In the era of information overload, personalized recommender systems are essential, particularly in critical domains such as skincare where incorrect suggestions have large physical risks. This presents a specialized problem whose demands for accuracy, explainability, and safety in the algorithms are unprecedented. This paper presents an extensive technical roadmap to the researcher, systematically examining the developmental history of recommender algorithms, covering the principal collaborative filtering and content-based filtering algorithms, the latent factor revolution with matrix factorization algorithms, and finishing with the newest deep learning and graph neural network-based algorithms for these systems. Some of this work covers the newest areas of research into how present systems can be trained to become "trustworthy decision partners", discussing causal inference for debiasing techniques, explainability techniques for building trust in users, and multi-dimensional, performance measures beyond accuracy. Using skin-care as a core subject, this paper examines how far the above paradigms are applicable to a very complex and critical real-world scenario. This will also provide an interesting view of future developments in hyper-personalized recommendation.

This paper introduces a novel SEIRS-type differential model that incorporates significant real-world factors such as vaccination, hospitalization, and vital dynamics. The model is described by a system of nonlinear ordinary differential equations with time-dependent parameters and coefficients. First, fundamental biological properties of the model, including the existence, uniqueness, and non-negativity of its solution, are established. In addition, using official COVID-19 data from Bulgaria, a special inverse problem for the differential model is formulated and investigated through the construction of an appropriate family of time-discrete inverse problems. As a result, the model parameters are identified, and the model is validated using real-world data. The presented numerical experiments confirm that the proposed methodology performs well in real-world applications with actual data. A very good agreement between computed and officially reported data with respect to the l2 and l∞ norms is obtained. The model and its simulation tools are adaptable and can be applied to datasets from other countries, provided suitable epidemiological data are available.

The article examines the crisis of historical science in Belarus and historical higher education in the context of authoritarian realities and explores the problems of historical education, as well as proposes the main principles of its future reform in the New Belarus. Based on autoethnographic reflection and analysis of the discourse of institutional materials, the article highlights the key problems of historical science and education in modern Belarus, and proposes the main principles for their solution. The article highlights universal (freedom of speech, human rights), general scientific (autonomy of universities, expertness of the scientific community, bureaucracy of science) and special historical problems (disciplinary boundaries, ethics of science, the problem of plagiarism, etc.) of historical science and education in Belarus, and suggests ways to solve them. The study points to ideological control in Belarus over historical science and education, the problems of erosion of ethical norms. A long‑term strategy for reforming historical science and education is proposed based on autonomy, self‑reflection and self‑organization of the historical community in the New Belarus.

Introduction. In the 1920s and 1930s, economically developed countries were engulfed in a period of global economic instability characterized by declining industrial production, widespread unemployment, overproduction, falling prices, and other challenges. This turmoil underscored the urgent need for state regulation of economic processes occurring within their territories. During this period, various mechanisms of influence – both administrative and economic – were devised and implemented to steer economic activity. Among these regulatory models was W. Leontief's pioneering “input-output” model, which provided a comprehensive description of the economy of an entire country or individual regions. For this groundbreaking work, Leontief was awarded the Nobel Prize in Economics in 1973. Our scientists, including those affiliated with the Institute of Cybernetics, made significant contributions to advancing and applying the theory of inter-industry balance. Notably, M.V. Mikhalevich focused extensively on studying and developing Leontief’s inverse models. These inverse models play a crucial role in production planning by determining the necessary gross output to meet a specified aggregated demand. They also facilitate the analysis of how changes in production technology affect output volumes. Overall, the inverse models serve as a key instrument in inter-sectoral balance by linking final demand to gross production through the inverse matrix of the total cost coefficients. The purpose of the research is to study the modification of Leontief’s classical “input-output” model through its optimization-based extension developed by M.V. Mikhalevich, incorporating structural and technological shifts, institutional changes, wage levels, and profit shares across various industries. This study seeks to justify the applicability of the modified model for strategic planning of inter-sectoral proportions within an economic policy framework focused on growth without cost inflation. Additionally, it involves the development of AMPL implementations to solve optimization problems related to structural and technological changes in the inter-sectoral balance, utilizing the AMPL (A Modeling Language for Mathematical Programming) through solver SNOPT and BARON on server NEOS. Results. The AMPL implementation has been developed to solve optimization problems of structural and technological changes in the inter-industry balance. The effectiveness of solving test problems using modern versions of solvers on the NEOS server has been investigated. Conclusions. The inter-industry models for planning structural and technological changes discussed in the article give rise to complex optimization problems characterized by non-convex objective functions and nonlinear constraints. In order to address these challenges an AMPL implementation of the optimization models for structural and technological changes in the inter-industry balance was developed. Computational results obtained with the SNOPT and BARON solvers on the NEOS server demonstrated the effectiveness of this approach in solving specialized problems. Keywords: modified ‘input-output’ models, modelling of inter-industry balance, aggregated demand, optimization, AMPL-implementation, NEOS.

