Nonlinear multicore waveguiding structures with balanced gain and loss

We study existence, stability, and dynamics of linear and nonlinear stationary modes propagating in radially symmetric multicore waveguides with balanced gain and loss. We demonstrate that, in general, the system can be reduced to an effective PT-symmetric dimer with asymmetric coupling. In the linear case, we find that there exist two modes with real propagation constants before an onset of the PT-symmetry breaking while other modes have always the propagation constants with nonzero imaginary parts. This leads to a stable (unstable) propagation of the modes when gain is localized in the core (ring) of the waveguiding structure. In the case of nonlinear response, we show that an interplay between nonlinearity, gain, and loss induces a high degree of instability, with only small windows in the parameter space where quasistable propagation is observed. We propose a novel stabilization mechanism based on a periodic modulation of both gain and loss along the propagation direction that allows bounded light propagation in the multicore waveguiding structures.

Isomorphism Problems for the Baire Function Spaces of Topological Spaces

Let a compact Hausdorff space X contain a non-empty perfect subset. If α < β and β is a countable ordinal, then the Banach space Bα (X) of all bounded real-valued functions of Baire class α on X is a proper subspace of the Banach space Bβ (X). In this paper it is shown that: 1. Bα (X) has a representation as C(bα X), where bα X is a compactification of the space P X – the underlying set of X in the Baire topology generated by the Gδ -sets in X. 2. If 1 ≤ α < β ≤ Ω, where Ω is the first uncountable ordinal number, then Bα (X) is uncomplemented as a closed subspace of Bβ (X). These assertions for X = [0, 1] were proved by W. G. Bade [4] and in the case when X contains an uncountable compact metrizable space – by F.K.Dashiell [9]. Our argumentation is one non-metrizable modification of both Bade’s and Dashiell’s methods.

Growing Neural Networks Using Nonconventional Activation Functions

In the paper, an ontogenic artificial neural network (ANNs) is proposed. The network uses orthogonal activation functions that allow significant reducing of computational complexity. Another advantage is numerical stability, because the system of activation functions is linearly independent by definition. A learning procedure for proposed ANN with guaranteed convergence to the global minimum of error function in the parameter space is developed. An algorithm for structure network structure adaptation is proposed. The algorithm allows adding or deleting a node in real-time without retraining of the network. Simulation results confirm the efficiency of the proposed approach.

Teaching our children when to eat:how parental feeding practices inform the development of emotional eating-a longitudinal experimental design

Background: Emotional eating in children has been related to the consumption of energy-dense foods and obesity, but the development of emotional eating in young children is poorly understood. Objectives: We evaluated whether emotional eating can be induced in 5-7-y-old children in the laboratory and assessed whether parental use of overly controlling feeding practices at 3-5 y of age predicts a greater subsequent tendency for children to eat under conditions of mild stress at ages 5-7 y. Design: Forty-one parent-child dyads were recruited to participate in this longitudinal study, which involved parents and children being observed consuming a standard lunch, completing questionnaire measures of parental feeding practices, participating in a research procedure to induce child emotion (or a control procedure), and observing children's consumption of snack foods. Results: Children at ages 5-7 y who were exposed to a mild emotional stressor consumed significantly more calories from snack foods in the absence of hunger than did children in a control group. Parents who reported the use of more food as a reward and restriction of food for health reasons with their children at ages 3-5 y were more likely to have children who ate more under conditions of negative emotion at ages 5-7 y. Conclusions: Parents who overly control children's food intake may unintentionally teach children to rely on palatable foods to cope with negative emotions. Additional research is needed to evaluate the implications of these findings for children's food intake and weight outside of the laboratory setting. This trial was registered at clinicaltrials.gov as NCT01122290.

"Trade creep" and implications of the Transatlantic Trade and Investment Partnership Agreement for the United Kingdom National Health Service

The ambitious and comprehensive Transatlantic Trade and Investment Partnership Agreement (TTIP/TAFTA) agreement between the European Union and United States is now being negotiated and may have far-reaching consequences for health services. The agreement extends to government procurement, investment, and further regulatory cooperation. In this article, we focus on the United Kingdom National Health Service and how these negotiations can limit policy space to change policies and to regulate in relation to health services, pharmaceuticals, medical devices, and health industries. The negotiation of TTIP/TAFTA has the potential to "harmonize" more corporate-friendly regulation, resulting in higher costs and loss of policy space, an example of "trade creep" that potentially compromises health equity, public health, and safety concerns across the Atlantic.