Misleading inferences from discretization of empty spacetime: Snyder-noncommutativity case study

Alternative approaches to the study of the quantum-gravity problem are handling the role of spacetime very differently. Some are focusing on the analysis of one or another novel formulation of "empty spacetime", postponing to later stages the introduction of particles and fields, while other approaches assume that spacetime should only be an emergent entity. We here argue that recent progress in the covariant formulation of quantum mechanics suggests that empty spacetime is not physically meaningful. We illustrate our general thesis in the specific context of the noncommutative Snyder spacetime, which is also of some intrinsic interest, since hundreds of studies were devoted to its analysis. We show that empty Snyder spacetime, described in terms of a suitable kinematical Hilbert space, is discrete, but this is only a formal artifact: the discreteness leaves no trace on the observable properties of particles on the physical Hilbert space.Comment: 6 page

Volume Entropy

Building on a technical result by Brunnemann and Rideout on the spectrum of the Volume operator in Loop Quantum Gravity, we show that the dimension of the space of the quadrivalent, diffeomorphism invariant states with no zero-volume nodes describing a region with total volume smaller than $V$, has \emph{finite} dimension, bounded by $V \log V$. This allows us to introduce the notion of "volume entropy" for this phase space: the von Neumann entropy associated to the measurement of volume.Comment: 5 pages, references added and some additional remark

A constraint on the dynamics of wealth concentration

In Ref. [1] the authors show that under minimal hypothesis, in a free, growing economy the wealth concentration as measured by the Gini coefficient $G_t$ is bounded to reach its maximum, $G_t \to 1$. Under their hypothesis the wealth growth is on average proportional to the wealth itself, thus leaving no room for a salary component independent of the individual's wealth. In addition the state of zero wealth is absorbing, meaning that once an individual loses all its wealth, it is forced to remain in that state. Here we further generalize the result of Ref. [1], introducing a salary component of wealth growth and thus allowing for the possibility to escape from the state of zero wealth. We arrive at the same conclusions of the previous study, unless a minimum salary component is introduced and kept proportional to the average wealth.Comment: New section adde

Covariant quantum mechanics applied to noncommutative geometry

We here report a result obtained in collaboration with Giovanni Amelino-Camelia, first shown in the paper [1]. Applying the manifestly covariant formalism of quantum mechanics to the much studied Snyder spacetime [2] we show how it is trivial in every physical observables, this meaning that every measure in this spacetime gives the same results that would be obtained in the flat Minkowski spacetime

Relative locality in a quantum spacetime and the pregeometry of κ\kappa-Minkowski

We develop a new description of the much-studied $\kappa$-Minkowski noncommutative spacetime, centered on representing on a single Hilbert space not only the $\kappa$-Minkowski coordinates, but also the associated differential calculus and the $\kappa$-Poincar\'e symmetry generators. In this "pregeometric" representation the relevant operators act on the kinematical Hilbert space of the covariant formulation of quantum mechanics, which we argue is the natural framework for studying the implications of the step from commuting spacetime coordinates to the $\kappa$-Minkowski case, where the spatial coordinates do not commute with the time coordinate. The empowerment provided by this kinematical-Hilbert space representation allows us to give a crisp characterization of the "fuzziness" of $\kappa$-Minkowski spacetime, whose most striking aspect is a relativity of spacetime locality. We show that relative locality, which had been previously formulated exclusively in classical-spacetime setups, for a quantum spacetime takes the shape of a dependence of the fuzziness of a spacetime point on the distance at which an observer infers properties of the event that marks the point.Comment: 10 pages. This is a more polished version of the manuscript. Technical results and Fig.1 unchanged. A Fig.2 has been added highlighting an analogy between relative simultaneity and relative localit

Textual analysis of a Twitter corpus during the COVID-19 pandemics

[EN] Text data gathered from social media are extremely up-to-date and have a great potential value for economic research. At the same time, they pose some challenges, as they require different statistical methods from the ones used for traditional data. The aim of this paper is to give a critical overview of three of the most common techniques used to extract information from text data: topic modelling, word embedding and sentiment analysis. We apply these methodologies to data collected from Twitter during the COVID-19 pandemic to investigate the influence the pandemic had on the Italian Twitter community and to discover the topics most actively discussed on the platform. Using these techniques of automated textual analysis, we are able to make inferences about the most important subjects covered over time and build real-time daily indicators of the sentiment expressed on this platform.Astuti, V.; Crispino, M.; Langiulli, M.; Marcucci, J. (2022). Textual analysis of a Twitter corpus during the COVID-19 pandemics. En 4th International Conference on Advanced Research Methods and Analytics (CARMA 2022). Editorial Universitat Politècnica de València. 276-276. http://hdl.handle.net/10251/18975927627

Efficient and accurate inference for mixtures of Mallows models with Spearman distance

The Mallows model occupies a central role in parametric modelling of ranking data to learn preferences of a population of judges. Despite the wide range of metrics for rankings that can be considered in the model specification, the choice is typically limited to the Kendall, Cayley or Hamming distances, due to the closed-form expression of the related model normalizing constant. This work instead focuses on the Mallows model with Spearman distance. An efficient and accurate EM algorithm for estimating finite mixtures of Mallows models with Spearman distance is developed, by relying on a twofold data augmentation strategy aimed at i) enlarging the applicability of Mallows models to samples drawn from heterogeneous populations; ii) dealing with partial rankings affected by diverse forms of censoring. Additionally, a novel approximation of the model normalizing constant is introduced to support the challenging model-based clustering of rankings with a large number of items. The inferential ability of the EM scheme and the effectiveness of the approximation are assessed by extensive simulation studies. Finally, we show that the application to three real-world datasets endorses our proposals also in the comparison with competing mixtures of ranking models.Comment: 20 pages, 6 Figures, 11 Table

Gravity's weight on worldline fuzziness

We investigate a connection between recent results in 3D quantum gravity, providing an effective noncommutative-spacetime description, and some earlier heuristic descriptions of a quantum-gravity contribution to the fuzziness of the worldlines of particles. We show that 3D-gravity-inspired spacetime noncommutativity reflects some of the features suggested by previous heuristic arguments. Most notably, gravity-induced worldline fuzziness, while irrelevantly small on terrestrial scales, could be observably large for propagation of particles over cosmological distances.Comment: 8 pages. This essay received an honorable mention in the 2012 Essay Competition of the Gravity Research Foundatio