Rigidity sensing plays a fundamental role in multiple cell functions ranging from migration, to proliferation and differentiation1-5. During migration, single cells have been reported to preferentially move toward more rigid regions of a substrate in a process termed durotaxis. Durotaxis could contribute to cell migration in wound healing and gastrulation, where local gradients in tissue rigidi...

It is often claimed that Kripke (1980) and Putnam (1975) established that many predicates, most importantly natural kind predicates, are like proper names in being rigid designators. This insight is generally regarded as having important consequences in the theory of necessary truths: the rigidity of terms such as 'Hesperus', 'Phosphorus', 'water' and 'H 2 O' is used in explaining why identity ...

The rigidity of a matrix M is the function R M (r), which, for a given r, gives the minimum number of entries of M which one has to change in order to reduce its rank to at most r. This notion has been introduced by Valiant in 1977 in connection with the complexity of computing linear forms. Despite more than 20 years of research, very little is known about the rigidity of matrices. Nonlinear l...

We develop a bipartite rigidity theory for bipartite graphs parallel to the classical rigidity theory for general graphs, and define for two positive integers k, l the notions of (k, l)-rigid and (k, l)-stress free bipartite graphs. This theory coincides with the study of Babson–Novik’s balanced shifting restricted to graphs. We establish bipartite analogs of the cone, contraction, deletion, an...