This book deals with the mathematical properties of dimensioned quantities, such as length, mass, voltage, and viscosity. Beginning with a careful examination of how one expresses the numerical results of a measurement and uses these results in subsequent manipulations, the author rigorously constructs the notion of dimensioned numbers and discusses their algebraic structure. The result is a unification of linear algebra and traditional dimensional analysis that can be extended from the scalars to which the traditional analysis is perforce restricted to multidimensional vectors of the sort frequently encountered in engineering, systems theory, economics, and other applications.
In this IBM Redbooks publication, we discuss and describe a multidimensional data warehousing infrastructure that can enable solutions for complex problems in an efficient and effective manner. The focus of this infrastructure is the InfoSphere Warehouse Cubing Services Feature. With this feature, DB2 becomes the data store for large volumes of data that you can use to perform multidimensional analysis, which enables viewing complex problems from multiple perspectives, which provides more information for management business decision making. This feature supports analytic tool interfaces from powerful data analysis tools, such as Cognos 8 BI, Microsoft Excel, and Alphablox. This is a significant capability that supports and enhances the analytics that clients use as they work to resolve problems with an ever growing scope, dimension, and complexity. Analyzing problems by performing more detailed queries on the data and viewing the results from multiple perspectives yields significantly more information and insight. Building multidimensional cubes based on underlying DB2 relational tables, without having to move or replicate the data, enables significantly more powerful data analysis with less work and leads to faster problem resolution with the capability for more informed management decision making. This capability is known as No Copy Analytics and is made possible with InfoSphere Warehouse Cubing Services.
Multidimensional Analytical Techniques in Environmental Research is a comprehensive resource on the many multidimensional analytical strategies to qualitatively and quantitatively assess and map the organic and inorganic pollutants in complex atmospheric, water and soil matrices. During the past two decades, the rapidly-evolving field of analytical instrumentation has produced sophisticated multidimensional tools capable of providing unique and in-depth knowledge on the chemical features of complex mixtures from these different environmental matrices. This book brings together the wealth of information in the current literature, assisting in the decision-making process by covering both the fundamentals and applications of these methodologies. Sections cover the wide variety of multidimensional analytical techniques, including multidimensional solution- and solid-state nuclear magnetic resonance (NMR) spectroscopy, ultrahigh-resolution mass spectrometry (MS), two-dimensional correlation spectroscopy, two-dimensional liquid and gas chromatography and capillary electrophoresis coupled to high-resolution detection techniques, and excitation-emission (EEM) fluorescence spectroscopy assisted by multiway data analysis tools, and the use of synchrotron-radiation-based techniques combined with other spectroscopic approaches to explore and map the speciation of elements.
Outlines a set of techniques that enables a researcher to explore the hidden structure of large databases. These techniques use proximities to find a configuration of points that reflect the structure in the data.
Part one of the authors' comprehensive and innovative work on multidimensional real analysis. This book is based on extensive teaching experience at Utrecht University and gives a thorough account of differential analysis in multidimensional Euclidean space. It is an ideal preparation for students who wish to go on to more advanced study. The notation is carefully organized and all proofs are clean, complete and rigorous. The authors have taken care to pay proper attention to all aspects of the theory. In many respects this book presents an original treatment of the subject and it contains many results and exercises that cannot be found elsewhere. The numerous exercises illustrate a variety of applications in mathematics and physics. This combined with the exhaustive and transparent treatment of subject matter make the book ideal as either the text for a course, a source of problems for a seminar or for self study.
Poverty is a paradoxical state. Recognizable in the eld for any sensitive observer who travels in remote rural areas and urban slums and meets marginalized people in a given society, poverty still remains a challenge to conceptual formalization and to measurement that is consistent with such formalization. The analysis of poverty is multidisciplinary. It goes from ethics to economics, from political science to human biology, and any type of measurement rests on mathematics. Moreover, poverty is multifaceted according to the types of deprivation, and it is also gender and age speci c. A vector of variables is required, which raises a substantial problem for individual and group comparisons necessary to equity analysis. Multidimension- ity also complicates the aggregation necessary to perform the ef ciency analysis of policies. In the case of income poverty, these two problems, equity and ef ciency, have bene ted from very signi cant progress in the eld of economics. Similar achievements are still to come in the area of multidimensional poverty. Within this general background, this book has a very modest and narrow-scoped objective. It proposes an operational methodology for measuring multidimensional poverty, independent from the conceptual origin, the size and the qualitative as well as the quantitative nature of the primary indicators used to describe the poverty of an individual, a household or a sociodemographic entity.
Unstructured text, as one of the most important data forms, plays a crucial role in data-driven decision making in domains ranging from social networking and information retrieval to scientific research and healthcare informatics. In many emerging applications, people's information need from text data is becoming multidimensional—they demand useful insights along multiple aspects from a text corpus. However, acquiring such multidimensional knowledge from massive text data remains a challenging task. This book presents data mining techniques that turn unstructured text data into multidimensional knowledge. We investigate two core questions. (1) How does one identify task-relevant text data with declarative queries in multiple dimensions? (2) How does one distill knowledge from text data in a multidimensional space? To address the above questions, we develop a text cube framework. First, we develop a cube construction module that organizes unstructured data into a cube structure, by discovering latent multidimensional and multi-granular structure from the unstructured text corpus and allocating documents into the structure. Second, we develop a cube exploitation module that models multiple dimensions in the cube space, thereby distilling from user-selected data multidimensional knowledge. Together, these two modules constitute an integrated pipeline: leveraging the cube structure, users can perform multidimensional, multigranular data selection with declarative queries; and with cube exploitation algorithms, users can extract multidimensional patterns from the selected data for decision making. The proposed framework has two distinctive advantages when turning text data into multidimensional knowledge: flexibility and label-efficiency. First, it enables acquiring multidimensional knowledge flexibly, as the cube structure allows users to easily identify task-relevant data along multiple dimensions at varied granularities and further distill multidimensional knowledge. Second, the algorithms for cube construction and exploitation require little supervision; this makes the framework appealing for many applications where labeled data are expensive to obtain.
Information and communication technologies play a crucial role in a number of modern industries. Among these, education has perhaps seen the greatest increases in efficiency and availability through Internet-based technologies. E-Learning as a Socio-Cultural System: A Multidimensional Analysis provides readers with a critical examination of the theories, models, and best practices in online education from a social perspective, evaluating blended, distance, and mobile learning systems with a focus on the interactions of their practitioners. Within the pages of this volume, teachers, students, administrators, policy makers, and IT professionals will all find valuable advice and enriching personal experiences in the field of online education.
This book highlights recent developments in multidimensional data visualization, presenting both new methods and modifications on classic techniques. Throughout the book, various applications of multidimensional data visualization are presented including its uses in social sciences (economy, education, politics, psychology), environmetrics, and medicine (ophthalmology, sport medicine, pharmacology, sleep medicine). The book provides recent research results in optimization-based visualization. Evolutionary algorithms and a two-level optimization method, based on combinatorial optimization and quadratic programming, are analyzed in detail. The performance of these algorithms and the development of parallel versions are discussed. The utilization of new visualization techniques to improve the capabilies of artificial neural networks (self-organizing maps, feed-forward networks) is also discussed. The book includes over 100 detailed images presenting examples of the many different visualization techniques that the book presents. This book is intended for scientists and researchers in any field of study where complex and multidimensional data must be represented visually.
