arXiv subjects

Andrew Duncan

Publications and source records attributed to Andrew Duncan.

36 records · Page 2Linked to original sources

arXiv2022

Expanding Accurate Person Recognition to New Altitudes and Ranges: The BRIAR Dataset

Face recognition technology has advanced significantly in recent years due largely to the availability of large and increasingly complex training datasets for use in deep learning models. These datasets, however, typically comprise images scraped from news sites or social media platforms and, therefore, have limited utility in more advanced security, forensics, and military applications. These applications require lower resolution, longer ranges, and elevated viewpoints. To meet these critical needs, we collected and curated the first and second subsets of a large multi-modal biometric dataset designed for use in the research and development (R&D) of biometric recognition technologies under extremely challenging conditions. Thus far, the dataset includes more than 350,000 still images and over 1,300 hours of video footage of approximately 1,000 subjects. To collect this data, we used Nikon DSLR cameras, a variety of commercial surveillance cameras, specialized long-rage R&D cameras, and Group 1 and Group 2 UAV platforms. The goal is to support the development of algorithms capable of accurately recognizing people at ranges up to 1,000 m and from high angles of elevation. These advances will include improvements to the state of the art in face recognition and will support new research in the area of whole-body recognition using methods based on gait and anthropometry. This paper describes methods used to collect and curate the dataset, and the dataset's characteristics at the current stage.

cs.CV↗

arXiv2022

Federated Bayesian Computation via Piecewise Deterministic Markov Processes

When performing Bayesian computations in practice, one is often faced with the challenge that the constituent model components and/or the data are only available in a distributed fashion, e.g. due to privacy concerns or sheer volume. While various methods have been proposed for performing posterior inference in such federated settings, these either make very strong assumptions on the data and/or model or otherwise introduce significant bias when the local posteriors are combined to form an approximation of the target posterior. By leveraging recently developed methods for Markov Chain Monte Carlo (MCMC) based on Piecewise Deterministic Markov Processes (PDMPs), we develop a computation -- and communication -- efficient family of posterior inference algorithms (Fed-PDMC) which provides asymptotically exact approximations of the full posterior over a large class of Bayesian models, allowing heterogenous model and data contributions from each client. We show that communication between clients and the server preserves the privacy of the individual data sources by establishing differential privacy guarantees. We quantify the performance of Fed-PDMC over a class of illustrative analytical case-studies and demonstrate its efficacy on a number of synthetic examples along with realistic Bayesian computation benchmarks.

stat.CO↗

arXiv2022

Density reconstruction from schlieren images through Bayesian nonparametric models

This study proposes a radically alternate approach for extracting quantitative information from schlieren images. The method uses a scaled, derivative enhanced Gaussian process model to obtain true density estimates from two corresponding schlieren images with the knife-edge at horizontal and vertical orientations. We illustrate our approach on schlieren images taken from a wind tunnel sting model, a supersonic aircraft in flight, and a high-order numerical shock tube simulation.

physics.flu-dyn↗

arXiv2022

Grassmann Stein Variational Gradient Descent

Stein variational gradient descent (SVGD) is a deterministic particle inference algorithm that provides an efficient alternative to Markov chain Monte Carlo. However, SVGD has been found to suffer from variance underestimation when the dimensionality of the target distribution is high. Recent developments have advocated projecting both the score function and the data onto real lines to sidestep this issue, although this can severely overestimate the epistemic (model) uncertainty. In this work, we propose Grassmann Stein variational gradient descent (GSVGD) as an alternative approach, which permits projections onto arbitrary dimensional subspaces. Compared with other variants of SVGD that rely on dimensionality reduction, GSVGD updates the projectors simultaneously for the score function and the data, and the optimal projectors are determined through a coupled Grassmann-valued diffusion process which explores favourable subspaces. Both our theoretical and experimental results suggest that GSVGD enjoys efficient state-space exploration in high-dimensional problems that have an intrinsic low-dimensional structure.

