Search results for: mathematical reasoning

Authors: Ahmed Tarek, Ahmed Alveed

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In the theory of computing, there are a wide variety of direct and indirect proof techniques. However, mathematical induction (MI) stands out to be one of the most powerful proof techniques for proving hypotheses, theorems, and new results. There are variations of mathematical induction-based proof techniques, which are broadly classified into three categories, such as structural induction (SI), weak induction (WI), and strong induction (SI). In this expository paper, several different variants of the mathematical induction techniques are explored, and the specific scenarios are discussed where a specific induction technique stands out to be more advantageous as compared to other induction strategies. Also, the essential difference among the variants of mathematical induction are explored. The points of separation among mathematical induction, recursion, and logical deduction are precisely analyzed, and the relationship among variations of recurrence relations, and mathematical induction are being explored. In this context, the application of recurrence relations, and mathematical inductions are considered together in a single framework for codewords over a given alphabet.

Keywords: alphabet, codeword, deduction, mathematical, induction, recurrence relation, strong induction, structural induction, weak induction

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Authors: Jennifer Wallbrown

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It’s not uncommon in the US to see news article headlines about public school teachers being scrutinized for what they are teaching or see the general public weighing in on whether or not they think certain controversial subjects should be addressed in the classroom- such as LGBTQ+ or multicultural literature. Even though this is a subject that has been written about and discussed for years, it continues to be a relevant topic in education as it continues to be a struggle to implement more diverse texts. Although it is valid for teachers to fear controversy when they attempt to create a more diverse or inclusive curriculum, it is a fight worth fighting because of the benefits students can gain from being exposed to a wide range of texts. This paper is different from others of its kind because it addresses many of the counterarguments often made to implementing LGBTQ+ or multicultural literature in secondary classrooms. It not only encourages educators to try to include more diverse texts, but it gives them the tools to address common concerns and be sound in their reasoning for choosing these texts. This can be of interest to those educators who are not English teachers because a truly diverse and inclusive curriculum would include other subjects as well- including history, art, and more. By the end of my proposed paper, readers will feel encouraged to choose more diverse and inclusive texts for their classrooms. They can also be confident that if met with opposition or controversy, as is sometimes common when implementing new texts, that they have sound arguments and reasoning for why they chose to include these texts. This reasoning is that, based on the research, studies have found there are benefits to students studying texts about those different from themselves, because it teaches them empathy and helps fight prejudice.

Keywords: education, diverse, inclusive, multicultural, lgbtq+, pedagogy

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Authors: Wen Li, Zhengyu Bai, Qi Zhang

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The demand for smart scheduling platform in agriculture, particularly in the scheduling process of machinery equipment, is high. With the continuous development of agricultural machinery equipment technology, a large number of agricultural machinery equipment and agricultural machinery cooperative service organizations continue to appear in China. The large area of cultivated land and a large number of agricultural activities in the central and western regions of China have made the demand for smart and efficient agricultural machinery equipment scheduling platforms more intense. In this study, we design and implement a platform for agricultural machinery equipment scheduling to allocate agricultural machinery equipment resources reasonably. With agricultural machinery equipment scheduling platform taken as the research object, we discuss its research significance and value, use the service blueprint technology to analyze and characterize the agricultural machinery equipment schedule workflow, the network analytic method to obtain the demand platform function requirements, and divide the platform functions through the platform function division diagram. Simultaneously, based on the case-based reasoning (CBR) algorithm, the equipment scheduling module of the agricultural machinery equipment scheduling platform is realized; finally, a design scheme of the agricultural machinery equipment scheduling platform architecture is provided, and the visualization interface of the platform is established via VB programming language. It provides design ideas and theoretical support for the construction of a modern agricultural equipment information scheduling platform.

Keywords: case-based reasoning, service blueprint, system design, ANP, VB programming language

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Authors: Sagir M. Yusuf, Chris Baber

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In this paper, we describe how Bayesian inferential reasoning will contributes in obtaining a well-satisfied prediction for Distributed Constraint Optimization Problems (DCOPs) with uncertainties. We also demonstrate how DCOPs could be merged to multi-agent knowledge understand and prediction (i.e. Situation Awareness). The DCOPs functions were merged with Bayesian Belief Network (BBN) in the form of situation, awareness, and utility nodes. We describe how the uncertainties can be represented to the BBN and make an effective prediction using the expectation-maximization algorithm or conjugate gradient descent algorithm. The idea of variable prediction using Bayesian inference may reduce the number of variables in agents’ sampling domain and also allow missing variables estimations. Experiment results proved that the BBN perform compelling predictions with samples containing uncertainties than the perfect samples. That is, Bayesian inference can help in handling uncertainties and dynamism of DCOPs, which is the current issue in the DCOPs community. We show how Bayesian inference could be formalized with Distributed Situation Awareness (DSA) using uncertain and missing agents’ data. The whole framework was tested on multi-UAV mission for forest fire searching. Future work focuses on augmenting existing architecture to deal with dynamic DCOPs algorithms and multi-agent information merging.

