Inferring Latent States and Refining Force Estimates via Hierarchical Dirichlet Process Modeling in Single Particle Tracking Experiments

Optical microscopy provides rich spatio-temporal information characterizing in vivo molecular motion. However, effective forces and other parameters used to summarize molecular motion change over time in live cells due to latent state changes, e.g., changes induced by dynamic micro-environments, photobleaching, and other heterogeneity inherent in biological processes. This study focuses on techniques for analyzing Single Particle Tracking (SPT) data experiencing abrupt state changes. We demonstrate the approach on GFP tagged chromatids experiencing metaphase in yeast cells and probe the effective forces resulting from dynamic interactions that reflect the sum of a number of physical phenomena. State changes are induced by factors such as microtubule dynamics exerting force through the centromere, thermal polymer fluctuations, etc. Simulations are used to demonstrate the relevance of the approach in more general SPT data analyses. Refined force estimates are obtained by adopting and modifying a nonparametric Bayesian modeling technique, the Hierarchical Dirichlet Process Switching Linear Dynamical System (HDP-SLDS), for SPT applications. The HDP-SLDS method shows promise in systematically identifying dynamical regime changes induced by unobserved state changes when the number of underlying states is unknown in advance (a common problem in SPT applications). We expand on the relevance of the HDP-SLDS approach, review the relevant background of Hierarchical Dirichlet Processes, show how to map discrete time HDP-SLDS models to classic SPT models, and discuss limitations of the approach. In addition, we demonstrate new computational techniques for tuning hyperparameters and for checking the statistical consistency of model assumptions directly against individual experimental trajectories; the techniques circumvent the need for "ground-truth" and subjective information.Comment: 25 pages, 6 figures. Differs only typographically from PLoS One publication available freely as an open-access article at http://journals.plos.org/plosone/article?id=10.1371/journal.pone.013763

Competition and innovation: an inverted U relationship

This paper investigates the relationship between product market competition (PMC) and innovation. A Schumpeterian growth model is developed in which firms innovate ‘step-by-step’, and where both technological leaders and their followers engage in R&D activities. In this model, competition may increase the incremental profit from innovating; on the other hand, competition may also reduce innovation incentives for laggards. This model generates four main predictions which we test empirically. First, the relationship between product market competition (PMC) and innovation is an inverted U-shape: the escape competition effect dominates for low initial levels of competition, whereas the Schumpeterian effect dominates at higher levels of competition. Second, the equilibrium degree of technological ‘neck-and-neckness’ among firms should decrease with PMC. Third, the higher the average degree of ‘neck-and-neckness’ in an industry, the steeper the inverted-U relationship between PMC and innovation in that industry. Fourth, firms may innovate more if subject to higher debt-pressure, especially at lower levels of PMC. We confront these four predictions with a new panel data set on UK firms’ patenting activity at the US patenting office. The inverted U relationship, the neck and neck, and the debt pressure predictions are found to accord well with observed behavior in the data

Competition and innovation: an inverted U relationship?

This paper investigates the relationship between product market competition and innovation. It uses the radical policy reforms in the UK as instruments for changes in product market competition, and finds a robust inverted-U relationship between competition and patenting. It then develops an endogenous growth model with step-by-step innovation that can deliver this inverted-U pattern. In this model, competition has an ambiguous effect on innovation. On the one hand, it discourages laggard firms from innovating, as it reduces their rents from catching up with the leaders in the same industry. On the other hand, it encourages neck-and-neck firms to innovate in order to escape competition with their rival. The inverted-U pattern results from the interplay between these two effects, together with the effect of competition on the equilibrium industry structure. The model generates two additional predictions: on the relationship between competition and the average technological distance between leaders and followers across industries; and on the relationship between the distance of an industry to its technological frontier and the steepness of the inverted-U. Both predictions are supported by the data

Hard gamma ray emission from blazars

The gamma-ray emission expected from compact extragalactic sources of nonthermal radiation is examined. The highly variable objects in this class should produce copious amounts of self-Compton gamma-rays in the compact relativistic jet. This is shown to be a likely interpretation of the hard gamma-ray emission recently detected from the quasar 3C 279 during a period of strong nonthermal flaring at lower frequencies. Ways of discriminating between the self-Compton model and other possible gamma-ray emission mechanisms are discussed

