Graph Of Function Research Articles

A Novel Classification Framework Using the Graph Representations of Electroencephalogram for Motor Imagery Based Brain-Computer Interface

The motor imagery (MI) based brain-computer interfaces (BCIs) have been proposed as a potential physical rehabilitation technology. However, the low classification accuracy achievable with MI tasks is still a challenge when building effective BCI systems. We propose a novel MI classification model based on measurement of functional connectivity between brain regions and graph theory. Specifically, motifs describing local network structures in the brain are extracted from functional connectivity graphs. A graph embedding model called Ego-CNNs is then used to build a classifier, which can convert the graph from a structural representation to a fixed-dimensional vector for detecting critical structure in the graph. We validate our proposed method on four datasets, and the results show that our proposed method produces high classification accuracies in two-class classification tasks (92.8% for dataset 1, 93.4% for dataset 2, 96.5% for dataset 3, and 80.2% for dataset 4) and multiclass classification tasks (90.33% for dataset 1). Our proposed method achieves a mean Kappa value of 0.88 across nine participants, which is superior to other methods we compared it to. These results indicate that there is a local structural difference in functional connectivity graphs extracted under different motor imagery tasks. Our proposed method has great potential for motor imagery classification in future studies.

Использование метода комплексного электрического модуля для определения релаксационных параметров диэлектриков с высокой электропроводностью

The paper submits that the method of a complex electrical module allows to investigate the characteristics of relaxation processes in dielectrics having high electrical conductivity. The method makes it possible to determine the relaxation parameters of dielectrics when relaxation peaks are absent in the frequency dependence of dielectric losses ε”(f). In turn, relaxation peaks can be detected on the frequency dependences M”(f). In addition, a function graph M’(f) is plotted. Simultaneous approximation of the curves M”(f) and M’(f) in the frequency range corresponding to the maximum M” by the Havriliak–Negami equation for the electrical module makes it possible to determine the relaxation parameters α, β, τ0.

Segmentation and identification of spectral and statistical textures for computer medical diagnostics in dermatology.

An important component of the computer systems of medical diagnostics in dermatology is the device for recognition of visual images (DRVI), which includes identification and segmentation procedures to build the image of the object for recognition. In this study, the peculiarities of the application of detection, classification and vector-difference approaches for the segmentation of textures of different types in images of dermatological diseases were considered. To increase the quality of segmented images in dermatologic diagnostic systems using a DRVI, an improved vector-difference method for spectral-statistical texture segmentation has been developed. The method is based on the estimation of the number of features and subsequent calculation of a specific texture feature, and it uses wavelets obtained by transforming the graph of the power function at the stage of contour segmentation. Based on the above, the authors developed a modulus for spectral-statistical texture segmentation, which they applied to segment images of psoriatic disease; the Pratt's criterion was used to assess the quality of segmentation. The reliability of the classification of the spectral-statistical texture images was confirmed by using the True Positive Rate (TPR) and False Positive Rate (FPR) metrics calculated on the basis of the confusion matrix. The results of the experimental research confirmed the advantage of the proposed vector-difference method for the segmentation of spectral-statistical textures. The method enables further supplementation of the vector of features at the stage of identification through the use of the most informative features based on characteristic points for different degrees and types of psoriatic disease.

Seizure Onset Zone Identification From iEEG: A Review

This paper discusses the various methods of identifying the seizure onset zone (SOZ) from the intracranial electroencephalography (iEEG) data. Epilepsy, also known as seizure disorder, is a neurological condition caused due to disruption in the regular electrical communication within the neuron network. With almost a third of epileptic conditions being drug-resistant and several cases with no known cause, there is a need to resort to alternative treatment methods such as neurostimulation or surgical resection. Both these methods require the identification of regions within the brain that need to be stimulated or resected. For most of the patients, this corresponds to the part that initiates the seizure. These are called seizure onset zone (SOZ) or epileptogenic zone (EZ). Epileptologists locate the SOZ by analyzing the iEEG data of patients suffering from seizures. This, however, is time-consuming and can be prone to human error. Thus, there has been significant research on the automatic detection of SOZ. High-frequency oscillations (HFOs), characterized by iEEG oscillations above 80 Hz, are one of the most promising candidates for identifying SOZ. Functional connectivity and graph theory measures have also distinguished SOZ and non-SOZ regions using different features. Newer works on phase-amplitude coupling have also shown promising results. With the increased data availability, it has also become possible to build supervised learning algorithms to improve the predictive power of anomaly detection algorithms used to localize SOZ.