Keywords: DCOP, multi-agent reasoning, Bayesian reasoning, swarm intelligence

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Authors: Abubakar Sa’adatu Mohammed

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This paper reports on a study of problem solving differences between expert and novice Problem solvers for effective physics teaching. Significant differences were found both at the conceptual level and at the level of critical thinking, creative thinking and reasoning. It is suggested for a successful solution of a problem, conceptual knowledge alone may not be sufficient. There is the need of the knowledge of how the conceptual knowledge should be applied (problem solving skills). It is hoped that this research might contribute to efforts of exploring ways for students to acquire a powerful conceptual toolkit based on experts like problem solvers approach for effective teaching delivery.

Keywords: conceptual knowledge, procedural knowledge, critical thinking, creative thinking, reasoning ability

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Authors: Jaime E. Fernandez, Pablo J. Valverde

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This paper presents a methodological approach that aims to contrast/validate theoretical results from a corruption network game through probabilistic analysis of simulated microdata using Bayesian Networks (BNs). The research develops a public corruption model in a game theory framework. Theoretical results suggest a series of 'optimal settings' of model's exogenous parameters that boost the emergence of corruption. The paper contrasts these outcomes with probabilistic inference results based on BNs adjusted over simulated microdata. Principal findings indicate that probabilistic reasoning based on BNs significantly improves parameter specification and causal analysis in a public corruption game.

Keywords: Bayesian networks, probabilistic reasoning, public corruption, theoretical games

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Authors: Sagir M. Yusuf, Chris Baber

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In this paper, we describe how to achieve knowledge understanding and prediction (Situation Awareness (SA)) for multiple-agents conducting searching activity using Bayesian inferential reasoning and learning. Bayesian Belief Network was used to monitor agents' knowledge about their environment, and cases are recorded for the network training using expectation-maximisation or gradient descent algorithm. The well trained network will be used for decision making and environmental situation prediction. Forest fire searching by multiple UAVs was the use case. UAVs are tasked to explore a forest and find a fire for urgent actions by the fire wardens. The paper focused on two problems: (i) effective agents’ path planning strategy and (ii) knowledge understanding and prediction (SA). The path planning problem by inspiring animal mode of foraging using Lévy distribution augmented with Bayesian reasoning was fully described in this paper. Results proof that the Lévy flight strategy performs better than the previous fixed-pattern (e.g., parallel sweeps) approaches in terms of energy and time utilisation. We also introduced a waypoint assessment strategy called k-previous waypoints assessment. It improves the performance of the ordinary levy flight by saving agent’s resources and mission time through redundant search avoidance. The agents (UAVs) are to report their mission knowledge at the central server for interpretation and prediction purposes. Bayesian reasoning and learning were used for the SA and results proof effectiveness in different environments scenario in terms of prediction and effective knowledge representation. The prediction accuracy was measured using learning error rate, logarithm loss, and Brier score and the result proves that little agents mission that can be used for prediction within the same or different environment. Finally, we described a situation-based knowledge visualization and prediction technique for heterogeneous multi-UAV mission. While this paper proves linkage of Bayesian reasoning and learning with SA and effective searching strategy, future works is focusing on simplifying the architecture.

Keywords: Levy flight, distributed constraint optimization problem, multi-agent system, multi-robot coordination, autonomous system, swarm intelligence

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Authors: Ian O'Loughlin

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Memory networks aim to integrate some of the recent successes in machine learning with a dynamic memory base that can be updated and deployed in artificial reasoning tasks. These models involve training networks to identify, update, and operate over stored elements in a large memory array in order, for example, to ably perform question and answer tasks parsing real-world and simulated discourses. This family of approaches still faces numerous challenges: the performance of these network models in simulated domains remains considerably better than in open, real-world domains, wide-context cues remain elusive in parsing words and sentences, and even moderately complex sentence structures remain problematic. This innovation, employing an array of stored and updatable ‘memory’ elements over which the system operates as it parses text input and develops responses to questions, is a compelling one for at least two reasons: first, it addresses one of the difficulties that standard machine learning techniques face, by providing a way to store a large bank of facts, offering a way forward for the kinds of long-term reasoning that, for example, recurrent neural networks trained on a corpus have difficulty performing. Second, the addition of a stored long-term memory component in artificial reasoning seems psychologically plausible; human reasoning appears replete with invocations of long-term memory, and the stored but dynamic elements in the arrays of memory networks are deeply reminiscent of the way that human memory is readily and often characterized. However, this apparent psychological plausibility is belied by a recent turn in the study of human memory in cognitive science. In recent years, the very notion that there is a stored element which enables remembering, however dynamic or reconstructive it may be, has come under deep suspicion. In the wake of constructive memory studies, amnesia and impairment studies, and studies of implicit memory—as well as following considerations from the cognitive neuroscience of memory and conceptual analyses from the philosophy of mind and cognitive science—researchers are now rejecting storage and retrieval, even in principle, and instead seeking and developing models of human memory wherein plasticity and dynamics are the rule rather than the exception. In these models, storage is entirely avoided by modeling memory using a recurrent neural network designed to fit a preconceived energy function that attains zero values only for desired memory patterns, so that these patterns are the sole stable equilibrium points in the attractor network. So although the array of long-term memory elements in memory networks seem psychologically appropriate for reasoning systems, they may actually be incurring difficulties that are theoretically analogous to those that older, storage-based models of human memory have demonstrated. The kind of emergent stability found in the attractor network models more closely fits our best understanding of human long-term memory than do the memory network arrays, despite appearances to the contrary.

