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2. Zero Forcing with Random Sets

Author

Curtis, Bryan, Gan, Luyining, Haddock, Jamie, Lawrence, Rachel, and Spiro, Sam

Subjects
Mathematics - Combinatorics, 05C15, 05C05, 05C31
Abstract

Given a graph $G$ and a real number $0\le p\le 1$, we define the random set $B_p(G)\subset V(G)$ by including each vertex independently and with probability $p$. We investigate the probability that the random set $B_p(G)$ is a zero forcing set of $G$. In particular, we prove that for large $n$, this probability for trees is upper bounded by the corresponding probability for a path graph. Given a minimum degree condition, we also prove a conjecture of Boyer et.\ al.\ regarding the number of zero forcing sets of a given size that a graph can have., Comment: 22 pages, 5 figures

Published
2022

6. Teachers with PhDs carrying out research on their teaching practice : the experience of participants on the Researchers in Schools Programme

Author

Lawrence, Rachel, Winch, Christopher Andrew, and Gibbons, Simon James

Abstract

This project is about a group of teachers carrying out research on their teaching practice. My starting point was that engaging with research can play an important part in teacher learning (BERA-RSA, 2014, p.3). The process of carrying out research on one's teaching practice can help to build teachers' morale and sense of professionalism (Mincu, 2015, p.265). There is a great deal of research on teachers carrying out research on their practice, this study offers a new perspective because it focuses on teachers who are on the Researchers in Schools programme. Researchers in Schools is a route into teaching and three-year training programme exclusively for PhD graduates. It is the first programme to gather teachers with PhDs together in this way, and as such it offers an opportunity to study this sub-set of teachers. My research question is 'How did carrying out a research project on their teaching practice help RIS participants develop their thinking?' The question may shed light on whether the participants were able to transfer their research skills from the PhD context to research on their teaching practice. I proposed that as participants had engaged in research at PhD level, they were likely to be 'research literate' (BERA-RSA, p.40). I reasoned that participants might be able to use these skills to help them reflect on their teaching practice and to inform their thinking. If so, at an individual level they would be able to contribute to creating 'research-rich' schools (BERARSA, p.40), where innovation and creativity are encouraged and teachers drive change rather than having it 'done' to them (BERA-RSA, 2014, p.40). The project involved one-hour interviews with 12 participants in the 2016 cohort of the RIS programme. I analysed the interviews using the 'constant comparative method' of analysis (Thomas, 2013, p.235). The findings from the interviews suggest that participants were 'research literate' (BERARSA, 2014, p.40) and they were able to transfer some of their research skills to their research on their teaching practice. Participants reported that they were confident in their ability to frame a research question and find relevant academic literature to help them answer the question. They stressed the importance of evaluating the literature and considering the context in which the research had taken place. Participants also appeared to have 'scholarship-informed dispositions' (Gewirtz, 2014, p.12) and scholarly habits. They appeared to be 'comfortable with theory' and able to 'think in disciplined ways' (Gewirtz, 2014, p. 13). Participants exhibited a 'healthy scepticism' (BERA-RSA, 2014, p.40) about research. It seems that doing a research project on their teaching practice helped participants to draw on their research expertise and reflect on how it was relevant to their teaching practice. The data from the interviews suggests that the wider context in which the participants completed their research projects was significant. The participants' thinking was influenced by the RIS training that they took part in, and the community of their RIS peers. It seems that participants in the cohort helped each other to form their identity as 'RIS teachers'. When they described what this meant to them, they identified certain characteristics of 'RIS teachers.' This included a preference for using data to inform their thinking about their teaching, being reflective about their teaching, and being confident to share their weaknesses with each other. I will argue that it is important that the participants completed their training as a cohort, as it allowed participants to acknowledge both their researcher and teacher identities in the training sessions. The findings from this study may lay the groundwork for further research about how to help teachers with PhDs connect their research experience with their teaching and use it to benefit the pupils that they teach.

