Dr. Carlo Cafaro, SUNY Poly applied mathematics assistant professor, collaborated with Dr. Domenico Felice (SUNY Poly Visiting Scientist and former Postdoctoral Researcher at the Max Planck Institute for Mathematics in the Sciences in Leipzig-Germany) on a work published in Mathematics.  

Mathematics is a peer-reviewed, open access journal which provides an advanced forum for studies related to mathematics and is published semimonthly online by MDPI (Multidisciplinary Digital Publishing Institute).

The research paper, “Explicit Information Geometric Calculations of the Canonical Divergence of a Curve”, is a formal proof-oriented mathematical work with a clear pedagogical flavor for the information geometry community.

Information geometry concerns the study of a dual structure (g, ∇, ∇∗) upon a smooth manifold M. Such a geometry is totally encoded within a potential function usually referred to as a divergence or contrast function of (g, ∇, ∇∗). Even though infinitely many divergences induce on M the same dual structure, when the manifold is dually flat, a canonical divergence is well defined and was originally introduced by Shun-Ichi Amari and Hiroshi Nagaoka. In this paper, Felice and Cafaro presented explicit non-trivial differential geometry-based proofs concerning the canonical divergence for a special type of dually flat manifold represented by an arbitrary 1-dimensional path γ. Highlighting the geometric structure of such a particular canonical divergence, their study could suggest a way to select a general canonical divergence by using the information from a general dual structure in a minimal way.

The paper belongs to the Special Issue entitled “New Advances in Differential Geometry and Optimizations on Manifolds,” guest-edited by Dr. Constantin Udriste and Dr. Vladimir Rovenski. The Special Issue belongs to the section “Computational and Applied Mathematics” of Mathematics. 

The team’s published research can be read here: https://www.mdpi.com/2227-7390/10/9/1452/htm