The Atlas of Irish Mathematics: Limerick (Dec 2017)
On 15 Dec 2017, the Annals of Irish Mathematics & Mathematicians turned three years old. It then accounted for just over 3600 people, reflecting an average growth rate of 100 people per month. One of AIMM's spinoff features is The Atlas of Irish Mathematics, which highlights some of the more notable careers, county by county. One goal of the series of blogs of which this is the fourth is to make that wealth of information more accessible and digestible for a wide audiencehence six regional blogs per year entire island has been covered.
Earlier in 2017, we took a look at the careers of some mathematically trained people from Donegal, Wexford and Armagh. This month, we focus on people associated with Limerick. Since the county is home to one of the island's newer universities—the University of Limerick (UL) in the city of the same name—it has provided longterm career options for numerous people whose origins are elsewhere, ranging from Mallow to Moscow. Many of those academics are also documented below. As a result, this is a much longer "county blog" than the previous ones, accounting as it does for 70 people.
The scope of this roundup is a pointer to future challenges when Dublin, Belfast and Cork people will be documented. The numbers for each of those will be substantially larger and may necessitate being broken up into several blogs for each of those university cities.
As usual, those listed here started with a degree in maths or a related field, unless otherwise indicated. Of course, some lives (and careers) drifted far from the mathematics studied in university.
There are undoubtedly instances where the designation "born in Limerick" could refer to the city or more generally to the county; but we simply don't know which is more accurate. Hence, some county births may be mistakenly attributed to the city. Corrections and comments, as always, are welcome.
The information below is extracted from the Gallery of Irish Mathematics & Mathematicians. For Limerick associated people, extensive assistance has been provided by Eugene Gath of UL.
Last updated 22 Feb 2020.
0. James Baggott (17711805) was born in Ballingarry, where he taught as a hedgemaster. He corresponded with Laplace. Bio1 / Bio 2  
1. Matthew Collins (17711849) was born in Ballingarry, Limerick, and educated at TCD, where he served as Professor of Maths. Obit  
2. John Walsh (1786?1847) was born in Shandrumm, Limerick, and became a teacher in Cork. His mathematically eccentric ways drew the attention of both De Morgan and Boole, the latter writing about him that "he laboured under a peculiar mental hallucination". He submitted, without success, a significant number of papers to learned societies, one resulting in an unfavourable report by Poisson and Cauchy. MacTutor  
3. Henry Hickman Harte (17901848) was born in Limerick. He was educated at TCD, where he was served as Donegall Lecturer before moving on to parish work in Tyrone. He published translations of Laplace's Système du Monde & Poisson's Mécanique. Wikipedia  
4. Andrew Searle Hart (18111890) was born 14 Mar in Limerick. He was educated at TCD, and spent his entire career there, rising to the rank of viceprovost. He published treatises on hydrostatics and mechanics, as well as papers on geodesic lines and curves. Wikipedia DIB  
5. Matthew Collins (1814?1888?) was born in Limerick, and educated at TCD. He taught at the Mechanics Institute of Liverpool then at TCD for many decades. He authored A tract on the possible and impossible cases of quadratic duplicate inequalities in the diophantice analysis. Gen Probs Maths Book  
6. John Casey (18201891) was born 12 May in Coolattin, Limerick. He was selfeducated until middle age, when, unusually for a Catholic in that period, he graduated from TCD. He later opted to teach at the Catholic University of Ireland, rather than at TCD where he was also offered a position. He was one of the founders of the modern geometry of triangles and circles, wrote seven books on geometry, and is also remembered for a theorem generalising Ptolomy's theorem. Wikipedia MacTutor  
7. Thomas Power (1859? to at least 1921) was born in Limerick. He taught maths at St Patrick's College in Thurles, and later in Limerick. Census1 Census2  
8. Jane McCutcheon (18681956) was born 8 Sep in Limerick city. She was educated at QUB and taught in Belfast. Census1 Census2  
9. John Enright (1876?1940) was born in Limerick city and was educated to master's level at UCD. He taught at Knockbeg College, Carlow, then in Longford and Dublin, and later at UCD. Census 1 Census 2  