ЗАСТОСУВАННЯ СКМ MAPLE ДЛЯ ПОБУДОВИ 3D ГРАФІКІВ В ЗАДАЧАХ ОБЧИСЛЕННЯ ОБ’ЄМУ ФІГУР

Every year the number of works devoted to the search for methods and techniques for introducing computer mathematics systems for teaching higher mathematics is increasing. The main place among them is occupied by the Maple computer mathematics system, which is one of the leaders in universal systems and allows the user to use an intelligent environment for mathematical research. This paper emphasizes that the most valuable developments of a theoretical and applied nature on the use of computer mathematics systems in teaching higher mathematics should include materials related to improving visibility, as well as the formation of students' skills and abilities in solving typical problems of higher mathematics. The problems of introduction and adaptation of the Maple computer mathematics system in the educational process of the institu-tion of higher education in teaching the course of higher mathematics are considered. The use of the Maple computer mathematics system provides an oppor-tunity to optimize the educational process and activate the organization of students' independent work to consolidate the educa-tional material. The paper adapts the use of the Maple computer mathematics system graphics package capabilities to build 3D graphics in order to improve clarity in the tasks of calculating the volume of a spatial figure. Part of the mathematical apparatus and the developed code fragments in the Maple computer mathematics system make it possible to automatically obtain the line of intersection of graphs of functions, build the corresponding surfaces and figures when solving typical problems of higher mathematics. The paper substantiates the need to design educational problems of a new type, taking into account the need to use modern information and communication technologies for solving them, in particular Maple computer mathematics systems.

APPLICATION OF IGS GEOGEBRA IN THE STUDY OF HIGHER MATHEMATICS BY STUDENTS OF TECHNICAL INSTITUTIONS OF HIGHER EDUCATION

Introduction. Recently, the use of various packages of computer mathematics systems to improve the efficiency of the educational process has become relevant, especially during distance learning. One of the most promising areas in the technology of higher mathematics is the introduction and development of interactive geometric environments, and, as a consequence, to identify effective ways to use them in the educational process. The use of software is especially relevant in higher mathematics classes. The above software packages help to perform calculations in a short time, allow you to build graphs of functions and three-dimensional bodies and more. Purpose. Possibilities of application of the interactive geometric environment GeoGebra for the purpose of the organization of research activity of students of technical specialties during employment in higher mathematics are considered Methods. The article substantiates the relevance of using the cognitive-visual approach in the process of teaching students of technical specialties of higher mathematics in institution of higher education, considers the essence of this approach, as well as its implementation in teaching higher mathematics using educational software products using interactive geometric environment GeoGebra Results. Possibilities of separate software products of professional and educational purpose are considered, advantages of the interactive geometrical environment GeoGebra are listed, the example of its use in the course of training of higher mathematics of students of technical institution of higher education is given, namely: possibilities of application for the purpose of organization of research activity of students. in particular, remote, and the use of second-order image curves, which allows the visualization of geometric objects under study. Also, the stages of the process of preparation for the application of the interactive geometric environment GeoGebra were identified. Originality. For the first time with students majoring in 151 Automation and Computer-Integrated Technologies, we used distance learning to study one of the problems of solving problems using the interactive geometric environment GeoGebra. Conclusion. Solving our geometric problems, performed using the interactive geometric environment GeoGebra, allows students to see not only the visual construction of geometric objects, but also to form elements of the algorithm for solving practical problems in analytical geometry and lay the foundation for calculation the length of the arc, the area of the figure, the volumes of bodies in parallel section and the body of rotation, the surface area of the body of rotation, which is discussed in the next section "Application of the definite integral". The dynamic capabilities of GeoGebra to study the change in the shape of the projections of the spatial curve when changing the parameters in the equations of surfaces. The use of GeoGebra to solve problems in the course of higher mathematics in technical free economic education increases the motivation and interest of students, creates conditions for the formation of research skills, prepares students for the effective use of ICT in their future careers.

