A particle system approach to aggregation phenomena

Inspired by a PDE-ODE system of aggregation developed in the biomathematical literature, an interacting particle system representing aggregation at the level of individuals is investigated. It is proved that the empirical density of the individual converges to solution of the PDE-ODE system

Advance Directives: regarding the recovery of subjectivity between independence and self-narration

After 41 years from the approval of the first living will law in 1976 in California, on December 22nd 2017 the bill on “Rules on in- formed consent and advance directives” has been approved in Italy. The applicability of the law highlights a lack of a univocal methodol- ogy regarding the recovery process of the patient’s subjective dimension under a testamentary will; so, it seemed useful to highlight the passages that occur between the drafting and the use of an advance directive in an existential phenomenological prospective. Is the individual who freely drafts an A.D., choosing to decide now for the future, the same per- son for which the provisions were outlined? The goal of this paper is to offer an ethical reading of the ontological issue that illness can raises

The Navier–Stokes–Vlasov–Fokker–Planck System as a Scaling Limit of Particles in a Fluid

Convergence of a system of particles, interacting with a fluid, to Navier–Stokes–Vlasov–Fokker–Planck system is studied. The interaction between particles and fluid is described by Stokes drag force. The empirical measure of particles is proved to converge to the Vlasov–Fokker–Planck component of the system and the velocity of the fluid coupled with the particles converges in the uniform topology to the the Navier–Stokes component. A new uniqueness result for the PDE system is added

A Novel Averaging Principle Provides Insights in the Impact of Intratumoral Heterogeneity on Tumor Progression

Typically stochastic differential equations (SDEs) involve an additive or multiplicative noise term. Here, we are interested in stochastic differential equations for which the white noise is nonlinearly integrated into the corresponding evolution term, typically termed as random ordinary differential equations (RODEs). The classical averaging methods fail to treat such RODEs. Therefore, we introduce a novel averaging method appropriate to be applied to a specific class of RODEs. To exemplify the importance of our method, we apply it to an important biomedical problem, in particular, we implement the method to the assessment of intratumoral heterogeneity impact on tumor dynamics. Precisely, we model gliomas according to a well-known Go or Grow (GoG) model, and tumor heterogeneity is modeled as a stochastic process. It has been shown that the corresponding deterministic GoG model exhibits an emerging Allee effect (bistability). In contrast, we analytically and computationally show that the introduction of white noise, as a model of intratumoral heterogeneity, leads to monostable tumor growth. This monostability behavior is also derived even when spatial cell diffusion is taken into account