stat.ML↗

arXiv2022

Limit groups over coherent right-angled Artin groups

A new class of groups $\mathcal{C}$, containing all coherent RAAGs and all toral relatively hyperbolic groups, is defined. It is shown that, for a group $G$ in the class $\mathcal{C}$, the $\mathbb{Z}[t]$-exponential group $G^{\mathbb{Z}[t]}$ may be constructed as an iterated centraliser extension. Using this fact, it is proved that $G^{\mathbb{Z}[t]}$ is fully residually $G$ (i.e. it has the same universal theory as $G$) and so its finitely generated subgroups are limit groups over $G$. If $\mathbb{G}$ is a coherent RAAG, then the converse also holds - any limit group over $\mathbb{G}$ embeds into $\mathbb{G}^{\mathbb{Z}[t]}$. Moreover, it is proved that limit groups over $\mathbb{G}$ are finitely presented, coherent and CAT$(0)$, so in particular have solvable word and conjugacy problems.

math.GR↗

arXiv2021

Bayesian Mass Averaging in Rigs and Engines

This paper introduces the Bayesian mass average and details its computation. Owing to the complexity of flow in an engine and the limited instrumentation and the precision of the sensor apparatus used, it is difficult to rigorously calculate mass averages. Building upon related work, this paper views any thermodynamic quantity's spatial variation at an axial plane in an engine (or a rig) as a Gaussian random field. In cases where the mass flow rate is constant in the circumferential direction but can be expressed via a polynomial or spline radially, this paper presents an analytical calculation of the Bayesian mass average. In cases where the mass flow rate itself can be expressed as a Gaussian random field, a sampling procedure is presented to calculate the Bayesian mass average. Examples of the calculation of the Bayesian mass average for temperature are presented, including with a real engine case study where velocity profiles are inferred from stagnation pressure measurements.

physics.flu-dyn↗

arXiv2021

Bayesian Assessments of Aeroengine Performance with Transfer Learning

Aeroengine performance is determined by temperature and pressure profiles along various axial stations within an engine. Given limited sensor measurements both along and between axial stations, we require a statistically principled approach to inferring these profiles. In this paper we detail a Bayesian methodology for interpolating the spatial temperature or pressure profile at axial stations within an aeroengine. The profile at any given axial station is represented as a spatial Gaussian random field on an annulus, with circumferential variations modelled using a Fourier basis and radial variations modelled with a squared exponential kernel. This Gaussian random field is extended to ingest data from multiple axial measurement planes, with the aim of transferring information across the planes. To facilitate this type of transfer learning, a novel planar covariance kernel is proposed, with hyperparameters that characterise the correlation between any two measurement planes. In the scenario where precise frequencies comprising the temperature field are unknown, we utilise a sparsity-promoting prior on the frequencies to encourage sparse representations. This easily extends to cases with multiple engine planes whilst accommodating frequency variations between the planes. The main quantity of interest, the spatial area average is readily obtained in closed form. We term this the Bayesian area average and demonstrate how this metric offers far more precise averages than a sector area average -- a widely used area averaging approach. Furthermore, the Bayesian area average naturally decomposes the posterior uncertainty into terms characterising insufficient sampling and sensor measurement error respectively. This too provides a significant improvement over prior standard deviation based uncertainty breakdowns.

cs.CE↗

arXiv2019

Spatial Flow-Field Approximation Using Few Thermodynamic Measurements Part II: Uncertainty Assessments

