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Matroid varieties are the closures in the Grassmannian of sets of points defined by specifying which Pl\"ucker coordinates vanish and which don't --- the set of nonvanishing Pl\"ucker coordinates forms a well-studied object called a…
Recent advances in bipartite consensus on matrix-weighted networks, where agents are divided into two disjoint sets with those in the same set agreeing on a certain value and those in different sets converging to opposite values, have…
Recent developments in cloud storage architectures have originated new models of online storage as cooperative storage systems and interconnected clouds. Such distributed environments involve many organizations, thus ensuring…
In this paper, we propose a new type of matroids, namely covering matroids, and investigate the connections with the second type of covering-based rough sets and some existing special matroids. Firstly, as an extension of partitions,…
A spectrahedron is the positivity region of a linear matrix pencil and thus the feasible set of a semidefinite program. We propose and study a hierarchy of sufficient semidefinite conditions to certify the containment of a spectrahedron in…
This paper presents the first formalisation of the precise subtyping relation for asynchronous multiparty sessions. We show that our subtyping relation is sound (i.e., guarantees safe process replacement) and also complete: any extension of…
We consider a combinatorial question about searching for an unknown ideal $\mu$ within a known pointed poset $\lambda$. Elements of $\lambda$ may be queried for membership in $\mu$, but at most $k$ positive queries are permitted. We provide…
Secret Sharing techniques are now the building blocks of several security protocols. A (t;n) threshold secret sharing scheme is one in which t or more participant can join together to retrieve the secret.Traditional single secret sharing…
Matroids and semigraphoids are discrete structures abstracting and generalizing linear independence among vectors and conditional independence among random variables, respectively. Despite the different nature of conditional independence…
Cloud computing has changed the way enterprises store, access and share data. Data is constantly being uploaded to the cloud and shared within an organization built on a hierarchy of many different individuals that are given certain data…
Many real-world networks exhibit a multicores-periphery structure, with densely connected vertices in multiple cores surrounded by a general periphery of sparsely connected vertices. Identification of the multicores-periphery structure can…
We study some properties of a serial (i.e. one-by-one) symmetric exchange of elements of two disjoint bases of a matroid. We show that any two elements of one base have a serial symmetric exchange with some two elements of the other base.…
We present initial results on a comprehensive model of structured communications, in which self- adaptation and security concerns are jointly addressed. More specifically, we propose a model of self-adaptive, multiparty communications with…
We explore the structure of multipartite quantum systems which are entangled in multiple degrees of freedom. We find necessary and sufficient conditions for the characterization of tripartite systems and necessary conditions for any number…
In this PhD thesis we propose an algorithmic approach to the study of the Hilbert scheme. Developing algorithmic methods, we also obtain general results about Hilbert schemes. In Chapter 1 we discuss the equations defining the Hilbert…
Smart matter consists of many sensors, computers and actuators embedded within materials. These microelectromechanical systems allow properties of the materials to be adjusted under program control. In this context, we study the behavior of…
Property $(P)$, introduced in recent work and rooted in the classical theory of Parter vertices, concerns the existence of a nonsingular matrix $A\in S(G)$ for which every vertex of $G$ is a $P$-vertex. Previous investigations have fully…
We clarify the mathematical structure underlying unitary $t$-designs. These are sets of unitary matrices, evenly distributed in the sense that the average of any $t$-th order polynomial over the design equals the average over the entire…
In the matroid secretary problem we are given a stream of elements and asked to choose a set of elements that maximizes the total value of the set, subject to being an independent set of a matroid given in advance. The difficulty comes from…
Networks are a fundamental tool for understanding and modeling complex systems in physics, biology, neuroscience, engineering, and social science. Many networks are known to exhibit rich, lower-order connectivity patterns that can be…