arXiv subjects

Todd Mullen

Publications and source records attributed to Todd Mullen.

5 recordsLinked to original sources

arXiv2023

A statistical significance testing approach for measuring term burstiness with applications to domain-specific terminology extraction

A term in a corpus is said to be ``bursty'' (or overdispersed) when its occurrences are concentrated in few out of many documents. In this paper, we propose Residual Inverse Collection Frequency (RICF), a statistical significance test inspired heuristic for quantifying term burstiness. The chi-squared test is, to our knowledge, the sole test of statistical significance among existing term burstiness measures. Chi-squared test term burstiness scores are computed from the collection frequency statistic (i.e., the proportion that a specified term constitutes in relation to all terms within a corpus). However, the document frequency of a term (i.e., the proportion of documents within a corpus in which a specific term occurs) is exploited by certain other widely used term burstiness measures. RICF addresses this shortcoming of the chi-squared test by virtue of its term burstiness scores systematically incorporating both the collection frequency and document frequency statistics. We evaluate the RICF measure on a domain-specific technical terminology extraction task using the GENIA Term corpus benchmark, which comprises 2,000 annotated biomedical article abstracts. RICF generally outperformed the chi-squared test in terms of precision at k score with percent improvements of 0.00% (P@10), 6.38% (P@50), 6.38% (P@100), 2.27% (P@500), 2.61% (P@1000), and 1.90% (P@5000). Furthermore, RICF performance was competitive with the performances of other well-established measures of term burstiness. Based on these findings, we consider our contributions in this paper as a promising starting point for future exploration in leveraging statistical significance testing in text analysis.

cs.IR↗

arXiv2021

An Analogue of Quasi-Transitivity for Edge-Coloured Graphs

We extend the notion of quasi-transitive orientations of graphs to 2-edge-coloured graphs. By relating quasi-transitive $2$-edge-colourings to an equivalence relation on the edge set of a graph, we classify those graphs that admit a quasi-transitive $2$-edge-colouring. As a contrast to Ghouilá-Houri's classification of quasi-transitively orientable graphs as comparability graphs, we find quasi-transitively $2$-edge-colourable graphs do not admit a forbiddden subgraph characterization. Restricting the problem to comparability graphs, we show that the family of uniquely quasi-transitively orientable comparability graphs is exactly the family of comparabilty graphs that admit no quasi-transitive $2$-edge-colouring.

math.CO↗

arXiv2020

Complete Graphs and Polyominoes

In the chip-firing variant, Diffusion, chips flow from places of high concentration to places of low concentration (or equivalently, from the rich to the poor). We explore this model on complete graphs, determining the number of different ways that chips can be distributed on an unlabelled complete graph and demonstrate connections to polyominoes.

math.CO↗

arXiv2020

Counting Path Configurations in Parallel Diffusion

Parallel Diffusion is a variant of Chip-Firing introduced in 2018 by Duffy et al. In Parallel Diffusion, chips move from places of high concentration to places of low concentration through a discrete-time process. At each time step, every vertex sends a chip to each of its poorer neighbours, allowing for some vertices to perhaps fall into debt (represented by negative stack sizes). In their recent paper, Long and Narayanan proved a conjecture from the original paper by Duffy et al. that every Parallel Diffusion process eventually, after some pre-period, exhibits periodic behaviour. With this result, we are now able to count the number of these periods that exist up to a definition of isomorphism. We determine a recurrence relation for calculating this number for a path of any length. If $T_n$ is the number of configurations with period length 2 that can exist on $P_n$ up to isomorphism and $n$ is an integer greater than 4, we conclude that $T_n = 3T_{n-1} + 2T_{n-2} + T_{n-3} - T_{n-4}$.

math.CO↗

arXiv2020

Diffusion: Quiescence and Perturbation

Originally proposed by Duffy et al., Diffusion is a variant of chip-firing in which chips from flow from places of high concentration to places of low concentration. In the variant, Perturbation Diffusion, the first step involves a "perturbation" in which some number of vertices send chips to each of their respective neighbours even though the rules of Diffusion only permit for chips to be sent from richer vertices to poorer vertices. Perturbation Diffusion allows us to expand our study of Diffusion by asking new questions such as ``Given an initial configuration, which vertices, when perturbed, will return the initial configuration after some number of steps in Diffusion." We give some results in this paper that begin to answer this question in the specific case of every vertex initially having 0 chips. We characterize some of the ways a graph can reach such a state in Perturbation Diffusion before focusing on paths in particular with more specific results.

math.CO↗