Toward a Vector-Based Representation of Dispositions

The article discusses prerequisites for the application of the ontological approach to the construction of digital twins, taking into account the available results in the field of ontological engineering of energy systems. It is proposed to use the accumulated experience in developing mathematical models of energy objects and systems of different levels, as well as experience in building ontologies of tasks and methods, ontological models for describing and accumulating expert knowledge for building and integrating mathematical, imitation and ontological models as the basis for digital twins. Basic concepts in the field of digital twins are introduced, the main types of digital twins and their difference from “digital shadows” are considered. The stages of the transition to digital twins are proposed, the most important of which is the ontological engineering of the subject area, which ends with the construction of the corresponding ontological models. Examples of heuristic ontologies are given as a result of ontological engineering of the subject area related to heat power engineering. An example of a logical ontology in XML for a thermal power plant is given. The novelty of the proposed approach lies in the fact that when creating digital twins, the structuring of the knowledge of the subject area is preliminarily performed using ontological models, on the basis of which the information and mathematical models are then built constituting the basis of digital twins and software systems driven by ontologies are developed.

In this study, a satisfaction index estimation model is proposed integrating structural equation modeling and mathematical programming methods with fuzzy customer data. Firstly, a deep literature survey is conducted in this field of study. Then, a new model is proposed by taking into consideration gaps in the literature. The estimation model is composed of five stages and first stage is building conceptual model in which measurement and latent variables are introduced. At the second stage, a fuzzy evaluation method is developed for decreasing subjectivity in customer data. At the third stage, for measurement variables that are directly observed, a measurement model is developed with Linear Structural Relations. In the solution of the measurement model maximum likelihood algorithm is used. In the solution of structural model that is composed of latent variables that are not directly observed, a mathematical estimation model is developed in this study at the fourth stage. Mathematical model is coded in ILOG Cplex Optimization Studio. In the mathematical model that minimizes estimation errors, structural relations and measurement variable weights (precedence coefficients) are defined as constraints. At the fifth and last stage, index scores are calculated with mathematical model outputs. Application of the model is carried out in public sector at a local government service point. In the application model, service quality, innovation, communication, satisfaction and cost perception dimensions are used. Application results are discussed for both measurement and latent variables in detail. The results of model we developed are also compared with an alternative model outcomes and we show that we achieve optimum estimation capability with minimum estimation errors.

Progress in Industrial Mathematics at ECMI 2000

This study is important in terms of the fact that the production of a dried product with good quality and minimum process drying cost is dependent on individual or combinations of several drying conditions. However, if drying is not properly conducted at favourable drying conditions, it generates product quality-related problems for the consumer and food market. Thus, this study focused on the optimization and evaluation of the main and interactive effects of drying air temperature (DAT), air velocity (DAV), relative humidity (RH), and drying time (DRT) on the cabinet-tray hot air drying and quality attributes of chili pepper using the four-factors-five-level-rotatable central composite experimental design of response surface methodology. The drying kinetics was also modeled using known empirical drying models (Page, Newton, Logarithmic, and Henderson and Pabis). The drying conditions utilized are DAV (0 - 2 m/s), RH (60 - 80 %), DAT (40 - 80 °C), and DRT (180 - 900 min), while the moisture content (MC), carbohydrate content (CHC), total plate count (TPLC), and protein content (PTC) were the considered product quality attributes. The results showed that the most significant drying process conditions that exerted a more pronounced main and interactive effects on the dried chili pepper quality attributes are drying process time and drying air temperature. Second-order quadratic regression model adequately predicted the quality attributes of the dried chili pepper. The optimum process conditions for the production of dried chili pepper with minimum MC (9.93 %) and TPLC (40.10 CFU/g) as well as maximum PTC (7.88 %) and CHC (24.66 %) were obtained to be DAT, 61.59 °C, DAV, 0.70 m/s, RH, 68.39. %, and DRT, 729.63 min. The Page model best describe the drying kinetics. The drying treatments generally retained the protein and carbohydrate contents (nutritional properties) in the dried chili pepper product as well as reduced the microbial load to the acceptable limit allowed for consumption.
 HIGHLIGHTS
 
