Triangular Distribution Research Articles

Evaluation of geothermal resources potential in the uplifted mountain of Guangdong province using the Monte Carlo simulation

Geothermal energy is a kind of renewable energy with the characteristics of stability, zero carbon emissions, less land occupation, and localization. It has enormous development potential in the transition from traditional fossil energy to renewable energy, especially in Guangdong, geothermal resources are also abundant. However, the existing resource potential evaluation is relatively broad, and the uncertainty of the distribution of geothermal resources is not considered. Therefore, accurately and scientifically assessing the potential of geothermal resources is currently a research focus, Monte Carlo simulation is an ideal solution to quantitatively measure the distribution of geothermal resources through probability distributions. In this study, based on the volume method, considering the uncertainty of geothermal resource distribution parameters, Monte Carlo simulation was introduced, and the triangular distribution and uniform distribution model were used to simulate the input parameters of geothermal fields, and the potential of uplifted mountain geothermal resources in this area was evaluated. The results show that the fracture-banded reservoir geothermal resources are 5.648–5.867 × 1016 kJ (mean 5.743 × 1016 kJ), the karst-layered reservoir geothermal resources are 5.089–5.536 × 1015 kJ (mean 5.328 × 1015 kJ), finally the uplifted mountain geothermal resources potential of Guangdong are 6.176–6.399 × 1016 kJ (mean 6.275 × 1016 kJ). It quantitatively shows that the existing uplifted mountainous geothermal resources potential in Guangdong Province is enormous, the total amount of uplifted mountainous geothermal resources is equal to 2.11–2.18 × 105 Ten thousand tons of standard coal (mean 2.14 × 105 Ten thousand tons of standard coal).

Short term follow-up of unstable femoral neck fractures in young adults treated with femoral neck system and cannulated compression screws

To investigate the clinical efficacy of femoral neck system(FNS) and three cannulated compression screws(CCS) in the treatment of unstable femoral neck fractures in young adults. The clinical data of 52 young and middle-aged patients with unstable femoral neck fractures admitted from August 2018 to August 2021 were reviewed and analyzed. All patients were divided into two groups according to the internal fixation method, 25 cases were treated with FNS fixation, 27 cases were treated with closed reduction and 3 CCS inverted triangular distribution. The operation time, incision length, intraoperative bleeding, hospitalization expenses and fracture reduction quality of two groups were recorded and compared;The patients were followed up regularly after operation. The fracture healing time, complete weight-bearing time and postoperative complications(nonunion, femoral neck shortening, femoral head necrosis) of two groups were compared. The Harris score was used to evaluate hip function 6 months after surgery. The operation was successfully completed in both groups. The patients in FNS group had more bleeding, longer incision length and higher hospitalization cost than CCS group(P<0.01). There ware no significant difference in operation time and Garden index between two groups(P>0.05). Patients in both groups were followed up for 6 to 32 months.The fracture healing time in FNS group was less than that in CCS group, the time of complete weight bearing after surgery was earlier than that in CCS group, and the hip Harris score was higher than that in CCS group (P<0.01). There were no internal fixation fracture complications in two groups during follow-up. In the FNS group, there were 4 cases of avascular necrosis of the femoral head and 2 cases of femoral neck shortening, of which 3 cases underwent total hip replacement due to avascular necrosis of the femoral head. In the CCS group, there were 2 cases of nonunion, 9 cases of avascular necrosis of the femoral head, and 11 cases of femoral neck shortening, among which 5 cases underwent total hip replacement due to nonunion and avascular necrosis of the femoral head. With simple operation, rotational stability and angular stability, FNS enables patients to start functional exercise as early as possible and reduces the incidence of postoperative complications of unstable femoral neck fracture. It is a new choice for the treatment of unstable femoral neck fracture in young adults.

Sustainable production-inventory system for perishables under dynamic fuel pricing and preservation technology investment.

