This paper proposes the Trajectory-Information Exchange Multi-Bernoulli (T-IEMB) filter to estimate sets of alive and all trajectories in track-before-detect applications with nested superpositional measurements. This measurement model has a nested architecture with two layers. The first layer includes superpositional hidden variables which are then mapped in the second layer to the conditional mean and covariance of the measurement, enabling it to model a broad range of measurement models. This paper also presents a Gaussian implementation of the T-IEMB filter, which performs the update by approximating the conditional moments of the measurement model, a computationally light filtering solution. Simulation results for a non-Gaussian radar-based tracking scenario demonstrate the performance of two Gaussian T-IEMB implementations, which provide improved tracking performance compared to state-of-the-art particle filters for track-before-detect, at a reduced computational cost.

Understanding the confidence with which a machine learning model classifies an input datum is an important, and perhaps under-investigated, concept. In this paper, we propose a new calibration metric, the Entropic Calibration Difference (ECD). Based on existing research in the field of state estimation, specifically target tracking (TT), we show how ECD may be applied to binary classification machine learning models. We describe the relative importance of under- and over-confidence and how they are not conflated in the TT literature. Indeed, our metric distinguishes under- from over-confidence. We consider this important given that algorithms that are under-confident are likely to be 'safer' than algorithms that are over-confident, albeit at the expense of also being over-cautious and so statistically inefficient. We demonstrate how this new metric performs on real and simulated data and compare with other metrics for machine learning model probability calibration, including the Expected Calibration Error (ECE) and its signed counterpart, the Expected Signed Calibration Error (ESCE).

Quantitative proteomics plays a central role in uncovering regulatory mechanisms, identifying disease biomarkers, and guiding the development of precision therapies. These insights are often obtained through complex Bayesian models, whose inference procedures are computationally intensive, especially when applied at scale to biological datasets. This limits the accessibility of advanced modelling techniques needed to fully exploit proteomics data. Although Sequential Monte Carlo (SMC) methods offer a parallelisable alternative to traditional Markov Chain Monte Carlo, their high-performance implementations often rely on specialised hardware, increasing both financial and energy costs. We address these challenges by introducing an opportunistic computing framework for SMC samplers, tailored to the demands of large-scale proteomics inference. Our approach leverages idle compute resources at the University of Liverpool via HTCondor, enabling scalable Bayesian inference without dedicated high-performance computing infrastructure. Central to this framework is a novel Coordinator-Manager-Follower architecture that reduces synchronisation overhead and supports robust operation in heterogeneous, unreliable environments. We evaluate the framework on a realistic proteomics model and show that opportunistic SMC delivers accurate inference with weak scaling, increasing samples generated under a fixed time budget as more resources join. To support adoption, we release CondorSMC, an open-source package for deploying SMC samplers in opportunistic computing environments.

When performing Bayesian inference using Sequential Monte Carlo (SMC) methods, two considerations arise: the accuracy of the posterior approximation and computational efficiency. To address computational demands, Sequential Monte Carlo Squared (SMC^2) is well-suited for high-performance computing (HPC) environments. The design of the proposal distribution within SMC^2 can improve accuracy and exploration of the posterior as poor proposals may lead to high variance in importance weights and particle degeneracy. The Metropolis-Adjusted Langevin Algorithm (MALA) uses gradient information so that particles preferentially explore regions of higher probability. In this paper, we extend this idea by incorporating second-order information, specifically the Hessian of the log-target. While second-order proposals have been explored previously in particle Markov Chain Monte Carlo (p-MCMC) methods, we are the first to introduce them within the SMC^2 framework. Second-order proposals not only use the gradient (first-order derivative), but also the curvature (second-order derivative) of the target distribution. Experimental results on synthetic models highlight the benefits of our approach in terms of step-size selection and posterior approximation accuracy when compared to other proposals.

Bayesian inference with Markov Chain Monte Carlo (MCMC) is challenging when the likelihood function is irregular and expensive to compute. We explore several sampling algorithms that make use of subset evaluations to reduce computational overhead. We adapt the subset samplers for this setting where gradient information is not available or is unreliable. To achieve this, we introduce data-driven proxies in place of Taylor expansions and define a novel computation-cost aware adaptive controller. We undertake an extensive evaluation for a challenging disease modelling task and a configurable task with similar irregularity in the likelihood surface. We find our improved version of Hierarchical Importance with Nested Training Samples (HINTS), with adaptive proposals and a data-driven proxy, obtains the best sampling error in a fixed computational budget. We conclude that subset evaluations can provide cheap and naturally-tempered exploration, while a data-driven proxy can pre-screen proposals successfully in explored regions of the state space. These two elements combine through hierarchical delayed acceptance to achieve efficient, exact sampling.

