70 resultados para C65 - Miscellaneous Mathematical Tools


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Linguistic modelling is a rather new branch of mathematics that is still undergoing rapid development. It is closely related to fuzzy set theory and fuzzy logic, but knowledge and experience from other fields of mathematics, as well as other fields of science including linguistics and behavioral sciences, is also necessary to build appropriate mathematical models. This topic has received considerable attention as it provides tools for mathematical representation of the most common means of human communication - natural language. Adding a natural language level to mathematical models can provide an interface between the mathematical representation of the modelled system and the user of the model - one that is sufficiently easy to use and understand, but yet conveys all the information necessary to avoid misinterpretations. It is, however, not a trivial task and the link between the linguistic and computational level of such models has to be established and maintained properly during the whole modelling process. In this thesis, we focus on the relationship between the linguistic and the mathematical level of decision support models. We discuss several important issues concerning the mathematical representation of meaning of linguistic expressions, their transformation into the language of mathematics and the retranslation of mathematical outputs back into natural language. In the first part of the thesis, our view of the linguistic modelling for decision support is presented and the main guidelines for building linguistic models for real-life decision support that are the basis of our modeling methodology are outlined. From the theoretical point of view, the issues of representation of meaning of linguistic terms, computations with these representations and the retranslation process back into the linguistic level (linguistic approximation) are studied in this part of the thesis. We focus on the reasonability of operations with the meanings of linguistic terms, the correspondence of the linguistic and mathematical level of the models and on proper presentation of appropriate outputs. We also discuss several issues concerning the ethical aspects of decision support - particularly the loss of meaning due to the transformation of mathematical outputs into natural language and the issue or responsibility for the final decisions. In the second part several case studies of real-life problems are presented. These provide background and necessary context and motivation for the mathematical results and models presented in this part. A linguistic decision support model for disaster management is presented here – formulated as a fuzzy linear programming problem and a heuristic solution to it is proposed. Uncertainty of outputs, expert knowledge concerning disaster response practice and the necessity of obtaining outputs that are easy to interpret (and available in very short time) are reflected in the design of the model. Saaty’s analytic hierarchy process (AHP) is considered in two case studies - first in the context of the evaluation of works of art, where a weak consistency condition is introduced and an adaptation of AHP for large matrices of preference intensities is presented. The second AHP case-study deals with the fuzzified version of AHP and its use for evaluation purposes – particularly the integration of peer-review into the evaluation of R&D outputs is considered. In the context of HR management, we present a fuzzy rule based evaluation model (academic faculty evaluation is considered) constructed to provide outputs that do not require linguistic approximation and are easily transformed into graphical information. This is achieved by designing a specific form of fuzzy inference. Finally the last case study is from the area of humanities - psychological diagnostics is considered and a linguistic fuzzy model for the interpretation of outputs of multidimensional questionnaires is suggested. The issue of the quality of data in mathematical classification models is also studied here. A modification of the receiver operating characteristics (ROC) method is presented to reflect variable quality of data instances in the validation set during classifier performance assessment. Twelve publications on which the author participated are appended as a third part of this thesis. These summarize the mathematical results and provide a closer insight into the issues of the practicalapplications that are considered in the second part of the thesis.

