(CDT Student names in bold)

2024

Coarse extrinsic curvature of Riemannian submanifolds

           Authors: Marc Arnaudon, Xue-Mei Li, Benedikt Petko

Weak Convergence Analysis of Online Neural Actor-Critic Algorithms

           Authors: Samuel Chun-Hei Lam, Justin Sirignano, Ziheng Wang

Deep Neural Network Initialization with Sparsity Inducing Activations

          Authors: Ilan Price, Nicholas Daultry Ball, Samuel C.H. Lam, Adam C. Jones, Jared Tanner

Neural Networks-based Random Vortex Methods for Modelling Incompressible Flows

           Authors: Vladislav Cherepanov and Sebastian W. Ertel

Random vortex dynamics and Monte-Carlo simulations for wall-bounded viscous flows

           Authors: Vladislav Cherepanov, Sebastian W. Ertel, Zhongmin Qian and Jiang-Lun Wu

On the dynamics of the boundary vorticity for incompressible viscous flows

          Authors: Vladislav Cherepanov, Jian-Guo Liu and Zhongmin Qian

Conditioned stochastic stability of equilibrium states on uniformly expanding repellers

          Authors: Bernat Bassols Cornudella, Matheus Manzatto de Castro and Jeroen S. W. Lamb

Universality classes for percolation models with long-range correlations

          Authors: Christopher Chalhoub, Alexander Drewitz, Alexis Prévost, Pierre-François Rodriguez

Constructive proofs for some semilinear PDEs on H²(e^{|x|²/4} , ℝ^d)

          Authors: Maxime Breden (École Polytechnique, Paris) and Hugo Chu

Optimal Portfolio Choice with Cross-Impact Propagators

          Authors: Eduardo Abi Jaber, Eyal Neuman and Sturmius Tuschmann

Partially Stochastic Infinitely Deep Bayesian Neural Networks

         Authors: Sergio Calvo-Ordonez, Matthieu Meunier, Francesco Piatti, Yuantao Shi

2023

Noise-induced chaos: A conditioned random dynamics perspective

         Authors: Bernat Bassols-Cornudella and Jeroen S. W. Lamb

VolGAN: a generative model for arbitrage-free implied volatility surfaces

         Authors: Milena Vuletić and Rama Cont (working paper)

Learning Lie Group Symmetry Transformations with Neural Networks

        Authors: Alex Gabel, Victoria Klein, Riccardo Valperga, Jeroen S. W. Lamb, Kevin Webster, Rick Quax and  Efstratios Gavves 

Narratives from GPT-derived Networks of News, and a link to Financial Markets Dislocations

       Authors: Deborah Miori and Constantin Petrov

Kernel Limit of Recurrent Neural Networks Trained on Ergodic Data Sequences

       Authors: Samuel Chun-Hei Lam, Justin Sirignano, Konstantinos Spiliopoulos

Likelihood-based inference and forecasting for trawl processes: a stochastic optimization approach. arXiv preprint arXiv:2308.16092 (2023) (with software: Ambit stochastics - a Github repository dedicated to the study of ambit fields and trawl processes  https://github.com/danleonte/Ambit_Stochastics, doi:10.5281/zenodo.7081978.)

       Authors: Dan Leonte and Almut ED Veraart

​​​​​​Binomial Cayley Graphs and Applications to Dynamics on Finite Spaces

Authors: Bernat Bassols-Cornudella, Francesco Viganò

Monte-Carlo method for incompressible fluid flows past obstacles

         Authors: Vladislav Cherepanov, Zhongmin Qian

Random Young towers and quenched decay of correlations for predominantly expanding multimodal circle maps

Author: Matheus M. Castro, Giuseppe Tenaglia

On the fluctuations of an SDE system modelling grid cells

Author: Andrea Clini

SHAPER: Can You Hear the Shape of a Jet?