Expected level of self-Compton scattering in radio loud quasars

Radio-loud quasars usually contain parsec-scale nonthermal jets. The most compact emission region ('the core'), and perhaps some of the moving 'knots', are expected to be efficient producers of inverse Compton scattered X-rays and gamma-rays since many of the synchrotron photons will upscatter before escaping. Through multifrequency flux density observations and Very Long Baseline Interferometry (VLBI) measurements of angular sizes, one can predict the flux density of this self-Compton high-energy emission. It is not always the case that the brightest synchrotron sources are also the brightest X-ray and gamma-ray sources. Perhaps a better predictor of high-energy brightness is the ratio of hard X-ray to high-frequency radio emission. Using the synchrotron self-Compton relations, we predict the gamma-ray fluxes of several sources we expect to be detected by the Energetic Gamma Ray Experiment Telescope (EGRET). More accurate predictions will be made when we complete a program of contemporaneous radio-submillimeter and X-ray observations during the course of the EGRET all-sky survey

A Multiwavelength Investigation of Unidentified EGRET Sources

Statistical studies indicate that the 271 point sources of high-energy gamma rays belong to two groups: a Galactic population and an isotropic extragalactic population. Many unidentified extragalactic sources are certainly blazars, and it is the intention of this work to uncover gamma-ray blazars missed by previous attempts. Until recently, searches for blazar counterparts to unidentified EGRET sources have focused on finding AGN that have 5-GHz radio flux densities S_5 near or above 1 Jy. However, the recent blazar identification of 3EG J2006-2321 (S_5 = 260 mJy) and other work suggest that careful studies of weaker flat-spectrum sources may be fruitful. In this spirit, error circles of 4 high-latitude unidentified EGRET sources have been searched for 5-GHz sources. The gamma-ray sources are 3EG J1133+0033, 3EG J1212+2304, 3EG J1222+2315, and 3EG J1227+4302. Within the error contours of each of the four sources are found 6 radio candidates; by observing the positions of the radio sources with the 0.81-m Tenagra II telescope it is determined that 14 of these 24 radio sources have optical counterparts with R < 22. Eight of these from two different EGRET sources have been observed in the B, V, and R bands in more than one epoch and the analysis of these data is ongoing. Any sources that are found to be variable will be the objects of multi-epoch polarimetry studies.Comment: 6 pages, 2 tables. To appear in Astrophysics & Space Scienc

The star-formation rate in the host of GRB 990712

We have observed the host galaxy of GRB 990712 at 1.4 GHz with the Australia Telescope Compact Array, to obtain an estimate of its total star-formation rate. We do not detect a source at the position of the host. The 2 sigma upper limit of 70 microJy implies that the total star-formation rate is lower than 100 Msun/yr, using conservative values for the spectral index and cosmological parameters. This upper limit is in stark contrast with recent reports of radio/submillimeter-determined star-formation rates of roughly 500 Msun/yr for two other GRB host galaxies. Our observations present the deepest radio-determined star-formation rate limit on a GRB host galaxy yet, and show that also from the unobscured radio point-of-view, not every GRB host galaxy is a vigorous starburst.Comment: A&A Letters, in press, 5 pages; a high-resolution color gif version of the paper figure is also supplie

Differential effects of Alzheimer\u27s disease and Huntington\u27s disease on the performance of mental rotation

he ability to spatially rotate a mental image was compared in patients with Alzheimer\u27s disease (AD; n = 18) and patients with Huntington\u27s disease (HD; n = 18). Compared to their respective age-matched normal control (NC) group, the speed, but not the accuracy, of mental rotation abnormally decreased with increasing angle of orientation for patients with HD. In contrast, the accuracy, but not the speed, of rotation abnormally decreased with increasing angle of orientation for patients with AD. Additional analyses showed that these unique patterns of performance were not attributable to different speed/accuracy trade-off sensitivities. This double dissociation suggests that the distinct brain regions affected in the two diseases differentially contribute to speed and accuracy of mental rotation. Specifically, the slowing exhibited by HD patients may be mediated by damage to the basal ganglia, whereas the spatial manipulation deficit of AD patients may reflect pathology in parietal and temporal lobe association cortices important for visuospatial processing. (JINS, 2005, 11, 30–39.