10. Éamon de Valera (18821975) was born 14 Oct in New York, and grew up in Bruree, Limerick. He earned a maths degree in Dublin from the Royal University of Ireland. He taught at Maynooth and at Caryfort College, as well as at various schools, before turning to nationalist activities, and ultimately entering a long career in politics. In 1940, as Taoiseach, he initiated the foundation of the Dublin Institute for Advanced Studies. Wikipedia MacT UCD UCC  
11. Gerald Foley (18861982) was born 1 Apr in Askeaton, Limerick, and was educated at TCD, where he was a Scholar. His career was mostly spent in the police, first in the RIC and later in a leadership role in Palestine. DIB Link  
12. Physicist Thomas Nevin (19061986) was born 4 Oct in Bristol, and grew up in in Limerick city. He was educated at UCD, starting his studies in mathematical science. He lectured at UCD for almost half a century, in time serving as department head and dean. He revived the spectroscopy laboratory and started the nuclear emulsion group. Wikipedia Web UCD  
13. Applied mathematician Paddy Quinlan (19192001) was born 7 Dec in Kilmallock, Limerick, and was educated at UCC and Caltech. His 1949 PhD on "A Fourier Integral Approach to an Aeolotropic Medium" was done with Romeo Martel & Frederick Converse. He lectured at UCC for four decades, supervising numerous theses there. He also served as a member of Seanad Éireann, from 1957 to 1977. Wikipedia Obit  
14. Meteorologist Sean Connolly (19322008) was born in Bruff, Limerick, and was educated to master's level at UCG. His entire career was spent in the met office, mainly in Aviation Forecasting at Shannon, rising to become Head of Aviation Services.  
15. Tom Ambrose was born in Newcastle West, Limerick, and was educated at UCD and TCD. His original research was on electromagnetic interactions, and he taught for four decades at Kevin St (later DIT). For most of that time he also taught at UCD. Interview  
16. Michael A. Hayes (19362017) was born on 2 Aug in Kilfinane, Limerick. He grew up there and in Limerick city, and was educated at UCG (where he earned an NUI Travelling Studentship Prize) and at Brown. After some years at the University of East Anglia, he became head of mathematical physics at UCD, where he worked for a quarter of a century. His research was in elasticity theory and the kinematics of deformation. He coauthored the book Bivectors and Waves in Mechanics and Optics (Chapman & Hall, 1993). NUIG recently established a prize in continuum mechanics in his memory. Obit IUTUM 

17. Applied mathematician Frank Hodnett (19392011) was born 15 Oct in Cork and was educated at UCC and at Leeds. Upon completing his PhD in 1967 on "Magnetogasdynamic Problems Associated with Electric Arcs and the Slow Compressible Flow Past a Circular Cylinder" with Allin Goldsworthy, he spent a few years at the University of Connecticut. In 1974, he joined the staff at NIHE Limerick (later UL), where he worked for three decades. He rose to become department head, supervised several theses and edited two conference proceedings.  
18. Mick Wallace was born in Limerick, and was educated at UCG. After a decade at Kevin St, he joined the staff at NIHE Limerick (later UL) where he taught for over three decades, rising to department head. His interests are in statistics and quality control. Along with Eamonn Murphy, he founded the National Centre for Quality Management which brought a lot of stats to bear in industry in the midWest in the 1990s.  
19. Paddy MacNeice (19401970) was born in Limerick, and was educated at UCD, first in engineering and then in maths. He taught at UCD for several years before his untimely death.  
20. Gerry Beggan was born in Limerick, and was first educated at UCD. He worked for the department of education, then for almost three decades at UCG's education department, earning his doctorate from ???? along the way. Interview  
21. Mathematics education expert John O'Donoghue was born in Nenagh, Tipperary, and educated at St John Fisher College in Rochester, at Rensselaer Polytechnic and at Loughborough. His 1978 PhD on "Educating and Training Mathematics Teachers for Secondary Schools in Ireland: a New Perspective on Teacher Education" was done with Avi Bajpai. His career was mostly spent at Thomond College and then at UL, where he supervised over 30 theses at master's and PhD level, and coauthored two books. He was founding codirector of the National Centre for Excellence in Mathematics and Science Teaching and Learning (NCEMSTL). UL Interview  
22. Liam O'Callaghan was born in Effin, Limerick, and was educated at UCD and Wesleyan University. His 1976 PhD on "Topological Endohomeomorphism and Compactness Properties of Products and Generalized SigmaProducts" was done with Bill Comfort. He spent most of his career in the aerospace software industry.  
