Additive Convolution Research Articles

Conditionally monotone cumulants via shuffle algebra

In this work, we study conditional monotone cumulants and additive convolution in the shuffle-algebraic approach to non-commutative probability. We describe c-monotone cumulants as an infinitesimal character and identify the c-monotone additive convolution as an associative operation in the set of pairs of characters in the dual of a double tensor Hopf algebra. In this algebraic framework, we understand previous results on c-monotone cumulants and prove a combinatorial formula that relates c-free and c-monotone cumulants. We also identify the notion of [Formula: see text]-Boolean cumulants in the shuffle-algebraic approach and introduce the corresponding notion of [Formula: see text]-monotone cumulants as a particular case of c-monotone cumulants.

Stability of Cauchy–Stieltjes Kernel Families by Free and Boolean Convolutions Product

Let F(νj)={Qmjνj,mj∈(m−νj,m+νj)}, j=1,2, be two Cauchy–Stieltjes Kernel (CSK) families induced by non-degenerate compactly supported probability measures ν1 and ν2. Introduce the set of measures F=F(ν1)⊞F(ν2)={Qm1ν1⊞Qm2ν2,m1∈(m−ν1,m+ν1)andm2∈(m−ν2,m+ν2)}. We show that if F remains a CSK family, (i.e., F=F(μ) where μ is a non-degenerate compactly supported measure), then the measures μ, ν1 and ν2 are of the Marchenko–Pastur type measure up to affinity. A similar conclusion is obtained if we substitute (in the definition of F) the additive free convolution ⊞ by the additive Boolean convolution ⊎. The cases where the additive free convolution ⊞ is replaced (in the definition of F) by the multiplicative free convolution ⊠ or the multiplicative Boolean convolution are also studied.

Density of the Free Additive Convolution of Multi-cut Measures

Abstract We consider the free additive convolution semigroup $\lbrace \mu ^{\boxplus t}:\,t\ge 1\rbrace $ and determine the local behavior of the density of $\mu ^{\boxplus t}$ at the endpoints and at any singular point of its support. We then study the free additive convolution of two multi-cut probability measures and show that its density decays either as a square root or as a cubic root at any endpoint of its support. The probability measures considered in this paper satisfy a power law behavior with exponents strictly between $-1$ and $1$ at the endpoints of their supports.

Выбор альтернативы в принятии управленческих решений методом оценочных таблиц

The proposed methodology is based on the method of evaluation tables using expert assessments. The method makes it quite easy to convert criteria of various dimensions into dimensionless ones for subsequent comparison and integral evaluation, for example, using an additive convolution criterion. Management decision options are alternatives that are compared according to specific evaluation parameters (criteria). An example of constructing a normalized matrix of pairwise comparison of criteria is shown. The research material allows for a numerical assessment of various alternatives with sufficient reliability.

Choice of machine learning models for predicting the development of psychological disorders in people with hypothireosis and hyperthireosis

The subject of this article is endocrinological diseases, namely, the analysis of complications in people with hypothyroidism and hyperthyroidism. It is known that these diseases occur asymptomatically or in a way that may indicate other possible diseases, so people do not suspect what exactly they are suffering from. Later, the diseases develop to the point where complications occur in the body, some of the most dangerous of which are psychological disorders: depression, mania, aggression, etc. Therefore, the aim of this work is to develop methods for predicting the occurrence of neurological deterioration in people who have already been diagnosed with endocrinological diseases. The article solves the problem of choosing the best models for predicting the occurrence of psychological disorders in people with endocrinological problems. Machine learning methods that are widespread in the medical field were analyzed and one of them was chosen that more optimally solves all the tasks of the task. The selection of criteria took into account potential problems with medical and psychological data. The method used was linear additive convolution, which is used to select the best alternatives according to the results, with the Pareto principle, which aims to exclude less suitable alternatives because all the features have lower values than in other options. For the experiment, all features were converted into quantitative ones to calculate convolution values. The evaluation criteria are given in the paper. The following results were obtained: the forecasting model in further study of this problem will be a random forest. Conclusions: the forecasting methods were studied and a more optimal model was chosen using linear additive convolution, namely, the random forest algorithm, its advantages and disadvantages were considered. A more detailed analysis of its development will be presented in the following articles. A mathematical description of the chosen forecasting method is provided, which includes potential ways of implementation and steps for building an algorithm for one of these methods.