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The aim of the present set of longitudinal studies was to explore 3-7-year-old children.s Spontaneous FOcusing on Numerosity (SFON) and its relation to early mathematical development. The specific goals were to capture in method and theory the distinct process by which children focus on numerosity as a part of their activities involving exact number recognition, and individual differences in this process that may be informative in the development of more complex number skills. Over the course of conducting the five studies, fifteen novel tasks were progressively developed for the SFON assessments. In the tasks, confounding effects of insufficient number recognition, verbal comprehension, other procedural skills as well as working memory capacity were aimed to be controlled. Furthermore, how children.s individual differences in SFON are related to their development of number sequence, subitizing-based enumeration, object counting and basic arithmetic skills was explored. The effect of social interaction on SFON was tested. Study I captured the first phase of the 3-year longitudinal study with 39 children. It was investigated whether there were differences in 3-year-old children.s tendency to focus on numerosity, and whether these differences were related to the children.s development of cardinality recognition skills from the age of 3 to 4 years. It was found that the two groups of children formed on the basis of their amount of SFON tendency at the age of 3 years differed in their development of recognising and producing small numbers. The children whose SFON tendency was very predominant developed faster in cardinality related skills from the age of 3 to 4 years than the children whose SFON tendency was not as predominant. Thus, children.s development in cardinality recognition skills is related to their SFON tendency. Studies II and III were conducted to investigate, firstly, children.s individual differences in SFON, and, secondly, whether children.s SFON is related to their counting development. Altogether nine tasks were designed for the assessments of spontaneous and guided focusing on numerosity. The longitudinal data of 39 children in Study II from the age of 3.5 to 6 years showed individual differences in SFON at the ages of 4, 5 and 6 years, as well as stability in children.s SFON across tasks used at different ages. The counting skills were assessed at the ages of 3.5, 5 and 6 years. Path analyses indicated a reciprocal tendency in the relationship between SFON and counting development. In Study III, these results on the individual differences in SFON tendency, the stability of SFON across different tasks and the relationship of SFON and mathematical skills were confirmed by a larger-scale cross-sectional study of 183 on average 6.5-year-old children (range 6;0-7;0 years). The significant amount of unique variance that SFON accounted for number sequence elaboration, object counting and basic arithmetic skills stayed statistically significant (partial correlations varying from .27 to .37) when the effects of non-verbal IQ and verbal comprehension were controlled. In addition, to confirm that the SFON tasks assess SFON tendency independently from enumeration skills, guided focusing tasks were used for children who had failed in SFON tasks. It was explored whether these children were able to proceed in similar tasks to SFON tasks once they were guided to focus on number. The results showed that these children.s poor performance in the SFON tasks was not caused by their deficiency in executing the tasks but on lacking focusing on numerosity. The longitudinal Study IV of 39 children aimed at increasing the knowledge of associations between children.s long-term SFON tendency, subitizing-based enumeration and verbal counting skills. Children were tested twice at the age of 4-5 years on their SFON, and once at the age of 5 on their subitizing-based enumeration, number sequence production, as well as on their skills for counting of objects. Results showed considerable stability in SFON tendency measured at different ages, and that there is a positive direct association between SFON and number sequence production. The association between SFON and object counting skills was significantly mediated by subitizing-based enumeration. These results indicate that the associations between the child.s SFON and sub-skills of verbal counting may differ on the basis of how significant a role understanding the cardinal meanings of number words plays in learning these skills. The specific goal of Study V was to investigate whether it is possible to enhance 3-year old children.s SFON tendency, and thus start children.s deliberate practice in early mathematical skills. Participants were 3-year-old children in Finnish day care. The SFON scores and cardinality-related skills of the experimental group of 17 children were compared to the corresponding results of the 17 children in the control group. The results show an experimental effect on SFON tendency and subsequent development in cardinality-related skills during the 6-month period from pretest to delayed posttest in the children with some initial SFON tendency in the experimental group. Social interaction has an effect on children.s SFON tendency. The results of the five studies assert that within a child.s existing mathematical competence, it is possible to distinguish a separate process, which refers to the child.s tendency to spontaneously focus on numerosity. Moreover, there are significant individual differences in children.s SFON at the age of 3-7 years. Moderate stability was found in this tendency across different tasks assessed both at the same and at different ages. Furthermore, SFON tendency is related to the development of early mathematical skills. Educational implications of the findings emphasise, first, the importance of regarding focusing on numerosity as a separate, essential process in the assessments of young children.s mathematical skills. Second, the substantial individual differences in SFON tendency during the childhood years suggest that uncovering and modeling this kind of mathematically meaningful perceiving of the surroundings and tasks could be an efficient tool for promoting young children.s mathematical development, and thus prevent later failures in learning mathematical skills. It is proposed to consider focusing on numerosity as one potential sub-process of activities involving exact number recognition in future studies.

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The main objective of this study was to develop mathematical model capable to describe the effect of ultrastructural features on the longitudinal modulus of elasticity of softwood fiber. Another objective was to identify, based on ultrastructural features, a potential explanatory factor for the mechanical difference between Norway spruce and Scots pine fibers and to demonstrate its influence utilizing developed modelling tools. According to the literature, the main difference between the pine and spruce fibers is the pit structure, which is clearly different in these fibers. The spruce fiber contains a lot of tiny pits, whereas the pits of the pine fiber are larger and the total number of them is smaller. The effect of the pits on the longitudinal modulus of elasticity of fiber is studied with both the analytical and the numerical model. The results show that, although the spruce fiber seems to contain clearly more pits, larger pits appearing in the pine fiber turn out to have a stronger influence on the longitudinal modulus of elasticity of the fiber. The effect of local variation of microfibril angle which occurs near the pits seems to be minor. Moreover, the results suggest that spruce fibers may have higher ultimate strength due to the more uniform straining behavior.

