Related papers: Separations of sets
Similarly to $\beta$-adic van der Corput sequences, abstract van der Corput sequences can be defined for abstract numeration systems. Under some assumptions, these sequences are low discrepancy sequences. The discrepancy function is…
It is well known that not every combinatorial configuration admits a geometric realization with points and lines. Moreover, some of them do not even admit realizations with pseudoline arrangements, i.e., they are not topological. In this…
Fusions are a simple way of combining logics. For normal modal logics, fusions have been investigated in detail. In particular, it is known that, under certain conditions, decidability transfers from the component logics to their fusion.…
We consider a compositional construction of approximate abstractions of interconnected control systems. In our framework, an abstraction acts as a substitute in the controller design process and is itself a continuous control system. The…
We introduce a new class of structured symmetric matrices by extending the notion of perfect elimination ordering from graphs to weighted graphs or matrices. This offers a common framework capturing common vertex elimination orderings of…
A pseudoline is a homeomorphic image of the real line in the plane so that its complement is disconnected. An arrangement of pseudolines is a set of pseudolines in which every two cross exactly once. A drawing of a graph is pseudolinear if…
In this paper, we propose a compositional approach to construct opacity-preserving finite abstractions (a.k.a symbolic models) for networks of discrete-time nonlinear control systems. Particularly, we introduce new notions of simulation…
Rough sets were proposed to deal with the vagueness and incompleteness of knowledge in information systems. There are may optimization issues in this field such as attribute reduction. Matroids generalized from matrices are widely used in…
The study of networks plays a crucial role in investigating the structure, dynamics, and function of a wide variety of complex systems in myriad disciplines. Despite the success of traditional network analysis, standard networks provide a…
Network systems consist of subsystems and their interconnections, and provide a powerful framework for analysis, modeling and control of complex systems. However, subsystems may have high-dimensional dynamics, and the amount and nature of…
The bipartition polynomial of a graph is a generalization of many other graph polynomials, including the domination, Ising, matching, independence, cut, and Euler polynomial. We show in this paper that it is also a powerful tool for proving…
A split graph is a graph whose vertex set can be partitioned into a clique and an independent set. A split comparability graph is a split graph which is transitively orientable. In this work, we characterize split comparability graphs in…
Deduction systems and graph rewriting systems are compared within a common categorical framework. This leads to an improved deduction method in diagrammatic logics.
Abstraction is the process of extracting the essential features from raw data while ignoring irrelevant details. It is well known that abstraction emerges with depth in neural networks, where deep layers capture abstract characteristics of…
Abstraction is a commonly used process to represent some low-level system by a more coarse specification with the goal to omit unnecessary details while preserving important aspects. While recent work on abstraction in the situation…
Abstraction plays a key role in concept learning and knowledge discovery; this paper is concerned with computational abstraction. In particular, we study the nature of abstraction through a group-theoretic approach, formalizing it as…
We define a decomposition of link projections whose pieces we call atoroidal graphs. We describe a surgery operation on these graphs and show that all atoroidal graphs can be generated by performing surgery repeatedly on a family of well…
Partial duality generalizes the fundamental concept of the geometric dual of an embedded graph. A partial dual is obtained by forming the geometric dual with respect to only a subset of edges. While geometric duality preserves the genus of…
We present an approach for representing abstract argumentation frameworks based on an encoding into classical higher-order logic. This provides a uniform framework for computer-assisted assessment of abstract argumentation frameworks using…
The paper deals with a construction of a separating system of rational invariants for finite dimensional generic algebras. In the process of dealing an approach to a rough classification of finite dimensional algebras is offered by…