Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

We present a novel statistical method and a prototype computational implementation for estimating the diffusion coefficient from single particle tracking (SPT) data. Our method is based on anchored Brownian motion which is a novel representation that relaxes the restrictions of conventional Brownian motion. Our method is fully developed in Bayesian terms and allows for robust estimation of diffusion coefficient and quantification of the uncertainly propagated from limited data quantity and quality as appropriate for the analysis of live-cell SPT data. We compare our methods with conventional Brownian motion and demonstrate superior performance in estimating the correct value of the diffusion coefficient. Finally, we benchmark our methods with SPT data from in cellulo and in silico experiments.

Interactions between cytosolic biomolecules and the bacterial inner membrane are fundamental to many cellular processes, yet directly measuring their binding kinetics in living cells remains challenging. Conventional two-dimensional single-molecule tracking analyses can be insufficient, particularly when membrane association does not markedly alter the diffusion rate. Here, we present a method to recover membrane interaction kinetics from three-dimensional single-molecule trajectories in rod-shaped bacteria. Using simulated 3D tracking data, we identify membrane-associated motion by quantifying how well short trajectory segments follow the circular curvature of the cell membrane. The resulting measure is further analyzed using a hidden Markov modeling framework, enabling robust discrimination between cytosolic and membrane-bound states and capturing the dynamics of state transitions without requiring diffusion-rate changes or direct colocalization with membrane markers. This work establishes a general framework for extracting membrane interaction kinetics from 3D single-molecule tracking data in live bacteria, and highlights the value of realistic microscopy simulations for quantitative interpretation and systematic bias assessment.

The spatial resolution of optical imaging systems is fundamentally restricted by the diffraction limit. However, in widefield live-cell microscopy, the achievable resolution is further constrained by the specimen motion, which indicates the existence of a fundamental spatio-temporal resolution trade-off between signal accumulation during the full frame integration and the resulting motion blur. To improve the fidelity with which moving objects can be imaged, a quantitative understanding of this spatio-temporal trade-off is necessary. Here, we present a systematic analysis of motion-induced resolution dynamics measured with spectral signal-to-noise ratio (SSNR). We developed a simulation framework which models the image formation of objects undergoing arbitrary motion, to evaluate the degradation of the spatial resolution under translational and rotational dynamics. Our results demonstrate that for translating objects, the spatial resolution is anisotropically reduced as a function of the orientation of the object relative to the motion vector, leading to the spectral signal-to-noise ratio degrading by up to 50% and the resolution by up to 40% for a 90{degrees} change in the motion direction. Furthermore, we show that for rotational motion, conventional radially averaged metrics such as the Fourier Ring Correlation are not able to quantify the effects of angular blur. On the other hand, the SSNR is able to accurately quantify this degradation. These findings underscore the necessity of an object-oriented imaging approach, in which acquisition parameters such as exposure time are tuned to specific biological spatio-temporal characteristics to optimize the trade-off between motion blur and spatial fidelity.

