Revisiting Multi-Subject Random Effects in fMRI: Advocating Prevalence Estimation

Random Effects analysis has been introduced into fMRI research in order to generalize findings from the study group to the whole population. Generalizing findings is obviously harder than detecting activation in the study group since in order to be significant, an activation has to be larger than the inter-subject variability. Indeed, detected regions are smaller when using random effect analysis versus fixed effects. The statistical assumptions behind the classic random effects model are that the effect in each location is normally distributed over subjects, and "activation" refers to a non-null mean effect. We argue this model is unrealistic compared to the true population variability, where, due to functional plasticity and registration anomalies, at each brain location some of the subjects are active and some are not. We propose a finite-Gaussian--mixture--random-effect. A model that amortizes between-subject spatial disagreement and quantifies it using the "prevalence" of activation at each location. This measure has several desirable properties: (a) It is more informative than the typical active/inactive paradigm. (b) In contrast to the hypothesis testing approach (thus t-maps) which are trivially rejected for large sample sizes, the larger the sample size, the more informative the prevalence statistic becomes. In this work we present a formal definition and an estimation procedure of this prevalence. The end result of the proposed analysis is a map of the prevalence at locations with significant activation, highlighting activations regions that are common over many brains

Projections onto translation—Invariant subspaces of L1(G)

AbstractLet G be a locally compact abelian group. A translation-invariant subspace in L1(G) may or may not be complemented depending on the structure of its hull in Ĝ. Techniques for deciding this complementation problem in a variety of situations are developed and illustrated with examples. A complete characterization is obtained for those ideals with a discrete hull

Gene identification for the cblD defect of vitamin B12 metabolism

Background Vitamin B12 (cobalamin) is an essential cofactor in several metabolic pathways. Intracellular conversion of cobalamin to its two coenzymes, adenosylcobalamin in mitochondria and methylcobalamin in the cytoplasm, is necessary for the homeostasis of methylmalonic acid and homocysteine. Nine defects of intracellular cobalamin metabolism have been defined by means of somatic complementation analysis. One of these defects, the cblD defect, can cause isolated methylmalonic aciduria, isolated homocystinuria, or both. Affected persons present with multisystem clinical abnormalities, including developmental, hematologic, neurologic, and metabolic findings. The gene responsible for the cblD defect has not been identified. Methods We studied seven patients with the cblD defect, and skin fibroblasts from each were investigated in cell culture. Microcell-mediated chromosome transfer and refined genetic mapping were used to localize the responsible gene. This gene was transfected into cblD fibroblasts to test for the rescue of adenosylcobalamin and methylcobalamin synthesis. Results The cblD gene was localized to human chromosome 2q23.2, and a candidate gene, designated MMADHC (methylmalonic aciduria, cblD type, and homocystinuria), was identified in this region. Transfection of wild-type MMADHC rescued the cellular phenotype, and the functional importance of mutant alleles was shown by means of transfection with mutant constructs. The predicted MMADHC protein has sequence homology with a bacterial ATP-binding cassette transporter and contains a putative cobalamin binding motif and a putative mitochondrial targeting sequence. Conclusions Mutations in a gene we designated MMADHC are responsible for the cblD defect in vitamin B12 metabolism. Various mutations are associated with each of the three biochemical phenotypes of the disorder

Differentiating Orlicz spaces with rare bases of rectangles

In the current paper, we study how the speed of convergence of a sequence of angles decreasing to zero influences the possibility of constructing a rare differentiation basis of rectangles in the plane, one side of which makes with the horizontal axis an angle belonging to the given sequence, that differentiates precisely a fixed Orlicz space

Planetary Radio Interferometry and Doppler Experiment (PRIDE) Technique: a Test Case of the Mars Express Phobos Fly-by. 2. Doppler tracking: Formulation of observed and computed values, and noise budget

Context. Closed-loop Doppler data obtained by deep space tracking networks (e.g., NASA's DSN and ESA's Estrack) are routinely used for navigation and science applications. By "shadow tracking" the spacecraft signal, Earth-based radio telescopes involved in Planetary Radio Interferometry and Doppler Experiment (PRIDE) can provide open-loop Doppler tracking data when the dedicated deep space tracking facilities are operating in closed-loop mode only. Aims. We explain in detail the data processing pipeline, discuss the capabilities of the technique and its potential applications in planetary science. Methods. We provide the formulation of the observed and computed values of the Doppler data in PRIDE tracking of spacecraft, and demonstrate the quality of the results using as a test case an experiment with ESA's Mars Express spacecraft. Results. We find that the Doppler residuals and the corresponding noise budget of the open-loop Doppler detections obtained with the PRIDE stations are comparable to the closed-loop Doppler detections obtained with the dedicated deep space tracking facilities

Multidimensional Binning Techniques for a Two Parameter Trilinear Gauge Coupling Estimation at LEP II

This paper describes two generalization schemes of the Optimal Variables technique in estimating simultaneously two Trilinear Gauge Couplings. The first is an iterative procedure to perform a 2-dimensional fit using the linear terms of the expansion of the probability density function with respect to the corresponding couplings, whilst the second is a clustering method of probability distribution representation in five dimensions. The pair production of W's at 183 GeV center of mass energy, where one W decays leptonically and the other hadronically, was used to demonstrate the optimal properties of the proposed estimation techniques.Comment: (25 pages, 11 figures

A reactive system for open terrain navigation: Performance and limitations

We describe a core system for autonomous navigation in outdoor natural terrain. The system consists of three parts: a perception module which processes range images to identify untraversable regions of the terrain, a local map management module which maintains a representation of the environment in the vicinity of the vehicle, and a planning module which issues commands to the vehicle controller. Our approach is to use the concept of 'early traversability evaluation', and on the use of reactive planning for generating commands to drive the vehicle. We argue that our approach leads to a robust and efficient navigation system. We illustrate our approach by an experiment in which a vehicle travelled autonomously for one kilometer through unmapped cross-country terrain

Modeling and Analysing Respondent Driven Sampling as a Counting Process

Respondent-driven sampling (RDS) is an approach to sampling design and analysis which utilizes the networks of social relationships that connect members of the target population, using chain-referral methods to facilitate sampling. RDS typically leads to biased sampling, favoring participants with many acquaintances. Naive estimates, such as the sample average, which are uncorrected for the sampling bias, will themselves be biased. To compensate for this bias, current methodology suggests inverse-degree weighting, where the "degree" is the number of acquaintances. This stems from the fundamental RDS assumption that the probability of sampling an individual is proportional to their degree. Since this assumption is tenuous at best, we propose to harness the additional information encapsulated in the time of recruitment, into a model-based inference framework for RDS. This information is typically collected by researchers, but ignored. We adapt methods developed for inference in epidemic processes to estimate the population size, degree counts and frequencies. While providing valuable information in themselves, these quantities ultimately serve to debias other estimators, such a disease's prevalence. A fundamental advantage of our approach is that, being model-based, it makes all assumptions of the data-generating process explicit. This enables verification of the assumptions, maximum likelihood estimation, extension with covariates, and model selection. We develop asymptotic theory, proving consistency and asymptotic normality properties. We further compare these estimators to the standard inverse-degree weighting through simulations, and using real-world data. In both cases we find our estimators to outperform current methods. The likelihood problem in the model we present is convex, and thus efficiently solvable. We implement these estimators in an R package, chords, available on CRAN.Comment: 16 page