23. Statistician Eamonn Murphy (brother of Oliver below) was born in Limerick city and was first educated at St Pat's, Drumcondra, whereupon he taught primary school in Limerick for many years. His 1987 PhD on "An Empirical Study of Information Technology as an Aid to the Teaching of Mathematics in the Primary School" was done at UCD. Along with Mick Wallace, he cofounded the National Centre for Quality Management at NIHE Limerick (now UL). This brought a lot of stats to bear in industry in the midWest in the 1990s. UL IT  
24. Eoghan MacAogáin was born in Dublin and educated at TCD, where he was a Scholar, and at Warwick. He career was spent teaching first at Thomond College and then at UL. He is also a flute player with two albums to his name.  
25. Theoretical physicist Charles Nash was born in London, and grew up in Limerick city. He was educated at TCD and Cambridge. His 1973 PhD on "Contributions to Deep Inelastic Scattering" was done with John Polkinghorne. He taught at TCD and Imperial before settling at Maynooth, from which he recently retired after 36 years. He has authored three books, including Topology and Geometry for Physicists (Academic Press, 1983). Maynooth Symposium  
26. Mathematical physicist Bob Critchley (19482007) was born on 8 November in London and was educated at Oxford and DIAS. His 1974 Oxford doctorate on "Some Applications of Representations of the Canonical Commutation Relations" was completed in Dublin with John Lewis. He settled at NIHE Limerick (later UL) where he worked for three decades. He was active in Computer Aided Learning for many years, and also taught for the Open University. Prize  
27. Pat O'Sullivan was born in Cork and educated entirely at Maynooth. His 1976 PhD was done with Tigran Tchrakian. His entire career was spent at Mary Immaculate College, where his interests ranged from financial mathematics to differential equations and numerical methods, as well as computer use in maths education. MIC  
28. Des Penny was born in Limerick, and was educated at UCC, where he won an NUI Travelling Studentship Prize, and at the University of Utah, from which he earned his PhD in 1975. Most of his career was spent on the physics and engineering staff at Southern Utah University. SUU1 SUU2  
29. Michael Barry was born in Limerick city and was educated at UCD, where he won an NUI Travelling Studentship Prize, and at Notre Dame. His 1976 PhD on "Parabolic Subgroups of Groups of Lie Type" was done with Warren Wong. His career started at Carysfort College, following which he has spent three decades at Allegheny College in Pennsylvania. Allegheny  
30. Gerry Enright was born in Kanturk, Cork, and was educated at UCG and Cambridge. His 1977 PhD on "The Structure and Subgroups of the Fischer Groups F_{22} and F_{23}" was done with John H. Conway. His entire career was spent at Mary Immaculate College, where his interests spanned finite simple sporadic groups, mathematics education, and computers in education. MIC  
31. Applied mathematician Dick Sheehy was born in Limerick city and was educated entirely at UCC, earning his 1979 PhD on "The EdgeFunction Method for Free Vibrations of Isotropic Plates" with Paddy Quinlan and Michael O'Callaghan. His career was spent at CIT, from which he recently retired.  
32. Gordon Lessells was born 9 Nov in Fraserburgh, Aberdeenshire, Scotland, and was educated at Aberdeen and Oxford. He has been on the staff at NIHE Limerick (now UL) for 35 years, having been at UCC before that. He has long played a leadership role in the Irish Mathematical Olympiad.  
