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- Giovanni Petri, Paul Expert, +4 authors Francesco Vaccarino
- Journal of the Royal Society, Interface
- 2014

Networks, as efficient representations of complex systems, have appealed to scientists for a long time and now permeate many areas of science, including neuroimaging (Bullmore and Sporns 2009 Nat.â€¦ (More)

- Giovanni Petri, Martina Scolamiero, Irene Donato, Francesco Vaccarino
- PloS one
- 2013

The statistical mechanical approach to complex networks is the dominant paradigm in describing natural and societal complex systems. The study of network properties, and their implications onâ€¦ (More)

- Jacopo Binchi, Emanuela Merelli, Matteo Rucco, Giovanni Petri, Francesco Vaccarino
- Electr. Notes Theor. Comput. Sci.
- 2014

Complex networks equipped with topological data analysis are one of the promising tools in the study of biological systems (e.g. evolution dynamics, brain correlation, breast cancer diagnosis, etc. .â€¦ (More)

Abstract. Let R be a commutative ring and let n, m be two positive integers. Let AR(n, m) be the polynomial ring in the commuting independent variables xi(j) with i = 1, . . . , m ; j = 1, . . . , nâ€¦ (More)

It is well known that over an infinite field the ring of symmetric functions in a finite number of variables is isomorphic to the one of polynomial functions on a single matrix that are invariants byâ€¦ (More)

- Alice Patania, Francesco Vaccarino, Giovanni Petri
- EPJ Data Science
- 2017

Propelled by a fast evolving landscape of techniques and datasets, data science is growing rapidly. Against this background, topological data analysis (TDA) has carved itself a niche for the analysisâ€¦ (More)

We show that the ring of multisymmetric functions over a commutative ring is isomorphic to the ring generated by the coefficients of the characteristic polynomial of polynomials in commuting genericâ€¦ (More)

- Irene Donato, Matteo Gori, +4 authors Francesco Vaccarino
- Physical review. E
- 2016

Persistent homology analysis, a recently developed computational method in algebraic topology, is applied to the study of the phase transitions undergone by the so-called mean-field XY model and byâ€¦ (More)

- Jean-Gabriel Young, Giovanni Petri, Francesco Vaccarino, Alice Patania
- Physical review. E
- 2017

Simplicial complexes are now a popular alternative to networks when it comes to describing the structure of complex systems, primarily because they encode multinode interactions explicitly. With thisâ€¦ (More)

Let R be a commutative ring and let n, m be two positive integers. Let AR(n, m) := R[x11, . . . , x1m, . . . , xn1, . . . , xnm] be the polynomial ring in the commuting independent variables x11, . .â€¦ (More)