Who am I? This question on identity has plagued the philosophers over time. This is not only a metaphysical question but also a psychological problem regarding our identity. We are not concerned about our own identity but also about the identity of other person. The question is that why the identity of a person is considered a problem at all. We find that there are many things which can be easily identified, and it is clear that identification of these things is not considered as a problem. The philosophers are not concerned about the identity of material things or any physical objects, then why is it that they regard the identity of a person as a special problem. In the case of the material things, we can identify them by their spatio-temporal characteristics. Let us take an example of a table or a book. I can identify a table of my room as the same table which I saw yesterday by its spatio-temporal continuity. It occupies the same place which it occupied yesterday and hence there is temporal continuity. I can individuate it from another table which is visibly similar with the table of my room by their spatial character because two different tables have occupied two different places at the same time. But it may be said that a person has a spatial character because a person has a body and the body must occupy a particular place. So, a body can be regarded as a physical object, but a person is not just a body.

ABSTRACT The study examines the applicability of the Dzhumabaev parametrization method to multipoint boundary value problems for a Duffing‐type integro‐differential operator equation. The original problem is reformulated as an equivalent parametric multipoint problem, which was then decomposed into two subproblems: A nonlinear special Cauchy problem and a system of nonlinear algebraic equations. The special Cauchy problem is addressed via linearization at fixed parameter values and solved through a sequence of stepwise linear approximations. The solutions obtained are subsequently employed to construct the right‐hand side of the algebraic system and its associated Jacobi matrix. On this basis, a new approach for solving the original problem is developed. The efficiency and convergence of the proposed approach were confirmed through a numerical example.

One of the important aspects of drug addiction problems in society is the development of scientific methodologies and practical measures aimed at managing the emerging situation, the threat of the threat and ways to combat the consequences of the addiction in order to create a standard preventive space in the conditions of. The purpose of this study is to examine a set of legal, organizational, methodological and medical aspects for the formation of a standard methodological core within the framework of a preventive space that unites the efforts of all subjects of drug prevention in the regions. According to the authors, the processes of reorganization and centralization of the regional narcological service (State Budgetary Healthcare Institution «Republican Center for Health and Narcology» of the Ministry of Health of the Kabardino-Balkarian Republic) have taken place; management competencies in the formation of specialized tasks have been determined, where system-forming connections and relationships will apparently form a methodological basis in a single preventive space. The researchers came to the conclusion that the peculiarities of legal regulation of psychiatric and narcological medical care contribute to the emergence of special problems that manifest themselves with uncertain restrictions in the guarantees, rights and status of patients and organizations, which requires regulation at the federal level. The authors came to the conclusion that the most effective implementation of the concept of preliminary preliminary space is possible at the external level, since it is here that the possibility of delegating powers from state authorities to subjects of the Russian Federation of local governments is normatively enshrined. It is this redistribution of functions that creates legal and organizational prerequisites for the systematic implementation of measures aimed at preventing drug addiction, taking into account the specifics of the territory and interdepartmental interaction. The regional level is the link between federal strategies and the municipal territory, and in order to create a permanent preventive space, it is necessary to combine the efforts of all participants in the preventive process at the meso (regional) level.

This study utilizes approximation techniques to address a boundary value problem involving a differential equation with a delayed argument. The problem is approached through analytical techniques by transforming it firstly into an equivalent integral equation. Specifically, we derive a Fredholm–Volterra integral equation that encapsulates the delayed behavior inherent in the original differential equation. The Fredholm operator in this equation features a degenerate kernel, which enables simplification and facilitates the construction of successive approximations. To solve this integral equation, we employ the two-sided convergence method, a powerful iterative technique that generates two sequences of approximate solutions—lower and upper bounds—that converge monotonically toward the exact solution. This method is particularly well-suited for problems with delayed arguments, as it ensures both stability and convergence under appropriate conditions on the kernel functions. The main objective of the study is to demonstrate the applicability and accuracy of the Simple Two-Sided Convergence Method for this class of boundary value problems. A numerical example is presented to illustrate the theoretical results, and the obtained approximations are compared with the exact analytical solution. All computations were carried out using Maple, ensuring precise numerical evaluation.

