Canonical form of m-by-2-by-2 matrices over a field of characteristic other than two

We give a canonical form of m-by-2-by-2 matrices for equivalence over any field of characteristic not two.Comment: 6 page

Recruitment dynamics in adaptive social networks

We model recruitment in adaptive social networks in the presence of birth and death processes. Recruitment is characterized by nodes changing their status to that of the recruiting class as a result of contact with recruiting nodes. Only a susceptible subset of nodes can be recruited. The recruiting individuals may adapt their connections in order to improve recruitment capabilities, thus changing the network structure adaptively. We derive a mean field theory to predict the dependence of the growth threshold of the recruiting class on the adaptation parameter. Furthermore, we investigate the effect of adaptation on the recruitment level, as well as on network topology. The theoretical predictions are compared with direct simulations of the full system. We identify two parameter regimes with qualitatively different bifurcation diagrams depending on whether nodes become susceptible frequently (multiple times in their lifetime) or rarely (much less than once per lifetime)

One-Pot 3D Printing of Robust Multimaterial Devices

Polymer 3D printing is a broad set of manufacturing methods that permit the fabrication of complex architectures, and, as a result, numerous efforts focus on formulating processible chemistries that produce desirable material behavior in printed parts. However, current resin chemistries typically result in a single fixed set of properties once fully polymerized, a fact that poses significant engineering challenges to obtaining multimaterial devices. As an alternative to single-property materials, we introduce a ternary sequential reaction scheme that exhibits diverse multimaterial properties by profoundly altering the polymer microstructure from within a single resin composition. In this system, the photodosage during 3D printing sets both the shape and extent of conversion for each subsequent reaction. This different polymerization mechanisms of the subsequent stages yield disparate crosslink densities and viscoelastic properties. As a result, our materials possess Young's Moduli spanning over three orders of magnitude (400 kPa < E < 1.6 GPa) with smooth transitions between soft and stiff regions. We successfully pattern a 500x change in modulus in under a millimeter while the sequential assembly of our polymer networks ensures robust interfaces and enhances toughness by 10x compared to the single property materials. Most importantly, the final objects remain stable to UV and thermal aging, a key limitation to applications of previous multimaterial chemistries. We demonstrate the ability to 3D print intricate multimaterial architectures by fabricating a soft, wearable braille display.Comment: 54 pages including supplemental information, 5 main text figure

Formation of dislocations and hardening of LiF under high-dose irradiation with 5–21 MeV 12C ions

R. Zabels, I. Manika, J. Maniks, and R.Grants acknowledge the national project IMIS2, and A. Dauletbekova, M. Baizhumanov, and M. Zdorovets the Ministry of Education and Science of the Republic of Kazakhstan for the financial support.The emergence of dislocations and hardening of LiF crystals irradiated to high doses with 12C ions have been investigated using chemical etching, AFM, nanoindentation, and thermal annealing. At fluences ensuring the overlapping of tracks (Ф ≥6 × 1011 ions/cm2), the formation of dislocation-rich structure and ion-induced hardening is observed. High-fluence (1015 ions/cm2) irradiation with 12C ions causes accumulation of extended defects and induces hardening comparable to that reached by heavy ions despite of large differences in ion mass, energy, energy loss, and track morphology. The depth profiles of hardness indicate on a notable contribution of elastic collision mechanism (nuclear loss) in the damage production and hardening. The effect manifests at the end part of the ion range and becomes significant at high fluences (≥1014 ions/cm2).IMIS2; Ministry of Education and Science of the Republic of Kazakhstan; Institute of Solid State Physics, University of Latvia as the Center of Excellence has received funding from the European Union’s Horizon 2020 Framework Programme H2020-WIDESPREAD-01-2016-2017-TeamingPhase2 under grant agreement No. 739508, project CAMART

Structure of magnetic fields in intracluster cavities

Observations of clusters of galaxies show ubiquitous presence of X-ray cavities, presumably blown by the AGN jets. We consider magnetic field structures of these cavities. Stability requires that they contain both toroidal and poloidal magnetic fields, while realistic configurations should have vanishing magnetic field on the boundary. For axisymmetric configurations embedded in unmagnetized plasma, the continuity of poloidal and toroidal magnetic field components on the surface of the bubble then requires solving the elliptical Grad-Shafranov equation with both Dirichlet and Neumann boundary conditions. This leads to a double eigenvalue problem, relating the pressure gradients and the toroidal magnetic field to the radius of the bubble. We have found fully analytical stable solutions. This result is confirmed by numerical simulation. We present synthetic X-ray images and synchrotron emission profiles and evaluate the rotation measure for radiation traversing the bubble.Comment: 10 pages, 13 figures, accepted by MNRA

Accumulation of radiation defects and modification of micromechanical properties under MgO crystal irradiation with swift 132Xe ions

