Concept Of Probability Research Articles

Ortaokul Öğrencilerinin Olasılıksal Akıl Yürütme Beceri Düzeylerinin Bazı Değişkenler Açısından İncelenmesi

In this study, it was aimed to determine sixth, seventh and eighth grade students’ levels of probabilistic
 reasoning and to investigate these levels in relation to gender, grade level and mathematics achievement. The
 study employed the descriptive survey and relational survey models with study group comprised of a total of
 286 students. For determination of the students’ levels of probabilistic reasoning, the probabilistic reasoning
 scale used developed by researchers. The probabilistic reasoning was examined for six key concepts called
 sample space, experimental probability of an event, theoretical probability of an event, probability comparisons,
 conditional probability and independence. In the determination of the students’ levels of probabilistic reasoning,
 descriptive statistics were used and with Chi-square analysis, the relationships between these levels and the
 variables to be determined. As a result of the analyses, it was found that the students had the most 3rd level
 reasoning skills in the concepts of the theoretical probability of an event and probability comparisons. A
 relationship was found between the gender variable and only the sample space. A relationship was found in all
 concepts with the grade level. There was a relationship between the mathematics achievement and the concepts
 except independence and the experimental probability of an event.

Realizing the value in "non-standard" parts of the qPCR standard curve by integrating fundamentals of quantitative microbiology.

The real-time polymerase chain reaction (PCR), commonly known as quantitative PCR (qPCR), is increasingly common in environmental microbiology applications. During the COVID-19 pandemic, qPCR combined with reverse transcription (RT-qPCR) has been used to detect and quantify SARS-CoV-2 in clinical diagnoses and wastewater monitoring of local trends. Estimation of concentrations using qPCR often features a log-linear standard curve model calibrating quantification cycle (Cq) values obtained from underlying fluorescence measurements to standard concentrations. This process works well at high concentrations within a linear dynamic range but has diminishing reliability at low concentrations because it cannot explain "non-standard" data such as Cq values reflecting increasing variability at low concentrations or non-detects that do not yield Cq values at all. Here, fundamental probabilistic modeling concepts from classical quantitative microbiology were integrated into standard curve modeling approaches by reflecting well-understood mechanisms for random error in microbial data. This work showed that data diverging from the log-linear regression model at low concentrations as well as non-detects can be seamlessly integrated into enhanced standard curve analysis. The newly developed model provides improved representation of standard curve data at low concentrations while converging asymptotically upon conventional log-linear regression at high concentrations and adding no fitting parameters. Such modeling facilitates exploration of the effects of various random error mechanisms in experiments generating standard curve data, enables quantification of uncertainty in standard curve parameters, and is an important step toward quantifying uncertainty in qPCR-based concentration estimates. Improving understanding of the random error in qPCR data and standard curve modeling is especially important when low concentrations are of particular interest and inappropriate analysis can unduly affect interpretation, conclusions regarding lab performance, reported concentration estimates, and associated decision-making.

Toward nonprobabilistic explanations of learning and decision-making.

Referring to probabilistic concepts (such as randomness, sampling, and probability distributions among others) is commonplace in contemporary explanations of how people learn and make decisions in the face of environmental unknowns. Here, we critically evaluate this practice and argue that such concepts should only play a relatively minor part in psychological explanations. To make this point, we provide a theoretical analysis of what people need to do in order to deal with unknown aspects of a typical decision-making task (a repeated-choice gamble). This analysis reveals that the use of probabilistic concepts in psychological explanations may and often does conceal essential, nonprobabilistic steps that people need to take to attempt to solve the problems that environmental unknowns present. To give these steps a central role, we recast how people solve these problems as a type of hypothesis generation and evaluation, of which using probabilistic concepts to deal with unknowns is one of many possibilities. We also demonstrate some immediate practical consequences of our proposed approach in two experiments. This perspective implies a shift in focus toward nonprobabilistic aspects of psychological explanations. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

