Organized by: Maria Bruna (University of Cambridge, United Kingdom), Ulrich Dobramysl (University of Cambridge, United Kingdom), Simon Garnier (New Jersey Institute of Technology, USA)

• Meg Crofoot (Max Planck Institute of Animal Behavior & University of Konstanz, Germany)
  "Locomotor compromise underlies coordination in heterogeneous groups on the move"
When members of a group differ in locomotor capacity, coordinating collective movement poses a challenge: some individuals may have to move faster (or slower) than their preferred speed to remain together. Such compromises have energetic repercussions yet research in collective behavior has largely neglected locomotor consensus costs. Here we integrate high-resolution tracking of wild baboon locomotion and movement with simulations to demonstrate that size-based variation in locomotor capacity poses an obstacle to collective movement. While all baboons modulate their gait and move-pause dynamics during collective movement, the costs of maintaining cohesion are disproportionately borne by smaller group members. Although consensus costs are not distributed equally, all group-mates do make locomotor compromises, suggesting a shared decision-making process drives the pace of collective movement in this highly despotic species. These results highlight the importance of considering how social dynamics and locomotor capacity interact to shape the movement ecology of group-living species.
• Colin Torney (School of Mathematics & Statistics, University of Glasgow, United Kingdom)
  "Inferring microscale properties of interacting systems from macroscale observations"
Emergent dynamics of complex systems are observed throughout nature and society. The coordinated motion of bird flocks, the spread of opinions, fashions and fads, or the dynamics of an epidemic, are all examples of complex macroscale phenomena that arise from fine-scale interactions at the individual level. In many scenarios, observations of the system can only be made at the macroscale, while we are interested in creating and fitting models of the microscale dynamics. This creates a challenge for inference as a formal mathematical link between the micro and macro scale is rarely available. In this talk, I will describe an inferential framework that bypasses the need for a formal link between scales and instead uses sparse Gaussian process regression to learn the drift and diffusion terms of an empirical Fokker-Planck equation which describes the time evolution of the probability density of a macroscale variable. This gives access to the likelihood of the microscale properties of the system and a second Gaussian process can then be used to emulate the log-likelihood surface, allowing the implementation of a fast, adaptive MCMC sampler which iteratively refines the emulator when needed. The performance of the method can be illustrated by applying it to simple models of collective motion.
• Yuko Ulrich (Institute of Integrative Biology, ETH Zurich, Switzerland)
  "Behavioral organization in heterogeneous groups of a social insect"
The composition of social groups has profound effects on their function, from collective decision-making to foraging efficiency. But few social systems afford sufficient control over group composition to precisely quantify its effects on individual and collective behavior. Here we combine experimental and theoretical approaches to study the effect of group composition on individual behavior and division of labor (DOL) in a social insect. Experimentally, we use automated behavioral tracking to monitor 120 colonies of clonal raider ants, with controlled variation in three key correlates of social insect behavior: genotype, age, and morphology. We find that each of these sources of heterogeneity generates a distinct pattern of behavioral organization, including the amplification or dampening of inherent behavioral differences in mixed colonies. Theoretically, we use a well-studied model of DOL to explore potential mechanisms underlying the experimental findings. We find that the simplest implementation of this model, which assumes that heterogeneous individuals differ only in response thresholds, could only partially recapitulate the empirically observed patterns of behavior. However, the full spectrum of observed phenomena was recapitulated by extending the model to incorporate two factors that are biologically meaningful but theoretically rarely considered: variation among workers in task performance efficiency and among larvae in task demand. Our results thus show that different sources of heterogeneity within social groups can generate different, sometimes non-intuitive, behavioral effects, but that relatively simple models can capture these dynamics and thereby begin to elucidate the basic organizational principles of DOL in social insects.
• Adrien Blanchet (Toulouse School of Economics, France)
  "Mathematical model of disinformation"
For a couple of decades, the social network revolution has dramatically changed the way in which people access or share information. Information appears now to be decentralised, spreads faster and faster and seems difficult to control, predict or even understand. However the understanding of the spreading of information is absolutely crucial as it shapes the modern society: the opinion of citizens, the consumption of consumers, the behaviour of agents, or the political decisions. The problem of disinformation is fundamental and has been identified by the World Economic Forum as one of the threats to the economy. In this talk we will present a model of such phenomenon based on a game theory framework and using optimal transport and we will present an ongoing project. Co-authors: G. Carlier, F. Santambroggio, P. Mossay

Organized by: Hong Duong (University of Birmingham, UK), The Anh Han (Teesside University, UK)

• Hye Jin Park (Asia Pacific Center for Theoretical Physics, Korea)
  "Extinction dynamics from meta-stable coexistences in an evolutionary game"
• Jorge Peña (Institute for Advanced Study in Toulouse, University of Toulouse 1 Capitole, France)
  "Evolutionary dynamics of discrete public goods under threshold uncertainty"
• Isamu Okada (Soka University, Japan)
  "Social dilemma, scoring dilemma, and punishment dilemma in indirect reciprocity"
• Marco A. Javarone (University College London, UK)
  "Cooperative behaviours and sources of noise"

