This paper is dedicated to employ novel technique of deep learning for machines failures prediction. General idea of how to transform sensor data into suitable data set for prediction is presented. Then, neural network architecture that is very successful in solving such problems is derived. Finally, we present a case study for real industrial data of a gas turbine, including results of the experiments.

The use of machine learning methods in the case of incomplete data is an important task in many scientific fields, like medicine, biology, or face recognition. Typically, missing values are substituted with artificial values that are estimated from the known samples, and the classical machine learning algorithms are applied. Although this methodology is very common, it produces less informative data, because artificially generated values are treated in the same way as the known ones. In this paper, we consider a probabilistic representation of missing data, where each vector is identified with a Gaussian probability density function, modeling the uncertainty of absent attributes. This representation allows to construct an analogue of RBF kernel for incomplete data. We show that such a kernel can be successfully used in regression SVM. Experimental results confirm that our approach capture relevant information that is not captured by traditional imputation methods.

A novel model of dynamically programmed attributed regular grammars, DPAR, for the ECG diagnosis justification purposes is presented in the paper. A formal model, power properties and a case of DPAR grammar are described. The formalism of DPAR grammars allows to differentiate between certain subclasses of ECG phenomena.

In this paper we present a theorem concerning an equivalent statement of the Jacobian Conjecture in terms of Picard-Vessiot extensions. Our theorem completes the earlier work of T. Crespo and Z. Hajto which suggested an effective criterion for detecting polynomial automorphisms of affine spaces. We show a simplified criterion and give a bound on the number of wronskians determinants which we need to consider in order to check if a given polynomial mapping with non-zero constant Jacobian determinant is a polynomial automorphism. Our method is specially efficient with cubic homogeneous mappings introduced and studied in fundamental papers by H. Bass, E. Connell, D.Wright and L. Drużkowski

For a positive integer n, n-expandable deep pushdown automata always contain no more than n occurrences of non-input symbols in their pushdowns during any computation. As its main result, the present paper demonstrates that these automata are as powerful as the same automata with only two non-input pushdown symbols - $ and #, where # always appears solely as the pushdown bottom. The paper demonstrates an infinite hierarchy of language families that follows from this main result. The paper also points out that if # is the only non-input symbol in these automata, then they characterize the family of regular languages. In its conclusion, the paper suggests open problems and topics for the future investigation.

Size of the data is often a challenge in real-life applications. Especially when working with time series data, when next sample is produced every few milliseconds and can include measurement from hundreds of sensors, one has to take the dimensionality of the data into consideration. In this work, we compare various dimensionality reduction methods for time series data and check their performance on failure detection task. We work on sensory data coming from existing machines.