Skills for Prospective Civil Engineers: Mastery of Current and Future Situations

This study aims to explore the competency mastery of prospective civil engineers based on the 3rd edition of the Civil Engineering Body of Knowledge and predict the future skills needed for prospective civil engineers in the next 10-20 years. A quantitative approach with a survey method was carried out to answer the first research objective. The questionnaire is filled out by prospective civil engineers who are final-year students of bachelor’s in civil engineering. Next, a descriptive analysis was conducted to provide an overview of the mastery of competencies. Finally, the Systematic Literature Review (SLR) method was carried out to answer the second research objective. The analyzed literature uses the Scopus Database with keywords that describe future work skills and competencies. Then the articles were then filtered using the PRISMA Diagram and analyzed with the help of the R program to produce a word cloud that describes the types of future skills needed. The research results show that 1) civil engineer candidates must increase competence in the application of natural sciences, humanities aspects for Civil Engineering, mechanics and fluids problems, formulation of solutions to problems relevant to Civil Engineering, engineering economics, probability concepts, and statistics. 2) They must develop future skills needed for prospective civil engineers: critical thinking, communication, professionalism, problem-solving, leadership, teamwork, collaboration, and the principle of sustainability. The findings of this study serve as evaluation material and recommendations for civil engineering education providers to prepare prospective civil engineers with a global outlook.

Establishment of outdoor thermal comfort index groups for quantifying climate impact on construction accidents

The construction industry is significantly influenced by various outdoor weather factors, which affect the thermal comfort of workers and, subsequently their productivity and health. Existing studies regarding outdoor thermal comfort only consider the daytime or a specific season. However, this study considers all seasons and regions based on accident data and aims to analyze the relationship between construction accidents and the outdoor thermal comfort index based on the frequency and probabilities by using accident data from the construction industry. In addition, Physiological equivalent temperature groups based on their impact on accidents are developed to classify the accident probability by climate index level. This study is conducted in the following five steps: (i) collection of data, (ii) calculation of the outdoor thermal comfort, (iii) calculation of the relative frequency, and (iv) conducting statistical analyses. As a result of the relative probability analysis, which is the concept of probability, it was found that the probability of accidents was the highest at PET temperature of 34.7 °C and 2.95. That is, as the PET temperature decreases or increases, the relative frequency indicating the probability of an accident increases. In addition, seven outdoor thermal comfort index grades were classified based on relative frequency.

Ramsey and Keynes revisited

Abstract This paper re-assesses Ramsey’s influence on Keynes. It is argued that the Standard View has restricted attention to the implications for probability theory of Ramsey’s criticisms of Keynes’s concepts of logical probability-relations and non-numerical probabilities. Building on the work of both Coates (1996) and Misak (2016), an Alternative View is proposed in which Ramsey’s influence on Keynes is seen as principally philosophical. Specifically, the Alternative View recognises Ramsey’s adoption of the logical pragmatist philosophy of C. S. Peirce from 1924 onwards with a dispositional theory of belief in which beliefs are treated not only as useful mental habits that can successfully guide future actions but also as able to provide true explanations of observed empirical facts. The textual evidence is examined, particularly Keynes’s biographical essay on Ramsey, which, it is argued, supports the contention that Keynes fully appreciated and was sympathetic to Ramsey’s pragmatism especially the importance of vague knowledge and the need for the development of human logic as the study of reasonable human behaviour.

Probabilistic modeling of threshold stress intensity factor for fatigue endurance reliability prediction

This study develops a probabilistic model for the threshold stress intensity factor range, which is a critical parameter in infinite fatigue life design under material flaws. The model is based on the proposed concept of probability of propagation in the probabilistic framework, allowing for deriving the probability density function of the threshold intensity factor range. The uncertainty in fatigue crack growth can naturally be incorporated into the resulting distribution. By further introducing the derived distribution into the Kitagawa–Takahashi diagram, the fatigue endurance reliability model can be established in a rational manner. With the first-order asymptotic approximation, the analytical form of fatigue endurance reliability index is obtained. The usefulness of the overall method is demonstrated using realistic engineering application examples.