Published
2022

9. Figure 1 from PIGA Mutations and Glycosylphosphatidylinositol Anchor Dysregulation in Polyposis-Associated Duodenal Tumorigenesis

Author

Meuser, Elena, primary, Chang, Kyle, primary, Walters, Angharad, primary, Hurley, Joanna J., primary, West, Hannah D., primary, Perry, Iain, primary, Mort, Matthew, primary, Reyes-Uribe, Laura, primary, Truscott, Rebekah, primary, Jones, Nicholas, primary, Lawrence, Rachel, primary, Jenkins, Gareth, primary, Giles, Peter, primary, Dolwani, Sunil, primary, Al-Sarireh, Bilal, primary, Hawkes, Neil, primary, Short, Emma, primary, Williams, Geraint T., primary, Taggart, Melissa W., primary, Luetchford, Kim, primary, Lynch, Patrick M., primary, Terlouw, Diantha, primary, Nielsen, Maartje, primary, Walton, Sarah-Jane, primary, Latchford, Andrew, primary, Clark, Susan K., primary, Sampson, Julian R., primary, Vilar, Eduardo, primary, and Thomas, Laura E., primary

Published
2024
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10. Supplementary Table S3 from PIGA Mutations and Glycosylphosphatidylinositol Anchor Dysregulation in Polyposis-Associated Duodenal Tumorigenesis

Author

Meuser, Elena, primary, Chang, Kyle, primary, Walters, Angharad, primary, Hurley, Joanna J., primary, West, Hannah D., primary, Perry, Iain, primary, Mort, Matthew, primary, Reyes-Uribe, Laura, primary, Truscott, Rebekah, primary, Jones, Nicholas, primary, Lawrence, Rachel, primary, Jenkins, Gareth, primary, Giles, Peter, primary, Dolwani, Sunil, primary, Al-Sarireh, Bilal, primary, Hawkes, Neil, primary, Short, Emma, primary, Williams, Geraint T., primary, Taggart, Melissa W., primary, Luetchford, Kim, primary, Lynch, Patrick M., primary, Terlouw, Diantha, primary, Nielsen, Maartje, primary, Walton, Sarah-Jane, primary, Latchford, Andrew, primary, Clark, Susan K., primary, Sampson, Julian R., primary, Vilar, Eduardo, primary, and Thomas, Laura E., primary

Published
2024
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11. Supplementary Figure S5 from PIGA Mutations and Glycosylphosphatidylinositol Anchor Dysregulation in Polyposis-Associated Duodenal Tumorigenesis

Author

Meuser, Elena, primary, Chang, Kyle, primary, Walters, Angharad, primary, Hurley, Joanna J., primary, West, Hannah D., primary, Perry, Iain, primary, Mort, Matthew, primary, Reyes-Uribe, Laura, primary, Truscott, Rebekah, primary, Jones, Nicholas, primary, Lawrence, Rachel, primary, Jenkins, Gareth, primary, Giles, Peter, primary, Dolwani, Sunil, primary, Al-Sarireh, Bilal, primary, Hawkes, Neil, primary, Short, Emma, primary, Williams, Geraint T., primary, Taggart, Melissa W., primary, Luetchford, Kim, primary, Lynch, Patrick M., primary, Terlouw, Diantha, primary, Nielsen, Maartje, primary, Walton, Sarah-Jane, primary, Latchford, Andrew, primary, Clark, Susan K., primary, Sampson, Julian R., primary, Vilar, Eduardo, primary, and Thomas, Laura E., primary

Published
2024
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12. Data from PIGA Mutations and Glycosylphosphatidylinositol Anchor Dysregulation in Polyposis-Associated Duodenal Tumorigenesis