33. Applied mathematician Andrew Fowler was born in Belfast, and educated at Oxford. In 1977 he completed his doctorate on "Glacier Dynamics" with Alan Tayler. He worked at TCD and MIT before returning to teach at Oxford. For the past decade he has been on the staff at UL, specialising in mathematical modelling. He has supervised several theses and written two books, including Mathematical Geoscience (Springer, 2011). UL  
34. Applied mathematician and computer scientist Liam Tuohey was born in Kilmallock, Limerick, and was educated entirely at UCC, completing his PhD in 1982 on "Application of the Edge Function Method to Potential Problems in Three Dimensions" with Paddy Quinlan. The early part of his career was spent in the aerospace industy, then he joined the computer science staff DCU. DCU  
35. Diarmuid O'Driscoll was born in Millstreet, Cork, and educated at UCC, where he was awarded an NUI Travelling Studentship Prize. His entire career has been spent at Mary Immaculate College, where he currently serves as department head. His interests have ranged from IT in the primary school curriculum to regression analysis and measurement error models. MIC  
36. John Kinsella was born in Dublin and educated entirely at UCD, earning his 1980 PhD on "Crossing Symmetry for Production Amplitudes and Sum Rules for Partial Waves" with John Kennedy. He then joined the staff at NIHE Limerick (now UL), where his interests include constrained optimisation. He has supervised 2 PhD students. UL  
37. Electrical engineer Mark Burke was born in Dublin, and was educated at UCD (BE 1975?, ME 1976?), and at Northwestern (PhD 1980). His thesis on "Optimal Inputs for the Identification of Linear Systems" was done under Zenonas Rekasius. His career was mostly spent in the maths department at NIHE Limerick/UL. His interests include control theory and nonlinear dynamics. UL  
38. Statistician Gerard Scallan was born in Limerick and was educated at UCG, where he won an NUI Travelling Studentship. After some postgraduate studies at both Graz and Stanford, he settled in Paris, where he specialises in modelling techniques for both scorecards and financial models. Scorplus  
39. Avril Hegarty (née Reynolds) was born in Dublin and educated at TCD and UL. Her 2003 PhD on "Bayesian Disease Mapping using Product Partition Models" was done with Don Barry. Her career has been spent at UL, where she specialises in applying maths to the biomechanics and technology sectors. UL  
40. Ray Johnstone was born in Limerick and was educated at UCG, where he won an NUI Travelling Studentship Prize. After some postgraduate studies at Leeds, he settled in the USA, where he works in the software industry.  
41. Statistician Don Barry was born in Cork and was educated at UCC, where he won an NUI Travelling Studentship, and then at Yale. His 1983 PhD on "NonParametric Bayesian Regression" was done with John Hartigan. He started his career at UCC, where he served as department head, and then he moved to UL, where he recently completed a decade as president. He has supervised several PhDs. HSE  
42. Alan Hegarty was born in Dublin and was educated at TCD. Following his 1986 PhD on "Analysis of Finite Difference Methods for TwoDimensional Elliptic Singular Perturbation Problems" done with John Miller, he joined the staff at NIHE Limerick (now UL), where he currently serves as head of department. His main research interest is on the numerical solution of singular perturbation problems, and he has coedited one conference proceedings book. UL  
43. Eugene Gath was born 10 Mar in Dublin and grew up mostly there and just outside Waterford city. He was educated at UCD, where he won an NUI Travelling Studentship Prize, and at MIT. His 1989 PhD on "Exact Results in Quantum Field Theory: The Spinor Lehmann Representation in Antide Sitter Space and the Superconformal Thirring Ghosts" was done with Dan Freedman. Most of his career has been spent at UL, where his original focus on relativity, conformal field theory and string theory has given way to applications of mathematics and statistics, especially financial mathematics. UL  
44. Applied mathematician Eugene Benilov was born 22 Jul in Moscow, Russia, and was educated there, earning his 1988 PhD on "Instability of Ideal Fluid Flows over an Uneven Bottom" at the Shirshov Institute of Oceanology, with V. E. Zakharov. After a spell in Australia (and two years at Warwick) he settled at UL. He has supervised numerous theses, and was part of the team that solved a longstanding mystery about sinking bubbles in glasses of stout. UL Bubbles  
45. Theoretical physicist Diarmuid Ó Sé was born in Limerick city and grew up nearby in Ardnacrusha, Clare. He was educated at Maynooth, finishing his 1986 PhD on "Classical Gauge Field Solutions and Their Topological Properties" with Tigran Tchrakian at DIAS. His career has been spent in IT Carlow, where his interests have broadened to include maths learning support and management science. IT Carlow  
46. Hubert O'Driscoll was born in Doon, Limerick and was first educated at UCD—where he qualified as a vet before persuing maths—and at Notre Dame. His 1989 PhD on "Isomorphisms of saturated subgroups of PO_{6}" was done with Alex Hahn. His career has been spent as a veterinarian in rural Limerick. Vet  
47. Applied mathematician Stephen B. O'Brien was born in Cork and educated at UCC and Oxford. His 1992 doctorate on "Free Boundary Problems from Industry" with Alan Tayler was done after he'd worked for a while for Philips in Holland. He has long been at UL, where he currently codirects the Mathematics Applications Consortium for Science and Industry (MACSI). He has supervised numerous theses. UL  
48. Bernd Kreussler was born in Germany and educated entirely at Humboldt University in Berlin. His 1989 doctorate on "Twistorräume und kleine Auflösungen von Doppelüberlagerungen des ℙ^{3}, die über einer Quartik mit genau 13 gewöhnlichen Doppelpunkten verzweigt sind" was done with Herbert Kurke. After a decade on the staff at Kaiserslautern, he settled at Mary Immaculate College, where his interests include complex algebraic geometry and homological algebra as well as homological mirror symmetry. He has coauthored two books, including "Vector Bundles on Degenerations of Elliptic Curves and YangBaxter Equations" (AMS, 2012). He is very active in the Irish Mathematical Olympiad. MIC  
49. Cliff Nolan was born in Cork city and educated at UCG, TCD and Rice. His 1997 PhD on "Global Analysis of Linearized Inversion for the Acoustic Wave Equation" was done with William Symes. Since then he has mostly been at UL, where his interests include inverse problems, microlocal analysis, and anisotropic wave propagation and scattering. He also maintains an adjunct research position at Rensselaer Polytechnic.  
