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Nonlinear superposition formulae of integrable partial differential equations by the singular manifold method
We study by the singular manifold method a few 1+1-dimensional partial differential equations which possess N-soliton solutions for arbitrary N, i.e....
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Results for Sr2RuO4
In this chapter, we focus on our results for the elementary excitations and Cooper pairing in strontium ruthenate (...
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Bilinear Formalism in Soliton Theory
A brief survey of the bilinear formalism discovered by Hirota is given. First, the procedure to obtain soliton solutions of nonlinear evolution...
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Critical Phenomena in a Small World
We consider the behavior of various systems on a small-world network near a critical point. Our starting point is a different, nonrandom system with...
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Who Is the Best Connected Scientist?A Study of Scientific Coauthorship Networks
Using data from computer databases of scientific papers in physics, biomedical research, and computer science, we have constructed networks of...
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Scholarly Information Network
I review the background and some recent trends of a particular scholarly information network, ar**v.org, and discuss some of its implications for new...
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Information Theory of Complex Networks: On Evolution and Architectural Constraints
Complex networks are characterized by highly heterogeneous distributions of links, often pervading the presence of key properties such as robustness...
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The Small World Phenomenonin Hybrid Power Law Graphs
The small world phenomenon, that consistently occurs in numerous existing networks, refers to two similar but different properties — small average...
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Nonlinear Waves, Solitons, and IST
These lectures are written for a wide audience with diverse backgrounds. The subject is approached from a general perspective and overly detailed...
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Integrability – and How to Detect It
We present a physicist’s approach to integrability and its detection. Starting from specific examples we present a working definition of what is...
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Extremal Properties of Random Structures
The extremal characteristics of random structures, including trees, graphs, and networks, are discussed. A statistical physics approach is employed...
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Spectral Analysis of Random Networks
We review a general approach that describes the spectra of eigenvalues for random graphs with a local tree-like structure. The exact equations to the...
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Theory of Cooper Pairing Due to Exchange of Spin Fluctuations
It is of general interest whether singlet high- \(T_{\rm c}\)...
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Modeling Calcium Waves
We present an introduction to the mathematics of calcium waves, both intracellular and intercellular. After a discussion of the earlier models I...
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Regulation of IP 3 Receptors by IP 3 and Ca 2+
Inositol 1,4,5-trisphosphate ( IP 3) receptors are intracellular Ca 2+ channels that mediate release of Ca 2+ from intracellular stores. The channels...
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Hormone-Mediated Intercellular Calcium Signalling in an Insect Salivary Gland – Pathways and Mechanisms
The salivary glands of the blowfly Calliphora vicina are a favourable preparation for investigations into spatio-temporal Ca 2+ dynamics in an intact...
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From Simple to Complex Ca 2+ Oscillations: Regulatory Mechanisms and Theoretical Models
Intracellular Ca 2+ oscillations most often appear as regular spikes. However, complex Ca 2+ oscillations in the form of bursting or chaos have also...
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Entropy, Quasiequilibrium, and Projectors Field
Projection operators Py contribute both to the invariance equation (3.2), and to the film extension of the dynamics (4.5). Limiting results, exact...
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Introduction
Nonlinear systems model all but the simplest physical phenomena. In the classical theory, the tools of Poisson geometry appear in an essential way,...