## Ton Coolen

#### ACC (Ton) Coolen

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###### Professor,

###### Physics of machine learning and complex systems

###### Department of Biophysics, DCN

###### Faculty of Science, Radboud University

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###### Director,

###### Saddle Point Science Europe BV

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###### Email:

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ton.coolen@saddlepointscience.com

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###### Office addresses:

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Department of Biophysics, Donders Institute

Huygens Gebouw, Heyendaalseweg 135

6525 AJ Nijmegen, The Netherlands

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Saddle Point Science Europe BV

UBC Building, Mercator Science Park

Toernooiveld 100

6525 EC Nijmegen, The Netherlands

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##### RESEARCH

Active Themes

Active Projects

Mathematical biomedicine and survival analysis, with applications to cancer research

Statistical mechanics of disordered and heterogeneous many-particle systems

Stochastic processes on complex networks or graphs, and generation of tailored random graphs

Medical statistics

Bayesian analysis of survival data in presence of latent cohort heterogeneity, beyond the visible covariates (e.g. heterogeneity in associations or base hazard rates), and with competing risks (i.e. informative censoring). Theory of overfitting and overfitting-correction protocols in time-to-event regression models, and Bayesian discriminant analysis for very high-dimensional covariates.

Mathematical immunology

Dynamics and statics of large immune system networks in the finite connectivity regime. We want to improve our understanding of the adaptive immune system, with a long-term view to aid intelligent reprogramming of this powerful but so far clinically under-utilised system.

Currently dormant themes

Mathematical analysis of natural and synthetic neural information processing systems

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Non-equilibrium statistical mechanics of minority games - agent based models for financial markets

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Generation of primary and secondary structure in heteropolymers

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Stationary state probability distributions of nonequilibrium stochastic processes

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Theory of cellular signalling processes

Cellular signalling networks (proteomic, gene regulatory, metabolic) are highly complex interacting many-variable systems. I try to adapt the mathematical tools from heterogeneous many-particle systems in theoretical physics to proteome and interactome cell biology, such as generating functional analysis

(based on path integrals).

Analysis of loopy sparse random graph ensembles

Nearly all of our mathematical methods for analysing sparse graphs (cavity methods, belief propagation, standard replica methods, etc) assume that these graphs are locally tree-like. No exact methods exist for calculating e.g. eigenvalue spectra or ensemble entropies for graphs with many short loops. I am developing a new method for this, based on a flavour of replica analysis with imaginary replica dimension.

Equilibrium and non-equilibrium analysis of processes on complex loopy graphs

I try to use the methods of the previous project to derive exact results for complex dynamical systems on finitely connected loopy graphs. The idea is to approximate any given graph by an ensemble of random graphs which share with the original graph the full degree sequence and the eigenvalue spectrum (so they have identical local connectivity and identical closed path statistics of any length).

##### PUBLICATIONS

Books

Books in preparation

Principles of survival analysis (with JE Barrett and L Holmberg)

All research and review papers

ACC Coolen, R Kuehn and P Sollich

Theory of neural information processing systems

(Oxford University Press, July 2005)

ACC Coolen

The mathematical theory of minority games: statistical mechanics of interacting agents

(Oxford University Press, January 2005)

ACC Coolen, A Annibale and K Roberts

Generating random networks and graphs

(Oxford University Press, April 2017)

Selected recent research papers

ACC Coolen, J Barrett, P Paga and C Perez Vicente. J Phys A 50 (2017), 375001

Replica analysis of overfitting in regression models for time-to-event data.

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M Sheikh and ACC Coolen. Journal of Classification (2017), submitted.

Accurate Bayesian data classification without hyperparameter cross-validation.

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F Aguirre Lopez, P Barucca, M Fekom and ACC Coolen. J Phys A 51 (2018), 085101

Exactly solvable random graph ensemble with extensively many short cycles.

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A Grigoriadis et al. J Path: Clin Res 4 (2018), 39-54

Histological scoring of immune and stromal features in breast and axillary lymph

nodes is prognostic for distant metastasis in lymph node-positive breast cancers

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A Mozeika and ACC Coolen. Phys Rev E98 (2018), 042133

Mean-field theory of Bayesian clustering

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##### PUBLICATIONS

Books

Books in preparation

Principles of survival analysis (with M Jonker and L Holmberg)

Statistical physics of heterogeneous many-particle systems (with A Annibale)

Books planned

Introduction to the replica method

Dynamics of heterogeneous many-particle systems

(with A Annibale and A Mozeika)

All research and review papers

Below you find links to:

A full list of my publications

PDFs of recently published papers, organised by year

PDFs of recently published papers, organised by topic

ACC Coolen, R Kuehn and P Sollich

Theory of neural information processing systems

(Oxford University Press, July 2005)

ACC Coolen

The mathematical theory of minority games: statistical mechanics of interacting agents

(Oxford University Press, January 2005)

ACC Coolen, A Annibale and K Roberts

Generating random networks and graphs

(Oxford University Press, April 2017)

Selected recent research papers

E Massa, A Mozeika and ACC Coolen, J Phys A (2024) in press.