In the production and inventory management of perishables, environmental considerations are gaining prominence. By reducing carbon emissions from various supply chain processes, such as production, transportation, warehousing, and waste disposal of perishable items, the present study aims to minimize the overall cost to the manufacturer through an optimized investment in green technology. Additionally, cycle time and preservation technology investment are optimized to decrease deterioration and revenue loss in order to minimize cost. The originality of the present research lies in the following considerations. Due to an increase in fuel price, the transportation cost of every subsequent order will also increase, thus resulting in an increase of average delivery cost in a production cycle. We investigate the impact of changes in fuel prices on transportation costs and production inventory model policies due to the volatile nature of fuel prices. The function of transportation cost can be used to calculate transport costs in the future. The deterioration rate is a random variable with a double triangular distribution. Precisely, the demand for any product depends on the product's price; therefore, linear price-dependent demand is considered. Per unit production cost is a function of direct material cost, tooling cost, and manpower cost. Taking into account all the aforementioned parameters, this paper simultaneously optimizes green technology investment, preservation investment, and cycle time. To achieve the solution of the proposed sustainable production system, an optimization technique for the nonlinear function is employed. Finally, numerical experiments are conducted to validate the model. A special case of a numerical example demonstrates that the expected value of the total average cost is reduced by 10.723% when investments are made in both green and preservation technology, whereas investments in green technology alone result in a cost reduction of only 2.15%. Then, managerial implications and a discussion of findings are proposed after a sensitivity analysis that examines the model's response to key parameter variation. The study concludes with a discussion of the limitations of current work and possible future scopes.

Uncertainty clustering internal validity assessment using Fréchet distance for unsupervised learning

Knowing the number of clusters a priori is one of the most challenging aspects of unsupervised learning. Clustering Internal Validity Indices (CIVIs) evaluate partitions in unsupervised algorithms based on metrics like compactness, separation, and density. However, specialized CIVIs for specific applications have been designed, and there is no general CIVI that works in all scenarios. The absence of CIVIs based on crisp uncertainty metrics is especially critical in decision-making processes that involve ambiguity, non-convex distributions, outliers, and overlapping data. To address this problem, we propose a novel Uncertainty Fréchet (UF) CIVI that assesses the certainty of a well-defined partition. UF leverages uncertainty fingerprints based on Type-2 fuzzy Gaussian Mixture Models (T2FGMM) and the Fréchet distance between clusters to introduce a metric that evaluates partition quality. We integrate UF into a merging methodology that combines similar clusters within a partition, allowing us to determine the number of clusters without the need to run the clustering algorithms iteratively as other CIVIs require. We undertake a comprehensive evaluation of our proposal on 5,250 convex, 36 non-convex synthetic datasets, and five benchmark real datasets. In addition, we apply UF in a real-world scenario that involves high uncertainty: Passive Acoustic Monitoring (PAM) of ecosystems, which aims to study ecological transformations through acoustic recordings. The results show that UF exhibits notable performance in synthetic and real-world scenarios, obtaining an Adjusted Mutual Information (AMI) score higher than 0.88 for normal, uniform, gamma, and triangular distribution datasets. In the PAM application, UF identifies the transformation of ecosystems through sound using clustering algorithms and UF, achieving an F1 score of 0.84. Therefore, results show that the UF index is a suitable tool for researchers and practitioners working with highly uncertain data.

Design and Motion Process of Air-Sieve Castor Cleaning Device Based on Discrete Element Method

In order to improve the cleaning effect of the castor shelling mixture, an air-sieve castor cleaning device was developed. The structure of the cleaning device was optimized by experiment and simulation based on the discrete element method. The results show that the sieving efficiency of the square distribution is 98.23% and the loss rate is 2.39%, both of which are better than the triangular distribution. The sieving efficiency in the condition of a 14 mm sieve hole diameter is 98.23%. For the conditions of 15 mm and 16 mm sieve hole diameters, the sieving efficiencies are 96.64% and 96.69%, respectively. Therefore, a sieve hole diameter of 14 mm is more beneficial for the sieving of castor capsules. The sieving efficiency is 94.0–99.5%, and the loss rate is 0.5–3.0% under 5–9° sieve inclination. The cleaning effect is better through comprehensive analysis when the sieve surface inclination is 8°. The parameters of maximum sieving efficiency combination, minimum loss rate combination, and optimal cleaning effect were obtained by optimizing the operating parameters of the cleaning device. The operating parameters were adjusted, and then the three combinations of parameters were tested. It is found that the impurity content of castor seeds is within 1%, which meets the requirements of the device design. This study can provide a reference for developing high-efficiency castor cleaning devices.