Particle Filters (PFs) are commonly used Sequential Monte Carlo (SMC) algorithms to process a never-ending stream of measurements relating to a nonlinear non-Gaussian state space model. Fixed-Lag SMC (FL-SMC) is an extension to the PF that allows for re-processing of historic data. FL-SMC is widely flexible, such that it can solve problems that are challenging for standard PFs. However, FL-SMC also inherits the challenges (in terms of maximizing accuracy and efficiency) that can limit PFs' efficacy when using a poor choice of the proposal distribution: this can be especially evident in strongly nonlinear scenarios. One alternative is to employ Sequential Markov Chain Monte Carlo (S-MCMC) methods, for which the literature offers a wider selection of efficient proposal distributions. However, S-MCMC does not inherently have the broad applicability of FL-SMC. In this paper, we present the Fixed-Lag No-U-Turn Sampler, an SMC framework that combines FL-SMC and No-U-Turn Sampler (NUTS), a gradient-based MCMC method. We show that, when compared with several variants of PFs, including one that employs Particle Flow, several variants of FL-SMC, and S-MCMC, our proposed approach provides significant accuracy and efficiency improvements, at the price of a moderate run-time overhead.

Markov Chain Monte Carlo (MCMC) is a method for drawing samples from non-standard probability distributions. Hamiltonian Monte Carlo (HMC) is a popular variant of MCMC that uses gradient information to explore the target distribution. The Sequential Monte Carlo (SMC) sampler is an alternative sampling method which, unlike MCMC, can readily utilise parallel computing architectures. It is typical within SMC literature to target a tempered distribution using a proposal with an accept/reject mechanism. In this letter, we show how the proposal used in the No-U-Turn Sampler (NUTS), an advanced variant of HMC, can be incorporated into an SMC sampler without an accept/reject mechanism. Empirical results show that this can remove the need for tempering and gives rise to accurate estimates being generated in fewer iterations which motivates this technique being deployed on parallel hardware.

By facilitating the generation of samples from arbitrary probability distributions, Markov Chain Monte Carlo (MCMC) is, arguably, the tool for the evaluation of Bayesian inference problems that yield non-standard posterior distributions. In recent years, however, it has become apparent that Sequential Monte Carlo (SMC) samplers have the potential to outperform MCMC in several ways. SMC samplers are better suited to highly parallel computing architectures and also feature various tuning parameters that are not available to MCMC. One such parameter – the 'L-kernel' – is a user-defined probability distribution that can be used to influence the efficiency of the sampler. In the current paper, the authors explain how to derive an expression for the L-kernel that minimises the variance of the estimates realised by an SMC sampler. Various approximation methods are then proposed to aid the implementation of the proposed L-kernel. The improved performance of the resulting algorithm is demonstrated in multiple scenarios. For the examples shown in the current paper, the use of an approximately optimal L-kernel has reduced the variance of the SMC estimates by up to 99 % while also reducing the number of times that resampling was required by between 65% and 70%. Python code and code tests accompanying this manuscript are available through the Github repository https://github.com/plgreenLIRU/SMC_approx_optL.

It has been widely documented that the sampling and resampling steps in particle filters cannot be differentiated. The reparameterisation trick was introduced to allow the sampling step to be reformulated into a differentiable function. We extend the reparameterisation trick to include the stochastic input to resampling therefore limiting the discontinuities in the gradient calculation after this step. Knowing the gradients of the prior and likelihood allows us to run particle Markov Chain Monte Carlo (p-MCMC) and use the No-U-Turn Sampler (NUTS) as the proposal when estimating parameters. We compare the Metropolis-adjusted Langevin algorithm (MALA), Hamiltonian Monte Carlo with different number of steps and NUTS. We consider three state-space models and show that NUTS improves the mixing of the Markov chain and can produce more accurate results in less computational time.

