There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

抗原变异可使得多种致病微生物易于逃避宿主免疫应答。表达在感染红细胞表面的恶性疟原虫红细胞表面蛋白1（PfPMP1）与感染红细胞、内皮细胞、树突状细胞以及胎盘的单个或多个受体作用，在黏附及免疫逃避中起关键的作用。每个单倍体基因组var基因家族编码约60种成员，通过启动转录不同的var基因变异体为抗原变异提供了分子基础。

疟原虫var基因转换速率变化导致抗原变异[英]／Paul H, Robert P, Christodoulou Z, et al//Proc Natl Acad Sci U S A

Inspired by empirical studies of networked systems such as the Internet, social networks, and biological networks, researchers have in recent years developed a variety of techniques and models to help us understand or predict the behavior of these systems. Here we review developments in this field, including such concepts as the small-world effect, degree distributions, clustering, network correlations, random graph models, models of network growth and preferential attachment, and dynamical processes taking place on networks.

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The Structure and Function of Complex Networks

Deposits of clastic carbonate-dominated (calciclastic) sedimentary slope systems in the rock record have been identified mostly as linearly-consistent carbonate apron deposits, even though most ancient clastic carbonate slope deposits fit the submarine fan systems better. Calciclastic submarine fans are consequently rarely described and are poorly understood. Subsequently, very little is known especially in mud-dominated calciclastic submarine fan systems. Presented in this study are a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) that reveals a >250 m thick calciturbidite complex deposited in a calciclastic submarine fan setting. Seven facies are recognised from core and thin section characterisation and are grouped into three carbonate turbidite sequences. They include: 1) Calciturbidites, comprising mostly of highto low-density, wavy-laminated bioclast-rich facies; 2) low-density densite mudstones which are characterised by planar laminated and unlaminated muddominated facies; and 3) Calcidebrites which are muddy or hyper-concentrated debrisflow deposits occurring as poorly-sorted, chaotic, mud-supported floatstones. These

Phd by thesis

http://www.maths.qmul.ac.uk/%7Elatora/report_06.pdf

Complex networks: Structure and dynamics

* Established textbook
 * Continues to lead its readers to some of the hottest topics of contemporary mathematical research

This established reference work continues to lead its readers to some of the hottest topics of contemporary mathematical research.This new edition introduces and explains the ideas of the parabolic methods that have recently found such a spectacular success in the work of Perelman at the examples of closed geodesics and harmonic forms. It also discusses further examples of geometric variational problems from quantum field theory, another source of profound new ideas and methods in geometry.


From the reviews:
"This book provides a very readable introduction to Riemannian geometry and geometric analysis. The author focuses on using analytic methods in the study of some fundamental theorems in Riemannian geometry, e.g., the Hodge theorem, the Rauch comparison theorem, the Lyusternik and Fet theorem and the existence of harmonic mappings. With the vast development of the mathematical subject of geometric analysis, the present textbook is most welcome. [..] The book is made more interesting by the perspectives in various sections." Mathematical Reviews

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Riemannian geometry and geometric analysis

1 Introduction.- 1.1 Examples of Riemannian manifolds of negative or nonpositive sectional curvature.- Appendix to 1.1: Symmetric spaces of noncompact type.- 1.2 Mordell and Shafarevitch type problems.- 1.3 Geometric superrigidity.- 2 Spaces of nonpositive curvature.- 2.1 Local properties of Riemannian manifolds of nonpositive sectional curvature.- 2.2 Nonpositive curvature in the sense of Busemann.- 2.3 Nonpositive curvature in the sense of Alexandrov.- 3 Convex functions and centers of mass.- 3.1 Minimizers of convex functions.- 3.2 Centers of mass.- 3.3 Convex hulls.- 4 Generalized harmonic maps.- 4.1 The definition of generalized harmonic maps.- 4.2 Minimizers of generalized energy functional.- 5 Bochner-Matsushima type identities for harmonic maps and rigidity theorems.- 5.1 The Bochner formula for harmonic one-forms and harmonic maps.- 5.2 A Matsushima type formula for harmonic maps.- 5.3 Geometrie superrigidity.

Nonpositive Curvature: Geometric and Analytic Aspects

Part 1 Examples, definitions, and elementary results: Plateau's problem two dimensional conformally invariant variational problems harmonic maps, conformal maps and holomorphic quadratic differentials some applications of holomorphic quadratic differentials surfaces in R3 the Gauss map. Part 2 Regularity and uniqueness results: harmonic co-ordinates uniqueness of harmonic maps continuity of weak solutions removability of isolated singularities higher regularity the Hartmann-Wintner lemma and some of its consequences asymptotic expansions at branch points estimates from below for the functional determinant of univarlent harmonic mappings. Part 3 Conformal representation: conformal representation of surfaces homeomorphic to S2 and circular domains and closed surfaces of higher genus. Part 4 Existence results: the local existence theorem - an easy proof of the existence of energy minimizing maps the general existence theorem corollaries and consequences of the general existence theorem - boundary conditions nonexistence results - existence of maps with holomorphic quadratic differentials another proof of the existence of unstable minimal surfaces the Plateau-Douglas problem in Riemannian manifolds. Part 5 Harmonic maps between surfaces: the existence of harmonic diffeomorphisms local computations consequences for nonpositively curved image metrics harmonic diffeomorphisms Kneser's Theorem harmonic maps and branched coverings. Part 6 Harmonic maps and Teichmuller spaces: the basic definitions the topological and differentiable structure of Teichmuller's Theorem the complex structure the energy as a function of the domain metric the metric structure the Weil-Petersson metric Kahler property.

Two-dimensional geometric variational problems

Spectral properties of coupled map lattices are described. Conditions for the stability of spatially homogeneous chaotic solutions are derived using linear stability analysis. Global stability analysis results are also presented. The analytical results are supplemented with numerical examples. The quadratic map is used for the site dynamics with different coupling schemes such as global coupling, nearest neighbor coupling, intermediate range coupling, random coupling, small world coupling and scale free coupling.

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Spectral properties and synchronization in coupled map lattices.

We consider networks of coupled maps where the connections between units involve time delays. We show that, similar to the undelayed case, the synchronization of the network depends on the connection topology, characterized by the spectrum of the graph Laplacian. Consequently, scale-free and random networks are capable of synchronizing despite the delayed flow of information, whereas regular networks with nearest-neighbor connections and their small-world variants generally exhibit poor synchronization. On the other hand, connection delays can actually be conducive to synchronization, so that it is possible for the delayed system to synchronize where the undelayed system does not. Furthermore, the delays determine the synchronized dynamics, leading to the emergence of a wide range of new collective behavior which the individual units are incapable of producing in isolation.

/pdf/delays-connection-topology-and-synchronization-of-coupled-ultgwd8o05.pdf

Jürgen Jost

Papers

Riemannian geometry and geometric analysis

Nonpositive Curvature: Geometric and Analytic Aspects

Two-dimensional geometric variational problems

Spectral properties and synchronization in coupled map lattices.

Delays, Connection Topology, and Synchronization of Coupled Chaotic Maps