The conduct of the sample average when the first moment is infinite

Many books about probability and statistics only mention the weak and the strong law of large numbers for samples from distributions with finite expectation. However, these laws also hold for distributions with infinite expectation and then the sample average has to go to infinity with increasing sample size.\ud \ud Being curious about the way in which this would happen, we simulated increasing samples (up to n= 40000) from three distributions with infinite expectation. The results were somewhat surprising at first sight, but understandable after some thought. Most statisticians, when asked, seem to expect a gradual increase of the average with the size of the sample. So did we. In general, however, this proves to be wrong and for different parent distributions different types of conduct appear from this experiment.\ud \ud The samples from the "absolute Cauchy"-distribution are most interesting from a practical point of view: the average takes a high jump from time to time and decreases in between. In practice it might well happen, that the observations causing the jumps would be discarded as outlying observations

Experiential, Distributional and Dependency-based Word Embeddings have Complementary Roles in Decoding Brain Activity

We evaluate 8 different word embedding models on their usefulness for predicting the neural activation patterns associated with concrete nouns. The models we consider include an experiential model, based on crowd-sourced association data, several popular neural and distributional models, and a model that reflects the syntactic context of words (based on dependency parses). Our goal is to assess the cognitive plausibility of these various embedding models, and understand how we can further improve our methods for interpreting brain imaging data. We show that neural word embedding models exhibit superior performance on the tasks we consider, beating experiential word representation model. The syntactically informed model gives the overall best performance when predicting brain activation patterns from word embeddings; whereas the GloVe distributional method gives the overall best performance when predicting in the reverse direction (words vectors from brain images). Interestingly, however, the error patterns of these different models are markedly different. This may support the idea that the brain uses different systems for processing different kinds of words. Moreover, we suggest that taking the relative strengths of different embedding models into account will lead to better models of the brain activity associated with words.Comment: accepted at Cognitive Modeling and Computational Linguistics 201

T-Cell Compartmentalization and Functional Adaptation in Autoimmune Inflammation: Lessons From Pediatric Rheumatic Diseases

Chronic inflammatory diseases are characterized by a disturbed immune balance leading to recurring episodes of inflammation in specific target tissues, such as the joints in juvenile idiopathic arthritis. The tissue becomes infiltrated by multiple types of immune cell, including high numbers of CD4 and CD8 T-cells, which are mostly effector memory cells. Locally, these T-cells display an environment-adapted phenotype, induced by inflammation- and tissue-specific instructions. Some of the infiltrated T-cells may become tissue resident and play a role in relapses of inflammation. Adaptation to the environment may lead to functional (re)programming of cells and altered cellular interactions and responses. For example, specifically at the site of inflammation both CD4 and CD8 T-cells can become resistant to regulatory T-cell-mediated regulation. In addition, CD8 and CD4 T-cells show a unique profile with pro- and anti-inflammatory features coexisting in the same compartment. Also regulatory T-cells are neither homogeneous nor static in nature and show features of functional differentiation, and plasticity in inflammatory environments. Here we will discuss the recent insights in T-cell functional specialization, regulation, and clonal expansion in local (tissue) inflammation

Dosimetric verification of the anisotropic analytical algorithm for radiotherapy treatment planning

BACKGROUND AND PURPOSE: To investigate the accuracy of photon dose calculations performed by the Anisotropic Analytical Algorithm, in homogeneous and inhomogeneous media and in simulated treatment plans. MATERIALS AND METHODS: Predicted dose distributions were compared with ionisation chamber and film measurements for a series of increasingly complex situations. Initially, simple and complex fields in a homogeneous medium were studied. The effect of inhomogeneities was investigated using a range of phantoms constructed of water, bone and lung substitute materials. Simulated treatment plans were then produced using a semi-anthropomorphic phantom and the delivered doses compared to the doses predicted by the Anisotropic Analytical Algorithm. RESULTS: In a homogeneous medium, agreement was found to be within 2% dose or 2mm dta in most instances. In the presence of heterogeneities, agreement was generally to within 2.5%. The simulated treatment plan measurements agreed to within 2.5% or 2mm. Conclusions: The accuracy of the algorithm was found to be satisfactory at 6MV and 10MV both in homogeneous and inhomogeneous situations and in the simulated treatment plans. The algorithm was more accurate than the Pencil Beam Convolution model, particularly in the presence of low density heterogeneities

Toward in vivo dosimetry in external beam radiotherapy using x‐ray acoustic computed tomography: A soft‐tissue phantom study validation

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/146485/1/mp13070_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/146485/2/mp13070.pd