DEVELOPMENT OF A MULTICRITERIA MODEL OF DISTRIBUTION OF ADMISSION QUOTAS

Objective. The main problem of higher education institutions is that there is a well-developed system of approval and distribution of admission control figures between educational organizations, but there is no unified system of distribution of budgetary and paid places within enlarged groups of directions and specialties (UGSS). In this regard, it is proposed to develop a multi-criteria model for the distribution of budgetary and paid places within the USGS, which will be a tool for analyzing the demand for certain directions among applicants and considering the risks of not filling the directions, which may be allocated more than the number of applicants.
 Method or methodology of work. The research is based on multi-criteria optimization, data normalization, additive convolution, construction of the BCG matrix.
 Results. The developed model makes it possible to compile the optimal distribution for the university, which can be used both for a specific USGS and for the whole university, which is ensured by multilevel optimization, which was used to solve the problem. Also the model allows to take into account the risks of not filling the places and minimize them.
 Scope of application of the results. The results of the study can be applied in the field of enrollment forecasting.

Time gap of the impact of risk insurance, life insurance and reinsurance on social progress: The case of Ukraine

The paper examines, using the example of Ukraine from 2003 to 2020, how and to what extent the development of various segments of the insurance market (risk insurance, life insurance, and reinsurance) influences the overall level of social progress. It also identifies the time gaps through which this influence manifests. The study creates a single measure that looks at various aspects such as social class differences, spending patterns, income changes, and government social spending (their standardized values, weighed by the principal component method, integrated through additive convolution). Using VAR modeling, the impact of the development indicators of different segments of the insurance market (risk insurance, life insurance, and reinsurance) at the current moment and with lags of one, two, and three years is investigated, as well as the level of social progress in Ukraine in previous years. The modeling confirms that social reforms yield significant results for social progress only after three years, similarly to the increase in the number of insurance companies. Given insurers’ assets and payout levels, their growth in life insurance has a faster impact on social progress than in risk, while the opposite is true for premiums. Insurance premiums transferred to Ukrainian reinsurers negatively and slowly (over three years) affect social progress, and to non-resident reinsurers – positively and faster (within a year). Across most indicators, life insurance not only influences Ukraine’s social progress more quickly than others but also provides a more substantial social effect.

О реализации нечеткой модели оценки лояльности потребителей для организаций электроэнергетики на основе метода аддитивной свертки

The relevance of developing models and tools that take into account the growing role of electricity consumers in order to increase the competitiveness of electric power industry organizations based on the creation of artifi-cial intelligence systems that provide ample opportunities for structuring demand, taking into account the main and additional types of activities, contributing to the formation of development programs for organizations, is emphasized. The developed models for assessing consumer loyalty are characterized, the approach most of-ten used for their formation is determined, and their peculiarity is their application to multi-product sales. It is emphasized that the choice of tools for implementing a model for assessing consumer loyalty for electric pow-er industry organizations is associated with the influence of technical, social and economic factors that deter-mine the use of “soft” modeling. It is shown that the most appropriate method for implementing the model is the additive convolution method. An algorithm for implementing a fuzzy model is presented based on the selected method and the proposed criterion for determining loyal consumers. An example of assessing the loyalty of electricity consumers of an energy sales organization is shown, consumers with a high level of loyalty, includ-ing behavioral and cognitive, are identified in order to formulate proposals for participation in programs for the development of the digital environment and the use of additional services.

Information System Concept for a Sports and Game Mobile Application with Elements of Artificial Motivation to Lead a More Active Lifestyle

The article presents the idea of a sports and gaming mobile application. The proposed concept has a number of indisputable advantages over the analogue products. The main one is the presence of a mechanism of artificial motivation to lead a more active lifestyle. This approach is especially relevant for modern children and teenagers, most of whom prefer virtual entertainment. The analysis of approaches and methods for encouraging and retaining the user of the mobile application was carried out based on the studied literature. The problem of reducing the physical activity of the population is highlighted. Based on the model of additive convolution for the problem of multi-criteria optimization, the feasibility of implementing the system and its superiority over similar software products presented on the market are substantiated. The expected implementation effects of the system are formulated. Mathematical model for substantiation of educational and physical culture and health effects are proposed. Decomposition of the system into subsystems was carried out using Gain-Sarson DFD-notation. The skeleton architecture of the application has been developed and substantiated. The UML activity diagram of the main process of system functioning has been developed. One of the possible options for implementing the system is proposed: the model of the project life cycle is chosen and substantiated, the stages of its implementation are determined, and the list of minimum necessary human resources is assigned. Implementation of the proposed application will have positive sports, health and educational effects. In addition to improving physical fitness, users will increase their awareness of the achievements of world-famous athletes and the sports they represent. The proposed mechanics for a gradual transition from regular walks to runs will minimize the chance of injury. The implementation of the proposed application is the first step for quantitative and qualitative analysis of physical activity of users. On the basis of statistical data, which is going to be collected in the following versions of the system, it is possible to determine to what extent the use of modern technologies and gamification mechanisms can motivate people to a more active lifestyle. The basis for this stage is the model presented in this paper.

