Opinion formation on evolving network. The DPA method applied to a nonlocal cross-diffusion PDE-ODE system

We study a system of nonlocal aggregation cross-diffusion PDEs that describe the evolution of opinion densities on a network. The PDEs are coupled with a system of ODEs that describe the time evolution of the agents on the network. Firstly, we apply the Deterministic Particle Approximation (DPA) method to the aforementioned system in order to prove the existence of solutions under suitable assumptions on the interactions between agents. Later on, we present an explicit model for opinion formation on an evolving network. The opinions evolve based on both the distance between the agents on the network and the 'attitude areas,' which depend on the distance between the agents' opinions. The position of the agents on the network evolves based on the distance between the agents' opinions. The goal is to study radicalization, polarization, and fragmentation of the population while changing its open-mindedness and the radius of interaction

Pointwise universal Gysin formulae and applications towards Griffiths' conjecture

Let $X$ be a complex manifold, $(E,h)\to X$ be a rank $r$ holomorphic Hermitian vector bundle, and $\rho$ be a sequence of dimensions 0 = \rho_0 < \rho_1 < \cdots < \rho_m = r. Let $Q_{\rho,j}$, $j=1,\dots,m$, be the tautological line bundles over the (possibly incomplete) flag bundle $\mathbb{F}_{\rho}(E) \to X$ associated to $\rho$, endowed with the natural metrics induced by that of $E$, with Chern curvatures $\Xi_{\rho,j}$. We show that the universal Gysin formula \textsl{\`{a} la} Darondeau--Pragacz for the push-forward of a homogeneous polynomial in the Chern classes of the $Q_{\rho,j}$'s also holds pointwise at the level of the Chern forms $\Xi_{\rho,j}$ in this Hermitianized situation. As an application, we show the strong positivity of several polynomials in the Chern forms of a Griffiths (semi)positive vector bundle not previously known, thus giving some new evidences towards a conjecture by Griffiths, which in turn can be seen as a pointwise Hermitianized version of the Fulton--Lazarsfeld theorem on numerically positive polynomials for ample vector bundles

SPLITTING SCHEMES & SEGREGATION IN REACTION-(CROSS-)DIFFUSION SYSTEMS

International audienceOne of the most fascinating phenomena observed in reaction-diffusion systems is the emergence of segregated solutions, i.e. population densities with disjoint supports. We analyse such a reaction cross-diffusion system. In order to prove existence of weak solutions for a wide class of initial data without restriction about their supports or their positivity, we propose a variational splitting scheme combining ODEs with methods from optimal transport. In addition, this approach allows us to prove conservation of segregation for initially segregated data even in the presence of vacuum

Quantifying the relative importance of climate and habitat on structuring the species and taxonomic diversity of aquatic plants in a biodiversity hotspot of tropical Asia

It has not been well known how climate and habitat variables will influence the distribution of plant species to some extents at mesoscales. In this report, by using the distribution of aquatic plants in Western Ghats, a biodiversity hotspot in tropical Asian region, I quantify the relative importance of climate and habitat variables on structuring spatially species richness and taxonomic diversity patterns using structural equation modeling. All the sampling qudrats in the region used for the study has a spatial resolution of 0.5 latitude × 0.5 longitude. The results showed that species richness is high in both northern and southern part of the region, while low in the middle part. In contrast, taxonomic distinctiveness is relatively homogeneous over all the sampling quadrats in the region. Structural equation modeling suggested that taxonomic distinctiveness patterns of aquatic plants in the region follow temperature (partial regression coefficient=0.31, p<0.05) and elevational (partial regression coefficient=0.31, p<0.05) gradients, while richness patterns cannot be explained by any of the currently used variables. In conclusion, environmental variables that are related to taxonomic distinctiveness would not be related to richness, given the fact that these two quantities are orthogonal more or less. Both climate and habitat are equally influential on taxonomic distinctiveness patterns for aquatic plants in Western Ghats of India

Germinação de sementes de alface submetidas a condicionamento osmótico durante o armazenamento

In some species the osmopriming technique allows rapid and uniform germination of seeds. This research studies the efficiency of osmopriming on the germination of lettuce seeds. Seeds of the cultivars Mesa 659, Nabuco RS and Verônica were osmoprimed with a mannitol solution (0.35 mol) for periods of 3, 4, 5, and 6 days, at the temperature of 20ºC and under daylight. After priming seeds were dried for 12 hours in an oven at 32ºC. Evaluation of osmopriiming efficiency was performed by the standard germination test 0, 10, 20, 30, 60 and 90 days after priming, in a complete randomized design with four replications, 50 seeds per replicate. Data were submitted to analysis of variance in a factorial arrangement 2 × 5 × 6 (2 levels of vigor; 5 periods of osmopriming and 6 periods of storage after drying). The effect of osmopriming on lettuce seeds varied depending on the cultivar and priming period.Em algumas espécies a técnica do condicionamento osmótico permite a obtenção de uma germinação rápida e uniforme. A pesquisa teve por objetivo verificar a eficiência do condicionamento osmótico de sementes de alface sobre a sua germinação. Sementes dos cultivares Mesa 659, Nabuco RS e Verônica, com dois níveis de viabilidade, foram submetidas ao condicionamento osmótico em solução (0,35 mol) de manitol por períodos de 3, 4, 5 e 6 dias sob 20ºC e em presença de luz. A seguir, as sementes foram submetidas à secagem (32ºC) por 12 horas em estufa com circulação de ar. As avaliações foram feitas pelo teste padrão de germinação aos 0, 10, 20, 30, 60 e 90 dias após o condicionamento e secagem das sementes. Utilizou-se o delineamento experimental inteiramente casualizado, com quatro repetições de 50 sementes, em esquema fatorial 2 × 5× 6, (dois níveis de vigor; cinco períodos de condicionamento osmótico e seis períodos de armazenamento após secagem). A resposta de sementes de alface ao condicionamento osmótico varia em função do cultivar e do período de condicionamento osmótico