Organized by: Esteban Hernandez-Vargas (Instituto de Matematicas, UNAM, Unidad Juriquilla, Queretaro, Mexico., Mexico), Jorge X. Velasco-Hernandez (Instituto de Matematicas, UNAM, Unidad Juriquilla, Queretaro, Mexico., Mexico)

• Jan Fuhrmann (Jülich Supercomputing Centre, Forschungszentrum Jülich, Jülich, Germany, Germany)
  "Modeling the COVID-19 epidemic in Germany"
The novel corona virus SARS-CoV-2 that causes the disease COVID19 was first identified in Hubei province, China, in 2019 and has since spread around the globe. Its virulence and the morbidity associated with has caused the WHO to declare this new respiratory disease a pandemic in March 2020. From a modeling perspective this pandemic poses several challenges. As with most new infectious diseases, many parameters are not particularly well known. Alarmingly high numbers of known infectious and COVID-19 related deaths led to contact reductions among the population, partly by increased caution, partly mandated by authorities. And the infection often leading to mild, non-specific symptoms - or even no symptoms at all - makes it all but impossible to estimate the ratio of detected cases among all infections. We shall discuss some of the data available from public domain sources and show how ordinary differential equation models can be used to reproduce these data, generate short term forecasts, and simulate possible further courses of the epidemic for different scenarios. Particular emphasis will be put on the relevance of detection ratios and how they are affected by test strategies and case numbers.
• Lubna Pinky (University of Tennessee Health Science Center, Memphis, TN 38163, USA, USA)
  "Quantifying Dose-, Strain-, and Tissue-Specific Kinetics of Parainfluenza Virus Infection"
Human parainfluenza viruses (HPIVs) are a leading cause of acute respiratory infection hospitalization in children, yet little is known about how dose, strain, tissue tropism, and individual heterogeneity affects the processes driving growth and clearance kinetics. Longitudinal measurements are possible by using reporter sendai viruses, murine parainfluenza counterpart, that express luciferase, where the insertion location yields a wild-type-like or attenuated phenotype. Bioluminescence measurements from individual animals infected with either strain suggests that there is a rapid increase in expression followed by a peak, biphasic clearance, and resolution. However, these kinetics vary between individuals and with dose, strain, and whether the infection was initiated in the upper and/or lower respiratory tract. To quantify the differences, we translated the bioluminescence measurements from the nasopharynx, trachea, and lung into viral loads and used a mathematical model together with nonlinear mixed effects approach to define the mechanisms distinguishing each scenario. The results confirmed a higher rate of virus production with the wild-type-like virus compared to its attenuated counterpart, and suggested that low doses result in disproportionately fewer infected cells. The analyses indicated faster infectivity and infected cell clearance rates in the lung and that higher viral doses, and concomitantly higher infected cell numbers, resulted in more rapid clearance. Infected cell clearance was also highly variable amongst individuals, which was particularly evident during infection in the lung. These critical differences provide important insight into distinct HPIV dynamics, and show how bioluminescence data combined with quantitative analyses can be used to dissect host-, virus-, and dose-dependent effects.
• Fernando Saldaña (Instituto de Matematicas UNAM at Juriquilla, Mexico, Mexico)
  "A model for vaccine escape under unequal vaccine access"
Currently, there are concerns that without adequate vaccine distribution, the SARS-CoV-2 variants will grow and mutate, curbing the progress that has been made since the vaccine has been made available. In this work, we present a mathematical model to study vaccine escape evolution in structured host populations. We find that vaccine escape mutants are less likely to come from vaccinated regions where there is a strong selection pressure for vaccine escape and more likely to come from a neighboring unvaccinated region where there is no selection for escape.
• Suneet Singh Jhutty (Frankfurt Institute for Advanced Studies, Frankfurt am Main, Germany., Germany)
  "Mapping of Influenza Infection from Blood Data with Machine Learning Methods"
Seasonal and pandemic influenza causes enormous economic loss, health complications and death. The measurement of clinical markers for influenza and its respective immune responses is time-consuming and almost impossible to perform. Here, we show for first time the proof applicability and implementation of machine learning algorithms to infer the viral load and immune markers in the lung compartment based on hematology data of mice infected with influenza H1N1. Our results show that even with high variability in the data, the model prediction to track the infection in the host is possible. Platelets and granulocytes play an essential role to track influenza infection. The proposed in silico tool paved the way towards a better prognosis of influenza infections and possibly other respiratory diseases.

