arXiv subjects

Alexander Campbell

Publications and source records attributed to Alexander Campbell.

12 recordsLinked to original sources

arXiv2026

A convenient model category for bicategories

We introduce and study the model category of flexible $2$-categories, which is Quillen equivalent to Lack's model category of $2$-categories, but enjoys several excellent properties not shared by the latter. In particular, every object of this model category is cofibrant, it is a monoidal model category with respect to its cartesian closed structure, and its full subcategory of fibrant objects is equivalent to the category of bicategories and normal pseudofunctors.

math.CT↗

arXiv2026

Parity complexes redux

We fix the notion of parity complex by a judicious selection from among the axioms originally considered by Street. We show that parity complexes so defined, together with the morphisms of parity complexes defined by Verity, form a category equivalent to the category of strong Steiner complexes (n\'es augmented directed complexes with strongly loop-free unital bases). To this end, we isolate the purely combinatorial structure possessed by the bases of free augmented directed complexes. This analysis reveals the essential advantage of Steiner's formalism to be that the role of subsets in Street's formalism is played instead by multisets.

math.CT↗

arXiv2023

DynDepNet: Learning Time-Varying Dependency Structures from fMRI Data via Dynamic Graph Structure Learning

Graph neural networks (GNNs) have demonstrated success in learning representations of brain graphs derived from functional magnetic resonance imaging (fMRI) data. However, existing GNN methods assume brain graphs are static over time and the graph adjacency matrix is known prior to model training. These assumptions contradict evidence that brain graphs are time-varying with a connectivity structure that depends on the choice of functional connectivity measure. Incorrectly representing fMRI data with noisy brain graphs can adversely affect GNN performance. To address this, we propose DynDepNet, a novel method for learning the optimal time-varying dependency structure of fMRI data induced by downstream prediction tasks. Experiments on real-world fMRI datasets, for the task of sex classification, demonstrate that DynDepNet achieves state-of-the-art results, outperforming the best baseline in terms of accuracy by approximately 8 and 6 percentage points, respectively. Furthermore, analysis of the learned dynamic graphs reveals prediction-related brain regions consistent with existing neuroscience literature.

cs.LG↗

arXiv2023

DBGDGM: Dynamic Brain Graph Deep Generative Model

Graphs are a natural representation of brain activity derived from functional magnetic imaging (fMRI) data. It is well known that clusters of anatomical brain regions, known as functional connectivity networks (FCNs), encode temporal relationships which can serve as useful biomarkers for understanding brain function and dysfunction. Previous works, however, ignore the temporal dynamics of the brain and focus on static graphs. In this paper, we propose a dynamic brain graph deep generative model (DBGDGM) which simultaneously clusters brain regions into temporally evolving communities and learns dynamic unsupervised node embeddings. Specifically, DBGDGM represents brain graph nodes as embeddings sampled from a distribution over communities that evolve over time. We parameterise this community distribution using neural networks that learn from subject and node embeddings as well as past community assignments. Experiments demonstrate DBGDGM outperforms baselines in graph generation, dynamic link prediction, and is comparable for graph classification. Finally, an analysis of the learnt community distributions reveals overlap with known FCNs reported in neuroscience literature.

cs.LG↗

arXiv2021

An investigation of pre-upsampling generative modelling and Generative Adversarial Networks in audio super resolution

There have been several successful deep learning models that perform audio super-resolution. Many of these approaches involve using preprocessed feature extraction which requires a lot of domain-specific signal processing knowledge to implement. Convolutional Neural Networks (CNNs) improved upon this framework by automatically learning filters. An example of a convolutional approach is AudioUNet, which takes inspiration from novel methods of upsampling images. Our paper compares the pre-upsampling AudioUNet to a new generative model that upsamples the signal before using deep learning to transform it into a more believable signal. Based on the EDSR network for image super-resolution, the newly proposed model outperforms UNet with a 20% increase in log spectral distance and a mean opinion score of 4.06 compared to 3.82 for the two times upsampling case. AudioEDSR also has 87% fewer parameters than AudioUNet. How incorporating AudioUNet into a Wasserstein GAN (with gradient penalty) (WGAN-GP) structure can affect training is also explored. Finally the effects artifacting has on the current state of the art is analysed and solutions to this problem are proposed. The methods used in this paper have broad applications to telephony, audio recognition and audio generation tasks.

eess.AS↗

arXiv2021

High Frequency EEG Artifact Detection with Uncertainty via Early Exit Paradigm

Electroencephalography (EEG) is crucial for the monitoring and diagnosis of brain disorders. However, EEG signals suffer from perturbations caused by non-cerebral artifacts limiting their efficacy. Current artifact detection pipelines are resource-hungry and rely heavily on hand-crafted features. Moreover, these pipelines are deterministic in nature, making them unable to capture predictive uncertainty. We propose E4G, a deep learning framework for high frequency EEG artifact detection. Our framework exploits the early exit paradigm, building an implicit ensemble of models capable of capturing uncertainty. We evaluate our approach on the Temple University Hospital EEG Artifact Corpus (v2.0) achieving state-of-the-art classification results. In addition, E4G provides well-calibrated uncertainty metrics comparable to sampling techniques like Monte Carlo dropout in just a single forward pass. E4G opens the door to uncertainty-aware artifact detection supporting clinicians-in-the-loop frameworks.