Development and Application of Methodology for Quantification of Overbreaks in Hard Rock Tunnel Construction

A methodology for determining overbreaks in hard rock tunnel construction using the drill-and-blast technique is presented in this paper. The methodology was developed for and applied to crystalline medium- to thick-bedded limestone, but it can be used in any jointed hard rock mass. Overbreaks are inevitable in hard rock tunnelling in a low-confinement environment (shallow tunnels up to several hundred meters deep) as a result of wedge failures along unfavourably oriented discontinuities caused by blasting. It is widely accepted in engineering practise that overbreaks will be inevitable even if smooth contour blasting is applied. If not controlled, overbreaks can result in extreme financial and time costs; and determining, predicting, and mitigating them is the key to successful tunnel construction in hard rock. Technological overbreaks, which are caused by the inappropriate use of drill-and-blast excavation, are not easily distinguished from the inevitable overbreaks dictated by the geological conditions with which they interfere and overlap. A methodology was developed with the aim of distinguishing the two causes of overbreaks, which can be applied in any phase of tunnel construction for evaluation or mitigation. The analysis of key inputs, including geological face mapping, shear strength tests along discontinuities of the rock mass, and their spatial orientation relative to tunnel advancement and survey overbreak measurements, is presented in this paper. Due to the stochastic and statistical nature of the problem, a probabilistic concept was also applied as part of the method so that the probability of failure around unprotected tunnel sections could be determined. The so-called stability criterion is introduced to distinguish between stable and unstable sections in terms of the probabilistic safety factor. The quantification of overbreaks, including the threshold value distinguishing technological from geological overbreaks, is proposed. The application of the methodology, demonstrated on an 8.1 km long section of a 12 km long pressure tunnel in hard rock, is presented in the paper.

A model‐free approach to continuous‐time finance

AbstractWe present a pathwise approach to continuous‐time finance based on causal functional calculus. Our framework does not rely on any probabilistic concept. We introduce a definition of continuous‐time self‐financing portfolios, which does not rely on any integration concept and show that the value of a self‐financing portfolio belongs to a class of nonanticipative functionals, which are pathwise analogs of martingales. We show that if the set of market scenarios is generic in the sense of being stable under certain operations, such self‐financing strategies do not give rise to arbitrage. We then consider the problem of hedging a path‐dependent payoff across a generic set of scenarios. Applying the transition principle of Rufus Isaacs in differential games, we obtain a pathwise dynamic programming principle for the superhedging cost. We show that the superhedging cost is characterized as the solution of a path‐dependent equation. For the Asian option, we obtain an explicit solution.

A SIMPLE APPROACH FOR MULTI-CRITERIA DECISION-MAKING ON BASIS OF PROBABILITY THEORY

In the present paper, a new concept of favorable probability is proposed first, and a simplified approach for multi-criteria decision-making is developed on basis of probability theory. It assumes that all the performance indexes of all alternatives can be divided into beneficial and unbeneficial types in the multi-criteria decision-making, and each performance index of all alternative makes its contribution to a partial favorable probability in positively or negatively correlative manners linearly upon its type of beneficial or unbeneficial; the partial favorable probability of each performance index with the same physical meaning is normalized in the alternative group; the product of all partial favorable probability of an alternative makes the total favorable probability of the alternative. As a consequence, all the alternatives can be ranked according to their total favorable probability comparatively in the multi-criteria decision-making. As application examples of the new method, the quantitative assessment of multi-criteria selection for effective dwelling house walls, project managers and contractor for construction works are given in detail, satisfied results are obtained.

Calculation of average acquisition probability for spiral–circular composite scanning in free space optical communication

This study investigates the acquisition probability calculation method for spiral–circular composite scanning (SCCS) in free space optical communication. The concepts of effective coverage area (ECA) and average acquisition probability (AAP) are proposed. Owing to the fast movement of the fine tracking system (FTS) of the transmitting terminal, the beam width of the transmitter is enlarged from the perspective of the receiving terminal, and the ECA is actually the enlarged area. Based on the concept of ECA, the SCCS can be considered as the traditional spiral scanning (TSS) with an enlarged beam. Then the AAP calculation method is presented to describe the acquisition probability by considering the field of uncertainty (FOU) and platform vibration simultaneously. Furthermore, the AAP builds up a connection between two existing concepts of acquisition probabilities and includes them as special cases. The effectiveness of the proposed method is validated by Monte Carlo simulations.

