Linear mixed models with endogenous covariates: modeling sequential treatment effects with application to a mobile health study

Mobile health is a rapidly developing field in which behavioral treatments are delivered to individuals via wearables or smartphones to facilitate health-related behavior change. Micro-randomized trials (MRT) are an experimental design for developing mobile health interventions. In an MRT the treatments are randomized numerous times for each individual over course of the trial. Along with assessing treatment effects, behavioral scientists aim to understand between-person heterogeneity in the treatment effect. A natural approach is the familiar linear mixed model. However, directly applying linear mixed models is problematic because potential moderators of the treatment effect are frequently endogenous---that is, may depend on prior treatment. We discuss model interpretation and biases that arise in the absence of additional assumptions when endogenous covariates are included in a linear mixed model. In particular, when there are endogenous covariates, the coefficients no longer have the customary marginal interpretation. However, these coefficients still have a conditional-on-the-random-effect interpretation. We provide an additional assumption that, if true, allows scientists to use standard software to fit linear mixed model with endogenous covariates, and person-specific predictions of effects can be provided. As an illustration, we assess the effect of activity suggestion in the HeartSteps MRT and analyze the between-person treatment effect heterogeneity

The shape of Fe Kα\alpha line emitted from relativistic accretion disc around AGN black holes

The relativistically broadened Fe K$\alpha$ line, originating from the accretion disc in a vicinity of a super massive black hole, is observed in only less than 50\% of type 1 Active Galactic Nuclei (AGN). In this study we investigate could this lack of detections be explained by the effects of certain parameters of the accretion disc and black hole, such as the inclination, the inner and outer radius of disc and emissivity index. In order to determine how these parameters affect the Fe K $\alpha$ line shape, we simulated about 60,000 Fe K $\alpha$ line profiles emitted from the relativistic disc. Based on simulated line profiles, we conclude that the lack of the Fe K$\alpha$ line detection in type 1 AGN could, be caused by the specific emitting disc parameters, but also by the limits in the spectral resolution and sensitivity of the X-ray detectors.Comment: Based on the talk presented Balkan Workshop BW2018 (10-14 June 2018, Ni\v{s}, Serbia), accepted for publishing in International Journal of Modern Physics A, 8 figures, 1 table, 15 page

Controlling the Local Spin-Polarization at the Organic-Ferromagnetic Interface

By means of ab initio calculations and spin-polarized scanning tunneling microscopy experiments we show how to manipulate the local spin-polarization of a ferromagnetic surface by creating a complex energy dependent magnetic structure. We demonstrate this novel effect by adsorbing organic molecules containing pi(pz)-electrons onto a ferromagnetic surface, in which the hybridization of the out-of-plane pz atomic type orbitals with the d-states of the metal leads to the inversion of the spin-polarization at the organic site due to a pz - d Zener exchange type mechanism. As a key result, we demonstrate that it is possible to selectively inject spin-up and spin-down electrons from the same ferromagnetic surface, an effect which can be exploited in future spintronic devices

Unstable recurrent patterns in Kuramoto-Sivashinsky dynamics

We undertake a systematic exploration of recurrent patterns in a 1-dimensional Kuramoto-Sivashinsky system. For a small, but already rather turbulent system, the long-time dynamics takes place on a low-dimensional invariant manifold. A set of equilibria offers a coarse geometrical partition of this manifold. A variational method enables us to determine numerically a large number of unstable spatiotemporally periodic solutions. The attracting set appears surprisingly thin - its backbone are several Smale horseshoe repellers, well approximated by intrinsic local 1-dimensional return maps, each with an approximate symbolic dynamics. The dynamics appears decomposable into chaotic dynamics within such local repellers, interspersed by rapid jumps between them.Comment: 11 pages, 11 figure

Impact of chromophores on colour appearance in a computational skin model

Early diagnosis of skin cancer offers the patient more favorable treatment options. Color fidelity of skin images is a major concern for dermatologists as adoption of digital dermatoscopes is increasing rapidly. Accurate color depiction of the lesion and surrounding skin are vital in diagnostic evaluation of a lesion. We previously introduced VCT-Derma, a pipeline for dermatological Virtual Clinical Trials (VCTs) including detailed and flexible models of human skin and lesions, which represent the patient in the entire dermatoscopy-based diagnostic process. However, those initial models of skin and lesions did not properly account for tissue colors. Our new skin model accounts for tissue color appearance by incorporating chromophores (e.g., melanin, blood) into the tissue model, and simulating the optical properties of the various skin layers. The physical properties of the skin and lesion were selected from clinically plausible values. The model and simulated dermatoscope images were created in open modelling software, assuming a linear camera model. We have assumed ambient white lighting, with a 6mm distance to the camera. Our model of color appearance was characterised by comparing the brightness of the lesion to its depth. The brightness of the lesion is compared through the variability of the mean gray values of a cropped region around the lesion. We compare two skin models, one without extensive chromophore content and one with. Our preliminary evaluation of increasing chromophore content shows promise based on the results presented here. Further refinement and validation of the model is ongoing