arXiv subjects

Robin Evans

Publications and source records attributed to Robin Evans.

At least 19 recordsLinked to original sources

arXiv2026

Beam Squinting Effects in Super Wideband Communication Systems

Beam squint, the frequency-dependent shift of the main beam, poses a major challenge for wideband antenna arrays. This paper focuses on the beam squint effects in super wideband (SW) systems, where high mutual coupling (MC) effects are present. These high MC effects complicate beamforming (BF) by creating frequency-dependent phase relationships that invalidate conventional approaches. To accurately model MC effects, this paper uses a circuit-theoretic framework for tightly coupled SW uniform linear arrays (ULAs). We derive closed-form expressions for the average received signal-to-noise ratio (SNR) with BF in conventional half-wavelength spaced, weakly coupled arrays and validate them. Extending our analysis to tightly coupled SW arrays, we demonstrate that, in contrast to conventional weakly coupled arrays, the effective true time delays exhibit a nonlinear dependence on frequency due to coupling-induced phase shifts. A comparative analysis reveals that strong MC in SW arrays significantly reduces squint in phase-controlled BF, extending the usable bandwidth considerably.

eess.SP↗

arXiv2026

MCAnalysis: An Open-Source Package for Preprocessing, Modelling, and Visualisation of Menstrual Cycle Effects in Digital Health Data

The menstrual cycle influences numerous physiological and psychological outcomes, yet standardised, open-source statistical methods for quantifying these cyclic effects remain lacking. We developed mcanalysis, an open-source package in R and Python implementing a Fourier-basis generalised additive model (GAM) for menstrual cycle research. The package provides a complete pipeline: processing period dates, labelling cycle days relative to menstruation onset, filtering physiologically plausible cycles, normalising outcomes to individual means, fitting cyclic GAMs with bootstrap confidence intervals, and identifying turning points to generate phase-specific linear trend estimates. We demonstrate the package on 15 wearable and self-reported outcomes using data from the Juli chronic health management application (N = 2,816 users). Nine of 15 outcomes showed evidence of association with the menstrual cycle (p < 0.05), spanning physiological (HRV p < 0.001, oxygen saturation p = 0.002), sleep (p = 0.003), symptom (migraine p < 0.001, headache p = 0.005), mood (EMA mood p = 0.024, PHQ-8 lack of energy p = 0.008, mania p = 0.041), and activity (hours outside p = 0.019) domains. No tested confounders were significantly associated with cycle-normalised outcomes. mcanalysis provides a standardised, reproducible approach to menstrual cycle analysis for users at all levels of statistical expertise. The package is freely available at https://github.com/kyradelray/mcanalysis, with a no-code web interface at https://kyradelray.shinyapps.io/mcanalysis/.

stat.AP↗

arXiv2025

Dynamic Length FSK Waveforms for Joint Communications and Radar

Motivated by the constant modulus property of frequency shift keying (FSK) based waveforms and the stabilisation of its radar performance with an increase in the number of subpulses, in this paper an FSK-based dynamic subpulse number joint communications and radar waveform design is proposed. From a communications point of view, the system operates based on traditional FSK modulation. From a sensing point of view, although the subpulses are continuously generated and transmitted, radar waveforms are dynamically formed by monitoring the flatness of the spectrum which in turn guarantees the accuracy of the delay estimation. Other constraints on the waveform length are used to ensure satisfactory values of the root mean square time duration, ambiguity function sidelobe levels and prevent overly long waveforms. To provide an estimation of the probability of generating extremely long waveforms, the distribution of the number of subpulses is approximated using a Brownian motion process and an existing result on its one-sided exit density. Numerical examples are provided to evaluate the accuracy of the approximate distribution, as well as the ambiguity function sidelobe levels and the delay and Doppler shift estimation performance of the transmitted waveforms.

eess.SP↗

arXiv2025

Using Gaussian Mixtures to Model Evolving Multi-Modal Beliefs Across Social Media