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The desire to create a statistical or mathematical model, which would allow predicting the future changes in stock prices, was born many years ago. Economists and mathematicians are trying to solve this task by applying statistical analysis and physical laws, but there are still no satisfactory results. The main reason for this is that a stock exchange is a non-stationary, unstable and complex system, which is influenced by many factors. In this thesis the New York Stock Exchange was considered as the system to be explored. A topological analysis, basic statistical tools and singular value decomposition were conducted for understanding the behavior of the market. Two methods for normalization of initial daily closure prices by Dow Jones and S&P500 were introduced and applied for further analysis. As a result, some unexpected features were identified, such as a shape of distribution of correlation matrix, a bulk of which is shifted to the right hand side with respect to zero. Also non-ergodicity of NYSE was confirmed graphically. It was shown, that singular vectors differ from each other by a constant factor. There are for certain results no clear conclusions from this work, but it creates a good basis for the further analysis of market topology.

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Syftet med denna studie är att granska hur användningen av smarttelefoner kan stöda elevens reflektion av sin egen slöjdprocess och samtidigt se hur eleven dokumenterar sin slöjdprocess med hjälp av Talking Tools (TT). Fokus i denna studie ligger på dokumentation av elevens slöjdprocess, men jag behandlar även presentation av slöjdprodukter och olika möjligheter till och sätt på hur eleverna använder TT på en smarttelefon i slöjdundervisningen. En förändring i hur informations- och kommunikationsteknik (IKT) används sker och kommer även att ske i fortsättningen i grundskolan. Då en ny läroplan för den grundläggande utbildningen tas i bruk år 2016 kommer IKT att ha en avsevärt större roll. Denna förändring lägger press på lärare och på skolan överlag för att skapa ändamålsenliga metoder i användningen av IKT. Studien baserar sig på intervjuer med elever som använt TT under ett arbetsområde i slöjden. Elva elever presenterade först sina slöjdprodukter för forskaren varefter eleverna intervjuades. Eleverna hade tillgång till sina slöjdbloggar gjorda i TT under intervjutillfällena. Intervjuerna filmades och lades ihop med bloggarna för att förenkla analysen av materialet. I den här undersökningen framkom att dokumentationen av slöjdprocessen bidrog till en reflektion av när bilder och texter från bloggarna användes under presentationerna. Då kraven på dokumenteringen av arbetet i skolan blir högre i och med läroplanen 2016 tror jag att Talking Tools kan vara ett hjälpmedel för elever och lärare i förverkligandet av bland annat användningen av IKT i arbetet i skolan. Detta förutsätter att eleverna ges tid för användningen samt att tekniken fungerar.

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Marketing communications has gone through significant changes during the last decades and new online tools have been leading this change for the last decade. Now, in the digital age, if wanting to be successful companies need to experiment new things and seize the opportunities online provides and adapt to the new environment. However, during this time the marketing communication mix and the meanings given to the various components of it have not changed dramatically, and personal selling, direct marketing, sales promotion, advertising and public relations activities are still regarded as important tools in the marketing communications mix. The purpose of this study was to examine business-to-business marketing communications and the tools used by companies in their marketing communications efforts in the digital age and in a global environment. The research questions dealt with the marketing communication tools and their roles as well as the role of online marketing communication and the way it has shaped the field of b2b marketing communications. In order to answer these questions, qualitative approach was chosen and the data was collected by theme interviews with six representatives of Finnish global companies from the b2b sector being interviewed. The theoretical framework covers the general field of b2b marketing communications and its main elements. The online environment as well as the concept of a global marketplace and integrated approach to marketing communication activities is also discussed. The theory was supported by the interviews regarding the activities and roles of the marketing communication tools and both theory as well as the interviews found personal selling to be a vital tool. However, the importance of online has grown and online marketing activities have risen right next to personal selling. The use of analytics and marketing automation was found to be of great interest in the interviews and they were seen as a growing domain in b2b marketing communications. The importance of targeted and personalised messages from relevant medias was a repeating theme as was the customer-centric approach in marketing communication activities. Also, offline and online tools and channels were seen as something that should be treated together as an entity rather than as separate activities. Relevant content created according to the needs of the customer with the gathered data from analytics were seen as the future of b2b marketing communications. Online has added its input to the more traditionally perceived tools and they are executed within the framework of the digital age. Nevertheless, even though online has increased its presence in the b2b marketing communications mix, the more traditionally perceived marketing communication tools, especially personal selling, have not lost their meaning or place in the b2b marketing communication mix.