Demba Ba, Akshunna S. Dogra, Rikab Gambhir, Abiy Tasissa, Jesse Thaler

Fluctuations of stochastic PDEs with long-range correlations

Author: Luca Gerolla, Martin Hairer, Xue-Mei Li

Calibration of Local Volatility Models with Stochastic Interest Rates using Optimal Transport

Gregoire Loeper, Jan Obloj, Benjamin Joseph

Smooth vs. Physical Solutions of the Navier-Stokes Equation

Authors: James Glimm, Jarret Petrillo, Min Chul Lee

DeFi: data-driven characterisation of Uniswap v3 ecosystem & an ideal crypto law for liquidity pools

Authors: Deborah Miori, Mihai Cucuringu

Execution and Statistical Arbitrage with Signals in Multiple Automated Market Makers

Authors: Álvaro Cartea, Fayçal Drissi, Marcello Monga

Coarse Ricci curvature of weighted Riemannian manifolds

Authors: Marc Arnaudon, Xue-Mei Li, Benedikt Petko

Singular SPDEs on Homogeneous Lie Groups

Authors: Avi Mayorcas, Harprit Singh

Strong convergence of parabolic rate 1 of discretisations of stochastic Allen-Cahn-type equations

Authors: Máté Gerencsér, Harprit Singh

Authors: Jeroen S.W. Lamb, Giuseppe Tenaglia, Dmitry Turaev

Looking forwards and backwards: dynamics and genealogies of locally regulated populations

Authors: Alison M. Etheridge, Thomas G. Kurtz, Ian Letter, Peter L. Ralph, Terence Tsui Ho Lung 

Towards Evology: a Market Ecology Agent-Based Model of US Equity Mutual Funds II

Authors: Aymeric Vie, J. Doyne Farmer

Fin-GAN: Forecasting and Classifying Financial Time Series via Generative Adversarial Networks

Authors: Milena Vuletić, Felix Prenzel, Mihai Cucuringu

Dynamics of market making algorithms in dealer markets: Learning and tacit collusion

Authors: Rama Cont, Wei Xiong

Random neural networks for rough volatility

Authors: Antoine Jacquier, Zan Zuric

 

2022

Learning reversible symplectic dynamics

        Authors: Riccardo Valperga, Kevin Webster, Dmitry Turaev, Victoria Klein and Jeroen S.W. Lamb

The Lyapunov spectrum for conditioned random dynamical systems

Authors: Matheus M. Castro, Dennis Chemnitz, Hugo Chu, Maximilian Engel, Jeroen S. W. Lamb, Martin Rasmussen

On the quasi-ergodicity of absorbing Markov chains with unbounded transition densities, including random logistic maps with escape

Authors: Matheus M. Castro, Vincent P. H. Goverse, Jeroen S. W. Lamb, Martin Rasmussen

The mean field limit of stochastic differential equation systems modelling grid cells

Authors: José A. Carrillo, Andrea Clini, Susanne Solem

Porous media equations with nonlinear gradient noise and Dirichlet boundary conditions

Authors: Andrea Clini

The entropy production of stationary diffusions

Authors: Lancelot Da Costa, Grigorios A. Pavliotis

Path integrals, particular kinds, and strange things

Authors: Karl Friston, Lancelot Da Costa, Dalton A. R. Sakthivadivel, Conor Heins, Grigorios A. Pavliotis, Maxwell Ramstead, Thomas Parr

Modelling non-reinforced preferences using selective attention

Authors: Noor Sajid, Panagiotis Tigas, Zafeirios Fountas, Qinghai Guo, Alexey Zakharov, Lancelot Da Costa

Sparse coupling and Markov blankets: A comment on “How particular is the physics of the Free Energy Principle?” by Aguilera, Millidge, Tschantz and Buckley

Authors: Conor Heins, Lancelot Da Costa

On Bayesian Mechanics: A Physics of and by Beliefs

Authors: Maxwell J D Ramstead, Dalton A R Sakthivadivel, Conor Heins, Magnus Koudahl, Beren Millidge, Lancelot Da Costa, Brennan Klein, Karl J Friston

The free energy principle made simpler but not too simple

Authors: Karl Friston, Lancelot Da Costa, Noor Sajid, Conor Heins, Kai Ueltzhöffer, Grigorios A. Pavliotis, Thomas Parr

Geometric Methods for Sampling, Optimisation, Inference and Adaptive Agents

Authors: Alessandro Barp, Lancelot Da Costa, Guilherme França, Karl Friston, Mark Girolami, Michael I. Jordan, Grigorios A. Pavliotis

A mixed generative model of auditory word repetition

Authors: Noor Sajid, Emma Holmes, Lancelot Da Costa, Cathy Price, Karl Friston

How Active Inference Could Help Revolutionise Robotics

Authors: Lancelot Da Costa, Pablo Lanillos, Noor Sajid, Karl Friston, Shujhat Khan

