arXiv subjects

Jason Brown

Publications and source records attributed to Jason Brown.

At least 19 recordsLinked to original sources

arXiv2026

Come Together: Analyzing Popular Songs Through Statistical Embeddings

Statistical modeling of popular music presents a unique challenge due to the complexity of song structures, which cannot be easily analyzed using conventional statistical tools. However, recent advances in data science have shown that converting non-standard data objects into real vector-valued embeddings enables meaningful statistical analysis. In this work, we demonstrate an approach based on logistic principal component analysis to construct embeddings from global song features, allowing for standard multivariate analysis. We apply this method to a corpus of Lennon and McCartney songs from 1962-1966, using embeddings derived from chords, melodic notes, chord and pitch transitions, and melodic contours. Our analysis explores how these song embeddings cluster by Beatles album, how songwriting styles evolved over time, and whether Lennon and McCartney's compositions exhibited convergence or divergence. This embedding-based approach offers a powerful framework for statistically examining musical structure and stylistic development in popular music.

stat.AP↗

arXiv2025

Comparing loose bimodules and double barrels using pseudo-models of enhanced sketches

(Pseudo) double categories have two sorts of morphisms: tight ones which compose strictly, and loose ones which compose up to coherent isomorphism. In this paper, we consider bimodules between double categories in the loose direction. We provide two formulation of this concept -- first as pseudo-bimodules between pseudo-categories in the 2-category of categories, and second as double barrels generalizing Joyal's definition of bimodules between categories as functors into the walking arrow -- and prove these two formulations equivalent. In order to prove this equivalence, we define a notion of \emph{pseudo-model} of an enhanced sketch, which may be of independent interest. We then consider some double category theory unlocked by the theory of loose bimodules: loose adjunctions, and loose limits.

math.CT↗

arXiv2025

Exploring Gaps in the APS: Direct Minimal Pair Analysis in LLM Syntactic Assessments

Recent studies probing the Argument from the Poverty of the Stimulus (APS) have applied Large Language Models (LLMs) to test the learnability of complex syntax through surprisal-based metrics. However, divergent conclusions raise questions concerning the insights these metrics offer. While Wilcox et al. (2024) used direct minimal pair comparisons (the "wh-effect") to demonstrate that models successfully generalise knowledge of filler-gap dependencies, Lan et al. (2024) used a Difference-in-Differences (DiD) metric and found that models largely fail on parasitic gaps (PGs). This paper argues that the direct minimal pair approach offers greater diagnostic transparency. We demonstrate this by generating a full 8-permutation paradigm of refined PG stimuli and evaluating the GPT-2 model used in previous studies with a systematic Wilcox-style wh-effect analysis. Our results show that GPT-2 succeeds across all four tested conditions, indicating robust knowledge of filler-gap licensing principles even in complex PG environments. This finding, which contrasts with the more ambiguous results from DiD-style metrics, suggests that the choice of evaluation metric is critical for assessing an LLM's syntactic competence.

cs.CL↗

arXiv2025

Evaluating The Impact of Stimulus Quality in Investigations of LLM Language Performance

Recent studies employing Large Language Models (LLMs) to test the Argument from the Poverty of the Stimulus (APS) have yielded contrasting results across syntactic phenomena. This paper investigates the hypothesis that characteristics of the stimuli used in recent studies, including lexical ambiguities and structural complexities, may confound model performance. A methodology is proposed for re-evaluating LLM competence on syntactic prediction, focusing on GPT-2. This involves: 1) establishing a baseline on previously used (both filtered and unfiltered) stimuli, and 2) generating a new, refined dataset using a state-of-the-art (SOTA) generative LLM (Gemini 2.5 Pro Preview) guided by linguistically-informed templates designed to mitigate identified confounds. Our preliminary findings indicate that GPT-2 demonstrates notably improved performance on these refined PG stimuli compared to baselines, suggesting that stimulus quality significantly influences outcomes in surprisal-based evaluations of LLM syntactic competency.

cs.CL↗

arXiv2025

Biological Processing Units: Leveraging an Insect Connectome to Pioneer Biofidelic Neural Architectures

