ELEMENTS OF ‘‘FUZZY LOGIC’’ AS A COMPONENT OF PROFESSIONAL AND PEDAGOGICAL TRAINING OF FUTURE MATHEMATICS AND INFORMATICS TEACHERS

Introduction: the article describes the application of fuzzy logic in the teaching of mathematics. This theory has a great creative ability to solve various pedagogical tasks for the implementation of the developing and applied functions of school mathematical education. The purpose of the article is to identify the possibilities of including the theory of fuzzy logic in the composition of professional training for future teachers of mathematics and computer science with the definition of content and methodological features. Materials and Methods: normative and programmatic documents describing the implementation of the training of future teachers of mathematics and computer science were studied during the writing of the article. The authors looked through the results of sociological surveys of students. Theoretical analysis and comparison of domestic and foreign approaches to the study of fuzzy logic were used, as well as analysis of the content and features of the professional training process for future teachers of mathematics and com¬puter science. Pedagogical measurements, generalization of the experience of teaching special subjects at the Penza State University, and pedagogical experiments were involved. Results: the need to study the elements of fuzzy mathematics in the school and the appropriateness of including this subject in the content of professional preparation of future mathematics and computer science teachers was demonstrated. Methodological prerequisites for studying this topic are defined, the Using Elements of Fuzzy Logic to Solve Pedagogical Problems intensive course is developed. Discussion and Conclusions: the fuzzy logic course allows to strengthen the motivational and developing potential of teachers of mathematics and computer science at school and university due to the non-conventionality of the involved thinking techniques and the possibility of connecting diverse subject interrelations. As the main way of preparing future teachers of mathematics and computer science for teaching students the elements of fuzzy mathematics, it is advisable to consider an elective course that includes elements of fuzzy logic and their pedagogical applications. Students used the materials quite effectively in the course of their practical work as teachers of mathematics and computer science in high school

Combination of Low-Temperature Electrosurgical Unit and Extractive Electrospray Ionization Mass Spectrometry for Molecular Profiling and Classification of Tissues

Real-time molecular navigation of tissue surgeries is an important goal at present. Combination of electrosurgical units and mass spectrometry (MS) to perform accurate molecular visualization of biological tissues has been pursued by many research groups. Determination of molecular tissue composition at a particular location by surgical smoke analysis is now of increasing interest for clinical use. However, molecular analysis of surgical smoke is commonly lacking molecular specificity and is associated with significant carbonization and chemical contamination, which are mainly related to the high temperature of smoke at which many molecules become unstable. Unlike traditional electrosurgical tools, low-temperature electrosurgical units allow tissue dissection without substantial heating. Here, we show that low-temperature electrosurgical units can be used for desorption of molecules from biological tissues without thermal degradation. The use of extractive electrospray ionization technique for the ionization of desorbed molecules allowed us to obtain mass spectra of healthy and pathological tissues with high degree of differentiation. Overall, the data indicate that the described approach has potential for intraoperative use

Validation of Breast Cancer Margins by Tissue Spray Mass Spectrometry

Current methods for the intraoperative determination of breast cancer margins commonly suffer from the insufficient accuracy, specificity and/or low speed of analysis, increasing the time and cost of operation as well the risk of cancer recurrence. The purpose of this study is to develop a method for the rapid and accurate determination of breast cancer margins using direct molecular profiling by mass spectrometry (MS). Direct molecular fingerprinting of tiny pieces of breast tissue (approximately 1 × 1 × 1 mm) is performed using a home-built tissue spray ionization source installed on a Maxis Impact quadrupole time-of-flight mass spectrometer (qTOF MS) (Bruker Daltonics, Hamburg, Germany). Statistical analysis of MS data from 50 samples of both normal and cancer tissue (from 25 patients) was performed using orthogonal projections onto latent structures discriminant analysis (OPLS-DA). Additionally, the results of OPLS classification of new 19 pieces of two tissue samples were compared with the results of histological analysis performed on the same tissues samples. The average time of analysis for one sample was about 5 min. Positive and negative ionization modes are used to provide complementary information and to find out the most informative method for a breast tissue classification. The analysis provides information on 11 lipid classes. OPLS-DA models are created for the classification of normal and cancer tissue based on the various datasets: All mass spectrometric peaks over 300 counts; peaks with a statistically significant difference of intensity determined by the Mann–Whitney U-test (p < 0.05); peaks identified as lipids; both identified and significantly different peaks. The highest values of Q2 have models built on all MS peaks and on significantly different peaks. While such models are useful for classification itself, they are of less value for building explanatory mechanisms of pathophysiology and providing a pathway analysis. Models based on identified peaks are preferable from this point of view. Results obtained by OPLS-DA classification of the tissue spray MS data of a new sample set (n = 19) revealed 100% sensitivity and specificity when compared to histological analysis, the “gold” standard for tissue classification. “All peaks” and “significantly different peaks” datasets in the positive ion mode were ideal for breast cancer tissue classification. Our results indicate the potential of tissue spray mass spectrometry for rapid, accurate and intraoperative diagnostics of breast cancer tissue as a means to reduce surgical intervention