A Triclustering Approach for Time Evolving Graphs

This paper introduces a novel technique to track structures in time evolving graphs. The method is based on a parameter free approach for three-dimensional co-clustering of the source vertices, the target vertices and the time. All these features are simultaneously segmented in order to build time segments and clusters of vertices whose edge distributions are similar and evolve in the same way over the time segments. The main novelty of this approach lies in that the time segments are directly inferred from the evolution of the edge distribution between the vertices, thus not requiring the user to make an a priori discretization. Experiments conducted on a synthetic dataset illustrate the good behaviour of the technique, and a study of a real-life dataset shows the potential of the proposed approach for exploratory data analysis

Graph-based approaches to word sense induction

This thesis is a study of Word Sense Induction (WSI), the Natural Language Processing (NLP) task of automatically discovering word meanings from text. WSI is an open problem in NLP whose solution would be of considerable benefit to many other NLP tasks. It has, however, has been studied by relatively few NLP researchers and often in set ways. Scope therefore exists to apply novel methods to the problem, methods that may improve upon those previously applied. This thesis applies a graph-theoretic approach to WSI. In this approach, word senses are identifed by finding particular types of subgraphs in word co-occurrence graphs. A number of original methods for constructing, analysing, and partitioning graphs are introduced, with these methods then incorporated into graphbased WSI systems. These systems are then shown, in a variety of evaluation scenarios, to return results that are comparable to those of the current best performing WSI systems. The main contributions of the thesis are a novel parameter-free soft clustering algorithm that runs in time linear in the number of edges in the input graph, and novel generalisations of the clustering coeficient (a measure of vertex cohesion in graphs) to the weighted case. Further contributions of the thesis include: a review of graph-based WSI systems that have been proposed in the literature; analysis of the methodologies applied in these systems; analysis of the metrics used to evaluate WSI systems, and empirical evidence to verify the usefulness of each novel method introduced in the thesis for inducing word senses

Controlling and leveraging small-scale information in tomographic galaxy-galaxy lensing

The tangential shear signal receives contributions from physical scales in the galaxy-matter correlation function well below the transverse scale at which it is measured. Since small scales are difficult to model, this non-locality has generally required stringent scale cuts or new statistics for cosmological analyses. Using the fact that uncertainty in these contributions corresponds to an uncertainty in the enclosed projected mass around the lens, we provide an analytic marginalization scheme to account for this. Our approach enables the inclusion of measurements on smaller scales without requiring numerical sampling over extra free parameters. We extend the analytic marginalization formalism to retain cosmographic ("shear-ratio") information from small-scale measurements that would otherwise be removed due to modeling uncertainties, again without requiring the addition of extra sampling parameters. We test the methodology using simulated likelihood analysis of a DES Year 5-like galaxy-galaxy lensing and galaxy clustering datavector. We demonstrate that we can remove parameter biases due to the presence of an un-modeled 1-halo contamination of the galaxy-galaxy lensing signal, and use the shear-ratio information on small scales to improve cosmological parameter constraints.Comment: 10 pages, 5 figure, submitted to MNRAS. Comments welcom

Clustering of Galaxies with f(R) gravity

Based on thermodynamics, we discuss the galactic clustering of expanding Universe by assuming the gravitational interaction through the modified Newton's potential given by $f(R)$ gravity. We compute the corrected $N$-particle partition function analytically. The corrected partition function leads to more exact equations of states of the system. By assuming that system follows quasi-equilibrium, we derive the exact distribution function which exhibits the $f(R)$ correction. Moreover, we evaluate the critical temperature and discuss the stability of the system. We observe the effects of correction of $f(R)$ gravity on the power law behavior of particle-particle correlation function also. In order to check feasibility of an $f(R)$ gravity approach to the clustering of galaxies, we compare our results with an observational galaxy cluster catalog.Comment: 14 pages, 8 figures, 1 table; accepted for publication on MNRA