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1. Noncommutative Choquet theory: A Survey

Author

Davidson, Kenneth R. and Kennedy, Matthew

Subjects
Mathematics - Operator Algebras, Mathematics - Functional Analysis, Primary 46A55, 46L07, 47A20, Secondary 46L52, 47L25
Abstract

We survey noncommutative Choquet theory and some of its applications., Comment: To appear in "Operator Theory" edited by Daniel Alpay, Fabrizio Colombo and Irene Sabadini with Springer Nature. 27 pages

Published
2024

3. Intermediate subalgebras for reduced crossed products of discrete groups

Author

Kennedy, Matthew and Ursu, Dan

Subjects
Mathematics - Operator Algebras, Mathematics - Functional Analysis
Abstract

Let $\alpha : \Gamma \curvearrowright A$ be an action of a discrete group $\Gamma$ on a unital C*-algebra $A$ by *-automorphisms and let $A \rtimes_{\alpha,\lambda} \Gamma$ denote the corresponding reduced crossed product C*-algebra. Assuming that $\Gamma$ satisfies the approximation property, we establish a sufficient and (almost always) necessary condition on the action $\alpha$ for the existence of a Galois correspondence between intermediate C*-algebras for the inclusion $A \subseteq A \rtimes_{\alpha,\lambda} \Gamma$ and partial subactions of $\alpha$. This condition, which we refer to as pointwise residual proper outerness, is a natural noncommutative generalization of freeness., Comment: 29 pages

Published
2024

5. An extension property for noncommutative convex sets and duality for operator systems

Author

Humeniuk, Adam, Kennedy, Matthew, and Manor, Nicholas

Subjects
Mathematics - Operator Algebras, Mathematics - Functional Analysis, 46A55, 46L07, 46L52, 47L25, 47L50
Abstract

We characterize inclusions of compact noncommutative convex sets with the property that every continuous affine function on the smaller set can be extended to a continuous affine function on the larger set with a uniform bound. As an application of this result, we obtain a simple geometric characterization of (possibly nonunital) operator systems that are dualizable, meaning that their dual can be equipped with an operator system structure. We further establish some permanence properties of dualizability, and provide a large new class of dualizable operator systems. These results are new even when specialized to ordinary compact convex sets.

Published
2023

8. Frontmatter

Author

Kennedy, Matthew

Published
2007

12. Index

Author

Kennedy, Matthew

Published
2007

13. Cover

Author

Kennedy, Matthew

Published
2007

17. Epilogue

Author

Kennedy, Matthew

Published
2007

29. Inserting agility in system development

Author

Kennedy, Matthew R. and Ward, Dan, LtCol

Subjects
PROCUREMENT - Defense Dept - United States - Methodology, PROGRAM PLANNING - Methodology, INFORMATION TECHNOLOGY - Methodology
Abstract

illus por tab bibliog

Published
2012

30. Evaluating open source software

Author

Kennedy, Matthew

Subjects
COMPUTERS - Software - Design, COMPUTERS - Military Applications - Design
Abstract

illus

Published
2010

32. The ideal intersection property for essential groupoid C*-algebras

Author

Kennedy, Matthew, Kim, Se-Jin, Li, Xin, Raum, Sven, and Ursu, Dan

Subjects
Mathematics - Operator Algebras, Mathematics - Dynamical Systems, Mathematics - Group Theory
Abstract

We characterise, in several complementary ways, \'etale groupoids with locally compact Hausdorff space of units whose essential groupoid C*-algebra has the ideal intersection property, assuming that the groupoid is topologically transitive and either Hausdorff or $\sigma$-compact. This leads directly to a characterisation of the simplicity of this C*-algebra which, for Hausdorff groupoids, agrees with the reduced groupoid C*-algebra. Specifically, we prove for topologically transitive groupoids that the ideal intersection property is equivalent to the absence of essentially confined amenable sections of isotropy groups. For topologically transitive groupoids with compact space of units we moreover show that this is equivalent to the uniqueness of equivariant pseudo-expectations. A key technical idea underlying our results is a new notion of groupoid action on C*-algebras including the essential groupoid C*-algebra itself. For minimal groupoids, we further obtain a relative version of Powers averaging property. Examples arise from suitable group representations into simple groupoid \Cstar-algebras. This is illustrated by the example of the quasi-regular representation of Thompson's group $\mathrm{T}$ with respect to Thompson's group $\mathrm{F}$, which satisfies the relative Powers averaging property in the Cuntz algebra $\mathcal{O}_2$., Comment: 59 pages; v3: corrected a mistake from previous versions and the literature, assumption of topological transitivity added to some main results. v2: reorganised introduction, added some results, minor corrections, added references