The preferred stride ratio (PSR), defined as the ratio of step length to cadence, is approximately invariant across a wide range of walking speeds in healthy adults but breaks down at slow speeds. The lower speed boundary at which this constancy is broken was estimated by Murakami and Otaka (2017) to be approximately 62 m min-1 ({approx} 1.03 m s-1) on the basis of unstandardised K-means cluster analysis applied to data from 21 healthy adults at five speed conditions. The present report re-examines this estimate using the digitised individual-level scatter of Fig. 1-A and the published group-level statistics of Table 1 of that study, applying three breakpoint estimators in parallel: (i) unstandardised K-means (replicating the original method), (ii) a Gaussian mean-and-variance changepoint estimator, and (iii) a piecewise-linear regression on PSR. Applied directly to the digitised scatter (n = 84 resolved markers from a total of 105; 44 of 44 slow-walk markers, 40 of 61 normal-walk markers), the unstandardised K-means estimator returned 62.0 m min-1, matching the originally reported value to the reported precision; the mean-and-variance changepoint estimator returned 55 m min-1; and the piecewise-linear estimator was numerically unstable on the raw heteroscedastic data. To quantify uncertainty, 5 000 Monte Carlo realisations of synthetic individual-level data were generated from a bivariate truncated-normal model conditioned on the published condition means and standard deviations and on the published within-cluster speed-PSR correlations. The Monte Carlo distributions gave median estimates of 61 m min-1 (95 % MC interval 55-67) for unstandardised K-means, 39 m min-1 (29-53) for the mean-and-variance changepoint estimator, and 35 m min-1 (19-49) for piecewise-linear regression. Under a log-normal sensitivity model the corresponding intervals were 60 [55, 66], 34 [20, 58], and 19 [5, 42] m min-1. The likelihood-based estimator placed the central tendency substantially below 62 m min-1, and its Monte Carlo intervals did not include the original boundary under either marginal-distribution model. An additional robust heteroscedastic segmented profile-likelihood analysis on log-PSR yielded lower Monte Carlo median breakpoints across all model specifications, although the full-variance intervals overlapped the original K-means boundary. The qualitative finding of Murakami and Otaka -- that PSR constancy breaks down at slow walking speeds -- is supported by the present reanalysis. The original 62 m min-1 boundary is reproduced under the unstandardised K-means estimator, where it reflects the location of the largest density gap in the published five-condition speed sampling rather than a formally estimated changepoint; estimators formally designed for changepoint detection localise the joint PSR mean-and-variance transition substantially below this value. O_FIG O_LINKSMALLFIG WIDTH=162 HEIGHT=200 SRC="FIGDIR/small/720900v2_fig1.gif" ALT="Figure 1"> View larger version (41K): org.highwire.dtl.DTLVardef@2bb53dorg.highwire.dtl.DTLVardef@187d9bborg.highwire.dtl.DTLVardef@1e7a6a0org.highwire.dtl.DTLVardef@16c587b_HPS_FORMAT_FIGEXP M_FIG O_FLOATNOFigure 1.C_FLOATNO Reproduction and likelihood-based extension of the boundary reported in Murakami and Otaka [5]. (A) Digitised individual-level scatter from Fig. 1-A of [5] (n = 84 resolved markers from a total of 105: 44 of 44 slow-walk markers and 40 of 61 normal-walk markers). The dashed vertical line marks the value 62.4 m min-1 as drawn in the original figure. (B) PSR variance amplification across the five speed conditions, expressed as Var(PSR)/Var(PSR)Preferred, on a logarithmic vertical axis. (C) Distributions of the breakpoint estimates over N = 5 000 Monte Carlo realisations under the bivariate truncated-normal model with cluster-specific within-cluster correlations: unstandardised K-means (median 61 m min-1), the Gaussian mean-and-variance changepoint estimator (median 39 m min-1), and piecewise-linear regression on PSR (median 35 m min-1). The dashed vertical line marks 62.4 m min-1. (D) Sensitivity of each estimator to the choice of marginal-distribution model (truncated normal vs. log-normal); error bars are 95 % Monte Carlo simulation intervals. (E) PSR mean {+/-} SD across the five speed conditions (Table 1 of [5], height-adjusted). C_FIG O_TBL View this table: org.highwire.dtl.DTLVardef@24fe39org.highwire.dtl.DTLVardef@ae8fdborg.highwire.dtl.DTLVardef@66a473org.highwire.dtl.DTLVardef@b6ad84org.highwire.dtl.DTLVardef@139bca7_HPS_FORMAT_FIGEXP M_TBL O_FLOATNOTable 1.C_FLOATNO O_TABLECAPTIONSource data reproduced from Murakami and Otaka [5], height-adjusted, n = 21 per condition. C_TABLECAPTION C_TBL

Optical microscopy is fundamental to modern life-science research, yet interpreting its results requires precise modelling of point spread functions (PSFs) within complex environments. This manuscript introduces a versatile and efficient approach to wave-optical PSF calculations that extends existing frameworks by incorporating detection PSF modelling through the principle of reciprocity. Accompanying this work is a free MATLAB software package centred on a single, minimalistic core function, PlaneWaveExc.m, which utilizes a plane-wave superposition based on the Richards-Wolf model. Despite its simplicity, the framework accounts for "real-life" complexities such as systemic aberrations, arbitrary amplitude and phase modulations, and stratified media with complex-valued refractive indices. We demonstrate the softwares broad applicability through diverse case studies, including single-molecule imaging, STED microscopy, the segmented aperture of the James Webb Space Telescope, and coherent wide-field iSCAT microscopy. Each example is supported by dedicated scripts to facilitate adaptation for specific research needs.

