Even after decades of quantum computing development, examples generally useful algorithms with exponential speedups over classical counterparts are scarce. Recent progress in for linear-algebra positioned machine learning (QML) as a potential source such improvements. Yet, an unexpected recent series "dequantization" results has equally rapidly removed the promise several QML algorithms. This r...

My most significant recent work is in the field of applied topology. While the early development of topology was firmly rooted in applications, many of its later advances have been driven by purely mathematical motivations. More recently there is a growing awareness that some of its powerful tools may be just what is needed to help address outstanding problems in diverse modern applications. I ...

In this paper we propose a methodology for deriving a model of a complex system by exploiting the information extracted from Topological Data Analysis. Central to our approach is the S[B] paradigm in which a complex system is represented by a two-level model. One level, the structural S one, is derived using the newly introduced quantitative concept of Persistent Entropy. The other level, the b...

My research concerns the theoretical foundations of topological data analysis (TDA). Work done in the last several years on theory and applications of TDA has demonstrated that TDA offers a principled, flexible, and computationally viable framework for studying coarse-scale global geometric features of data [17, 26, 13, 7, 11, 10, 8, 24]. Moreover, the tools of TDA have proven to be very well s...

Pathogenic bacteria present a large disease burden on human health. Control of these pathogens is hampered by rampant lateral gene transfer, whereby pathogenic strains may acquire genes conferring resistance to common antibiotics. Here we introduce tools from topological data analysis to characterize the frequency and scale of lateral gene transfer in bacteria, focusing on a set of pathogens of...