Markov Chain Monte Carlo (MCMC) is a powerful method for drawing samples from non-standard probability distributions and is utilized across many fields and disciplines. Methods such as Metropolis-Adjusted Langevin (MALA) and Hamiltonian Monte Carlo (HMC), which use gradient information to explore the target distribution, are popular variants of MCMC. The Sequential Monte Carlo (SMC) sampler is an alternative sampling method which, unlike MCMC, can readily utilise parallel computing architectures and also has tuning parameters not available to MCMC. One such parameter is the L-kernel which can be used to minimise the variance of the estimates from an SMC sampler. In this letter, we show how the proposal used in the No-U-Turn Sampler (NUTS), an advanced variant of HMC, can be incorporated into an SMC sampler to improve the efficiency of the exploration of the target space. We also show how the SMC sampler can be optimized using both a near-optimal L-kernel and a Hamiltonian proposal

The Transverse Energy Spread Spectrometer (TESS) was designed primarily to study the mean transverse energy spread of electrons emitted from photocathode electron sources at both room and liquid nitrogen temperatures as a function of quantum efficiency through analysis of the photoemission footprint. By reconfiguring the potentials applied to different detector elements, TESS can also be used to measure the mean longitudinal energy spread of photoemitted electrons. Initial plans were to use electrostatic wire meshes as a retarding element which prevents the detection of electrons with insufficient energy to overcome a variable potential barrier. However, this method has proved impractical and a new method has been proposed in which the photocathode bias potential is swept (effectively from a state of no electron emission to full emission) and the emitted photocurrent is then detected by using a photoemitted charge collector. In this article, we present the TESS set-up and analyze this new method to measure the longitudinal energy distribution curve. Experimental results are presented and compared to simulated results by utilising a custom designed tracking code.

Fibre based Optical Beam Loss Monitors (oBLMs) are on-line devices used in-situ to measure losses along a beamline. The technology is based on the detection of Cherenkov radiation, produced inside quartz fibres placed alongside the beampipe, from the interaction of secondary showers generated from losses hitting the vacuum pipe. This contribution presents ongoing developments of an oBLM system installed along the Compact Linear Accelerator for Research and Applications (CLARA). The oBLM system consists of 4 channels which allows for sub-metre loss resolution with two dimensional coverage along the entirety of the beam line, as opposed to conventional localised BLM systems. The system was first commissioned to measure dark current from the injector. The ability of the system to locate longitudinal positions of known beam loss locations has also been measured and has shown excellent agreement. We present measurements acquired from the detector during regular operation and during dedicated beam tests. We also discuss the incorporation of the monitor into the accelerator diagnostics system and its use in assisting accelerator characterisation and performance.