Uncertainty quantification (UQ) in computational heart models is essential for reliable cardiac digital twins (DTs) in personalized medicine, yet remains challenging. Traditional Monte Carlo and stochastic Galerkin methods often become impractical in the high-dimensional, nonlinear state variable and parameter spaces of cardiac electrophysiology and mechanics. This article introduces a framework for learning a joint probability density over cardiac observables and model parameters, enabling the characterization of statistical dependencies across a large number of variables in patient-specific cardiac DTs. By sampling from this density and conditioning on available data, useful predictive distributions can be constructed, allowing uncertainty to be propagated through the model and quantified in terms of variability. Conditional regression can then be performed directly on this learned density, enabling systematic exploration of interdependencies among observables for both predictive inference and model design. The statistical methodology adopts a geometry-aware generative learning framework, recently introduced by the authors, that decouples the learning of data geometry from sampling. First it identifies a low-dimensional latent representation that captures the intrinsic structure of the data and its multiscale geometric features. A stochastic differential equation is then formulated directly in the low-dimensional latent space to generate samples efficiently; these are subsequently mapped back to the high-dimensional space of cardiac states and parameters through a smooth lifting operator. We demonstrate the approach on a ventricular arrhythmia prediction benchmark, where the learned joint probability density enables the construction of predictive distributions over key parameters (e.g., conductivities, fibrosis patterns) through sampling and conditioning. This enables uncertainty to be propagated and quantified through sampling and conditioning on the learned joint density, with substantially fewer model evaluations than conventional UQ methods.

We introduce a workflow to identify oligomeric structures that are recorded with single-molecule localization microscopy (SMLM) under cryogenic conditions. Typically, these oligomers are assumed to consist of protomers arranged as equilateral two-dimensional polygons and every protomer is labeled with a dye molecule for visualization. Unlike previous work, we consider scenarios in which the sample plane has an unknown orientation relative to the focal plane. Our contribution is a high-precision plane-fitting algorithm to determine the sample plane, combined with geometrical transformations and two circle-fitting algorithms to identify the oligomeric structures. Our simulations on synthetic data demonstrate that the proposed workflow achieves high accuracy in estimating both the unknown tilted plane and the oligomer size.

Digital holographic microscopy systems in a common-path configuration, compared to systems with a separate reference arm, offer a compact design and resistance to disturbances. They can operate with partially coherent illumination, reducing speckle noise. However, they are limited by the overlapping of the object beam and its laterally shifted replica. As a result, images from different regions of the object overlap on the detector, preventing imaging of dense samples. We present the wavelength-scanning replica-removal method, which solves this problem by enabling the separation of information from both replicas and thereby doubling the effective field of view (FOV). The wavelength-scanning multi-shear replica removal algorithm plays a key role in reconstructing the undisturbed phase from a series of holograms recorded with variable shears. The shear value is controlled by changing the illumination wavelength. This enabled the development of two measurement modes: time-domain wavelength scanning for high-quality imaging, and a single-shot mode with frame division into color channels to improve temporal resolution. The method was validated using resolution tests and biological samples - neurons and dynamic yeast cultures. By combining the advantages of the common-path configuration with dense-structure imaging and dynamic processes, the proposed method constitutes a versatile tool for quantitative phase microscopy.

