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

다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

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

/pdf/determining-lyapunov-exponents-from-a-time-series-3bxxq6d0wt.pdf

Determining Lyapunov exponents from a time series

It is shown that a recently developed hybrid modeling approach that combines machine learning (ML) with an atmospheric global circulation model (AGCM) can serve as a basis for capturing atmospheric processes not captured by the AGCM. This power of the approach is illustrated by three examples from a decades‐long climate simulation experiment. The first example demonstrates that the hybrid model can produce sudden stratospheric warming, a dynamical process of nature not resolved by the low resolution AGCM component of the hybrid model. The second and third example show that introducing 6‐hr cumulative precipitation and sea surface temperature (SST) as ML‐based prognostic variables improves the precipitation climatology and leads to a realistic ENSO signal in the SST and atmospheric surface pressure.

A Hybrid Atmospheric Model Incorporating Machine Learning Can Capture Dynamical Processes Not Captured by Its Physics‐Based Component

The resistive wall stability of an electron beam is studied, and application of the theory to the modified betatron accelerator is considered. Only flute‐like perturbations are analyzed (n=0, l≥1, where n and l are the toroidal and poloidal mode numbers, respectively). Included in the analysis are the effects of relativistic velocities, equilibrium and perturbed self‐electromagnetic fields, and resonant particle effects due to density and velocity profiles. The principal results are (1) l≥2 modes are much more difficult to stabilize than is the l=1 mode; (2) the velocity gradient along the beam can provide an important stabilizing mechanism; (3) the stabilizing effect of the density gradient is reduced by relativistic effects; and (4) magnetic perturbations can be important even for nonrelativistic beams.

Resistive wall flute stability of magnetically guided relativistic electron beams

/pdf/short-wavelength-reverberant-wave-systems-for-enhanced-3cudkr0rm2.pdf

Short-wavelength Reverberant Wave Systems for Enhanced Reservoir Computing

Chaos in Dynamical Systems: One-dimensional maps

The Brillouin flow equilibrium in magnetically insulated lines is a state in which field-emitted electrons, confined to a sheath near the cathode by a magnetic field, drift laminarly at the ?? x ?? velocity in the self-consistent fields of the anode-cathode gap. Herein, this state is perturbed by a TM disturbance traveling along the direction of electron flow. Asymptotic expansions of all quantities of interest in some small parameter are performed in the long wavelength limit. First order quantities are seen to be governed by the Korteweg-deVries' equation, which admits soliton solutions. In the appropriate limits of either infinite wavelength or vanishingly small amplitude, the results contained herein are seen to agree with other analyses, based, respectively, upon either the nondispersive telegraphers' equations or a linearized analysis.

Edward Ott

Papers

A Hybrid Atmospheric Model Incorporating Machine Learning Can Capture Dynamical Processes Not Captured by Its Physics‐Based Component

Resistive wall flute stability of magnetically guided relativistic electron beams

Short-wavelength Reverberant Wave Systems for Enhanced Reservoir Computing

Chaos in Dynamical Systems: One-dimensional maps

Long Wavelength, Nonlinear Perturbations of the Brillouin Flow Equilibrium on Magnetically Insulated Lines