Keywords: artificial reasoning, human memory, machine learning, neural networks

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Authors: Mariamawit T. Belete

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Cereal production and marketing are the means of livelihood for millions of households in Ethiopia. However, cereal production is constrained by technical and socio-economic factors. Among the technical factors, cereal crop diseases are the major contributing factors to the low yield. The aim of this research is to develop an integration of data mining and knowledge based system for sorghum anthracnose disease diagnosis that assists agriculture experts and development agents to make timely decisions. Anthracnose diagnosing systems gather information from Melkassa agricultural research center and attempt to score anthracnose severity scale. Empirical research is designed for data exploration, modeling, and confirmatory procedures for testing hypothesis and prediction to draw a sound conclusion. WEKA (Waikato Environment for Knowledge Analysis) was employed for the modeling. Knowledge based system has come across a variety of approaches based on the knowledge representation method; case-based reasoning (CBR) is one of the popular approaches used in knowledge-based system. CBR is a problem solving strategy that uses previous cases to solve new problems. The system utilizes hidden knowledge extracted by employing clustering algorithms, specifically K-means clustering from sampled anthracnose dataset. Clustered cases with centroid value are mapped to jCOLIBRI, and then the integrator application is created using NetBeans with JDK 8.0.2. The important part of a case based reasoning model includes case retrieval; the similarity measuring stage, reuse; which allows domain expert to transfer retrieval case solution to suit for the current case, revise; to test the solution, and retain to store the confirmed solution to the case base for future use. Evaluation of the system was done for both system performance and user acceptance. For testing the prototype, seven test cases were used. Experimental result shows that the system achieves an average precision and recall values of 70% and 83%, respectively. User acceptance testing also performed by involving five domain experts, and an average of 83% acceptance is achieved. Although the result of this study is promising, however, further study should be done an investigation on hybrid approach such as rule based reasoning, and pictorial retrieval process are recommended.

Keywords: sorghum anthracnose, data mining, case based reasoning, integration

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Authors: Zhanxing Li, Liqi Zhu

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Authorities often intervene in children’s property conflicts, which may affect young children’s ownership understanding. First possession is a typical rule of ownership judgment. We recruited Chinese preschoolers as subjects and investigated their ownership reasoning regarding first possession, by setting three conditions via a conflicting cues method, in which a third party (mother or peer friend)’s testimony was always opposite to the cue of first possession (authority/non-authority testimony condition), or only the cue of first possession was present (no testimony condition). In Study A, we examined forty-two 3- and 5-year olds’ attribution and justification of ownership. The results showed while 5-year olds gave more support for the first possessor as the owner across three conditions, 3-year olds’ choice for the first possessor had no difference from the non-first possessor in the authority testimony condition. Moreover, 3-year olds tended to justify by reference to what mother said in the authority testimony condition, 5-year olds consistently referred to the first possession in three conditions. In Study B, we added two ownership questions to quantify children’s ability of ownership reasoning with four age groups (n = 32 for the 3-year-olds, n = 33 for the 4-year-olds, n = 27 for the 5-year olds and n = 30 for the adults) to explore the developmental trajectory further. It revealed that while 5-year olds’ performances were similar to the adults’ and always judged the first possessor as owner in three conditions, 3- and 4-year olds’ performed at chance level in the authority testimony condition. The results imply that Chinese young preschooler’s ownership reasoning was susceptible to authority’s testimony. Family authority may play an important role in diluting children’s adherence to ownership principles, which will be helpful for children to learn to share with others.

Keywords: authority, ownership judgment, preschoolers, testimony

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Authors: Liming Chen, Baoxin Xu, Zhaoyun Ding, Bin Liu, Xianqiang Zhu

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In the era of big data, public investors are faced with more complicated information related to investment decisions than ever before. To survive in the fierce competition, it has become increasingly urgent for investors to combine multi-source knowledge and evaluate the companies’ true value efficiently. For this, a rule-based ontology reasoning method is proposed to support steel companies’ value assessment. Considering the delay in financial disclosure and based on cost-benefit analysis, this paper introduces the supply chain enterprises financial analysis and constructs the ontology model used to value the value of steel company. In addition, domain knowledge is formally expressed with the help of Web Ontology Language (OWL) language and SWRL (Semantic Web Rule Language) rules. Finally, a case study on a steel company in China proved the effectiveness of the method we proposed.

Keywords: financial ontology, steel company, supply chain, ontology reasoning

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Authors: Pi-Hsia Hung

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The development of mathematical competency has individual benefits as well as benefits to the wider society. Children who begin school behind their peers in their understanding of number, counting, and simple arithmetic are at high risk of staying behind throughout their schooling. The development of effective strategies for improving the educational trajectory of these individuals will be contingent on identifying areas of early quantitative knowledge that influence later mathematics achievement. A computer-based quantity assessment was developed in this study to investigate the characteristics of 2nd and 3rd grade slow learners in quantity. The concept of quantification involves understanding measurements, counts, magnitudes, units, indicators, relative size, and numerical trends and patterns. Fifty-five tasks of quantitative reasoning—such as number sense, mental calculation, estimation and assessment of reasonableness of results—are included as quantity problem solving. Thus, quantity is defined in this study as applying knowledge of number and number operations in a wide variety of authentic settings. Around 1000 students were tested and categorized into 4 different performance levels. Students’ quantity ability correlated higher with their school math grade than other subjects. Around 20% students are below basic level. The intervention design implications of the preliminary item map constructed are discussed.