A large part of current research and innovation capacity depends on high quality electron beams. Electron accelerators are found in many applications from cancer therapy, cargo scanners, high energy particle colliders, synchrotron light sources to free electron lasers. Electron beams also offer exciting opportunities for developments at the cutting edge of science, for example on novel accelerating schemes which promise accelerating gradients several orders of magnitude higher than what can be realised with conventional radiofrequency accelerators. Whilst R&D into the optimisation of electron accelerators has been performed over many decades, further improvements are still required so their potential can be fully exploited. This includes studies into advanced instrumentation to yield more precise information about the beam itself, novel simulation tools that model the physics of emission and interaction processes, as well as improved beam generation and shaping schemes to enhance the achievable beam brightness. In the frame of this PhD work, different areas of electron beams and associated technologies have been studied whilst still pertaining to the same question: How can we better understand the generation, control and use of electron beams? The thesis is split into three main sections: After a general introduction to the subject, studies into electron emission and initial beam shaping are covered in chapter 2, before the results from investigations into novel beam loss detection techniques are presented in chapter 3. In any accelerator based light source, maintaining the beam quality is crucial. The electron source itself is a key element that determines the achievable beam quality. A variety of source materials are currently under test across many institutes to better understand emission characteristics and to identify the best materials and optimum preparation methods. Here, one experimental set-up at the Cockcroft Institute has been considered. The Transverse Energy Spread Spectrometer (TESS) apparatus uses electrostatic elements to measure both the transverse and longitudinal energy properties of electron beams generated from photocathodes. This then provides detailed information about the electron emission process and allows optimisation of beam generation schemes. To enhance the understanding of the experimental data, a dedicated particle tracking code has been developed which uses accurate maps obtained from simulation or experiment to represent all electromagnetic fields of the set-up. This code has then been used to study two different techniques to measure the longitudinal energy spread of electrons emitted from gallium arsenide. The first technique was to use a wire mesh as an energy filter which the electrons must pass through, the second was to generate a potential difference between the cathode source and detector system. Experimental results are presented for both techniques and the analysis is supplemented with simulations. Monte Carlo results are in good agreement with experimental data, however, through this analysis it is found that using the meshes as a wire filter may not be an efficient method of measuring the longitudinal energy distribution curve as a result of the potential distribution surrounding the wire meshes. The second method is sufficient to the task however the resolution of the technique may be affected by focusing effects around the meshes. Measurement and detection of beam loss is important for any accelerator as unwanted losses yield reduced beam transmission and cause higher background noise. It is crucial in high energy accelerators where unwanted loss particles could easily damage parts of the accelerator and the experiments. Currently used techniques, however, are often limited in their dynamic range, spatial and time resolution, radiation hardness and can be expensive. A detector based on optical fibres with photodetector readout has been studied as part of this work as a detector for a future electron-positron collider. It can cover large distances at the expense of many smaller localised detectors. The ultimate performance of this detector is strongly affected by the light sensor at the fibre end. This in turn limits the performance to locate beam loss intensity and position and hence ultimately limits the understanding of beam loses along an accelerator. To this end Silicon Photomultipliers have been studied as an advanced light sensor that shows great promise for beam loss applications. Preliminary models are compared to experimental data and it is shown that the detector performance in this application is limited by the finite number of pixels available to fire along with pixel recovery/dead time. Measurements carried out at the CLIC Test Facility at CERN using an optical fibre systems are presented and used to assess the system’s performance to specific beam structures. Several techniques are used to analyses signals recorded by multiple detectors however it is found that the layout of optical fibres, which could not be changed, limited full understanding, however, these results are the basis of later experiments which fully measure the effect of a fibre optic beam loss monitor to different beam structures and additional changes to the set-up, which may aid further tests, are covered.

Wire meshes are used across many disciplines to accelerate and focus charged particles, however, analytical solutions are non-exact and few codes exist which simulate the exact fields around a mesh with physical sizes. A tracking code based in Matlab-Simulink using field maps generated using finite element software has been developed which tracks electrons or ions through electrostatic wire meshes. The fields around such a geometry are presented as an analytical expression using several basic assumptions, however, it is apparent that computational calculations are required to obtain realistic values of electric potential and fields, particularly when multiple wire meshes are deployed. The tracking code is flexible in that any quantitatively describable particle distribution can be used for both electrons and ions as well as other benefits such as ease of export to other programs for analysis. The code is made freely available and physical examples are highlighted where this code could be beneficial for different applications.

Challenges of arbitrary waveform signal detection by SiPM in beam loss monitoring systems 2

Sergey Vinogradov, Lee Devlin, Eduardo Nebot del Busto, Maria Kastriotou, and Carsten P. Welsch a,b Department of Physics, University of Liverpool Liverpool L69 7ZE, United Kingdom Cockcroft Institute of Accelerator Science and Technology Daresbury Sci-Tech, Warrington WA4 4AD, United Kingdom P.N. Lebedev Physical Institute of the Russian Academy of Sciences Leninsky pr. 53, Moscow 119991, Russia CERN CH-1211, Geneve 23, Switzerland E-mail: Sergey.Vinogradov@liverpool.ac.uk, Vin@lebedev.ru

Non–invasive, highly accurate and reliable beam monitors are a desired aim of any beam diagnostics design. Knowledge of beam parameters is essential in fundamental research, industrial or medical applications with varying demands. It’s also extremely critical in the optimization of ion beams used for cancer treatment. Ocular tumour treatment at the Clatterbridge Cancer Centre (CCC) uses a 60 MeV proton beam. Disturbances introduced to a beam by intercepting devices risk affecting its energy and deteriorating the energy spread, thereby limiting the effectiveness of the treatment. The advantageous semi-circular structure of the LHCb Vertex Locator (VELO) detector has been investigated in the QUASAR Group as an interesting option for a noninvasive online beam monitor. The method relies on beam ‘halo’ measurements without disturbing the part of the beam used for treatment. This contribution discusses the measurement method, setup design and integration within the CCC treatment beam line and outlines the preliminary experimental results of the performance of the monitor.