## >> Publications at DIEP

###### DIEP aims at performing groundbreaking interdisciplinary research that connects different fields and â€‹shines light on aspects of emergence. Below you find a list of publications of some of the researchers associated with DIEP starting in late 2020.

## >> Topological waves in passive and active fluids on curved surfaces: a unified picture

## by R. Green, J. Armas, Jan de Boer, Luca Giomi | November 2020

###### A study of hydrodynamics on curved surfaces and the emergence of topological edge modes - hydrodynamic waves confined to the equators of surfaces, such as Kelvin and Yanai waves on the surface of the Earth.

## >> Topology and broken Hermiticity

## by C. Coulais, R. Fleury and J. van Wezel | November 2020

###### A review paper on topological phases of matter published in Nature, following one of the DIEP workshops. In recent years, however, there has been a considerable push to explore the consequences of topology and symmetries in non-conservative, non-equilibrium or non-Hermitian systems. A plethora of driven artificial materials has been reported, blurring the lines between a wide variety of fields in physics and engineering, including condensed matter, photonics, phononics, optomechanics, as well as electromagnetic and mechanical metamaterials.

## >> Learning to Collude in a Pricing Duopoly

## by J. Meylahn and A. den Boer | January 2021

###### We design and analyze a pricing algorithm that learns to collude (charge higher than competitive prices) when it "competes" against itself and learns to price according to a best-response when playing against opponents in a certain class. This poses a threat to consumer welfare since the implementation of the algorithm would be legal under current anti-trust legislation.

## >> Exact epidemic models from a tensor product formulation

## by W. Merbis | February 2021

###### A general framework for the exact description of stochastic systems on networks is presented and applied to many well-known compartmental models of epidemiology. The formulation is inspired by methods from quantum mechanics and represents the state of the population as a vector in the tensor product space of N individual probability vector spaces. The transitions between different states, as specified by the compartmental model as well as the interaction network, are obtained by taking suitable linear combinations of tensor products of smaller matrices. Several mean-field approximations known in the literature are recovered from the exact formulation. In addition, we show how the exact transition rate matrix for the susceptible-infected (SI) model can be used to find analytic solutions for SI outbreaks on finite trees and the cycle graph.

## >> Multiscale molecular kinetics by coupling Markov state models and reaction-diffusion dynamics

## by M. J. del Razo, M. Dibak, C. SchÃ¼tte, F. NoÃ© | March 2021

###### Computing large time- and length-scale kinetics of interacting molecules is fundamental to understand biomolecular processes, such as protein-drug binding and virus capsid formation. In general, direct simulation of such processes at scales relevant to life is computationally unfeasible. Long-time dynamics of small to intermediate molecules/complexes can be estimated with Markov models parametrized with large ensembles of short simulations. However, these are still limited to small length-scales. To model multiple molecules at large lengthscales, particle-based reaction-diffusion is more suitable but lacks molecular detail. To combine the best of both, this work develops a general framework to couple Markov state models of molecular kinetics with particle-based reaction-diffusion simulations, which is capable of efficiently simulating large time and length-scales with great accuracy.

## >> Two-community noisy Kuramoto model with general interaction strengths. I & II (two papers)

## by S. Achterhof, J. Meylahn | March 2021

###### We study the noisy Kuramoto model on a two-community network. Making this simple adjustment to the standard noisy Kuramoto model leads to an increase in the richness of the model by making it possible for there to be up to four possible steady-state solutions in parts of the parameter space. We introduce a geometric interpretation of the self-consistency equations which allows us to identify all bifurcation points and so leads to a full classification of the phase diagram. Making this change in the underlying network structure of the interaction of the model gives rise to new phenomena like non-symmetrically synchronized solutions.

## >> Independent Markov Decomposition: Towards modeling kinetics of biomolecular complexes

## by T. Hempel, M. J. del Razo, C. T. Lee, B. C. Taylor, R. E. Amaro, F. NoÃ© | March 2021

###### Molecular simulations of proteins are often coarse-grained into Markov state models (MSMs), in which each protein configuration is assigned to a state and the transitions between states are inferred from the molecular simulations. As we explore larger and more complex biological systems, the number of states will face a combinatorial explosion, rendering it impossible to gather sufficient data to parametrize the MSM. In this work, we introduce an approach to decompose a system of interest into separable subsystems. We show that MSMs built for each sub-system, that are cheaper to parametrize, can be later coupled to reproduce the behaviors of the global system. To aid in the choice of decomposition we also describe a score to quantify its goodness. This decomposition strategy has the promise to enable robust modeling of complex biomolecular systems.

## >> Probabilities with Gaps and Gluts

## by D. Klein, O. Majer, S. R. Rad | April 2021

###### The paper studies probabilities in non-classical contexts where one is faced with incomplete or even contradictory information. In classical logic, strong completeness is assumed for information that ensures the truth of either A or Â¬A (the negation of A) for any A. Even worse when dealing with contradictory information the classical setting is trivialized and does not allow for any meaningful inference. In this paper we follow up on some recent approaches in the literature to investigate non-standard probabilities in situations of incomplete or contradictory information and study the formal machinery that allows for meaningful inference in these scenarios. We do in particular study conditionalisation and learning in this setting and sketch the contours of a theory of belief aggregation for these non-standard probabilities. To apper in Journal of Philosophical Logic.

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