Keywords: mathematics assessment, mathematical cognition, quantity, number sense, validity

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Authors: Angela Oktavia Suryani, Bernadeth Gloria, Edwin Sutamto, Jessica Kristianty, Ni Made Rai Sapitri, Patricia Catherine Agla, Sitti Arlinda Rochiadi

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It was found that some blogs or personal websites in Indonesia sell standardized intelligence tests (for example, Progressive Matrices (PM), Intelligence Structure Test (IST), and Culture Fair Intelligence Test (CFIT)) and other psychological tests, together with the manual and the key answers for public. Individuals can buy and prepare themselves for selection or recruitment with the real test. This action drives people to lie to the institution (education or company) and also to themselves. It was also found that those tests are old. Some items are not relevant with the current context, for example a question about a diameter of a certain coin that does not exist anymore. These problems motivate us to develop a new intelligence battery test, namely of Multiple Aptitude Battery (MAB). The battery test was built by using Thurstone’s Primary Mental Abilities theory and intended to be used by high schools students, university students, and worker applicants. The battery tests consist of 9 subtests. In the current study we examine six subtests, namely Reading Comprehension, Verbal Analogies, Numerical Inductive Reasoning, Numerical Deductive Reasoning, Mechanical Ability, and Two Dimensional Spatial Reasoning for university students. The study included 1424 data from students recruited by convenience sampling from eight faculties at Atma Jaya Catholic University of Indonesia. Classical and modern test approaches (Item Response Theory) were carried out to identify the item difficulties of the items and confirmatory factor analysis was applied to examine their internal validities. The validity of each subtest was inspected by using convergent–discriminant method, whereas the reliability was examined by implementing Kuder–Richardson formula. The result showed that the majority of the subtests were difficult in medium level, and there was only one subtest categorized as easy, namely Verbal Analogies. The items were found homogenous and valid measuring their constructs; however at the level of subtests, the construct validity examined by convergent-discriminant method indicated that the subtests were not unidimensional. It means they were not only measuring their own constructs but also other construct. Three of the subtests were able to predict academic performance with small effect size, namely Reading Comprehension, Numerical Inductive Reasoning, and Two Dimensional Spatial Reasoning. GPAs in intermediate level (GPAs at third semester and above) were considered as a factor for predictive invalidity. The Kuder-Richardson formula showed that the reliability coefficients for both numerical reasoning subtests and spatial reasoning were superior, in the range 0.84 – 0.87, whereas the reliability coefficient for the other three subtests were relatively below standard for ability test, in the range of 0.65 – 0.71. It can be concluded that some of the subtests are ready to be used, whereas some others are still need some revisions. This study also demonstrated that the convergent-discrimination method is useful to identify the general intelligence of human.

Keywords: intelligence, psychometric examination, multiple aptitude battery, university students

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Authors: Fausto Morais

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Artificial intelligence has been widely used in law. Programs are able to classify suits, to identify decision-making patterns, to predict outcomes, and to formalize legal arguments as well. In Brazil, the artificial intelligence victor has been classifying cases to supreme court’s standards. When those programs act doing those tasks, they simulate some kind of legal decision and legal arguments, raising doubts about how artificial intelligence can be integrated into legal reasoning. Taking this into account, the following three issues are identified; the problem of hypernormatization, the argument of legal anthropocentrism, and the artificial legal principles. Hypernormatization can be seen in the Brazilian legal context in the Supreme Court’s usage of the Victor program. This program generated efficiency and consistency. On the other hand, there is a feasible risk of over standardizing factual and normative legal features. Then legal clerks and programmers should work together to develop an adequate way to model legal language into computational code. If this is possible, intelligent programs may enact legal decisions in easy cases automatically cases, and, in this picture, the legal anthropocentrism argument takes place. Such an argument argues that just humans beings should enact legal decisions. This is so because human beings have a conscience, free will, and self unity. In spite of that, it is possible to argue against the anthropocentrism argument and to show how intelligent programs may work overcoming human beings' problems like misleading cognition, emotions, and lack of memory. In this way, intelligent machines could be able to pass legal decisions automatically by classification, as Victor in Brazil does, because they are binding by legal patterns and should not deviate from them. Notwithstanding, artificial intelligent programs can be helpful beyond easy cases. In hard cases, they are able to identify legal standards and legal arguments by using machine learning. For that, a dataset of legal decisions regarding a particular matter must be available, which is a reality in Brazilian Judiciary. Doing such procedure, artificial intelligent programs can support a human decision in hard cases, providing legal standards and arguments based on empirical evidence. Those legal features claim an argumentative weight in legal reasoning and should serve as references for judges when they must decide to maintain or overcome a legal standard.