50. Oliver P. Murphy (brother of Eamonn above) was born in Limerick city and was educated at Mary Immaculate College (BEd 1980) and later at UCC (MA, PhD 1995). His doctorate on "A Robust Model Fitting Technique" was done with Don Barry. Since then he has taught both maths and business studies at IT Tralee, and currently serves as president there. 

51. Ali Ansari was born in Karachi, Pakistan and grew up there and in the United Arab Emirates. He arrived in Limerick in time to do his Leaving Cert and was educated entirely at NIHE/UL. Following his PhD 2001 "On the Use of Shishkin Meshes to Obtain Parameter Robust Numerical Solutions of Singularly Perturbed Differential Equations" under Alan Hegarty he remained on the staff there for a few years, supervising one PhD himself. The rest of his career has been spent at the Gulf University for Science and Technology in Kuwait, where he has served as department head and dean. GUST  
52. Pat Doody was born in Ballingarry, Limerick, and was educated at UL, where in 1999 he did his PhD on "Bounding and Controlling the Generalisation Error in Feedforward Neural Networks" under John Kinsella. He has long taught statistics at IT Tralee, and is currenly involved with the Intelligent Mechatronics and RFID (IMaR) Gateway project there. LI  
53. Natalia Kopteva was born 22 Aug in Moscow, and was educated at Moscow State University, earning her 1997 PhD on "Uniform grid methods for certain singularly perturbed equations on layeradapted grids" with Vladimir Andreev. She has taught at UL for fifteen years, and has coedited one conference proceedings book. Her area of research is numerical analysis for partial differential equations. UL  
54. Statistician Ailish Hannigan was born in Limerick, and was educated at UL and UCD. Her 1997 PhD on "Survival Analysis—A New Approach to Analysing Three Year Caries Clinical Trials" was done with Don Barry. Most of her career has been spent at UL, first in maths and now on the biostats staff. UL  
55. Statistician Kevin Hayes was born in Dublin and was educated entirely at TCD. His PhD was done with John Haslett. His entire career has been spent at UL. His main research area is in the statistical analysis of curve data as applied to the area of human biomechanics. UL  
56. Applied mathematician James Gleeson was born 19 Apr in Nenagh, Tipperary, and was educated at UCD and Caltech. His 1999 PhD on "Random Advection of a Passive Scalar" was done with Phil Saffman. He started his career at UCC before settling at the University of Limerick, where he currently codirects the Mathematics Applications Consortium for Science and Industry (MACSI). He has supervised many theses. UL  
57. Mathematical educator Olivia Fitzmaurice (née Gill) was born on 19 Oct in Kilnaleck, Cavan, and was educated at UL and Maynooth. Her 2006 PhD was on "What Counts as Service Mathematics?: An Investigation into the 'Mathematics Problem' in Ireland" was done with John O'Donoghue. After some secondary teaching, she returned to UL. Her research areas include adult learners of mathematics, service mathematics, the Irish Mathematics Learning Support Network (IMLSN) and mathematics in initial teacher education. UL  
58. Norbert Hoffmann was born in Germany and educated at Göttingen and Bonn. His 2002 doctorate "On vector bundles over algebraic and arithmetic curves" was done with Gerd Faltings. After a decade at the Free University of Berlin he settled at Mary Immaculate College in Limerick. His research interests are in algebraic vector bundles and principal bundles and in moduli spaces and moduli stacks. MIC  
59. Statistician Helen Purtill (née Mac Mullen) was born on 26 May in Killybegs, Donegal, and was educated at DCU and at Sheffield Hallam. Her 2000 PhD on "Schwarz Domain Decomposition Methods for Singularly Perturbed Differential Equations" was done with Eugene O'Riordan at DCU. She has long been based at UL, where she is actively involved in interdisciplinary research with numerous collaborators. UL  
60. Mathematical finance expert Bernard Murphy was educated at UCD, starting in engineering and later getting a masters in economics, then he taught at UL for over two decades. Along the way he earned a PhD at Warwick.  
