On an Asymptotic Series of Ramanujan

An asymptotic series in Ramanujan's second notebook (Entry 10, Chapter 3) is concerned with the behavior of the expected value of $\phi(X)$ for large $\lambda$ where $X$ is a Poisson random variable with mean $\lambda$ and $\phi$ is a function satisfying certain growth conditions. We generalize this by studying the asymptotics of the expected value of $\phi(X)$ when the distribution of $X$ belongs to a suitable family indexed by a convolution parameter. Examples include the problem of inverse moments for distribution families such as the binomial or the negative binomial.Comment: To appear, Ramanujan

Riociguat treatment in patients with chronic thromboembolic pulmonary hypertension: Final safety data from the EXPERT registry

Objective: The soluble guanylate cyclase stimulator riociguat is approved for the treatment of adult patients with pulmonary arterial hypertension (PAH) and inoperable or persistent/recurrent chronic thromboembolic pulmonary hypertension (CTEPH) following Phase

Independent yet overlapping pathways ensure the robustness and responsiveness of trans-Golgi network functions in <em>Arabidopsis</em>.

The trans-Golgi-network (TGN) has essential housekeeping functions in secretion, endocytosis and protein sorting, but also more specialized functions in plant development. How the robustness of basal TGN function is ensured while specialized functions are differentially regulated is poorly understood. Here, we investigate two key regulators of TGN structure and function, ECHIDNA and the Transport Protein Particle II (TRAPPII) tethering complex. An analysis of physical, network and genetic interactions suggests that two network communities are implicated in TGN function and that ECHIDNA and TRAPPII belong to distinct yet overlapping pathways. Whereas ECHIDNA and TRAPPII colocalized at the TGN in interphase cells, their localization diverged in dividing cells. Moreover, ECHIDNA and TRAPPII localization patterns were mutually independent. TGN structure, endocytosis and sorting decisions were differentially impacted in echidna and trappii mutants. Our analyses point to a partitioning of specialized TGN functions, with ECHIDNA being required for cell elongation and TRAPPII for cytokinesis. Two independent pathways able to compensate for each other might contribute to the robustness of TGN housekeeping functions and to the responsiveness and fine tuning of its specialized functions

Estimating Discrete Joint Probability Distributions for Demographic Characteristics at the Store Level Given Store Level Marginal Distributions and a City-Wide Joint Distribution

This paper provides a solution to the problem of estimating a joint distribution using the associated marginal distributions and a related joint distribution. The particular application we have in mind is estimating joint distributions of demographic characteristics corresponding to market areas for individual retail stores. Marginal distributions are generally available at the census tract level, but joint distributions are only available for Metropolitan Statistical Areas which are generally much larger than the market for a single retail store. Joint distributions over demographics are an important input into mixed logit demand models for aggregate data. Market shares that vary systematically with demographics are essential for relieving the restrictions imposed by the Independence from Irrelevant Alternative property of the logit model. We approach this problem by formulating a parametric function that incorporates both the city-wide joint distributional information and marginal information specific to the retail store’s market area. To estimate the function, we form moment conditions equating the moments of the parametric function to observed data, and we input these into a GMM objective. In one of our illustrations we use four marginal demographic distributions from each of eight stores in Dominick’s Finer Foods data archive to estimate a four dimensional joint distribution for each store. Our results show that our GMM approach produces estimated joint distributions that differ substantially from the product of marginal distributions and emit marginals that closely match the observed marginal distributions. Mixed logit demand estimates are also presented which show the estimates to be sensitive to the formulation of the demographics distribution. Copyright Springer Science + Business Media, Inc. 2005mixed logit, discrete joint probability distributions, generalized method of moments,

Item Response Theory with Estimation of the Latent Population Distribution Using Spline-Based Densities

item response theory, marginal maximum likelihood, latent variable, population distribution, density estimation, splines,