Keywords: artificial intelligence, artificial legal principles, hypernormatization, legal anthropocentrism argument, legal reasoning

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Authors: Abderrahmane Khiat, Moussa Benaissa

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Due to the increasing number of sources of information available on the web and their distribution and heterogeneity, ontology alignment became a very important and inevitable problem to ensure semantic interoperability. Instance-based ontology alignment is based on the comparison of the extensions of concepts; and represents a very promising technique to find semantic correspondences between entities of different ontologies. In practice, two situations may arise: ontologies that share many common instances and ontologies that share few or do not share common instances. In this paper, we describe an approach to manage the latter case. This approach exploits the reasoning on ontologies in order to create a corpus of common instances. We show that it is theoretically powerful because it is based on description logics and very useful in practice. We present the experimental results obtained by running our approach on ontologies of OAEI 2012 benchmark test. The results show the performance of our approach.

Keywords: description logic inference, instance-based ontology alignment, semantic interoperability, semantic web

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Authors: Hafida Bouarfa, Mohamed Abed

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The main object of our work is the development and the validation of a system indicated Fuzzy Vulnerability. Fuzzy Vulnerability uses a fuzzy representation in order to tolerate the imprecision during the description of construction. At the the second phase, we evaluated the similarity between the vulnerability of a new construction and those of the whole of the historical cases. This similarity is evaluated on two levels: 1) individual similarity: bases on the fuzzy techniques of aggregation; 2) Global similarity: uses the increasing monotonous linguistic quantifiers (RIM) to combine the various individual similarities between two constructions. The third phase of the process of Fuzzy Vulnerability consists in using vulnerabilities of historical constructions narrowly similar to current construction to deduce its estimate vulnerability. We validated our system by using 50 cases. We evaluated the performances of Fuzzy Vulnerability on the basis of two basic criteria, the precision of the estimates and the tolerance of the imprecision along the process of estimation. The comparison was done with estimates made by tiresome and long models. The results are satisfactory.

Keywords: case based reasoning, fuzzy logic, fuzzy case based reasoning, seismic vulnerability

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Authors: Agarana Michael C., Akinlabi Esther T., Pule Kholopane

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Innovation in manufacturing process technologies and associated product design affects the prospects for manufacturing today and in near future. In this study some theoretical methods, useful as tools in advanced manufacturing, are considered. In particular, some basic Mathematical, Operational Research, Heuristic, and Statistical techniques are discussed. These techniques/methods are very handy in many areas of advanced manufacturing processes, including process planning optimization, modelling and analysis. Generally the production rate requires the application of Mathematical methods. The Emerging Trends Processes in Advanced Manufacturing can be enhanced by using Mathematical Modelling and Optimization techniques.

Keywords: mathematical modelling, optimization, emerging trends, advanced manufacturing

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Authors: Lisa Kasmer

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Teachers’ instructional decisions shape the structure and content of mathematics lessons and influence the mathematics that students are given the opportunity to learn. Therefore, it is important to better understand how teachers make instructional decisions and thus find new ways to help practicing and future teachers give their students a more effective and robust learning experience. Understanding the relationship between teachers’ instructional decisions and their goals, resources, and orientations (beliefs) is important given the heightened focus on geometric transformations in the middle school mathematics curriculum. This work is significant as the development and support of current and future teachers need more effective ways to teach geometry to their students. The following research questions frame this study: (1) As middle school mathematics teachers plan and enact instruction related to teaching transformations, what thinking processes do they engage in to make decisions about teaching transformations with or without a coordinate system and (2) How do the goals, resources and orientations of these teachers impact their instructional decisions and reveal about their understanding of teaching transformations? Teachers and students alike struggle with understanding transformations; many teachers skip or hurriedly teach transformations at the end of the school year. However, transformations are an important mathematical topic as this topic supports students’ understanding of geometric and spatial reasoning. Geometric transformations are a foundational concept in mathematics, not only for understanding congruence and similarity but for proofs, algebraic functions, and calculus etc. Geometric transformations also underpin the secondary mathematics curriculum, as features of transformations transfer to other areas of mathematics. Teachers’ instructional decisions in terms of goals, orientations, and resources that support these instructional decisions were analyzed using open-coding. Open-coding is recognized as an initial first step in qualitative analysis, where comparisons are made, and preliminary categories are considered. Initial codes and categories from current research on teachers’ thinking processes that are related to the decisions they make while planning and reflecting on the lessons were also noted. Surfacing ideas and additional themes common across teachers while seeking patterns, were compared and analyzed. Finally, attributes of teachers’ goals, orientations and resources were identified in order to begin to build a picture of the reasoning behind their instructional decisions. These categories became the basis for the organization and conceptualization of the data. Preliminary results suggest that teachers often rely on their own orientations about teaching geometric transformations. These beliefs are underpinned by the teachers’ own mathematical knowledge related to teaching transformations. When a teacher does not have a robust understanding of transformations, they are limited by this lack of knowledge. These shortcomings impact students’ opportunities to learn, and thus disadvantage their own understanding of transformations. Teachers’ goals are also limited by their paucity of knowledge regarding transformations, as these goals do not fully represent the range of comprehension a teacher needs to teach this topic well.