Construction Work Efficiency Analysis—Application of Probabilistic Approach and Machine Learning for Formworks Assembly

Analyses of efficiency are vital for planning and monitoring the duration and costs of construction works, as well as the entire construction project. This paper introduces a combined quantitative (probabilistic) and qualitative (machine learning-based) approach to the problem. The proposed approach covers probabilistic analysis based on fitting a triangular distribution to empirical data, followed by the application of support vector machines (SVM). Following the theoretical assumptions, the paper also presents an application of the proposed approach for formwork assembly as an exemplary construction work. This is based on real-life data, including conditions, characteristics, and features of formwork assembly work recorded on a construction site. As a result of the study, triangular distributions were fitted to data representing efficiencies of formwork assembly for three different types of structural members made of reinforced concrete. The parameters (a—minimum, m—peak and b—maximum values of efficiency measured as square meters of an assembled formwork per hour) of the fitted distributions for the particular real-life data were as follows: for columns a = 0.100, m = 1.450, b = 1.900, for walls a = 0.700, m = 1.995, b = 3.300 and for slabs a = 0.200, m = 2.125, b = 3.200. The obtained distributions allow us to assess the probability of achieving efficiency not less than a certain assumed critical value. The study also developed two SVM models—the first based on so-called C-classification and the second based on ν-classification—capable of recognising with satisfactory accuracy whether the efficiency of formworks assembly works for certain conditions, characteristics, and features of works are above or below median values computed based on previously fitted distributions. The performance of both developed models in terms of proper classification, either for training or testing, was above 80%.

An application of a smart production system to control deteriorated inventory

Deteriorating products require different handling procedures. Handling procedure includes prevention of the natural deterioration rate of the product. The production of deteriorating products requires prevention technology for those products to use for a long time. Overproduction of deteriorating types of products causes more trouble in preventing deterioration. This study uses a smart production system to control the production of deteriorating products. A controllable production rate controls the production of deteriorating products, and preservation technology reduces the deterioration rate of products. Preservation technology helps extend the life of products, but it requires a specific temperature-controlled environment to work at maximum efficiency. Transportation of these products uses refrigerated transportation to maintain the quality during the transportation time. The purpose of using all these features for deteriorating products is to reduce the deterioration rate, which helps to reduce waste generation from production. Besides, imperfect products from the production system pass through a remanufacturing process to support the waste reduction process. A sustainable supply chain management model under the above-stated strategies is described here. A classical optimization is used to find global optimum solution of the objective function. Then, the total cost of the supply chain is optimized using unique solutions of production rate, number of deliveries, delivery lot size, system reliability, and preservation investment. Global optimum solutions are established theoretically, and few propositions are developed. Some special cases, case studies, and a comparison graph are provided to validate the results. The beta distribution provides the minimum total cost of the system than uniform, gamma, triangular, and double triangular distribution. Smart production allows 72% system reliability with a negligible amount of imperfect products. Besides, the proposed policy gain 22.72% more profit than exiting literature. The model is more realistic through convex 3D graphs, sensitivity analyses, and managerial insights.

Risk assessment in railway rolling stock planning

Rolling stock planning is one of the steps in the traffic planning process considered from the railway undertaking's point of view. It is directly related to the efficiency of rolling stock utilisation, which should be ensured at the highest possible level in the case of rail transport. The planning work stage is subject to certain risks (threats and opportunities), which, if they materialise, will impact it. It, therefore, makes sense to carry out analyses that can anticipate specific events in good time and introduce appropriate countermeasures in advance. This article aims to conduct a risk assessment process concerning rolling stock planning. It was assumed that the considerations were carried out based on the M_o_R (Management of Risk) methodology. Based on this methodology, risk identifica-tion and risk analysis (estimation of risk impact) were carried out. Risk assessment was carried out using the Monte Carlo simulation method. The work identified sixteen risks that represent threats. The principle of risk description was used to identify risks. It requires indicating for each risk the reason for its occurrence and the effect it may have. As a part of risk estimation, variables were selected to assess each risk's impact on the objectives of the stage. Publicly available statistical data were used to define the variables. The variables were expressed in monetary units. The work identified five variables describing impact, which were assigned to the individual risks. As a trian-gular probability distribution was used for the variability of impact description, the variable's minimum, most likely, and maximum value was identified. A risk assessment was carried out for only two impact description varia-bles (for those variables used to describe the impact of the most significant number of risks). For each variable, statistical parameters were indicated and analysed. The resulting value of the variable describing the impact was then read out for each percentile, and the expected value of the risk was calculated. A detailed risk assessment was made for the lower, middle and upper quartiles. A histogram of the incidence of each variable value was presented, and an assessment was made.

