Related papers: Formalising Sensor Topologies for Target Counting
A topological approach to stratification learning is developed for point cloud data drawn from a stratified space. Given such data, our objective is to infer which points belong to the same strata. First we define a multi-scale notion of a…
This paper introduces mathematical models of \sensors\ for mobile robots based on visibility. Serving a purpose similar to the pinhole camera model for computer vision, the introduced models are expected to provide a useful, idealized…
Detecting small targets at range is difficult because there is not enough spatial information present in an image sub-region containing the target to use correlation-based methods to differentiate it from dynamic confusers present in the…
Model counting is the problem of computing the number of models that satisfy a given propositional theory. It has recently been applied to solving inference tasks in probabilistic logic programming, where the goal is to compute the…
Modal logics have proved useful for many reasoning tasks in symbolic artificial intelligence (AI), such as belief revision, spatial reasoning, among others. On the other hand, mathematical morphology (MM) is a theory for non-linear analysis…
In current practice a formal analysis of hybrid system models is assertion-based. The work presented here is based on features that look beyond functional correctness toward a quantitative evaluation of behavioral attributes. A feature…
Real-time systems are computing systems in which the meeting of their requirements is vital for their correctness. Consequently, if the real-time requirements of these systems are poorly understood and verified, the results can be…
The best possible precision is one of the key figures in metrology, but this is established by the exact response of the detection apparatus, which is often unknown. There exist techniques for detector characterisation, that have been…
Formal explainability guarantees the rigor of computed explanations, and so it is paramount in domains where rigor is critical, including those deemed high-risk. Unfortunately, since its inception formal explainability has been hampered by…
We develop a sequential-topological study of rational points of schemes of finite type over local rings typical in higher dimensional number theory and algebraic geometry. These rings are certain types of multidimensional complete fields…
The concept of $typed$ $topology$ is introduced. In a typed topological space, some open sets are assigned "types", and topological concepts such as closure, connectedness can be defined using types. A finite data set in $R^2$ is a…
For autonomous robots to navigate a complex environment, it is crucial to understand the surrounding scene both geometrically and semantically. Modern autonomous robots employ multiple sets of sensors, including lidars, radars, and cameras.…
Topic modeling is a popular method used to describe biological count data. With topic models, the user must specify the number of topics $K$. Since there is no definitive way to choose $K$ and since a true value might not exist, we develop…
Post-selection strategies have been proposed with the aim of amplifying weak signals, which may help to overcome detection thresholds associated with technical noise in high-precision measurements. Here we use an optical setup to…
We present a novel method to explicitly incorporate topological prior knowledge into deep learning based segmentation, which is, to our knowledge, the first work to do so. Our method uses the concept of persistent homology, a tool from…
A more realistic object detection paradigm, Open-World Object Detection, has arisen increasing research interests in the community recently. A qualified open-world object detector can not only identify objects of known categories, but also…
There is now a large body of techniques, many based on formal methods, for describing and realizing complex robotics tasks, including those involving a variety of rich goals and time-extended behavior. This paper explores the limits of what…
Continuous first-order logic is used to apply model-theoretic analysis to analytic structures (e.g. Hilbert spaces, Banach spaces, probability spaces, etc.). Classical computable model theory is used to examine the algorithmic structure of…
Languages based on the theory of timed automata are a well established approach for modelling and analysing real-time systems, with many applications both in industrial and academic context. Model checking for timed automata has been…
Suppose one wants to monitor a domain with sensors, each sensing a small ball-shaped region, but the domain is hazardous enough that one cannot control the placement of the sensors. A prohibitively large number of randomly placed sensors…