О НЕКОТОРЫХ ПОНЯТИЯХ И ТЕОРЕМАХ МАТЕМАТИЧЕСКОГО АНАЛИЗА

The article presents the results obtained by the author in search of innovative forms and methods of presenting educational and methodological information in order to achieve a better understanding, assimilation and consolidation of the educational material read by students, and at the output – the ability to apply the knowledge gained in practice. Based on the axiom of continuity of the set of real numbers, definitions of a continuous set, a discontinuous set with a jump and with a gap are given. As well as the examples. The use of symbolism and the laws of mathematical logic, as also the equivalence of the necessary condition for the existence of a mathematical concept and a sufficient condition for the non-existence of this concept, allowed us to obtain a number of significant results with regard to the continuity of the function, the local extremum of the function and the inflection point of the function graph in the Roll theorem. The article shows the existence of an alternative to the standard form of presentation of the necessary condition for the continuity of a function at a point and the necessary condition for the continuity of a function on a set. A new criterion for the continuity of a function on a set is presented, which greatly simplifies the study of a function for continuity on a set. The consequence of the criterion was a new definition of the continuity of a function on a set. Heaviside and Dirichlet functions are given as an example. Some concepts and theorems set forth in the article are used by the author in classes on mathematical analysis.

Predicting Logarithm of Real Numbers to any Real Number Base

This paper aims to propose an algorithm that can predict the values of logarithmic function for any domain and for any bases with minimum possible error using basic mathematical operations. It talks about a univariate quadratic function that overlaps with the graph of the common logarithmic function to some extent, and using this resemblance to fullest advantage. It proposes a formula and certain algorithms based on the same formula.

Physics Simulation with Excel Spreadsheet

this study present several examples of using Excel spreadsheets to study and simulate physical phenomena, namely projectile motion, falling motion in The air, The wave function of particles in a one-dimensional box, and nuclear radioactive decay. Spreadsheets are used to analyze the motion of projectiles with and without resistance, falling objects with different terminal velocities, graphs of wave functions and probabilities with different values of n, i.e. n=1 to n=4, and nuclear decay with different probability values of P. The use of excel spreadsheets has proven to be very useful in the physics learning process, namely the rapid response to changes in data and graphs, according to the values given

Kriteria Buku Referensi Media Pembelajaran Matematika Yang Diperlukan Bagi Guru-Guru SMP Di Mataram

The purpose of this study was to determine the criteria for a mathematics learning media reference book that is needed for junior high school mathematics teachers in the city of Mataram. The research begins with a survey on whether learning mathematics requires media, then identifies the frequency with which teachers use media in learning mathematics, as well as the reasons teachers never or rarely use media in learning mathematics. Based on the survey, it was found that teachers need reference books to develop mathematics learning media, so it is necessary to develop the criteria for the required reference books. Furthermore, a literature review was conducted to compare the needs (ideal conditions) for Learning Media reference books with the current state (real conditions). Conclusion The results of the study show that the materials that require media are: arithmetic operations Integers and fractions, Linear Equations, Sets and Venn Diagrams, geometry, Function values, function graph sketches, slopes of lines, Pythagoras, circles, tangents, inner circles and the outer circle of a triangle, the properties of geometric figures, similarity, congruence, cylinders, cones, and spheres. In addition, the media needed are Concept Maps, Informative Power Points, Interactive Power Points, Student Worksheets, Learning Videos, Teaching Aids, and GeoGebra. Furthermore, the criteria for a valid book were developed based on the results of the study which included 4 aspects, namely material aspects, language, presentation of material, and graphics

Theoretical Study and Numerical Experiment on the Influence of Trend Changes on Correlation Coefficient