Damage Identification in Plane Multi-storey Reinforced Concrete Frame

Objective: In this paper, a new method for damage detection in reinforced concrete multi-storey frames is presented. Methods: The proposed new methodology is a hybrid technique consisting of two parts. The first step involves determining the seismic pushover capacity curve of the structure, and the second step includes formulating the diagram of the instantaneous eigenfequencies of the structure in the nonlinear regime. With reference to this diagram, more details are given in the text. To estimate the equivalent target displacement defined at the top of the structure, which corresponds to the instantaneous eigenfrequencies of a structure with damage, the diagram of these eigenfrequencies is combined with the seismic pushover capacity curve of the structure. Thus, the target displacement at the top of the frame is calculated. Result: The advantage of the proposed methodology is that using this target displacement, the final picture of the damage in the structure is estimated from the two pushover analyses, with positive and negative signs of the floor lateral forces corresponding to triangular distribution in elevation. For clarification, an example of a three-storey R/C frame is presented as a paradigm. Conclusion: Using the proposed methodology, the locations of damage in the structure are successfully identified, as well as the Damage Stiffness Matrix is estimated with high accuracy.

Canonical triangular interval type-2 fuzzy set linguistic distribution assessment TODIM approach: A case study of FMEA for electric vehicles DC charging piles

Linguistic distribution assessment (LDA) plays a prominent role in describing the subjective uncertainties and objective distribution of decision-maker (DM) opinions. Although there have been several studies on LDA, few of these studies have paid attention to the different understandings of language semantics provided by DMs. To address the issue, type-2 (T2) fuzzy sets (T2FSs) are a well-known approach because T2FSs can accurately model the understanding of individuals with linguistic uncertainty. A trapezium (or trapezoidal) interval type-2 fuzzy set (TrIT2FS) is a common application of T2 fuzzy logic. Accordingly, this paper discusses a novel LDA called a canonical triangular interval type-2 fuzzy set (CTriIT2FS)-LDA in a T2 fuzzy environment. The CTriIT2FS-LDA combines a CTriIT2FS simplified from a TrIT2FS with LDA, which can simplify the computation while retaining their advantages. To facilitate the calculation of the CTriIT2FS-LDA, the basic operations of the CTriIT2FSs and the CTriIT2F-LDA, such as the defuzzied (crisp) function, distance measurement, and entropy measurement, are defined. Based on the TODIM approach, a CTriIT2F-LDA-TODIM is developed for FMEA for interval type-2 fuzzy environments. Furthermore, the proposed approach is applied in a practical case for FMEA for the electric vehicle DC charging piles of the State Grid Corporation of China.

Propagation Mechanism of Deep-Water Impulse Waves Generated by Landslides in V-Shaped River Channels of Mountain Valleys: Physical Model of Regular Rigid Block

Landslide-induced impulse waves in alpine valleys are a significant risk to large-scale dam and reservoir engineering projects in the surrounding area. In this study, a 1 : 200-scale physical model of landslide-induced impulse waves in a V-shaped river channel was established, and 18 groups of tests were conducted to evaluate the influence of different parameters, such as the volume and shape of the landslide body, water entry velocity, and water depth of the reservoir. Based on the test results, a dimensionless formula was established for the first wave height of impulse waves caused by a deep-water landslide in a V-shaped channel. An energy conversion law was determined for the impact of landslide-induced impulse waves on the reservoir bank. Finally, a distribution law was obtained for the initial maximum pressure caused by landslide-induced impulse waves along the water depth on the opposite bank. The theoretical predictions of the dimensionless formula showed good agreement with the experimental results, and the energy conversion rate of the landslide-induced impulse waves initially increased and then decreased with an increasing Froude number. The maximum dynamic water pressure showed a triangular distribution with increasing water depth below the surface of the still water body. The impact pressure of the impulse waves on the slope on the opposite bank increased with the water entry velocity. This study provides a scientific basis for the risk prevention and control of landslide-induced impulse waves in river channels feeding into reservoirs.

