arXiv subjects

Avalon Campbell-Cousins

Publications and source records attributed to Avalon Campbell-Cousins.

4 recordsLinked to original sources

arXiv2025

Multiplex Nodal Modularity: A novel network metric for the regional analysis of amnestic mild cognitive impairment during a working memory binding task

Modularity is a well-established concept for assessing community structures in various single and multi-layer networks, including those in biological and social domains. Brain networks are known to exhibit community structure at local, meso, and global scale. However, modularity is limited as a metric to a global scale describing the overall strength of community structure, overlooking important variations in community structure at node level. To address this limitation, we extended modularity to individual nodes. This novel measure of nodal modularity (nQ) captures both mesoscale and local-scale changes in modularity. We hypothesized that nQ would illuminate granular changes in the brain due to diseases such as Alzheimer's disease (AD), which are known to disrupt the brain's modular structure. We explored nQ in multiplex networks of a visual short-term memory binding task in fMRI and DTI data in the early stages of AD. While limited by sample size, changes in nQ for individual regions of interest (ROIs) in our fMRI networks were predominantly observed in visual, limbic, and paralimbic systems in the brain, aligning with known AD trajectories and linked to amyloid-$β$ and tau deposition. Furthermore, observed changes in white-matter microstructure in our DTI networks in parietal and frontal regions may compliment studies of white-matter integrity in poor memory binders. Additionally, nQ clearly differentiated MCI from MCI converters indicating that nQ may be sensitive to this key turning point of AD. Our findings demonstrate the utility of nQ as a measure of localized group structure, providing novel insights into task and disease-related variability at the node level. Given the widespread application of modularity as a global measure, nQ represents a significant advancement, providing a granular measure of network organization applicable to a wide range of disciplines.

q-bio.NC↗

arXiv2024

Graph Permutation Entropy: Extensions to the Continuous Case, A step towards Ordinal Deep Learning, and More

Nonlinear dynamics play an important role in the analysis of signals. A popular, readily interpretable nonlinear measure is Permutation Entropy. It has recently been extended for the analysis of graph signals, thus providing a framework for non-linear analysis of data sampled on irregular domains. Here, we introduce a continuous version of Permutation Entropy, extend it to the graph domain, and develop a ordinal activation function akin to the one of neural networks. This is a step towards Ordinal Deep Learning, a potentially effective and very recently posited concept. We also formally extend ordinal contrasts to the graph domain. Continuous versions of ordinal contrasts of length 3 are also introduced and their advantage is shown in experiments. We also integrate specific contrasts for the analysis of images and show that it generalizes well to the graph domain allowing a representation of images, represented as graph signals, in a plane similar to the entropy-complexity one. Applications to synthetic data, including fractal patterns and popular non-linear maps, and real-life MRI data show the validity of these novel extensions and potential benefits over the state of the art. By extending very recent concepts related to permutation entropy to the graph domain, we expect to accelerate the development of more graph-based entropy methods to enable nonlinear analysis of a broader kind of data and establishing relationships with emerging ideas in data science.

nlin.CD↗

arXiv2024

Graph-Based Permutation Patterns for the Analysis of Task-Related fMRI Signals on DTI Networks in Mild Cognitive Impairment

Permutation Entropy ($PE$) is a powerful nonlinear analysis technique for univariate time series. Recently, Permutation Entropy for Graph signals ($PEG$) has been proposed to extend PE to data residing on irregular domains. However, $PEG$ is limited as it provides a single value to characterise a whole graph signal. Here, we introduce a novel approach to evaluate graph signals \emph{at the vertex level}: graph-based permutation patterns. Synthetic datasets show the efficacy of our method. We reveal that dynamics in graph signals, undetectable with $PEG$, can be discerned using our graph-based patterns. These are then validated in DTI and fMRI data acquired during a working memory task in mild cognitive impairment, where we explore functional brain signals on structural white matter networks. Our findings suggest that graph-based permutation patterns in individual brain regions change as the disease progresses, demonstrating potential as a method of analyzing graph-signals at a granular scale.

q-bio.NC↗

arXiv2020

Deconstructing Legal Text_Object Oriented Design in Legal Adjudication

Rules are pervasive in the law. In the context of computer engineering, the translation of legal text to algorithmic form is seemingly direct. In large part, law may be a ripe field for expert systems and machine learning. For engineers, existing law appears formulaic and logically reducible to "if, then" statements. The underlying assumption is that the legal language is both self-referential and universal. Moreover, description is considered distinct from interpretation; that in describing the law, the language is seen as quantitative and objectifiable. Nevertheless, is descriptive formal language purely dissociative? From the logic machine of the 1970s to the modern fervor for artificial intelligence (AI), governance by numbers is making a persuasive return. Could translation be possible? The project follows a fundamentally semantic conundrum: what is the significance of "meaning" in legal language? The project, therefore, tests translation by deconstructing sentences from existing legal judgments to their constituent factors. Definitions are then extracted in accordance with the interpretations of the judges. The intent is to build an expert system predicated on alleged rules of legal reasoning. The authors apply both linguistic modelling and natural language processing technology to parse the legal judgments. The project extends beyond prior research in the area, combining a broadly statistical model of context with the relative precision of syntactic structure. The preliminary hypothesis is that, by analyzing the components of legal language with a variety of techniques, we can begin to translate law to numerical form.

cs.IR↗