Keywords: coordinate plane, geometric transformations, instructional decisions, middle school mathematics

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Authors: Sonia Anand Knowlton

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There are some cases where we as a society feel deeply uncomfortable with the use of Artificial Intelligence (AI) tools in the judicial decision-making process, and justifiably so. A perfect example is COMPAS, an algorithmic model that predicts recidivism rates of offenders to assist in the determination of their bail conditions. COMPAS turned out to be extremely racist: it massively overpredicted recidivism rates of Black offenders and underpredicted recidivism rates of white offenders. At the same time, there are certain uses of AI in the judicial decision-making process that many would feel more comfortable with and even support. Take, for example, a “super-breathalyzer,” an (albeit imaginary) tool that uses AI to deliver highly detailed information about the subject of the breathalyzer test to the legal decision-makers analyzing their drunk-driving case. This article evaluates the point at which a judge’s use of AI tools begins to undermine the public’s trust in the administration of justice. It argues that the answer to this question depends on whether the AI tool is in a role in which it must perform a moral evaluation of a human being.

Keywords: artificial intelligence, judicial reasoning, morality, technology, algorithm

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Authors: Marko Batic, Nikola Tomasevic, Sanja Vranes

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One of the strongholds in the ubiquitous efforts related to the energy conservation and energy efficiency improvement is represented by the retrofit of high energy consumers in buildings. In general, HVAC systems represent the highest energy consumers in buildings. However they usually suffer from mal-operation and/or malfunction, causing even higher energy consumption than necessary. Various Fault Detection and Diagnosis (FDD) systems can be successfully employed for this purpose, especially when it comes to the application at a single device/unit level. In the case of more complex systems, where multiple devices are operating in the context of the same building, significant energy efficiency improvements can only be achieved through application of comprehensive FDD systems relying on additional higher level knowledge, such as their geographical location, served area, their intra- and inter- system dependencies etc. This paper presents a comprehensive FDD system that relies on the utilization of common knowledge repository that stores all critical information. The discussed system is deployed as a test-bed platform at the two at Fiumicino and Malpensa airports in Italy. This paper aims at presenting advantages of implementation of the knowledge base through the utilization of ontology and offers improved functionalities of such system through examples of typical queries and reasoning that enable derivation of high level energy conservation measures (ECM). Therefore, key SPARQL queries and SWRL rules, based on the two instantiated airport ontologies, are elaborated. The detection of high level irregularities in the operation of airport heating/cooling plants is discussed and estimation of energy savings is reported.

Keywords: airport ontology, knowledge management, ontology modeling, reasoning

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Authors: Angana Chatterjee

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The feminist scholars point out the various problematic issues in the traditional mainstream western thought and theories. The thought practices behind the discriminatory and oppressive social practices are based on concepts that play a pivotal role in theorisation. Therefore, many feminist philosophers take up reformation or reconceptualisation projects. Such projects have bearings on various aspects of philosophical thought, namely, ontology, epistemology, logic, ethics, social, political thought, and so on. In tune with this spirit, the present paper suggests a well-established thought pattern which is not western but has got the potential to deal with the problems of mainstream western thought culture that are identified by the feminist critics. The Indian thought pattern is theorised in the domain of Indian logic, which is a study of inference patterns. As, in the Indian context, the inference is considered as a source of knowledge, certain epistemological questions are linked with the discussion of inference. One of the key epistemological issues is one regarding justification. The study about the nature of derivation of knowledge from available evidence, and the nature of the evidence itself, are integral parts of the discipline called Indian logic. But if we contrast the western tradition of thought with the Indian one, we can find that the Indian logic has got some peculiar features which may be shown to deal with the problems identified by the feminist scholars in western thought culture more plausibly. The tradition of western logic, starting from Aristotle, has been maintaining sharp differences between two forms of reasoning, namely, deductive and inductive. These two different forms of reasoning have been theorised and dealt with separately within the domain of the study called ‘logic.’ There are various philosophical problems that are raised around concepts and issues regarding both deductive and inductive reasoning. Indian logic does not distinguish between deduction and induction as thought patterns, but their distinction is very usual to make in the western tradition. Though there can be found various interpretations about this peculiarity of Indian thought pattern, these mixed patterns were actually very close to the cross-cultural pattern in which human beings would tend to argue or infer from the available data or evidence. The feminist theories can successfully operate in the domain of lived experience if they make use of such a mixed pattern of reasoning or inference. By offering sound inferential knowledge on contextual evidences, the Indian thought pattern is potent to serve the feminist purposes in a meaningful way.

Keywords: feminist thought, Indian logic, inference, justification, mixed thought pattern

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Authors: Adrian W. Chew

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This paper argues that education policy analysis tends to be steered towards empiricist oriented approaches, which place emphasis on objective and measurable data. However, this paper argues that empiricist oriented approaches are generally based on inductive and/or deductive reasoning, which are unable to generate new ideas/knowledge. This paper will outline the logical structure of induction, deduction, and abduction, and argues that only abduction provides possibilities for the creation of new ideas/knowledge. This paper proposes the neologism of ‘informed guessing’ as a reformulation of abduction, and also as an approach to education policy analysis. On one side, the signifier ‘informed’ encapsulates the idea that abductive policy analysis needs to be informed by descriptive conceptualization theory to be able to make relations and connections between, and within, observed phenomenon and unobservable general structures. On the other side, the signifier ‘guessing’ captures the cyclical and unsystematic process of abduction. This paper will end with a brief example of utilising ‘informed guessing’ for a policy analysis of school choice lotteries in the United States.