Static numerical simulation of radial deformation of ultra-thin dicing blade

Grinding with dicing blade is an important method to cut or slot electronic and optical devices. The deformation of grinding tools will definitely affect the processing of workpiece. However, this effect has been disregarded during processing. In order to improve the machining accuracy in the precision grinding method, this deformation is worth considering. In this research, the grinding state of the ultra-thin dicing blade was simplified as a static problem. The force model of the ultra-thin dicing blade during grinding was established, which centrifugal force was adopted in the whole blade and triangular distribution grinding forces were adopted in the grinding area. The radial deformation of the ultra-thin dicing blade was determined by finite element simulation, and the influence of grinding parameters on its radial deformation was analyzed. The simulation results showed that the grinding area of the ultra-thin dicing blade occurred radial expansion deformation at high rotational speed (more than 8000 rpm), and the value could reach 1.75 μm (rotational speed at 23,000 rpm, feed speed at 600 mm/min, and grinding depth at 0.12 mm). The deformation increased in a form of power function with the increase of rotational speed, and decreased linearly with the increase of feed speed and grinding depth. This work can provide reference data for deformation compensation, which is helpful to improve the dimensional accuracy of grinding groove.

Effect of vortex generator spanwise height distribution pattern on aerodynamic characteristics of a straight wing

Vortex generator (VG) is a passive flow control technology, which can effectively inhibit flow separation. Recently, significant research efforts have been devoted to the study on the application of VG in airfoil, wing/blade and aircraft flow separation inhibition. However, the research on the variable height distribution of VG along the wingspan still lacks. This study focuses on the experimental investigation of the influence of variable height distribution of ramp VG on aerodynamic characteristics. First, VG was designed, such that it was composed of two parts, one fixed region and one deformed region, which allowed for height modification. The height of VGs along the wingspan presented equal-height, triangular and trapezoidal distribution, forming a total of 15 VG layouts. Then, the connection mode of the model, the change of angle of attack and the collection and processing of aerodynamic data were introduced. Finally, a wind tunnel experiment was performed to investigate the influence of height distribution of VG on aerodynamic characteristics of wing. The experimental results show that: (1) the height distribution of the three types of VGs could inhibit the stall flow and improve the aerodynamic performance of the wing; (2) “Triangular translation 3” and “Trapezoidal translation 2” were the best layouts, both of which could increase the maximum lift coefficient, delay stall, and significantly increase the lift-to-drag ratio at high angle of attack; (3) the influence of VG height and position factors on wing stall characteristics was analyzed by using the rough set theory, and the key position information of VG arrangement was provided. This study indicates that the variable height distribution is obviously better than the equal height distribution, which can provide ideas and references for the active control of variable height distribution of VGs.

Random Orthogonal Search with Triangular and Quadratic Distributions (TROS and QROS): Parameterless Algorithms for Global Optimization

In this paper, the behavior and performance of Pure Random Orthogonal Search (PROS), a parameter-free evolutionary algorithm (EA) that outperforms many existing EAs on the well-known benchmark functions with finite-time budget, are analyzed. The sufficient conditions to converge to the global optimum are also determined. In addition, we propose two modifications to PROS, namely Triangular-Distributed Random Orthogonal Search (TROS) and Quadratic-Distributed Random Orthogonal Search (QROS). With our local search mechanism, both modified algorithms improve the convergence rates and the errors of the obtained solutions significantly on the benchmark functions while preserving the advantages of PROS: parameterless, excellent computational efficiency, ease of applying to all kinds of applications, and high performance with finite-time search budget. The experimental results show that both TROS and QROS are competitive in comparison to several classic metaheuristic optimization algorithms.

