Dualization of a monotone Boolean function on a finite lattice can be represented by transforming the set of its minimal 1 values to the set of its maximal 0 values. In this paper we consider finite lattices given by ordered sets of their meet and join irreducibles (i.e., as a concept lattice of a formal context). We show that in this case dualization is equivalent to the enumeration of so-called minimal hypotheses. In contrast to usual dualization setting, where a lattice is given by the ordered set of its elements, dualization in this case is shown to be impossible in output polynomial time unless P = NP. However, if the lattice is distributive, dualization is shown to be possible in subexponential time.
We propose a new mathematical growth model of primary tumor and primary metastases which may help to improve predicting accuracy of breast cancer process using an original mathematical model referred to CoM-IV and corresponding software. The CoM-IV model and predictive software: a) detect different growth periods of primary tumor and primary metastases; b) make forecast of patient survival; c) have higher average prediction accuracy than the other tools; d) can improve forecasts on survival of BC and facilitate optimisation of diagnostic tests. The CoM-IV enables us, for the first time, to predict the whole natural history of primary tumor and primary metastases growth on each stage (pT1, pT2, pT3, pT4) considering only on primary tumor sizes. Summarising: CoM-IV a) describes correctly primary tumor and primary distant metastases growth of IV (T1-4N0-3M1) stage with (N1-3) or without regional metastases in lymph nodes (N0); b) facilitates the understanding of the appearance period and manifestation of primary metastases.
Nowadays, mind mapping is rather popular educational technique. Like any other learning tools, mind maps became a part of modern educational trends like blended learning and computer-supported collaborative learning. Lots of mind mapping software tools are adopted to teaching and learning routines such as educational content delivery or assessment. This paper focuses on the additional automatic evaluation of digital educational mind maps gained from the existing procedures of assessments. The review of automatic graders which support the evaluation process demonstrates that some systematical work is done in automation grading by comparing students’ mind maps with a template. But lots of questions about automatic mind maps’ scoring by retrieving the data from a scored mind map are still open. This paper introduces the automatic grader for educational mind maps (AGEMM) which acts like a teacher’s assistant and calculates several quantitative metrics. The AGEMM is implemented as a web-service and interacted with mind maps prepared in the Coggle web-service through its API. The AGEMM is adopted to a bachelor course. Results demonstrate that scores from the AGEMM may be transformed to scales or criterial levels which are used to evaluation. Moreover, the AGEMM application revealed several problems and shew lines of development which we discuss in the paper.
The cornerstone of retail banking risk management is the estimation of the expected losses when granting a loan to the borrower. The key driver for loss estimation is probability of default (PD) of the borrower. Assessing PD lies in the area of classification problem. In this paper we apply FCA query-based classification techniques to Kaggle open credit scoring data. We argue that query based classification allows one to achieve higher classification accuracy as compared to applying classical banking models and still to retain interpretability of model results, whereas black-box methods grant better accuracy but diminish interpretability.