A Class of Nonconvex Penalties Preserving Overall Convexity in Optimization-Based Mean Filtering

$\ell_1$ mean filtering is a conventional, optimization-based method to estimate the positions of jumps in a piecewise constant signal perturbed by additive noise. In this method, the $\ell_1$ norm penalizes sparsity of the first-order derivative of the signal. Theoretical results, however, show that in some situations, which can occur frequently in practice, even when the jump amplitudes tend to $\infty$, the conventional method identifies false change points. This issue is referred to as stair-casing problem and restricts practical importance of $\ell_1$ mean filtering. In this paper, sparsity is penalized more tightly than the $\ell_1$ norm by exploiting a certain class of nonconvex functions, while the strict convexity of the consequent optimization problem is preserved. This results in a higher performance in detecting change points. To theoretically justify the performance improvements over $\ell_1$ mean filtering, deterministic and stochastic sufficient conditions for exact change point recovery are derived. In particular, theoretical results show that in the stair-casing problem, our approach might be able to exclude the false change points, while $\ell_1$ mean filtering may fail. A number of numerical simulations assist to show superiority of our method over $\ell_1$ mean filtering and another state-of-the-art algorithm that promotes sparsity tighter than the $\ell_1$ norm. Specifically, it is shown that our approach can consistently detect change points when the jump amplitudes become sufficiently large, while the two other competitors cannot.Comment: Submitted to IEEE Transactions on Signal Processin

Hydrogen reliquefiers for lunar storage systems

Reliquifier application to eliminate propellant boil off losses in space and lunar storage system

The Influence of Irregularity on the Values of Demand Modifier Factor in ASCE 41-06

In the past two decades, many investigations have been made on the methods related to the seismic retrofitting of the structures. As the real nonlinear behaviors of the elements are considered in these methods, the values of internal forces determined in the members are equal to the real ones. In the structural seismic linear analysis methods the elements behaviors are still assumed linear. In this regard, the passage of structure through yield point borders and the displacement increasing are correspondent to the forces elevation. In FEMA codes, the factors such as demand modifier (m) or increasing capacity ones are presented applying the effects of elements nonlinear behaviors in linear method analysis. In this research the factors recommended in ASCE 41-06 are studied focusing on several symmetrical and asymmetrical concrete moment resisting frame moldings (5, 7 and 10 stories structures) and linear & non linear time history analysis (7 records). In this regard, the method used for scaling earthquake records is the current method presented in UBC97, “nonlinear dynamic analysis (RHA)”. According to this research there is direct relation between irregularity and increasing the amount of distribution among the results. In this way by increasing the eccentricity, difference between obtained results and recommended values will be more than the case with less irregularity

Successive Concave Sparsity Approximation for Compressed Sensing

In this paper, based on a successively accuracy-increasing approximation of the $\ell_0$ norm, we propose a new algorithm for recovery of sparse vectors from underdetermined measurements. The approximations are realized with a certain class of concave functions that aggressively induce sparsity and their closeness to the $\ell_0$ norm can be controlled. We prove that the series of the approximations asymptotically coincides with the $\ell_1$ and $\ell_0$ norms when the approximation accuracy changes from the worst fitting to the best fitting. When measurements are noise-free, an optimization scheme is proposed which leads to a number of weighted $\ell_1$ minimization programs, whereas, in the presence of noise, we propose two iterative thresholding methods that are computationally appealing. A convergence guarantee for the iterative thresholding method is provided, and, for a particular function in the class of the approximating functions, we derive the closed-form thresholding operator. We further present some theoretical analyses via the restricted isometry, null space, and spherical section properties. Our extensive numerical simulations indicate that the proposed algorithm closely follows the performance of the oracle estimator for a range of sparsity levels wider than those of the state-of-the-art algorithms.Comment: Submitted to IEEE Trans. on Signal Processin

Lagrangian structure of flows in the Chesapeake Bay:Challenges and perspectives on the analysis of estuarine flows

In this work we discuss applications of Lagrangian techniques to study transport properties of flows generated by shallow water models of estuarine flows. We focus on the flow in the Chesapeake Bay generated by Quoddy (see Lynch and Werner, 1991), a finite-element (shallow water) model adopted to the bay by Gross et al. (2001). The main goal of this analysis is to outline the potential benefits of using Lagrangian tools for both understanding transport properties of such flows, and for validating the model output and identifying model deficiencies. We argue that the currently available 2-D Lagrangian tools, including the stable and unstable manifolds of hyperbolic trajectories and techniques exploiting 2-D finite-time Lyapunov exponent fields, are of limited use in the case of partially mixed estuarine flows. A further development and efficient implementation of three-dimensional Lagrangian techniques, as well as improvements in the shallow-water modelling of 3-D velocity fields, are required for reliable transport analysis in such flows. Some aspects of the 3-D trajectory structure in the Chesapeake Bay, based on the Quoddy output, are also discussed

Intrinsic localized modes in the charge-transfer solid PtCl

We report a theoretical analysis of intrinsic localized modes in a quasi-one-dimensional charge-transfer-solid $[Pt(en)_2][Pt(en)_2 Cl_2](ClO_4)_4$(PtCl). We discuss strongly nonlinear features of resonant Raman overtone scattering measurements on PtCl, arising from quantum intrinsic localized (multiphonon) modes (ILMs) and ILM-plus-phonon states. We show, that Raman scattering data displays clear signs of a non-thermalization of lattice degrees-of-freedom, manifested in a nonequilibrium density of intrinsic localized modes.Comment: 4 pages, 4 figures, REVTE

Transparency of 0.2% GdCl3 Doped Water in a Stainless Steel Test Environment

The possibility of neutron and neutrino detection using water Cerenkov detectors doped with gadolinium holds the promise of constructing very large high-efficiency detectors with wide-ranging application in basic science and national security. This study addressed a major concern regarding the feasibility of such detectors: the transparency of the doped water to the ultraviolet Cerenkov light. We report on experiments conducted using a 19-meter water transparency measuring instrument and associated materials test tank. Sensitive measurements of the transparency of water doped with 0.2% GdCl3 at 337nm, 400nm and 420nm were made using this instrument. These measurements indicate that GdCl3 is not an appropriate dopant in stainless steel constructed water Cerenkov detectors.Comment: 17 pages, 11 figures, corrects typos, changes formatting, adds error bars to figure