Determining the Accuracy of the Triangular and PERT Distributions

The Triangular and PERT (Program Evaluation Review Technique) distribution probability density functions are commonly used in decision and risk analyses. These distributions are popular because they are each specified by only three points (two support bounds and the mode) that are believed to be easy to assess from experts or data. In this paper, we carefully analyze how close the Triangular and PERT distributions are to other distributions sharing the same support and mode and show that the errors induced by the Triangular and PERT distributions are significant. We further show that distributions that are characterized by the median tend to provide a better fit than do those that are characterized by the mode. Funding: This research was supported by the Equinor Fellows Program and the Operating System 2.0 research program developed by the Construction Industry Institute.

Soft labelling based on triangular distributions for ordinal classification

Recently, solving ordinal classification problems using machine learning and deep learning techniques has acquired important attention. There are many real-world problems in different areas of knowledge where a categorical variable needs to be predicted, and the existing categories follow an order associated with the nature of the problem: e.g. medical diagnosis with different states of a disease, or industrial quality assessment with different levels of quality. In these problems, it is quite common that the final label for each sample is determined by a group of experts with different opinions, and all opinions are usually summarised in a single crisp label by means of a given statistic (e.g. the median or the mode). Applying standard ordinal classifiers to these crisp labels could result in overfitting, as the labelling information is considered as totally certain. In this work, we propose a unimodal regularisation approach based on soft labelling, i.e. the ordinal information is used to introduce the inherent uncertainty of the label fusion. Specifically, said regularisation is based on using triangular distributions to simulate the aforementioned fusion of the expert opinions, where a parameter is used to decide the amount of probability that is assigned to the target category and the adjacent ones (according to the ordinal scale). The strategy could be applied to the loss function used by any ordinal classification learning algorithm, but we focus on deep learning in this paper. The proposal is compared to a baseline approach for nominal classification tasks and other state-of-the-art unimodal regularisation methods, and the experimental validation includes six benchmark datasets and five performance metrics. The results along with the statistical analysis show that the proposed methodology significantly outperforms the rest of the methods.

Performance evaluation of steel-concrete composite structures designed in poorly graded soils

In this study, the seismic behavior of steel concrete composite buildings in a specific region was investigated. For this purpose, 5-, 10-, 15- and 20-storey composite moment-resisting framed structures were designed. Moment-resisting composite framed structures are modeled with concrete-filled steel tube columns and designed and modeled using composite beams. The buildings are designed according to ÇYTHYE-2016 and TBEC-2018 regulations at design levels with high ductility. In the design of the designed structures, the peak ground acceleration value is 0.79 g, and the design ground is planned as ZE class. SeismoStruct software was used for the design and performance evaluation of the structures. During the performance evaluations of the structures, nonlinear static pushover and incremental dynamic analyzes were used. Uniform and triangular load distributions are adopted in the static pushover analysis and 16 earthquake ground motions are used in the incremental dynamic analysis. Evaluation of the effect of the number of stories on the earthquake behavior of composite moment-resisting framed structures was investigated using the non-linear analyzes mentioned. Accordingly, lateral response, overstrength factors, ductility, and dynamic behavior factor values for composite frame structures were calculated and presented using the relevant analysis results. It has been calculated that the behavior factor of all moment-resisting composite framed structures can perform well above the design assumptions, whereas moment-resistant composite framed structures absorb seismic energy by using inelastic deformations. Ductility is almost 30% higher than the design assumption for international standards. As a result, it was concluded that these structures could continue to serve theoretically.