Author

Meuser, Elena, primary, Chang, Kyle, primary, Walters, Angharad, primary, Hurley, Joanna J., primary, West, Hannah D., primary, Perry, Iain, primary, Mort, Matthew, primary, Reyes-Uribe, Laura, primary, Truscott, Rebekah, primary, Jones, Nicholas, primary, Lawrence, Rachel, primary, Jenkins, Gareth, primary, Giles, Peter, primary, Dolwani, Sunil, primary, Al-Sarireh, Bilal, primary, Hawkes, Neil, primary, Short, Emma, primary, Williams, Geraint T., primary, Taggart, Melissa W., primary, Luetchford, Kim, primary, Lynch, Patrick M., primary, Terlouw, Diantha, primary, Nielsen, Maartje, primary, Walton, Sarah-Jane, primary, Latchford, Andrew, primary, Clark, Susan K., primary, Sampson, Julian R., primary, Vilar, Eduardo, primary, and Thomas, Laura E., primary

Published
2024
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13. Figure 3 from PIGA Mutations and Glycosylphosphatidylinositol Anchor Dysregulation in Polyposis-Associated Duodenal Tumorigenesis

Author

Meuser, Elena, primary, Chang, Kyle, primary, Walters, Angharad, primary, Hurley, Joanna J., primary, West, Hannah D., primary, Perry, Iain, primary, Mort, Matthew, primary, Reyes-Uribe, Laura, primary, Truscott, Rebekah, primary, Jones, Nicholas, primary, Lawrence, Rachel, primary, Jenkins, Gareth, primary, Giles, Peter, primary, Dolwani, Sunil, primary, Al-Sarireh, Bilal, primary, Hawkes, Neil, primary, Short, Emma, primary, Williams, Geraint T., primary, Taggart, Melissa W., primary, Luetchford, Kim, primary, Lynch, Patrick M., primary, Terlouw, Diantha, primary, Nielsen, Maartje, primary, Walton, Sarah-Jane, primary, Latchford, Andrew, primary, Clark, Susan K., primary, Sampson, Julian R., primary, Vilar, Eduardo, primary, and Thomas, Laura E., primary

Published
2024
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14. Figure 2 from PIGA Mutations and Glycosylphosphatidylinositol Anchor Dysregulation in Polyposis-Associated Duodenal Tumorigenesis

Author

Meuser, Elena, primary, Chang, Kyle, primary, Walters, Angharad, primary, Hurley, Joanna J., primary, West, Hannah D., primary, Perry, Iain, primary, Mort, Matthew, primary, Reyes-Uribe, Laura, primary, Truscott, Rebekah, primary, Jones, Nicholas, primary, Lawrence, Rachel, primary, Jenkins, Gareth, primary, Giles, Peter, primary, Dolwani, Sunil, primary, Al-Sarireh, Bilal, primary, Hawkes, Neil, primary, Short, Emma, primary, Williams, Geraint T., primary, Taggart, Melissa W., primary, Luetchford, Kim, primary, Lynch, Patrick M., primary, Terlouw, Diantha, primary, Nielsen, Maartje, primary, Walton, Sarah-Jane, primary, Latchford, Andrew, primary, Clark, Susan K., primary, Sampson, Julian R., primary, Vilar, Eduardo, primary, and Thomas, Laura E., primary

Published
2024
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16. Counting Arcs in Projective Planes via Glynn's Algorithm

Author

Kaplan, Nathan, Kimport, Susie, Lawrence, Rachel, Peilen, Luke, and Weinreich, Max

Subjects
Mathematics - Combinatorics, 51E20, 51E15, 51A35
Abstract

An $n$-arc in a projective plane is a collection of $n$ distinct points in the plane, no three of which lie on a line. Formulas counting the number of $n$-arcs in any finite projective plane of order $q$ are known for $n \le 8$. In 1995, Iampolskaia, Skorobogatov, and Sorokin counted $9$-arcs in the projective plane over a finite field of order $q$ and showed that this count is a quasipolynomial function of $q$. We present a formula for the number of $9$-arcs in any projective plane of order $q$, even those that are non-Desarguesian, deriving Iampolskaia, Skorobogatov, and Sorokin's formula as a special case. We obtain our formula from a new implementation of an algorithm due to Glynn; we give details of our implementation and discuss its consequences for larger arcs., Comment: 19 pages, to appear in Journal of Geometry

Published
2016
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17. Simplicial Reaction Networks and Dynamics on Graphs