Published
2021

33. Nonunital operator systems and noncommutative convexity

Author

Kennedy, Matthew, Kim, Se-Jin, and Manor, Nicholas

Subjects
Mathematics - Operator Algebras, Mathematics - Functional Analysis
Abstract

We establish the dual equivalence of the category of (potentially nonunital) operator systems and the category of pointed compact nc (noncommutative) convex sets, extending a result of Davidson and the first author. We then apply this dual equivalence to establish a number of results about operator systems, some of which are new even in the unital setting. For example, we show that the maximal and minimal C*-covers of an operator system can be realized in terms of the C*-algebra of continuous nc functions on its nc quasistate space, clarifying recent results of Connes and van Suijlekom. We also characterize "C*-simple" operator systems, i.e. operator systems with simple minimal C*-cover, in terms of their nc quasistate spaces. We develop a theory of quotients of operator systems that extends the theory of quotients of unital operator algebras. In addition, we extend results of the first author and Shamovich relating to nc Choquet simplices. We show that an operator system is a C*-algebra if and only if its nc quasistate space is an nc Bauer simplex with zero as an extreme point, and we show that a second countable locally compact group has Kazhdan's property (T) if and only if for every action of the group on a C*-algebra, the set of invariant quasistates is the quasistate space of a C*-algebra., Comment: 48 pages

Published
2021

34. Amenability, proximality and higher order syndeticity

Author

Kennedy, Matthew, Raum, Sven, and Salomon, Guy

Subjects
Mathematics - Group Theory, Mathematics - Dynamical Systems, Mathematics - Functional Analysis, Mathematics - Operator Algebras
Abstract

We show that the universal minimimal proximal flow and the universal minimal strongly proximal flow of a discrete group can be realized as the Stone spaces of translation invariant Boolean algebras of subsets of the group satisfying a higher order notion of syndeticity. We establish algebraic, combinatorial and topological dynamical characterizations of these subsets that we use to obtain new necessary and sufficient conditions for strong amenability and amenability. We also characterize dense orbit sets, answering a question of Glasner, Tsankov, Weiss and Zucker., Comment: 42 pages; minor changes

Published
2020

39. Lack of regional pathways impact on surgical delay: Analysis of the Orthopaedic Trauma Hospital Outcomes–Patient Operative Delays (ORTHOPOD) study

