Deterministic continutation of stochastic metastable equilibria via Lyapunov equations and ellipsoids

Numerical continuation methods for deterministic dynamical systems have been one of the most successful tools in applied dynamical systems theory. Continuation techniques have been employed in all branches of the natural sciences as well as in engineering to analyze ordinary, partial and delay differential equations. Here we show that the deterministic continuation algorithm for equilibrium points can be extended to track information about metastable equilibrium points of stochastic differential equations (SDEs). We stress that we do not develop a new technical tool but that we combine results and methods from probability theory, dynamical systems, numerical analysis, optimization and control theory into an algorithm that augments classical equilibrium continuation methods. In particular, we use ellipsoids defining regions of high concentration of sample paths. It is shown that these ellipsoids and the distances between them can be efficiently calculated using iterative methods that take advantage of the numerical continuation framework. We apply our method to a bistable neural competition model and a classical predator-prey system. Furthermore, we show how global assumptions on the flow can be incorporated - if they are available - by relating numerical continuation, Kramers' formula and Rayleigh iteration.Comment: 29 pages, 7 figures [Fig.7 reduced in quality due to arXiv size restrictions]; v2 - added Section 9 on Kramers' formula, additional computations, corrected typos, improved explanation

Put on your poker face? Neural systems supporting the anticipation for expressive suppression and cognitive reappraisal

It is a unique human ability to regulate negative thoughts and feelings. Two well-investigated emotion-regulation strategies (ERSs), cognitive reappraisal and expressive suppression, are associated with overlapping prefrontal neural correlates, but differ temporally during the emotion-generation process. Although functional imaging studies have mainly investigated these ERS as a reaction to an emotion-inducing event, the intention to regulate upcoming negative emotions might already be associated with differences in neural activity. Hence, event-related functional magnetic resonance imaging was recorded in 42 participants while they completed an emotion-regulation paradigm. During this task, participants were instructed to proactively prepare to use a specific ERS knowing that a negative, high-arousing image would appear after the preparation period. As expected, the results demonstrated prefrontal and parietal activation while participants were suppressing or reappraising their emotions (family-wise error (FWE)-corrected). The intention to suppress emotions was associated with increased activation in the right inferior frontal gyrus, bilateral putamen, pre-supplementary motor area and right supramarginal gyrus (FWE-corrected). This enhanced proactive inhibitory control: (i) predicted decreased motoric activity during the actual suppression of emotional expressions and (2) trended toward a significant association with how successfully participants suppressed their emotions. However, neural correlates of preparatory control for cognitive reappraisal were not observed, possibly because contextual cues about the upcoming emotional stimulus are necessary to proactively start to cognitively reinterpret the situation

Use of control umbilicals as a deployment mode for free flying telerobotic work systems

Work to date on telerobotic work systems for use in space generally consider two deployment modes, free flying, or fixed within a limited work envelope. Control tethers may be employed to obtain a number of operational advantages and added flexibility in the basing and deployment of telerobotic work systems. Use of a tether allows the work system to be separated into two major modules, the remote work package and the control module. The Remote Work Package (RWP) comprises the free flying portion of the work system while the Control Module (CM) remains at the work system base. The chief advantage of this configuration is that only the components required for completion of the work task must be located at the work site. Reaction mass used in free flight is stored at the Control module and supplied to the RWP through the tether, eliminating the need for the RWP to carry it. The RWP can be made less massive than a self contained free flying work system. As a result, reaction mass required for free flight is lower than for a self contained free flyer

"Third places" and social interaction in deprived neighbourhoods in Great Britain

This paper explores social interaction in local ‘public’ social spaces such as local shops, pubs, cafés, and community centres in deprived neighbourhoods. More specifically, it examines the importance, role and function of these places, which have been described by Oldenberg and Brissett (Qual Sociol 5(4):265–284, 1982), Oldenburg (Urban design reader. Architectural Place, Oxford, 2007) as being “third places” of social interaction after the home (first) and workplace (second). It does so by drawing on data gleaned from in-depth interviews with 180 residents in six deprived areas neighbourhoods across Great Britain, conducted as part of a study of the links between poverty and place funded by the Joseph Rowntree Foundation. The paper notes that local third places are an important medium for social interaction in these areas, although their importance appears to vary by population group. It notes that shops appear to be a particularly important social space. It also identifies some of the barriers to social interaction within third places and concludes by highlighting some of the key implications for policy to emerge from the research

Dependence of Galaxy Shape on Environment in the Sloan Digital Sky Survey

Using a sample of galaxies from the Sloan Digital Sky Survey (SDSS) Data Release 4, we study the trends relating surface brightness profile type and apparent axis ratio to the local galaxy environment. We use the SDSS parameter `fracDeV' to quantify the profile type. We find that galaxies with M_r > -18 are mostly described by exponential profiles in all environments. Galaxies with -21 < M_r < -18 mainly have exponential profiles in low density environments and de Vaucouleurs profiles in high density environments. The most luminous galaxies, with M_r < -21, are mostly described by de Vaucouleurs profiles in all environments. For galaxies with M_r < -19, the fraction of de Vaucouleurs galaxies is a monotonically increasing function of local density, while the fraction of exponential galaxies is monotonically decreasing. For a fixed surface brightness profile type, apparent axis ratio is frequently correlated with environment. As the local density of galaxies increases, we find that for -20 < M_r < -18, galaxies of all profile types become slightly rounder, on average; for -22 < M_r < -20, galaxies with exponential profiles tend to become flatter, while galaxies with de Vaucouleurs profiles become rounder; for M_r < -22, galaxies with exponential profiles become flatter, while the de Vaucouleurs galaxies become rounder in their inner regions, yet exhibit no change in their outer regions. We comment on how the observed trends relate to the merger history of galaxies.Comment: 23 pages, 7 figures, accepted by Ap