Network Planning Analysis Using CPM and PERT Methods on Optimization of Time and Cost

The shipbuilding industry is the most important industry to support sea transportation in the context of maritime development. As a company engaged in shipping, the function of the shipyard is as a place for shipbuilding, ship repair, and ship maintenance. One of the activities carried out by PT. DNC as a shipyard company is to repair TK Aek Sigala-gala. Ship repair is a process of repairing or replacing ship materials that cannot be used to avoid risks that occur in the sea when the ship sails. In the implementation of project activities, the company must understand the right network so that there are no problems scheduling, planning and controlling project activities. This study aims to solve the problems faced by the company, is the delay in completion time. The data used is secondary data related to the sequence and relationship of activities, execution time, and cost budget plan (RAB). This study uses CPM and PERT methods to determine the optimal turn around time using critical path and probability concepts. The results of the CPM and PERT methods are activities on the critical path with an optimal duration of 98 days. The crashing method is to reduce the duration to 72 days with savings of Rp. 16,351,708. if the project implementer does not crash, the penalty that must be paid is Rp. 3,072,963,905.

Novo rešenje problema višekriterijumskog celobrojnog programiranja pomoću višekriterijumske optimizacije zasnovane na verovatnoći

Introduction/purpose: In this paper, a new solution for solving a multiobjective integer programming problem with probabilistic multi - objective optimization is formulated. Furthermore, discretization by means of the good lattice point and sequential optimization are employed for a successive simplifying treatment and deep optimization. Methods: In probabilistic multi - objective optimization, a new concept of preferable probability has been introduced to describe the preference degree of each performance utility of a candidate; each performance utility of a candidate contributes a partial preferable probability and the product of all partial preferable probabilities deduces the total preferable probability of a candidate; the total preferable probability thus transfers a multi-objective problem into a single-objective one. Discretization by means of the good lattice point is employed to conduct discrete sampling for a continuous objective function and sequential optimization is used to perform deep optimization. At first, the requirements of integers in the treatment could be given up so as to simply conduct above procedures. Finally, the optimal solutions of the input variables must be rounded to the nearest integers. Results: This new scheme is used to deal with two production problems, i.e., maximizing profit while minimizing pollution and determining a purchasing plan for spending as little money as possible while getting as large amount of raw materials as possible. Promising results are obtained for the above two problems from the viewpoint of the probability theory for simultaneous optimization of multiple objectives. Conclusion: This method properly considers simultaneous optimization of multiple objectives in multi-objective integer programming, which naturally reflects the essence of multi-objective programming, and opens a new way of solving multi-objective problems.

Theology and thermodynamics of life and mind in the scientific legacy of Nikolay Ivanovich Kobozev

Nikolay Ivanovich Kobozev (1903–1974), Professor of Moscow State University, famous Russian physico-chemist, specialist in the field of thermodynamics. In his works devoted to thermodynamics of information and thinking, he emphasized the incompatibility between the entropy law for molecular structures, including molecular machinery of the mind, and the law of identity for thinking. In order to compensate for the molecular entropy, the mind should receive a negative entropy or antientropy, which is defined on the basis of the extended concept of thermodynamic probability. The latter is defined as a number of procedures (algorithms) that can be used to produce a physico-chemical system from its elementary components. For non-algorithmic systems, the entropy is negative. In order to model processing and production of information, N. I. Kobozev postulated the existence in a brain of a strongly degenerate Fermi gas of superlight Ψ-particles (psychons), thus being one of the first scientists who emphasized the importance of quantum processes for the physics of mind. In all its levels, life contains an antientropic component, which distinguishes it from the non-living matter. According to Kobozev, ‘human mind cannot be the result of evolutionary transformation of information function into thinking. The latter must be given to us, and not acquired in the course of evolution’. Since the source of information is the God Himself, the N. I. Kobozev’s works correspond to the theocentric scientific worldview and they can well be considered as theological construction in natural sciences.

