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pro vyhledávání: '"Harrington, Heather A."'
Persistent homology (PH) studies the topology of data across multiple scales by building nested collections of topological spaces called filtrations, computing homology and returning an algebraic object that can be vizualised as a barcode--a multiset
Externí odkaz:
http://arxiv.org/abs/2411.08201
Directed graphs can be studied by their associated directed flag complex. The homology of this complex has been successful in applications as a topological invariant for digraphs. Through comparison with path homology theory, we derive a homotopy-lik
Externí odkaz:
http://arxiv.org/abs/2411.04572
This paper illustrates a further application of topological data analysis to the study of self-organising models for chemical and biological systems. In particular, we investigate whether topological summaries can capture the parameter dependence of
Externí odkaz:
http://arxiv.org/abs/2409.20491
We investigate the geometry of a family of log-linear statistical models called quasi-independence models. The toric fiber product is useful for understanding the geometry of parameter inference in these models because the maximum likelihood degree i
Externí odkaz:
http://arxiv.org/abs/2405.13897
The challenge of selecting the most relevant features of a given dataset arises ubiquitously in data analysis and dimensionality reduction. However, features found to be of high importance for the entire dataset may not be relevant to subsets of inte
Externí odkaz:
http://arxiv.org/abs/2404.06993
Autor:
Byrne, Helen, Harrington, Heather, Ovchinnikov, Alexey, Pogudin, Gleb, Rahkooy, Hamid, Soto, Pedro
Differential equation models are crucial to scientific processes. The values of model parameters are important for analyzing the behaviour of solutions. A parameter is called globally identifiable if its value can be uniquely determined from the inpu
Externí odkaz:
http://arxiv.org/abs/2402.04241
Autor:
Puente, Luis David García, Gross, Elizabeth, Harrington, Heather A, Johnston, Matthew, Meshkat, Nicolette, Millán, Mercedes Pérez, Shiu, Anne
Motivated by the question of how biological systems maintain homeostasis in changing environments, Shinar and Feinberg introduced in 2010 the concept of absolute concentration robustness (ACR). A biochemical system exhibits ACR in some species if the
Externí odkaz:
http://arxiv.org/abs/2401.00078
We investigate algebraic and topological signatures of networks of coupled oscillators. Translating dynamics into a system of algebraic equations enables us to identify classes of network topologies that exhibit unexpected behaviors. Many previous st
Externí odkaz:
http://arxiv.org/abs/2312.16069
Plants are a paradigm for active shape control in response to stimuli. For instance, it is well-known that a tilted plant will eventually straighten vertically, demonstrating the influence of both an external stimulus, gravity, and an internal stimul
Externí odkaz:
http://arxiv.org/abs/2309.08950
Autor:
Reise, Wojciech, Fernández, Ximena, Dominguez, Maria, Harrington, Heather A., Beguerisse-Díaz, Mariano
We present a topological audio fingerprinting approach for robustly identifying duplicate audio tracks. Our method applies persistent homology on local spectral decompositions of audio signals, using filtered cubical complexes computed from mel-spect
Externí odkaz:
http://arxiv.org/abs/2309.03516