Multicriteria ranking and selection in rank gradations of objects measured in different types of scales

To solve multi-criteria applied problems related to the construction of ratings of organizations, the choice of effective objects (alternatives, solutions), the initial data of which are presented in different types (quantitative, ordinal) measurement scales, the use of a generalized criterion in the form of an additive convolution of particular criteria is incorrect. In this regard, methods for narrowing the initial set of objects, as well as methods for constructing the resulting ranking (Kemeny-Snell medians), have become widespread. However, if the initial estimates of objects are transformed into the resulting homogeneous scale i.e., if there is a scale with the same scope of criteria, then the use of an additive aggregation mechanism in this case will be correct. An ordinal rank scale can serve as such a resultant scale. The paper substantiates a method in which the results of the transformation of quantitative (point) estimates of objects in the gradation of the rank scale when solving multi-criteria problems will be invariant for any quantitative transformations of the original scales. The preservation of the ordering of objects according to generalized estimates in the form of the sum of ranks according to equally important criteria is proved. At the same time, object orderings based on relationships with the k-th order of strict preference are also preserved. Illustrative examples are given.

Multicriteria Optimization of Software Development Platform Selection

The problem of multicriteria optimization of tech stack selection in a non-linear software development environment is formalized. Approaches to solving the problem based on the formation of a compromise area of local quality criteria, additive convolution of vector criteria and their scalarization are considered. An aggregate quality criterion of the software development platform is proposed. It allows taking into account the nonlinearities of the external environment in the framework of solving the problem of extremal control. The coordinates of the vector criteria are piecewise continuous functions A comparative analysis of various approaches to changing the software development tech stack in the face of significant disturbances in the development tools market has been carried out. The possibilities of boxed solutions, custom development and Open Source software development in ensuring information security of the software development environment are shown. The information stability of a software development project using Less Code tools is established and the advantages of technological solutions are shown. The analysis of the adequacy of the obtained solutions was carried out using the Open Source Less Code of the Jmix platform. The data of a comparative analysis of the budgets of the Less Code platform and custom software from vendors are given, which showed the benefits of using Open Source software development tools for long-term operation of the development platform.

Public health and national security proxies: Case of European countries

The COVID-19 pandemic has spurred transformations aimed at ensuring the effectiveness of the public health system and highlighted the need for a deeper study of the causal relationships between the parameters of healthcare system effectiveness and the national security. The aim of this study is to identify causal and temporal patterns in the impact of various types of healthcare expenditures on the components of national security. The study was conducted on a sample of 34 European countries for 2000-2021. In order to achieve the research objectives, integral indicators of economic, social, and environmental security were developed based on a complex combination of principal component analysis, Fishburn formula and additive convolution. Panel data regression modelling was employed to identify causal relationships between health care expenditures and those integral indicators. Finally, distributional-lag modelling (testing for the presence of a lag of up to 3 years) identified temporal patterns of the relationship between the indicators. Causal and temporal patterns of the relationship between health care expenditures and components of national security of the state were determined according to the modelling results.

