Publications & Presentations





Emergent Transdisciplinary Methodology for Effective Collaboration in Ecological Economics, Sustainability 2023, 15(9), 7522.

Regarding Oslington's Assessment of Lonergan's Economics, Method: Journal of Lonergan Studies, to appear.

On the Operative Presence of Eight Tasks in Economics, Method: Journal of Lonergan Studies, to appear.

Two Sample Lessons for Introducing Two-Circuit Economics (with John Benton), Bent on Futurology, 2022.

Contributor, Dictionary of Ecological Economics, Edward Elgar Publishing, to appear.

Anatomy of Economic Activity: There are Two Main FlowsAmerican Review of Political Economy, January, 2019.


Method in Theology, chapter 5, "Functional Specialties," Journal of Macrodynamic Analysis, vol. 16 (2022): 110-132.

Beginnings with Philip McShane: A Progress-Oriented Tribute, Divyadaan: Journal of Philosophy and Education: 33/1 (2022), 141–146. Courtesy of editors, also available at Journal of Macrodynamic Analysisvol. 15 (2022): 141 - 146.

Philip McShane’s Invitation to the Academy and the Economy, 47th Boston Lonergan Workshop, June 20–25, 2021, Divyadaan: Journal of Philosophy and Education, to appear. Preprint is available at:

Editors’ Introduction, Philip McShane, Randomness, Statistics and Emergence, 2nd edition (Vancouver: Axial Publishing, 2021 (1st edition: (Dublin: Gill and Macmillan Ltd., 1970)).

The notion of a thing (with Meghan Allerton), Journal of Macrodynamic Analysis, vol. 14 (2020): 95–109.

Heuristic notions of space and time (with James Duffy and Robert Henman), Journal of Macrodynamic Analysis, vol. 14 (2020): 65–94.

Assembling the Meaning of Probability (with. James Duffy and Cecilia Maloney), Journal of Macrodynamic Analysis, vol. 13 (2020): 84-118.

Effective Dialectical Analysis (with James Duffy, Alexendra Gillis, Robert Henman and William Zanardi), Journal of Macrodynamic Analysis13 (2020): 21–44.

Searching for a Philosophy of History, Divyadaan: Journal of Philosophy and Education, 30/2 (2019): 1-22.

Toward the Positive Anthropocene Age. Closing the Gap, Divyadaan: Journal of Philosophy and Education. Vol. 28, No. 2, 2017, 299-320.

Lonergan's Core Shift in Theological Method, Divyadaan: Journal of Philosophy and Education. Vol. 27, No. 2, 2016, 123-144.

Interpreting Lonergan’s Fifth Chapter of Insight, “Space and Time,” in P. Brown and J. Duffy, eds., Seeding Global Collaboration (Vancouver, Axial Publishing, 2016): 29-44.

Reaching for Collaboration in Insight, Journal of Macrodynamic Analysis, Vol. 8 (2014): 11-29.

Community Climbing: Toward Functional Collaboration, Journal of Macrodynamic Analysis, Vol. 8 (2014): 45-66. See also, The Second Latin American Lonergan Workshop, The Human Good (tr. into Spanish by Benjamin Luján, “La Escalada Comunitaria: Haciauna Colaboración Funcional,” Segundo Taller Latino americano, El Bien Humano, 13-14 Junio 2013, UIA Ciudad de México), Bernard Lonergan Latinoamérica Online Publications,

Generalized Empirical Method in the Biological Sciences, Dialogues in Philosophy, Mental and Neurosciences, Vol. 7, Issue 1 (2014): 31.

Fledgling Functional Foundations for the Biology of the Adult Pigeon, Revista de Filosofía, Año 45 No. 135, Universidad Iberoamericana, México (2013): 123-152.

Invitation to Functional Collaboration: Dynamics of Progress in the Sciences, Technologies and Arts, Journal of Macrodynamic Analysis, Vol. 7 (2012): 94-122.

The Twin Paradox (in special relativity) – Working Toward Functional Interpretation, Journal of Macrodynamic Analysis, Vol. 4 (2004): 1-25.

Reflections on Progress in Mathematics, Journal of Macrodynamic Analysis, Festchchrift edition, Vol. 3 (2003): 97-116.

From Schrödinger to Dirac: On relations and statistics, B.N. Prasad Centenary, Commemoration Bull. Allahabad Math. Soc., Indian Journal of Mathematics, Vol.15 (2000): 69-100.

Mathematics Pedagogy

On Mathematical Understanding, Supplement to, T. Quinn, Z. Boudhraa and S. Rai, Basic Insights in Vector Calculus, with a Supplement on Mathematical Understanding (Hoboken, NJ: World Scientific Publishing Co. Pte. Ltd., to appear).

Variation of Parameters in Differential Equations - A Variation in Making Sense of Variation of Parameters (with S. Rai), Problems, Resources and Issues in Mathematics Undergraduate Studies (PRIMUS), 2013, 23(1):25-44.

On Two Types of Learning (in mathematics) and Implications for Teaching, On Learning Problems in Mathematics, Research Council on Mathematics Learning, Mathematical Association of America, FOCUS, Fall 2004, 31-43.

Getting Started in Calculus, Problems, Resources and Issues in Mathematics Undergraduate Studies (PRIMUS), Vol. 13, Issue 1, March, 2003, 55 – 74.

Mathematics and Applications of Mathematics

A direct method for computing extreme value (Gumbel) parameters for gapped biological sequence alignments (with Z. Sinkala), International Journal of Bioinformatics Research and Applications (IJBRA), Vol. 10, No. 2 (2014): 177-189.

A Practical Approach for Computing the Active Site of the Ribonucleoside Hydrolase of E. coli Encoded by rihC (with Anthony Farone, Mary Farone, Paul Kline, Zachariah Sinkala), in Advances in Computational Biology, Advances in Experimental Medicine and Biology, Vol. 680 (2010): 437-443.