 Effects of drying conditions on dried chili pepper quality attributes were evaluated using response surface method (RSM)
 Dried chili pepper quality attributes were optimized using RSM
 Drying conditions retained the quality attributes of dried chili pepper
 Microbial load of dried chili pepper was within the acceptable limit for consumption
 A mathematical model was developed for the dried chili pepper quality attributes’ prediction
 
 GRAPHICAL ABSTRACT

Pulsed ultraviolet (PUV) light technology holds the potential for surface decontamination of foods. In this study, the survival of L. monocytogenes and some quality attributes (color, moisture, water activity, and antioxidant activity) of sliced mushrooms subjected to PUV light were modeled using data obtained from a previous study. Three mathematical models, log‐linear model, Weibull model, and log‐logistic model were used to describe the inactivation of L. monocytogenes with respect to fluence (J/cm2) at three treatment distances (5, 8, and 13 cm) from the quartz window of the PUV‐light system. Weibull model (R2adj: 0.8598–0.9820, root mean square error [RMSE]: 0.09–0.24) described the inactivation better compared to log‐linear model (R2adj: 0.7205–0.9072, RMSE: 0.22) and log‐logistic model (R2adj: 0.4871–0.7629, RMSE: 0.24–0.46). The survival curves of L. monocytogenes at all treatment distances showed upward concavity. These findings indicate that the survival of L. monocytogenes on sliced mushrooms subjected to PUV light follows a non‐linear trend, and the Weibull model may be a useful tool to predict the behavior of L. monocytogenes on mushroom surface subjected to PUV light. For the quality attributes, zero‐order kinetics (R2: 0.8500–0.9974, mean square error (MSE): 1.55*10−8–2.3124) described the changes slightly better compared to first‐order kinetics (R2: 0.8451–0.9974, MSE: 1.55*10−8–2.3867).Practical ApplicationsPulsed UV light is one of the most effective methods for the control of different pathogenic microorganisms on surfaces of food products. The parameters related to the kinetics of the inactivation of the pathogenic microorganisms in foods such as mushroom are of great importance to maintain food safety. Mathematical models provide practical information about not only tested variables but also untested ones. Process evaluation with mathematical models is useful to verify the effectiveness of the food safety applications. In this study, inactivation of L. monocytogenes on sliced mushroom surface was modeled using log‐linear, Weibull, and log‐logistic models. In addition, zero‐order and first‐order kinetics were applied to quality attributes of sliced mushroom in order to better understand the effect of pulsed UV light application.

Botanical beverages are made from plant extracts that can be packaged to extend their shelf-life. The shelf-life of foods and beverages can be estimated by mathematical modelling, usually by employing linear equation model. To accurately estimate the shelf-life, it is necessary to determine the indicators. This study aimed to determine the shelf-life indicators of a botanical beverage made from red ginger and garlic which were prepared under boiling condition and packaged in glass bottles at hot condition. The product was stored at 27, 33, and 40°C and their quality attributes comprising sensory, visual consistency, viscosity, pH, and total microbe were observed weekly. The data obtained were mathematically modeled using linear equations to determine the order of the reaction (n) and the rate constant (k) of the change in quality attributes. The coefficient of determination (R2) for the equation of change in quality attributes at 27, 33, and 40°C were 0.19, 0.21, 0.62; 0.10, 0.01, 0.01; 0.02, 0.19, 0.89 respectively for viscosity, pH, and total microbe. The total microbe is the most appropriate quality indicator for estimating shelf-life of this botanical beverage.