We use Gaussian mixtures to model formation and evolution of multi-modal beliefs and opinion uncertainty across social networks. In this model, opinions evolve by Bayesian belief update when incorporating exogenous factors (signals from outside sources, e.g., news articles) and by non-Bayesian mixing dynamics when incorporating endogenous factors (interactions across social media). The modeling enables capturing the richness of behavior observed in multi-modal opinion dynamics while maintaining interpretability and simplicity of scalar models. We present preliminary results on opinion formation and uncertainty to investigate the effect of stubborn individuals (as social influencers). This leads to a notion of centrality based on the ease with which an individual can disrupt the flow of information across the social network.

eess.SY↗

arXiv2025

How trust networks shape students' opinions about the proficiency of artificially intelligent assistants

The rising use of educational tools controlled by artificial intelligence (AI) has provoked a debate about their proficiency. While intrinsic proficiency, especially in tasks such as grading, has been measured and studied extensively, perceived proficiency remains underexplored. Here it is shown through Monte Carlo multi-agent simulations that trust networks among students influence their perceptions of the proficiency of an AI tool. A probabilistic opinion dynamics model is constructed, in which every student's perceptions are described by a probability density function (PDF), which is updated at every time step through independent, personal observations and peer pressure shaped by trust relationships. It is found that students infer correctly the AI tool's proficiency $\theta_{\rm AI}$ in allies-only networks (i.e.\ high trust networks). AI-avoiders reach asymptotic learning faster than AI-users, and the asymptotic learning time for AI-users decreases as their number increases. However, asymptotic learning is disrupted even by a single partisan, who is stubbornly incorrect in their belief $\theta_{\rm p} \neq \theta_{\rm AI}$, making other students' beliefs vacillate indefinitely between $\theta_{\rm p}$ and $\theta_{\rm AI}$. In opponents-only (low trust) networks, all students reach asymptotic learning, but only a minority infer $\theta_{\rm AI}$ correctly. AI-users have a small advantage over AI-avoiders in reaching the right conclusion. In mixed networks, students may exhibit turbulent nonconvergence and intermittency, or achieve asymptotic learning, depending on the relationships between partisans and AI-users. The educational implications of the results are discussed briefly in the context of designing robust usage policies for AI tools, with an emphasis on the unintended and inequitable consequences which arise sometimes from counterintuitive network effects.

physics.soc-ph↗

arXiv2024

Rician Channel Modelling for Super Wideband MIMO Communications

Recent developments in Multiple-Input-Multiple-Output (MIMO) technology include packing a large number of antenna elements in a compact array to access the bandwidth benefits provided by higher mutual coupling (MC). The resulting super-wideband (SW) systems require a circuit-theoretic framework to handle the MC and channel models which span extremely large bands. Hence, in this paper, we make two key contributions. First, we develop a physically-consistent Rician channel model for use with SW systems. Secondly, we express the circuit-theoretic models in terms of a standard MIMO model, so that insights into the effects of antenna layouts, MC, and bandwidth can be made using standard communication theory. For example, we show the bandwidth widening resulting from the new channel model. In addition, we show that MC distorts line-of-sight paths which has beamforming implications. We also highlight the interaction between spatial correlation and MC and show that tight coupling reduces spatial correlations at low frequencies.

cs.IT↗

arXiv2024

A fast score-based search algorithm for maximal ancestral graphs using entropy

\emph{Maximal ancestral graph} (MAGs) is a class of graphical model that extend the famous \emph{directed acyclic graph} in the presence of latent confounders. Most score-based approaches to learn the unknown MAG from empirical data rely on BIC score which suffers from instability and heavy computations. We propose to use the framework of imsets \citep{studeny2006probabilistic} to score MAGs using empirical entropy estimation and the newly proposed \emph{refined Markov property} \citep{hu2023towards}. Our graphical search procedure is similar to \citet{claassen2022greedy} but improved from our theoretical results. We show that our search algorithm is polynomial in number of nodes by restricting degree, maximal head size and number of discriminating paths. In simulated experiment, our algorithm shows superior performance compared to other state of art MAG learning algorithms.

