Biological materials such as extracellular matrix scaffolds, cancer cells, and tissues are often assumed to respond elastically for simplicity; the viscoelastic response is quite commonly ignored. Extracellular matrix mechanics including the viscoelasticity has turned out to be a key feature of cellular behavior and the entire shape and function of healthy and diseased tissues, such as cancer. The interference of cells with their local microenvironment and the interaction among different cell types relies both on the mechanical phenotype of each involved element. However, there is still not yet clearly understood how viscoelasticity alters the functional phenotype of the tumor extracellular matrix environment. Especially the biophysical technologies are still under ongoing improvement and further development. In addition, the effect of matrix mechanics in the progression of cancer is the subject of discussion. Hence, the topic of this review is especially attractive to collect the existing endeavors to characterize the viscoelastic features of tumor extracellular matrices and to briefly highlight the present frontiers in cancer progression and escape of cancers from therapy. Finally, this review article illustrates the importance of the tumor extracellular matrix mechano-phenotype, including the phenomenon viscoelasticity in identifying, characterizing, and treating specific cancer types.

In this thesis we improve and extend an algebraic technique pioneered by M. Gaudin. The technique is based on an infinite dimensional Lie algebra and a related family of mutually commuting Hamiltonians. In order to find energy eigenvalues of such Hamiltonians one has to solve the equations of Bethe ansatz. However, in most cases analytical solutions are not available. In this study we examine a special case for which analytical solutions of Bethe ansatz equations are not needed. Instead, some special properties of these equations are utilized to evaluate the energy eigenvalues. We use this method to find exact expressions for the energy eigenvalues of a class of interacting boson models. In addition to that, we also introduce a q-deformation of the algebra of Gaudin. This deformation leads us to another family of mutually commuting Hamiltonians which we diagonalize using algebraic Bethe ansatz technique. The motivation for this deformation comes from a relationship between Gaudin algebra and a spin extension of the integrable model of F. Calogero. Observing this relation, we then consider a well known periodic version of Calogero&#039 / s model which is due to B. Sutherland. The search for a Gaudin-like algebraic structure which is in a similar relationship with the spin extension of Sutherland&#039 / s model naturally leads to the above mentioned q-deformation of Gaudin algebra. The deformation parameter q and the periodicity d of the Sutherland model are related by the formula q=i{pi}/d.

Editorial on the Research Topic. Editorial: Editor’s Pick 2021: Highlights in Cell Adhesion and Migration.