Identifying the active site of ribonucleoside hydrolase of E. coli encoded by rihC (with A. Farone, M. Farone, A. Khaliq, P. Kline, Z. Sinkala), Proceedings of The 2009 International Conference on Bioinformatics & Computational Biology: BIOCOMP2009, Vol. I, eds. H.R. Arabnia and M. Q. Yang (Athens, GA, CSREA Press, 2009): 216-218.

Dynamics of prostate cancer stem cells with diffusion and organism response (with Z. Sinkala), Biosystems, Vol. 96, Issue 1, April 2009, 69-79.

Investigation of granular segregation in a horizontal rotating tube from an energy perspective [with Boles, W. (1st author).; Robertson, W; Martin, J; Siebert, E; Underwood, T; Clayton, M], Proceedings of the Earth and Space Conference, American Society of Civil Engineers, March 2008.

Natural networks and the GoogleTM search engine, Journal of the Tennessee Academy of Science, Vol. 82, Issue 1-2, January – April 2007.

Stability of multi-delay systems of differential equations: characteristic equations and applications, International Journal of Pure and Applied Mathematics (with. S. Rai), Vol. 18, No. 2, 2005, 171-196.

A four dimensional system of functional differential equations for the dynamics of CD4+ T-cells and HIV-1 (with S. Rai), International Journal of Differential Equations and Applications, Vol. 9, No. 1, 2004, 1-56.

A Solution of Ovsiannikov’s reduction problem (with S. Rai and C. C. Sastri), International Journal of Differential Equations and Applications, Vol. 4, No. 2, 2002, 157-169.

Remarks on partially invariant solutions of differential equations (with S. Rai and C. C. Sastri), Communications in Applied Analysis, Vol. 4, No. 4, 2000, 475-480.

Factorisation in approximately poly-normal C*-algebras: products of positive operators, Journal of Natural Geometry, Math. Res. Unit, University of London, Vol. 14, 1998, 93-132.

Factorisation of n-normal operators: products of positive operators, Proc. of the Roy. Irish Academy, Vol. 95A, 1995, 89-108.

Products of decomposable positive operators, Canadian Journal of Mathematics, Vol. 46, No. 4, 1994, 854-871.


Discovering Mathematics Workshop, Archimedes to Lebesgue, under Manual for Project Portal to Success in Engineering, Fund for the Improvement of Postsecondary Education (FIPSE), Montgomery College, Rockville, Maryland, 2007 – 2009 (non-refereed).

Introduction to Graph Theory and its Applications, Mini-Courses in Mathematical Sciences, Division of Science, Engineering and Mathematics, Montgomery College, Rockville, MD, Fall 2004 (non-refereed).


Public Lecture (with John Benton), "Economics Actually for Owen Sound and Beyond: Today and Tomorrow, Sustainable and Inclusive," Owen Sound and North Grey Union Public Library, Owen Sound, Ontario, Canada, March 26, 2024.

Anatomy of Economic Activity: There are Two Main Flows, International Confederation of Associations for Pluralism in Economics, Drexel University, Philadelphia, January 4th, 2018.

(1) Hintings of Lonergan’s Amazingly Remote Meaning; (2) Toward the Tower of Able: Lonergan’s Dream; (3) Remarks on the Future Science of Functional Communications; and (4) Reflections on the Challenge of Reading Lonergan. Four talks given at the Lonergan Workshop in Korea, Sogang University, Seoul, S. Korea, May 22-May 26, 2017.

Why Functional Collaboration, Sixth International Lonergan Conference, Functional Collaboration in the Academy: Advancing Bernard Lonergan’s Central Achievement, University of British Columbia, Vancouver, Canada. July 21-25, 2014.

Community Climbing: Toward Functional Collaboration, Segundo Taller Latinoamericano, El Bien Humano, Universidad Iberoamericana, Ciudad de México, 13-14 de junio de 2013.

Reaching for Collaboration in Insight, Lonergan Research Institute Graduate Seminar, Regis College, University of Toronto, November 16, 2012.

Functional Foundations of Biology, Halifax Lonergan Conference 2012, Moving Lonergan Studies into Functional Talk, St. Mary’s University, Halifax, NS, July 16-20, 2012.

Introduction to Two-Flow Economics, Owen Sound District Secondary School, Owen Sound, Ontario, June 2012.

Invitation to Functional Collaboration, Vancouver Lonergan Conference 2011, Lonergan's Final Specification of Cosmopolis: Implementing the Longer Global Cycles of Incline, University of British Columbia, July 11-15, 2011.

Introduction to Functional Division of Labour in Biology, Owen Sound District Secondary School, Owen Sound, Ontario, June 2011.

What is Description? (with John Benton), Vancouver Lonergan Conference 2010, Education and Functional Collaboration, University of British Columbia, July 5 – 9, 2010.

Generalized Empirical Methods, St. Mary’s University, Lonergan Conference: Global Functional Collaboration, July 6-10, 2009.

Today’s Pedagogy in Mathematics and the Need for Functional Specialization, 50th Anniversary of Lonergan’s Halifax Lectures -- Lonergan’s Leading Ideas, St. Mary’s University, Halifax, Nova Scotia, May 30 – June 1, 2008.

Re-structuring Education in Mathematics and Physics, Crises of Sciences, Cultures and Theologies: Constructive Re-orientations, University of British Columbia, August 15-19, 2005.

Foundations of Geometry, Boston College, 32nd Annual Lonergan Conference, June 19-24, 2005.

Method in Mathematics, 20th Annual Fallon Memorial Lonergan Symposium, March 31-April 2, 2005.


Practical Economics (with J. Benton).