If four points in this order, lie on a circle , there is an interesting and useful result, called Ptolemy’s Theorem, which links the lengths of the legs of the quadrilateral with the lengths of its diagonals, by the equality This result may be generalized if the points are replaced by circles that touch the circle The result is known as Generalized Ptolemy’s Theorem (GPT), also known as Casey’s Theorem. This relatively less-known result may be used to prove several geometric results. In this paper, we apply GPT to partially known special problems, demonstrating the efficiency of this proving tool. We also compare it with other ways of proving the results, omitting the GPT. Finally, we also expect that one can pose similar geometric problems, where GPT can efficiently be used as a solving tool.

Soil disturbance as a result of military action can range from a short-term reduction in fertility to complete destruction of the soil. A special problem is the restoration of agricultural soils. The most promising way to solve this issue is to use phytoextraction and phytostabilization methods, especially those that combine remediation measures with simultaneous economic benefits. R e cently, among phytoextraction strategies, preference has been given to growing plants that do not have the ability to hyperacc u mulate, but which , due to their rapid growth and the formation of a large biomass, can remove toxicants from the soil in large quantities. The idea of combining the restoration of contaminated lands with the production of biomass for phytomining and renewable energy is especially attractive. Phytostabilization strategies can be implemented using useful plants that do not acc u mulate pollutants in the final raw material, for example, some agricultural, forage and pasture crops ( Vicia villosa , Secale cereale , Zea majus , Lupinus luteus , Festuca sp . , Lolium perenne , etc.), energy crops ( Spartina pectinata , Miscanthus sp., etc.), essential oil plants ( Mentha×piperita , Melissa officinalis , Marrubium vulgare ). The attention of scientists is also drawn to the search for promising soil additives and the study of their application rates in order to improve soil conditions and increase biomass yields.

This paper develops the linear-algebraic foundations of the Convex Least Squares Programming (CLSP) estimator and constructs its modular two-step convex optimization framework, capable of addressing ill-posed and underdetermined problems. After reformulating a problem in its canonical form, A(r)z(r)=b, Step 1 yields an iterated (if r>1) minimum-norm least-squares estimate z^(r)=(AZ(r))†b on a constrained subspace defined by a symmetric idempotent Z (reducing to the Moore–Penrose pseudoinverse when Z=I). The optional Step 2 corrects z^(r) by solving a convex program, which penalizes deviations using a Lasso/Ridge/Elastic net-inspired scheme parameterized by α∈[0,1] and yields z^*. The second step guarantees a unique solution for α∈(0,1] and coincides with the Minimum-Norm BLUE (MNBLUE) when α=1. This paper also proposes an analysis of numerical stability and CLSP-specific goodness-of-fit statistics, such as partial R2, normalized RMSE (NRMSE), Monte Carlo t-tests for the mean of NRMSE, and condition-number-based confidence bands. The three special CLSP problem cases are then tested in a 50,000-iteration Monte Carlo experiment and on simulated numerical examples. The estimator has a wide range of applications, including interpolating input–output tables and structural matrices.

ABSTRACT In the early years of the Second World War, rising workplace discontent, perceived communist influence, and war weariness sparked a suite of investigations into civilian mood and behaviour in the volatile west of Scotland. This article examines three ways the general domestic population was monitored in Scotland’s industrial heartland: by the police, via a state-private partnership, and by a special interest group. In doing so, this article hopes to reshape knowledge of the domestic intelligence sphere in wartime Britain, and illuminate the extent to which Allied societies were subject to counter-measures to undermine perceived ‘subversive’ activities.

Aerodigestive fistulas represent a major challenge in clinical practice. This problem is burdened with severe morbidity and mortality, despite recent advantages in endoscopic endoluminal repair techniques. Special problems are fistulas localized higher, engaging the proximal esophagus and trachea, which in adults most often result from post-intubation injury. Surgery is generally demanding and reserved for the patients in whom other, less invasive options fail. Hereby, we present a case of post-intubation tracheoesophageal fistula, successfully treated with endoscopic vascular plug placement.

