The scattering map in two coupled piecewise-smooth systems, with numerical application to rocking blocks

We consider a non-autonomous dynamical system formed by coupling two piecewise-smooth systems in \RR^2 through a non-autonomous periodic perturbation. We study the dynamics around one of the heteroclinic orbits of one of the piecewise-smooth systems. In the unperturbed case, the system possesses two $C^0$ normally hyperbolic invariant manifolds of dimension two with a couple of three dimensional heteroclinic manifolds between them. These heteroclinic manifolds are foliated by heteroclinic connections between $C^0$ tori located at the same energy levels. By means of the {\em impact map} we prove the persistence of these objects under perturbation. In addition, we provide sufficient conditions of the existence of transversal heteroclinic intersections through the existence of simple zeros of Melnikov-like functions. The heteroclinic manifolds allow us to define the {\em scattering map}, which links asymptotic dynamics in the invariant manifolds through heteroclinic connections. First order properties of this map provide sufficient conditions for the asymptotic dynamics to be located in different energy levels in the perturbed invariant manifolds. Hence we have an essential tool for the construction of a heteroclinic skeleton which, when followed, can lead to the existence of Arnol'd diffusion: trajectories that, on large time scales, destabilize the system by further accumulating energy. We validate all the theoretical results with detailed numerical computations of a mechanical system with impacts, formed by the linkage of two rocking blocks with a spring

Spectral Efficiency of One-Bit Sigma-Delta Massive MIMO

We examine the uplink spectral efficiency of a massive MIMO base station employing a one-bit Sigma-Delta ( \Sigma \Delta ) sampling scheme implemented in the spatial rather than the temporal domain. Using spatial rather than temporal oversampling, and feedback of the quantization error between adjacent antennas, the method shapes the spatial spectrum of the quantization noise away from an angular sector where the signals of interest are assumed to lie. It is shown that, while a direct Bussgang analysis of the \Sigma \Delta approach is not suitable, an alternative equivalent linear model can be formulated to facilitate an analysis of the system performance. The theoretical properties of the spatial quantization noise power spectrum are derived for the \Sigma \Delta array, as well as an expression for the spectral efficiency of maximum ratio combining (MRC). Simulations verify the theoretical results and illustrate the significant performance gains offered by the \Sigma \Delta approach for both MRC and zero-forcing receivers

Knowledge management activities in social enterprises: lessons for small and non-profit firms

Purpose: This paper explores what Social Enterprises (SEs) in the UK know and how they acquire, convert, apply and protect this knowledge. This will enable them to manage their knowledge effectively, hence improve their practices and maximize the creation of social, environmental and economic value. Design/methodology/approach: This study follows a qualitative approach, comprising of 21 interviews with founders and senior members of SEs in UK. Findings: The results show that the investigated SEs have KM practices similar to the already identified in SMEs, associated with informality, reliance on external sources and focus on socialisation activities, but they have unique challenges on managing their knowledge related to their hybrid mission, to include social and economic objectives, and their closed relationship with stakeholders. Research limitations/implications: As there is limited research on Knowledge Management (KM) practices in SEs; they were defined based on previous studies in large, private and public companies. Therefore, not all practices may be included. This research is a starting point in the study of KM in SEs. Practical implications: This study identifies knowledge activities that enable the creation of social, environmental and economic value in SEs. This allows SEs, small firms and non-profit organisations to review their current practices and develop plans for their further improvement. Social implications: Originality/value: This paper is one of the first empirical studies exploring KM practices in SEs, highlighting their informal nature as well as their impact in and on the enterprise

Commissioning of the electron injector for the AWAKE experiment

The advanced wakefield experiment (AWAKE) at CERN is the first proton beam-driven plasma wakefield acceleration experiment. The main goal of AWAKE RUN 1 was to demonstrate seeded self-modulation (SSM) of the proton beam and electron witness beam acceleration in the plasma wakefield. For the AWAKE experiment, a 10-meter-long Rubidium-vapor cell together with a high-power laser for ionization was used to generate the plasma. The plasma wakefield is driven by a 400 GeV/c proton beam extracted from the super proton synchrotron (SPS), which undergoes a seeded self-modulation process in the plasma. The electron witness beam used to probe the wakefields is generated from an S-band RF photo-cathode gun and then accelerated by a booster structure up to energies between 16 and 20 MeV. The first run of the AWAKE experiment revealed that the maximum energy gain after the plasma cell is 2 GeV, and the SSM mechanism of the proton beam was verified. In this paper, we will present the details of the AWAKE electron injector. A comparison of the measured electron beam parameters, such as beam size, energy, and normalized emittance, with the simulation results was performed

New results in nonlinear state estimation using extended unbiased fir filtering

This paper discusses two algorithms of extended unbiased FIR (EFIR) filtering of nonlinear discrete-time state-space models used in tracking and state estimation. The basic algorithm employs the extended nonlinear state and observation equations. The modified algorithm utilizes the nonlinear-to-linear conversion of the observation equation which is provided using a batch EFIR filter having small memory. Unlike the extended Kalman filter (EKF), both EFIR algorithms ignore the noise statistics and demonstrate better robustness against temporary model uncertainties. These algorithms require an optimal horizon in order to minimize the mean square error. Applications are given for robot indoor self-localization utilizing radio frequency identification tags

Bioevents correlation of planktic foraminifers and radiolarians from the Cenomanian to Turonian, southeastern Mexico

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Serine threonine kinase receptor associated protein regulates early follicle development in the mouse ovary.