stat.ML↗

arXiv2022

Towards standard imsets for maximal ancestral graphs

The imsets of Studen\'y (2005) are an algebraic method for representing conditional independence models. They have many attractive properties when applied to such models, and they are particularly nice for working with directed acyclic graph (DAG) models. In particular, the 'standard' imset for a DAG is in one-to-one correspondence with the independences it induces, and hence is a label for its Markov equivalence class. We first present a proposed extension to standard imsets for maximal ancestral graph (MAG) models, using the parameterizing set representation of Hu and Evans (2020). In these cases the imset provides a scoring criteria by measuring the discrepancy for a list of independences that define the model; this gives an alternative to the usual BIC score that is also consistent, and much easier to compute. We also show that, of independence models that do represent the MAG, the imset we give is minimal. Unfortunately, for some graphs the representation does not represent all the independences in the model, and in certain cases does not represent any at all. For these general MAGs, we refine the reduced ordered local Markov property Richardson (2003) by a novel graphical tool called _power DAGs_, and this results in an imset that induces the correct model and which, under a mild condition, can be constructed in polynomial time.

stat.ME↗

arXiv2022

Selection, Ignorability and Challenges With Causal Fairness

In this paper we look at popular fairness methods that use causal counterfactuals. These methods capture the intuitive notion that a prediction is fair if it coincides with the prediction that would have been made if someone's race, gender or religion were counterfactually different. In order to achieve this, we must have causal models that are able to capture what someone would be like if we were to counterfactually change these traits. However, we argue that any model that can do this must lie outside the particularly well behaved class that is commonly considered in the fairness literature. This is because in fairness settings, models in this class entail a particularly strong causal assumption, normally only seen in a randomised controlled trial. We argue that in general this is unlikely to hold. Furthermore, we show in many cases it can be explicitly rejected due to the fact that samples are selected from a wider population. We show this creates difficulties for counterfactual fairness as well as for the application of more general causal fairness methods.

stat.ML↗

arXiv2022

Continuous gravitational waves in the lab: recovering audio signals with a table-top optical microphone

Gravitational-wave observatories around the world are searching for continuous waves: persistent signals from sources such as spinning neutron stars. These searches use sophisticated statistical techniques to look for weak signals in noisy data. In this paper, we demonstrate these techniques using a table-top model gravitational-wave detector: a Michelson interferometer where sound is used as an analog for gravitational waves. Using signal processing techniques from continuous-wave searches, we demonstrate the recovery of tones with constant and wandering frequencies. We also explore the use of the interferometer as a teaching tool for educators in physics and electrical engineering by using it as an "optical microphone" to capture music and speech. A range of filtering techniques used to recover signals from noisy data are detailed in the Supplementary Material. Here, we present highlights of our results using a combined notch plus Wiener filter and the statistical log minimum mean-square error (logMMSE) estimator. Using these techniques, we easily recover recordings of simple chords and drums, but complex music and speech are more challenging. This demonstration can be used by educators in undergraduate laboratories and can be adapted for communicating gravitational-wave and signal-processing topics to non-specialist audiences.

gr-qc↗

arXiv2021

Combined Radar and Communications with Phase-Modulated Frequency Permutations

This paper focuses on the combined radar and communications problem and conducts a thorough analytical investigation on the effect of phase and frequency change on the communication and sensing functionality. First, we consider the classical stepped frequency radar waveform and modulate data using M-ary phase shift keying (MPSK). Two important analytical tools in radar waveform design, namely the ambiguity function (AF) and the Fisher information matrix (FIM) are derived, based on which, we make the important conclusion that MPSK modulation has a negligible effect on radar local accuracy. Next, we extend the analysis to incorporate frequency permutations and propose a new signalling scheme in which the mapping between incoming data and waveforms is performed based on an efficient combinatorial transform called the Lehmer code. We also provide an efficient communications receiver based on the Hungarian algorithm. From the communications perspective, we consider the optimal maximum likelihood (ML) detector and derive the union bound and nearest neighbour approximation on the block error probability. From the radar sensing perspective, we discuss the broader structure of the waveform based on the AF derivation and quantify the radar local accuracy based on the FIM. Extensive numerical examples are provided to illustrate the accuracy of our results.