RESEARCH ON METHODS OF DETERMINING CUSTOMER LOYALTY AND ASSESSING THEIR LEVEL OF SATISFACTION

The subject of research in the article is methods of data collection and processing to assess the level of customer satisfaction and loyalty to the company, as well as the possibility of evaluating the collected data. The purpose of the work is the analysis of methods for determining customer loyalty and assessing their level of satisfaction, the development of a unified assessment algorithm based on various types of data. The article deals with the following tasks: analysis of information acquisition methods – questionnaires and reviews, evaluation methods definition and comparison questionnaires with closed answers, reviews and open answers’ text tonality evaluation methods analysis using an artificial intelligence, development of an algorithm for determining a unified evaluation and conducting an experiment. The following methods are used: theoretical research methods for determining existing data collection methods, as well as methods for assessing the level of customer loyalty and satisfaction using CSI, CSAT indexes, NLP methods for determining the text tonality, bringing the calculated values to one scale, determining the method of a unified assessment; empirical research methods for conducting an experiment, determining and proving the feasibility of applying the method. The following results were obtained: a method of assessing customer loyalty and their level of satisfaction based on the analysis of various types of information with further results unification was proposed. Various types of date are responses to questionnaires and user reviews. The questionnaires are analyzed using KPI, and reviews – using artificial intelligence methods. After normalizing the results (bringing them to one scale), the additive convolution method is used to unify the overall result. A prototype of the software system has been developed, which allows you to carry out a full cycle from collecting information to calculating both KPI-metrics and a unified assessment. Conclusions: Experimentally, it was determined that the method of assessing customer loyalty and their level of satisfaction based on the unification of a comprehensive assessment of various types of data is efficient and can be used to optimize business processes by reducing time and efforts spent on analyzing the gathered data. The use of this method is fully justified, since the measurement error is low, and the margin of error is acceptable.

Real natural exponential families and generalized orthogonality

In this article, we use the notion of generalized orthogonality for a sequence of polynomials introduced by Bryc, Fakhfakh, and Mlotkowski (2019) to extend the characterizations of the Feinsilver, Meixner, and Shanbhag based on orthogonal polynomials. These new versions subsume the real natural exponential families (NEFs) having polynomial variance function in the mean of arbitrary degree. We also relate generalized orthogonality to Sheffer systems. We show that the generalized orthogonality of Sheffer systems occurs if and only if the associated classical additive convolution semigroup of probability measures generates NEFs with polynomial variance function. In addition, we use the raising and lowering operators for quasi-monomial polynomials associated with NEFs to give a characterization of NEFs with polynomial variance function of arbitrary degree.

COMPARISON OF SIGNAL RECOGNITION METHODS BY COMBINED USE OF APPROPRIATE EVALUATION CRITERIA WITHIN THE ADDITIVE CONVOLUTION

Existing signal recognition methods have both their advantages and disadvantages, which are found when recognizing signals from classes defined by different characteristic standards. Therefore, for signals from different classes, the indicators of recognition quality by one method or another can differ significantly. There is a need to create a more balanced method capable of providing the necessary stability relative to the accuracy and reliability of the final results in the process of recognizing signals from various classes. As such signal recognition method, the article proposes to use an approach based on the combine using of weighted signal proximity criteria within the additive convolution. Euclidean distances between reference points are used as evaluation criteria, which are used in the context of applying the four most well-known recognition methods: the amplitude method (the trivial Euclid method), the DDTW method using the values of the first derivatives, and methods based on the Wavelet transform and the Fourier transform.

MRP-Net: Seizure detection method based on modified recurrence plot and additive attention convolution neural network

Electroencephalographic (EEG) signals play an important role in the detection of seizures in epilepsy, and accurate detection of seizures can buy patients valuable treatment time. However, most seizure detection methods ignore the nonlinear, implicit characteristics of EEG, which has some impact on the accuracy of detection. Therefore, in this paper, we propose an EEG epilepsy detection network (MRP-Net) based on modified recurrence plot (MRP) and additive attention convolution neural network. This network can fully take into account the nonlinear, occult characteristics of EEG which can be mapped to the two-dimensional plane and served as the input of additive attention convolution neural network to automatically learn, analyze, and extract the EEG characteristics of seizures. The performance of the proposed method was evaluated on the Bonn University dataset and the SWEC-ETHZ short-term dataset. Sensitivity, specificity and accuracy were 100% in multiple detection tasks in the University of Bonn single-channel EEG dataset. The sensitivity, specificity and accuracy of SWEC’s short-term, multi-channel EEG dataset were 99.77%, 99.57% and 99.69%, respectively, higher than the latest methods (3.76%, 4.73% and 4.27%). The results of the experiments show that the network in this paper is superior and universal in epilepsy detection.