Organized by: Luca Calatroni (Laboratoire I3S, CNRS, UCA & Inria Sophia Antipolis Méditerranée, France), Mathieu Desroches (MathNeuro Project-Team, Inria Sophia Antipolis Méditerranée & Université Côté d’Azur, France), Valentina Franceschi (Dipartimento di Matematica, Università degli Studidi Padova, Italy), Dario Prandi (Université Paris-Saclay, CNRS, CentraleSupélec, L2S, France)
Note: this minisymposia has multiple sessions. The second session is MS17-NEUR.

• Laurent Perrinet (INT, CNRS - Aix-Marseille Université, France)
  "Pooling in a predictive model of V1 explains functional and structural diversity across species"
Neurons in the primary visual cortex are selective to orientation with various degrees of selectivity to the spatial phase, from high selectivity in simple cells to low selectivity in complex cells. Various computational models have suggested a possible link between the presence of phase invariant cells and the existence of cortical orientation maps in higher mammals’ V1. These models, however, do not explain the emergence of complex cells in animals that do not show orientation maps. In this study, we build a model of V1 based on a convolutional network called Sparse Deep Predictive Coding (SDPC) and show that a single computational mechanism, pooling, allows the SDPC model to account for the emergence of complex cells as well as cortical orientation maps in V1, as observed in distinct species of mammals. By using different pooling functions, our model developed complex cells in networks that exhibit orientation maps (e.g., like in carnivores and primates) or not (e.g., rodents and lagomorphs). The SDPC can therefore be viewed as a unifying framework that explains the diversity of structural and functional phenomena observed in V1. In particular, we show that orientation maps emerge naturally as the most cost-efficient structure to generate complex cells under the predictive coding principle.
• Rufin VanRullen (CerCo, CNRS and ANITI, Universite de Toulouse, France)
  "Deep predictive coding for more robust and human-like vision"
I will report on a series of experiments with deep convolutional neural networks augmented with feedback connections. The dynamics of the network are governed by predictive coding objectives, similar to those that have been proposed to explain neural activity in the brain. Compared to the standard feed-forward networks, these predictive coding networks can be more robust to noise and against certain adversarial attacks. They also respond to visual illusions (in particular, illusory contours from Kanisza shapes) in a way that is more similar to biological perception.
• Yuri Elias Rodrigues (INRIA/IPMC/Université Côte d'Azur, France)
  "Modelling the experimental heterogeneity of synaptic plasticity"
Discovering the rules of synaptic plasticity is an important step for understanding brain learning. Existing plasticity models are either 1) top-down and interpretable, but not flexible enough to account for experimental data, or 2) bottom-up and biologically realistic, but too intricate to interpret and hard to fit data. We fill the gap between these approaches by uncovering a new plasticity rule based on a geometrical readout mechanism that flexibly maps synaptic enzyme dynamics to plasticity outcomes. We apply this readout to a multi-timescale model of hippocampal synaptic plasticity induction that includes electrical dynamics, calcium, CaMKII and Calcineurin, and accurate representation of intrinsic noise sources. Using a single set of model parameters, we demonstrate the robustness of this plasticity rule by reproducing nine published ex vivo experiments covering various spike-timing and frequency-dependent plasticity induction protocols, animal ages, and experimental conditions. Our model should facilitate experimental design since each variable identify a biological counterpart bridging experiment and simulation.
• Halgurd Taher (Inria Sophia Antipolis-Méditerranée Research Centre, France)
  "Bursting in a next generation neural mass model with synaptic dynamics: a slow-fast approach"
We report a detailed analysis on the emergence of bursting in a recently developed neural mass model, that takes short-term synaptic plasticity into account. Neural mass models are capable of mimicking the collective dynamics of large scale neuronal populations in terms of a few macroscopic variables like mean membrane potential and firing rate. The one being used here particularly important, as it represents an exact meanfield limit of synaptically coupled quadratic integrate & fire neurons, a canonical model for type I excitability. In absence of synaptic dynamics, a periodic external current with a slow frequency ϵ can lead to burst-like dynamics. The firing patterns can be understood using techniques of singular perturbation theory, specifically slow-fast dissection. In the model with synaptic dynamics the separation of timescales leads to a variety of slow-fast phenomena and their role for bursting is rendered inordinately more intricate. Canards are one of the main slow-fast elements on the route to bursting. They describe trajectories evolving nearby otherwise repelling invariant sets of the system and are found in the transition region from subthreshold dynamics to bursting. For values of the timescale separation nearby the singular limit ϵ → 0, we report peculiar jump-on canards, which block a continuous transition to bursting. In the biologically more plausible regime this transition becomes continuous and bursts emerge via consecutive spike-adding. The onset of bursting is of complex nature and involves mixed-type like torus canards, that form the very first spikes of the burst and revolve nearby repelling limit cycles. We provide numerical evidence for the same mechanisms to be responsible for the emergence of bursting in the quadratic & fire network with plastic synapses. The main conclusions apply for the network, thanks to the exactness of the meanfield limit.