Dan P. Guralnik

Postdoctoral fellow ( my CV )

Contact: guraldan at seas.upenn.edu

I owe my training (B.A., M.Sc. and Ph.D. in Mathematics) to my great professors and TAs at the Math department of the Technion — IIT in Haifa, Israel. Following postdocs at Vanderbilt and at the University of Oklahoma, I decided to attempt a transition into the applied domain, following a long-time interest in the mathematical foundations of cognition. Specifically, I was interested in the role Topology might play in exposing and explaining high-level, symbolic reasoning as an emergent phenomenon, “bootstrapped”, so to speak, from the lowest level control structures which the scientific consensus still directly relates to cognition: the interactions among neurons and the interactions between neurons and their environments.

Joining Kod*Lab in the fall of 2011 as part of the CHASE MURI framework introduced me to a menagerie of problems in data analysis and representation with fundamental connections to information theory and complexity theory on the one hand and topology and geometry in curvature bounded from above on the other, with potential applications ranging from controlling swarms,  through new methods for unsupervised clustering/classification, to life-long learning.

Below is a selection of projects, current and past, all joined by the common thread of geometry being used to encode formal information structures.

Current Projects

Universal Memory-and-Control Architectures

With Daniel E. Koditschek, Siqi Huang (Penn CIS-CGGT masters program graduate) and Darius Rodgers (Penn ESE Junior)

Funded in part by AFOSR CHASE MURI, by NSF-CABiR, and by AFRL SIRCUS.

Mathematical Foundations of Distance-based Clustering

With Jared Culbertson (AFRL) and Peter Stiller (Texas A&M)

Funded by AFOSR

Information Theory and Estimation of Distance-Based Hierarchies

Estimation of Distance-Based Hierarchies in the Presence of Noise.

with Dekang Zhu (NUDT), Xuezhi Wang (RMIT), Xiang Li (NUDT) and Bill Moran (University of Melbourne)  

Entropy-Based Control of Hierarchical Classification Schemes.

with Bill Moran (University of Melbourne), Ali Pezeshki and Lorenzo DeCarli (Colorado State University)

Earlier Projects

Navigation in Tree Space

with Omur Arslan (lead; now at Max Planck, Tübingen) and Daniel E. Koditschek

The NNI graph for the space of binary trees on 4 leaves (right). The edges of the graph are Nearest-Neighbor Interchanges, or NNI moves (left).

Hierarchical Navigation in Euclidean Space

with Omur Arslan (lead; now at Max Planck, Tübingen), Yuliy Baryshnikov (UIUC) and Daniel E. Koditschek

Rank-Rigidity of CAT(0) Groups

with Eric L. Swenson (Brigham Young University)