Perceived Barriers by Hispanic Mothers in Obtaining Primary Health Care for Their Childern

Purpose: Hispanic mothers tend to over use hospital emergency services and under use primary care providers when seeking health care for their children. In order to change this health care utilization behavior, researchers must understand the barriers to health care perceived by Hispanic mothers. Design: In this non-experimental survey study, a non-probability, purposive sampling of 45 Hispanic mothers at a rural county pediatric clinic were surveyed. Methods: Using the Health Belief Model (HBM) as its framework an 18-item survey examined, barriers to health care, cues to action, subjects\u27 knowledge, family satisfaction, access, and likelihood of action. Findings: The data suggest that long waiting periods for clinical appointments, limited clinical hours, and lengthy waiting room delays are the major perceived barriers by these Hispanic mothers

Embedding and approximation theorems for echo state networks

Echo State Networks (ESNs) are a class of single layer recurrent neural networks that have enjoyed recent attention. In this paper we prove that a suitable ESN, trained on a series of measurements of an invertible dynamical system, induces a C1 map from the dynamical system's phase space to the ESN's reservoir space. We call this the Echo State Map. We then prove that the Echo State Map is generically an embedding with positive probability. Under additional mild assumptions, we further conjecture that the Echo State Map is almost surely an embedding. For sufficiently large, and specially structured, but still randomly generated ESNs, we prove that there exists a linear readout layer that allows the ESN to predict the next observation of a dynamical system arbitrarily well. Consequently, if the dynamical system under observation is structurally stable then the trained ESN will exhibit dynamics that are topologically conjugate to the future behaviour of the observed dynamical system. Our theoretical results connect the theory of ESNs to the delay-embedding literature for dynamical systems, and are supported by numerical evidence from simulations of the traditional Lorenz equations. The simulations confirm that, from a one dimensional observation function, an ESN can accurately infer a range of geometric and topological features of the dynamics such as the eigenvalues of equilibrium points, Lyapunov exponents and homology groups.Comment: 24 pages, 9 figure

Echo State Networks Trained by Tikhonov Least Squares are L2 Approximators of Ergodic Dynamical Systems

Echo State Networks (ESNs) are a class of single-layer recurrent neural networks with randomly generated internal weights, and a single layer of tuneable outer weights, which are usually trained by regularised linear least squares regression. Remarkably, ESNs still enjoy the universal approximation property despite the training procedure being entirely linear. In this paper, we prove that an ESN trained on a sequence of observations from an ergodic dynamical system (with invariant measure ) using Tikhonov least squares regression against a set of targets, will approximate the target function in the norm. In the special case that the targets are future observations, the ESN is learning the next step map, which allows time series forecasting. We demonstrate the theory numerically by training an ESN using Tikhonov least squares on a sequence of scalar observations of the Lorenz system

Arbuscular mycorrhizal fungi as mediators of ecosystem responses to nitrogen deposition: A trait-based predictive framework

Anthropogenic nitrogen (N) deposition is exposing plants and their arbuscular mycorrhizal fungi (AMFs) to elevated N availability, often leading to shifts in communities of AMF. However, physiological trade-offs among AMF taxa in their response to N enrichment vs the ability to acquire other soil nutrients could have negative effects on plant and ecosystem productivity. It follows that information on the functional traits of AMF taxa can be used to generate predictions of their potential role in mediating ecosystem responses to N enrichment. Arbuscular mycorrhizal fungi taxa that produce extensive networks of external hyphae should forage for N and phosphorus (P) more effectively, but these services incur greater carbon (C) costs to the plant. If N enrichment ameliorates plant nutrient limitation, then plants may reduce C available for AMF, which in turn could eliminate AMF taxa with large extensive external hyphae from the soil community. As a result, the remaining AMF taxa may confer less P benefit to their host plants. Using a synthesis of data from the literature, we found that the ability of a taxon to persist in the face of increasing soil N availability was particularly high in isolates from the genus Glomus, but especially low among the Gigasporaceae. Across AMF genera, our data support the prediction that AMF with a tolerance for high soil N may confer a lower P benefit to their host plant. Relationships between high N tolerance and production of external hyphae were mixed. Synthesis. If the relationship between N tolerance and plant P benefit is widespread, then shifts in arbuscular mycorrhizal fungi communities associated with N deposition could have negative consequences for the ability of plants to acquire P and possibly other nutrients via a mycorrhizal pathway. Based on this relationship, we predict that arbuscular mycorrhizal fungi responses could constrain net primary productivity in P-limited ecosystems exposed to N enrichment. This prediction could be tested in future empirical and modelling studies

Learning strange attractors with reservoir systems

This paper shows that the celebrated embedding theorem of Takens is a particular case of a much more general statement according to which, randomly generated linear state-space representations of generic observations of an invertible dynamical system carry in their wake an embedding of the phase space dynamics into the chosen Euclidean state space. This embedding coincides with a natural generalized synchronization that arises in this setup and that yields a topological conjugacy between the state-space dynamics driven by the generic observations of the dynamical system and the dynamical system itself. This result provides additional tools for the representation, learning, and analysis of chaotic attractors and sheds additional light on the reservoir computing phenomenon that appears in the context of recurrent neural networks.</p

Learning strange attractors with reservoir systems

This paper shows that the celebrated embedding theorem of Takens is a particular case of a much more general statement according to which, randomly generated linear state-space representations of generic observations of an invertible dynamical system carry in their wake an embedding of the phase space dynamics into the chosen Euclidean state space. This embedding coincides with a natural generalized synchronization that arises in this setup and that yields a topological conjugacy between the state-space dynamics driven by the generic observations of the dynamical system and the dynamical system itself. This result provides additional tools for the representation, learning, and analysis of chaotic attractors and sheds additional light on the reservoir computing phenomenon that appears in the context of recurrent neural networks.</p

Chaos on compact manifolds: Differentiable synchronizations beyond the Takens theorem

This paper shows that a large class of fading memory state-space systems driven by discrete-time observations of dynamical systems defined on compact manifolds always yields continuously differentiable synchronizations. This general result provides a powerful tool for the representation, reconstruction, and forecasting of chaotic attractors. It also improves previous statements in the literature for differentiable generalized synchronizations, whose existence was so far guaranteed for a restricted family of systems and was detected using H\"older exponent-based criteria.Comment: 13 pages letter and 4 captioned figure

Learning strange attractors with reservoir systems

This paper shows that the celebrated Embedding Theorem of Takens is a particular case of a much more general statement according to which, randomly generated linear state-space representations of generic observations of an invertible dynamical system carry in their wake an embedding of the phase space dynamics into the chosen Euclidean state space. This embedding coincides with a natural generalized synchronization that arises in this setup and that yields a topological conjugacy between the state-space dynamics driven by the generic observations of the dynamical system and the dynamical system itself. This result provides additional tools for the representation, learning, and analysis of chaotic attractors and sheds additional light on the reservoir computing phenomenon that appears in the context of recurrent neural networks.Comment: 36 pages, 11 figure