A Spectral Triple for a Solenoid Based on the Sierpinski Gasket

The Sierpinski gasket admits a locally isometric ramified self-covering. A semifinite spectral triple is constructed on the resulting solenoidal space, and its main geometrical features are discussed

Spectral triples for noncommutative solenoidal spaces from self-coverings

Examples of noncommutative self-coverings are described, and spectral triples on the base space are extended to spectral triples on the inductive family of coverings, in such a way that the covering projections are locally isometric. Such triples are shown to converge, in a suitable sense, to a semifinite spectral triple on the direct limit of the tower of coverings, which we call noncommutative solenoidal space. Some of the self-coverings described here are given by the inclusion of the fixed point algebra in a C$^*$-algebra acted upon by a finite abelian group. In all the examples treated here, the noncommutative solenoidal spaces have the same metric dimension and volume as on the base space, but are not quantum compact metric spaces, namely the pseudo-metric induced by the spectral triple does not produce the weak$^*$ topology on the state space.Comment: v3: the paper will appear in the Journal of Mathematical Analysis and Applications, 42 pages, no figure

The Emotional and Chromatic Layers of Urban Smells

People are able to detect up to 1 trillion odors. Yet, city planning is concerned only with a few bad odors, mainly because odors are currently captured only through complaints made by urban dwellers. To capture both good and bad odors, we resort to a methodology that has been recently proposed and relies on tagging information of geo-referenced pictures. In doing so for the cities of London and Barcelona, this work makes three new contributions. We study 1) how the urban smellscape changes in time and space; 2) which emotions people share at places with specific smells; and 3) what is the color of a smell, if it exists. Without social media data, insights about those three aspects have been difficult to produce in the past, further delaying the creation of urban restorative experiences.Comment: 11 pages, 18 figures, final version published in the Proceedings of the Tenth International Conference on Web and Social Media (ICWSM 2016

The Shortest Path to Happiness: Recommending Beautiful, Quiet, and Happy Routes in the City

When providing directions to a place, web and mobile mapping services are all able to suggest the shortest route. The goal of this work is to automatically suggest routes that are not only short but also emotionally pleasant. To quantify the extent to which urban locations are pleasant, we use data from a crowd-sourcing platform that shows two street scenes in London (out of hundreds), and a user votes on which one looks more beautiful, quiet, and happy. We consider votes from more than 3.3K individuals and translate them into quantitative measures of location perceptions. We arrange those locations into a graph upon which we learn pleasant routes. Based on a quantitative validation, we find that, compared to the shortest routes, the recommended ones add just a few extra walking minutes and are indeed perceived to be more beautiful, quiet, and happy. To test the generality of our approach, we consider Flickr metadata of more than 3.7M pictures in London and 1.3M in Boston, compute proxies for the crowdsourced beauty dimension (the one for which we have collected the most votes), and evaluate those proxies with 30 participants in London and 54 in Boston. These participants have not only rated our recommendations but have also carefully motivated their choices, providing insights for future work.Comment: 11 pages, 7 figures, Proceedings of ACM Hypertext 201

Smelly Maps: The Digital Life of Urban Smellscapes

Smell has a huge influence over how we perceive places. Despite its importance, smell has been crucially overlooked by urban planners and scientists alike, not least because it is difficult to record and analyze at scale. One of the authors of this paper has ventured out in the urban world and conducted smellwalks in a variety of cities: participants were exposed to a range of different smellscapes and asked to record their experiences. As a result, smell-related words have been collected and classified, creating the first dictionary for urban smell. Here we explore the possibility of using social media data to reliably map the smells of entire cities. To this end, for both Barcelona and London, we collect geo-referenced picture tags from Flickr and Instagram, and geo-referenced tweets from Twitter. We match those tags and tweets with the words in the smell dictionary. We find that smell-related words are best classified in ten categories. We also find that specific categories (e.g., industry, transport, cleaning) correlate with governmental air quality indicators, adding validity to our study.Comment: 11 pages, 7 figures, Proceedings of 9th International AAAI Conference on Web and Social Media (ICWSM2015

A spectral triple for a solenoid based on the Sierpinski Gasket

The Sierpinski gasket admits a locally isometric ramified self-covering. A semifinite spectral triple is constructed on the resulting solenoidal space, and its main geometrical features are discussed

Spectral triples on irreversible C∗C^*-dynamical systems

Given a spectral triple on a $C^*$-algebra $\mathcal A$ together with a unital injective endomorphism $\alpha$, the problem of defining a suitable crossed product $C^*$-algebra endowed with a spectral triple is addressed. The proposed construction is mainly based on the works of Cuntz and of Hawkins, Skalski, White and Zacharias, and on our previous papers. The embedding of $\alpha(\mathcal A)$ in $\mathcal A$ can be considered as the dual form of a covering projection between noncommutative spaces. A main assumption is the expansiveness of the endomorphism, which takes the form of the local isometricity of the covering projection and is expressed via the compatibility of the Lip-norms on $\mathcal A$ and $\alpha(\mathcal A)$.Comment: 25 pages, to appear in the International Journal of Mathematic

Multidimensional Tie Strength and Economic Development

The strength of social relations has been shown to affect an individual’s access to opportunities. To date, however, the correspondence between tie strength and population’s economic prospects has not been quantified, largely because of the inability to operationalise strength based on Granovetter’s classic theory. Our work departed from the premise that tie strength is a unidimensional construct (typically operationalized with frequency or volume of contact), and used instead a validated model of ten fundamental dimensions of social relationships grounded in the literature of social psychology. We built state-of-the-art NLP tools to infer the presence of these dimensions from textual communication, and analyzed a large conversation network of 630K geo-referenced Reddit users across the entire US connected by 12.8M social ties created over the span of 7 years. We found that unidimensional tie strength is only weakly correlated with economic opportunities ([Formula: see text] ), while multidimensional constructs are highly correlated ([Formula: see text] ). In particular, economic opportunities are associated to the combination of: (i) knowledge ties, which bridge geographically distant groups, facilitating the knowledge dissemination across communities; and (ii) social support ties, which knit geographically close communities together, and represent dependable sources of social and emotional support. These results point to the importance of developing high-quality measures of tie strength in network theory