DeHyFoNet: Deformable Hybrid Network for Formula Detection in Scanned Document Images

This work presents an approach for detecting mathematical formulas in scanned document images. The proposed approach is end-to-end trainable. Since many OCR engines cannot reliably work with the formulas, it is essential to isolate them to obtain the clean text for information extraction from the document. Our proposed pipeline comprises a hybrid task cascade network with deformable convolutions and a Resnext101 backbone. Both of these modifications help in better detection. We evaluate the proposed approaches on the ICDAR-2017 POD and Marmot datasets and achieve an overall accuracy of 96% for the ICDAR-2017 POD dataset. We achieve an overall reduction of error of 13%. Furthermore, the results on Marmot datasets are improved for the isolated and embedded formulas. We achieved an accuracy of 98.78% for the isolated formula and 90.21% overall accuracy for embedded formulas. Consequently, it results in an error reduction rate of 43% for isolated and 17.9% for embedded formulas.

Software tool for recognition of Ukrainian-language scientific articles

The problem of computer recognition, both separately printed characters and whole texts, which may contain mathematical formulas, and further saving the resulting document in the "Latex" format, is considered. The developed software implements the ability to recognize printable Latin, Cyrillic, Greek letters and special mathematical symbols. For this, a multilayer convolutional neural network built using the Keras machine learning library and additional validation heuristics are used. To improve the quality of neural network recognition, a sophisticated image processing mechanism has been developed that helps to remove noise from the image, eliminate errors associated with the inclination of characters, and correct character defects associated with the quality of the input image. Also implemented are mechanisms for collecting individual characters into words or mathematical formulas, reproducing the position of signs of indices and degrees, forming ordinary fractions and expressions under the root sign. The results of the recognized text are saved in a file with the simultaneous construction of the "latex" document structure. To demonstrate the capabilities of the developed software, a graphical user interface has been added, with which you can select and inspect the input image even before the start of recognition. During testing of the software, the recognition of images of different types was carried out: completely textual, mathematical formulas without text, mathematical formulas that are between blocks of text.

VALUE AT RISK AS A TOOL FOR ECONOMIC-MANAGERIAL DECISION-MAKING IN THE PROCESS OF TRADING IN THE FINANCIAL MARKET

Research background: Risk is an integral part of the world of financial markets today. One of the best known and widespread methods of quantifying the risk of a securities portfolio is the concept of value at risk (VaR). The method quantifies the maximum possible loss of a securities portfolio for specific variables. We used the work of Carol Alexander as a basis for our contribution, whence we borrowed mathematical formulas and derivatives of normal linear VaR and VaR scaling. Purpose of the article: The aim of this study is to design our own method of using the VaR calculation in the trading process and to practically verify the explanatory power of such calculation. To meet this goal, we used our own designed and adjusted formulas to calculate normal linear VaR and scaling VaR. Methods: The purpose of these adjusted formulas is to calculate specific levels of significance of specific scenarios of the course of trading positions, which represent the probability of their occurrence. Subsequently, we used regression analysis and constructed two regression models to verify that the significance levels themselves were significant variables, and that they could explain the variability of the explanatory variable to such an extent that they could be considered as strong predictors in the trading process. Findings & Value added: Based on such research, we find that the resulting levels of significance of our proposed VaR calculation formulas are significant. Based on the compiled regression models, we also find that the dependence we identified is a strong one and can therefore be considered as systematic. Nevertheless, the materiality levels could explain only a small proportion of the variability of the variable being explained, and therefore could not be considered as strong predictors and thus involved in the trading process itself.

On Estimating Reliability of a Stress – Strength Model in Case of Rayleigh Pareto Distribution

The stress – strength model is one of the models that are used to compute reliability. In this paper, we derived mathematical formulas for the reliability of the stress – strength model that follows Rayleigh Pareto (Rayl. – Par) distribution. Here, the model has a single component, where strength Y is subjected to a stress X, represented by moment, reliability function, restricted behavior, and ordering statistics. Some estimation methods were used, which are the maximum likelihood, ordinary least squares, and two shrinkage methods, in addition to a newly suggested method for weighting the contraction. The performance of these estimates was studied empirically by using simulation experimentation that could give more varieties for different-sized samples for stress and strength. The most interesting finding indicates the superiority of the proposed shrinkage estimation method.