Author

Stevenson, Iain, Yoong, Andrel, Rankin, Iain, Dixon, James, Lim, Jun Wei, Sattar, Mariam, McDonald, Stephen, Scott, Sharon, Davies, Helen, Jones, Louise, Nolan, Michelle, McGinty, Rebecca, Stevenson, Helene, Bowe, David, Sim, Francis, Vun, James, Strain, Ritchie, Giannoudis, Vasileios, Talbot, Christopher, Gunn, Christopher, Le, Ha Phuong Do, Bradley, Matthew, Lloyd, William, Hanratty, Brian, Lim, Yizhe, Brookes-Fazakerley, Steven, Varasteh, Amir, Francis, Jonathan, Choudhry, Nameer, Malik, Sheraz, Vats, Amit, Evans, Ashish, Garner, Madeleine, King, Stratton, Zbaeda, Mohamed, Diamond, Owen, Baker, Gavin, Napier, Richard, Guy, Stephen, McCauley, Gordon, King, Samuel, Edwards, Gray, Lin, Benjamin, Davoudi, Kaveh, Haines, Samuel, Raghuvanshi, Manav, Buddhdev, Pranai, Karam, Edward, Nimmyel, Enoch, Ekanem, George, Lateef, Razaq, Jayadeep, JS, Crowther, Ian, Mazur, Karolina, Hafiz, Nauman, Khan, Umair, Chettiar, Krissen, Ibrahim, Amr, Gopal, Prasanth, Tse, Shannon, Lakshmipathy, Raj, Towse, Claudia, Al-Musawi, Hashim, Walmsley, Matthew, Aspinall, Will, Metcalfe, James, Moosa, Aliabbas, Crome, George, Abdelmonem, Mohamed, Lakpriya, Sathya, Hawkins, Amanda, Waugh, Dominic, Kennedy, Matthew, Elsagheir, Mohamed, Kieffer, Will, Oyekan, Adekinte, Collis, Justin, Raad, Marjan, Raut, Pramin, Baker, Markus, Gorvett, Alexander, Gleeson, Hannah, Fahmy, John, Walters, Sam, Tinning, Craig, Chaturvedi, Abhishek, Russell, Heather, Alsawada, Osama, Sinnerton, Robert, Crane, Evan, Warwick, Catherine, Dimascio, Lucia, Ha, Taegyeong Tina, King, Thomas, Engelke, Daniel, Chan, Matthew, Gopireddy, Rajesh, Deo, Sunny, Vasarhelyi, Ferenc, Jhaj, Jasmeet, Dogramatzis, Kostas, McCartney, Sarah, Ardolino, Toni, Fraig, Hossam, Hiller-Smith, Ryan, Haughton, Benjamin, Greenwood, Heather, Stephenson, Nicola, Chong, Yuki, Sleat, Graham, Saedi, Farid, Gouda, Joe, Ravi, Sanjeev Musuvathy, Henari, Shwan, Imam, Sam, Howell, Charles, Theobald, Emma, Wright, Jan, Cormack, Jonathan, Borja, Karlou, Wood, Sandy, Khatri, Amulya, Bretherton, Chris, Tunstall, Charlotte, Lowery, Kathryn, Holmes, Benjamin, Nichols, Jennifer, Bashabayev, Beibit, Wildin, Clare, Sofat, Rajesh, Thiagarajan, Aarthi, Abdelghafour, Karim, Nicholl, James, Abdulhameed, Ahmed, Duke, Kathryn, Maling, Lucy, McCann, Matthew, Masud, Saqib, Marshman, James, Moreau, Joshua, Cheema, Kanwalnaini, Rageeb, Peter Morad, Mirza, Yusuf, Kelly, Andrew, Hassan, Abdul, Christie, Alexander, Davies, Angharad, Tang, Cary, Frostick, Rhiannon, Pemmaraju, Gopalakrishna, Handford, Charles, Chauhan, Govind, Dong, Huan, Choudri, Mohammed Junaid, Loveday, David, Bawa, Akshdeep, Baldwick, Cheryl, Roberton, Andrew, Burden, Eleanor, Nagi, Sameer, Johnson-Lynn, Sarah, Guiot, Luke, Kostusiak, Milosz, Appleyard, Thomas, Mundy, Gary, Basha, Amr, Abdeen, Bashar, Robertson-Smith, Bill, Hussainy, Haydar Al, Reed, Mike, Jamalfar, Aral, Flintoft, Emily, McGovern, Julia, Alcock, Liam, Koziara, Michal, Ollivere, Benjamin, Zheng, Amy, Atia, Fady, Goff, Thomas, Slade, Henry, Teoh, Kar, Shah, Nikhil, Al-Obaedi, Ossama, Jamal, Bilal, Bell, Stuart, Macey, Alistair, Brown, Cameron, Simpson, Cameron, Alho, Roberto, Wilson, Victoria, Lewis, Charlotte, Blyth, Daniel, Chapman, Laura, Woods, Lisa, Katmeh, Rateb, Pasapula, Chandra, Youssef, Hesham, Tan, Jerry, Famure, Steven, Grazette, Andrew, Lloyd, Adam, Beaven, Alastair, Jackowski, Anna, Piper, Dani, Lotfi, Naeil, Chakravarthy, Jagannath, Elzawahry, Ahmed, Trew, Christopher, Neo, Chryssa, Elamin-Ahmed, Hussam, Ashwood, Neil, Wembridge, Kevin, Eyre-Brook, Alistair, Greaves, Amy, Watts, Anna, Stedman, Tobias, Ker, Andrew, Wong, Li