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

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

Complex networks: Structure and dynamics

We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

1980 Preface * 1999 Preface * 1999 Acknowledgements * Introduction * 1 Circular Logic * 2 Phase Singularities (Screwy Results of Circular Logic) * 3 The Rules of the Ring * 4 Ring Populations * 5 Getting Off the Ring * 6 Attracting Cycles and Isochrons * 7 Measuring the Trajectories of a Circadian Clock * 8 Populations of Attractor Cycle Oscillators * 9 Excitable Kinetics and Excitable Media * 10 The Varieties of Phaseless Experience: In Which the Geometrical Orderliness of Rhythmic Organization Breaks Down in Diverse Ways * 11 The Firefly Machine 12 Energy Metabolism in Cells * 13 The Malonic Acid Reagent ('Sodium Geometrate') * 14 Electrical Rhythmicity and Excitability in Cell Membranes * 15 The Aggregation of Slime Mold Amoebae * 16 Numerical Organizing Centers * 17 Electrical Singular Filaments in the Heart Wall * 18 Pattern Formation in the Fungi * 19 Circadian Rhythms in General * 20 The Circadian Clocks of Insect Eclosion * 21 The Flower of Kalanchoe * 22 The Cell Mitotic Cycle * 23 The Female Cycle * References * Index of Names * Index of Subjects

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/596B270197FE27DE5FABB598B6210622/S0025557200150892a.pdf/div-class-title-span-class-italic-the-geometry-of-biological-time-span-by-a-t-winfree-pp-544-dm68-corrected-second-printing-1990-isbn-3-540-52528-9-springer-div.pdf

The geometry of biological time , by A. T. Winfree. Pp 544. DM68. Corrected Second Printing 1990. ISBN 3-540-52528-9 (Springer)

We develop a method for the multifractal characterization of nonstationary time series, which is based on a generalization of the detrended fluctuation analysis (DFA). We relate our multifractal DFA method to the standard partition function-based multifractal formalism, and prove that both approaches are equivalent for stationary signals with compact support. By analyzing several examples we show that the new method can reliably determine the multifractal scaling behavior of time series. By comparing the multifractal DFA results for original series with those for shuffled series we can distinguish multifractality due to long-range correlations from multifractality due to a broad probability density function. We also compare our results with the wavelet transform modulus maxima method, and show that the results are equivalent.

Multifractal Detrended Fluctuation Analysis of Nonstationary Time Series

Hybrid dynamical systems characterized by discrete switching of smooth dynamics have been used to model various rhythmic phenomena. However, the phase reduction theory, a fundamental framework for analyzing the synchronization of limit-cycle oscillations in rhythmic systems, has mostly been restricted to smooth dynamical systems. Here we develop a general phase reduction theory for weakly perturbed limit cycles in hybrid dynamical systems that facilitates analysis, control, and optimization of nonlinear oscillators whose smooth models are unavailable or intractable. On the basis of the generalized theory, we analyze injection locking of hybrid limit-cycle oscillators by periodic forcing and reveal their characteristic synchronization properties, such as ultrafast and robust entrainment to the periodic forcing and logarithmic scaling at the synchronization transition. We also illustrate the theory by analyzing the synchronization dynamics of a simple physical model of biped locomotion.

Phase reduction theory for hybrid nonlinear oscillators

We theoretically study the synchronization between collective oscillations exhibited by two weakly interacting groups of nonidentical phase oscillators with internal and external global sinusoidal couplings of the groups. Coupled amplitude equations describing the collective oscillations of the oscillator groups are obtained by using the Ott–Antonsen ansatz, and then coupled phase equations for the collective oscillations are derived by phase reduction of the amplitude equations. The collective phase coupling function, which determines the dynamics of macroscopic phase differences between the groups, is calculated analytically. We demonstrate that the groups can exhibit effective antiphase collective synchronization even if the microscopic external coupling between individual oscillator pairs belonging to different groups is in-phase, and similarly effective in-phase collective synchronization in spite of microscopic antiphase external coupling between the groups.

