Tensor multivariate trace inequalities and their applications

In linear algebra, the trace of a square matrix is defined as the sum of elements on the main diagonal. The trace of a matrix is the sum of its eigenvalues (counted with multiplicities), and it is invariant under the change of basis. This charac-terization can be used to define the trace of a tensor in general. Trace inequalities are mathematical relations between different multivariate trace functionals involving linear operators. These relations are straightforward equalities if the involved linear operators commute, however, they can be difficult to prove when the non-commuting linear operators are involved. Given two Hermitian tensors H1 and H2 that do not commute. Does there exist a method to transform one of the two tensors such that they commute without completely destroying the structure of the original tensor? The spectral pinching method is a tool to resolve this problem. In this work, we will apply such spectral pinching method to prove several trace inequalities that extend the Araki–Lieb–Thirring (ALT) inequality, Golden–Thompson(GT) inequality and logarithmic trace inequality to arbitrary many tensors. Our approaches rely on complex interpolation theory as well as asymptotic spectral pinching, providing a transpar-ent mechanism to treat generic tensor multivariate trace inequalities. As an example application of our tensor extension of the Golden–Thompson inequality, we give the tail bound for the independent sum of tensors. Such bound will play a fundamental role in high-dimensional probability and statistical data analysis

Energy-Efficient Non-Orthogonal Transmission under Reliability and Finite Blocklength Constraints

This paper investigates an energy-efficient non-orthogonal transmission design problem for two downlink receivers that have strict reliability and finite blocklength (latency) constraints. The Shannon capacity formula widely used in traditional designs needs the assumption of infinite blocklength and thus is no longer appropriate. We adopt the newly finite blocklength coding capacity formula for explicitly specifying the trade-off between reliability and code blocklength. However, conventional successive interference cancellation (SIC) may become infeasible due to heterogeneous blocklengths. We thus consider several scenarios with different channel conditions and with/without SIC. By carefully examining the problem structure, we present in closed-form the optimal power and code blocklength for energy-efficient transmissions. Simulation results provide interesting insights into conditions for which non-orthogonal transmission is more energy efficient than the orthogonal transmission such as TDMA.Comment: accepted by IEEE GlobeCom workshop on URLLC, 201

The Potential Economic Impact of Avian Flu Pandemic on Taiwan

This study analyzes the potential consequences of an outbreak of avian influenza (H5N1) on Taiwan¡¦s macro economy and individual industries. Both the Input-Output (IO) Analysis Model and Computable General Equilibrium (CGE) Model are used to simulate the possible damage brought by lowering domestic consumption, export, and labor supply. The simulation results indicates that if the disease is confined within the poultry sector, then the impact on real GDP is around -0.1%~-0.4%. Once it becomes a human-to-human pandemic, the IO analysis suggests that the potential impacts on real GDP would be as much as -4.2%~-5.9% while labor demand would decrease 4.9%~6.4%. In the CGE analysis, which allows for resource mobility and substitutions through price adjustments, the real GDP and labor demand would contract 2.0%~2.4% and 2.2%~2.4%, respectively, and bringing down consumer prices by 3%. As for the individual sector, the outbreak will not only damage the poultry sector and its upstream and downstream industries, but also affect the service sectors including wholesale, retail, trade, air transportation, restaurants, as well as healthcare services. These results can be used to support public investment in animal disease control measures.Avian Flu Pandemic, Input-output Model, Computable General Equilibrium Model, Livestock Production/Industries,

Chapter 37 Introduction to Section 6

This handbook addresses a growing list of challenges faced by regions and cities in the Pacific;Rim, drawing connections around the what, why, and how questions that are fundamental;to sustainable development policies and planning practices. These include the connection;between cities and surrounding landscapes, across different boundaries and scales; the persistence;of environmental and development inequities; and the growing impacts of global;climate change, including how physical conditions and social implications are being anticipated;and addressed. Building upon localized knowledge and contextualized experiences,;this edited collection brings attention to place-;based;approaches across the Pacific Rim and;makes an important contribution to the scholarly and practical understanding of sustainable;urban development models that have mostly emerged out of the Western experiences. Nine;sections, each grounded in research, dialogue, and collaboration with practical examples and;analysis, focus on a theme or dimension that carries critical impacts on a holistic vision of city-;landscape;development, such as resilient communities, ecosystem services and biodiversity,;energy, water, health, and planning and engagement.;This international edited collection will appeal to academics and students engaged in;research involving landscape architecture, architecture, planning, public policy, law, urban;studies, geography, environmental science, and area studies. It also informs policy makers,;professionals, and advocates of actionable knowledge and adoptable ideas by connecting;those issues with the Sustainable Development Goals (SDGs);of the United Nations. The;collection of writings presented in this book speaks to multiyear collaboration of scholars;through the APRU Sustainable Cities and Landscapes (SCL);Program and its global network,;facilitated by SCL Annual Conferences and involving more than 100 contributors;from more than 30 institutions

New Efficient Approach to Solve Big Data Systems Using Parallel Gauss–Seidel Algorithms

In order to perform big-data analytics, regression involving large matrices is often necessary. In particular, large scale regression problems are encountered when one wishes to extract semantic patterns for knowledge discovery and data mining. When a large matrix can be processed in its factorized form, advantages arise in terms of computation, implementation, and data-compression. In this work, we propose two new parallel iterative algorithms as extensions of the Gauss–Seidel algorithm (GSA) to solve regression problems involving many variables. The convergence study in terms of error-bounds of the proposed iterative algorithms is also performed, and the required computation resources, namely time-and memory-complexities, are evaluated to benchmark the efficiency of the proposed new algorithms. Finally, the numerical results from both Monte Carlo simulations and real-world datasets are presented to demonstrate the striking effectiveness of our proposed new methods

Chapter 37 Introduction to Section 6

This handbook addresses a growing list of challenges faced by regions and cities in the Pacific;Rim, drawing connections around the what, why, and how questions that are fundamental;to sustainable development policies and planning practices. These include the connection;between cities and surrounding landscapes, across different boundaries and scales; the persistence;of environmental and development inequities; and the growing impacts of global;climate change, including how physical conditions and social implications are being anticipated;and addressed. Building upon localized knowledge and contextualized experiences,;this edited collection brings attention to place-;based;approaches across the Pacific Rim and;makes an important contribution to the scholarly and practical understanding of sustainable;urban development models that have mostly emerged out of the Western experiences. Nine;sections, each grounded in research, dialogue, and collaboration with practical examples and;analysis, focus on a theme or dimension that carries critical impacts on a holistic vision of city-;landscape;development, such as resilient communities, ecosystem services and biodiversity,;energy, water, health, and planning and engagement.;This international edited collection will appeal to academics and students engaged in;research involving landscape architecture, architecture, planning, public policy, law, urban;studies, geography, environmental science, and area studies. It also informs policy makers,;professionals, and advocates of actionable knowledge and adoptable ideas by connecting;those issues with the Sustainable Development Goals (SDGs);of the United Nations. The;collection of writings presented in this book speaks to multiyear collaboration of scholars;through the APRU Sustainable Cities and Landscapes (SCL);Program and its global network,;facilitated by SCL Annual Conferences and involving more than 100 contributors;from more than 30 institutions