Related papers: The gradient flow of the polarization measure. Wit…
We establish two versions of Vizing's theorem for Borel multi-graphs whose vertex degrees and edge multiplicities are uniformly bounded by respectively $\Delta$ and $\pi$. The ``approximate'' version states that, for any Borel probability…
Studying and understanding social networks is crucial for accurately defining ideological polarization, since they enable precise modeling of social structures. One of the limitations of many methods for quantifying polarization on networks…
Uncertainty propagation and filtering can be interpreted as gradient flows with respect to suitable metrics in the infinite dimensional manifold of probability density functions. Such a viewpoint has been put forth in recent literature, and…
A polarity of a projective plane is a map, often assumed to be involutive, mapping a generic point to a generic line and reciprocally. The most classical polarity is the polarity with respect to a conic, but other exist: the harmonic…
We re-consider the polarization of the star light that may arise during microlensing events due to the high gradient of magnification across the atmosphere of the source star, by exploring the full range of microlensing and stellar physical…
Political polarization is perceived as a threat to democracies. Using the Galam model of opinion dynamics deployed in a five-dimensional parameter space, I show that polarization is the byproduct of an essential hallmark of a vibrant…
A commonly used characteristic of statistical dependence of adjacency relations in real networks, the clustering coefficient, evaluates chances that two neighbours of a given vertex are adjacent. An extension is obtained by considering…
We discuss different proposals for the degree of polarization of quantum fields. The simplest approach, namely making a direct analogy with the classical description via the Stokes operators, is known to produce unsatisfactory results.…
Political polarization, a key driver of social fragmentation, has drawn increasing attention for its role in shaping online and offline discourse. Despite significant efforts, accurately measuring polarization within ideological…
We give an explicit sequence of polarizations such that for every measurable function, the sequence of iterated polarizations converge to the symmetric rearrangement of the initial function.
Polarization is a troubling phenomenon that can lead to societal divisions and hurt the democratic process. It is therefore important to develop methods to reduce it. We propose an algorithmic solution to the problem of reducing…
We have derived the relationship between polarization and intensity fluctuations due to point sources. In the case of a Poisson distribution of a population with uniform evolution properties and constant polarization degree, polarization…
The estimation of class prevalence, i.e., the fraction of a population that belongs to a certain class, is a very useful tool in data analytics and learning, and finds applications in many domains such as sentiment analysis, epidemiology,…
We prove the convergence of a particle method for the approximation of diffusive gradient flows in one dimension. This method relies on the discretisation of the energy via non-overlapping balls centred at the particles and preserves the…
We say that a population is perfectly polarized when divided in two groups of the same size and opposite opinions. In this paper, we propose a methodology to study and measure the emergence of polarization from social interactions. We begin…
Deliberative processes are often discussed as increasing or decreasing polarization. This approach misses a different, and arguably more diagnostic, dimension of opinion change: whether deliberation reshuffles who agrees with whom, or…
Under the formalism of annealed averaging of the partition function, a type of random multifractal measures with their multipliers satisfying exponentially distributed is investigated in detail. Branching emerges in the curve of generalized…
Ascertaining the physical state of a system is vital in order to understand and predict its behaviour. Tomography is a standard approach used to determine the form of an unknown state. Here we show that an alternative approach, based on…
A measure of complexity based on a probabilistic description of physical systems is proposed. This measure incorporates the main features of the intuitive notion of such a magnitude. It can be applied to many physical situations and to…
Interestingness measures provide information that can be used to prune or select association rules. A given value of an interestingness measure is often interpreted relative to the overall range of the values that the interestingness…