# 7th "Summer" School on Applied Mathematics and Informatics - Invited Tutorial Speakers

### Ľubomír Snoha (Slovakia)

Department of Mathematics
Faculty of Natural Sciences
Matej Bel University, Banská Bystrica

### Tentative topics:Obstacles to minimality

Let (X,f) be a dynamical system given by a space X and a continuous map f: X -> X. If x in X, the orbit of the point x is the set {x, f(x), f^2(x), ...}. If every orbit is dense in X, the system is called minimal. We also say that the map f itself is minimal. If a space X admits a minimal map, we call it a minimal space.

One of the important problems in topological dynamics is to decide whether a given space admits a minimal map/homeomorphism or not. We will give some examples and we will discuss some obstacles to minimality of a map/space.

### Marek Gagolewski (Poland)

Faculty of Mathematics and Information Science
Warsaw University of Technology
and
Department of Stochastic Methods
Systems Research Institute

### Tentative topic: Clustering on MSTs

Cluster analysis is one of the most commonly applied unsupervised machine learning techniques. Its aim is to automatically discover an underlying structure of a data set represented by a partition of its elements: mutually disjoint and nonempty subsets are determined in such a way that observations within each group are ``similar'' and entities in distinct clusters ``differ'' as much as possible from each other.
It turns out that two state-of-the-art clustering algorithms -- namely the Genie and HDBSCAN* methods -- can be computed based on the minimum spanning tree (MST) of the pairwise dissimilarity graph. Both of them are not only resistant to outliers and produce high-quality partitions, but also are relatively fast to compute.
The aim of this tutorial is to discuss some key issues of hierarchical clustering and explore their relations with graph and data aggregation theory.

### Eduard Sojka (Czech Republic)

Department of Computer science
Faculty of Electrical Engineering and Computer Science
VSB - Technical University of Ostrava

### Tentative Topic: Recognising the objects in the point clouds and depth maps using the 3D models

The problem can be regarded as challenging. The point clouds and the depth maps are now available thanks to the various types of sensors. The 3D models of the objects that are to be recognised can be easily produced by various CAD systems, for example. Recognising the objects described in this way in various environments seems to be possible. In the industrial context, it is a key task for automation of production. In spite of its clear usefulness, the solution to the problem is difficult if it should work in practice and in a real-life environment. The following recognition chain is discussed: (1) Computing the key points. (2) Computing the descriptors at the key points. (3) Reducing the descriptor size based on the principal component analysis. (4) Finding the correspondences between the key points of the scene and the key points of particular models. (5) Filtering the correspondences. (6) Recognizing the objects and their position based on the set of correspondences. (7) Verifying the recognition and the position that were found in the previous step. Several methods for solving each step are discussed. Notes on parallel CUDA implementation are presented too since a highly parallel implementation is inevitable. Practical demonstration is carried out.