., Skelton, Megan, Armour, Cherie, Bradley, John, Buckman, Joshua E.J., Davies, Molly R., Hirsch, Colette R., Hotopf, Matthew, Hübel, Christopher, Jones, Ian R., Kalsi, Gursharan, Kingston, Nathalie, Krebs, Georgina, Lin, Yuhao, Monssen, Dina, McIntosh, Andrew M., Mundy, Jessica R., Peel, Alicia J., Rimes, Katharine A., Rogers, Henry C., Smith, Daniel J., ter Kuile, Abigail R., Thompson, Katherine N., Veale, David, Wingrove, Janet, Walters, James T.R., Breen, Gerome, and Eley, Thalia C.

Published
2022
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