cs.IT↗

arXiv2021

Frequency Permutations for Joint Radar and Communications

This paper presents a new joint radar and communication technique based on the classical stepped frequency radar waveform. The randomization in the waveform, which is achieved by using permutations of the sequence of frequency tones, is utilized for data transmission. A new signaling scheme is proposed in which the mapping between incoming data and waveforms is performed based on an efficient combinatorial transform called the Lehmer code. Considering the optimum maximum likelihood (ML) detection, the union bound and the nearest neighbour approximation on the communication block error probability is derived for communication in an additive white Gaussian noise (AWGN) channel. The results are further extended to incorporate the Rician fading channel model, of which the Rayleigh fading channel model is presented as a special case. Furthermore, an efficient communication receiver implementation is discussed based on the Hungarian algorithm which achieves optimum performance with much less operational complexity when compared to an exhaustive search. From the radar perspective, two key analytical tools, namely, the ambiguity function (AF) and the Fisher information matrix are derived. Furthermore, accurate approximations to the Cramer-Rao lower bounds (CRLBs) on the delay and Doppler estimation errors are derived based on which the range and velocity estimation accuracy of the waveform is analysed. Numerical examples are used to highlight the accuracy of the analysis and to illustrate the performance of the proposed waveform.

cs.IT↗

arXiv2020

Faster algorithms for Markov equivalence

Maximal ancestral graphs (MAGs) have many desirable properties; in particular they can fully describe conditional independences from directed acyclic graphs (DAGs) in the presence of latent and selection variables. However, different MAGs may encode the same conditional independences, and are said to be \emph{Markov equivalent}. Thus identifying necessary and sufficient conditions for equivalence is essential for structure learning. Several criteria for this already exist, but in this paper we give a new non-parametric characterization in terms of the heads and tails that arise in the parameterization for discrete models. We also provide a polynomial time algorithm ($O(ne^{2})$, where $n$ and $e$ are the number of vertices and edges respectively) to verify equivalence. Moreover, we extend our criterion to ADMGs and summary graphs and propose an algorithm that converts an ADMG or summary graph to an equivalent MAG in polynomial time ($O(n^{2}e)$). Hence by combining both algorithms, we can also verify equivalence between two summary graphs or ADMGs.

math.CO↗

arXiv2019

Ground-Based Gravitational-Wave Astronomy in Australia: 2019 White Paper

The past four years have seen a scientific revolution through the birth of a new field: gravitational-wave astronomy. The first detection of gravitational waves---recognised by the 2017 Nobel Prize in Physics---provided unprecedented tests of general relativity while unveiling a previously unknown class of massive black holes, thirty times more massive than the Sun. The subsequent detection of gravitational waves from a merging binary neutron star confirmed the hypothesised connection between binary neutron stars and short gamma-ray bursts while providing an independent measurement of the expansion of the Universe. The discovery enabled precision measurement of the speed of gravity while shedding light on the origin of heavy elements. At the time of writing, the Laser Interferometer Gravitational-wave Observatory (LIGO) and its European partner, Virgo, have published the detection of eleven gravitational-wave events. New, not-yet-published detections are announced on a nearly weekly basis. This fast-growing catalogue of gravitational-wave transients is expected to yield insights into a number of topics, from the equation of state of matter at supra-nuclear densities to the fate of massive stars. The science potential of 3G observatories is enormous, enabling measurements of gravitational waves from the edge of the Universe and precise determination of the neutron star equation of state. Australia is well-positioned to help develop the required technology. The Mid-term Review for the Decadal plan for Australian astronomy 2016-2025 should consider investment in a scoping study for an Australian Gravitational-Wave Pathfinder that develops and validates core technologies required for the global 3G detector network.