The complete connectome of the Drosophila larva brain offers a unique opportunity to investigate whether biologically evolved circuits can support artificial intelligence. We convert this wiring diagram into a Biological Processing Unit (BPU), a fixed recurrent network derived directly from synaptic connectivity. Despite its modest size 3,000 neurons and 65,000 weights between them), the unmodified BPU achieves 98% accuracy on MNIST and 58% on CIFAR-10, surpassing size-matched MLPs. Scaling the BPU via structured connectome expansions further improves CIFAR-10 performance, while modality-specific ablations reveal the uneven contributions of different sensory subsystems. On the ChessBench dataset, a lightweight GNN-BPU model trained on only 10,000 games achieves 60% move accuracy, nearly 10x better than any size transformer. Moreover, CNN-BPU models with ~2M parameters outperform parameter-matched Transformers, and with a depth-6 minimax search at inference, reach 91.7% accuracy, exceeding even a 9M-parameter Transformer baseline. These results demonstrate the potential of biofidelic neural architectures to support complex cognitive tasks and motivate scaling to larger and more intelligent connectomes in future work.

cs.NE↗

arXiv2024

GLL: A Differentiable Graph Learning Layer for Neural Networks

Standard deep learning architectures used for classification generate label predictions with a projection head and softmax activation function. Although successful, these methods fail to leverage the relational information between samples for generating label predictions. In recent works, graph-based learning techniques, namely Laplace learning, have been heuristically combined with neural networks for both supervised and semi-supervised learning (SSL) tasks. However, prior works approximate the gradient of the loss function with respect to the graph learning algorithm or decouple the processes; end-to-end integration with neural networks is not achieved. In this work, we derive backpropagation equations, via the adjoint method, for inclusion of a general family of graph learning layers into a neural network. The resulting method, distinct from graph neural networks, allows us to precisely integrate similarity graph construction and graph Laplacian-based label propagation into a neural network layer, replacing a projection head and softmax activation function for general classification task. Our experimental results demonstrate smooth label transitions across data, improved generalization and robustness to adversarial attacks, and improved training dynamics compared to a standard softmax-based approach.

cs.LG↗

arXiv2024

Learning Surface Terrain Classifications from Ground Penetrating Radar

Terrain classification is an important problem for mobile robots operating in extreme environments as it can aid downstream tasks such as autonomous navigation and planning. While RGB cameras are widely used for terrain identification, vision-based methods can suffer due to poor lighting conditions and occlusions. In this paper, we propose the novel use of Ground Penetrating Radar (GPR) for terrain characterization for mobile robot platforms. Our approach leverages machine learning for surface terrain classification from GPR data. We collect a new dataset consisting of four different terrain types, and present qualitative and quantitative results. Our results demonstrate that classification networks can learn terrain categories from GPR signals. Additionally, we integrate our GPR-based classification approach into a multimodal semantic mapping framework to demonstrate a practical use case of GPR for surface terrain classification on mobile robots. Overall, this work extends the usability of GPR sensors deployed on robots to enable terrain classification in addition to GPR's existing scientific use cases.

cs.RO↗

arXiv2023

Holographic imaging of antiferromagnetic domains with in-situ magnetic field

Lensless coherent x-ray imaging techniques have great potential for high-resolution imaging of magnetic systems with a variety of in-situ perturbations. Despite many investigations of ferromagnets, extending these techniques to the study of other magnetic materials, primarily antiferromagnets, is lacking. Here, we demonstrate the first (to our knowledge) study of an antiferromagnet using holographic imaging through the "holography with extended reference by autocorrelation linear differential operation" technique. Energy-dependent contrast with both linearly and circularly polarised x-rays are demonstrated. Antiferromagnetic domains and topological textures are studied in the presence of applied magnetic fields, demonstrating quasi-cyclic domain reconfiguration up to 500 mT.

cond-mat.mes-hall↗

arXiv2021

Maximal Intervals of Decrease and Inflection Points for Node Reliability

The \textit{node reliability} of a graph $G$ is the probability that at least one node is operational and that the operational nodes can all communicate in the subgraph that they induce, given that the edges are perfectly reliable but each node operates independently with probability $p\in[0,1]$. We show that unlike many other notions of graph reliability, the number of maximal intervals of decrease in $[0,1]$ is unbounded, and that there can be arbitrarily many inflection points in the interval as well.