Siang, Fullarton, Mairi, Phelan, Sean, Choudry, Qaisar, Qureshi, Alham, Moulton, Lawrence, Cadwallader, Craig, Jenvey, Cara, Aqeel, Aqeel, Francis, Daniel, Simpson, Robin, Phillips, Jon, Matthews, Edward, Thomas, Ellen, Williams, Mark, Jones, Robin, White, Tim, Ketchen, Debbie, Bell, Katrina, Swain, Keri, Chitre, Amol, Lum, Joann, Syam, Kevin, Dupley, Leanne, O'Brien, Sarah, Ford, David, Chapman, Taya, Zahra, Wajiha, Guryel, Enis, McLean, Elizabeth, Dhaliwal, Kawaljit, Regan, Nora, Berstock, James, Deano, Krisna, Donovan, Richard, Blythe, Andrew, Salmon, Jennifer, Craig, Julie, Hickland, Patrick, Matthews, Scott, Brown, William, Borland, Steven, Aminat, Akinsemoyin, Stamp, Gregory, Zaheen, Humayoon, Jaibaji, Monketh, Egglestone, Anthony, Sampalli, Sridhar Rao, Goodier, Henry, Gibb, Julia, Islam, Saad, Ranaboldo, Tom, Theivendran, Kanthan, Bond, Georgina, Richards, Joanna, Sanghera, Ranjodh, Robinson, Karen, Fong, Angus, Tsang, Bonita, Dalgleish, James, McGregor-Riley, Jonathan, Barkley, Sarah, Eardley, William, Elhassan, Almutasim, Tyas, Ben, Chandler, Henry, McVie, James, Wei, Nicholas, Negus, Oliver, Baldock, Thomas, Ravi, Kuppuswamy, Qazzaz, Layth, Mohamed, Muawia, Sivayoganthan, Sriharan, Poole, William, Slade, George, Beaumont, Hugo, Beaumont, Oliver, Taha, Rowa, Lever, Caroline, Sood, Abhay, Moss, Maximillian, Khatir, Mohammed, Trompeter, Alex, Jeffers, Aisha, Brookes, Charlotte, Dadabhoy, Maria, Bhattacharya, Rajarshi, Singh, Abhinav, Beer, Alexander, Hodgson, Harry, Rahman, Kashed, Barter, Reece, Mackinnon, Thomas, Frasquet-Garcia, Antonio, Aldarragi, Ameer, Warner, Christian, Pantelides, Christopher, Attwood, Joseph, Al-Uzri, Muntadhir, Qaoud, Qaiys Abu, Green, Stephen, Osborne, Alex, Griffiths, Alexandra, Emmerson, Benjamin, Slater, Duncan, Altahoo, Hasan, Scott, Helen, Rowland, David, O'Donnell, Janine, Edwards, Taff, Hafez, Ahmed, Khan, Basharat, Crane, Emily, Axenciuc, Rostislav, Al-Habsi, Ruqaiya, McAlinden, Gavan, Sterne, Jonathan, Wong, Matthew Lynch, Patil, Sunit, Ridha, Ali, Rasidovic, Damir, Searle, Henry, Choudhry, Jamaal, Farhan-Alanie, Muhamed M, Tanagho, Andy, Sharma, Sidharth, Thomas, Suresh, Smith, Ben, McMullan, Mark, Winstanley, Robert, Mirza, Saqeb, Hamlin, Katharine, Elgayar, Lugman, Larsen, Matthew P, Eissa, Mohamed, Stevens, Samuel, Hopper, Graeme P, Fang Soh, Terrence Chi, Doorgakant, Ashtin, Yogeswaran, Apimaan, Myatt, Darren, Mahon, Joseph, Ward, Nicholas, Reid, Susan, Deierl, Krisztian, Brogan, Declan, Little, Max, Deakin, Sue, Baines, Elliott, Jones, Georgie, Boulton, Helen, Douglas, Trixie, Jeyaseelan, Lucky, Abdale, Abdirizak, Islam, Aminul, Atkinson, Kate V, Mohamedfaris, Khalid, Mmerem, Kingsley, Jamal, Shazil, Wharton, Danielle, Rana, Anurag, McAllister, Ross, Sasi, Sijith, Thomas, Terin, Pillai, Anand, Flaherty, David, Khan, Munir, Akkena, Sudheer, Shandala, Yaseen, Lankester, Benedict, Hainsworth, Louis, Ahmed, Hussam Elamin, Walshaw, Thomas, Walker, Reece, and Eardley, William G.P.

