A Java High Performance Tool For Topological Data Analysis
On the edge between top-down and bottom-up approaches there is the new emergent S[B] paradigm for modeling self-adaptive systems . In the S[B] paradigm a model has two levels of description, namely the S global or structural level and the B local or behavioral level, which are entangled in order to express the behavior of the system as a whole. The S level describes how the system evolves following global information coming from the environment in which it is operating and from the interactions and the evolutions of the entities of the B level. In the S[B] fashion, the B-level adapts itself according to the higher level rules. The S-level constraints the B-level. On the behavioral level, adaptation is expressed by firing a higher-order transition, meaning that the S-level switches to a different set of constraints and the B-level has adapted it behavior by reaching a state that meets the new constraints. This adaptation is not necessarily instantaneous. Moreover, the S-level can exhibit adaptation by switching from a model to another or by redefining the set of invariants.
The S[B] methodology has been successfully applied for modeling the Idiotypic Network (IN), a network based model of the human immune system. The application of the methodology revealed when the IN reacts to external stimuli. Moreover the methodology identified the main classes of antibodies, i.e. the antibodies that are necessary for reaching the immune memory, and how do they are functional connected. The methodology is also used for identifying classes of equivalent behaviors among different simulations of IN.
For more details please refer to:
 MERELLI, EMANUELA AND RUCCO, MATTEO AND SLOOT, PETER AND TESEI, LUCA. Topological Characterization of Complex Systems: Using Persistent Entropy. Entropy, 17(10):6872–6892, 2015.
 EMANUELA MERELLI, MARCO PETTINI, AND MARIO RASETTI. Topology driven modeling: the IS metaphor. Natural Computing, pages 1–10, 2014.
 EMANUELA MERELLI AND MARIO RASETTI. Non locality, Topology, Formal Languages: New Global Tools to Handle Large Data Sets. Procedia Computer Science, 18:90–99, 2013.
Even if the S[B] paradigm has been introduced for dealing with complex self adaptive software system, we guess that it can be easily used for modeling not only software complex systems. Indeed, we derived a new methodology based on S[B] and Persistent entropy. With respect to the literature, the newly S[B] methodology is on the edge between the two classical approaches and it aims to extract both qualitative and quantitative information at the meso-scale: between the micro-scale and the macro-scale. The methodology is based on topological data analysis (TDA), advanced data analysis (machine learning, statistics) and the S[B] paradigm. The rationale behind this methodology is that the S[B] paradigm is able to formalize the adaptabilities of a complex self-adaptive system, topological data analysis is the right machinery for deciphering the relationships among the entities that form a complex system and persistent entropy theory can be used for linking the dynamics of a whole system together the patterns discovered by TDA. The adaptability can be observed both at the structural level and at the behavioral level. In the former case, the system switches from a model to another. The states of a system are characterized by sets of invariants that are imposed by the structural level. In the behavioral adaptability, the system moves from a state to another by performing intermediate actions that allow to satisfy the invariants of the new state. The S level dynamics is represented by the newly defined Persistent Entropy Automaton (PEA). The picture below represents the methodology.