An Extension of the Gamma Test Statistics to Binary Variables and Some Applications

In this paper, we discuss the problem of estimating the minimum error reachable by a regression model given a dataset, prior to learning. More specifically, we extend the Gamma Test estimates of the variance of the noise from the continuous case to the binary case. We give some heuristics for further possible extensions of the theory in the continuous case with the [Formula: see text]-norm and conclude with some applications and simulations. From the point of view of machine learning, the result is relevant because it gives conditions under which there is no need to learn the model in order to predict the best possible performance.

The number of failed components in a coherent working system when the lifetimes are discretely distributed

In this paper, we study the number of failed components of a coherent system. We consider the case when the component lifetimes are discrete random variables that may be dependent and non-identically distributed. Firstly, we compute the probability that there are exactly i, $$i=0,\ldots ,n-k,$$ i = 0 , … , n - k , failures in a k-out-of-n system under the condition that it is operating at time t. Next, we extend this result to other coherent systems. In addition, we show that, in the most popular model of independent and identically distributed component lifetimes, the obtained probability corresponds to the respective one derived in the continuous case and existing in the literature.

CONTINUOUS CASE STUDY AS AN EFFECTIVE METHOD OF ENGLISH LANGUAGE LEARNING BY FUTURE ENGINEERS

The present paper addresses the issue of teaching foreign language as an indispensable course at university. One of the demands to the training of future engineers is to prepare them for solving professional tasks and situations. A continuous case study method is one of the forms of problem-based learning which allows teachers to model fragments of future professional activity, its multicultural context. We suggest a continuous case study method as a powerful tool for modelling real professional activities, which contributes to the formation of professionally oriented English-language competence of future engineers. In our article, we aim to reveal the essence and stages of using the method of continuous case studies at English classes. We outlined the following methods: analysis, synthesis, generalization, systematization, inference, observation. In order to verify our statement, we conducted a continuous case study on the topic “Refutation of inaccurate information on technical operation and repair of lifting mechanisms at the enterprise”. As shown by the results of our research, a continuous case study method is a way of development of a professionally oriented English-language competence of the future engineers by involving them in solving imaginary professionally oriented problems through simulated engineering environment. It has been found that the use of a continuous case study method in the course “Practical Course of Foreign Language for Professional (Scientific) Purposes” contributes to the improvement of the future engineers’ professionally oriented foreign-language competencies in listening, speaking, reading; professionally oriented sociocultural, linguistic, educational, strategic and pragmatic competencies.

Automated seizure diagnosis system based on feature extraction and channel selection using EEG signals

Seizure is an abnormal electrical activity of the brain. Neurologists can diagnose the seizure using several methods such as neurological examination, blood tests, computerized tomography (CT), magnetic resonance imaging (MRI) and electroencephalogram (EEG). Medical data, such as the EEG signal, usually includes a number of features and attributes that do not contains important information. This paper proposes an automatic seizure classification system based on extracting the most significant EEG features for seizure diagnosis. The proposed algorithm consists of five steps. The first step is the channel selection to minimize dimensionality by selecting the most affected channels using the variance parameter. The second step is the feature extraction to extract the most relevant features, 11 features, from the selected channels. The third step is to average the 11 features extracted from each channel. Next, the fourth step is the classification of the average features using the classification step. Finally, cross-validation and testing the proposed algorithm by dividing the dataset into training and testing sets. This paper presents a comparative study of seven classifiers. These classifiers were tested using two different methods: random case testing and continuous case testing. In the random case process, the KNN classifier had greater precision, specificity, positive predictability than the other classifiers. Still, the ensemble classifier had a higher sensitivity and a lower miss-rate (2.3%) than the other classifiers. For the continuous case test method, the ensemble classifier had higher metric parameters than the other classifiers. In addition, the ensemble classifier was able to detect all seizure cases without any mistake.

Spectrum of the q-Schrödinger equation by means of the variational method based on the discrete q-Hermite I polynomials

In this work, the [Formula: see text]-Schrödinger equations with symmetric polynomial potentials are considered. The spectrum of the model is obtained for several values of [Formula: see text], and the limiting case as [Formula: see text] is considered. The Rayleigh–Ritz variational method is adopted to the system. The discrete [Formula: see text]-Hermite I polynomials are handled as basis in this method. Furthermore, the following potentials with numerous results are presented as applications: [Formula: see text]-harmonic, purely [Formula: see text]-quartic and [Formula: see text]-quartic oscillators. It is also shown that the obtained results confirm the ones that exist in the literature for the continuous case.

Continuous Empirical Wavelets Systems

The recently proposed empirical wavelet transform was based on a particular type of filter. In this paper, we aim to propose a general framework for the construction of empirical wavelet systems in the continuous case. We define a well-suited formalism and then investigate some general properties of empirical wavelet systems. In particular, we provide some sufficient conditions to the existence of a reconstruction formula. In the second part of the paper, we propose the construction of empirical wavelet systems based on some classic mother wavelets.