math.CO↗

arXiv2020

Extension to the Beraha-Kahane-Weiss Theorem with Applications

The beautiful Beraha-Kahane-Weiss theorem has found many applications within graph theory, allowing for the determination of the limits of root of graph polynomials in settings as vast as chromatic polynomials, network reliability, and generating polynomials related to independence and domination. Here we extend the class of functions to which the BKW theorem can be applied, and provide some applications in combinatorics.

math.CO↗

arXiv2020

Roots of Two-Terminal Reliability

Assume that the vertices of a graph $G$ are always operational, but the edges of $G$ are operational independently with probability $p \in[0,1]$. For fixed vertices $s$ and $t$, the \emph{two-terminal reliability} of $G$ is the probability that the operational subgraph contains an $(s,t)$-path, while the \emph{all-terminal reliability} of $G$ is the probability that the operational subgraph contains a spanning tree. Both reliabilities are polynomials in $p$, and have very similar behaviour in many respects. However, unlike all-terminal reliability, little is known about the roots of two-reliability polynomials. In a variety of ways, we shall show that the nature and location of the roots of two-terminal reliability polynomials have significantly different properties than those held by roots of the all-terminal reliability.

math.CO↗

arXiv2020

SpaceNet 6: Multi-Sensor All Weather Mapping Dataset

Within the remote sensing domain, a diverse set of acquisition modalities exist, each with their own unique strengths and weaknesses. Yet, most of the current literature and open datasets only deal with electro-optical (optical) data for different detection and segmentation tasks at high spatial resolutions. optical data is often the preferred choice for geospatial applications, but requires clear skies and little cloud cover to work well. Conversely, Synthetic Aperture Radar (SAR) sensors have the unique capability to penetrate clouds and collect during all weather, day and night conditions. Consequently, SAR data are particularly valuable in the quest to aid disaster response, when weather and cloud cover can obstruct traditional optical sensors. Despite all of these advantages, there is little open data available to researchers to explore the effectiveness of SAR for such applications, particularly at very-high spatial resolutions, i.e. <1m Ground Sample Distance (GSD). To address this problem, we present an open Multi-Sensor All Weather Mapping (MSAW) dataset and challenge, which features two collection modalities (both SAR and optical). The dataset and challenge focus on mapping and building footprint extraction using a combination of these data sources. MSAW covers 120 km^2 over multiple overlapping collects and is annotated with over 48,000 unique building footprints labels, enabling the creation and evaluation of mapping algorithms for multi-modal data. We present a baseline and benchmark for building footprint extraction with SAR data and find that state-of-the-art segmentation models pre-trained on optical data, and then trained on SAR (F1 score of 0.21) outperform those trained on SAR data alone (F1 score of 0.135).

eess.IV↗

arXiv2019

Interference mitigation techniques for a dense heterogeneous area network in machine-to-machine communications

With the advent of Machine-to-Machine (M2M) communications, various networking consumer industrial and autonomous systems exchange messages in the real world in order to achieve their objectives. Parts of these systems are comprised of short-range wireless networks in the form of clusters that collectively cover a large geographical area. In these clusters, the nodes that represent the cluster heads need to deal with two types of communications: one is within the cluster and the other is from the cluster to the sink node. As the number of clusters increases, it takes multiple hops for the cluster head to forward data to the sink node, thus resulting in a low packet delivery rate and throughput. To solve this problem, we propose a heterogeneous area network in which the cluster head is equipped with two types of radios: the IEEE 802.15.4 and IEEE 802.11 radios. The former is for the devices within the cluster to communicate, whereas the latter is for the cluster heads to communicate to the sink node. Although the IEEE 802.11 links increase the link capacity, the IEEE 802.11 radio and the IEEE 802.15.4 radio might share the 2.4 GHz unlicensed band, thus giving rise to the inter-network collisions or interference. To tackle this problem and to maintain decent Qualityof-Service (QoS) for the network, we subsequently present two interference mitigation techniques, in which a Blank Burst (BB) period is proposed so that the IEEE 802.15.4 radios can be suspended while the IEEE 802.11 radios are active. Simulation results show the proposed two methods can effectively mitigate the inter-network collisions and are superior to the existing technique, which uses an adaptive aggregation technique to mitigate the inter-network collisions.