/pdf/phase-synchronization-between-collective-rhythms-of-globally-2u0ma48yxi.pdf

Phase synchronization between collective rhythms of globally coupled oscillator groups: Noiseless nonidentical case

Phase reduction framework for limit-cycling systems based on isochrons has been used as a powerful tool for analyzing rhythmic phenomena. Recently, the notion of isostables, which complements the isochrons by characterizing amplitudes of the system state, i.e., deviations from the limit-cycle attractor, has been introduced to describe transient dynamics around the limit cycle [Wilson and Moehlis, Phys. Rev. E 94, 052213 (2016)]. In this study, we introduce a framework for a reduced phase-amplitude description of transient dynamics of stable limit-cycling systems. In contrast to the preceding study, the isostables are treated in a fully consistent way with the Koopman operator analysis, which enables us to avoid discontinuities of the isostables and to apply the framework to system states far from the limit cycle. We also propose a new, convenient bi-orthogonalization method to obtain the response functions of the amplitudes, which can be interpreted as an extension of the adjoint covariant Lyapunov vector to transient dynamics in limit-cycling systems. We illustrate the utility of the proposed reduction framework by estimating optimal injection timing of external input that efficiently suppresses deviations of the system state from the limit cycle in a model of a biochemical oscillator.

/pdf/phase-amplitude-reduction-of-transient-dynamics-far-from-1las3x81se.pdf

Phase-amplitude reduction of transient dynamics far from attractors for limit-cycling systems

As shown by Alan Turing in 1952, differential diffusion may destabilize uniform distributions of reacting species and lead to emergence of patterns. While stationary Turing patterns are broadly known, the oscillatory instability, leading to traveling waves in continuous media and sometimes called the wave bifurcation, remains less investigated. Here, we extend the original analysis by Turing to networks and apply it to ecological metapopulations with dispersal connections between habitats. Remarkably, the oscillatory Turing instability does not lead to wave patterns in networks, but to spontaneous development of heterogeneous oscillations and possible extinction of species. We find such oscillatory instabilities for all possible food webs with three predator or prey species, under various assumptions about the mobility of individual species and nonlinear interactions between them. Hence, the oscillatory Turing instability should be generic and must play a fundamental role in metapopulation dynamics, providing a common mechanism for dispersal-induced destabilization of ecosystems.

/pdf/dispersal-induced-destabilization-of-metapopulations-and-4dkk2nqttj.pdf

Dispersal-induced destabilization of metapopulations and oscillatory Turing patterns in ecological networks

In large random networks, each eigenvector of the Laplacian matrix tends to localize on a subset of network nodes having similar numbers of edges, namely, the components of each Laplacian eigenvector take relatively large values only on a particular subset of nodes whose degrees are close. Although this localization property has significant consequences for dynamical processes on random networks, a clear theoretical explanation has not yet been established. Here we analyze the origin of localization of Laplacian eigenvectors on random networks by using a perturbation theory. We clarify how heterogeneity in the node degrees leads to the eigenvector localization and that there exists a clear degree-eigenvalue correspondence, that is, the characteristic degrees of the localized nodes essentially determine the eigenvalues. We show that this theory can account for the localization properties of Laplacian eigenvectors on several classes of random networks, and argue that this localization should occur generally in networks with degree heterogeneity.

/pdf/localization-of-laplacian-eigenvectors-on-random-networks-3wbt0neoby.pdf

Hiroya Nakao

Papers

Phase reduction theory for hybrid nonlinear oscillators

Phase synchronization between collective rhythms of globally coupled oscillator groups: Noiseless nonidentical case

Phase-amplitude reduction of transient dynamics far from attractors for limit-cycling systems

Dispersal-induced destabilization of metapopulations and oscillatory Turing patterns in ecological networks

Localization of Laplacian eigenvectors on random networks.