The approach to create power system digital twins is presented by the example of energy supply of a geographically localized R&D facility. In this paper, the six-layer digital twin architecture is proposed and its prototype software implementation is described. The architecture consists of an ontological model, a digital single line diagram, electronic documentation, master data, load measurement data, and mathematical models and simulations. The paper describes problems and principles of ontological modeling of the prosumer infrastructure, including customer load, low-voltage distribution network sections, small-scale generation equipment, and electric energy storage devices. The optimal configuration of the hybrid power supply system with renewable energy sources was computed using the digital twin that was composed according to the presented approach. For machine-readable representation of the digital twin, the ontological modeling language OWL is used.

Development of predictive models for quality and maturation stage attributes of wine grapes using vis-nir reflectance spectroscopy

We describe a postacquisition, attribute-based quality assessment method for brain magnetic resonance imaging (MRI) images. It is based on the application of Bayes theory to the relationship between entropy and image quality attributes. The entropy feature image of a slice is segmented into low- and high-entropy regions. For each entropy region, there are three separate observations of contrast, standard deviation, and sharpness quality attributes. A quality index for a quality attribute is the posterior probability of an entropy region given any corresponding region in a feature image where quality attribute is observed. Prior belief in each entropy region is determined from normalized total clique potential (TCP) energy of the slice. For TCP below the predefined threshold, the prior probability for a region is determined by deviation of its percentage composition in the slice from a standard normal distribution built from 250 MRI volume data provided by Alzheimer's Disease Neuroimaging Initiative. For TCP above the threshold, the prior is computed using a mathematical model that describes the TCP-noise level relationship in brain MRI images. Our proposed method assesses the image quality of each entropy region and the global image. Experimental results demonstrate good correlation with subjective opinions of radiologists for different types and levels of quality distortions.

Mathematical knowledge is a term often used to describe various components of mathematical science, such as theorems, lemmas, axioms, proofs, etc.. By the term “knowledge from mathematical modeling” we understand the definition of a huge amount of knowledge, which is formalized both within the framework of a specific mathematical model and in the process of its construction, as well as related procedures of practical use. Compared to other forms of knowledge, such as rules, solution trees, mathematical knowledge is more abstract and more structured. In general, the ontological approach to mathematical modeling refers to the use of ontology, as it is based on the terms of mathematical modeling and descriptions of relationships between the main processes of its course.. The general ontological approach to mathematical modeling from an applied point of view does not allow to manage the processes of building mathematical models, because it can only be used to describe the area of mathematical modeling. From an applied point of view, most basic forms of mathematical knowledge are either embedded in specific software tools, such as models of aggregate operation in simulation software, or must be formally interpreted into a more general mathematical tool, following appropriate syntactic rules. Most of this type of knowledge relates to specific modeling tasks and is clearly implemented with the help of appropriate procedural descriptions, rather than declarative representations, unlike the philosophical vision of mathematical modeling. The paper substantiates the use of the ontological approach as an effective tool for managing the processes of building mathematical models based on interval data and using these models for applied problems. The use of the ontological model made it possible to formalize the process of obtaining, storing and using knowledge obtained in the process of mathematical modeling. The article also presents the features of building a software architecture for mathematical modeling based on interval analysis and an ontological approach. The technology for creating software based on the developed ontological add-on for mathematical modeling using interval data for various objects, as well as various forms of user interface implementation, is described. A number of diagrams illustrating the peculiarities of using the ontological approach based on interval data are presented and the peculiarities of its interpretation in applied fields, in particular, in the tasks of environmental monitoring, are described.

