Categories without structures

The popular view according to which Category theory provides a support for Mathematical Structuralism is erroneous. Category-theoretic foundations of mathematics require a different philosophy of mathematics. While structural mathematics studies invariant forms (Awodey) categorical mathematics studies covariant transformations which, generally, don t have any invariants. In this paper I develop a non-structuralist interpretation of categorical mathematics and show its consequences for history of mathematics and mathematics education.Comment: 28 page

Fast and robust image feature matching methods for computer vision applications

Service robotic systems are designed to solve tasks such as recognizing and manipulating objects, understanding natural scenes, navigating in dynamic and populated environments. It's immediately evident that such tasks cannot be modeled in all necessary details as easy as it is with industrial robot tasks; therefore, service robotic system has to have the ability to sense and interact with the surrounding physical environment through a multitude of sensors and actuators. Environment sensing is one of the core problems that limit the deployment of mobile service robots since existing sensing systems are either too slow or too expensive. Visual sensing is the most promising way to provide a cost effective solution to the mobile robot sensing problem. It's usually achieved using one or several digital cameras placed on the robot or distributed in its environment. Digital cameras are information rich sensors and are relatively inexpensive and can be used to solve a number of key problems for robotics and other autonomous intelligent systems, such as visual servoing, robot navigation, object recognition, pose estimation, and much more. The key challenges to taking advantage of this powerful and inexpensive sensor is to come up with algorithms that can reliably and quickly extract and match the useful visual information necessary to automatically interpret the environment in real-time. Although considerable research has been conducted in recent years on the development of algorithms for computer and robot vision problems, there are still open research challenges in the context of the reliability, accuracy and processing time. Scale Invariant Feature Transform (SIFT) is one of the most widely used methods that has recently attracted much attention in the computer vision community due to the fact that SIFT features are highly distinctive, and invariant to scale, rotation and illumination changes. In addition, SIFT features are relatively easy to extract and to match against a large database of local features. Generally, there are two main drawbacks of SIFT algorithm, the first drawback is that the computational complexity of the algorithm increases rapidly with the number of key-points, especially at the matching step due to the high dimensionality of the SIFT feature descriptor. The other one is that the SIFT features are not robust to large viewpoint changes. These drawbacks limit the reasonable use of SIFT algorithm for robot vision applications since they require often real-time performance and dealing with large viewpoint changes. This dissertation proposes three new approaches to address the constraints faced when using SIFT features for robot vision applications, Speeded up SIFT feature matching, robust SIFT feature matching and the inclusion of the closed loop control structure into object recognition and pose estimation systems. The proposed methods are implemented and tested on the FRIEND II/III service robotic system. The achieved results are valuable to adapt SIFT algorithm to the robot vision applications

Grounding semantics in robots for Visual Question Answering

In this thesis I describe an operational implementation of an object detection and description system that incorporates in an end-to-end Visual Question Answering system and evaluated it on two visual question answering datasets for compositional language and elementary visual reasoning

The use of data-mining for the automatic formation of tactics

This paper discusses the usse of data-mining for the automatic formation of tactics. It was presented at the Workshop on Computer-Supported Mathematical Theory Development held at IJCAR in 2004. The aim of this project is to evaluate the applicability of data-mining techniques to the automatic formation of tactics from large corpuses of proofs. We data-mine information from large proof corpuses to find commonly occurring patterns. These patterns are then evolved into tactics using genetic programming techniques

Information Technology and Pragmatic Analysis

Similarity method has been in science for several centuries. The basis of the study is closely connected with mathematical linguistics. This approach has allowed obtaining new results in the analytical geometry, which, in turn, is used in different applications in information technology. The results are described briefly. Binary relations in linguistics and geometry are compared with the position of system analysis. The modified hypothesis of space as a binary structure is put forward on the basis of singular linear transformations. The hypothesis of the human sensory system is given shortly. Architecture computing appliance for solving this class of problems is proposed. The modified method is also applied in pattern recognition. The presence of symmetry in natural languages is shown briefly