Scientific Endeavors of A.M. Mathai: An Appraisal on the Occasion of his Eightieth Birthday, April 2015

A.M. Mathai is Emeritus Professor of Mathematics and Statistics at McGill University, Canada, and Director of the Centre for Mathematical and Statistical Sciences, India. He has published over 300 research papers and more than 25 books on topics in mathematics, statistics, physics, astrophysics, chemistry, and biology. He is a Fellow of the Institute of Mathematical Statistics, National Academy of Sciences of India, President of the Mathematical Society of India, and a Member of the International Statistical Institute. He is the founder of the Canadian Journal of Statistics and the Statistical Society of Canada. He is instrumental in the implementation of the United Nations Basic Space Science Initiative. The paper is an attempt to capture the broad spectrum of scientific endeavors of Professor A.M. Mathai at the occasion of his anniversary.Comment: 21 pages, LaTe

Approximate Inference for Constructing Astronomical Catalogs from Images

We present a new, fully generative model for constructing astronomical catalogs from optical telescope image sets. Each pixel intensity is treated as a random variable with parameters that depend on the latent properties of stars and galaxies. These latent properties are themselves modeled as random. We compare two procedures for posterior inference. One procedure is based on Markov chain Monte Carlo (MCMC) while the other is based on variational inference (VI). The MCMC procedure excels at quantifying uncertainty, while the VI procedure is 1000 times faster. On a supercomputer, the VI procedure efficiently uses 665,000 CPU cores to construct an astronomical catalog from 50 terabytes of images in 14.6 minutes, demonstrating the scaling characteristics necessary to construct catalogs for upcoming astronomical surveys.Comment: accepted to the Annals of Applied Statistic

What A Polygon Can\u27t Tell You: Shifting From Area-Level To Point-Level Investigation Of Residential Segregation Patterns

The study of segregation is essential for understanding how place influences life outcomes. However, traditional segregation indices rely heavily on the use of areal units for calculation, which risks introducing both measurement and interpretation error. Researchers suggest that individual-level data avoids many of the problems facing traditional area-level indices. In this Dissertation, I use the recent release of the complete 1940 Census to investigate the potential problems with measuring segregation with areal units and develop a new method for measuring segregation at the individual level. In Chapter 1, I investigate the potential impact the modifiable areal unit problem (MAUP) may have on accurately measuring segregation when using areal unit indices. In Chapter 2, I develop a new measure of segregation, the Shortest Path Isolation (SPI) index, which captures the degree of racial isolation from the perspective of what an individual would experience. Using the SPI index developed in Chapter 2, Chapter 3 investigates how individual-level racial isolation in 1940 West Philadelphia is associated with access to neighborhood resources by race. Given that our understanding is only as good as our measurement, it is imperative that our measures accurately reflect our perceptions of segregation

Network Centralities in Polycentric Urban Regions: Methods for the Measurement of Spatial Metrics

The primary aim of this thesis is to explain the complex spatial organisations of polycentric urban regions (PURs). PURs are a form of regional morphology that often evolves from post-industrial structures and describe a subnational area featuring a plurality of urban centres. As of today, the analysis of the spatial organisation of PURs constitutes a hitherto uncharted territory. This is due to PURs’ inherent complexity that poses challenges for their conceptualisation. In this context, this thesis reviews theories on the spatial organisation of regions and cities and seeks to make a foundational methodological contribution by joining space syntax and central place theory in the conceptualisation of polycentric urban regions. It takes into account human agency embedded in the physical space, as well as the reciprocal effect of the spatial organisation for the emergence of centralities and demonstrates how these concepts can give insights into the fundamental regional functioning. The thesis scrutinises the role that the spatial organisation plays in such regions, in terms of organising flows of goods and people, ordering locational occupation and fostering centres of commercial activity. It proposes a series of novel measurements and techniques to analyse large and messy datasets. This includes a method for the application of large-scale volunteered geographic information in street network analysis. This is done, in the context of two post-industrial regions: the German Ruhr Valley and the British Nottinghamshire, Derbyshire and Yorkshire region. The thesis’ contribution to the understanding of regional spatial organisation and the study of regional morphology lies in the identification of spatial structural features of socio-economic potentials of regions and particular areas within them. It constitutes the first comparative study of comprehensive large-scale regional spatial networks and presents a framework for the analysis of regions and the evaluation of the predictive potential of spatial networks for socio-economic patterns and the location of centres in regional contexts

Frontiers in Psychology / Imprecise Uncertain Reasoning : A Distributional Approach

The contribution proposes to model imprecise and uncertain reasoning by a mental probability logic that is based on probability distributions. It shows how distributions are combined with logical operators and how distributions propagate in inference rules. It discusses a series of examples like the Linda task, the suppression task, Doherty's pseudodiagnosticity task, and some of the deductive reasoning tasks of Rips. It demonstrates how to update distributions by soft evidence and how to represent correlated risks. The probabilities inferred from different logical inference forms may be so similar that it will be impossible to distinguish them empirically in a psychological study. Second-order distributions allow to obtain the probability distribution of being coherent. The maximum probability of being coherent is a second-order criterion of rationality. Technically the contribution relies on beta distributions, copulas, vines, and stochastic simulation.(VLID)311645

Using the R Package Spatstat to Assess Inhibitory Effects of Microregional Hypoxia on the Infiltration of Cancers of the Head and Neck Region by Cytotoxic T Lymphocytes

(1) Background: The immune system has physiological antitumor activity, which is partially mediated by cytotoxic T lymphocytes (CTL). Tumor hypoxia, which is highly prevalent in cancers of the head and neck region, has been hypothesized to inhibit the infiltration of tumors by CTL. In situ data validating this concept have so far been based solely upon the visual assessment of the distribution of CTL. Here, we have established a set of spatial statistical tools to address this problem mathematically and tested their performance. (2) Patients and Methods: We have analyzed regions of interest (ROI) of 22 specimens of cancers of the head and neck region after 4-plex immunofluorescence staining and whole-slide scanning. Single cell-based segmentation was carried out in QuPath. Specimens were analyzed with the endpoints clustering and interactions between CTL, normoxic, and hypoxic tumor areas, both visually and using spatial statistical tools implemented in the R package Spatstat. (3) Results: Visual assessment suggested clustering of CTL in all instances. The visual analysis also suggested an inhibitory effect between hypoxic tumor areas and CTL in a minority of the whole-slide scans (9 of 22, 41%). Conversely, the objective mathematical analysis in Spatstat demonstrated statistically significant inhibitory interactions between hypoxia and CTL accumulation in a substantially higher number of specimens (16 of 22, 73%). It showed a similar trend in all but one of the remaining samples. (4) Conclusion: Our findings provide non-obvious but statistically rigorous evidence of inhibition of CTL infiltration into hypoxic tumor subregions of cancers of the head and neck. Importantly, these shielded sites may be the origin of tumor recurrences. We provide the methodology for the transfer of our statistical approach to similar questions. We discuss why versions of the Kcross and pcf.cross functions may be the methods of choice among the repertoire of statistical tests in Spatstat for this type of analysis