Published
2023
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40. 60 hours in the breach

Author

Kennedy, Matthew W., Capt and Wood, McKinley C., 1stLt

Subjects
ARMORED WARFARE, OPERATION - Iraqi Freedom, IRAQ WAR, 2003, TASK FORCES
Abstract

illus

Published
2003

41. Noncommutative Choquet simplices

Author

Kennedy, Matthew and Shamovich, Eli

Subjects
Mathematics - Operator Algebras, Mathematics - Dynamical Systems, Mathematics - Functional Analysis, Mathematics - Group Theory
Abstract

We introduce a notion of noncommutative Choquet simplex, or briefly an nc simplex, that generalizes the classical notion of a simplex. While every simplex is an nc simplex, there are many more nc simplices. They arise naturally from C*-algebras and in noncommutative dynamics. We characterize nc simplices in terms of their geometry and in terms of structural properties of their corresponding operator systems. There is a natural definition of nc Bauer simplex that generalizes the classical definition of a Bauer simplex. We show that a compact nc convex set is an nc Bauer simplex if and only if it is affinely homeomorphic to the nc state space of a unital C*-algebra, generalizing a classical result of Bauer for unital commutative C*-algebras. We obtain several applications to noncommutative dynamics. We show that the set of nc states of a C*-algebra that are invariant with respect to the action of a discrete group is an nc simplex. From this, we obtain a noncommutative ergodic decomposition theorem with uniqueness. Finally, we establish a new characterization of discrete groups with Kazhdan's property (T) that extends a result of Glasner and Weiss. Specifically, we show that a discrete group has property (T) if and only if for every action of the group on a unital C*-algebra, the set of invariant states is affinely homeomorphic to the state space of a unital C*-algebra., Comment: 46 pages

Published
2019

42. Dynamic Cell Structure via Recursive-Recurrent Neural Networks

Author

Qian, Xin, Kennedy, Matthew, and Klabjan, Diego

Subjects
Computer Science - Machine Learning, Computer Science - Neural and Evolutionary Computing, Statistics - Machine Learning
Abstract

In a recurrent setting, conventional approaches to neural architecture search find and fix a general model for all data samples and time steps. We propose a novel algorithm that can dynamically search for the structure of cells in a recurrent neural network model. Based on a combination of recurrent and recursive neural networks, our algorithm is able to construct customized cell structures for each data sample and time step, allowing for a more efficient architecture search than existing models. Experiments on three common datasets show that the algorithm discovers high-performance cell architectures and achieves better prediction accuracy compared to the GRU structure for language modelling and sentiment analysis.

Published
2019

43. Noncommutative Choquet theory

Author

Davidson, Kenneth R. and Kennedy, Matthew

Subjects
Mathematics - Operator Algebras, Mathematics - Functional Analysis, Primary 46A55, 46L07, 47A20, Secondary 46L52, 47L25
Abstract

We introduce a new and extensive theory of noncommutative convexity along with a corresponding theory of noncommutative functions. We establish noncommutative analogues of the fundamental results from classical convexity theory, and apply these ideas to develop a noncommutative Choquet theory that generalizes much of classical Choquet theory. The central objects of interest in noncommutative convexity are noncommutative convex sets. The category of compact noncommutative sets is dual to the category of operator systems, and there is a robust notion of extreme point for a noncommutative convex set that is dual to Arveson's notion of boundary representation for an operator system. We identify the C*-algebra of continuous noncommutative functions on a compact noncommutative convex set as the maximal C*-algebra of the operator system of continuous noncommutative affine functions on the set. In the noncommutative setting, unital completely positive maps on this C*-algebra play the role of representing measures in the classical setting. The continuous convex noncommutative functions determine an order on the set of unital completely positive maps that is analogous to the classical Choquet order on probability measures. We characterize this order in terms of the extensions and dilations of the maps, providing a powerful new perspective on the structure of completely positive maps on operator systems. Finally, we establish a noncommutative generalization of the Choquet-Bishop-de Leeuw theorem asserting that every point in a compact noncommutative convex set has a representing map that is supported on the extreme boundary. In the separable case, we obtain a corresponding integral representation theorem., Comment: 83 pages; various minor changes

