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

中枢神経系疾患の治療は正常細胞（ニューロン）の機能維持を目的とするが，脳血管障害のように機能障害の原因が細胞の死滅に基づくことは多い．一方，脳腫瘍の治療においては薬物療法や放射線療法といった腫瘍細胞の死滅を目標とするものが大きな位置を占める．いずれの場合にも，細胞死の機序を理解することは各種病態や治療法の理解のうえで重要である．現在のところ最も研究の進んでいる細胞死の型はアポトーシスである．そのなかで重要な位置を占めるミトコンドリアにおける反応および抗アポトーシス因子について概要を紹介する．

Neuroscience 細胞死：最近の知見

The synchronization of chaotic systems

Gamma rhythms are commonly observed in many brain regions during both waking and sleep states, yet their functions and mechanisms remain a matter of debate. Here we review the cellular and synaptic mechanisms underlying gamma oscillations and outline empirical questions and controversial conceptual issues. Our main points are as follows: First, gamma-band rhythmogenesis is inextricably tied to perisomatic inhibition. Second, gamma oscillations are short-lived and typically emerge from the coordinated interaction of excitation and inhibition, which can be detected as local field potentials. Third, gamma rhythm typically concurs with irregular firing of single neurons, and the network frequency of gamma oscillations varies extensively depending on the underlying mechanism. To document gamma oscillations, efforts should be made to distinguish them from mere increases of gamma-band power and/or increased spiking activity. Fourth, the magnitude of gamma oscillation is modulated by slower rhythms. Such cross-frequency coupling may serve to couple active patches of cortical circuits. Because of their ubiquitous nature and strong correlation with the "operational modes" of local circuits, gamma oscillations continue to provide important clues about neuronal population dynamics in health and disease.

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Mechanisms of Gamma Oscillations

Semiconductor lasers are fast dynamical systems that can operate in time scales on the order of picoseconds. Recently there has been much interest in situations where two such lasers are coupled optically via injection of their emitted light into each other, both for fundamental and technological purposes. In this case, and when the distances separating the lasers are larger than tens of centimeters, the coupling signals take longer than nanoseconds to reach the receiver laser, which implies that delays in the coupling become non-negligible with respect to the intrinsic dynamics of the lasers. It is well known that such delay-coupled lasers exhibit different kinds of lag synchronization [1], where one of the lasers advances the dynamics of the other, while both the sign and amount of the lag depends on the details of the coupling architecture that links the lasers. Moreover, in the case of mutual injection, coupling is known to destabilize the otherwise stable lasers, and if the laser frequencies are close enough to each other, the resulting dynamics exhibits a special type of lag synchronization in which the leader and laggard roles of the dynamics alternates irregularly between the two lasers [2].

Lag Syncronization in Delay-Coupled Semiconductor Lasers

Reservoir computers are powerful tools for chaotic time series prediction. They can be trained to approximate phase space flows and can thus both predict future values to a high accuracy, as well as reconstruct the general properties of a chaotic attractor without requiring a model. In this work, we show that the ability to learn the dynamics of a complex system can be extended to systems with co-existing attractors, here a 4-dimensional extension of the well-known Lorenz chaotic system. We demonstrate that a reservoir computer can infer entirely unexplored parts of the phase space: a properly trained reservoir computer can predict the existence of attractors that were never approached during training and therefore are labelled as unseen. We provide examples where attractor inference is achieved after training solely on a single noisy trajectory.

Model-free inference of unseen attractors: Reconstructing phase space features from a single noisy trajectory using reservoir computing

6 pages, 4 figures.-- PACS: 02.30.Ks – Delay and functional equations; 05.45.Tp – Time series analysis; 05.45.-a – Nonlinear dynamics and chaos; 02.50.Fz – Stochastic analysis.

/pdf/delay-system-identification-using-permutation-entropy-and-4bt2vyqqv7.pdf

Delay system identification using permutation entropy and statistical complexity: resonance-like behavior in a noise environment

We analyze the synchronization properties in network elements based on semiconductor lasers mutually interacting with a finite time delay. The role of symmetry for the occurrence of particular synchronization solutions ? including zero-lag synchronization - is discussed and illustrated.

Synchronization properties of network elements based on mutually delay-coupled semiconductor lasers

This paper analyzes the coherence properties of a short external cavity semiconductor laser (ECSL) system in dependence on the feedback ratio, the pump level and laser parameters with respect to their influence on the coherence properties. Based on the findings, the authors are able to control and optimize the coherence properties of the laser system. Hence, short cavity ECSL systems offer novel perspectives for the utilization as light sources for applications where defined or even variable coherence properties are required.

Ingo Fischer

Papers

Lag Syncronization in Delay-Coupled Semiconductor Lasers

Model-free inference of unseen attractors: Reconstructing phase space features from a single noisy trajectory using reservoir computing

Delay system identification using permutation entropy and statistical complexity: resonance-like behavior in a noise environment

Synchronization properties of network elements based on mutually delay-coupled semiconductor lasers

Coherence properties of a short external cavity semiconductor laser system: design of a light source with widely tunable coherence length