When one of two time series undergoes an obvious change in trend, the correlation coefficient between the two will be distorted. In the context of global warming, most meteorological time series have obvious linear trends, so how do variations in these trends affect the correlation coefficient? In this paper, the correlation between time series with trend changes is studied theoretically and numerically. Adopting the trend coefficient, which reflects the nature and size of the trend change, we derive a formula r = f(k, l) for the correlation coefficient of time series X and Y with respective trend coefficients k and l. Analysis of the function graph shows that the changes in correlation coefficient with respect to the trend coefficients produce a twisted saddle surface, and the saddle point coordinates are given by the trend coefficients of time series X and Y with the opposite signs. The curve f(k, l) = f(0, 0) divides the coordinate planes into regions where f(k, l) > f(0, 0) and f(k, l) < f(0, 0). When the trend coefficients k and l are very small and the correlation coefficient is also very small, then k > 0 and l > 0 (or k < 0 and l < 0) amplifies a positive correlation, whereas k > 0 and l < 0 (or k < 0 and l > 0) amplifies a negative correlation, as found in previous research. Finally, experiments using meteorological data verify the reliability and effectiveness of the theory.

Analisis Miskonsepsi Siswa SMP pada Materi Relasi dan Fungsi Ditinjau dari Gaya Kognitif FI Dan FD

Misconception occurs when a person's conception of material differs from the conception stated by experts in the field. The misconceptions are related to the cognitive style of students. The purpose of this study was to describe the misconceptions experienced by students with Field-Independent (FI) and Field-Dependent (FD) cognitive styles on the topics of relations and functions. This type of research was qualitative research. The research subjects are students of class VIII-I SMPN 1 Jogoroto. Data collection techniques were tests and interviews. The results showed that the misconceptions of FI students were the concept of function, the concept of function in the arrow diagram, and the concept of function graphs and non-function graphs. The misconceptions experienced by FD students were the concept of function, the concept of function in the arrow diagram, the concept of codomain and range, the concepts of function graphs and non-function graphs.

Bifurcations in a Time-Delayed Birhythmic Biological System with Fractional Derivative and Lévy Noise

The birhythmic oscillation is of great significance in biology and engineering, and this paper presents a bifurcation analysis in a time-delayed birhythmic oscillator containing fractional derivative and Lévy noise. The numerical method is used to explore the influence of various parameters on the bifurcation of the birhythmic system, and the role of fractional derivative and Lévy noise in inducing or inhibiting birhythmicity in a time-delayed birhythmic biological system is examined in this work. First, we use a numerical method to calculate the fractional derivative, which has a fast calculation speed. Then the McCulloch algorithm is employed to generate Lévy random numbers. Finally, the stationary probability density function graph of the amplitude is obtained by Monte Carlo simulation. The results show that the fractional damping and Lévy noise can effectively control the characteristics of the birhythmic oscillator, and the change of the parameters (except the skewness parameter) can cause the system bifurcation. In addition, this article further discusses the interaction of fractional derivative and time delay in a birhythmic system with Lévy noise, proving that adjusting parameters of time delay can lead to abundant bifurcations. Our research may help to further explore the bifurcation phenomenon of birhythmic biological system, and has a practical significance.

Measuring the derivative using surfaces

Abstract Students need a robust understanding of the derivative for upper-division mathematics and science courses, including thinking about derivatives as ratios of small changes in multivariable and vector contexts. In Raising Calculus to the Surface activities, multivariable calculus students collaboratively discover properties of derivatives by using tangible tools to solve context-rich problems. In this paper, we present examples of student reasoning about derivatives during the first of a sequence of three Raising Calculus activities. In this sequence, students work collaboratively on dry-erasable surfaces (tangible graphs of functions of two variables) using an inclinometer, a tool that can measure derivatives in any direction on the surfaces, to invent procedures to determine derivatives in any direction. Since students are not given algebraic expressions for the underlying functions, they must coordinate conceptual and geometric notions of derivatives, building on their understandings from introductory differential calculus. We discuss examples of student reasoning that demonstrate how the activity supports student realization of the need to define a path, attend to direction and the orientation of the coordinate axes and recognize covariation between related quantities. This first activity enables students to initially recognize the ratio of small changes approach to derivatives. We briefly describe how students utilize the ratio of small changes approach in subsequent activities as they measure partial derivatives on surfaces (using an inclinometer) and on contour maps.