Universality of Winning Tickets: A Renormalization Group Perspective

Authors: William T. Redman, Tianlong Chen, Zhangyang Wang, Akshunna S. Dogra

Hamiltonian neural networks for solving equations of motion

Authors: Marios Mattheakis, David Sondak, Akshunna S. Dogra, Pavlos Protopapas

Convergence of policy gradient methods for finite-horizon stochastic linear-quadratic control problems

Authors: Michael Giegrich, Christoph Reisinger, Yufei Zhang

Learning reversible symplectic dynamics

Authors: Riccardo Valperga, Kevin Webster, Victoria Klein, Dmitry Turaev, Jeroen S. W. Lamb

Axioms for Quantum Gauge Fields

Authors: Min Chul Lee, James Glimm

Simulation methods and error analysis for trawl processes and ambit fields

Authors: Dan Leonte, Almut E. D. Veraart

On the fractal dimensions for deterministic and random substitution graph systems

Authors: Ziyu Li

The Short-Term Predictability of Returns in Order Book Markets: a Deep Learning Perspective

Authors: Lorenzo Lucchese, Mikko Pakkanen, Almut Veraart

An SPDE with Robin-type boundary for a system of elastically killed diffusions on the positive half-line

Authors: Ben Hambly, Julian Meier, Andreas Sojmark

McKean-Vlasov Equations with Positive Feedback through Elastic Stopping Times

Authors: Ben Hambly, Julian Meier

Fast and Slow Optimal Trading with Exogenous Information

Authors: Alessandro Micheli, Eyal Neuman

SEC Form 13F-HR: Statistical investigation of trading imbalances and profitability analysis

Authors: Deborah Miori, Mihai Cucuringu

Returns-Driven Macro Regimes and Characteristic Lead-Lag Behaviour between Asset Classes

Authors: Deborah Miori, Mihai Cucuringu

Decentralised Finance and Automated Market Making: Execution and Speculation

Authors: Álvaro Cartea, Fayçal Drissi, Marcello Monga

Decentralised Finance and Automated Market Making: Permanent Loss and Optimal Liquidity Provision

Authors: Álvaro Cartea, Fayçal Drissi, Marcello Monga

Analysis and modeling of client order flow in limit order markets

Rama Cont, Mihai Cucuringu, Vacslav Glukhov, Felix Prenzel

Asymptotic Analysis of Deep Residual Networks

Authors: Rama Cont, Alain Rossier, Renyuan Xu

Convergence and Implicit Regularization Properties of Gradient Descent for Deep Residual Networks

Authors: Rama Cont, Alain Rossier, RenYuan Xu

Quantitative Universal Approximation Bounds for Deep Belief Networks

Authors: Julian Sieber, Johann Gehringer

On the (Non-)Stationary Density of Fractional-Driven Stochastic Differential Equations

Authors: Xue-Mei Li, Fabien Panloup, Julian Sieber

Markov decision processes with observation costs

Authors: Christoph Reisinger, Jonathan Tam

Topologies on unparameterised path space

Authors: Thomas Cass, William F. Turner

Towards Evology: a Market Ecology Agent-Based Model of US Equity Mutual Funds

Authors: Aymeric Vie, Maarten Scholl, Alissa M. Kleinnijenhuis, Doyne J. Farmer

Simulation of Arbitrage-Free Implied Volatility Surfaces

Authors: Rama Cont, Milena Vuletic

Continuous-time stochastic gradient descent for optimizing over the stationary distribution of stochastic differential equations

Authors: Ziheng Wang, Justin Sirignano

A Forward Propagation Algorithm for Online Optimization of Nonlinear Stochastic Differential Equations

Authors: Ziheng Wang, Justin Sirignano

Interactions of market making algorithms: a study on perceived collusion

Authors: Wei Xiong, Rama Cont

Random vortex dynamics via functional stochastic differential equations

Authors: Zhongmin Qian, Endre Süli, Yihuang Zhang

Volatility forecasting with machine learning and intraday commonality

Authors: Chao Zhang, Yihuang Zhang, Mihai Cucuringu, Zhongmin Qian

Random vortex dynamics via functional stochastic differential equations

Authors: Zhongmin Qian, Endre Süli, Yihuang Zhang

2021

Existence and uniqueness of quasi-stationary and quasi-ergodic measures for absorbing Markov processes: a Banach lattice approach

Authors: Matheus M. Castro, Jeroen S. W. Lamb, Guillermo Olicón Méndez, Martin Rasmussen

The mean field limit of stochastic differential equation systems modelling grid cells

