Estimation and prediction in generalized linear mixed models are often hampered by intractable high dimensional integrals. This paper provides a framework to solve this intractability, using asymptotic expansions when the number of random effects is large. To that end, we first derive a modified Laplace approximation when the number of random effects is increasing at a lower rate than the sampl...

We study the parametrized post-Newtonian (PPN) limit of higher-derivative-torsion Modified Teleparallel Gravity. start from covariant formulation modified Gravity by restoring spin connection theory. Then, we perform expansion tetrad field around Minkowski background and find perturbed equations. compute PPN metric for higher-order theories which allows us to show that at this more general clas...

The Painlevé expansion for the second Painlevé equation (PII) and fourth Painlevé equation (PIV) have two branches. The singular manifold method therefore requires two singular manifolds. The double singular manifold method is used to derive Miura transformations from PII and PIV to modified Painlevé type equations for which auto-Bäcklund transformations are obtained. These auto-Bäcklund transf...

We propose an empirical method for estimating term weights directly from relevance judgements, avoiding various standard but potentially troublesome assumptions. It is common to assume, for example, that weights vary with term frequency (t f ) and inverse document frequency (idf) in a particular way, e.g., t f . idf, but the fact tha t there are so many variants of this formula in the literatur...

In this study, a stochastic model for transient saturated–unsaturated flow is developed based on the Karhunen-Loeve expansion of the input random soil properties combined with a perturbation method. The log-transformed saturated hydraulic conductivity f ðxÞ and the soil pore size distribution parameter aðxÞ are assumed to be normal random functions with known covariances. We decompose f ðxÞ and...

BACKGROUND 2-deoxy-2-[(18)F]fluoro-D-glucose-positron emission tomography ((18)F-FDG-PET) is applied in the clinic for infection assessment and is under consideration for investigating the inflammatory/immune response in lymphoid tissue in animal models of viral infection. Assessing changes in (18)F-FDG uptake of lymph nodes (LNs), primary lymphoid tissues targeted during viral infection, requi...

This paper introduces a fast high-resolution imaging algorithm designed for ultra-wideband radar, and combines modified Kirchhoff migration and frequency-wavenumber (F-K) migration. The proposed algorithm also uses the texture method and inverse boundary scattering transform to calculate efficiently the integral arising in modified Kirchhoff migration, and thus enabling the integral in the F-K ...

Background: 2-deoxy-2-[F]fluoro-D-glucose-positron emission tomography (F-FDG-PET) is applied in the clinic for infection assessment and is under consideration for investigating the inflammatory/immune response in lymphoid tissue in animal models of viral infection. Assessing changes in F-FDG uptake of lymph nodes (LNs), primary lymphoid tissues targeted during viral infection, requires suitabl...

I examine how two specific examples of modified gravity explanations of cosmic acceleration help us understand some general problems confronting cosmological tests of gravity: how do we distinguish modified gravity from dark energy if they can be made formally equivalent? how do we parameterize deviations according to physical principles with sufficient generality, yet focus cosmological tests ...