The main goal of this paper is twofold. First, we want to demonstrate how the forward and backward Feynman-Kac equations can be extended to account for the general form of Markov processes described by the differential Chapman-Kolmogorov equations. Second, we demonstrate specialization of these equations for different models of Markov processes, ranging from classical diffusion to more computationally challenging jump diffusion with drift, regime switching, and hybrid systems with resetting. To illustrate the power of the extended Feynman-Kac formalism, we consider different settings corresponding to various models of the stochastic process. We provide the closed-form solutions to the respective problems for an arbitrary initial (final) condition. For deterministic initial (final) conditions, the obtained results reduce to the known solutions to the respective special problems derived by different methods. We study the model with mean reversion and uncorrelated pre- and postjump states. This model is antipodal to both continuous diffusion and random walks. It is most appropriate when physical reality involves strong exogenous shocks with exponential relaxation to the mean value between these shocks, leading to a significant departure from conventional modeling assumptions. Finally, we demonstrate how naturally the generalized Feynman-Kac equations can be specialized to treat resetting (as a particular case of the uncorrelated states model) in stochastic hybrid systems.

The demand for creative ways to increase woman citizens’ access to quality of healthcare, is growing. The physical and mental changes that accompany aging present special health problems for women. A viable solution to these problems is artificial intelligence (ai), which offers cutting-edge instruments and platforms designed especially to meet the medical requirements of women. ai is being widely used in the creation of healthcare platforms and technologies that are tailored to the unique requirements of women. Among these are intelligent health monitoring devices, which enable continuous assessment of woman’s health condition by tracking and analyzing biometric data in real-time. These systems can recognize anomalous patterns and send out notifications for prompt medical attention using machine learning techniques. For example, smart wearables that track heart rate, activity level, and sleep quality allow medical professionals to closely monitor patients’ physical conditions, perhaps preventing serious health problems before they emerge. Even with the obvious advantages, there are several obstacles to overcome when integrating ai-driven solutions into the current healthcare systems. The difficulty of integrating new technology with conventional systems is one of the main problems. A lot of the infrastructures used in healthcare today are not entirely capable of integrating ai technology, which could cause problems with data security and administration. The broad application of ai in healthcare is also hampered by ethical issues with the usage of personal data and protecting user privacy. In summary, ai has the potential to greatly improve the standard and accessibility of healthcare for women. ai may be used to provide this vulnerable demographic with better and more accurate healthcare services by addressing the issues and putting methods in place that work.

Introduction. The article examines the specifics of cognitive activity of students with autism spectrum disorders (ASD) in the course of mastering natural science disciplines, including the process of performing mathematical tasks. The necessity of a differentiated approach in teaching, taking into account the cognitive sphere of this category of children, is substantiated in order to increase the capabilities of each student in mastering the program material. Categories of errors and difficulties are identified, reflecting the special problems that arise in the educational activity of children with ASD and requiring systematic pedagogical work.Materials and methods. The theoretical part of the study is based on the analysis of scientific publications devoted to the peculiarities of the development of natural sciences by students with ASD. The data of own empirical research based on the analysis of the results of annual control works in mathematics performed by students with ASD, studying in the fourth, sixth and eighth grades of a general education school, are given. The works of 55 students with ASD aged 11-16 years old, studying according to the variant of the adapted educational program 8.2, intended for children with ASD, who do not have intellectual disabilities, are considered. The study also used data from questionnaires filled out by teachers who conducted the tests. Thus, the study is based on a synthesis of scientific literature and a quantitative and qualitative analysis of the results obtained through empirical research.Results. A summary of current research data has identified two main categories of cognitive challenges faced by children with ASD that must be taken into account when teaching them science: difficulties related to executive function deficits and difficulties related to verbal comprehension and social perception deficits. These two categories account for almost half of the errors made by students with ASD in math tests. The article provides an overview of the main types of errors in each category. In addition, the results of an empirical study showed that the proportion of errors related to executive function deficits decreases over the course of education, as does the proportion of "non-specific" errors for children with ASD, which are related to a lack of knowledge and computational skills. However, the proportion of errors caused by deficits in verbal comprehension and social perception increases from year to year.Discussion and conclusions. The data of the empirical study based on the assessment of errors and difficulties in the performance of students with ASD of control works in mathematics, allowed to analyze their specificity and assign to different categories. At the same time, the difficulties of one of the identified categories, associated with the deficiencies of verbal understanding and social perception, were the most stable and, accordingly, require special attention of teachers at all stages of education of children with ASD. By summarizing and analyzing the data obtained from the teachers' questionnaires, it was possible to identify a set of methods and techniques aimed at systematically addressing the challenges faced by children with ASD in the process of learning science subjects. The results of the study indicate that methods and techniques aimed at improving verbal understanding and social perception are the most relevant, as these specific problems for students with ASD are the most resistant to pedagogical interventions in our study.