Author

Lawrence, Rachel

Subjects
Computer science, Mathematics, Dynamical systems, Graph theory, Minimum rank, Reaction networks, Theory of computing, Zero Forcing
Abstract

Reaction networks are a powerful tool for modeling the behavior of a wide variety of real-world systems, including population dynamics and chemical processes, as well as algorithms for sampling combinatorial objects. While many such systems have well-understood equilibrium states, the long-standing conjecture that these states will always be achieved remains open. This thesis presents the class of simplicial reaction networks, which includes a wide variety of natural combinatorial examples of use in theoretical computer science. It shows how simplicial structures can be used to understand and control the equilibrium behavior of the network as a whole, and discusses related progress towards the Global Attractor Conjecture. Finally, this thesis presents additional work exploring combinatorial approaches to the Inverse Eigenvalue Problem on graphs, including the randomized Zero Forcing algorithm and a lower bound for the Minimum Rank problem.

Published
2023

18. PIGA mutations and glycosylphosphatidylinositol anchor dysregulation in polyposis-associated duodenal tumorigenesis

Author

Meuser, Elena, primary, Chang, Kyle, additional, Walters, Angharad, additional, Hurley, Joanna J., additional, West, Hannah D., additional, Perry, Iain, additional, Mort, Matthew, additional, Reyes-Uribe, Laura, additional, Truscott, Rebekah, additional, Jones, Nicholas, additional, Lawrence, Rachel, additional, Jenkins, Gareth, additional, Giles, Peter, additional, Dolwani, Sunil, additional, Al-Sarireh, Bilal, additional, Hawkes, Neil, additional, Short, Emma, additional, Williams, Geraint T., additional, Taggart, Melissa W., additional, Luetchford, Kim, additional, Lynch, Patrick M., additional, Terlouw, Diantha, additional, Nielsen, Maartje, additional, Walton, Sarah-Jane, additional, Latchford, Andrew, additional, Clark, Susan K., additional, Sampson, Julian R., additional, Vilar, Eduardo, additional, and Thomas, Laura E., additional

Published
2024
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22. Discovery, preclinical validation and early human imaging with [11C]AZ14193391 – the first blood-brain barrier permeable and subtype selective PARP1 PET radioligand

Author

Cortes Gonzalez, Miguel Angel, primary, Jucaite, Aurelija, additional, Cselenyi, Zsolt, additional, Johnstrom, Peter, additional, Pike, Andy, additional, Högnäsbacka, Antonia, additional, Dahl, Kenneth, additional, Balazs, Amber, additional, Degorce, Sébastien, additional, Ghosh, Avipsa, additional, Hande, Sudir, additional, Johannes, Jeffrey, additional, Staniewska, Anna, additional, Leo, Elizabetta, additional, Hammerlik, Petra, additional, Davies, Barry, additional, Cosulich, Sabrina, additional, Swales, John, additional, Lawrence, Rachel, additional, Stenkrona, Per, additional, Farde, Lars, additional, Halldin, Christer, additional, and Schou, Magnus, additional

Published
2023
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25. Protocol for a Prospective Study Evaluating Circulating Tumour Cells Status to Predict Radical ProstatectomyTreatment Failure in Localised Prostate Cancer Patients (C- ProMeta-1)

Author

Al-Hammouri, Tarek, primary, Almeida-Magana, Ricardo, additional, Lawrence, Rachel, additional, Duffy, Tom, additional, White, Laura, additional, Burke, Edwina, additional, Kudahetti, Sakunthala, additional, Collins, Justin, additional, Rajan, Prabhakar, additional, Berney, Daniel, additional, Gabe, Rhian, additional, Shaw, Greg, additional, and Lu, Yong-Jie, additional

Published
2023
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28. O-69 - Discovery, preclinical validation and early human imaging with [11C]AZ14193391 – the first blood-brain barrier permeable and subtype selective PARP1 PET radioligand

