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Optimization Algorithms on Matrix Manifolds
Many problems in the sciences and engineering can be rephrased as optimization problems on matrix search spaces endowed with a so-called manifold structure. This book shows how to exploit the special structure of such problems to develop efficient numerical algorithms. It places careful emphasis on both the numerical formulation of the algorithm and its differential geometric abstraction--illustrating how good algorithms draw equally from the insights of differential geometry, optimization, and numerical analysis. Two more theoretical chapters provide readers with the background in differential geometry necessary to algorithmic development. In the other chapters, several well-known optimizat...
An Introduction to Optimization on Smooth Manifolds
Optimization on Riemannian manifolds-the result of smooth geometry and optimization merging into one elegant modern framework-spans many areas of science and engineering, including machine learning, computer vision, signal processing, dynamical systems and scientific computing. This text introduces the differential geometry and Riemannian geometry concepts that will help students and researchers in applied mathematics, computer science and engineering gain a firm mathematical grounding to use these tools confidently in their research. Its charts-last approach will prove more intuitive from an optimizer's viewpoint, and all definitions and theorems are motivated to build time-tested optimization algorithms. Starting from first principles, the text goes on to cover current research on topics including worst-case complexity and geodesic convexity. Readers will appreciate the tricks of the trade for conducting research and for numerical implementations sprinkled throughout the book.
Model Reduction of Complex Dynamical Systems
This contributed volume presents some of the latest research related to model order reduction of complex dynamical systems with a focus on time-dependent problems. Chapters are written by leading researchers and users of model order reduction techniques and are based on presentations given at the 2019 edition of the workshop series Model Reduction of Complex Dynamical Systems – MODRED, held at the University of Graz in Austria. The topics considered can be divided into five categories: system-theoretic methods, such as balanced truncation, Hankel norm approximation, and reduced-basis methods; data-driven methods, including Loewner matrix and pencil-based approaches, dynamic mode decomposit...
Recent Advances in Optimization and its Applications in Engineering
Mathematical optimization encompasses both a rich and rapidly evolving body of fundamental theory, and a variety of exciting applications in science and engineering. The present book contains a careful selection of articles on recent advances in optimization theory, numerical methods, and their applications in engineering. It features in particular new methods and applications in the fields of optimal control, PDE-constrained optimization, nonlinear optimization, and convex optimization. The authors of this volume took part in the 14th Belgian-French-German Conference on Optimization (BFG09) organized in Leuven, Belgium, on September 14-18, 2009. The volume contains a selection of reviewed articles contributed by the conference speakers as well as three survey articles by plenary speakers and two papers authored by the winners of the best talk and best poster prizes awarded at BFG09. Researchers and graduate students in applied mathematics, computer science, and many branches of engineering will find in this book an interesting and useful collection of recent ideas on the methods and applications of optimization.
ULSI Process Integration 6
ULSI Process Integration 6 covers all aspects of process integration. Sections are devoted to 1) Device Technologies, 2) Front-end-of-line integration (gate stacks, shallow junctions, dry etching, etc.), 3) Back-end-of-line integration (CMP, low-k, Cu interconnect, air-gaps, 3D packaging, etc.), 4) Alternative channel technologies (Ge, III-V, hybrid integration), and 5) Emerging technologies (CNT, graphene, polymer electronics, nanotubes).
Dielectrics in Nanosystems -and- Graphene, Ge/III-V, Nanowires and Emerging Materials for Post-CMOS Applications 3
This issue of ECS Transactions will cover the following topics in (a) Graphene Material Properties, Preparation, Synthesis and Growth; (b) Metrology and Characterization of Graphene; (c) Graphene Devices and Integration; (d) Graphene Transport and mobility enhancement; (e) Thermal Behavior of Graphene and Graphene Based Devices; (f) Ge & III-V devices for CMOS mobility enhancement; (g) III.V Heterostructures on Si substrates; (h) Nano-wires devices and modeling; (i) Simulation of devices based on Ge, III-V, nano-wires and Graphene; (j) Nanotechnology applications in information technology, biotechnology and renewable energy (k) Beyond CMOS device structures and properties of semiconductor nano-devices such as nanowires; (l) Nanosystem fabrication and processing; (m) nanostructures in chemical and biological sensing system for healthcare and security; and (n) Characterization of nanosystems; (f) Nanosystem modeling.
Silicon Photonic Modulators for Low-power Applications
In this book, silicon photonic integrated circuits are combined with electro-optic organic materials for realizing energy-efficient modulators with unprecedented performance. These silicon-organic hybrid Mach-Zehnder modulators feature a compact size, sub-Volt drive voltages, and they support data rates up to 84 Gbit/s. In addition, a wet chemical waveguide fabrication scheme and an efficient fiber-chip coupling scheme are presented.
Silicon and Silicide Nanowires
Nanoscale materials are showing great promise in various electronic, optoelectronic, and energy applications. Silicon (Si) has especially captured great attention as the leading material for microelectronic and nanoscale device applications. Recently, various silicides have garnered special attention for their pivotal role in Si device engineering
Thermoplasmonics
An overview of thermoplasmonics including the underlying theory in nanophotonics and applications in nanoengineering and nanomedicine.
