Related papers: Pointwise intersection in neighbourhood modal logi…
This paper introduces a new definition of multiscale neighborhoods in 3D point clouds. This definition, based on spherical neighborhoods and proportional subsampling, allows the computation of features with a consistent geometrical meaning,…
Let X be a smooth complete intersection. Suppose p and q are general points of X, we consider conics in X passing through p and q. We show the moduli space of these conics is a smooth complete intersection. The main ingredients of the proof…
Analysis and manipulation of trained neural networks is a challenging and important problem. We propose a symbolic representation for piecewise-linear neural networks and discuss its efficient computation. With this representation, one can…
When streets are designed according to the shared space principle, road user are encouraged to interact spontaneously with each other for negotiating the space. These interaction mechanisms do not follow clearly defined traffic rules but…
In this article we develop intersection theory in terms of the $\mathcal{B}$-group of a reduced analytic space. This group was introduced in a previous work as an analogue of the Chow group; it is generated by currents that are direct…
Numerical algebraic geometry has a close relationship to intersection theory from algebraic geometry. We deepen this relationship, explaining how rational or algebraic equivalence gives a homotopy. We present a general notion of witness set…
We study the axiomatisability of the iteration-free fragment of Propositional Dynamic Logic with Intersection and Tests. The combination of program composition, intersection and tests makes its proof-theory rather difficult. We develop a…
This is an expository paper on the subject of the title. It assumes basic scheme theory, commutative and homological algebra.
The classical theory of the cross-ratio is a beautiful case study of the moduli of ordered points of the projective line and of invariants of the action of $PGL_2$. We generalize the theory of the cross-ratio to the setting of $S$-valued…
Recent years have witnessed the great success of deep learning on various point cloud analysis tasks, e.g., classification and semantic segmentation. Since point cloud data is sparse and irregularly distributed, one key issue for point…
The paper analyzes dynamic epistemic logic from a topological perspective. The main contribution consists of a framework in which dynamic epistemic logic satisfies the requirements for being a topological dynamical system thus interfacing…
A configuration of the triple $(\mathcal{P}, \mathcal{L}, \mathcal{I})$ on the incidence relation which holds the properties of "Any two points are incident with at most one line" and "Any two lines are incident with at most one point". In…
Based on methods of structural convergence we provide a unifying view of local-global convergence, fitting to model theory and analysis. The general approach outlined here provides a possibility to extend the theory of local-global…
We present an algebraic characterization of the complexity classes Logspace and Nlogspace, using an algebra with a composition law based on unification. This new bridge between unification and complexity classes is rooted in proof theory…
With the progress of the urbanisation process, the urban transportation system is extremely critical to the development of cities and the quality of life of the citizens. Among them, it is one of the most important tasks to judge traffic…
This chapter presents a state-of-the-art survey of relationships, traditionally referred to as `bridges', between interpolation properties for propositional logics -- including superintuitionistic, modal, and substructural logics -- and…
In this paper we discuss the relationships between conditional and preferential logics and neural network models, based on a multi-preferential semantics. We propose a concept-wise multipreference semantics, recently introduced for…
We propose a novel, fully explainable neural approach to synthesis of combinatorial logic circuits from input-output examples. The carrying advantage of our method is that it readily extends to inductive scenarios, where the set of examples…
A graph $G=(V,E)$ is a geometric intersection graph if every node $v \in V$ is identified with a geometric object of some particular type, and two nodes are adjacent if the corresponding objects intersect. Geometric intersection graph…
In this paper, we propose an approach how connected and highly automated vehicles can perform cooperative maneuvers such as lane changes and left-turns at urban intersections where they have to deal with human-operated vehicles and…