## DIEP journal club

## Every second Thursday from 11am to 12:30pm | starting 14th of January 2021

## Organizers: Jácome Armas, Mauricio del Razo, Soroush Rafiee Rad, Janusz Meylahn and Wout Merbis

## Registration

###### To register for the DIEP journal club please fill out the form here. See full calendar of events here.

###### See recordings of all talks here.

## Programme:

###### Algorithmic collusion using Q-learning | 4th of February 2021

###### Janusz Meylahn, DIEP

###### Molecular kinetics as hybrid switching diffusions: a general framework for MSM/RD simulation | 14th of January 2021

Mauricio del Razo, DIEP

###### A novel approach to simulate simple protein-ligand systems at large time- and length-scales is to couple Markov state models (MSMs) of molecular kinetics with particle-based reaction-diffusion (PBRD) simulations; this approach is named MSM/RD. Current formulations of MSM/RD lack an underlying mathematical framework; they are limited to protein-ligand systems, where the ligand orientation and conformation switching are not taken into account; and they lack multi-particle extensions. In this work, we develop a general MSM/RD framework by coarse-graining molecular dynamics into hybrid switching diffusion processes, a class of stochastic process that integrates continuous dynamics and discrete events into the same process. This framework overcomes all the previous difficulties. We further implement and verify it for two toy models of protein-protein interaction and one multiparticle implementation to model the formation of pentameric ring molecules.

###### On Correlated Information | 28th of January 2021

###### Soroush Rafiee Rad, DIEP

###### We discuss a paper by Alexandru Baltag and Sonja Smets on correlated knowledge: https://www.researchgate.net/publication/226943513_Correlated_Knowledge_An_Epistemic-Logic_View_on_Quantum_Entanglement

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In this paper they model (classical and quantum) complex systems, and give a logical analysis of classical and quantum correlations using tools developed in the study of epistemic logics. They propose a logical system for reasoning about the information carried by a complex system consisting of different parts, and investigate the relationship between the information available in such a system as a whole and the information carried by each of its parts. In particular, their analysis distinguishes distributed information, that comes from pooling together all the information that can be observed in each separate part of the system, from correlated information, that is obtained by joint observations of the parts. This correlated information is only obtainable when the individual parts are combined and observed as a complex system, which allows information exchange between these parts. Similarly, for a set of individual agents with private information, correlated knowledge only emerges when they come together as a group, allowing for cooperation between them and the information dynamics that ensue. This is an instance of an emergent phenomena in information dynamics and epistemic logic and an example of logical analysis of such phenomena. This analysis elucidates the difference between classical and quantum information and provides an informational-logical characterization of 'quantum entanglement’.

###### Algorithmic pricing is becoming more and more integrated into the marketplace. The danger of this, according to some economists and lawyers, is that the algorithms may learn to collude spontaneously. This would take the form of the algorithms charging higher prices than would be competitive. In the article we will discuss this week, Calvano et al. conduct simulated experiments with a Q-learning algorithm. They show that the use of the algorithm by two firms in a duopoly leads to supra-competitive prices without the algorithm being explicitly programmed to do so. Surprisingly, the algorithm seems to respond to an exogenous "defection" with a "punishment" followed by a return to the supra-competitive price. A strategy of this kind (Reward and Punishment Scheme) is thought to be a crucial ingredient for stable collusion. The result that such a strategy spontaneously emerges when using Q-learning has received sufficient attention to warrant a follow-up publication in Science.

###### Coordination in polarised societies| 18th of February 2021

###### Vítor Vasconcelos, University of Amsterdam | See video here

###### Polarisation on various issues has increased in many western democracies since the 1980s. Beliefs about or observations of the behaviours and opinions of others drive individuals’ actions. These multiple social dynamics can support cooperative equilibria in the absence of enforcement by formal institutions, but they can also maintain harmful beliefs and behaviours. Through modelling and experiments, we explore the effects of polarisation on the likelihood that a society will coordinate on welfare-improving actions in a context where collective benefits are acquired only if enough individuals contribute—i.e., a coordination game. The talk will start with an analysis of competing complex-contagion processes and their role in generating different patterns in the distribution and segregation of ideas or opinions. Then, we will look into how heterogeneity of these opinions impacts collective action and the role of partial—and biased—information about others in improving the chances of collective success. Finally, we will show how different types of biases, not just the ones introduced by limited information but those intrinsic to human psychology, lead to suboptimal deadlocks.