Authors: José A. Carrillo, Andrea Clini, Susanne Solem

Memory and Markov Blankets

Authors: Thomas Parr, Lancelot Da Costa, Conor Heins, Maxwell James D. Ramstead, Karl J. Friston

Stochastic Chaos and Markov Blankets

Authors: Karl Friston, Conor Heins, Kai Ueltzhöffer, Lancelot Da Costa, Thomas Parr

A Drive towards Thermodynamic Efficiency for Dissipative Structures in Chemical Reaction Networks

Authors: Kai Ueltzhöffer, Lancelot Da Costa, Daniela Cialfi, Karl Friston

Active inference, Bayesian optimal design, and expected utility

Authors: Noor Sajid, Lancelot Da Costa, Thomas Parr, Karl Friston

Branching Time Active Inference: the theory and its generality

Authors: Théophile Champion, Lancelot Da Costa, Howard Bowman, Marek Grześ

Bayesian brains and the Rényi divergence

Authors: Noor Sajid, Francesco Faccio, Lancelot Da Costa, Thomas Parr, Jürgen Schmidhuber, Karl Friston

Bayesian Mechanics for Stationary Processes

Authors: Lancelot Da Costa, Karl Friston, Conor Heins, Grigorios A. Pavliotis

Signature asymptotics, empirical processes, and optimal transport

Authors: Thomas Cass, Remy Messadene

The dynamics of the Koopman-van Hove angular and linear momentum operators

Authors: Remy Messadene

Closed-Loop Nash Competition for Liquidity

Authors: Alessandro Micheli, Johannes Muhle-Karbe, Eyal Neuman

Scaling Properties of Deep Residual Networks

Authors: Alain-Sam Cohen, Rama Cont, Alain Rossier, Renyuan Xu

Mild Stochastic Sewing Lemma, SPDE in Random Environment, and Fractional Averaging

Authors: Xue-Mei Li, Julian Sieber

Functional Limit Theorems for Volterra Processes and Applications to Homogenization

Authors: Johann Gehringer, Xue-Mei Li, Julian Sieber

Modelling SARS-CoV-2 coevolution with genetic algorithms

Authors: Aymeric Vie

Emergence of more contagious COVID-19 variants from the coevolution of viruses and policy interventions

Authors: Aymeric Vie 

Population network structure impacts genetic algorithm optimisation performance

Authors: Aymeric Vie

Global Convergence of the ODE Limit for Online Actor-Critic Algorithms in Reinforcement Learning

Authors: Ziheng Wang, Justin Sirignano

Universality for the directed configuration model with random degrees: metric space convergence of the strongly connected components at criticality

Authors: Serte Donderwinkel, Zheneng Xie

Tracking the vortex motion by using Brownian fluid particles

Authors: Zhongmin Qian, Youchun Qiu, Yihuang Zhang

Large and moderate deviations for importance sampling in the Heston model

Authors: Marc Geha, Antoine Jacquier, Zan Zuric

Deep Hedging under Rough Volatility

Authors: Blanka Horvath, Josef Teichmann, Zan Zuric

2020

The relationship between dynamic programming and active inference: the discrete, finite-horizon case

Authors: Lancelot Da Costa, Noor Sajid, Thomas Parr, Karl Friston, Ryan Smith

Sophisticated Inference

Authors: Karl Friston, Lancelot Da Costa, Danijar Hafner, Casper Hesp, Thomas Parr

Some interesting observations on the free energy principle

Authors: Karl Friston, Lancelot Da Costa, Thomas Parr

Active inference on discrete state-spaces: a synthesis

Authors: Lancelot Da Costa, Thomas Parr, Noor Sajid, Sebastijan Veselic, Victorita Neacsu, Karl Friston

Evidence of Crowding on Russell 3000 Reconstitution Events

Authors: Alessandro Micheli, Eyal Neuman

Slow-Fast Systems with Fractional Environment and Dynamics

Authors: Xue-Mei Li, Julian Sieber

Formulae for the Derivative of the Poincaré Constant of Gibbs Measures

Authors: Julian Sieber

Qualities, challenges and future of genetic algorithms: a literature review

Authors: Aymeric Vie, Alissa M. Kleinnijenhuis, Doyne J. Farmer

Asymptotic strong Feller property and local weak irreducibility via generalized couplings

Authors: Oleg Butkovsky, Fabrice Wunderlich

Robust pricing and hedging via neural SDEs

Authors: Patryk Gierjatowicz, Marc Sabate-Vidales, David Šiška, Lukasz Szpruch, Žan Žurič