🍩 Database of Original & Non-Theoretical Uses of Topology

(found 5 matches in 0.001351s)

  2. Homological Scaffold via Minimal Homology Bases (2021)

    Marco Guerra, Alessandro De Gregorio, Ulderico Fugacci, Giovanni Petri, Francesco Vaccarino
    Abstract The homological scaffold leverages persistent homology to construct a topologically sound summary of a weighted network. However, its crucial dependency on the choice of representative cycles hinders the ability to trace back global features onto individual network components, unless one provides a principled way to make such a choice. In this paper, we apply recent advances in the computation of minimal homology bases to introduce a quasi-canonical version of the scaffold, called minimal, and employ it to analyze data both real and in silico. At the same time, we verify that, statistically, the standard scaffold is a good proxy of the minimal one for sufficiently complex networks.

  3. Topological Gene Expression Networks Recapitulate Brain Anatomy and Function (2019)

    Alice Patania, Pierluigi Selvaggi, Mattia Veronese, Ottavia Dipasquale, Paul Expert, Giovanni Petri
    Abstract Understanding how gene expression translates to and affects human behavior is one of the ultimate goals of neuroscience. In this paper, we present a pipeline based on Mapper, a topological simplification tool, to analyze gene co-expression data. We first validate the method by reproducing key results from the literature on the Allen Human Brain Atlas and the correlations between resting-state fMRI and gene co-expression maps. We then analyze a dopamine-related gene set and find that co-expression networks produced by Mapper return a structure that matches the well-known anatomy of the dopaminergic pathway. Our results suggest that network based descriptions can be a powerful tool to explore the relationships between genetic pathways and their association with brain function and its perturbation due to illness and/or pharmacological challenges., In this paper, we described a gene co-expression analysis pipeline that produces networks that we show to be closely related to either brain function and to neurotransmitter pathways. Our results suggest that this pipeline could be developed into a platform enabling the exploration of the effects of physiological and pathological alterations to specific gene sets, including profiling drugs effects.

  4. Unveiling Patterns of International Communities in a Global City Using Mobile Phone Data (2015)

    Paolo Bajardi, Matteo Delfino, André Panisson, Giovanni Petri, Michele Tizzoni
    Abstract We analyse a large mobile phone activity dataset provided by Telecom Italia for the Telecom Big Data Challenge contest. The dataset reports the international country codes of every call/SMS made and received by mobile phone users in Milan, Italy, between November and December 2013, with a spatial resolution of about 200 meters. We first show that the observed spatial distribution of international codes well matches the distribution of international communities reported by official statistics, confirming the value of mobile phone data for demographic research. Next, we define an entropy function to measure the heterogeneity of the international phone activity in space and time. By comparing the entropy function to empirical data, we show that it can be used to identify the city’s hotspots, defined by the presence of points of interests. Eventually, we use the entropy function to characterize the spatial distribution of international communities in the city. Adopting a topological data analysis approach, we find that international mobile phone users exhibit some robust clustering patterns that correlate with basic socio-economic variables. Our results suggest that mobile phone records can be used in conjunction with topological data analysis tools to study the geography of migrant communities in a global city.

  5. Topology Highlights Mesoscopic Functional Equivalence Between Imagery and Perception: The Case of Hypnotizability (2019)

    Esther Ibáñez-Marcelo, Lisa Campioni, Angkoon Phinyomark, Giovanni Petri, Enrica L. Santarcangelo
    Abstract The functional equivalence (FE) between imagery and perception or motion has been proposed on the basis of neuroimaging evidence of large spatially overlapping activations between real and imagined sensori-motor conditions. However, similar local activation patterns do not imply the same mesoscopic integration of brain regions, which can be described by tools from Topological Data Analysis (TDA). On the basis of behavioral findings, stronger FE has been hypothesized in the individuals with high scores of hypnotizability scores (highs) with respect to low hypnotizable participants (lows) who differ between each other in the proneness to modify memory, perception and behavior according to specific imaginative suggestions. Here we present the first EEG evidence of stronger FE in highs. In fact, persistent homology shows that the highs EEG topological asset during real and imagined sensory conditions is significantly more similar than the lows. As a corollary finding, persistent homology shows lower restructuring of the EEG asset in highs than in lows during both sensory and imagery tasks with respect to basal conditions. Present findings support the view that greater embodiment of mental images may be responsible for the highs greater proneness to respond to sensori-motor suggestions and to report involuntariness in action. In addition, findings indicate hypnotizability-related sensory and cognitive information processing and suggest that the psycho-physiological trait of hypnotizability may modulate more than one aspect of the everyday life.