Fixed effects model | EPFL Graph Search

In statistics, a fixed effects model is a statistical model in which the model parameters are fixed or non-random quantities. This is in contrast to random effects models and mixed models in which all or some of the model parameters are random variables. In many applications including econometrics and biostatistics a fixed effects model refers to a regression model in which the group means are fixed (non-random) as opposed to a random effects model in which the group means are a random sample from a population. Generally, data can be grouped according to several observed factors. The group means could be modeled as fixed or random effects for each grouping. In a fixed effects model each group mean is a group-specific fixed quantity. In panel data where longitudinal observations exist for the same subject, fixed effects represent the subject-specific means. In panel data analysis the term fixed effects estimator (also known as the within estimator) is used to r

Inverse problems in tumor modelling

Léo Aurélio Diserens

In this project, we deepen the analysis of a tumour growth model, recently proposed by Garcke et al. in [1]. This model describes tumour and healthy cells evolution as well as tumour cells’ nutrients, mixture velocity and pressure in the domain. Furthermore, it takes into account chemotaxis and apoptosis death of tumour cells, through a system of parabolic nonlinear PDE, that is a Cahn-Hilliard Darcy model, together with an advection-diffusion-reaction equation describing the evolution of nutrients. We perform a dimensional analysis and we build a numerical solver by use of the finite element method in space, a Backward Euler in time and a Newton method to tackle the nonlinearity. We perform several numerical simulations in order to recover results obtained in the article and to catch a general growth of the tumour depending on parameters of interest. Finally, a PDE-constrained optimization problem is formulated and solved, aiming at determining the shape of the tumur after a fixed time from an initial guess of its location. From the numerical simulations we obtained for the nutrients, we notice that the concentration of nutrients in an observable zone around the tumor region could possibly bring enough information to achieve this goal. Therefore, a previous numerical simulation of nutrients will be taken as a target, in order to recover the controlled tumor function, previously simulated numerically. In this respect, preliminary numerical results show that, to some extents, it is possible to identify the general shape of the tumor, even if the exact result of the numerical simulation could not be recovered.

2016

Scattering of wave maps from $\mathbb{R}^{2+1}$ to general targets

Joules Elie Nahas

We show that smooth, radially symmetric wave maps

U

from

\mathbb{R}^{2+1}

to a compact target manifold

N

, where

\partial_r U

and

\partial_t U

have compact support for any fixed time, scatter. The result will follow from the work of Christodoulou and Tahvildar-Zadeh, and Struwe, upon proving that for

\lambda' \in (0,1)

, energy does not concentrate in the set

K_\frac{5}{8}T,\frac{7}{8}T^{\lambda'} = \{(x,t) \in \mathbb R^{2+1} \vert \hspace{5pt} |x| \leq \lambda' t, t \in [(5/8)T,(7/8)T] \}.

Springer-Verlag2013

The longitudinal association between social functioning and theory of mind in first-episode psychosis

Daniela Herzig, Christine Mohr

IntroductionThere is some cross-sectional evidence that theory of mind ability is associated with social functioning in those with psychosis but the direction of this relationship is unknown. This study investigates the longitudinal association between both theory of mind and psychotic symptoms and social functioning outcome in first-episode psychosis.MethodsFifty-four people with first-episode psychosis were followed up at 6 and 12 months. Random effects regression models were used to estimate the stability of theory of mind over time and the association between baseline theory of mind and psychotic symptoms and social functioning outcome.ResultsNeither baseline theory of mind ability (regression coefficients: Hinting test 1.07 95% CI -0.74, 2.88; Visual Cartoon test -2.91 95% CI -7.32, 1.51) nor baseline symptoms (regression coefficients: positive symptoms -0.04 95% CI -1.24, 1.16; selected negative symptoms -0.15 95% CI -2.63, 2.32) were associated with social functioning outcome. There was evidence that theory of mind ability was stable over time, (regression coefficients: Hinting test 5.92 95% CI -6.66, 8.92; Visual Cartoon test score 0.13 95% CI -0.17, 0.44).ConclusionsNeither baseline theory of mind ability nor psychotic symptoms are associated with social functioning outcome. Further longitudinal work is needed to understand the origin of social functioning deficits in psychosis.

Taylor & Francis2014