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

Coating a spherical colloid with a nematic liquid crystal causes frustration-induced defects in the crystal. The thickness of this coating can be used to systematically control the number and orientation of these defects, which could be useful for engineering the microstructure of colloidal materials.

/pdf/frustrated-nematic-order-in-spherical-geometries-4ymx5sghoc.pdf

Frustrated nematic order in spherical geometries

We study the hydrodynamics of fluids composed of self-spinning objects such as chiral grains or colloidal particles subject to torques. These chiral active fluids break both parity and time-reversal symmetries in their non-equilibrium steady states. As a result, the constitutive relations of chiral active media display a dissipationless linear-response coefficient called odd (or equivalently, Hall) viscosity. This odd viscosity does not lead to energy dissipation, but gives rise to a flow perpendicular to applied pressure. We show how odd viscosity arises from non-linear equations of hydrodynamics with rotational degrees of freedom, once linearized around a non-equilibrium steady state characterized by large spinning speeds. Next, we explore odd viscosity in compressible fluids and suggest how our findings can be tested in the context of shock propagation experiments. Finally, we show how odd viscosity in weakly compressible chiral active fluids can lead to density and pressure excess within vortex cores.

/pdf/odd-viscosity-in-chiral-active-fluids-1jzofsy8gq.pdf

Odd viscosity in chiral active fluids.

Ensuring topological protection of the edge states in candidate topological insulators is complicated by the need to break time-reversal symmetry. Polar active liquids present an innovative solution to this problem, as a new metamaterial design shows. Liquids composed of self-propelled particles have been experimentally realized using molecular, colloidal or macroscopic constituents1,2,3,4,5. These active liquids can flow spontaneously even in the absence of an external drive6,7,8. Unlike spontaneous active flow9,10, the propagation of density waves in confined active liquids is not well explored. Here, we exploit a mapping between density waves on top of a chiral flow and electrons in a synthetic gauge field11,12 to lay out design principles for artificial structures termed topological active metamaterials. We design metamaterials that break time-reversal symmetry using lattices composed of annular channels filled with a spontaneously flowing active liquid. Such active metamaterials support topologically protected sound modes that propagate unidirectionally, without backscattering, along either sample edges or domain walls and despite overdamped particle dynamics. Our work illustrates how parity-symmetry breaking in metamaterial structure combined with microscopic irreversibility of active matter leads to novel functionalities that cannot be achieved using only passive materials.

/pdf/topological-sound-in-active-liquid-metamaterials-d7g8xnpeza.pdf

Topological sound in active-liquid metamaterials

This article discusses the concept of information and its intimate relationship with physics. After an introduction of all the necessary quantum mechanical and information theoretical concepts we analyse Landauer's principle which states that the erasure of information is inevitably accompanied by the generation of heat. We employ this principle to rederive a number of results in classical and quantum information theory whose rigorous mathematical derivations are difficult. This demonstrates the usefulness of Landauer's principle and provides an introduction to the physical theory of information.

The physics of forgetting: Landauer's erasure principle and information theory

States of self-stress—tensions and compressions of structural elements that result in zero net forces—play an important role in determining the load-bearing ability of structures ranging from bridges to metamaterials with tunable mechanical properties. We exploit a class of recently introduced states of self-stress analogous to topological quantum states to sculpt localized buckling regions in the interior of periodic cellular metamaterials. Although the topological states of self-stress arise in the linear response of an idealized mechanical frame of harmonic springs connected by freely hinged joints, they leave a distinct signature in the nonlinear buckling behavior of a cellular material built out of elastic beams with rigid joints. The salient feature of these localized buckling regions is that they are indistinguishable from their surroundings as far as material parameters or connectivity of their constituent elements are concerned. Furthermore, they are robust against a wide range of structural perturbations. We demonstrate the effectiveness of this topological design through analytical and numerical calculations as well as buckling experiments performed on two- and three-dimensional metamaterials built out of stacked kagome lattices.

https://www.pnas.org/content/pnas/112/25/7639.full.pdf

Vincenzo Vitelli

Papers

Frustrated nematic order in spherical geometries

Odd viscosity in chiral active fluids.

Topological sound in active-liquid metamaterials

The physics of forgetting: Landauer's erasure principle and information theory

Selective buckling via states of self-stress in topological metamaterials