27 research outputs found
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 , has \emph{finite}
dimension, bounded by . 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
Who is in equilibrium?
In order to describe the properties of the observed distribution of wealth in
a population, most economic models rely on the existence of an asymptotic
equilibrium state. In addition, the process generating the equilibrium
distribution is usually assumed to be ergodic, with a finite asymptotic average
and bounded inequality. Here we show, using data from Bank of Italy's Survey on
Household Income and Wealth and Forbes Italian billionaires lists, that the
last hypothesis is not justified in Italy. We find that, even if an equilibrium
asymptotic distribution exists, the average wealth has no finite asymptotic
value. As a consequence we find that - without changes in the parameters of the
wealth evolution process - wealth inequality is bound to diverge with time. In
addition we evaluate the equilibration time of the evolution process when its
parameters are chosen in order to admit both an equilibrium distribution and a
finite equilibrium average wealth. Even when both the equilibrium hypotheses
are satisfied, we find equilibration times much longer than the typical time
span between economic shocks
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
is bounded to reach its maximum, . 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 -Minkowski
We develop a new description of the much-studied -Minkowski
noncommutative spacetime, centered on representing on a single Hilbert space
not only the -Minkowski coordinates, but also the associated
differential calculus and the -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 -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 -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