Application of Random Radial Point Interpolation Method to Foundations Bearing Capacity Considering Progressive Failure

In conventional analyzes of foundations failure, strengh parameters are assumed constant. However, during the failure, soil resistance exhibits maximum and residual amounts, and its strength decreases prematurely by increasing the plastic strain. In addition to change soil strengh parameters in the progressive mechanism, the non-uniform nature of the soil also causes spatial variations of these parameters. Therefore, geotechnical systems should be considered in terms of the uncertainty of soil parameters values, uncertainly using the concepts of statistics and probabilities. The purpose of this study is to investigate foundations in meshless method. In this article, radial point interpolation method (RPIM), a meshless method is proposed for simulation of soil foundation. Difficulties of methods related to mesh are solved by using this method. A code has been developed based on this method and some examples are solved for analyzing the code. In this research, a RPIM in combination with a random field was used to model the spatial variations of soil strengh properties and foundation bearing capacity analysis. For probabilistic analysis, random field is also used to determine the cohesion and the friction angle as well as the dilation angle based on their mean values and standard deviation. In order to investigate the application of the point interpolation method with randomized radial functions, a foundation with definite geometry has been analyzed deterministic and probabilistic and its safety factor has been investigated. Based on the analysis of the progressive failure modeling, it is concluded that the actual failure of the soil and the occurrence of continuous displacements occur simultaneously with the formation of a progressive mechanism of soil failure and the arrival of the slipping path to the ground. In the following, probabilistic distribution functions of the safety factor were determined by probabilistic analysis and the production of random fields, and then the statistical parameters are calculated.

DEVELOPMENT AND EVALUATION OF A PROFESSIONAL DEVELOPMENT PROGRAM ON DESIGNING PARTICIPATORY ACTION RESEARCH PROJECTS FOR BASIC EDUCATION TEACHERS

Anchored on Evans’ professional development (PD) model, this study aimed to develop, implement, and evaluate a professional development program on designing participatory action research (PAR) projects for basic education teachers. The teachers are from Junior and Senior High School teaching English, Mathematics, and Science. The PD program consisted of ten in-person training sessions and virtual consultations which happened in between training on AR problem conceptualization and methodology for a 14-week period. Using the mixed-methods sequential explanatory (QUAN à qual) design, the study started with a professional needs assessment participated by 18 teachers from a secondary school as a basis for the planned PD program. The teachers underwent training sessions to develop a group or participatory AR proposal as evidence of their professional growth and program outcome. At the end of the program, the English, Mathematics, and Science teachers, respectively, developed and presented their AR proposals on the (a) design and evaluation of a gamified-based instruction towards improving vocabulary skill, (b) video-based instruction in teaching basic concepts of probability, and (c) investigating the effect of contextualized learning materials in developing students’ conceptual understanding of atoms. The post-assessment results, supported by interviews, revealed that the teachers displayed behavioural, attitudinal, and intellectual developments in AR. Based on the Department of Education’s criteria for evaluating PAR proposals, all three proposals were rated acceptable for implementation by a panel of evaluators. In conclusion, the PD design and evaluation framework were important factors that enabled the participating teachers to transform their AR competencies toward developing PAR proposals for improving teaching and research in their schools.

Leibniz’s Dual Concept of Probability

Leibniz uses the concept of probability in both epistemic and non-epistemic contexts, as do many of his contemporaries. Some commentators have claimed that this dual-use is inexact or confused. In this paper, I describe Leibniz’s understanding of the concept of probability and discuss its dual usage in his work. Then, building on Leibniz’s creation theory, in conjunction with Russell’s interpretation of the Principle of Sufficient Reason, I endeavor to justify this dual usage and to show that this justification is also valuable for the contemporary discussion of the concept of probability.