In this second part of our two-part paper, we provide a detailed, frequentist framework for propagating uncertainties within our multivariate linear least squares model. This permits us to quantify the impact of uncertainties in thermodynamic measurements---arising from calibrations and the data acquisition system---and the correlations therein, along with uncertainties in probe positions. We show how the former has a much larger effect (relatively) than uncertainties in probe placement. We use this non-deterministic framework to demonstrate why the well-worn metric for assessing spatial sampling uncertainty falls short of providing an accurate characterization of the effect of a few spatial measurements. In other words, it does not accurately describe the uncertainty associated with sampling a non-uniform pattern with a few circumferentially scattered rakes. To this end, we argue that our data-centric framework can offer a more rigorous characterization of this uncertainty. Our paper proposes two new uncertainty metrics: one for characterizing spatial sampling uncertainty and another for capturing the impact of measurement imprecision in individual probes. These metrics are rigorously derived in our paper and their ease in computation permits them to be widely adopted by the turbomachinery community for carrying out uncertainty assessments.

stat.AP↗

arXiv2019

Spatial Flow-Field Approximation Using Few Thermodynamic Measurements Part I: Formulation and Area Averaging

Our investigation raises an important question that is of relevance to the wider turbomachinery community: how do we estimate the spatial average of a flow quantity given finite (and sparse) measurements? This paper seeks to advance efforts to answer this question rigorously. In this paper, we develop a regularized multivariate linear regression framework for studying engine temperature measurements. As part of this investigation, we study the temperature measurements obtained from the same axial plane across five different engines yielding a total of 82 data-sets. The five different engines have similar architectures and therefore similar temperature spatial harmonics are expected. Our problem is to estimate the spatial field in engine temperature given a few measurements obtained from thermocouples positioned on a set of rakes. Our motivation for doing so is to understand key engine temperature modes that cannot be captured in a rig or in computational simulations, as the cause of these modes may not be replicated in these simpler environments. To this end, we develop a multivariate linear least squares model with Tikhonov regularization to estimate the 2D temperature spatial field. Our model uses a Fourier expansion in the circumferential direction and a quadratic polynomial expansion in the radial direction. One important component of our modeling framework is the selection of model parameters, i.e. the harmonics in the circumferential direction. A training-testing paradigm is proposed and applied to quantify the harmonics.

stat.AP↗

arXiv2017

Limit theorems for the Zig-Zag process

Markov chain Monte Carlo methods provide an essential tool in statistics for sampling from complex probability distributions. While the standard approach to MCMC involves constructing discrete-time reversible Markov chains whose transition kernel is obtained via the Metropolis- Hastings algorithm, there has been recent interest in alternative schemes based on piecewise deterministic Markov processes (PDMPs). One such approach is based on the Zig-Zag process, introduced in Bierkens and Roberts (2016), which proved to provide a highly scalable sampling scheme for sampling in the big data regime (Bierkens, Fearnhead and Roberts (2016)). In this paper we study the performance of the Zig-Zag sampler, focusing on the one-dimensional case. In particular, we identify conditions under which a Central limit theorem (CLT) holds and characterize the asymptotic variance. Moreover, we study the influence of the switching rate on the diffusivity of the Zig-Zag process by identifying a diffusion limit as the switching rate tends to infinity. Based on our results we compare the performance of the Zig-Zag sampler to existing Monte Carlo methods, both analytically and through simulations.

stat.CO↗

arXiv2015

Hybrid framework for the simulation of stochastic chemical kinetics

Stochasticity plays a fundamental role in various biochemical processes, such as cell regulatory networks and enzyme cascades. Isothermal, well-mixed systems can be modelled as Markov processes, typically simulated using the Gillespie Stochastic Simulation Algorithm (SSA). While easy to implement and exact, the computational cost of using the Gillespie SSA to simulate such systems can become prohibitive as the frequency of reaction events increases. This has motivated numerous coarse-grained schemes, where the "fast" reactions are approximated either using Langevin dynamics or deterministically. While such approaches provide a good approximation when all reactants are abundant, the approximation breaks down when one or more species exist only in small concentrations and the fluctuations arising from the discrete nature of the reactions becomes significant. This is particularly problematic when using such methods to compute statistics of extinction times for chemical species, as well as simulating non-equilibrium systems such as cell-cycle models in which a single species can cycle between abundance and scarcity. In this paper, a hybrid jump-diffusion model for simulating well- mixed stochastic kinetics is derived. It acts as a bridge between the Gillespie SSA and the chemical Langevin equation. For low reactant reactions the underlying behaviour is purely discrete, while purely diffusive when the concentrations of all species is large, with the two different behaviours coexisting in the intermediate region. A bound on the weak error in the classical large volume scaling limit is obtained, and three different numerical discretizations of the jump-diffusion model are described. The benefits of such a formalism are illustrated using computational examples.