Bound Estimation of Some Special Functions

This article estimates bounds of several special functions. It also gives mathematical proofs and graphs of the corresponding functions. The results are applicable in aspect of inequalities.

Geometric measure theory and differential inclusions

In this paper we consider Lipschitz graphs of functions which are stationary points of strictly polyconvex energies. Such graphs can be thought as integral currents, resp. varifolds, which are stationary for some elliptic integrands. The regularity theory for the latter is a widely open problem, in particular no counterpart of the classical Allard’s theorem is known. We address the issue from the point of view of differential inclusions and we show that the relevant ones do not contain the class of laminates which are used in [23] and [26] to construct nonregular solutions. Our result is thus an indication that an Allard’s type result might be valid for general elliptic integrands. We conclude the paper by listing a series of open questions concerning the regularity of stationary points for elliptic integrands.

Using digital tasks when teaching mathematics at school

The article discusses various types of digital math tasks to be performed on computers or tablets. The experience of creating digital tasks in mathematics with complex answers from the point of view of automatic verifcation: algebraic expressions, geometric constructions, graphs of functions, etc. is discussed. As an example of the use of digital tasks, the use of digital materials for preparing schoolchildren for the Unifed State Exam in mathematics of a profle level is considered. The article also discusses various forms of using simulators and tests in the educational process: supporting the independent activities of students in the full-time educational process, supporting online learning with a teacher in the context of the coronavirus pandemic, independent online learning without a teacher based on specially prepared and structured training courses. In the latter case, in addition to simulators, it is proposed to use other digital educational resources to increase the visibility of the educational material and organize self-control of learning outcomes: videos, slides, dynamic models, training exercises for problems with a detailed answer to the options for the USE control and measuring materials.

Functional Complex Networks Based on Operational Architectonics: Application on EEG-based Brain–computer Interface for Imagined Speech

A new method for analyzing brain complex dynamics and states is presented. This method constructs functional brain graphs and is comprised of two pylons: (a) Operational architectonics (OA) concept of brain and mind functioning. (b) Network neuroscience. In particular, the algorithm utilizes OA framework for a non-parametric segmentation of EEG signals, which leads to the identification of change points, namely abrupt jumps in EEG amplitude, called Rapid Transition Processes (RTPs). Subsequently, the time coordinates of RTPs are used for the generation of undirected weighted complex networks fulfilling a scale-free topology criterion, from which various network metrics of brain connectivity are estimated. These metrics form feature vectors, which can be used in machine learning algorithms for classification and/or prediction. The method is tested in classification problems on an EEG-based BCI data set, acquired from individuals during imagery pronunciation tasks of various words/vowels. The classification results, based on a Naïve Bayes classifier, show that the overall accuracies were found to be above chance level in all tested cases. This method was also compared with other state-of-the-art computational approaches commonly used for functional network generation, exhibiting competitive performance. The method can be useful to neuroscientists wishing to enhance their repository of brain research algorithms.

Recognition of flying small target based on enhanced quadratic time-frequency analysis

UAVs (Unmanned Aerial Vehicles, UAVs) are flying targets that sail at low altitudes, are slower and smaller in size. Nowadays, the task of detecting and distinguishing flying small targets is very difficult, so how to efficiently recognize flying small targets in real time is a key issue of current research. In order to solve this problem, this paper proposes a method of using pseudo-WVD and image fusion to represent the characteristics of UAVs. First, the SMMWR (Single-mode millimeter wave radar, SMMWR) equipment is used to collect the echo signals of various types of UAVs, and at the same time, the two-dimensional FFT is used to extract the target micro-motion signals in the distance dimension. Secondly, PWVD is used to generate time-frequency graphs of different window functions. Finally, the images fused based on principal component analysis are sent to AlexNet for training. The result proves that the accuracy of recognition rate based on AlexNet can be 93.75%.

On tameness of zonoids

We prove that in a globally subanalytic family of convex bodies the subfamily of zonoids is log-analytic, and in particular it is definable in the o–minimal structure generated by globally subanalytic sets and the graph of the exponential function. This result establishes a connection between Model theory and Functional analysis.