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At present, one of the main concerns of green network is to minimize the power consumption of network infrastructure. Surveys show that, the highest amount of power is consumed by the network devices during its runtime. However to control this power consumption it is important to know which factors has highest impact on this matter. This paper is focused on the measurement and modeling the power consumption of an Ethernet switch during its runtime considering various types of input parameters with all possible combinations. For the experiment, three input parameters are chosen. They are bandwidth, link load and number of connections. The output to be measured is the power consumption of the Ethernet switch. Due to the uncertain power consuming pattern of the Ethernet switch a fully-comprehensive experimental evaluation would require an unfeasible and cumbersome experimental phase. Because of that, design of experiment (DoE) method has been applied to obtain adequate information on the effects of each input parameters on the power consumption. The whole work consists of three parts. In the first part a test bed is planned with input parameters and the power consumption of the switch is measured. The second part is about generating a mathematical model with the help of design of experiment tools. This model can be used for measuring precise power consumption in different scenario and also pinpoint the parameters with higher influence in power consumption. And in the last part, the mathematical model is evaluated by comparing with the experimental values.

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This thesis introduces heat demand forecasting models which are generated by using data mining algorithms. The forecast spans one full day and this forecast can be used in regulating heat consumption of buildings. For training the data mining models, two years of heat consumption data from a case building and weather measurement data from Finnish Meteorological Institute are used. The thesis utilizes Microsoft SQL Server Analysis Services data mining tools in generating the data mining models and CRISP-DM process framework to implement the research. Results show that the built models can predict heat demand at best with mean average percentage errors of 3.8% for 24-h profile and 5.9% for full day. A deployment model for integrating the generated data mining models into an existing building energy management system is also discussed.

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Press forming is nowadays one of the most common industrial methods in use for producing deeper trays from paperboard. Demands for material properties like recyclability and sustainability have increased also in the packaging industry, but there are still limitations related to the formability of paperboard. A majority of recent studies have focused on material development, but the potential of the package manufacturing process can also be improved by the development of tooling and process control. In this study, advanced converting tools (die cutting tools and the press forming mould) are created for production scale paperboard tray manufacturing. Also monitoring methods that enable the production of paperboard trays with enhanced quality, and can be utilized in process control are developed. The principles for tray blank preparation, including creasing pattern and die cutting tool design are introduced. The mould heating arrangement and determination of mould clearance are investigated to improve the quality of the press formed trays. The effect of the spring back of the tray walls on the tray dimensions can be managed by adjusting the heat-related process parameters and estimating it at the mould design stage. This enables production speed optimization as the process parameters can be adjusted more freely. Real-time monitoring of pressing force by using multiple force sensors embedded in the mould structure can be utilized in the evaluation of material characteristics on a modified production machinery. Comprehensive process control can be achieved with a combination of measurement of the outer dimensions of the trays and pressing force monitoring. The control method enables detection of defects and tracking changes in the material properties. The optimized converting tools provide a basis for effective operation of the control system.

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The recent rapid development of biotechnological approaches has enabled the production of large whole genome level biological data sets. In order to handle thesedata sets, reliable and efficient automated tools and methods for data processingand result interpretation are required. Bioinformatics, as the field of studying andprocessing biological data, tries to answer this need by combining methods and approaches across computer science, statistics, mathematics and engineering to studyand process biological data. The need is also increasing for tools that can be used by the biological researchers themselves who may not have a strong statistical or computational background, which requires creating tools and pipelines with intuitive user interfaces, robust analysis workflows and strong emphasis on result reportingand visualization. Within this thesis, several data analysis tools and methods have been developed for analyzing high-throughput biological data sets. These approaches, coveringseveral aspects of high-throughput data analysis, are specifically aimed for gene expression and genotyping data although in principle they are suitable for analyzing other data types as well. Coherent handling of the data across the various data analysis steps is highly important in order to ensure robust and reliable results. Thus,robust data analysis workflows are also described, putting the developed tools andmethods into a wider context. The choice of the correct analysis method may also depend on the properties of the specific data setandthereforeguidelinesforchoosing an optimal method are given. The data analysis tools, methods and workflows developed within this thesis have been applied to several research studies, of which two representative examplesare included in the thesis. The first study focuses on spermatogenesis in murinetestis and the second one examines cell lineage specification in mouse embryonicstem cells.