Keywords: abductive reasoning, empiricism, informed guessing, policy analysis

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Authors: Rizky Oktaviana

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The main purpose of studying lies in improving students’ understanding. Teachers usually use written test to measure students’ understanding about learning material especially mathematical learning material. This common method actually has a lack point, such that in mathematics content, written test only show procedural steps to solve mathematical problems. Therefore, teachers unable to see whether students actually understand about mathematical concepts and the relation between concepts or not. One of the best tools to observe students’ understanding about the mathematical concepts is concept map. The goal of this research is to describe junior high school students understanding about mathematical concepts through Concept Maps based on the difference of mathematical ability. There were three steps in this research; the first step was choosing the research subjects by giving mathematical ability test to students. The subjects of this research are three students with difference mathematical ability, high, intermediate and low mathematical ability. The second step was giving concept mapping training to the chosen subjects. The last step was giving concept mapping task about the function to the subjects. Nodes which are the representation of concepts of function were provided in concept mapping task. The subjects had to use the nodes in concept mapping. Based on data analysis, the result of this research shows that subject with high mathematical ability has formal understanding, due to that subject could see the connection between concepts of function and arranged the concepts become concept map with valid hierarchy. Subject with intermediate mathematical ability has relational understanding, because subject could arranged all the given concepts and gave appropriate label between concepts though it did not represent the connection specifically yet. Whereas subject with low mathematical ability has poor understanding about function, it can be seen from the concept map which is only used few of the given concepts because subject could not see the connection between concepts. All subjects have instrumental understanding for the relation between linear function concept, quadratic function concept and domain, co domain, range.

Keywords: concept map, concept mapping, mathematical concepts, understanding

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Authors: V. Vargas-Alejo, L. E. Montero-Moguel

Abstract:

Understanding the concept of function has been important in mathematics education for many years. In this study, the models built by a group of five business administration and accounting undergraduate students when carrying out a population growth activity are analyzed. The theoretical framework is the Models and Modeling Perspective. The results show how the students included tables, graphics, and algebraic representations in their models. Using technology was useful to interpret, describe, and predict the situation. The first model, the students built to describe the situation, was linear. After that, they modified and refined their ways of thinking; finally, they created exponential growth. Modeling the activity was useful to deep on mathematical concepts such as covariation, rate of change, and exponential function also to differentiate between linear and exponential growth.

Keywords: covariation reasoning, exponential function, modeling, representations

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Authors: Yoon Suh Song

Abstract:

Though music education can broaden one’s capacity for mathematical performance, many countries lag behind in music education. Little empirical evidence is found to identify the connection between math and music. Therefore, this research was set out to explore what music-related variables are associated with mathematical performance. The result of our analysis is as follows: A Pearson's Correlation analysis revealed that PISA math score is strongly correlated with students' Intelligence Quotient (IQ). This lays the foundation for further research as to what factors in students’ IQ lead to a better performance in math.

Keywords: music education, mathematical performance, education, IQ

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Authors: Jaroslav Krutil, Simona Fialová, , František Pochylý

Abstract:

A nonlinear mathematical model of mutual fluid-structure interaction is presented in the work. The model is applicable to the general shape of sealing gaps. An in compressible fluid and turbulent flow is assumed. The shaft carries a rotational and procession motion, the gap is axially flowed through. The achieved results of the additional mass, damping and stiffness matrices may be used in the solution of the rotor dynamics. The usage of this mathematical model is expected particularly in hydraulic machines. The method of control volumes in the ANSYS Fluent was used for the simulation. The obtained results of the pressure and velocity fields are used in the mathematical model of additional effects.

Keywords: nonlinear mathematical model, CFD modeling, hydrodynamic sealing gap, matrices of mass, stiffness, damping

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Authors: Jay-R M. Mendoza

Abstract:

In almost all mathematics classrooms, students demonstrated discrepancies in their knowledge, skills, and understanding. OECD reports predicted that this continued to aggravate as not all teachers were sufficiently trained to handle this concentration. In response, the paper explored the potential of reSolve’s professional learning module 3 (PLM3) as an affordable and accessible professional development (PD) resource. Participants’ hands-on experience and exposure to PLM3 were audio recorded. After it was transcribed and examined and their work samples were analysed, there were four issues emerged: (1) criticality of conducting preliminary data collections and increasing the validity of inferences about what students can and cannot do by addressing the probabilistic nature of their performance; (2) criticality of the conclusion: a > b and/or (a-b) ∈ Z⁺ among students’ algebraic reasoning; (3) enabling and extending prompts provided by reSolve were found useful; and (4) dynamic adaptation of reSolve PLM3 through developing transferable skills and collaboration among teachers. PLM3 provided valuable insights on assessment, teaching, and planning to include all students in mathematics experiences.

Keywords: algebraic reasoning, building teacher capacity, including all students in mathematics experiences, professional development

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Authors: Juliana A. Knocikova, Yann Bouret, Médéric Argentina, Laurent Counillon

Abstract:

Cell volume, together with membrane potential and intracellular hydrogen ion concentration, is an essential biophysical parameter for normal cellular activity. Cell volumes can be altered by osmotically active compounds and extracellular tonicity. In this study, a simple mathematical model of osmotically induced cell swelling and shrinking is presented. Emphasis is given to water diffusion across the membrane. The mathematical description of the cellular behavior consists in a system of coupled ordinary differential equations. We compare experimental data of cell volume alterations driven by differences in osmotic pressure with mathematical simulations under hypotonic and hypertonic conditions. Implications for a future model are also discussed.