ПОРІВНЯННЯ АЛГОРИТМІВ КЛАСИФІКАЦІЇ BIG DATA МЕТОДАМИ ІМІТАЦІЙНОГО МОДЕЛЮВАННЯ

With the development of information transmission and storage technologies, the volumes of data that require processing and analysis are growing rapidly. Therefore, the task of developing algorithms for solving various artificial intelligence problems for Big Data volumes is urgent. In our works, this informal term "Big Data" refers to situations when known processing algorithms do not allow solving a problem in a practically acceptable time. With regard to classification tasks, such conditions are possible when the first place is not even high reliability (that is, the minimum number of errors), but productivity (classification speed). The well-known method of nearest neighbors is one of the most productive. However, the indicator of the order of growth (the number of typical operations) for it is K x M x N, where K is the number of nearest neighbors, M is the number of classes, N is the typical number of class elements. Along with this, we propose to consider algorithms based on the principles of M-means, where classes are replaced by only a small number of their characteristics. Among such algorithms, the article considers: the algorithm of class centers and the algorithm of adaptive rules. The order of growth for these algorithms is only M according to the number of classes. The comparative analysis of these algorithms is performed by the method of simulation modeling. Simulation models are implemented by the Adaptive Metrics program, developed at the Department of Software Engineering at DUITZ. In this program, the classification problem is solved using the example of the dichotomy problem for classes A and B. The program has the possibility of very flexible setting of models. Problems can be solved in 1-dimensional, 2-dimensional,..., 6-dimensional spaces. The distribution of factor values for classes A and B can have quite different statistical characteristics - from uniform and triangular distribution functions to functions approaching a normal distribution. The graphical interface of the program allows you to dynamically observe the solution of the classification problem in one-dimensional, two-dimensional and 6-dimensional projections. As a result of multiple runs of the program, it was established that the algorithms of the nearest neighbors slightly outperform the algorithms of class centers and adaptive rules according to the criterion of reliability, and also comply with the principle of compactness (concentration of the largest number of erroneous solutions in the hypercube of errors). Algorithms based on M-means principles significantly outperform this algorithm in terms of performance. Also, the algorithm of adaptive rules best corresponds to the principle of equality of classes and is the most productive of the considered ones.

Direct healthcare costs of non-metastatic castration-resistant prostate cancer in Italy.

The management of non-metastatic castration-resistant prostate cancer (nmCRPC) is rapidly evolving; however, little is known about the direct healthcare costs of nmCRPC. We aimed to estimate the cost-of-illness (COI) of nmCRPC from the Italian National Health Service perspective. Structured, individual qualitative interviews were carried out with clinical experts to identify what healthcare resources are consumed in clinical practice. To collect quantitative estimates of healthcare resource consumption, a structured expert elicitation was performed with clinical experts using a modified version of a previously validated interactive Excel-based tool, EXPLICIT (EXPert eLICItation Tool). For each parameter, experts were asked to provide the lowest, highest, and most likely value. Deterministic and probabilistic sensitivity analyses (PSA) were carried out to test the robustness of the results. Ten clinical experts were interviewed, and six of them participated in the expert elicitation exercise. According to the most likely estimate, the yearly cost per nmCRPC patient is €4,710 (range, €2,243 to €8,243). Diagnostic imaging (i.e., number/type of PET scans performed) had the highest impact on cost. The PSA showed a 50 percent chance for the yearly cost per nmCRPC patient to be within €5,048 using a triangular distribution for parameters, and similar results were found using a beta-PERT distribution. This study estimated the direct healthcare costs of nmCRPC in Italy based on a mixed-methods approach. Delaying metastases may be a reasonable goal also from an economic standpoint. These findings can inform decision-making about treatments at the juncture between non-metastatic and metastatic prostate cancer disease.

Continuous measurement of flow direction and streamflow based on travel time principles using a triangular distribution of acoustic tomography systems

Monitoring flood dynamics is important to provide optimal flood mitigation practices and understand their hydrological responses. Recently, applications of travel time principles have gained a growing interest in hydrological research and river engineering. In this study, flood dynamics were monitored using the fluvial acoustic tomography system (FAT), based on travel time principles. The primary objective of this study is to continuously measure the mean cross-sectional velocity, river flow direction, and river discharge using an innovative tomographic system during two flood events. In this regard, three FAT systems were placed in a gravel bed stream forming a triangle shape to measure stream velocity along two cross-sections. By investigating the magnitude of the cross-sectional mean velocity vectors and the cross-sectional areas, we proposed new equations to evaluate the expected flow direction. The performance of flow measurement by the FAT system was verified with another reference record. Importantly, we demonstrated that the minimum number of acoustic stations to determine river flow direction in unidirectional streams can be reduced to three stations which can be more practical and easier. Further, one of the novel aspects of this study is offering new guidelines to continuously estimate flow direction using a triangular distribution of tomographic systems. In general, this study presents a promising method for monitoring flow dynamics in rivers.