cs.NI↗

arXiv2018

On the Stability of Independence Polynomials

The independence polynomial of a graph is the generating polynomial for the number of independent sets of each size, and its roots are called {\em independence roots}. We investigate the stability of such polynomials, that is, conditions under which the roots lie in the left half-plane (all of the real roots of independence polynomial are negative and hence lie in this half-plane). We show stability for all independence polynomials of graphs with independence number at most three, but for larger independence number we show that the independence polynomials can have roots arbitrarily far to the right. We provide families of graphs whose independence polynomials are stable and ones that are not, utilizing various graph operations.

math.CO↗

arXiv2017

The shape of node reliability

Given a graph $G$ whose edges are perfectly reliable and whose nodes each operate independently with probability $p\in[0,1],$ the node reliability of $G$ is the probability that at least one node is operational and that the operational nodes can all communicate in the subgraph that they induce. We study analytic properties of the node reliability on the interval $[0,1]$ including monotonicity, concavity, and fixed points. Our results show a stark contrast between this model of network robustness and models that arise from coherent set systems (including all-terminal, two-terminal and K-terminal reliability).

math.CO↗

arXiv2017

On the roots of all-terminal reliability polynomials

Given a graph $G$ in which each edge fails independently with probability $q\in[0,1],$ the all-terminal reliability of $G$ is the probability that all vertices of $G$ can communicate with one another, that is, the probability that the operational edges span the graph. The all-terminal reliability is a polynomial in $q$ whose roots (all-terminal reliability roots) were conjectured to have modulus at most $1$ by Brown and Colbourn. Royle and Sokal proved the conjecture false, finding roots of modulus larger than $1$ by a slim margin. Here, we present the first nontrivial upper bound on the modulus of any all-terminal reliability root, in terms of the number of vertices of the graph. We also find all-terminal reliability roots of larger modulus than any previously known. Finally, we consider the all-terminal reliability roots of simple graphs; we present the smallest known simple graph with all-terminal reliability roots of modulus greater than $1,$ and we find simple graphs with all-terminal reliability roots of modulus greater than $1$ that have higher edge connectivity than any previously known examples.

math.CO↗

arXiv2016

A note on the real part of complex chromatic roots

A {\em chromatic root} is a root of the chromatic polynomial of a graph. While the real chromatic roots have been extensively studied and well understood, little is known about the {\em real parts} of chromatic roots. It is not difficult to see that the largest real chromatic root of a graph with $n$ vertices is $n-1$, and indeed, it is known that the largest real chromatic root of a graph is at most the tree-width of the graph. Analogous to these facts, it was conjectured in [8] that the real parts of chromatic roots are also bounded above by both $n-1$ and the tree-width of the graph. In this article we show that for all $k\geq 2$ there exist infinitely many graphs $G$ with tree-width $k$ such that $G$ has non-real chromatic roots $z$ with $\Re(z)>k$. We also discuss the weaker conjecture and prove it for graphs $G$ with $\chi(G)\geq n-3$.

math.CO↗

arXiv2016

On the real roots of $\sigma$-Polynomials

The $\sigma$-polynomial is given by $\sigma(G,x) = \sum_{i=\chi(G)}^{n} a_{i}(G)\, x^{i}$, where $a_{i}(G)$ is the number of partitions of the vertices of $G$ into $i$ nonempty independent sets. These polynomials are closely related to chromatic polynomials, as the chromatic polynomial of $G$ is given by $\sum_{i=\chi(G)}^{n} a_{i}(G)\, x(x-1) \cdots (x-(i-1))$. It is known that the closure of the real roots of chromatic polynomials is precisely $\{0,~1\} \bigcup [32/27,\infty)$, with $(-\infty,0)$, $(0,1)$ and $(1,32/27)$ being maximal zero-free intervals for roots of chromatic polynomials. We ask here whether such maximal zero-free intervals exist for $\sigma$-polynomials, and show that the only such interval is $[0,\infty)$ -- that is, the closure of the real roots of $\sigma$-polynomials is $(-\infty,0]$.

math.CO↗