Risk analysis of management of water systems in the Russian Federation

The management of the water management complex is based on the analysis of a large number of processes developing in systems that are techno-natural in nature, on the one hand, and in complex socio-economic systems affecting the whole society as a whole, on the other. The management methods implemented in practice today are based mainly on the analysis of the functioning of individual parts (individual processes) of the system, ideas about the processes under consideration are often not consistent, especially when it comes to technical and social systems. Regulatory management methods, including technical regulation, are considered separately. Socio-economic processes at different levels of temporal and spatial organization are investigated and predicted independently. At the same time, of course, regulatory legal knowledge is taken into account, but resource restrictions may fall out or be ignored, society is immune to instructions and recommendations lowered from above, legal nihilism takes place, the problem of qualification of decision-makers arises, etc.Certain possibilities for analyzing such situations are provided by risk theory methods. The purpose of the article is to analyze the risks arising at various stages of justifying water management measures, from design to strategies for the development of the industry as a whole. In particular, traditional methods of engineering calculations are considered, which ensure a given level of reliability of the designed water construction facilities in relation to hazardous impacts (loads), which are based on the concept of design probabilities. This approach provides a normative level of reliability, but does not guarantee the economic optimality of decisions made, is insufficient to implement the social functions of measures and structures, and is difficult to analyze environmental problems. Obtaining quantitative estimates of the parameters of structures and measures, carried out on the basis of probabilistic approaches, should be based at least on taking into account the possible consequences of decisions taken, as well as on damage assessments expressed in the form of relevant risks.

An Application of Relative Entropy in Structural Safety Analysis of Elastoplastic Beam under Fire Conditions

The main aim of this work is to propose a new algorithm of reliability assessment for steel civil engineering structures subjected to fire temperatures. This new algorithm is based upon the relative probabilistic entropy concept elaborated by Bhattacharyya, and this probabilistic distance is sought in-between extreme and admissible deformations of some structural beam subjected to higher temperatures. Similar to the First Order Reliability Method, this approach uses the first two probabilistic characteristics of the structural response, when structural output may be modelled with the use of Gaussian distribution. The probabilistic structural response is found here using hybrid computational technique–the Finite Element Method system ABAQUS with its fully coupled thermo-elastic analysis with 3D solid elements and probabilistic modules implemented in the computer algebra system MAPLE. The probabilistic response is determined via a triple stochastic analysis, which is based on the classical Monte-Carlo simulation, iterative generalized stochastic perturbation technique, and also using semi-analytical probabilistic calculus. Final determination of the relative entropy in the Serviceability Limit State of the given structure and its comparison with the results obtained using the FORM analysis enables to calibrate this new technique to numerical values proposed in the engineering designing codes. Hence, a more accurate probabilistic method may use some experimental-based admissible values included in the existing design of legal provisions.

THE HYPOTHETICAL LEARNING TRAJECTORY OF ENUMERATION RULES WITH ISLAMIC VALUES

<p>A context with Islamic values lies in can be used as a starting point in learning mathematics. The challenge is how teachers can deliver, formulate, and connect the mathematical content and the Islamic values in the learning activities. One of the learning approaches that can solve that challenge is Realistic Mathematics Education (RME) by implementing context as one of the activities. This study aims to design hypothetical learning trajectories (HLT) for supporting students in learning the rules of enumeration with the RME approach based on Islamic values. This study uses the first phase of design research (DR) methods. The first phase, namely preliminary design. The HLT is developed in this phase and will then be tested on students in experimental design, and the implemented results are analyzed in the retrospective analysis. Researchers began the study with a literature review, then obtained data about students' difficulties in the enumeration (counting) rule. Based on the review, researchers formulated activities into learning procedures and expected students and teachers’ responses, called HLT. The HLT of enumeration rules on data content with RME based on Islamic seen from the perspective of the four emerging modeling levels. At the first level – the 'situational level' – students explore the realistic context of determining the possible route to the mosque. The second level is the 'referential level' where the selection rules are used as a starting point for learning the concept of probability. At the third level – the 'general level' – students use diagrams to generalize the possible outcomes of an experiment and develop an understanding of multiplication rules. Finally, students develop their informal knowledge at the 'formal level' into formal concepts of multiplication rules.</p>