Electron-acoustic plasma waves: oblique modulation and envelope solitons

Theoretical and numerical studies are presented of the amplitude modulation of electron-acoustic waves (EAWs) propagating in space plasmas whose constituents are inertial cold electrons, Boltzmann distributed hot electrons and stationary ions. Perturbations oblique to the carrier EAW propagation direction have been considered. The stability analysis, based on a nonlinear Schroedinger equation (NLSE), reveals that the EAW may become unstable; the stability criteria depend on the angle $\theta$ between the modulation and propagation directions. Different types of localized EA excitations are shown to exist.Comment: 10 pages, 5 figures; to appear in Phys. Rev.

Conformally Invariant Fractals and Potential Theory

The multifractal (MF) distribution of the electrostatic potential near any conformally invariant fractal boundary, like a critical O(N) loop or a $Q$ -state Potts cluster, is solved in two dimensions. The dimension $\hat f(\theta)$ of the boundary set with local wedge angle $\theta$ is $\hat f(\theta)=\frac{\pi}{\theta} -\frac{25-c}{12} \frac{(\pi-\theta)^2}{\theta(2\pi-\theta)}$, with $c$ the central charge of the model. As a corollary, the dimensions $D_{\rm EP} =sup_{\theta}\hat f(\theta)$ of the external perimeter and $D_{\rm H}$ of the hull of a Potts cluster obey the duality equation $(D_{\rm EP}-1)(D_{\rm H}-1)={1/4}$. A related covariant MF spectrum is obtained for self-avoiding walks anchored at cluster boundaries.Comment: 5 pages, 1 figur

Property (T) and rigidity for actions on Banach spaces

We study property (T) and the fixed point property for actions on $L^p$ and other Banach spaces. We show that property (T) holds when $L^2$ is replaced by $L^p$ (and even a subspace/quotient of $L^p$), and that in fact it is independent of $1\leq p<\infty$. We show that the fixed point property for $L^p$ follows from property (T) when 1. For simple Lie groups and their lattices, we prove that the fixed point property for $L^p$ holds for any $1< p<\infty$ if and only if the rank is at least two. Finally, we obtain a superrigidity result for actions of irreducible lattices in products of general groups on superreflexive Banach spaces.Comment: Many minor improvement

Spectral and topological properties of a family of generalised Thue-Morse sequences

The classic middle-thirds Cantor set leads to a singular continuous measure via a distribution function that is know as the Devil's staircase. The support of the Cantor measure is a set of zero Lebesgue measure. Here, we discuss a class of singular continuous measures that emerge in mathematical diffraction theory and lead to somewhat similar distribution functions, yet with significant differences. Various properties of these measures are derived. In particular, these measures have supports of full Lebesgue measure and possess strictly increasing distribution functions. In this sense, they mark the opposite end of what is possible for singular continuous measures. For each member of the family, the underlying dynamical system possesses a topological factor with maximal pure point spectrum, and a close relation to a solenoid, which is the Kronecker factor of the system. The inflation action on the continuous hull is sufficiently explicit to permit the calculation of the corresponding dynamical zeta functions. This is achieved as a corollary of analysing the Anderson-Putnam complex for the determination of the cohomological invariants of the corresponding tiling spaces.Comment: Dedicated to Robert V. Moody on the occasion of his 70th birthday; revised and improved versio

Mosaic nanoparticles elicit cross-reactive immune responses to zoonotic coronaviruses in mice

Protection against SARS-CoV-2 and SARS-related emergent zoonotic coronaviruses is urgently needed. We made homotypic nanoparticles displaying the receptor-binding domain (RBD) of SARS-CoV-2 or co-displaying SARS-CoV-2 RBD along with RBDs from animal betacoronaviruses that represent threats to humans (mosaic nanoparticles; 4-8 distinct RBDs). Mice immunized with RBD-nanoparticles, but not soluble antigen, elicited cross-reactive binding and neutralization responses. Mosaic-RBD-nanoparticles elicited antibodies with superior cross-reactive recognition of heterologous RBDs compared to sera from immunizations with homotypic SARS-CoV-2–RBD-nanoparticles or COVID-19 convalescent human plasmas. Moreover, sera from mosaic-RBD–immunized mice neutralized heterologous pseudotyped coronaviruses equivalently or better after priming than sera from homotypic SARS-CoV-2–RBD-nanoparticle immunizations, demonstrating no immunogenicity loss against particular RBDs resulting from co-display. A single immunization with mosaic-RBD-nanoparticles provides a potential strategy to simultaneously protect against SARS-CoV-2 and emerging zoonotic coronaviruses

A proof of the Mazur-Orlicz theorem via the Markov-Kakutani common fixed point theorem, and vice versa

In this paper, we present a new proof of the Mazur-Orlicz theorem, which uses the Markov-Kakutani common fixed point theorem, and a new proof of the Markov-Kakutani common fixed point theorem, which uses the Mazur-Orlicz theorem

Random data wave equations

Nowadays we have many methods allowing to exploit the regularising properties of the linear part of a nonlinear dispersive equation (such as the KdV equation, the nonlinear wave or the nonlinear Schroedinger equations) in order to prove well-posedness in low regularity Sobolev spaces. By well-posedness in low regularity Sobolev spaces we mean that less regularity than the one imposed by the energy methods is required (the energy methods do not exploit the dispersive properties of the linear part of the equation). In many cases these methods to prove well-posedness in low regularity Sobolev spaces lead to optimal results in terms of the regularity of the initial data. By optimal we mean that if one requires slightly less regularity then the corresponding Cauchy problem becomes ill-posed in the Hadamard sense. We call the Sobolev spaces in which these ill-posedness results hold spaces of supercritical regularity. More recently, methods to prove probabilistic well-posedness in Sobolev spaces of supercritical regularity were developed. More precisely, by probabilistic well-posedness we mean that one endows the corresponding Sobolev space of supercritical regularity with a non degenerate probability measure and then one shows that almost surely with respect to this measure one can define a (unique) global flow. However, in most of the cases when the methods to prove probabilistic well-posedness apply, there is no information about the measure transported by the flow. Very recently, a method to prove that the transported measure is absolutely continuous with respect to the initial measure was developed. In such a situation, we have a measure which is quasi-invariant under the corresponding flow. The aim of these lectures is to present all of the above described developments in the context of the nonlinear wave equation.Comment: Lecture notes based on a course given at a CIME summer school in August 201

Changes in Global Gene Expression in Response to Chemical and Genetic Perturbation of Chromatin Structure

DNA methylation is important for controlling gene expression in all eukaryotes. Microarray analysis of mutant and chemically-treated Arabidopsis thaliana seedlings with reduced DNA methylation revealed an altered gene expression profile after treatment with the DNA methylation inhibitor 5-aza-2′ deoxycytidine (5-AC), which included the upregulation of expression of many transposable elements. DNA damage-response genes were also coordinately upregulated by 5-AC treatment. In the ddm1 mutant, more specific changes in gene expression were observed, in particular for genes predicted to encode transposable elements in centromeric and pericentromeric locations. These results confirm that DDM1 has a very specific role in maintaining transcriptional silence of transposable elements, while chemical inhibitors of DNA methylation can affect gene expression at a global level