This work has been carried out within the framework of the EUROfusion Consortium and has received funding from the Euratom research and training programme 2014-2018 and 2019-2020 under grant agreement No. 633053. The views and opinions expressed herein do not necessarily reflect those of the European Commission. A.A. also acknowledges support via the project GF AP05134257 of Ministry of Education and Science of the Republic of Kazakhstan .Accumulation of F-type defects under irradiation of MgO crystals by 0.23-GeV 132Xe ions with fluence varying by three orders of magnitude has been investigated via the spectra of optical absorption and low-temperature cathodoluminescence. The number of single centers continuously increases with fluence without any marks of saturation. At the highest fluence, a mean volume concentration of 3.1 × 1019 and 3.35 × 1019 cm−3 is reached for F and F+ centers, respectively. The F+ emission strongly dominates in the cathodoluminescence of irradiated MgO and its enhancement with fluence is detected. However, the creation efficiency of the F2 aggregate centers is very low and fluence dependence has a complicated shape. Radiation-induced changes of micro-mechanical properties of the same samples have been analysed; the depth profiles of hardening correlate with the ion energy loss. A joint contribution of ionization and impact mechanisms in the formation of structural defects under MgO irradiation with Xe ions is considered.H2020 Euratom 2019-2020,633053,2014-2018,GF AP05134257; Ministry of Education and Science of the Republic of Kazakhstan GF AP05134257; Institute of Solid State Physics, University of Latvia as the Center of Excellence has received funding from the European Union’s Horizon 2020 Framework Programme H2020-WIDESPREAD-01-2016-2017-TeamingPhase2 under grant agreement No. 739508, project CAMART

Epidemics in Adaptive Social Networks with Temporary Link Deactivation

Disease spread in a society depends on the topology of the network of social contacts. Moreover, individuals may respond to the epidemic by adapting their contacts to reduce the risk of infection, thus changing the network structure and affecting future disease spread. We propose an adaptation mechanism where healthy individuals may choose to temporarily deactivate their contacts with sick individuals, allowing reactivation once both individuals are healthy. We develop a mean-field description of this system and find two distinct regimes: slow network dynamics, where the adaptation mechanism simply reduces the effective number of contacts per individual, and fast network dynamics, where more efficient adaptation reduces the spread of disease by targeting dangerous connections. Analysis of the bifurcation structure is supported by numerical simulations of disease spread on an adaptive network. The system displays a single parameter-dependent stable steady state and non-monotonic dependence of connectivity on link deactivation rate

Simplified Models for LHC New Physics Searches

This document proposes a collection of simplified models relevant to the design of new-physics searches at the LHC and the characterization of their results. Both ATLAS and CMS have already presented some results in terms of simplified models, and we encourage them to continue and expand this effort, which supplements both signature-based results and benchmark model interpretations. A simplified model is defined by an effective Lagrangian describing the interactions of a small number of new particles. Simplified models can equally well be described by a small number of masses and cross-sections. These parameters are directly related to collider physics observables, making simplified models a particularly effective framework for evaluating searches and a useful starting point for characterizing positive signals of new physics. This document serves as an official summary of the results from the "Topologies for Early LHC Searches" workshop, held at SLAC in September of 2010, the purpose of which was to develop a set of representative models that can be used to cover all relevant phase space in experimental searches. Particular emphasis is placed on searches relevant for the first ~50-500 pb-1 of data and those motivated by supersymmetric models. This note largely summarizes material posted at http://lhcnewphysics.org/, which includes simplified model definitions, Monte Carlo material, and supporting contacts within the theory community. We also comment on future developments that may be useful as more data is gathered and analyzed by the experiments.Comment: 40 pages, 2 figures. This document is the official summary of results from "Topologies for Early LHC Searches" workshop (SLAC, September 2010). Supplementary material can be found at http://lhcnewphysics.or

Pcl-PRC2 is needed to generate high levels of H3-K27 trimethylation at Polycomb target genes

PRC2 is thought to be the histone methyltransferase (HMTase) responsible for H3-K27 trimethylation at Polycomb target genes. Here we report the biochemical purification and characterization of a distinct form of Drosophila PRC2 that contains the Polycomb group protein polycomblike (Pcl). Like PRC2, Pcl-PRC2 is an H3-K27-specific HMTase that mono-, di- and trimethylates H3-K27 in nucleosomes in vitro. Analysis of Drosophila mutants that lack Pcl unexpectedly reveals that Pcl-PRC2 is required to generate high levels of H3-K27 trimethylation at Polycomb target genes but is dispensable for the genome-wide H3-K27 mono- and dimethylation that is generated by PRC2. In Pcl mutants, Polycomb target genes become derepressed even though H3-K27 trimethylation at these genes is only reduced and not abolished, and even though targeting of the Polycomb protein complexes PhoRC and PRC1 to Polycomb response elements is not affected. Pcl-PRC2 is thus the HMTase that generates the high levels of H3-K27 trimethylation in Polycomb target genes that are needed to maintain a Polycomb-repressed chromatin state