astro-ph.IM↗

arXiv2019

Identifying Cognitive Radars -- Inverse Reinforcement Learning using Revealed Preferences

We consider an inverse reinforcement learning problem involving us versus an enemy radar equipped with a Bayesian tracker. By observing the emissions of the enemy radar,how can we identify if the radar is cognitive (constrained utility maximizer)? Given the observed sequence of actions taken by the enemy's radar, we consider three problems: (i) Are the enemy radar's actions (waveform choice, beam scheduling) consistent with constrained utility maximization? If so how can we estimate the cognitive radar's utility function that is consistent with its actions. We formulate and solve the problem in terms of the spectra (eigenvalues) of the state and observation noise covariance matrices, and the algebraic Riccati equation. (ii) How to construct a statistical test for detecting a cognitive radar (constrained utility maximization) when we observe the radar's actions in noise or the radar observes our probe signal in noise? We propose a statistical detector with a tight Type-II error bound. (iii) How can we optimally probe (interrogate) the enemy's radar by choosing our state to minimize the Type-II error of detecting if the radar is deploying an economic rational strategy, subject to a constraint on the Type-I detection error? We present a stochastic optimization algorithm to optimize our probe signal. The main analysis framework used in this paper is that of revealed preferences from microeconomics.

eess.SP↗

arXiv2019

Algebraic Properties of Gaussian HTC-identifiable Graphs

In this paper, we explore some algebraic properties of linear structural equation modelsthat can be represented by an HTC-identifiable graph. In particular, we prove that all mixedgraphs are HTC-identifiable if and only if all the regression coefficients can be recovered fromthe covariance matrix using straightforward linear algebra operations. We also find a set ofpolynomials that generates the ideal that encompasses all the equality constraints of the modelon the cone of positive definite matrices. We further prove that this set of polynomials are theminimal generators of said ideal for a subset of HTC-identifiable graphs.

math.ST↗

arXiv2017

Maximum likelihood estimation of the Latent Class Model through model boundary decomposition

The Expectation-Maximization (EM) algorithm is routinely used for the maximum likelihood estimation in the latent class analysis. However, the EM algorithm comes with no guarantees of reaching the global optimum. We study the geometry of the latent class model in order to understand the behavior of the maximum likelihood estimator. In particular, we characterize the boundary stratification of the binary latent class model with a binary hidden variable. For small models, such as for three binary observed variables, we show that this stratification allows exact computation of the maximum likelihood estimator. In this case we use simulations to study the maximum likelihood estimation attraction basins of the various strata. Our theoretical study is complemented with a careful analysis of the EM fixed point ideal which provides an alternative method of studying the boundary stratification and maximizing the likelihood function. In particular, we compute the minimal primes of this ideal in the case of a binary latent class model with a binary or ternary hidden random variable.

math.ST↗

arXiv2016

Convergence Analysis of Quantized Primal-dual Algorithm in Network Utility Maximization Problems

This paper investigates the asymptotic and non-asymptotic behavior of the quantized primal dual algorithm in network utility maximization problems, in which a group of agents maximize the sum of their individual concave objective functions under linear constraints. In the asymptotic scenario, we use the information theoretic notion of differential entropy power to establish universal lower bounds on the exponential convergence rates of joint primal dual, primal and dual variables under optimum achieving quantization schemes. These results provide trade offs between the speed of exponential convergence, the agents objective functions, the communication bit rates, and the number of agents and constraints. In the non-asymptotic scenario, we obtain lower bounds on the mean square distance of joint primal dual, primal and dual variables from the optimal solution for any finite time instance. These bounds hold regardless of the quantization scheme used.

math.OC↗