Let F be a field, let G be a simple graph on n vertices, and let S (G) be the class of all F -valued symmetric n × n matrices whose nonzero off-diagonal entries occur in exactly the positions corresponding to the edges of G. For each graph G, there is an associated minimum rank class, M R (G) consisting of all matrices A ∈ S (G) with rankA = mr (G), the minimum rank among all matrices in S (G)....

We implemented support for non-null types in Java according to the description in [1]. We built our implementation on top of the Polyglot Java compiler as a language extension. Our extension allows programmers to provide annotations specifying whether a variable is allowed to ever take on a null value and provides an augmented type system to enforce these guarantees. Once the separation between...

Let F be a field, let G be a simple graph on n vertices, and let S (G) be the class of all F -valued symmetric n × n matrices whose nonzero off-diagonal entries occur in exactly the positions corresponding to the edges of G. For each graph G, there is an associated minimum rank class, M R (G) consisting of all matrices A ∈ S (G) with rankA = mr (G), the minimum rank among all matrices in S (G)....

Let A and id="M2"> mathvariant="script">B be two closed linear relations acting between Banach spaces id="M3"> X id="M4"> Y , let id="M5"> λ a complex number. We study the stability of nullity deficiency id="M6"> when it is perturbed by id="M7"> . In particular, we sho...

Through a series of papers in the 1980’s, Bouchet introduced isotropic systems and the Tutte-Martin polynomial of an isotropic system. Then, Arratia, Bollobás, and Sorkin developed the interlace polynomial of a graph in [ABS00] in response to a DNA sequencing application. The interlace polynomial has generated considerable recent attention, with new results including realizing the original inte...

Abstract We study multivariate polynomials over ‘structured’ grids. Firstly, we propose an interpretation as to what it means for a finite subset of field be structured; do so by numerical parameter, the nullity. then extend several results – notably, Combinatorial Nullstellensatz and Coefficient Theorem structured The main point is that structure grid allows degree constraints on relaxed.