Quantum capacity under adversarial quantum noise: arbitrarily varying quantum channels

We investigate entanglement transmission over an unknown channel in the presence of a third party (called the adversary), which is enabled to choose the channel from a given set of memoryless but non-stationary channels without informing the legitimate sender and receiver about the particular choice that he made. This channel model is called arbitrarily varying quantum channel (AVQC). We derive a quantum version of Ahlswede's dichotomy for classical arbitrarily varying channels. This includes a regularized formula for the common randomness-assisted capacity for entanglement transmission of an AVQC. Quite surprisingly and in contrast to the classical analog of the problem involving the maximal and average error probability, we find that the capacity for entanglement transmission of an AVQC always equals its strong subspace transmission capacity. These results are accompanied by different notions of symmetrizability (zero-capacity conditions) as well as by conditions for an AVQC to have a capacity described by a single-letter formula. In he final part of the paper the capacity of the erasure-AVQC is computed and some light shed on the connection between AVQCs and zero-error capacities. Additionally, we show by entirely elementary and operational arguments motivated by the theory of AVQCs that the quantum, classical, and entanglement-assisted zero-error capacities of quantum channels are generically zero and are discontinuous at every positivity point.Comment: 49 pages, no figures, final version of our papers arXiv:1010.0418v2 and arXiv:1010.0418. Published "Online First" in Communications in Mathematical Physics, 201

Investigation of continuous-time quantum walk by using Krylov subspace-Lanczos algorithm

In papers\cite{js,jsa}, the amplitudes of continuous-time quantum walk on graphs possessing quantum decomposition (QD graphs) have been calculated by a new method based on spectral distribution associated to their adjacency matrix. Here in this paper, it is shown that the continuous-time quantum walk on any arbitrary graph can be investigated by spectral distribution method, simply by using Krylov subspace-Lanczos algorithm to generate orthonormal bases of Hilbert space of quantum walk isomorphic to orthogonal polynomials. Also new type of graphs possessing generalized quantum decomposition have been introduced, where this is achieved simply by relaxing some of the constrains imposed on QD graphs and it is shown that both in QD and GQD graphs, the unit vectors of strata are identical with the orthonormal basis produced by Lanczos algorithm. Moreover, it is shown that probability amplitude of observing walk at a given vertex is proportional to its coefficient in the corresponding unit vector of its stratum, and it can be written in terms of the amplitude of its stratum. Finally the capability of Lanczos-based algorithm for evaluation of walk on arbitrary graphs (GQD or non-QD types), has been tested by calculating the probability amplitudes of quantum walk on some interesting finite (infinite) graph of GQD type and finite (infinite) path graph of non-GQD type, where the asymptotic behavior of the probability amplitudes at infinite limit of number of vertices, are in agreement with those of central limit theorem of Ref.\cite{nko}.Comment: 29 pages, 4 figure

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.

Differential regulation of a MYB transcription factor is correlated with transgenerational epigenetic inheritance of trichome density in Mimulus guttatus

This is the peer reviewed version of the following article: Scoville, A. G., Barnett, L. L., Bodbyl-Roels, S., Kelly, J. K. and Hileman, L. C. (2011), Differential regulation of a MYB transcription factor is correlated with transgenerational epigenetic inheritance of trichome density in Mimulus guttatus. New Phytologist, 191: 251–263. doi:10.1111/j.1469-8137.2011.03656.x, which has been published in final form at http://doi.org/10.1111/j.1469-8137.2011.03656.x. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.Epigenetic inheritance, transgenerational transmission of traits not proximally determined by DNA sequence, has been linked to transmission of chromatin modifications and gene regulation, which are known to be sensitive to environmental factors. Mimulus guttatus increases trichome (plant hair) density in response to simulated herbivore damage. Increased density is expressed in progeny even if progeny do not experience damage. To better understand epigenetic inheritance of trichome production, we tested the hypothesis that candidate gene expression states are inherited in response to parental damage. Using M. guttatus recombinant inbred lines, offspring of leaf-damaged and control plants were raised without damage. Relative expression of candidate trichome development genes was measured in offspring. Line and parental damage effects on trichome density were measured. Associations between gene expression, trichome density, and response to parental damage were determined. We identified M. guttatus MYB MIXTA-like 8 as a possible negative regulator of trichome development. We found that parental leaf damage induces down-regulation of MYB MIXTA-like 8 in progeny, which is associated with epigenetically inherited increased trichome density. Our results link epigenetic transmission of an ecologically important trait with differential gene expression states – providing insight into a mechanism underlying environmentally induced ‘soft inheritance’