q-bio.MN↗

arXiv2015

Orientable and non-orientable genus $n$ Wicks forms over hyperbolic groups

In 1962 M.J. Wicks gave a precise description of the form a commutator could take in a free group or a free product and in 1973 extended this description to cover a product of two squares. Subsequently, lists of "Wicks forms" were found for arbitrary products of commutators and squares in free groups and free products, by Culler, Vdovina and other authors. Here we construct Wicks forms for products of commutators and squares in a hyperbolic group. As applications we give explicit lists of forms for a commutator and for a square, and find bounds on the lengths of conjugating elements required to express a quadratic tuple of elements of a hyperbolic group as a Wicks form.

math.GR↗

arXiv2014

Noise-induced multistability in chemical systems: Discrete vs Continuum modeling

The noisy dynamics of chemical systems is commonly studied using either the chemical master equation (CME) or the chemical Fokker-Planck equation (CFPE). The latter is a continuum approximation of the discrete CME approach. We here show that the CFPE may fail to capture the CME's prediction of noise-induced multistability. In particular we find a simple chemical system for which the CME's marginal probability distribution changes from unimodal to multimodal as the system-size decreases below a critical value, while the CFPE's marginal probability distribution is unimodal for all physically meaningful system sizes.

q-bio.QM↗

arXiv2013

Embeddings between partially commutative groups: two counterexamples

In this note we give two examples of partially commutative subgroups of partially commutative groups. Our examples are counterexamples to the Extension Graph Conjecture and to the Weakly Chordal Conjecture of Kim and Koberda, \cite{KK}. On the other hand we extend the class of partially commutative groups for which it is known that the Extension Graph Conjecture holds, to include those with commutation graph containing no induced $C_4$ or $P_3$. In the process, some new embeddings of surface groups into partially commutative groups emerge.

math.GR↗

arXiv2013

The subgroup membership problem in amalgamated products of finitely generated free groups

Stallings folding theory is modified, using double coset representatives, and to applied to the study of subgroups of amalgamated products of finite rank free groups. As a first application the subgroup membership problem for such groups is shown to be decidable. An algorithm for this problem is constructed and its complexity is analysed. Groups in this class are also shown to possess the Howson property.

math.GR↗

arXiv2012

Cyclic rewriting and conjugacy problems

Cyclic words are equivalence classes of cyclic permutations of ordinary words. When a group is given by a rewriting relation, a rewriting system on cyclic words is induced, which is used to construct algorithms to find minimal length elements of conjugacy classes in the group. These techniques are applied to the universal groups of Stallings pregroups and in particular to free products with amalgamation, HNN-extensions and virtually free groups, to yield simple and intuitive algorithms and proofs of conjugacy criteria.

math.GR↗

arXiv2008

Square free words as products of commutators

Elements of the commutator subgroup of a free group can be presented as values of canonical forms, called Wicks forms. We show that, starting from sufficiently high genus g, there is a sequence of words w(g) which can be presented by f(g) distinct Wicks forms, where f(g)>g!. Moreover we may choose these words w(g) to be square free.

math.GR↗

arXiv2002

Word Hyperbolic Semigroups

The study of word hyperbolic groups is a prominent topic in geometric group theory; however word hyperbolic groups are defined by a geometric condition which does not extend naturally to semigroups. We propose a linguistic definition. Roughly speaking a semigroup is word hyperbolic if its multiplication table is a context free language. For groups this definition is equivalent to the original geometric one. We also briefly consider word problems of semigroups.

math.GR↗