Topological & Algebraic Models of Social Interaction

Recent years have witnessed an explosion of research in the theory of evolutionary networks, with important implications in the analysis of dynamic social systems. We aim at stepping up this new science by considering mathematical models that are at once more general and more comprehensive than ordinary networks and graphs.

This research effort is the result of joint work of HoloMathics with two collaborators from Chapman University, Prof. D. C. Struppa and Prof. Lisa
Sparks, an internationally established mathematician and a leading expert in social communication, respectively.

An introductory article presenting the basic tenets of this approach can be found here.

Multimetric Clustering

Clustering is a familiar and extremely useful technique in Data Mining. This effort explores new clustering methodologies based on the notion of multimetric spaces.

Through our approach data sets can be seen from several different conceptual angles at once, affording analysts new and sometimes unexpected insights.

Hypergraph Ontology

Ontologies are generally modeled by Directed Acyclic Graphs, such as trees. We have extended this representation to include higher dimensional semantic relations between linguistic modules. The new set-up provides the conceptual tool for indexing unstructured text in a new fashion, a sort of semantic landscape that can be navigated, visualized and explored. Paths through this landscape could reveal new information, deeply concealed within and spread throughout the document set!

Hypergraph Ontology is a new milestone toward the creation of Semantic Browsers and other tools for the next generation of the World Wide Web. A survey paper on Hypergraph Ontology will soon be available on this page.

Large Networks Reconstruction

How can you grasp a huge network, such as the World Wide Web, if you only know some relatively small fragments thereof ? HoloMathics LLC, using state-of-the-art mathematical modeling tools, is creating new techniques to provide viable answers to this fundamental question.