Evaluation of effective resistances in pseudo-distance-regular resistor networks

In Refs.[1] and [2], calculation of effective resistances on distance-regular networks was investigated, where in the first paper, the calculation was based on the stratification of the network and Stieltjes function associated with the network, whereas in the latter one a recursive formula for effective resistances was given based on the Christoffel-Darboux identity. In this paper, evaluation of effective resistances on more general networks called pseudo-distance-regular networks [21] or QD type networks \cite{obata} is investigated, where we use the stratification of these networks and show that the effective resistances between a given node such as $\alpha$ and all of the nodes $\beta$ belonging to the same stratum with respect to $\alpha$ ($R_{\alpha\beta^{(m)}}$, $\beta$ belonging to the $m$-th stratum with respect to the $\alpha$) are the same. Then, based on the spectral techniques, an analytical formula for effective resistances $R_{\alpha\beta^{(m)}}$ such that $L^{-1}_{\alpha\alpha}=L^{-1}_{\beta\beta}$ (those nodes $\alpha$, $\beta$ of the network such that the network is symmetric with respect to them) is given in terms of the first and second orthogonal polynomials associated with the network, where $L^{-1}$ is the pseudo-inverse of the Laplacian of the network. From the fact that in distance-regular networks, $L^{-1}_{\alpha\alpha}=L^{-1}_{\beta\beta}$ is satisfied for all nodes $\alpha,\beta$ of the network, the effective resistances $R_{\alpha\beta^{(m)}}$ for $m=1,2,...,d$ ($d$ is diameter of the network which is the same as the number of strata) are calculated directly, by using the given formula.Comment: 30 pages, 7 figure

A symmetry group of a Thue-Morse quasicrystal

We present a method of coding general self-similar structures. In particular, we construct a symmetry group of a one-dimensional Thue-Morse quasicrystal, i.e., of a nonperiodic ground state of a certain translation-invariant, exponentially decaying interaction.Comment: 6 pages, Late

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

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

Conceptualisation, Development, Fabrication and In Vivo Validation of a Novel Disintegration Tester for Orally Disintegrating Tablets

Disintegration time is the key critical quality attribute for a tablet classed as an Orally Disintegrating Tablet (ODT). The currently accepted in vitro testing regimen for ODTs is the standard United States Pharmacopeia (USP) test for disintegration of immediate release tablets, which requires a large volume along with repeated submergence of the dosage form within the disintegration medium. The aim of this study was to develop an in vivo relevant ODT disintegration test that mimicked the environment of the oral cavity, including lower volume of disintegration medium, with relevant temperature and humidity that represent the conditions of the mouth. The results showed that the newly developed Aston test was able to differentiate between different ODTs with small disintegration time windows, as well as between immediate release tablets and ODTs. The Aston test provided higher correlations between ODT properties and disintegration time compared to the USP test method and most significantly, resulted in a linear in vitro/in vivo correlation (IVIVC) (R 2 value of 0.98) compared with a "hockey stick" profile of the USP test. This study therefore concluded that the newly developed Aston test is an accurate, repeatable, relevant and robust test method for assessing ODT disintegration time which will provide the pharmaceutical industry and regulatory authorities across the world with a pragmatic ODT testing regime