Exterior CT imaging is a special X-ray imaging problem that allows for nondestructive testing of relatively large tubular samples by using smaller detectors. However, due to the incomplete nature of the exterior projection data, the exterior CT imaging problem is highly challenging. In this study, we introduce a new CT reconstruction model for polychromatic spectrum exterior problems, called the Polychromatic Exterior Discrete Grayscale PAEDS (PE-DG-PAEDS) model. This model is based on the prior of discrete grayscale values in images and introduces a radial regularization term using polychromatic spectrum information for exterior CT reconstruction. Additionally, an alternating minimization method and the Discrete Algebraic Reconstruction Technique (DART) algorithm are used for alternating iterations to provide a solution algorithm for this model. Experiments conducted with both simulated and real data have validated the proposed model and algorithm. The results indicate that the method effectively suppresses artifacts associated with polychromatic X-ray CT exterior problem.

This paper presents an original approach through Transfer-Matrix Method applied for the calculus of the continuous circular plate embedded at the exterior circumference, charged with asymmetrical uniform load on the entire upper surface of the plate. Continuous circular plates are elements often found in practice, in the machine building, aeronautics, chemical industries (the bottoms of chemical reactors), and in petrochemical, mechanical, robotic, medical, military, nuclear, and aerospace industries. The calculus of continuous circular plates is a special problem both from the point of view of the theory of elasticity and from the point of view of the mathematical approach. The results obtained with Transfer-Matrix Method were compared and validated with those obtained from classical analytical calculation, the Theory of Elasticity. Transfer-Matrix Method is an elegant method and relatively easy to program. In future research, we want to validate our results with those given by the Finite Elements Method and those measured experimentally.

ABSTRACT Problems in moral philosophy and philosophy of religion can take on new forms in light of contemporary physical theories. Here we discuss how the problem of evil is transformed by the Everettian ‘Many-Worlds’ theory of quantum mechanics. We first present an Everettian version of the problem and contrast it to the problem in single-universe physical theories such as Newtonian mechanics and Bohmian mechanics. We argue that, pace Turner and Zimmerman, the Everettian problem of evil is no more extreme than the Bohmian one. The existence and multiplicity of (morally) terrible branches in the Everettian multiverse in contrast to the mere possibility of them in the Bohmian universe does not entail there is ‘more evil’ in the former than in the latter. Low probability in the Bohmian case and low branch weight in the Everettian case should modulate how we respond to them in exactly the same way. We suggest that the same applies to the divine decision of creating an Everettian multiverse. For an empirically adequate Everettian quantum mechanics that justifies the Born rule, there is no special problem of evil. In order for there to be a special Everettian problem of evil, the Everettian interpretation must already have been exposed to decisive refutation. In the process, we hope to show how attention to the details of physical and metaphysical theories can and should impact the way we think about problems in moral philosophy and philosophy of religion.

Aims: Ethiopia has the largest livestock population in Africa. To enhance the benefits of cattle, AI technologies have long been introduced into the country to improve the genetic potential of the indigenous cattle population. However, lack of recording scheme, wrong selection procedures, poor management of AI bulls, poor motivation and skills of inseminators are gaps in country and regional level. Therefore, this study was initiated to analyze factors affecting adoption of estrus synchronization and artificial insemination service in selected areas of Southern Ethiopia. Place and Duration of the Study: Southern Ethiopia from 2024 to 2025. Methodology: In total, 141 sample households were selected based on a systematic random sampling technique. The bivariate probit regression model was used to analyze the econometric data. Results: Education level, distance to AI station, heard information on failure of AI, mobile ownership, total family, and extension contact frequency were significant determinants of adoption of artificial insemination and estrous synchronization technology. Delay of AI technicians, shortage of supplementary feed, insufficient on-farm implementation of the services, indiscriminate application of AI, encountered failure, and insufficient equipment are challenges. In addition, inputs for the delivery of service, efficiency and specialization problems, shortage of technicians and limitation of access are constraints for sustainable utilization of AI and ES service. Conclusion: continuous training for AI technicians and farmers, focusing on on-farm implementation, fulfilling inputs and equipment, helping AITs to specialize on the area are required. In addition, working on improved/supplementary feed, provision of manuals for AITs in local language and raising awareness of farmers are necessary. Smoothening communication of farmers with AI technicians, and making AI centers functional at every time are also recommended.