IRIS Pol. TorinoIl sistema di repository digitale IRIS acquisisce, archivia, indicizza, conserva e rende accessibili prodotti digitali della ricerca.https://iris.polito.it2019-08-20T14:45:38Z2019-08-20T14:45:38Z10561Persistent homology analysis of phase transitionshttp://hdl.handle.net/11583/26427262018-09-03T08:59:52Z2016-01-01T00:00:00ZTitolo: Persistent homology analysis of phase transitions
Abstract: 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 by the ϕ4 lattice model, respectively. For both models the relationship between phase transitions and the topological properties of certain submanifolds of configuration space are exactly known. It turns out that these a priori known facts are clearly retrieved by persistent homology analysis of dynamically sampled submanifolds of configuration space.
2016-01-01T00:00:00ZModuli of linear representations, symmetric products and the non commutative Hilbert scheme
in
Geometric Methods in Representation Theory, II
Michel Brion Editor
Séminaires et Congrès 24-II (2012)http://hdl.handle.net/11583/23799022018-09-03T09:07:52Z2012-01-01T00:00:00ZTitolo: Moduli of linear representations, symmetric products and the non commutative Hilbert scheme
in
Geometric Methods in Representation Theory, II
Michel Brion Editor
Séminaires et Congrès 24-II (2012)
Abstract: Let k be a commutative ring and let R be a commutative k-algebra. Let A be a R-algebra. We discuss the connections between the coarse moduli space of the n-dimensional representations of A, the non-commutative Hilbert scheme on A and the affine scheme which represents multiplicative homogeneous polynomial laws of degree n on A. We build a norm map which specializes to the Hilbert-Chow morphism on the geometric points when A is commutative and k is an algebraically closed field. This generalizes the construction done by Grothendieck, Deligne and others. When k is an infinite field and A=k[x_1,,x_m ]is the free k-associative algebra on m letters, we give a simple description of this norm map
2012-01-01T00:00:00ZBlind separation of manufacturing variability with independent component analysis: a convolutive approachhttp://hdl.handle.net/11583/24131172018-09-03T09:10:53Z2011-01-01T00:00:00ZTitolo: Blind separation of manufacturing variability with independent component analysis: a convolutive approach
2011-01-01T00:00:00ZLinear representations, symmetric products and the commuting schemehttp://hdl.handle.net/11583/16461242018-09-03T07:53:50Z2007-01-01T00:00:00ZTitolo: Linear representations, symmetric products and the commuting scheme
2007-01-01T00:00:00ZShape partitioning based on symmetries detectionhttp://hdl.handle.net/11583/16466652018-09-03T07:53:46Z2007-01-01T00:00:00ZTitolo: Shape partitioning based on symmetries detection
2007-01-01T00:00:00ZThe ring of multisymmetric functionshttp://hdl.handle.net/11583/16461042018-09-03T07:53:52Z2005-01-01T00:00:00ZTitolo: The ring of multisymmetric functions
Abstract: We give a presentation (in terms of generators and relations) of the ring of multisymmetric functions that holds for any commutative ring R, thereby answering a classical question coming from works of F. Junker in the late nineteen century and then implicitly in H. Weyl book ``The classical groups."
2005-01-01T00:00:00ZSymmetric products as moduli spaces oflinear representationshttp://hdl.handle.net/11583/16472152018-09-03T07:54:25Z2007-01-01T00:00:00ZTitolo: Symmetric products as moduli spaces oflinear representations
2007-01-01T00:00:00ZData B Design to Evaluate a New Product Design and Development Processhttp://hdl.handle.net/11583/15544022018-09-03T07:52:11Z2005-01-01T00:00:00ZTitolo: Data B Design to Evaluate a New Product Design and Development Process
2005-01-01T00:00:00ZThe Hilbert–Chow morphism, symmetric product and the commuting varietyhttp://hdl.handle.net/11583/16461392018-09-03T08:32:42Z2006-01-01T00:00:00ZTitolo: The Hilbert–Chow morphism, symmetric product and the commuting variety
2006-01-01T00:00:00ZInsights into brain architectures from the homological scaffolds of functional connectivity networkshttp://hdl.handle.net/11583/26536362018-09-03T09:15:51Z2016-01-01T00:00:00ZTitolo: Insights into brain architectures from the homological scaffolds of functional connectivity networks
Abstract: In recent years, the application of network analysis to neuroimaging data has provided useful insights about the brain’s functional and structural organization in both health and disease. This has proven a significant paradigm shift from the study of individual brain regions in isolation. Graph-based models of the brain consist of vertices, which represent distinct brain areas, and edges which encode the presence (or absence) of a structural or functional relationship between each pair of vertices. By definition, any graph metric will be defined upon this dyadic representation of the brain activity. It is however unclear to what extent these dyadic relationships can capture the brain’s complex functional architecture and the encoding of information in distributed networks. Moreover, because network representations of global brain activity are derived from measures that have a continuous response (i.e. interregional BOLD signals), it is methodologically complex to characterize the architecture of functional networks using traditional graph-based approaches. In the present study, we investigate the relationship between standard network metrics computed from dyadic interactions in a functional network, and a metric defined on the persistence homological scaffold of the network, which is a summary of the persistent homology structure of resting-state fMRI data. The persistence homological scaffold is a summary network that differs in important ways from the standard network representations of functional neuroimaging data: i) it is constructed using the information from all edge weights comprised in the original network without applying an ad hoc threshold and ii) as a summary of persistent homology, it considers the contributions of simplicial structures to the network organization rather than dyadic edge-vertices interactions. We investigated the information domain captured by the persistence homological scaffold by computing the strength of each node in the scaffold and comparing it to local graph metrics traditionally employed in neuroimaging studies. We conclude that the persistence scaffold enables the identification of network elements that may support the functional integration of information across distributed brain networks.
2016-01-01T00:00:00Z