Wastewater is increasingly being recognized as an important data stream that can contribute to infectious disease surveillance and forecasting. With this recognition, a growing number of statistical inference approaches are being developed to use wastewater data to provide quantitative insights into epidemiological dynamics. However, few existing approaches have allowed for systematic integration of data streams for inference, for example by combining case incidence data and/or serological data with wastewater data. Furthermore, only a subset of existing approaches have been able to handle missing data without imputation and to handle datasets with different sampling times or intervals. Here, we develop a statistically rigorous, yet lightweight, approach to infer and forecast time-varying effective reproduction numbers (Rt values) using longitudinal wastewater virus concentrations either alone or jointly with additional data streams including case incidence data and serological data. Our approach relies on a state-space modeling approach for inference and forecasting, within the context of a simple bootstrap particle filter. We first describe the structure of our underlying disease transmission process model as well as our observation models. Using a mock dataset, we then show that Rt can be accurately estimated by interfacing this model with case incidence data, wastewater data, or a combination of these two data streams using the bootstrap particle filter. Of note, we show that these data streams alone do not allow for reconstruction of underlying infection dynamics due to structural parameter unidentifiability. We then apply our particle filter to a previously analyzed SARS-CoV-2 dataset from Zurich that includes case data and wastewater data. Our analyses of these real-world datasets indicate that incorporation of process noise (in the form of environmental stochasticity) into the state space model greatly improves our ability to reconstruct the latent variables of the model. We further show that underlying infection dynamics can be made identifiable through the incorporation of serological data and that the bootstrap particle filter can be used to make forecasts of Rt, case incidence, and wastewater virus concentrations. We hope that the inference approach presented here will lead to greater reliance on wastewater data for disease surveillance and forecasting that will aid public health practitioners in responding to infectious disease threats.

Symptom propagation occurs when the symptoms of secondary cases are related to those of the primary case as a result of epidemiological mechanisms. Determining whether - and to what extent - symptom propagation occurs requires data-driven methods. Here we quantify the strength of symptom propagation as the increase in risk of a secondary case developing severe symptoms if the primary case has severe symptoms. We first used synthetic results to determine the data requirements to robustly estimate the strength of symptom propagation and to investigate the effect of severity-dependent reporting bias. Categorising symptom severity into two group (mild or severe; asymptomatic or symptomatic), our estimation requires only four summary statistics - the number of primary-secondary case pairs of each combination of symptom presentations. Our analysis showed that a relatively small number (100) of synthetic primary-secondary case pairs was sufficient to obtain a reasonable estimate of the strength of symptom propagation and 1,000 pairs meant errors were consistently small across replicates. Our estimates were robust to severity-dependent reporting bias. We also explored how symptom propagation can be separated from other individual-level factors affecting severity, using age dependence as an example. Although synthetic data generated from an age-structured model led to overestimations of the strength of symptom propagation, allowing disease severity to be age-dependent restored the accuracy of parameter estimation. Finally, we applied our methodology to estimate the strength of symptom propagation from three publicly available data collected during the COVID-19 pandemic with data on presence or absence of symptoms: England households, Israel households, and Norway contact tracing. Our age-free methodology indicated a 12-17% increase in the risk of being symptomatic if infected by someone symptomatic. Our positive estimates for the strength of symptom propagation persisted when applying our age-dependent methodology to the two household data sets with age-structured information (England and Israel). These findings demonstrate evidence for symptom propagation of SARS-CoV-2 and provide consistent estimates for its strength. Our synthetic data analysis supports the conclusion that these correlations are not a result of reporting bias or age-dependent effects. This work provides a practical tool for estimating the strength of symptom propagation that has minimal data requirements, enabling application across a wide range of pathogens and epidemiological settings.

Micro-elastography is an optical technique that studies elastic waves for the mechanical characterisation of micrometric objects, such as cells. We propose to adapt this technique for the characterisation of millimetre-sized samples using a white light microscope. The objective is to perform a rapid, global characterisation of the elasticity of a biopsy. The millimetre-sized samples to be characterized are embedded in an agarose gel. A vibrator generates shear waves in this gel that transmit naturally inside the sample. This technique removes the need for precise manipulation of the wave source. A high-speed camera records the propagation of the waves in the sample. Their velocity is calculated using a noise correlation approach. Due to the lack of millimetric phantoms of calibrated elasticity, we choose to validate this method with a three step process. The experimental setup is first validated on homogeneous gels, then on biological samples of increasing elasticity, biopsies of beef liver hardened by heating, and finally on biological samples of clinical interest: biopsies of mouse endometrium. This method can be applied to all types of biological tissue, paving the way for rapid mechanical characterization of biopsies.