61. Applied mathematician Ray McNamara (19742004) was born in Scariff, Clare, and was educated entirely at NIHE/UL. His 2000 PhD on "Numerical Solutions of the Planetary Geostrophic Equations with Applications to Ocean Modelling" was done with Frank Hodnett. He then joined the staff at Mary Immaculate College where he worked until his early death. Run  
62. Applied mathematician Sarah Mitchell was born on 14 June in Bristol, England. Her education was entirely at Bath. Her 2003 PhD on "Coupling Transport and Chemistry: Numerics, Analysis and Applications" was done with Alastair Spence. She worked at the Universities of British Columbia and Cape Town before settling at UL, where she is currently department head. Her interests are in numerical and mathematical modelling of moving boundary problems relevant to solidification, melting and polymer diffusion. UL  
63. Ronan Flatley was born in Dublin and brought up in Sligo town and Letterkenny, Donegal. He was educated entirely at UCD—first in engineering—earning his 2012 PhD on "Symbol Algebras, Involutions and Trace Forms" with Thomas Unger & Dave Lewis. He now teaches at Mary Immaculate College, and his interests include central simple algebras with involution and the algebraic theory of quadratic forms. MIC  
64. Maths education expert Paddy Johnson was born in Laois and educated entirely at UL. In 2006, he completed his PhD on "An Investigation of Permanence and Exclusion in a TwoDimensional Discrete Time Competing Species Model" with Mark Burke. His career has been spent at UL, first in maths and now on the education staff. UL  
64. Romina Gaburro was born in Italy and was educated at Trieste and Manchester. Her 2003 PhD on "Anisotropic Conductivity Inverse Boundary Value Problems" was done with Bill Lionheart. She has long been on the UL staff, where her interests include inverse problems. UL Video  
66. Colin Wilmott was born in Pallaskenry, Limerick, and was educated at UCC and Royal Holloway. His 2006 PhD on "On Quantum Codes and Networks" was done with Peter Wild. After some positions at UCD, Duesseldorf and Masaryk, he settled at Nottingham Trent University, where his focus is on open quantum systems and the physics of information. NTU  
67. Statistitian Norma Bargary (née Coffey) was born 25 Feb in Cahir, Tipperary, and was educated entirely at UL. Her 2008 PhD was done with Kevin Hayes. After some postdoc positions she settled back at UL where her main area of interest is in the statistical modelling of timecourse/functional data using the mixed effects model, especially as applied to biological data. UL  
68. Alan McCarthy was born 2 Jan in Askeaton, Limerick, and educated entirely at UCC. Since completing his 2014 PhD on "Flat Surfaces on Finite Type in 3Sphere" with Martin Kilian he has taught at the University of New South Wales and then at the University of Notre Dame (Sidney). His areas of research are differential and discrete geometry. UND  
69. Statistician David Hawe was born in Limerick and educated at UL and UCC. In 2014 he completed his PhD on "Statistical Considerations in the Kinetic Analysis of PETFDG Brain Tumour Studies" with Finbarr O'Sullivan. He now teaches at CIT. CIT  
70. Statistician Kevin Burke was born in Tipperary and educated entirely at UL. His 2014 PhD on "MultiParameter Regression Survival Models" was done with MacKenzie & Murphy. He now teaches at UL where his research interests include survival analysis, i.e., is the statistical analysis of timetoevent data. UL 