Replica analysis of overfitting in regression models for time to event data: the impact of censoring

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E Massa, MA Jonker and ACC Coolen, J Phys A 55 (2022) 485002

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ACC Coolen, T Nikoletopoulos, S Arai and K Tanaka, Sublinear Computation Paradigm, Springer, 2022

Dynamical analysis of quantum annealing

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A Mozeika, M Sheikh, F Aguirre-Lopez, F Antenucci and ACC Coolen, Phys rev E 103 (2021), 042142

Exact results on high-dimensional linear regression via statistical physics

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ACC Coolen, M Sheikh, A Mozeika, F Aguirre-Lopez and F Antenucci,

J Phys A 53 (2020) 365001

Replica analysis of overfitting in generalized linear regression models

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F Aguirre Lopez and ACC Coolen, J Phys A 53 (2020), 065002

Imaginary replica analysis of loopy regular random graphs

M Sheikh and ACC Coolen. J Classification (2019), doi.org/10.1007/s00357-019-09316-6

Accurate Bayesian data classification without hyperparameter cross-validation.

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Leuven, 8 August 2005. Finitely connected vector spin systems with random matrix interactions.

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Cambridge, 10 Jan 2006. Dynamics on finitely connected random graphs.

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Fribourg, 8 Nov 2007. Applications of generating functional analysis to minority game models.

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Rome, 13 Feb 2008. A solvable model of the genesis of amino-acid sequences via coupled dynamics of folding and slow genetic variation.

Kyoto, 16 Sep 2009. Generating functional analysis of complex formation and dissociation in large protein interaction networks.

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Stockholm (NORDITA), 22 June 2010, and Roma (La Sapienza), 1 July 2010. Tailoring, counting, and generating structured random graphs.

Evora (Portugal), 16 Sept 2011. Controlled Markovian dynamics of graphs.

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London, 21 Feb 2012, 26 March 2012. What you see is not what you get: how sampling affects macroscopic features of biological networks.

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Bad Honnef (DPG Physics School), Sept 2012. Counting and generating tailored random graphs.

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Paris, 11 Dec 2013. Solvable immune network models on finitely connected graphs with many short loops

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Pisa, 8 Dec 2014. Bayesian clinical classification from high-dimensional data: signatures versus variability.

Boston, 20 May 2015, London, June 9 2015. New analytical tools for loopy sparse random graphs.

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Kyoto, 15 December 2015, London, June 9 2015. Replica methods for loopy sparse random graphs

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New York, 18 April 2016. Towards a theory of overfitting in proportional hazards regression for survival data.

Rochester (Mayo Clinic), 20 April 2016. Give me six hours to chop down a tree ... Statistical tools to meet the challenges of modern medical data.

Umea University, Sweden, 10 April 2017. Cohort heterogeneity and competing risks in cancer survival.

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Barcelona, 31 Aug 2017. Neural networks versus immune networks: interesting observations and new questions

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Eindhoven, 21 Sept 2017. Tailoring of random networks and graphs

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Krakow, 14 Nov 2018. Tools for understanding and manipulating cellular signalling networks

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Teddington, 18 Dec 2018. Open nonequilibrium problems in spin systems

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Belfast, 4 Sept 2019. Overfitting correction in multivariate survival analysis

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Sendai, 27 Oct 2019. Replica analysis of overfitting in survival analysis and other generalized linear models

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Kyoto, 1 Nov 2019. Imaginary replica analysis of loopy regular random graphs

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##### SOME SELECTED RECENT SEMINARS

##### TEACHING

Lecture courses

Postgraduate collaborators

Emanuele Massa

Mathematical theory of overfitting in survival analysis

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Mauricio Diaz-Ortiz

Methods for dealing with informative censoring by competing risks in inference models

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Shakeeb Majid

Methods for inference and prediction from longitudinal data

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Jasper Hof

Recurrent event models for bladder cancer outcome prediction from SNV data

##### SUPERVISION

##### AND

Former postgraduate collaborators

Postdoctoral collaborators

Hassan Pazira

Bayesian Federated Inference (BFI)

Harm Jonker, Stephen Laughton, Charles Mace, Nikos Skantzos, Alexander Heimel, Hirak Chakravorty, Jon Hatchett, Theodore Nikoletopoulos, Bastian Wemmenhove, Nima Shayeghi, Sabrina Rabello, Alexander Mozeika, Panos Papadopoulos, Mark Rowley, Kate Roberts, James Barrett, Akram Shalabi, Mansoor Sheikh, Fabian Aguirre-Lopez

Lecture notes

Modelling real-world complex systems (2021)

(Radboud University)

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Challenges of high dimensionality and heterogeneity in inference from modern medical data (2019) (Havana School lectures)

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Theory of complex networks (2016)

Statistical physics of tailored random graphs: entropies, processes and generation (2015)

(Barcelona Summerschool lectures)

Calculus 1 (2011)

Markov chains (2009)

Introductory quantum theory (2005)

Information theory in neural networks (2002)

Advanced neural networks (2002)

Path integral methods in the dynamics of disordered systems (1999)

Neural networks (1998)

Statistical mechanics of neural networks (1997)

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