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

Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

N G van Kampen 1981 Amsterdam: North-Holland xiv + 419 pp price Dfl 180 This is a book which, at a lower price, could be expected to become an essential part of the library of every physical scientist concerned with problems involving fluctuations and stochastic processes, as well as those who just enjoy a beautifully written book. It provides an extensive graduate-level introduction which is clear, cautious, interesting and readable.

https://iopscience.iop.org/article/10.1088/0031-9112/34/4/040/pdf

Stochastic Processes in Physics and Chemistry

Weyl and Dirac semimetals are three-dimensional phases of matter with gapless electronic excitations that are protected by topology and symmetry. As three-dimensional analogs of graphene, they have generated much recent interest. Deep connections exist with particle physics models of relativistic chiral fermions, and, despite their gaplessness, to solid-state topological and Chern insulators. Their characteristic electronic properties lead to protected surface states and novel responses to applied electric and magnetic fields. The theoretical foundations of these phases, their proposed realizations in solid-state systems, and recent experiments on candidate materials as well as their relation to other states of matter are reviewed.

Weyl and Dirac semimetals in three-dimensional solids

We theoretically study the quantum dynamics of transverse vibrations of a one-dimensional chain of trapped ions in harmonic potentials interacting via a Reggeon-type cubic nonlinearity that is nonunitary but preserves $\mathcal{P}\mathcal{T}$ symmetry. We propose the notion of quantum fragility for the dissipative structural phase transition that spontaneously breaks the $\mathcal{P}\mathcal{T}$ symmetry. In the quantum fragile regime, the nonlinearity dominates the response to mechanical perturbations and the chain supports neither the ordinary quantum phonons of a Luttinger liquid, nor the supersonic solitons that arise in classical fragile critical points in the absence of fluctuations. Quantum fluctuations, approximately captured within a one-loop renormalization group, give rise to mechanical excitations with a strongly momentum-dependent phonon velocity and dissipative spectral behavior. Observable signatures of the quantum fragile chain in trapped ion systems are discussed.

/pdf/soft-quantum-vibrations-of-a-pt-symmetric-nonlinear-ion-29indmqlqx.pdf

Soft quantum vibrations of a PT-symmetric nonlinear ion chain

The Stokeslet is the fundamental Green's function associated with point forces in viscous flows. It prescribes how the work done by external forces is balanced by the energy dissipated through velocity gradients. In ordinary fluids, viscosity is synonymous with energy dissipation. Yet, in fluids with broken microscopic time-reversal symmetry, the viscosity tensor can acquire a dissipationless contribution called odd viscosity. As the ratio between odd and dissipative viscosity diverges, energy balance requires that the resulting flow gradients become singular. Here, we find that these singularities give rise to additional contributions to the Stokeslet flow that persist even when the odd viscosity is small. In this limit, we solve for the flow past a sphere and illustrate the distinct effects of odd shear and rotational viscosities. When applied to many-body sedimentation, our analysis reveals the emergence of non-reciprocal hydrodynamic interactions and chiral modifications to particle trajectories.

Stokes flows in three-dimensional fluids with odd viscosity

We study the effect of thermal fluctuations in the XY-model on a surface with non vanishing mean curvature and zero Gaussian curvature. Unlike Gaussian curvature that typically frustrates orientational order, the extrinsic curvature of the surface can act as a local field that promotes long range order at low temperature. We find numerically that the transition from the high temperature isotropic phase to the true long range ordered phase is characterized by critical exponents consistent with those of the flat space Ising model in two dimensions, up to finite size effects. Our results suggest a versatile strategy to achieve geometric control of liquid crystal order by suitable design of the underlying curvature of a substrate or bounding surface.

Orientational order at finite temperature on undulated surfaces

Michel Fruchart,1, 2, ∗ Ming Han,1, 3 Colin Scheibner,1, 2 and Vincenzo Vitelli1, 2, 4, † James Franck Institute, University of Chicago, Chicago, Illinois 60637, USA Department of Physics, University of Chicago, Chicago, IL 60637, USA Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, USA Kadanoff Center for Theoretical Physics, University of Chicago, Chicago, IL 60637, USA

The odd ideal gas: Hall viscosity and thermal conductivity from non-Hermitian kinetic theory

The dynamics of a viscous liquid undergo a dramatic slowdown when it is cooled to form a solid glass. Recognizing the structural changes across such a transition remains a major challenge. Machine-learning methods, similar to those Facebook uses to recognize groups of friends, have now been applied to this problem.

Vincenzo Vitelli

Papers

Soft quantum vibrations of a PT-symmetric nonlinear ion chain

Stokes flows in three-dimensional fluids with odd viscosity

Orientational order at finite temperature on undulated surfaces

The odd ideal gas: Hall viscosity and thermal conductivity from non-Hermitian kinetic theory

Vitrification: Machines learn to recognize glasses