Opinion modeling on social media and marketing aspects

We introduce and discuss kinetic models of opinion formation on social networks in which the distribution function depends on both the opinion and the connectivity of the agents. The opinion formation model is subsequently coupled with a kinetic model describing the spreading of popularity of a product on the web through a social network. Numerical experiments on the underlying kinetic models show a good qualitative agreement with some measured trends of hashtags on social media websites and illustrate how companies can take advantage of the network structure to obtain at best the advertisement of their products

Phase transitions in a two parameter model of opinion dynamics with random kinetic exchanges

Recently, a model of opinion formation with kinetic exchanges has been proposed in which a spontaneous symmetry breaking transition was reported [M. Lallouache et al, Phys. Rev. E, {\bf 82} 056112 (2010)]. We generalise the model to incorporate two parameters, $\lambda$, to represent conviction and $\mu$, to represent the influencing ability of individuals. A phase boundary given by $\lambda=1-\mu/2$ is obtained separating the symmetric and symmetry broken phases: the effect of the influencing term enhances the possibility of reaching a consensus in the society. The time scale diverges near the phase boundary in a power law manner. The order parameter and the condensate also show power law growth close to the phase boundary albeit with different exponents. Theexponents in general change along the phase boundary indicating a non-universality. The relaxation times, however, become constant with increasing system size near the phase boundary indicating the absence of any diverging length scale. Consistently, the fluctuations remain finite but show strong dependence on the trajectory along which it is estimated.Comment: Version accepted for PRE; text modified, new figures and references adde

Gravitational wave emission from unstable accretion discs in tidal disruption events

Gravitational waves can be emitted by accretion discs if they undergo instabilities that generate a time varying mass quadrupole. In this work we investigate the gravitational signal generated by a thick accretion disc of 1\u2009M 99 around a static supermassive black hole of 106\u2009M 99, assumed to be formed after the tidal disruption of a solar type star. This torus has been shown to be unstable to a global non-axisymmetric hydrodynamic instability, the Papaloizou\u2013Pringle instability, in the case where it is not already accreting and has a weak magnetic field. We start by deriving analytical estimates of the maximum amplitude of the gravitational wave signal, with the aim to establish its detectability by the Laser Interferometer Space Antenna (LISA). Then, we compare these estimates with those obtained through a numerical simulation of the torus, made with a 3D smoothed particle hydrodynamics code. Our numerical analysis shows that the measured strain is two orders of magnitude lower than the maximum value obtained analytically. However, accretion discs affected by the Papaloizou\u2013Pringle instability may still be interesting sources for LISA, if we consider discs generated after deeply penetrating tidal disruptions of main-sequence stars of higher mas

Discovering intermediate massive black holes through tidally disrupted stars

Stars are spheres of gas held together by self-gravity. When flying by a black hole, however, the star self-binding force can be overwhelmed by the black hole tides and the star can be torn apart. This is a physically rich and fascinating event which will be described by first. introducing the concept. of black hole from a mathematical point of view. We will then dive into the physics of the tidal disruption and proceed describing the accompanying electromagnetic flare and gravitational wave burst in the frequency range of the Laser Interferometer Space Antenna. This empowers such events to discover the elusive black holes with mass intermediate between the solar and the million/billion solar masses