Ultrafast spatio-temporal dynamics of terahertz generation by ionizing two-color femtosecond pulses in gases

We present a combined theoretical and experimental study of spatio-temporal propagation effects in terahertz (THz) generation in gases using two-color ionizing laser pulses. The observed strong broadening of the THz spectra with increasing gas pressure reveals the prominent role of spatio-temporal reshaping and of a plasma-induced blue-shift of the pump pulses in the generation process. Results obtained from (3+1)-dimensional simulations are in good agreement with experimental findings and clarify the mechanisms responsible for THz emission

On the size of the Fe II emitting region in the AGN Akn 120

We present a reverberation analysis of the strong, variable optical Fe II emission bands in the spectrum of Akn 120, a low-redshift AGN which is one of the best candidates for such a study. On time scales of several years the Fe II line strengths follow the variations in the continuum strength. However, we are unable to measure a clear reverberation lag time for these Fe II lines on any time scale. This is due to the very broad and flat-topped nature of the Fe II cross correlation functions, as compared to the H-beta response which is much more sharply localized in time. Although there is some suggestion in the light curve of a 300-day response time, our statistical analysis does not pick up such a feature. We conclude that the optical Fe II emission does not come from a photoionization-powered region similar in size to the H-beta emitting region, but we cannot say for sure where it does come from. Our results are generally consistent either with emission from a photoionized region several times larger than the H-beta zone, or with emission from gas heated by some other means, perhaps responding only indirectly to the continuum variations.Comment: Accepted for publication in the Ap

Measurements of the reverse current of highly irradiated silicon sensors to determine the effective energy and current related damage rate

The reverse current of irradiated silicon sensors leads to self heating of the sensor and degrades the signal to noise ratio of a detector. Precise knowledge of the expected reverse current during detector operation is crucial for planning and running experiments in High Energy Physics. The dependence of the reverse current on sensor temperature and irradiation fluence is parametrized by the effective energy and the current related damage rate, respectively. In this study 18 n-in-p mini silicon strip sensors from companies Hamamatsu Photonics and Micron Semiconductor Ltd. were deployed. Measurements of the reverse current for different bias voltages were performed at temperatures of −32 ° C, −27 ° C and −23 ° C. The sensors were irradiated with reactor neutrons in Ljubljana to fluences ranging from 2×1014neq∕cm2 to 2×1016neq∕cm2 . The measurements were performed directly after irradiation and after 10 and 30 days of room temperature annealing. The aim of the study presented in this paper is to investigate the reverse current of silicon sensors for high fluences of up to 2×1016neq∕cm2 and compare the measurements to the parametrization models

On the use of blow up to study regularizations of singularities of piecewise smooth dynamical systems in R3\mathbb{R}^3

In this paper we use the blow up method of Dumortier and Roussarie \cite{dumortier_1991,dumortier_1993,dumortier_1996}, in the formulation due to Krupa and Szmolyan \cite{krupa_extending_2001}, to study the regularization of singularities of piecewise smooth dynamical systems \cite{filippov1988differential} in $\mathbb R^3$. Using the regularization method of Sotomayor and Teixeira \cite{Sotomayor96}, first we demonstrate the power of our approach by considering the case of a fold line. We quickly recover a main result of Bonet and Seara \cite{reves_regularization_2014} in a simple manner. Then, for the two-fold singularity, we show that the regularized system only fully retains the features of the singular canards in the piecewise smooth system in the cases when the sliding region does not include a full sector of singular canards. In particular, we show that every locally unique primary singular canard persists the regularizing perturbation. For the case of a sector of primary singular canards, we show that the regularized system contains a canard, provided a certain non-resonance condition holds. Finally, we provide numerical evidence for the existence of secondary canards near resonance.Comment: To appear in SIAM Journal of Applied Dynamical System

Photonic ring resonator filters for astronomical OH suppression

Ring resonators provide a means of filtering specific wavelengths from a waveguide, and optionally dropping the filtered wavelengths into a second waveguide. Both of these features are potentially useful for astronomical instruments. In this paper we focus on their use as notch filters to remove the signal from atmospheric OH emission lines from astronomical spectra, however we also briefly discuss their use as frequency combs for wavelength calibration and as drop filters for Doppler planet searches. We derive the design requirements for ring resonators for OH suppression from theory and finite difference time domain simulations. We find that rings with small radii (<10 microns) are required to provide an adequate free spectral range, leading to high index contrast materials such as Si and Si$_{3}$N$_{4}$. Critically coupled rings with high self-coupling coefficients should provide the necessary Q factors, suppression depth, and throughput for efficient OH suppression. We report on our progress in fabricating both Si and Si$_{3}$N$_{4}$ rings for OH suppression, and give results from preliminary laboratory tests. Our early devices show good control over the free spectral range and wavelength separation of multi-ring devices. The self-coupling coefficients are high (>0.9), but further optimisation is required to achieve higher Q and deeper notches, with current devices having $Q \approx 4000$ and $\approx 10$ dB suppression. The overall prospects for the use of ring resonators in astronomical instruments is promising, provided efficient fibre-chip coupling can be achieved.Comment: Submitted to Optics Express feature issue on Recent Advances in Astrophotonics (27 pages, 20 figs