###### Exact epidemic models form a tensor product formulation | 24th of February 2021

###### Wout Merbis, DIEP | See video here

###### A method for computing exact transition rate matrices for many well-known models of epidemic spreading on networks is presented. The state of the population is described as a tensor product of N individual probability vector spaces, with dimension equal to the number of compartments of the epidemiological model d. The transition rate matrix for the d^N-dimensional Markov chain is obtained by taking suitable linear combinations of tensor products of d-dimensional matrices. The resulting transition rate matrix is a sum over bilocal linear operators, which gives insight into the microscopic dynamics of the system. 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. We comment on possible applications of this formulation to the study of stochastic systems with many interacting constituents, such as the epidemic spreading process and other models of information spread on networks.

###### Beyond pairwise model for binary data: the search for simple spin models| 11th of March 2021

###### Clélia de Mulatier, University of Amsterdam

###### Finding the model that best captures the patterns hidden within noisy data is a central problem in science. To address this issue, information theory and Bayesian statistics provide two comparable rigorous methods to select the best of potential explanations for data. The selected model is the one that achieves the optimal balance between goodness-of-fit and simplicity. Yet in practice, the computational cost associated with fitting each of the many potential models and the difficulty of evaluating model complexity make it challenging to search for “the” best model. Besides, with a finite amount of data an important limitation comes from the large degeneracy of models that perform nearly optimally.

In this talk I will discuss these issues in the context of binary data, where pairwise spin models (Ising model) are widely used. To understand the features of simple models, we will study the information theoretic complexity of spin models with interactions of arbitrary order, which form a complete family of candidate models for binary data. We will highlight the existence of transformations between models with interactions of different orders that preserve model complexity and see that, contrary to common intuition, pairwise models are not necessarily the simplest spin models.

We will finally discuss the development of new complementary methods of model selection for binary data that take into account high order interactions. In particular, we will discuss the use of minimally complex models for which all quantities of interest – the model complexity, the maximum likelihood, the evidence, and the Fisher information matrix – can be computed easily. This approach contrasts with the statistical inference of pairwise models for which maximum likelihood estimates are already computationally challenging. We will illustrate these techniques on several datasets.

###### Formulating Emergence in the Physical Sciences -- a Philosopher's Perspective | 25th of March 2021

###### Sebastian De Haro, UvA

###### An important problem in the philosophy of emergence is the different uses that different authors make of the word ‘emergence’, and of the distinctions that they draw between different kinds of emergence. In this talk, I will review recent proposals, especially by Butterfield, to define emergence as novelty of behaviour relative to an appropriate comparison class, and to clarify the relation between emergence, reduction, and supervenience. Then I will present my own proposal for how to best define emergence in the physical sciences.

###### Light Production in a Unicellular Organism | 8th of April 2021

###### Mazi Jallal, University of Amsterdam

###### Bioluminescence (emission of light from living organisms) is a common form of communication in the ocean and land. It has evolved over forty times in history and can be found in multiple biological kingdoms like bacteria, fungi, and protozoa. Bioluminescence has been of interest to humankind for thousands of years and has been a source of commentary since ancient times, from Aristotle and Pliny the Elder to Shakespeare, Boyle and Darwin. While the internal biochemistry of light production by many organisms is well established, the manner by which fluid shear or mechanical forces trigger bioluminescence is still poorly understood. We will briefly review the history of the science of bioluminescence and then present our recent work on the bioluminescence of a single-celled organism, where we aim to understand the response (light production) to mechanical stimulation. We find a "viscoelastic" response in which light intensity depends on both the amplitude and rate of cell deformation, consistent with the action of stretch-activated ion channels. We also show how such a biological system can be modelled with a simple set of linear ordinary differential equations.

###### The non-Hermitian "split skin effect" | 15th of April 2021

###### Jasper van Wezel, UvA

###### From atomic chains, to lattices of cold atoms and metamaterials, non-reciprocal and non-conservative systems hosting waves can exhibit a dramatic phenomenon, known as the non-Hermitian skin effect in which all bulk modes are forced to one side of a finite system. Here, we demonstrate a driven mechanical chain that hosts a "split skin effect", in which an extensive fraction of the bulk modes localises on the side of the system opposite to the usual bulk mode localisation, and opposite to the driving in the chain.

This system realises a specific instance of a broad class of non-Hermitian, non-reciprocal systems in both classical and quantum mechanics, whose dynamics is governed by Toeplitz matrices. We present a theoretical analysis highlighting how both normal and split skin effect phases may arise in these systems, and how the localisation length of the various skin effect modes depends on the properties of the underlying Toeplitz matrix. Although our results clearly show the skin effect is not by itself topological in nature, we suggest an interpretation of the skin modes as topological edge modes of a hypothetical higher-dimensional system.