This book is about “Angiogenesis”. A process in which new vasculature is formed from pre-existing capillaries. Angiogenesis process is associated with the proliferation and growth of both physiologically normal and neoplastic tissues, through the formation of vascular supply, essential for delivering growth requirements such as oxygen and nutrients. The book describes more than 100 genes…
This book introduces analytical ultracentrifugation (AUC) as a whole, covering essential theoretical and practical aspects as well as its applications in both biological and non-biological systems. Comprehensive characterizations of macromolecules in a solution are now routinely required not only for understanding the solution system but also for producing a solution with better properties. Ana…
This book describes useful analytical methods by applying them to real-world problems rather than solving the usual over-simplified classroom problems. The book demonstrates the applicability of analytical methods even for complex problems and guides the reader to a more intuitive understanding of approaches and solutions. Although the solution of Partial Differential Equations by numerical …
This book focuses on the modeling and analysis of heat and fluid flow in microchannels and micro-systems, compiling a number of analytical and hybrid numerical-analytical solutions for models that account for the relevant micro-scale effects, with the corresponding experimental analysis validation when applicable. The volume stands as the only available compilation of easy to use analytically-b…
This volume contains a collection of research and survey papers written by some of the most eminent mathematicians in the international community and is dedicated to Helmut Maier, whose own research has been groundbreaking and deeply influential to the field. Specific emphasis is given to topics regarding exponential and trigonometric sums and their behavior in short intervals, anatomy of inte…
The book includes lectures given by the plenary and key speakers at the 9th International ISAAC Congress held 2013 in Krakow, Poland. The contributions treat recent developments in analysis and surrounding areas, concerning topics from the theory of partial differential equations, function spaces, scattering, probability theory, and others, as well as applications to biomathematics, queueing mo…
The purpose of this book is to present the classical analytic function theory of several variables as a standard subject in a course of mathematics after learning the elementary materials (sets, general topology, algebra, one complex variable). This includes the essential parts of Grauert–Remmert's two volumes, GL227(236) (Theory of Stein spaces) and GL265 (Coherent analytic sheaves) with a l…
This book provides an introduction to h-harmonics and Dunkl transforms. These are extensions of the ordinary spherical harmonics and Fourier transforms, in which the usual Lebesgue measure is replaced by a reflection-invariant weighted measure. The authors’ focus is on the analysis side of both h-harmonics and Dunkl transforms. Graduate students and researchers working in approximation the…
The main concern of the book is analysis of biological processes, the final stage of which is mathematical modeling, i.e. quantitative presentation of the processes in rigorous mathematical terms. It is designated for non-mathematicians. Mathematical models can be compared with experimental data thus verifying the validity of the models and finally of the initial assumptions and verbal descript…
Carolin Loos introduces two novel approaches for the analysis of single-cell data. Both approaches can be used to study cellular heterogeneity and therefore advance a holistic understanding of biological processes. The first method, ODE constrained mixture modeling, enables the identification of subpopulation structures and sources of variability in single-cell snapshot data. The second method …