eess.SP↗

arXiv2020

On truncated quasi-categories

For each $n \geq -1$, a quasi-category is said to be $n$-truncated if its hom-spaces are $(n-1)$-types. In this paper we study the model structure for $n$-truncated quasi-categories, which we prove can be constructed as the Bousfield localisation of Joyal's model structure for quasi-categories with respect to the boundary inclusion of the $(n+2)$-simplex. Furthermore, we prove the expected Quillen equivalences between categories and $1$-truncated quasi-categories and between $n$-truncated quasi-categories and Rezk's $(n,1)$-$Θ$-spaces.

math.CT↗

arXiv2020

A homotopy coherent cellular nerve for bicategories

The subject of this paper is a nerve construction for bicategories introduced by Leinster, which defines a fully faithful functor from the category of bicategories and normal pseudofunctors to the category of presheaves over Joyal's category $Θ_2$. We prove that the nerve of a bicategory is a $2$-quasi-category (a model for $(\infty,2)$-categories due to Ara), and moreover that the nerve functor restricts to the right part of a Quillen equivalence between Lack's model structure for bicategories and a Bousfield localisation of Ara's model structure for $2$-quasi-categories. We deduce that Lack's model structure for bicategories is Quillen equivalent to Rezk's model structure for $(2,2)$-$Θ$-spaces on the category of simplicial presheaves over $Θ_2$. To this end, we construct the homotopy bicategory of a $2$-quasi-category, and prove that a morphism of $2$-quasi-categories is an equivalence if and only if it is essentially surjective on objects and fully faithful. We also prove a Quillen equivalence between Ara's model structure for $2$-quasi-categories and the Hirschowitz--Simpson--Pellissier model structure for quasi-category-enriched Segal categories, from which we deduce a few more results about $2$-quasi-categories, including a conjecture of Ara concerning weak equivalences of $2$-categories.

math.CT↗

arXiv2019

Joyal's cylinder conjecture

For each pair of simplicial sets $A$ and $B$, the category $\mathbf{Cyl}(A,B)$ of cylinders (also called correspondences) from $A$ to $B$ admits a model structure induced from Joyal's model structure for quasi-categories. In this paper, we prove Joyal's conjecture that a cylinder $X \in \mathbf{Cyl}(A,B)$ is fibrant if and only if the canonical morphism $X \longrightarrow A \star B$ is an inner fibration, and that a morphism between fibrant cylinders in $\mathbf{Cyl}(A,B)$ is a fibration if and only if it is an inner fibration. We use this result to give a new proof of a characterisation of covariant equivalences due to Lurie, which avoids the use of the straightening theorem. In an appendix, we introduce a new family of model structures on the slice categories $\mathbf{sSet}/B$, whose fibrant objects are the inner fibrations with codomain $B$, which we use to prove some new results about inner anodyne extensions and inner fibrations.

math.CT↗

arXiv2019

A counterexample in quasi-category theory

We give an example of a morphism of simplicial sets which is a monomorphism, bijective on 0-simplices, and a weak categorical equivalence, but which is not inner anodyne. This answers an open question of Joyal. Furthermore, we use this morphism to refute a plausible description of the class of fibrations in Joyal's model structure for quasi-categories.

math.AT↗

arXiv2018

How strict is strictification?

The subject of this paper is the higher structure of the strictification adjunction, which relates the two fundamental bases of three-dimensional category theory: the $\mathbf{Gray}$-category of $2$-categories and the tricategory of bicategories. We show that -- far from requiring the full weakness provided by the definitions of tricategory theory -- this adjunction can be $\textit{strictly}$ enriched over the symmetric closed multicategory of bicategories defined by Verity. Moreover, we show that this adjunction underlies an adjunction of bicategory-enriched symmetric multicategories. An appendix introduces the symmetric closed multicategory of pseudo double categories, into which Verity's symmetric multicategory of bicategories embeds fully.

math.CT↗

arXiv2018

Skew-enriched categories

This paper introduces a skew variant of the notion of enriched category, suitable for enrichment over a skew-monoidal category, the main novelty of which is that the elements of the enriched hom-objects need not be in bijection with the morphisms of the underlying category. This is the natural setting in which to introduce the notion of locally weak comonad, which is fundamental to the theory of enriched algebraic weak factorisation systems. The equivalence, for a monoidal closed category $\mathcal{V}$, between tensored $\mathcal{V}$-categories and hommed $\mathcal{V}$-actegories is extended to the skew setting and easily proved by recognising both skew $\mathcal{V}$-categories and skew $\mathcal{V}$-actegories as equivalent to special kinds of skew $\mathcal{V}$-proactegory.

math.CT↗