Published
2019

44. ORthopaedic trauma hospital outcomes - Patient operative delays (ORTHOPOD) Study: The management of day-case orthopaedic trauma in the United Kingdom

Author

Stevenson, Iain, Yoong, Andrel, Rankin, Iain, Dixon, James, Lim, Jun Wei, Sattar, Mariam, McDonald, Stephen, Scott, Sharon, Davies, Helen, Jones, Louise, Nolan, Michelle, McGinty, Rebecca, Stevenson, Helene, Bowe, David, Sim, Francis, Vun, James, Strain, Ritchie, Giannoudis, Vasileios, Talbot, Christopher, Gunn, Christopher, Le, Ha Phuong Do, Bradley, Matthew, Lloyd, William, Hanratty, Brian, Lim, Yizhe, Brookes-Fazakerley, Steven, Varasteh, Amir, Francis, Jonathan, Choudhry, Nameer, Malik, Sheraz, Vats, Amit, Evans, Ashish, Garner, Madeleine, King, Stratton, Zbaeda, Mohamed, Diamond, Owen, Baker, Gavin, Napier, Richard, Guy, Stephen, McCauley, Gordon, King, Samuel, Edwards, Gray, Lin, Benjamin, Davoudi, Kaveh, Haines, Samuel, Raghuvanshi, Manav, Buddhdev, Pranai, Karam, Edward, Nimmyel, Enoch, Ekanem, George, Lateef, Razaq, Jayadeep, JS, Crowther, Ian, Mazur, Karolina, Hafiz, Nauman, Khan, Umair, Chettiar, Krissen, Ibrahim, Amr, Gopal, Prasanth, Tse, Shannon, Lakshmipathy, Raj, Towse, Claudia, Al-Musawi, Hashim, Walmsley, Matthew, Aspinall, Will, Metcalfe, James, Moosa, Aliabbas, Crome, George, Abdelmonem, Mohamed, Lakpriya, Sathya, Hawkins, Amanda, Waugh, Dominic, Kennedy, Matthew, Elsagheir, Mohamed, Kieffer, Will, Oyekan, Adekinte, Collis, Justin, Raad, Marjan, Raut, Pramin, Baker, Markus, Gorvett, Alexander, Gleeson, Hannah, Fahmy, John, Walters, Sam, Tinning, Craig, Chaturvedi, Abhishek, Russell, Heather, Alsawada, Osama, Sinnerton, Robert, Crane, Evan, Warwick, Catherine, Dimascio, Lucia, Ha, Taegyeong Tina, King, Thomas, Engelke, Daniel, Chan, Matthew, Gopireddy, Rajesh, Deo, Sunny, Vasarhelyi, Ferenc, Jhaj, Jasmeet, Dogramatzis, Kostas, McCartney, Sarah, Ardolino, Toni, Fraig, Hossam, Hiller-Smith, Ryan, Haughton, Benjamin, Greenwood, Heather, Stephenson, Nicola, Chong, Yuki, Sleat, Graham, Saedi, Farid, Gouda, Joe, Ravi, Sanjeev Musuvathy, Henari, Shwan, Imam, Sam, Howell, Charles, Theobald, Emma, Wright, Jan, Cormack, Jonathan, Borja, Karlou, Wood, Sandy, Khatri, Amulya, Bretherton, Chris, Tunstall, Charlotte, Lowery, Kathryn, Holmes, Benjamin, Nichols, Jennifer, Bashabayev, Beibit, Wildin, Clare, Sofat, Rajesh, Thiagarajan, Aarthi, Abdelghafour, Karim, Nicholl, James, Abdulhameed, Ahmed, Duke, Kathryn, Maling, Lucy, McCann, Matthew, Masud, Saqib, Marshman, James, Moreau, Joshua, Cheema, Kanwalnaini, Rageeb, Peter Morad, Mirza, Yusuf, Kelly, Andrew, Hassan, Abdul, Christie, Alexander, Davies, Angharad, Tang, Cary, Frostick, Rhiannon, Pemmaraju, Gopalakrishna, Handford, Charles, Chauhan, Govind, Dong, Huan, Choudri, Mohammed Junaid, Loveday, David, Bawa, Akshdeep, Baldwick, Cheryl, Roberton, Andrew, Burden, Eleanor, Nagi, Sameer, Johnson-Lynn, Sarah, Guiot, Luke, Kostusiak, Milosz, Appleyard, Thomas, Mundy, Gary, Basha, Amr, Abdeen, Bashar, Robertson-Smith, Bill, Hussainy, Haydar