Nonlinear sequential designs for logistic item response theory models with applications to computerized adaptive tests

Computerized adaptive testing is becoming increasingly popular due to advancement of modern computer technology. It differs from the conventional standardized testing in that the selection of test items is tailored to individual examinee's ability level. Arising from this selection strategy is a nonlinear sequential design problem. We study, in this paper, the sequential design problem in the context of the logistic item response theory models. We show that the adaptive design obtained by maximizing the item information leads to a consistent and asymptotically normal ability estimator in the case of the Rasch model. Modifications to the maximum information approach are proposed for the two- and three-parameter logistic models. Similar asymptotic properties are established for the modified designs and the resulting estimator. Examples are also given in the case of the two-parameter logistic model to show that without such modifications, the maximum likelihood estimator of the ability parameter may not be consistent.Comment: Published in at http://dx.doi.org/10.1214/08-AOS614 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Software development for flexible pavement thickness design based on aastho and road note 31

Nowadays, road and surface failure has become a critical issue in our country on the flexible pavement which reflects to a bad quality and error during design stage. The thickness design of flexible pavement has become crucial element in the overall efficiency of highway structure system to give a good performance and high serviceability under a traffic loading during the expected design period. The objectives of this study are to develop flexible pavement thickness design software for AASHTO and Road Note 31 by using Visual Basic 6.0. The result comparison between both methods was carried out shown in different of thickness and different percentage of cost evaluations between AASHTO and Road Note 31. This computer software could produce the design thickness of each layer for flexible pavement structure in graphical layout for both design methods. Therefore, the users can easily analyze and compared the result obtained to select the best design alternative between AASHTO and Road Note 31 based on cost and thickness different. The result analysis obtained from this computer software also can be saved and view in a report file to be printed or keep as soft copy for reference in the future. Besides, the result analysis obtained by this computer software is also been compared with the manual calculation (theory) and shown that the computer software has the same and exact result with the manual calculation (theory). Thus, the performance of this computer software was successful tested and validated. Therefore, computer software of flexible pavement thickness design is a very useful tool in highway engineering especially to design the thickness of flexible pavement. By applying the computer program, the design stage can be made in a very short time period of design process and help to minimize the error factor compare to manual calculation or conventional method. Computer software also can give a high accuracy and quality of result for pavement thickness design

Streaking and Wigner time delays in photoemission from atoms and surfaces

Streaked photoemission metrology allows the observation of an apparent relative time delay between the detection of photoelectrons from different initial electronic states. This relative delay is obtained by recording the photoelectron yield as a function of the delay between an ionizing ultrashort extended ultraviolet (XUV) pulse and a streaking infrared (IR) pulse. Theoretically, photoemission delays can be defined based on i) the phase shift the photoelectron wavefunction accumulates during the release and propagation of the photoelectron (``Wigner delay") and, alternatively, ii) the streaking trace in the calculated photoemission spectrum (``streaking delay"). We investigate the relation between Wigner and streaking delays in the photoemission from atomic and solid-surface targets. For solid targets and assuming a vanishing IR-skin depth, both Wigner and streaking delays can be interpreted as an average propagation time needed by photoelectrons to reach the surface, while the two delays differ for non-vanishing skin depths. For atomic targets, the difference between Wigner and streaking delays depends on the range of the ionic potential.Comment: 9 pages, 12 figures, submitted to Phys. Rev.

Achievable Angles Between two Compressed Sparse Vectors Under Norm/Distance Constraints Imposed by the Restricted Isometry Property: A Plane Geometry Approach

The angle between two compressed sparse vectors subject to the norm/distance constraints imposed by the restricted isometry property (RIP) of the sensing matrix plays a crucial role in the studies of many compressive sensing (CS) problems. Assuming that (i) u and v are two sparse vectors separated by an angle thetha, and (ii) the sensing matrix Phi satisfies RIP, this paper is aimed at analytically characterizing the achievable angles between Phi*u and Phi*v. Motivated by geometric interpretations of RIP and with the aid of the well-known law of cosines, we propose a plane geometry based formulation for the study of the considered problem. It is shown that all the RIP-induced norm/distance constraints on Phi*u and Phi*v can be jointly depicted via a simple geometric diagram in the two-dimensional plane. This allows for a joint analysis of all the considered algebraic constraints from a geometric perspective. By conducting plane geometry analyses based on the constructed diagram, closed-form formulae for the maximal and minimal achievable angles are derived. Computer simulations confirm that the proposed solution is tighter than an existing algebraic-based estimate derived using the polarization identity. The obtained results are used to derive a tighter restricted isometry constant of structured sensing matrices of a certain kind, to wit, those in the form of a product of an orthogonal projection matrix and a random sensing matrix. Follow-up applications to three CS problems, namely, compressed-domain interference cancellation, RIP-based analysis of the orthogonal matching pursuit algorithm, and the study of democratic nature of random sensing matrices are investigated.Comment: submitted to IEEE Trans. Information Theor

Constraints from Type IA Supernovae on {\lambda}-CDM Model in Randers-Finsler Space

Gravitational field equations in Randers-Finsler space of approximate Berwald type are investigated. A modified Friedmann equation and a new luminosity distance-redshift relation is proposed. A best-fit to the Type Ia supernovae (SNe) observations yields that the $\Omega_{\Lambda}$ in the $\Lambda$-CDM model is suppressed to almost zero. This fact indicates that the astronomical observations on the Type Ia SNe can be described well without invoking any form of dark energy. The best-fit age of the universe is given. It is in agreement with the age of our galaxy.Comment: 14 pages, 3 figure

Pion-nucleon Sigma Term in the Global Color Model of QCD

We study the pion-nucleon sigma term in vacuum and in nuclear matter in the framework of global color model of QCD. With the effective gluon propagator being taken as the $\delta$-function in momentum space of Munczek-Nomirovsky model, we estimate that the sigma term at chiral limit in the vacuum is 9/2 times the current quark mass and it decreases with the nuclear matter density. With the presently obtained in-medium pion-nucleon sigma term, we study the in-medium chiral quark condensate and obtain a reasonable variation behavior against the nuclear matter density.Comment: 17 pages, 3 figure