Stem cells and physical energies: can we really drive stem cell fate?

Adult stem cells are undifferentiated elements able to self-renew or differentiate to maintain tissue integrity. Within this context, stem cells are able to divide in a symmetric fashion, feature characterising all the somatic cells, or in an asymmetric way, which leads daughter cells to different fates. It is worth highlighting that cell polarity have a critical role in regulating stem cell asymmetric division and the proper control of cell division depends on different proteins involved in cell development, differentiation and maintenance of tissue homeostasis. Moreover, the interaction between cells and the extracellular matrix are crucial in influencing cell behavior, included in terms of mechanical properties as cytoskeleton plasticity and remodelling, and membrane tension. Finally, the activation of specific transcriptional program and epigenetic modifications contributes to cell fate determination, through modulation of cellular signalling cascades. It is well known that physical and mechanical stimuli are able to influence biological systems, and in this context, the effects of electromagnetic fields (EMFs) have already shown a considerable role, even though there is a lack of knowledge and much remains to be done around this topic. In this review, we summarize the historical background of EMFs applications and the main molecular mechanism involved in cellular remodelling, with particular attention to cytoskeleton elasticity and cell polarity, required for driving stem cell behavior

An elementary proof of uniqueness of the particle trajectories for solutions of a class of shear-thinning non-Newtonian 2D fluids

We prove some regularity results for a class of two dimensional non-Newtonian fluids. By applying results from [Dashti and Robinson, Nonlinearity, 22 (2009), 735-746] we can then show uniqueness of particle trajectories

Quantum graphs with singular two-particle interactions

We construct quantum models of two particles on a compact metric graph with singular two-particle interactions. The Hamiltonians are self-adjoint realisations of Laplacians acting on functions defined on pairs of edges in such a way that the interaction is provided by boundary conditions. In order to find such Hamiltonians closed and semi-bounded quadratic forms are constructed, from which the associated self-adjoint operators are extracted. We provide a general characterisation of such operators and, furthermore, produce certain classes of examples. We then consider identical particles and project to the bosonic and fermionic subspaces. Finally, we show that the operators possess purely discrete spectra and that the eigenvalues are distributed following an appropriate Weyl asymptotic law

Nonexistence of self-similar singularities for the 3D incompressible Euler equations

We prove that there exists no self-similar finite time blowing up solution to the 3D incompressible Euler equations. By similar method we also show nonexistence of self-similar blowing up solutions to the divergence-free transport equation in $\Bbb R^n$. This result has direct applications to the density dependent Euler equations, the Boussinesq system, and the quasi-geostrophic equations, for which we also show nonexistence of self-similar blowing up solutions.Comment: This version refines the previous one by relaxing the condition of compact support for the vorticit