Kinetic model for multidimensional opinion formation

In this paper, we deal with a kinetic model to describe the evolution of the opinion in a closed group with respect to a choice between multiple options, e.g. political parties, which takes into account two main mechanisms of opinion formation, namely, the interaction between individuals and the effect of the mass media. We numerically test the model in some relevant cases and eventually provide an existence and a uniqueness result for i

Distributional and classical solutions to the Cauchy Boltzmann problem for soft potentials with integrable angular cross section

This paper focuses on the study of existence and uniqueness of distributional and classical solutions to the Cauchy Boltzmann problem for the soft potential case assuming $S^{n-1}$ integrability of the angular part of the collision kernel (Grad cut-off assumption). For this purpose we revisit the Kaniel--Shinbrot iteration technique to present an elementary proof of existence and uniqueness results that includes large data near a local Maxwellian regime with possibly infinite initial mass. We study the propagation of regularity using a recent estimate for the positive collision operator given in [3], by E. Carneiro and the authors, that permits to study such propagation without additional conditions on the collision kernel. Finally, an $L^{p}$-stability result (with $1\leq p\leq\infty$) is presented assuming the aforementioned condition.Comment: 19 page

Formation and Propagation of Discontinuity for Boltzmann Equation in Non-Convex Domains

The formation and propagation of singularities for Boltzmann equation in bounded domains has been an important question in numerical studies as well as in theoretical studies. Consider the nonlinear Boltzmann solution near Maxwellians under in-flow, diffuse, or bounce-back boundary conditions. We demonstrate that discontinuity is created at the non-convex part of the grazing boundary, then propagates only along the forward characteristics inside the domain before it hits on the boundary again.Comment: 39 pages, 5 Figure

Protein crystals in adenovirus type 5-infected cells: requirements for intranuclear crystallogenesis, structural and functional analysis

Intranuclear crystalline inclusions have been observed in the nucleus of epithelial cells infected with Adenovirus serotype 5 (Ad5) at late steps of the virus life cycle. Using immuno-electron microscopy and confocal microscopy of cells infected with various Ad5 recombinants modified in their penton base or fiber domains, we found that these inclusions represented crystals of penton capsomers, the heteromeric capsid protein formed of penton base and fiber subunits. The occurrence of protein crystals within the nucleus of infected cells required the integrity of the fiber knob and part of the shaft domain. In the knob domain, the region overlapping residues 489–492 in the FG loop was found to be essential for crystal formation. In the shaft, a large deletion of repeats 4 to 16 had no detrimental effect on crystal inclusions, whereas deletion of repeats 8 to 21 abolished crystal formation without altering the level of fiber protein expression. This suggested a crucial role of the five penultimate repeats in the crystallisation process. Chimeric pentons made of Ad5 penton base and fiber domains from different serotypes were analyzed with respect to crystal formation. No crystal was found when fiber consisted of shaft (S) from Ad5 and knob (K) from Ad3 (heterotypic S5-K3 fiber), but occurred with homotypic S3K3 fiber. However, less regular crystals were observed with homotypic S35-K35 fiber. TB5, a monoclonal antibody directed against the Ad5 fiber knob was found by immunofluorescence microscopy to react with high efficiency with the intranuclear protein crystals in situ. Data obtained with Ad fiber mutants indicated that the absence of crystalline inclusions correlated with a lower infectivity and/or lower yields of virus progeny, suggesting that the protein crystals might be involved in virion assembly. Thus, we propose that TB5 staining of Ad-infected 293 cells can be used as a prognostic assay for the viability and productivity of fiber-modified Ad5 vectors

Age-structured gametocyte allocation links immunity to epidemiology in malaria parasites