Al, Reed, Mike, Jamalfar, Aral, Flintoft, Emily, McGovern, Julia, Alcock, Liam, Koziara, Michal, Ollivere, Benjamin, Zheng, Amy, Atia, Fady, Goff, Thomas, Slade, Henry, Teoh, Kar, Shah, Nikhil, Al-Obaedi, Ossama, Jamal, Bilal, Bell, Stuart, Macey, Alistair, Brown, Cameron, Simpson, Cameron, Alho, Roberto, Wilson, Victoria, Lewis, Charlotte, Blyth, Daniel, Chapman, Laura, Woods, Lisa, Katmeh, Rateb, Pasapula, Chandra, Youssef, Hesham, Tan, Jerry, Famure, Steven, Grazette, Andrew, Lloyd, Adam, Beaven, Alastair, Jackowski, Anna, Piper, Dani, Lotfi, Naeil, Chakravarthy, Jagannath, Elzawahry, Ahmed, Trew, Christopher, Neo, Chryssa, Elamin-Ahmed, Hussam, Ashwood, Neil, Wembridge, Kevin, Eyre-Brook, Alistair, Greaves, Amy, Watts, Anna, Stedman, Tobias, Ker, Andrew, Wong, Li Siang, Fullarton, Mairi, Phelan, Sean, Choudry, Qaisar, Qureshi, Alham, Moulton, Lawrence, Cadwallader, Craig, Jenvey, Cara, Aqeel, Aqeel, Francis, Daniel, Simpson, Robin, Phillips, Jon, Matthews, Edward, Thomas, Ellen, Williams, Mark, Jones, Robin, White, Tim, Ketchen, Debbie, Bell, Katrina, Swain, Keri, Chitre, Amol, Lum, Joann, Syam, Kevin, Dupley, Leanne, O'Brien, Sarah, Ford, David, Chapman, Taya, Zahra, Wajiha, Guryel, Enis, McLean, Elizabeth, Dhaliwal, Kawaljit, Regan, Nora, Berstock, James, Deano, Krisna, Donovan, Richard, Blythe, Andrew, Salmon, Jennifer, Craig, Julie, Hickland, Patrick, Matthews, Scott, Brown, William, Borland, Steven, Aminat, Akinsemoyin, Stamp, Gregory, Zaheen, Humayoon, Jaibaji, Monketh, Egglestone, Anthony, Sampalli, Sridhar Rao, Goodier, Henry, Gibb, Julia, Islam, Saad, Ranaboldo, Tom, Theivendran, Kanthan, Bond, Georgina, Richards, Joanna, Sanghera, Ranjodh, Robinson, Karen, Fong, Angus, Tsang, Bonita, Dalgleish, James, McGregor-Riley, Jonathan, Barkley, Sarah, Eardley, William, Elhassan, Almutasim, Tyas, Ben, Chandler, Henry, McVie, James, Wei, Nicholas, Negus, Oliver, Baldock, Thomas, Ravi, Kuppuswamy, Qazzaz, Layth, Mohamed, Muawia, Sivayoganthan, Sriharan, Poole, William, Slade, George, Beaumont, Hugo, Beaumont, Oliver, Taha, Rowa, Lever, Caroline, Sood, Abhay, Moss, Maximillian, Khatir, Mohammed, Trompeter, Alex, Jeffers, Aisha, Brookes, Charlotte, Dadabhoy, Maria, Bhattacharya, Rajarshi, Singh, Abhinav, Beer, Alexander, Hodgson, Harry, Rahman, Kashed, Barter, Reece, Mackinnon, Thomas, Frasquet-Garcia, Antonio, Aldarragi, Ameer, Warner, Christian, Pantelides, Christopher, Attwood, Joseph, Al-Uzri, Muntadhir, Qaoud, Qaiys Abu, Green, Stephen, Osborne, Alex, Griffiths, Alexandra, Emmerson, Benjamin, Slater, Duncan, Altahoo, Hasan, Scott, Helen, Rowland, David, O'Donnell, Janine, Edwards, Taff, Hafez, Ahmed, Khan, Basharat, Crane, Emily, Axenciuc, Rostislav, Al-Habsi, Ruqaiya, McAlinden, Gavan, Sterne, Jonathan, Wong, Matthew Lynch, Patil, Sunit, Ridha, Ali, Rasidovic, Damir, Searle, Henry, Choudhry, Jamaal, Farhan-Alanie, Muhamed M, Tanagho, Andy, Sharma, Sidharth, Thomas, Suresh, Smith, Ben, McMullan, Mark, Winstanley, Robert, Mirza, Saqeb, Hamlin, Katharine, Elgayar, Lugman, Larsen, Matthew P, Eissa, Mohamed, Stevens, Samuel, Hopper, Graeme P, Fang Soh, Terrence Chi, Doorgakant, Ashtin, Yogeswaran, Apimaan, Myatt, Darren, Mahon, Joseph, Ward, Nicholas, Reid, Susan, Deierl, Krisztian, Brogan, Declan, Little, Max, Deakin, Sue, Baines, Elliott, Jones, Georgie, Boulton, Helen, Douglas, Trixie, Jeyaseelan, Lucky, Abdale, Abdirizak, Islam, Aminul, Atkinson, Kate V, Mohamedfaris, Khalid, Mmerem, Kingsley, Jamal, Shazil, Wharton, Danielle, Rana, Anurag, McAllister, Ross, Sasi, Sijith, Thomas, Terin, Pillai, Anand, Flaherty, David, Khan, Munir, Akkena, Sudheer, Shandala, Yaseen, Lankester, Benedict, Hainsworth, Louis, Baldock, Thomas E., Walshaw, Thomas, Walker, Reece, and Eardley, William P.G.

