Identifying Barriers and Facilitators of Successful School-Based Mental Health and Behavioral Programs Delivered in the Context of Urban Poverty: A Qualitative Exploration of Perspectives from Service Providers and Youth

The goal of this study was to identify the barriers and facilitators of successful mental health and/or behavioral programs implemented within inner-city schools. The impetus for this study came from prior meta-analytic research which demonstrated programs being offered within inner-city schools, as a whole, showed very low effect sizes, with many of the programs offered to youth within these settings showing iatrogenic effects. The use of qualitative methods, specifically a phenomenological approach, provided an in-depth understanding of 1) service providers\u27 experience(s) delivering mental health and/or behavioral programs in inner-city schools; and, 2) low-income, urban youths\u27 experience(s) with receiving school-based mental health and/or behavioral programs. The current study\u27s research findings, which provide perspectives from both service providers and youth, was integrated and discussed in the context of: 1) factors that serve as barriers to successful program implementation and/or program outcomes, 2) factors that serve as facilitators of successful program implementation and/or program outcomes,3} impact of the program, 4) recommendations/implications for service providers who deliver programs in these settings, and 5) recommendations/implications for researchers who develop/adapt programs for implementation in these settings. Limitations of the current study and areas for future research were also discussed

Expected Number of Real Zeros of a Random Polynomial With Independent Identically Distributed Symmetric Long-Tailed Coefficients

We show that the expected number of real zeros of the nth degree polynomial with real independent identically distributed coefficients with common characteristic function φ(z) = e-A(ln|1/z|)^-a for 0 \u3c |z| \u3c 1 and φ(0) = 1, φ(z) ≡ 0 for 1 ≦ |z| \u3c ∞, with 1 \u3c a and A ≧ a(a-1), is (a-1)/(a-1/2) log(n) asymptotically as n → ∞

Accelerating Universe in Terms of Hankel Function Index

In this paper, $F(\nu)$ cosmology is proposed for the accelerating universe with asymptotic de Sitter expansion in terms of Hankel function index $\nu$. To some extent, both the initial expansion during early inflation and the current accelerated expansion can be studied with a vacuum cosmic fluid i.e. $\Lambda$ in the pure de Sitter phase. Observational data further support the notion of a quasi-vacuum fluid, rather than a pure vacuum, contributing to the quasi-de Sitter acceleration in both the early and late universe. By examining the asymptotic expansion of the Henkel function as an approximate solution of the Mukhanov-Sasaki equation, we seek a more detailed study of quasi-de Sitter solutions in cosmology containing vacuum-like fluid.Comment: 11 pages, 2 table

Level crossings and turning points of random hyperbolic polynomials

In this paper, we show that the asymptotic estimate for the expected number of K-level crossings of a random hyperbolic polynomial a1sinhx+a2sinh2x+⋯+ansinhnx, where aj(j=1,2,…,n) are independent normally distributed random variables with mean zero and variance one, is (1/π)logn. This result is true for all K independent of x, provided K≡Kn=O(n). It is also shown that the asymptotic estimate of the expected number of turning points for the random polynomial a1coshx+a2cosh2x+⋯+ancoshnx, with aj(j=1,2,…,n) as before, is also (1/π)logn

Random trigonometric polynomials with nonidentically distributed coefficients

This paper provides asymptotic estimates for the expected number of real zeros of two different forms of random trigonometric polynomials, where the coefficients of polynomials are normally distributed random variables with different means and variances. For the polynomials in the form of a 0 a 1 cos θ a 2 cos 2θ · · · a n cos nθ and a 0 a 1 cos θ b 1 sin θ a 2 cos 2θ b 2 sin 2θ · · · a n cos nθ b n sin nθ, we give a closed form for the above expected value. With some mild assumptions on the coefficients we allow the means and variances of the coefficients to differ from each others. A case of reciprocal random polynomials for both above cases is studied

Statistics of the Number of Zero Crossings : from Random Polynomials to Diffusion Equation

We consider a class of real random polynomials, indexed by an integer d, of large degree n and focus on the number of real roots of such random polynomials. The probability that such polynomials have no real root in the interval [0,1] decays as a power law n^{-\theta(d)} where \theta(d)>0 is the exponent associated to the decay of the persistence probability for the diffusion equation with random initial conditions in space dimension d. For n even, the probability that such polynomials have no root on the full real axis decays as n^{-2(\theta(d) + \theta(2))}. For d=1, this connection allows for a physical realization of real random polynomials. We further show that the probability that such polynomials have exactly k real roots in [0,1] has an unusual scaling form given by n^{-\tilde \phi(k/\log n)} where \tilde \phi(x) is a universal large deviation function.Comment: 4 pages, 3 figures. Minor changes. Accepted version in Phys. Rev. Let

Tracking Target Signal Strengths on a Grid using Sparsity

Multi-target tracking is mainly challenged by the nonlinearity present in the measurement equation, and the difficulty in fast and accurate data association. To overcome these challenges, the present paper introduces a grid-based model in which the state captures target signal strengths on a known spatial grid (TSSG). This model leads to \emph{linear} state and measurement equations, which bypass data association and can afford state estimation via sparsity-aware Kalman filtering (KF). Leveraging the grid-induced sparsity of the novel model, two types of sparsity-cognizant TSSG-KF trackers are developed: one effects sparsity through $\ell_1$-norm regularization, and the other invokes sparsity as an extra measurement. Iterative extended KF and Gauss-Newton algorithms are developed for reduced-complexity tracking, along with accurate error covariance updates for assessing performance of the resultant sparsity-aware state estimators. Based on TSSG state estimates, more informative target position and track estimates can be obtained in a follow-up step, ensuring that track association and position estimation errors do not propagate back into TSSG state estimates. The novel TSSG trackers do not require knowing the number of targets or their signal strengths, and exhibit considerably lower complexity than the benchmark hidden Markov model filter, especially for a large number of targets. Numerical simulations demonstrate that sparsity-cognizant trackers enjoy improved root mean-square error performance at reduced complexity when compared to their sparsity-agnostic counterparts.Comment: Submitted to IEEE Trans. on Signal Processin

Condensation of the roots of real random polynomials on the real axis

We introduce a family of real random polynomials of degree n whose coefficients a_k are symmetric independent Gaussian variables with variance = e^{-k^\alpha}, indexed by a real \alpha \geq 0. We compute exactly the mean number of real roots for large n. As \alpha is varied, one finds three different phases. First, for 0 \leq \alpha \sim (\frac{2}{\pi}) \log{n}. For 1 < \alpha < 2, there is an intermediate phase where grows algebraically with a continuously varying exponent, \sim \frac{2}{\pi} \sqrt{\frac{\alpha-1}{\alpha}} n^{\alpha/2}. And finally for \alpha > 2, one finds a third phase where \sim n. This family of real random polynomials thus exhibits a condensation of their roots on the real line in the sense that, for large n, a finite fraction of their roots /n are real. This condensation occurs via a localization of the real roots around the values \pm \exp{[\frac{\alpha}{2}(k+{1/2})^{\alpha-1} ]}, 1 \ll k \leq n.Comment: 13 pages, 2 figure