Asymptotic and numerical analysis for Holland and Simpson’s thin wire formalism

AbstractIn the context of simulation of electromagnetic propagation, the thin wire formalism of Holland and Simpson allows one to deal with scattering by perfectly conducting thin wires by coupling a standard FDTD method with a discrete 1D wave equation ruling the current inside the wires. This method can be very accurate, but it involves a fitting parameter that requires careful calibration.We propose a consistency analysis and derive a formula for the calibration of this parameter in the case of a simplified 2D analogue of the method of Holland and Simpson. Our proof relies on the observation that this method is actually a hidden version of the singular function method well known in the context of elliptic equations in domains with a singular boundary

Intrinsic and Extrinsic Modulators of the Epithelial to Mesenchymal Transition: Driving the Fate of Tumor Microenvironment

The epithelial to mesenchymal transition (EMT) is an evolutionarily conserved process. In cancer, EMT can activate biochemical changes in tumor cells that enable the destruction of the cellular polarity, leading to the acquisition of invasive capabilities. EMT regulation can be triggered by intrinsic and extrinsic signaling, allowing the tumor to adapt to the microenvironment demand in the different stages of tumor progression. In concomitance, tumor cells undergoing EMT actively interact with the surrounding tumor microenvironment (TME) constituted by cell components and extracellular matrix as well as cell secretome elements. As a result, the TME is in turn modulated by the EMT process toward an aggressive behavior. The current review presents the intrinsic and extrinsic modulators of EMT and their relationship with the TME, focusing on the non-cell-derived components, such as secreted metabolites, extracellular matrix, as well as extracellular vesicles. Moreover, we explore how these modulators can be suitable targets for anticancer therapy and personalized medicine