Author

Cortes Gonzalez, Miguel Angel, Jucaite, Aurelija, Cselenyi, Zsolt, Johnstrom, Peter, Pike, Andy, Högnäsbacka, Antonia, Dahl, Kenneth, Balazs, Amber, Degorce, Sébastien, Ghosh, Avipsa, Hande, Sudir, Johannes, Jeffrey, Staniewska, Anna, Leo, Elizabetta, Hammerlik, Petra, Davies, Barry, Cosulich, Sabrina, Swales, John, Lawrence, Rachel, Stenkrona, Per, Farde, Lars, Halldin, Christer, and Schou, Magnus

Published
2023
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32. Abstract 6302: Structure-based and property-based drug design of AZD9574, a CNS penetrant PARP1 selective inhibitor and trapper

Author

Ghosh, Avipsa, primary, Hande, Sudhir M., additional, Balazs, Amber, additional, Barratt, Derek, additional, Cosulich, Sabina, additional, Davies, Barry, additional, Degorce, Sébastien, additional, Embrey, Kevin, additional, Gill, Sonja, additional, Gunnarsson, Anders, additional, Illuzzi, Giuditta, additional, Johnström, Peter, additional, Lane, Jordan, additional, Larner, Carrie, additional, Lawrence, Rachel, additional, Leo, Elisabetta, additional, Madin, Andrew, additional, Martin, Elizabeth, additional, McWilliams, Lisa, additional, O’Connor, Lenka, additional, O’Connor, Mark, additional, Orme, Jonathan, additional, Pachl, Fiona, additional, Packer, Martin, additional, Pike, Andy, additional, Rawlins, Philip, additional, Schimpl, Marianne, additional, Schou, Magnus, additional, Staniszewska, Anna, additional, Yang, Wenzhan, additional, Yates, James, additional, Zhang, Andrew, additional, Zheng, XiaoLa, additional, Fawell, Stephen, additional, Hamerlik, Petra, additional, and Johannes, Jeffrey, additional

Published
2022
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35. The constitutionality of caps: upholding Missouri's right to jury trial and the non-economic damages debate.

Author

Lawrence, Rachel

Subjects
Medical personnel -- Malpractice, Limitation of damages -- Laws, regulations and rules, Right to trial by jury -- Laws, regulations and rules, Watts v. Lester E. Cox Medical Centers 376 S.W.3d 633 (Mo. 2012) (376 S.W.3d 633 (Mo. 2012)), Government regulation, Missouri. Revised Statutes (Mo. Rev. Stat. 538.210)
Abstract

Watts v. Lester E. Cox Medical Centers, 376 S.W.3d 633 (Mo. 2012) (en banc) I. INTRODUCTION Imagine a loved one who, through no fault of their own, suffers from the [...]

Published
2013

39. Examining Depression, Self-Stigma, Caregiver Role Identity, and Self-Compassion in Clergy Help-Seeking Attitudes.

Author

Sager, Kristen, Duan, Changming, Lawrence, Rachel, and Warlick, Craig A.

Subjects
CAREGIVERS, HELP-seeking behavior, CLERGY, ATTITUDE (Psychology), SENSATION seeking, MENTAL health
Abstract

Clergy provide guidance and support; they also experience psychological distress. While clergy may seek support, they underutilize professional psychological services. This study examines the relationships among depression, self-stigma of help-seeking, caregiver role identity, self-compassion, and attitudes toward psychological help-seeking in a majority Christian clergy sample. Self-compassion predicted self-stigma of help-seeking and was associated with depressive symptom levels, caregiver role identity, and help-seeking attitudes. Findings also revealed that caregiver role identity did not relate to clergy self-stigma, but caregiver role identity was associated with higher levels of depressive symptoms. Findings inform recommendations for supporting clergy mental health. [ABSTRACT FROM AUTHOR]

Published
2022
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43. Farmers' Spending on Variable Inputs Tends to Maximise Crop Yields, Not Profit

Author

READER, Mark, Lang, Ben, Hodge, Ian, Revoredo-Giha, Cesar, Lawrence, Rachel, Reader, Mark [0000-0002-4730-9035], Hodge, Ian [0000-0003-2679-3478], and Apollo - University of Cambridge Repository