Published
2023
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48. Cycling injuries requiring orthopaedic intervention during the first COVID-19 lockdown period: A multi-centre SCottish Orthopaedic Research collaborativE (SCORE) study

Author

Donoghue, Christopher J., Lee, Amanda, Bashyam, Jeswant, Greensmith, Thomas S., Macinnes, Alasdair, Pennington, Rachel, Sinnerton, Robert, Supparamaniam, Shreyas, Crome, Christopher R., Guiot, Luke, Harte, Collette, Kennedy, Matthew J., Noteman, Thomas W., Scicluna, Gabrielle, Wheelwright, Benjamin R.F., Torkington, Matthew S., Jamal, Bilal, Gill, Sarah L., Boddie, David E., Ashcroft, G. Patrick, Faulkner, Alastair, MacDonald, David R.W., Neilly, David W., Davies, Peter S.E., Ha, Taegyeong T., Stevenson, Iain M., and Jariwala, Arpit C.

Published
2022
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49. An infinite quantum Ramsey theorem

Author

Kennedy, Matthew, Kolomatski, Taras, and Spivak, Daniel

Subjects
Mathematics - Operator Algebras, Mathematical Physics, Mathematics - Combinatorics, Mathematics - Functional Analysis
Abstract

We prove an infinite Ramsey theorem for noncommutative graphs realized as unital self-adjoint subspaces of linear operators acting on an infinite dimensional Hilbert space. Specifically, we prove that if V is such a subspace, then provided there is no obvious obstruction, there is an infinite rank projection P with the property that the compression PVP is either maximal or minimal in a certain natural sense., Comment: 19 pages

Published
2017

50. Composition of PPT Maps

Author

Kennedy, Matthew, Manor, Nicholas A., and Paulsen, Vern I.

Subjects
Mathematics - Operator Algebras, Mathematical Physics, Mathematics - Functional Analysis
Abstract

M. Christandl conjectured that the composition of any trace preserving PPT map with itself is entanglement breaking. We prove that Christandl's conjecture holds asymptotically by showing that the distance between the iterates of any unital or trace preserving PPT map and the set of entanglement breaking maps tends to zero. Finally, for every graph we define a one-parameter family of maps on matrices and determine the least value of the parameter such that the map is variously, positive, completely positive, PPT and entanglement breaking in terms of properties of the graph. Our estimates are sharp enough to conclude that Christandl's conjecture holds for these families., Comment: 10 pages

Published
2017

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