Background Despite a long history of attempts to model malaria epidemiology, the over-riding conclusion is that a detailed understanding of host-parasite interactions leading to immunity is required. It is still not known what governs the duration of an infection and how within-human parasite dynamics relate to malaria epidemiology. Presentation of the hypothesis Immunity to Plasmodium falciparum develops slowly and requires repeated exposure to the parasite, which thus generates age-structure in the host-parasite interaction. An age-structured degree of immunity would present the parasite with humans of highly variable quality. Evolutionary theory suggests that natural selection will mould adaptive phenotypes that are more precise (less variant) in "high quality" habitats, where lifetime reproductive success is best. Variability in malaria parasite gametocyte density is predicted to be less variable in those age groups who best infect mosquitoes. Thus, the extent to which variation in gametocyte density is a simple parasite phenotype reflecting the complex within-host parasite dynamics is addressed. Testing the hypothesis Gametocyte densities and corresponding infectiousness to mosquitoes from published data sets and studies in both rural and urban Cameroon are analysed. The mean and variation in gametocyte density according to age group are considered and compared with transmission success (proportion of mosquitoes infected). Across a wide range of settings endemic for malaria, the age group that infected most mosquitoes had the least variation in gametocyte density, i.e. there was a significant relationship between the variance rather than the mean gametocyte density and age-specific parasite transmission success. In these settings, the acquisition of immunity over time was evident as a decrease in asexual parasite densities with age. By contrast, in an urban setting, there were no such age-structured relationships either with variation in gametocyte density or asexual parasite density. Implications of the hypothesis Gametocyte production is seemingly predicted by evolutionary theory, insofar as a reproductive phenotype (gametocyte density) is most precisely expressed (i.e. is most invariant) in the most infectious human age group. This human age group would thus be expected to be the habitat most suitable for the parasite. Comprehension of the immuno-epidemiology of malaria, a requisite for any vaccine strategies, remains poor. Immunological characterization of the human population stratified by parasite gametocyte allocation would be a step forward in identifying the salient immunological pathways of what makes a human a good habitat

Global existence and full regularity of the Boltzmann equation without angular cutoff

We prove the global existence and uniqueness of classical solutions around an equilibrium to the Boltzmann equation without angular cutoff in some Sobolev spaces. In addition, the solutions thus obtained are shown to be non-negative and $C^\infty$ in all variables for any positive time. In this paper, we study the Maxwellian molecule type collision operator with mild singularity. One of the key observations is the introduction of a new important norm related to the singular behavior of the cross section in the collision operator. This norm captures the essential properties of the singularity and yields precisely the dissipation of the linearized collision operator through the celebrated H-theorem

Modelling opinion formation by means of kinetic equations

In this chapter, we review some mechanisms of opinion dynamics that can be modelled by kinetic equations. Beside the sociological phenomenon of compromise, naturally linked to collisional operators of Boltzmann kind, many other aspects, already mentioned in the sociophysical literature or no, can enter in this framework. While describing some contributions appeared in the literature, we enlighten some mathematical tools of kinetic theory that can be useful in the context of sociophysics

Analysis and modelling of tsunami-induced tilt for the 2007, M = 7.6, Tocopilla and the 2010, M = 8.8 Maule earthquakes, Chile, from long-base tiltmeter and broadband seismometer records

We present a detailed study of tsunami-induced tilt at in-land sites, to test the interest and feasibility of such analysis for tsunami detection and modelling. We studied tiltmeter and broadband seismometer records of northern Chile, detecting a clear s

Sr2V3O9 and Ba2V3O9: quasi one-dimensional spin-systems with an anomalous low temperature susceptibility

The magnetic behaviour of the low-dimensional Vanadium-oxides Sr2V3O9 and Ba2V3O9 was investigated by means of magnetic susceptibility and specific heat measurements. In both compounds, the results can be very well described by an S=1/2 Heisenberg antiferromagnetic chain with an intrachain exchange of J = 82 K and J = 94 K in Sr2V3O9 and Ba2V3O9, respectively. In Sr2V3O9, antiferromagnetic ordering at T_N = 5.3 K indicate a weak interchain exchange of the order of J_perp ~ 2 K. In contrast, no evidence for magnetic order was found in Ba2V3O9 down to 0.5 K, pointing to an even smaller interchain coupling. In both compounds, we observe a pronounced Curie-like increase of the susceptibility below 30 K, which we tentatively attribute to a staggered field effect induced by the applied magnetic field. Results of LDA calculations support the quasi one-dimensional character and indicate that in Sr2V3O9, the magnetic chain is perpendicular to the structural one with the magnetic exchange being transferred through VO4 tetrahedra.Comment: Submitted to Phy. Rev.

Growth, optical and magnetic behavior of YMn0.35In0.65O3 thin film

The growth of YMn₀.₃₅In₀.₆₅O₃ thin films and their optical and magnetic behavior are reported. The YMn₀.₃₅In₀.₆₅O₃ thin film grows along the (0001) orientation with hexagonal structure similar to YMnO₃ on c-plane sapphire. The film shows paramagnetic behavior in the temperature range measured. The film exhibits a blue color due to the electronic transition in the red-green region of the visible spectrum. The development of such a relatively low cost, eco-friendly and highly stable chromophore can be used as a blue filter layer in color filter array. Copyright 2012 Author(s). This article is distributed under a Creative Commons Attribution 3.0 Unported License. [http://dx.doi.org/10.1063/1.4732131