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The Art of Random Walks
Einstein proved that the mean square displacement of Brownian motion is proportional to time. He also proved that the diffusion constant depends on the mass and on the conductivity (sometimes referred to Einstein’s relation). The main aim of this book is to reveal similar connections between the physical and geometric properties of space and diffusion. This is done in the context of random walks in the absence of algebraic structure, local or global spatial symmetry or self-similarity. The author studies the heat diffusion at this general level and discusses the following topics: The multiplicative Einstein relation, Isoperimetric inequalities, Heat kernel estimates Elliptic and parabolic Harnack inequality.
The Art of Random Walks
Einstein proved that the mean square displacement of Brownian motion is proportional to time. He also proved that the diffusion constant depends on the mass and on the conductivity (sometimes referred to Einstein's relation). The main aim of this book is to reveal similar connections between the physical and geometric properties of space and diffusion. This is done in the context of random walks in the absence of algebraic structure, local or global spatial symmetry or self-similarity. The author studies the heat diffusion at this general level and discusses the following topics: The multiplicative Einstein relation; Isoperimetric inequalities; Heat kernel estimates and Elliptic and parabolic Harnack inequality.
Operator Theory And Analysis Of Infinite Networks
This volume considers resistance networks: large graphs which are connected, undirected, and weighted. Such networks provide a discrete model for physical processes in inhomogeneous media, including heat flow through perforated or porous media. These graphs also arise in data science, e.g., considering geometrizations of datasets, statistical inference, or the propagation of memes through social networks. Indeed, network analysis plays a crucial role in many other areas of data science and engineering. In these models, the weights on the edges may be understood as conductances, or as a measure of similarity. Resistance networks also arise in probability, as they correspond to a broad class o...
Analysis and Geometry on Graphs and Manifolds
A contemporary exploration of the interplay between geometry, spectral theory and stochastics which is explored for graphs and manifolds.
Stability of Heat Kernel Estimates for Symmetric Non-Local Dirichlet Forms
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FM 2009: Formal Methods
th FM 2009, the 16 International Symposium on Formal Methods, marked the 10th an- versary of the First World Congress on Formal Methods that was held in 1999 in Toulouse, France. We wished to celebrate this by advertising and organizing FM 2009 as the Second World Congress in the FM series, aiming to once again bring together the formal methods communities from all over the world. The statistics displayed in the table on the next page include the number of countries represented by the Programme Committee members, as well as of the authors of submitted and accepted papers. Novel this year was a special track on tools and industrial applications. Subm- sions of papers on these topics were especially encouraged, but not given any special treatment. (It was just as hard to get a special track paper accepted as any other paper.) What we did promote, however, was a discussion of how originality, contri- tion, and soundness should be judged for these papers. The following questions were used by our Programme Committee.
Intelligent Computing
This book presents the proceedings of the Computing Conference 2019, providing a comprehensive collection of chapters focusing on core areas of computing and their real-world applications. Computing is an extremely broad discipline, encompassing a range of specialized fields, each focusing on particular areas of technology and types of application, and the conference offered pioneering researchers, scientists, industrial engineers, and students from around the globe a platform to share new ideas and development experiences. Providing state-of-the-art intelligent methods and techniques for solving real- world problems, the book inspires further research and technological advances in this important area.
Competitiveness in Research and Development
Competitiveness in Research and Development includes a unique comparative analysis of R&D and innovation systems of transition and developing economies. It also features a comprehensive and critical survey of international literature on the measurement of R&D and innovation performance.
