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Mathematical and graphical modelling of aerobatic flight trajectories

Linka A., Wroblewska A.

Journal of KONES

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2017

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Vol. 24, No. 3

181--187

EN

The article presents the current state of knowledge related to mathematical and graphical modelling of aircraft trajectories, particularly those of aerobatic flights. The first part of the article is an introduction to the subject of training and aerobatic flight. In the second chapter of this work, the authors describe the basic definitions related to mathematical modelling, rules for glider aerobatics (rules for the pilots and for the judges) and specification of navigation software, which is using during competitions. In the further part of the article the authors present example possibilities of application of the mathematical modelling tools in General Aviation and describe the possibilities of implementing the obtained models in selected navigation and tracking systems. In the same part of the article there is a description of the AeroSafetyShow Demonstrator PL – an intelligent system of flights supervision and safety (ASSD+PL), which will be using to compare the real flights trajectory and the models build trough the mathematical software. ASSD+PL in also only tracking system using by the judges at glider aerobatic World Championships. The aim of this article is to validate the applicability of the system comparing to the actual aircraft trajectory with the models referred to as ‘ideal’ for aerobatic purposes.

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On the key exchange and multivariate encryption with nonlinear polynomial maps of stable degree

Ustimenko V., Wroblewska A.

Annales Universitatis Mariae Curie-Skłodowska. Sectio AI, Informatica

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2013

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Vol. 13, no. 1

63--80

EN

We say that the sequence gn, n≥3, n→∞ of polynomial transformation bijective mapsof free module Kgn over commutative ring K is a sequence of stable degree if the order of gn is growing with n and the degree of each nonidentical polynomial map of kind gkn is an independent constant c. Transformation b = τgnkτ−1, where τ is the affine bijection, n is large and k is relatively small, can be used as a base of group theoretical Diffie-Hellman key exchange algorithm for the Cremona group C(Kn) of all regular automorphisms of Kn. The specific feature of this method is that the order of the base may be unknown for the adversary because of the complexity of its computation. The exchange can be implemented by tools of Computer Algebra (symbolic computations). The adversary can not use the degree of right handside in bx = d to evaluate unknown x in this form for the discrete logarithm problem. In the paper we introduce the explicit constructions of sequences of elements of stable degree for the cases c = 3 and c = n+2/4 for each commutative ring K containing at least 3 regular elements and discuss the implementation of related key exchange and multivariate map algorithms.

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Dynamical systems as the main instrument for the constructions of new quadratic families and their usage in cryptography

Ustimenko V., Wroblewska A.

Annales Universitatis Mariae Curie-Skłodowska. Sectio AI, Informatica

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2012

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Vol. 12, no. 3

65--74

EN

Let K be a finite commutative ring and f = f(n) a bijective polynomial map f(n) of the Cartesian power K^n onto itself of a small degree c and of a large order. Let f^y be a multiple composition of f with itself in the group of all polynomial automorphisms, of free module K^n. The discrete logarithm problem with the pseudorandom base f(n) (solvef^y = b for y) is a hard task if n is sufficiently large. We will use families of algebraic graphs defined over K and corresponding dynamical systems for the explicit constructions of such maps f(n) of a large order with c = 2 such that all nonidentical powers f^y are quadratic polynomial maps. The above mentioned result is used in the cryptographical algorithms based on the maps f(n) – in the symbolic key exchange protocols and public keys algorithms.

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Computer-aided interpretation of medical images: mammography case study

Przelaskowski A., Podsiadly-Marczykowska T., Wroblewska A., Boninski P., Bargiel P.

Machine Graphics and Vision

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2007

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Vol. 16, No. 3/4

347-375

EN

This paper presents the current limitations and challenges of computer-aided interpretation of radiological examinations. The analysis and the proposed improvements in interpretation arose from our experience, knowledge and observations with the collected suggestions and conclusions. The emphasized topics are as follows: computer understanding of human determinants of diagnosis, characteristics and enhancement of observer performance, diagnostic accuracy measures of image examinations, computer-aided diagnosis (CAD) systems, and numerical description of medical image-based content. All of these diagnosis support concepts can be integrated into an intelligent diagnosis interface and enhanced, basing on a formal description of semantic image content, i.e. ontology implied as a reliable, dynamic platform of medical knowledge, useful for diagnosis. CAD for mammography and content-based image indexing supported by the ontology were integrated for the needs of an enhanced diagnostic workstation applied in tele-information medical systems. A design of an effective human-machine interface has arisen as the leading problem of the current challenges.