Keywords: eukaryotic cell, mathematical modeling, osmosis, volume alterations

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Authors: Lam Pham, Peter Hubber, Russell Tytler

Abstract:

Students’ conceptual understandings of chemistry concepts/phenomena involve capability to coordinate across the three levels of Johnston’s triangle model. This triplet model is based on reasoning about chemical phenomena across macro, sub-micro and symbolic levels. In chemistry education, there is a need for further examining inquiry-based approaches that enhance students’ conceptual learning and problem solving skills. This research adopted a directed inquiry pedagogy based on students constructing and coordinating representations, to investigate senior school students’ capabilities to flexibly move across Johnston’ levels when learning dilution and molar concentration concepts. The participants comprise 50 grade 11 and 20 grade 10 students and 4 chemistry teachers who were selected from 4 secondary schools located in metropolitan Melbourne, Victoria. This research into classroom practices used ethnographic methodology, involved teachers working collaboratively with the research team to develop representational activities and lesson sequences in the instruction of a unit on solution chemistry. The representational activities included challenges (Representational Challenges-RCs) that used ‘representational tools’ to assist students to move across Johnson’s three levels for dilution phenomena. In this report, the ‘representational tool’ called ‘cross and portion’ model was developed and used in teaching and learning the molar concentration concept. Students’ conceptual understanding and problem solving skills when learning with this model are analysed through group case studies of year 10 and 11 chemistry students. In learning dilution concepts, students in both group case studies actively conducted a practical experiment, used their own language and visualisation skills to represent dilution phenomena at macroscopic level (RC1). At the sub-microscopic level, students generated and negotiated representations of the chemical interactions between solute and solvent underpinning the dilution process. At the symbolic level, students demonstrated their understandings about dilution concepts by drawing chemical structures and performing mathematical calculations. When learning molar concentration with a ‘cross and portion’ model (RC2), students coordinated across visual and symbolic representational forms and Johnson’s levels to construct representations. The analysis showed that in RC1, Year 10 students needed more ‘scaffolding’ in inducing to representations to explicit the form and function of sub-microscopic representations. In RC2, Year 11 students showed clarity in using visual representations (drawings) to link to mathematics to solve representational challenges about molar concentration. In contrast, year 10 students struggled to get match up the two systems, symbolic system of mole per litre (‘cross and portion’) and visual representation (drawing). These conceptual problems do not lie in the students’ mathematical calculation capability but rather in students’ capability to align visual representations with the symbolic mathematical formulations. This research also found that students in both group case studies were able to coordinate representations when probed about the use of ‘cross and portion’ model (in RC2) to demonstrate molar concentration of diluted solutions (in RC1). Students mostly succeeded in constructing ‘cross and portion’ models to represent the reduction of molar concentration of the concentration gradients. In conclusion, this research demonstrated how the strategic introduction and coordination of chemical representations across modes and across the macro, sub-micro and symbolic levels, supported student reasoning and problem solving in chemistry.

Keywords: cross and portion, dilution, Johnston's triangle, molar concentration, representations

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Authors: Ebenezer Joseph

Abstract:

Chess is a useful tool to enhance general and specific cognitive functioning in children. The present study aims to assess the impact of chess on cognitive in children and to measure the differential impact of socio-demographic factors like age and gender of the child on the effectiveness of the chess intervention.This research study used an experimental design to study the impact of the Training in Chess on the intelligence of children. The Pre-test Post-test Control Group Design was utilized. The research design involved two groups of children: an experimental group and a control group. The experimental group consisted of children who participated in the one-year Chess Training Intervention, while the control group participated in extra-curricular activities in school. The main independent variable was training in chess. Other independent variables were gender and age of the child. The dependent variable was the cognitive functioning of the child (as measured by IQ, working memory index, processing speed index, perceptual reasoning index, verbal comprehension index, numerical reasoning, verbal reasoning, non-verbal reasoning, social intelligence, language, conceptual thinking, memory, visual motor and creativity). The sample consisted of 200 children studying in Government and Private schools. Random sampling was utilized. The sample included both boys and girls falling in the age range 6 to 16 years. The experimental group consisted of 100 children (50 from Government schools and 50 from Private schools) with an equal representation of boys and girls. The control group similarly consisted of 100 children. The dependent variables were assessed using Binet-Kamat Test of Intelligence, Wechsler Intelligence Scale for Children - IV (India) and Wallach Kogan Creativity Test. The training methodology comprised Winning Moves Chess Learning Program - Episodes 1–22, lectures with the demonstration board, on-the-board playing and training, chess exercise through workbooks (Chess school 1A, Chess school 2, and tactics) and working with chess software. Further students games were mapped using chess software and the brain patterns of the child were understood. They were taught the ideas behind chess openings and exposure to classical games were also given. The children participated in mock as well as regular tournaments. Preliminary analysis carried out using independent t tests with 50 children indicates that chess training has led to significant increases in the intelligent quotient. Children in the experimental group have shown significant increases in composite scores like working memory and perceptual reasoning. Chess training has significantly enhanced the total creativity scores, line drawing and pattern meaning subscale scores. Systematically learning chess as part of school activities appears to have a broad spectrum of positive outcomes.

Keywords: chess, intelligence, creativity, children

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