Liquisolid pellets: Mixture experimental design assessment of critical quality attributes influencing the manufacturing performance via extrusion-spheronization

Introduction . Quality, along with efficacy and safety, are the key characteristics of a drug. Therefore, it is important in frame of pharmaceutical development to lay the foundation for obtaining a quality product and achieving the desired product characteristics. One of the tools used for this is the «Quality by design» approach (QbD) - quality through development. The ICH Q8 «Pharmaceutical development» manual defines it as a systematic approach to development that starts with pre-defined goals and focuses on understanding the product and process, as well as managing the process based on reliable scientific data and quality risk management. Aim . The aim of the research is to develop the composition of tablets based on clover meadow grass phytosubstance using the QbD tool with application of mathematical model that links the composition of tablets (CMA) with its quality attributes (CQA). Materials and methods . The research was based on the concept of quality by design/quality through development. The main method for conducting the development process was design of experiments method/experiment planning with creating of individual design. The experiment planning was performed in the software package JMP Pro 14 (ver. 14. 3. 0), SAS Institute Inc., USA. The method of risk analysis-failure mode and effects analysis (FMEA)/analysis of the types and consequences of failures was used for risk assessment in research. As methods of analysis of the tablet mixture and the tablets were used the following the tests: disintegration of tablets, crushing strength of tablets, determination of hygroscopicity, determination of Carr's and Hausner index. Results and discussion . The composition of tablets based on the clover meadow grass phytosubstance obtained by direct pressing was developed. In order to develop the composition of tablets in accordance with the ICH Q8 guidelines, the first step was to create a quality target product profile. To ensure the properties specified in the quality target product profile, the component composition of the developed tablets was selected based on the selected production technology and key characteristics of both the tablet mixture and the finished product. The risk assessment for the product composition determined that the quantitative content of 4 excipients are considered as critical quality attributes of materials (CMA). CMAs affect the critical quality attributes (CQA) of the dosage form, which determine the effectiveness of the composition. Based on the initial data analysis, optimal content boundaries for each component were established. Potentially critical qualitative characteristics of the drug under development (CQA) were identified. A mathematical model linking critical quality parameters and tablet composition was obtained and analyzed. Conclusion . Based on a mathematical model, the optimal composition of tablet mixture and tablets obtained from it was determined. The tablets quality indicators corresponding to the selected composition were calculated, and the adequacy of the obtained model was evaluated by comparing calculated and real indicators. It is shown that the calculation error does not exceed 10 %, and the proposed optimization algorithm and the model derived from it can be successfully used to optimize the composition of tablets.

A variety of topics are reviewed in the area of mathematical and computational modeling in biology, covering the range of scales from populations of organisms to electrons in atoms. The use of maximum entropy as an inference tool in the fields of biology and drug discovery is discussed. Mathematical and computational methods and models in the areas of epidemiology, cell physiology and cancer are surveyed. The technique of molecular dynamics is covered, with special attention to force fields for protein simulations and methods for the calculation of solvation free energies. The utility of quantum mechanical methods in biophysical and biochemical modeling is explored. The field of computational enzymology is examined.

Background and purpose As many other fields of science or perhaps more than them Mathematics needs abstract models to represent its core concepts and how they are related. Being abstract by nature, one could unadvisedly suppose that the task of building those conceptual models would be easier than the average case, which is not necessarily true. Mathematical modeling is a field of applied mathematics which form deep inroads into other disciplines. The availability of a formal ontology and derived benefits, such as the possibility of conducting automated reasoning about the ntological classes of the domains, greatly reduce the barrier of entry in the field for non-experts, while helping the establishment of a more precise and controlled vocabulary among the expert domains involved in mathematical modeling.

This paper presents a set of ontologies to organize concepts, categories, properties, and relationships that are typically used by designers for characterizing sensing and actuation devices that compose a given system architecture (SA). From the characterization of such devices, modeling can be done using the Architecture Analysis and Design Language (AADL). AADL supports modeling and analysis of functional and nonfunctional properties to evaluate quality attributes from ontology models. The paper also proposes an AADL property set that can be applied to sensors and actuators (S&A), based on previous researches with ontologies applied to sensor networks. Specific characteristics are provided to describe systems' quality attributes. This aims to be used for analyzing the designed architecture, and also its probable future evolution.