MISCONCEPTION ANALYSIS IN TERMS OF STUDENT LEARNING STYLES

This study aims to determine students' misconceptions in social arithmetic material when viewed from student learning styles. The population in this study was 28 students of class VII F MTs Negeri 5 Cirebon. The research form used in this study is qualitative research, with a research strategy that is a case study. Data collection techniques used were 1) the observation method, 2) the tests method, 3) the questionnaire method, 4) the interview method is conducted for students who experience misconceptions after adjusting to the student's learning style. The results of this study are 1) Students who have a visual learning style do not experience misconceptions in mathematical concepts, but students experience misconceptions in the process of counting and translation. 2) Students who have auditorial learning styles, there are no misconceptions in mathematical concepts, but students experience errors in the final calculation process. 3) Students who have kinesthetic learning styles it is suspected that students have conceptual misconceptions because students do not understand the concept of the process including students who do not understand the mathematical formulas and values that must be used and students do not understand calculations. In general, the causes of misconceptions in students who have visual learning styles, auditory and kinesthetic, are derived from student understanding and teacher learning methods.

Economic and mathematical models for forecasting the development of the space industry

The article examines a problem relevant to the national security of the state, the possibility of applying economic and mathematical models to predict the prospects for the development of the space industry. In modern conditions the, space industry is seen as the basis for innovative development and economic security of the state, which is the driving force of economic development. After all, in order to sustainably develop the economy and achieve the indicators planned by the government, it is necessary to have a clear idea of the mechanisms and function of the system as a whole and its individual parts. That is why competent forecasting of the main indicators of the development of the space industry with the identification of key factors influencing it is especially relevant at the present stage. Forecasting of indicators, based on the construction of economic and mathematical models of industry development. It is determined that the construction of this model begins with the development of a specification of the model, which includes a verbal description of the study, followed by a presentation of the process of its operation in the form of mathematical formulas. It is important to clearly formulate and define the problem, as well as to identify all the factors and patterns that characterize the functioning of the system. Economic and mathematical models can increase the efficiency of the planning system of the industry and increase the accuracy of the process of forecasting its development. The successful development of the space industry today becomes a necessary condition for preserving national sovereignty both in the military-political aspect and in the field of information security.

Exact mathematical Formula that connect 6 dimensionless physical constants

In this paper are a new formula for the Planck length ℓpℓ and a new formula for the Avogadro number NA. Also 9 Mathematical formulas that connect dimensionless physical constants. The 6 dimensionless physical constants are the Proton to Electron Mass Ratio μ,the Fine-structure constant α,the ratio Ν1 of electric force to gravitational force between electron and proton,the Avogadro number NA,the Gravitational coupling constant αG for the electron and the gravitational coupling constant αG(p) of proton.

Observations about Lithuanian state-level maturity examination in mathematics

The article presents several observations about the examination papers of the state-level Maturity Examinations in Mathematics in the years 2014–2021 in Lithuania. Some inaccuracies were observed in the appendix of the paper titled ``Mathematical formulas'', in the wordings of the problems. Also the issue of proof problems in the examination is discussed. The purpose of these observations is to draw attention to areas for improvement in the examination system. The article presents the subjective opinion of the authors.

On New Types of Multivariate Trigonometric Copulas

Copulas are useful functions for modeling multivariate distributions through their univariate marginal distributions and dependence structures. They have a wide range of applications in all fields of science that deal with multivariate data. While there is a plethora of copulas, those based on trigonometric functions, especially in dimensions greater than two, have received much less attention. They are, however, of interest because of the properties of oscillation and periodicity of the trigonometric functions, which can appear in certain models of correlation of natural phenomena. In order to fill this gap, this paper introduces and investigates two new types of “multivariate trigonometric copulas”. Their main theoretical properties are studied, and some perspectives for applications are sketched for future work. In particular, we show that the proposed copulas are symmetric, not associative, with no orthant dependence, and with copula densities that have wide oscillations, which remains an uncommon property in the field. The expressions of their multivariate Spearman’s rho are also determined. Furthermore, the first type of the proposed copulas has the interesting feature of having a multivariate Spearman’s rho equal to 0 for all of the dimensions. Some graphic evidence supports the findings. Some mathematical formulas involving the product of n trigonometric functions may be of independent interest.