Random Field Induced Order in Low Dimension I

Consider the classical XY model in a weak random external field pointing along the Y axis with strength $\epsilon$. We prove that the model defined on $\Z^3$ with nearest neighbor coupling exhibits residual magnetic order in the horizontal direction for arbitrarily weak random field strengths and, depending on field strength, sufficiently low temperature.Comment: 49 page

The changing Aboriginal and Torres Strait Islander population: evidence from the 2006–11 Australian Census Longitudinal Dataset

Abstract Populations change and grow through time. Keeping track of this change and associated improvements or worsening in outcomes is a key role for statistical agencies and researchers, and is necessary for an informed and evidence-based policy debate. This is no truer than for Aboriginal and Torres Strait Islander Australians (generally referred to as Indigenous Australians throughout the rest of this paper). Despite making up only a small percentage of the total Australian population, Indigenous people are a key focus of policy discussion in Australia, with a number of targets set by government against which progress is evaluated. The release of the Australian Census Longitudinal Dataset (ACLD) by the Australian Bureau of Statistics in the form of aggregate data in late 2013 and individual data in late 2014 provides an opportunity to better understand and evaluate the changing nature of the Indigenous population between 2006 and 2011. For the first time, it is possible to compare the identified Indigenous status for an individual in one year with their identified status in previous years using census data. Furthermore, the ACLD provides the first opportunity to look at the changing socioeconomic circumstances of Indigenous Australians, and compare these circumstances with the rest of the population. This paper provides a summary of such an analysis with the aim of spurring additional research and policy discussion

Localization for Linearly Edge Reinforced Random Walks

We prove that the linearly edge reinforced random walk (LRRW) on any graph with bounded degrees is recurrent for sufficiently small initial weights. In contrast, we show that for non-amenable graphs the LRRW is transient for sufficiently large initial weights, thereby establishing a phase transition for the LRRW on non-amenable graphs. While we rely on the description of the LRRW as a mixture of Markov chains, the proof does not use the magic formula. We also derive analogous results for the vertex reinforced jump process.Comment: 30 page

Improving Video Game Recommendations Using a Hybrid, Neural Network and Keyword Ranking Approach

Recommendations systems are software solutions for finding high-quality and relevant content for a given user type ranging from online shoppers, to music listeners, to video game players. Traditional recommendation systems use user review data to make recommendations, but we still want recommendations to perform well for new users with no review data. Currently, one of the problems that exists in recommendations is poor recommendation accuracy when only a small amount of data exists for a user, called the cold start problem. In this research we investigate solutions for the cold start problem in video game recommendations and we propose a solution that uses a hybrid neural network and keyword ranking approach. We evaluate this system with precision and recall metrics and compare the results to a traditional recommendation system. We present that this hybrid system offers performance gains when recommending to users who have low-medium previous reviews

Genomic analysis of macro- and micro-evolution in the reptilia

Recent advances in high-throughput, genomic sequencing allow unprecedented insight into the evolution of biodiversity. Chapter 1 of this thesis is a phylogenetic study of 1,145 sequenced loci, isolated using a novel high-throughput sequence capture methodology to address the phylogenetic position of turtles within tetrapods. The results reported here unambiguously place turtles as sister to archosaurs and resolve this long-standing question. Chapter 2 investigates the genetic basis of colorful pigmentation in the Green anole (Anolis carolinensis) by sequencing complete transcriptomes from the green dorsal, white ventral and pink dewlap skin. Anoles comprise an adaptive radiation of more than 400 species and color plays a central role in their ecology and evolution, but little is known about the genetic basis of colorful pigmentation in any vertebrate. This study identified 1,719 differentially expressed genes among the three differently colored tissues. Twenty-three of these genes are involved in melanin, pteridine, and carotenoid pigmentation pathways that contribute to the coloration of anole skin. Identifying candidate genes for colorful pigmentation is a significant advance that opens the field for comparative analysis in other taxa. To determine if the genes identified in Chapter 2 are involved in population divergence and speciation, Chapter 3 investigates the complete genomes of twenty individuals from two closely related subspecies of Anolis marmoratus. While the two subspecies differ markedly in pigmentation, this study found few genetic differences between populations except in five regions of the genome, which together contained 447 genes. Of these genes, only two, melanophilin (mlph) and 'cluster of differentiation 36' (cd36), are associated with pigmentation. The intersection of the genes identified in Chapter 2 and Chapter 3 includes both cd36 and mlph, suggesting that both are involved in divergence of coloration. Cd36 is of particular interest because it regulates the uptake of carotenoid pigments and is an important candidate gene contributing to carotenoid pigmentation. Together, this research demonstrates the power of genomic approaches to address fundamental questions in systematics, micro-evolution, and speciation. The findings bolster the emerging field of phylogenomics and broadly impact future research into the genetic basis of coloration in vertebrates

Simple random walk on long-range percolation clusters II: Scaling limits

Supported in part at the Technion by a Landau fellowship. Supported in part by an Alfred Sloan Fellowship in Mathematic