The molecular mechanisms involved in regulating the development of small, gonadotrophin-independent follicles are poorly understood; however, many studies have highlighted an essential role for TGFB ligands. Canonical TGFB signalling is dependent upon intracellular SMAD proteins that regulate transcription. STRAP has been identified in other tissues as an inhibitor of the TGFB-SMAD signalling pathway. Therefore, in this study we aimed to determine the expression and role of STRAP in the context of early follicle development. Using qPCR, Strap, Smad3 and Smad7 revealed similar expression profiles in immature ovaries from mice aged 4-16 days containing different populations of early growing follicles. STRAP and SMAD2/3 proteins co-localised in granulosa cells of small follicles using immunofluorescence. Using an established culture model, neonatal mouse ovary fragments with a high density of small non-growing follicles were used to examine the effects of Strap knockdown using siRNA and STRAP protein inhibition by immuno-neutralisation. Both interventions caused a reduction in the proportion of small, non-growing follicles and an increase in the proportion and size of growing follicles in comparison to untreated controls, suggesting inhibition of STRAP facilitates follicle activation. Recombinant STRAP protein had no effect on small, non-growing follicles, but increased the mean oocyte size of growing follicles in the neonatal ovary model and also promoted the growth of isolated preantral follicles in vitro Overall findings indicate STRAP is expressed in the mouse ovary and is capable of regulating development of small follicles in a stage-dependent manner

Public School Elementary Teachers’ Perspectives on Levels of Workplace Stress and Needed Supports

The problem addressed through this study was that public elementary school teachers in the United States have reported increasing levels of workplace stress. Teachers’ stress levels need to be studied and addressed because they affect students as well. The purpose of this basic qualitative study was to explore elementary public school K-3 teachers’ perspectives on their levels of workplace stress and institutional supports needed to reduce workplace stress. Coping-competence-context theory was the conceptual framework. Research questions explored elementary public school teachers’ perspectives on their levels of workplace stress, and their perspectives on the institutional supports needed to reduce workplace stress. Participants were selected purposefully in a sample of 13 K-3 U.S. public school teachers with 3 or more years of classroom experience. Data analysis procedures included interview transcription and the process of coding and categorizing data into emerging themes. Key results included teachers’ perspectives on stress and needed supports along three themes: time, balance, and institutional support. The reported average level of weekly stress was 6.4 on a scale of 1 to 10. Future studies may widen the geographic area and the representation of the sample. Implications for positive social change include aiding district leaders in developing institutional supports to assist elementary teachers and generating additional research on the influence stress has on their work. This study may lead to positive social change and fill a gap in practice by providing public school districts with the data to address K-3 elementary public school teachers’ perspectives on the institutional supports needed to reduce workplace stress

Validation of the TOLNet lidars: The Southern California Ozone Observation Project (SCOOP)

The North America-based Tropospheric Ozone Lidar Network (TOLNet) was recently established to provide high spatiotemporal vertical profiles of ozone, to better understand physical processes driving tropospheric ozone variability and to validate the tropospheric ozone measurements of upcoming spaceborne missions such as Tropospheric Emissions: Monitoring Pollution (TEMPO). The network currently comprises six tropospheric ozone lidars, four of which are mobile instruments deploying to the field a few times per year, based on campaign and science needs. In August 2016, all four mobile TOLNet lidars were brought to the fixed TOLNet site of JPL Table Mountain Facility for the 1-week-long Southern California Ozone Observation Project (SCOOP). This intercomparison campaign, which included 400¿h of lidar measurements and 18 ozonesonde launches, allowed for the unprecedented simultaneous validation of five of the six TOLNet lidars. For measurements between 3 and 10¿km¿a.s.l., a mean difference of 0.7¿ppbv (1.7¿%), with a root-mean-square deviation of 1.6¿ppbv or 2.4¿%, was found between the lidars and ozonesondes, which is well within the combined uncertainties of the two measurement techniques. The few minor differences identified were typically associated with the known limitations of the lidars at the profile altitude extremes (i.e., first 1¿km above ground and at the instruments' highest retrievable altitude). As part of a large homogenization and quality control effort within the network, many aspects of the TOLNet in-house data processing algorithms were also standardized and validated. This thorough validation of both the measurements and retrievals builds confidence as to the high quality and reliability of the TOLNet ozone lidar profiles for many years to come, making TOLNet a valuable ground-based reference network for tropospheric ozone profiling.Peer ReviewedPostprint (published version