Convergence in a multidimensional randomized Keynesian beauty contest

We study the asymptotics of a Markovian system of $N \geq 3$ particles in $[0,1]^d$ in which, at each step in discrete time, the particle farthest from the current centre of mass is removed and replaced by an independent $U [0,1]^d$ random particle. We show that the limiting configuration contains $N-1$ coincident particles at a random location $\xi_N \in [0,1]^d$. A key tool in the analysis is a Lyapunov function based on the squared radius of gyration (sum of squared distances) of the points. For d=1 we give additional results on the distribution of the limit $\xi_N$, showing, among other things, that it gives positive probability to any nonempty interval subset of $[0,1]$, and giving a reasonably explicit description in the smallest nontrivial case, N=3.Comment: 26 pages, 4 figure

The Crowded Page

The Crowded Page is an Internet-based humanities computing project whose goal is to create data-mining and visualization tools that will allow researchers to map out the intricate connections between the members of artistic and literary communities. In most accounts of literary and art history, a work of art or literature is said to be the product of a single creative mind. In an effort to make visible what is often obscured in traditional histories of art and literature, The Crowded Page seeks to take advantage of the unique capabilities of the digital medium to foreground the ways in which a complex network of friends, editors, neighbors, lovers, and fellow artists and writers informs the creative process

Hearts and Minds: Examining the Evolution of the Egyptian Excerebration and Evisceration Traditions through the IMPACT Mummy Database

Egyptian mummification and funerary rituals were a transformative process, making the deceased a pure being; free of disease, injury, and disfigurements, as well as ethical and moral impurities. Consequently, the features of mummification available to specific categories of individuals hold social and ideological significance. This study refutes long-held classical stereotypes, particularly dogmatic class associations; demonstrates the apocryphal nature of universal heart retention; and expands on the purposes of excerebration and evisceration implied by synthetic and radiological analyses. Features of the embalming traditions, specifically the variable excerebration and evisceration traditions, represented the Egyptian view of death. Fine-grain analyses, through primary imaging data for these traditions, have recently been made possible on a large scale through the development of a radiological mummy database. The IMPACT Radiological Mummy Database is a multi-institutional, collaborative research project devoted to the scientific study of mummified remains through primary data from medical imaging modalities. This first application of IMPACT addresses the evolution of Egyptian excerebration and evisceration, and how suites of features in mummies of differing age, sex, status, and location differ and how they relate to the fate of the recipient’s afterlife and to sociopolitical and ideological changes and interactions

Limiting behaviour of random spatial graphs and asymptotically homogeneous RWRE

We consider several random spatial graphs of the nearest-neighbour type, including the k- nearest neighbours graph, the on-line nearest-neighbour graph, and the minimal directed spanning tree. We study the large sample asymptotic behaviour of the total length of these graphs, with power-weighted edges. We give laws of large numbers and weak convergence results. We evaluate limiting constants explicitly. In Bhatt and Roy's minimal directed spanning tree (MDST) construction on random points in (0,1)(^2)， each point is joined to its nearest neighbour in the south-westerly direction. We show that the limiting total length (with power-weighted egdes) of the edges joined to the origin converges in distribution to a Dickman-type random variable. We also study the length of the longest edge in the MDST. For the total weight of the MDST, we give a weak convergence result. The limiting distribution is given a normal component plus a contribution due to boundary effects, which can be characterized by a fixed point equation. There is a phase transition in the limit law as the weight exponent increases. In the second part of this thesis, we give criteria for ergodicity, transience and null recurrence for the random walk in random environment (RWRE) on z+ = {0,1,2,...}, with reflection at the origin, where the random environment is subject to a vanishing perturbation from the so-called Sinai's regime. Our results complement existing criteria for random walks in random environments and for Markov chains with asymptotically zero drift, and are significantly different to these previously studied cases. Our method is based on a martingale technique 一 the method of Lyapunov functions

Loss of trust: The negative effects of leader discrimination and the mitigating effects of organizational response

This thesis focuses on how perceptions of leader discriminatory behavior influence trust in the leader and, subsequently, attitudes about the organization which the leader represents. This study builds on previous research findings by creating a 2 (discriminatory interaction) X 2 (procedural response) X 2 (distributive response) experimental design model with vignettes that focused a leader\u27s discriminatory or non-discriminatory behaviors and how the organization responds to accusations of such behavior. Participants (N = 293) were recruited from Amazon Mechanical Turk and randomly assigned to read one of the two vignettes describing a supervisor\u27s discriminatory or non-discriminatory behavior. After reporting perceptions shaped by the first vignette, participants were randomly assigned to read one for four possible vignettes that represent the organization\u27s actions and manipulates the procedural justice (whether an investigation was conducted or not) and the actions of the organization as seen as a form of distributive justice (whether the supervisor was fired or not). Results indicate that leader discriminatory behavior reduced trust and that through a trickle up process (Fulmer & Ostroff, 2017) the trust in the leader affected the trust and attraction to the organization that the leader was seen to represent. These impacts are further moderated by perceptions of procedural and distributive justice to any organizational intervention in response to reports of the discriminatory behavior. The actions and inactions of organizations prove to be an important factor in how employees perceive justice in response to perceptions of leader discriminatory behavior --Abstract, page iii