Finite State Graphon Games with Applications to Epidemics

We consider a game for a continuum of non-identical players evolving on a finite state space. Their heterogeneous interactions are represented with a graphon, which can be viewed as the limit of a dense random graph. A player’s transition rates between the states depend on their control and the strength of interaction with the other players. We develop a rigorous mathematical framework for the game and analyze Nash equilibria. We provide a sufficient condition for a Nash equilibrium and prove existence of solutions to a continuum of fully coupled forward-backward ordinary differential equations characterizing Nash equilibria. Moreover, we propose a numerical approach based on machine learning methods and we present experimental results on different applications to compartmental models in epidemiology.

Incorporating heterogeneous information in deep learning with informative meta-paths for community recommendations

Communities of interest promote knowledge sharing and discovery in social network platforms. However, platform users face difficulties of finding suitable communities, given their increasing number. Although recommendations have been proposed to help users find communities of interest, these methods ignore or exclude heterogeneous interactions between users and communities. In addition, widely used meta-paths help capture the complex semantic relation among entities but heavily rely on domain knowledge. In this study, we propose a novel recommendation model based on informative meta-path discovery in heterogeneous information networks and deep learning. Users, communities, relevant items and their relations are considered as entities in a heterogeneous information network, from where informative meta-paths are extracted on the basis of information theory to measure user-community similarities. Finally, similarities are incorporated in a deep learning model to predict whether target users join candidate communities. The proposed recommendation model is evaluated and compared against baseline methods using two data sets. Results demonstrate the superior performance of the present model in terms of precision, recall and F score.

A specific set of heterogeneous native interactions yields efficient knotting in protein folding

Native interactions are crucial for folding, and non-native interactions appear to be critical for efficiently knotting proteins. Therefore, it is important to understand both their roles in the folding of knotted proteins. It has been proposed that non-native interactions drive the correct order of contact formation, which is essential to avoid backtracking and efficiently self-tie. In this study we ask if non-native interactions are strictly necessary to tangle a protein, or if the correct order of contact formation can be assured by a specific set of native, but otherwise heterogeneous, interactions. In order to address this problem we conducted extensive Monte Carlo simulations of lattice models of proteinlike sequences designed to fold into a pre-selected knotted conformation embedding a trefoil knot. We were able to identify a specific set of heterogeneous native interactions that drives efficient knotting, and is able to fold the protein when combined with the remaining native interactions modeled as homogeneous. This specific set of heterogeneous native interactions is strictly enough to efficiently self-tie. A distinctive feature of these native interactions is that they do not backtrack, because their energies ensure the correct order of contact formation. Furthermore, they stabilize a knotted intermediate state, which is en-route to the native structure. Our results thus show that - at least in the context of the adopted model - non-native interactions are not necessary to knot a protein. However, when they are taken into account into protein energetics it is possible to find specific, non-local non-native interactions that operate as a scaffold that assists the knotting step.

The BioDynaMo Project

Computer simulations have become a very powerful tool for scientific research. Given the vast complexity that comes with many open scientific questions, a purely analytical or experimental approach is often not viable. For example, biological systems comprise an extremely complex organization and heterogeneous interactions across different spatial and temporal scales. In order to facilitate research on such problems, the BioDynaMo project aims at a general platform for computer simulations for biological research. Since scientific investigations require extensive computer resources, this platform should be executable on hybrid cloud computing systems, allowing for the efficient use of state-of-the-art computing technology. This chapter describes challenges during the early stages of the software development process. In particular, we describe issues regarding the implementation and the highly interdisciplinary as well as international nature of the collaboration. Moreover, we explain the methodologies, the approach, and the lessons learned by the team during these first stages.