Impact of coronavirus disease (COVID-19) on food security: bibliometric analysis and empirical evidence

Impact of coronavirus disease on sustainable growth and food security is dramatically negative. Despite significant number of publications focused on food security and coronavirus disease issues, a deeper analysis of food security damages activated by COVID-19 is necessary. This determines the main task of this research. Theoretical block of the study involves bibliometric analysis of relevant Scopus publications using VOSviewer. Empirical block of the study involves: 1) formation of Food Security Index for 15 European countries based on a combination of Principal Component Analysis, ranking, Fishburn formula and additive convolution; 2) panel data regression modelling aimed at clarifying impact of macroeconomic indicators and healthcare expenditures on food security during 2000–2021 (model 1), 2000–2019 (model 2) and 2020–2021 (model 3). Model 1 demonstrates that 1% increase in current health care expenditures leads to 0.003 units increase in Food Security Index; impact of the dummy variable characterizing COVID-19 pandemic is also positive. Model 2 demonstrates similar results. Model 3 confirms only positive and statistically significant impact of trade and agricultural land on Food Security Index. The results can be useful to government officials for adjusting political measures in food governance, political decision-making and good governance, recovery of sustainable growth in post-pandemic period.

The Impact of the Organization of Public Health Systems on the Ability of Countries to Resist the COVID-19 Pandemic: The Experience of Developed Countries of the World and Ukraine.

The purpose of the study is to analyze the presence of functional interrelationships between the level of funding of the healthcare sector and the country's ability to withstand any pandemic, using the example of the COVID-19 pandemic. Official indicators presented by the WHO, analytical reports by Numbeo (the world's largest cost-of-living database), and the Global Health Security Index were used for the study. Using these indicators, the authors analyzed the following: the level of the spread of coronavirus infections in the world's countries, the share of public expenditures on the development of the medical sphere in the GDP of the countries, and the development of the healthcare sector in 12 developed countries and Ukraine. These countries were grouped into three groups, based on the model of the organization of the healthcare sector (Beveridge model, Bismark model, Market (private) model). The Farrar-Glauber method was used to check for multicollinearity in the input dataset, and thirteen relevant indicators were selected. These indicators took part in the formation of the generalized characteristics of the country's medical sphere and the ability to resist the pandemic. The state of readiness of countries to resist the spread of coronavirus infections was assessed using the country's index of vulnerability to COVID-19 and the integral index of the development of medicine. Additive convolution was used in combination with sigma-limited parameterization to form an integral index of the country's vulnerability to COVID-19 and to determine the weights of each indicator. The convolution of indicators according to the Kolmogorov-Gabor polynomial was used to construct an integral index of the development of medicine. Thus, while analyzing the ability of countries to resist the pandemic in terms of models of organization of the healthcare sector, it should be noted that none of the models demonstrated absolute effectiveness in the fight against the mass spread of COVID-19. The calculations made it possible to determine the nature of the relationship between the integral indices of the development of medicine and the vulnerability of countries to COVID-19, as well as a country's potential ability to resist any pandemic and prevent the mass spread of infectious diseases.

Superconvergence and regularity of densities in free probability

The phenomenon of superconvergence, first observed in the central limit theorem of free probability, was subsequently extended to arbitrary limit laws for free additive convolution. We show that the same phenomenon occurs for the multiplicative versions of free convolution on the positive line and on the unit circle. We also show that a certain Hölder regularity, first demonstrated by Biane for the density of a free additive convolution with a semicircular law, extends to free (additive and multiplicative) convolutions with arbitrary freely infinitely divisible distributions.

Impact of Coronavirus Disease COVID-19 on the Relationship between Healthcare Expenditures and Sustainable Economic Growth.

The coronavirus disease (COVID-19) pandemic led to a catastrophic burden on the healthcare system and increased expenditures for the supporting medical infrastructure. It also had dramatic socioeconomic consequences. The purpose of this study is to identify the empirical patterns of healthcare expenditures' influence on sustainable economic growth in the pandemic and pre-pandemic periods. Fulfilment of the research task involves the implementation of two empirical blocks: (1) development of a Sustainable Economic Growth Index based on public health, environmental, social, and economic indicators using principal component analysis, ranking, Fishburne approach, and additive convolution; (2) modelling the impact of different kinds of healthcare expenditures (current, capital, general government, private, out-of-pocket) on the index using panel data regression modelling (random-effects GLS regression). Regression results in the pre-pandemic period show that the growth of capital, government, and private healthcare expenditures positively influence sustainable economic growth. In 2020-2021, healthcare expenditures did not statistically significantly influence sustainable economic growth. Consequently, more stable conditions allowed capital healthcare expenditures to boost economic growth, while an excessive healthcare expenditure burden damaged economic stability during the COVID-19 pandemic. In the pre-pandemic period, public and private healthcare expenditures ensured sustainable economic growth; out-of-pocket healthcare expenditures dominantly contributed to the pandemic period.