Subjects
bepress|Life Sciences|Agriculture|Agricultural Economics, productivity, oilseed rape, variable inputs, Life Sciences, marginal product, Agriculture, farm management, crops, fertilizer, AgriXiv|Life Sciences, Britain, bepress|Life Sciences|Agriculture, bepress|Life Sciences, wheat, AgriXiv|Life Sciences|Agriculture, AgriXiv|Life Sciences|Agriculture|Agricultural Economics, Agricultural Economics, crop protection
Abstract

We estimate the marginal returns to spending on Crop Variable Inputs (CVI) (such as fertilizers and crop protection), to explore whether observed spending maximises physical or economic returns to farmers. Data are taken from the Farm Business Survey for 2004-2013, where gross margins and input spending are available, in over 10,300 crops of conventional winter wheat or oilseed rape in England and Wales. Marginal spending on CVIs generate financial returns significantly less than £1 per marginal pound spent. This suggests that expenditure on CVIs exceeds an economic optimum that would maximise profit. However marginal physical products (crop yields) are positive, but small and significantly different from zero. This suggests that, on average, farmers approximately maximise yields. These results hold across a wide range of alternative economic models and two crop species. Similar results have been reported in estimations for Indian grain production and for maize in China. In practice, farmers are making decisions on input use in advance of having information on a variety of factors, including future yield, product quality and price, making it difficult to optimise input levels according to expected profit. Farmers may be consistently optimistic, prefer to avoid risk, or deliberately seek to maximise yields. Some farmers may put on the standard recommended application irrespective of input or expected output price. It is also possible that advice may sometimes aim to maximise yield, influenced by an incentive to encourage greater sales. Excessive input use both reduces private profits and is a cause of environmental damage. There are thus potential private as well as social benefits to be gained from optimising levels of input use., Rural Business Unit, Department of Land Economy, University of Cambridge

Published
2018
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45. Farmers’ spending on variable inputs tends to maximise crop yields, not profit

Author

Reader, Mark A., Revoredo-Giha, Cesar, Lawrence, Rachel J., Hodge, Ian D., and Galang, Ben

Subjects
marginal profit, fertiliser, agricultural productivity, Farm Management, marginal products, farm variable inputs, Crop Production/Industries, crop protection
Abstract

We estimate the marginal returns to spending on Crop Variable Inputs (CVI) (such as fertilizers and crop protection), to explore whether observed spending maximises physical or economic returns to farmers. Data are taken from the Farm Business Survey for 2004-2013, where gross margins and input spending are available, in over 10,300 crops of conventional winter wheat or oilseed rape in England and Wales. Marginal spending on CVIs generate financial returns significantly less than d1 per marginal pound spent. This suggests that expenditure on CVIs exceeds an economic optimum that would maximise profit. However marginal physical products (crop yields) are positive, but small and significantly different from zero. This suggests that, on average, farmers approximately maximise yields. These results hold across a wide range of alternative economic models and two crop species. Similar results have been reported in estimations for Indian grain production and for maize in China. In practice, farmers are making decisions on input use in advance of having information on a variety of factors, including future yield, product quality and price, making it difficult to optimise input levels according to expected profit. Farmers may be consistently optimistic, prefer to avoid risk, or deliberately seek to maximise yields. Some farmers may put on the standard recommended application irrespective of input or expected output price. It is also possible that advice may sometimes aim to maximise yield, influenced by an incentive to encourage greater sales. Excessive input use both reduces private profits and is a cause of environmental damage. There are thus potential private as well as social benefits to be gained from optimising levels of input use.

Published
2018
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49. Production day

Author

Lawrence, Rachel

Subjects
Editors, Journalists, News, opinion and commentary, Sports and fitness
Abstract

Byline: Rachel LawrenceSharing is caring!Anyone who walks into the Scroll office on a Saturday morning can depend on finding nearly two dozen staff members busy working on stories -- and [...]

Published
2018

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