Finding hypernetworks in directed hypergraphs

The term ‘‘hypernetwork’’ (more precisely, s-hypernetwork and (s, d)-hypernetwork) has been recently adopted to denote some logical structures contained in a directed hypergraph. A hypernetwork identifies the core of a hypergraph model, obtained by filtering off redundant components. Therefore, finding hypernetworks has a notable relevance both from a theoretical and from a computational point of view. In this paper we provide a simple and fast algorithm for finding s-hypernetworks, which substantially improves on a method previously proposed in the literature. We also point out two linearly solvable particular cases. Finding an (s, d)-hypernetwork is known to be a hard problem, and only one polynomially solvable class has been found so far. Here we point out that this particular case is solvable in linear time

Hypergraphs Demonstrate Anastomoses During Divergent Integration

Complex networks can be used to analyze structures and systems in the embryo. Not only can we characterize growth and the emergence of form, but also differentiation. The process of differentiation from precursor cell populations to distinct functional tissues is of particular interest. These phenomena can be captured using a hypergraph consisting of nodes represented by cell type categories and arranged as a directed cyclic graph (lineage hypergraph) and a complex network (spatial hypergraph). The lineage hypergraph models the developmental process as an n-ary tree, which can model two or more descendent categories per division event. A lineage tree based on the mosaic development of the nematode C. elegans (2-ary tree), is used to capture this process. Each round of divisions produces a new set of categories that allow for exchange of cells between types. An example from single-cell morphogenesis based on the cyanobacterial species Nostoc punctiforme (multiple discontinuous 2-ary tree) is also used to demonstrate the flexibility of this method. This model allows for new structures to emerge (such as a connectome) while also demonstrating how precursor categories are maintained for purposes such as dedifferentiation or other forms of cell fate plasticity. To understand this process of divergent integration, we analyze the directed hypergraph and categorical models, in addition to considering the role of network fistulas (spaces that conjoin two functional modules) and spatial restriction.Comment: 21 pages, 8 figure

Hypernetworks Analysis of RoboCup Interactions

Robotic soccer simulations are controlled environments in which the rich variety of interactions among agents make them good candidates to be studied as complex adaptive systems. The challenge is to create an autonomous team of soccer agents that can adapt and improve its behaviour as it plays other teams. By analogy with chess, the movements of the soccer agents and the ball form ever-changing networks as players in one team form structures that give their team an advantage. For example, the Defender’s Dilemma involves relationships between an attacker with the ball, a team-mate and a defender. The defender must choose between tackling the player with the ball, or taking a position to intercept a pass to the other attacker. Since these structures involve more that two interacting entities it is necessary to go beyond networks to multidimensional hypernetworks. In this context, this thesis investigates (i) is it possible to identify patterns of play, that lead a team to obtain an advantage ?, (ii) is it possible to forecast with a good degree of accuracy if a certain game action or sequence of game actions is going to be successful, before it has been completed ?, and (iii) is it possible to make behavioural patterns emerge in the game without specifying the behavioural rules in detail ? To investigate these research questions we devised two methods to analyse the interactions between robotic players, one based on traditional programming and one based on Deep Learning. The first method identified thousands of Defender’s Dilemma configurations from RoboCup 2D simulator games and found a statistically significant association between winning and the creation of the defender’s dilemma by the attackers of the winning team. The second method showed that a feedforward Artificial Neural Network trained on thousands of games can take as input the current game configuration and forecast to a high degree of accuracy if the current action will end up in a goal or not. Finally, we designed our own fast and simple robotic soccer simulator for investigating Reinforcement Learning. This showed that Reinforcement Learning using Proximal Policy Optimization could train two agents in the task of scoring a goal, using only basic actions without using pre-built hand-programmed skills. These experiments provide evidence that it is possible: to identify advantageous patterns of play; to forecast if an action or sequence of actions will be successful; and to make behavioural patterns emerge in the game without specifying the behavioural rules in detail