Pediatric glaucoma: current perspectives

Giorgio Marchini, Marco Toscani, Francesca Chemello Eye Clinic, Department of Neurological and Movement Sciences, University of Verona, Verona, Italy Abstract: "Childhood glaucoma" is a heterogeneous group of severe pediatric conditions often associated with significant visual loss and characterized by elevated intraocular pressure (IOP) and optic-disk cupping. Successful IOP control is crucial but challenging and most often achieved surgically, with medical therapy playing a supportive role. There are many classifications of childhood glaucoma, but they can simply be divided into primary, in which a developmental abnormality of the anterior chamber angle only exists, and secondary, in which aqueous outflow is reduced due to independent mechanisms that secondarily impair the function of the filtration angle. The worldwide prevalence of childhood blindness ranges from 0.03% in high-income countries to 0.12% in undeveloped countries. The majority of cases do not have an identified genetic mutation and, where the mutation is known, the genes often account for only a small proportion of cases. Several pathogenetic mechanisms are known to contribute to the development of childhood glaucoma. Whatever the cause, it results in a reduced aqueous outflow at the level of the trabecular meshwork. Age of onset and magnitude of the elevated IOP largely determine the clinical manifestation the high variability of clinical manifestations. Glaucoma from any cause in a neonate and infant is characterized by the classic triad of epiphora, photophobia, and blepharospasm, and could be associated with eye enlargement (buphthalmos) and Haab striae. The eye examination, usually performed under general anesthesia, includes: tonometry, anterior-segment examination, gonioscopy, corneal diameter and axial length measurement, dilated fundoscopy with optic-nerve-head evaluation. Medical therapy, considering the high frequency of side effects, is generally used as temporizing IOP-lowering treatment before surgery or as adjuvant treatment postoperatively in case of partially successful procedures for refractory glaucomas. Surgery is the nodal point of the management of refractory childhood glaucoma, so it is crucial to opt for a forward-looking strategy to reach the target IOP and minimize the visual loss. Keywords: childhood glaucoma, congenital glaucoma, glaucoma surgical therapy, childhood visual los

Optimal control of epidemic spreading in presence of social heterogeneity

The spread of COVID-19 has been thwarted in most countries through non-pharmaceutical interventions. In particular, the most effective measures in this direction have been the stay-at-home and closure strategies of businesses and schools. However, population-wide lockdowns are far from being optimal carrying heavy economic consequences. Therefore, there is nowadays a strong interest in designing more efficient restrictions. In this work, starting from a recent kinetic-type model which takes into account the heterogeneity described by the social contact of individuals, we analyze the effects of introducing an optimal control strategy into the system, to limit selectively the mean number of contacts and reduce consequently the number of infected cases. Thanks to a data-driven approach, we show that this new mathematical model permits to assess the effects of the social limitations. Finally, using the model introduced here and starting from the available data, we show the effectivity of the proposed selective measures to dampen the epidemic trends

ASYMPTOTIC FLOCKING DYNAMICS FOR THE KINETIC CUCKER-SMALE MODEL

In this paper, we analyse the asymptotic behavior of solutions of the continuous kinetic version of flocking by Cucker and Smale [16], which describes the collective behavior of an ensemble of organisms, animals or devices. This kinetic version introduced in [24] is here obtained starting from a Boltzmann-type equation. The large-time behavior of the distribution in phase space is subsequently studied by means of particle approximations and a stability property in distances between measures. A continuous analogue of the theorems of [16] is shown to hold for the solutions on the kinetic model. More precisely, the solutions will concentrate exponentially fast their velocity to their mean while in space they will converge towards a translational flocking solution

On the minimization problem of sub-linear convex functionals

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Adaptive Polynomial Harmonic Distortion Compensation in Current and Voltage Transformers Through Iteratively Updated QR Factorization

Measuring current and voltage harmonics has paramount importance for improving the power quality of distribution grids. However, the achieved accuracy strongly depends on the adopted instrument transformer (IT). This article proposes an adaptive technique that enables an effective compensation of both the filtering behavior and the harmonic distortion (HD) introduced by current and voltage transformers (VTs), namely the strongest nonlinear effect at low-order harmonics. The approach is based on a flexible, linear in the parameters polynomial modeling of HD in the frequency domain. Model complexity can be different from one harmonic to the other, and it is selected through an automatic iterative process to suit the nonlinear behavior at each specific harmonic order, while avoiding overfitting. In particular, the number of parameters is increased by progressively updating the QR factorization of the regressor matrix trough Householder reflections until a convergence condition is reached. Experimental tests performed on an inductive VT and current transformer (CT) highlight the effectiveness of the approach