Transparent and composite surfaces pose a fundamental challenge for stereo photogrammetry: optically smooth glass produces no detectable surface features under visible illumination, making three-dimensional reconstruction impossible without surface preparation. This excludes optical components such as lenses and cover glasses, composite assemblies, and semi-translucent biological specimens from non-contact geometric measurement. Here we show that coherent speckle illumination at 266 nm overcomes this limitation by exploiting wavelength-dependent scatter enhancement, generating sufficient backscattered signal on surfaces that are entirely invisible under visible illumination. We developed a multispectral stereo system and evaluated three illumination modalities under identical acquisition conditions. On transparent glass, both visible modalities produce complete reconstruction failure, recovering only non-transparent holder structures. Ultraviolet speckle illumination at 266 nm enables dense reconstruction of the same surfaces. We demonstrate recovery of an uncoated plano-convex lens with a fitted radius of 30.946 mm and point-cloud standard deviation of 106.5 {micro}m, defect detection on a transparent cover glass without surface preparation, and reconstruction of a semi-translucent biological specimen. On metrology-grade reference objects, ultraviolet speckle achieves a standard deviation of 116 {micro}m and completeness exceeding 93%, approaching the performance of optimised visible structured illumination. These results establish ultraviolet speckle photogrammetry as an enabling approach of optical metrology to otherwise uncooperative surfaces, with relevance to optical manufacturing inspection and biological surface analysis.

Standard analysis of amyotrophic lateral sclerosis (ALS) clinical trials evaluates therapeutic efficacy by comparing linear slopes of total ALS Functional Rating Scale (ALSFRS) scores between treatment arms. This approach compresses multidomain ordinal data into a single scalar trajectory, discarding distributional structure. When subgroup-level trends differ in timing or direction, such aggregation can attenuate or eliminate them, a phenomenon known as Simpsons paradox. Here we apply Shannon entropy, computed from item-level score distributions within each ALSFRS functional domain following the framework established in [8], to the PRO-ACT database, stratified by treatment arm (Active: n = 4,581; Placebo: n = 2,931; 19 monthly time points). The entropy trajectories of drug-treated and placebo populations diverge visibly and systematically across all four functional domains (Bulbar, Fine Motor, Gross Motor, Respiratory). In the Fine Motor domain, the placebo population reaches peak entropy at month 8 and reverses, while the active population does not peak until month 13, a five-month delay in the populations transit toward functional loss. This divergence is model-independent: it is present in the raw Shannon entropy trajectories before any dynamical model is applied. A permutation test shuffling patient-level arm labels (n = 1,000 permutations) confirms that the total integrated absolute divergence across all four domains exceeds the null distribution at p < 0.001 (observed: 4.48; null: 2.03 {+/-} 0.33; 7.5 standard deviations above the null mean), with Fine Motor (p = 0.001) and Respiratory (p < 0.001) individually significant. The quantity that differs between arms, the shape and timing of the populations distributional evolution, does not exist as a measurable quantity in the total-score linear-slope framework used to evaluate these trials. Whether this signal reflects genuine treatment effects, compositional artifacts from pooling heterogeneous trials, or both cannot be determined from the anonymized public database alone. What can be determined is that the standard ALS clinical trial endpoint makes an implicit assumption, that the distributional information it discards is uninformative, and the present results demonstrate empirically that this assumption is false.

Short-horizon epidemic forecasting is difficult when surveillance series are highly nonstationary and affected by structural change and evolving reporting conditions. This study evaluates statistical models for global daily COVID-19 incidence using a rolling-origin benchmark designed to approximate real-time forecasting under such conditions. Using global incidence data from 22 January to 27 July 2020, we compare naive, seasonal naive, drift, ARIMA(log1p), ETS(log1p), and Prophet(log1p) forecasts at horizons h [isin] {1, 3, 7, 14} days. Structural phases are identified retrospectively on a variance-stabilized scale and used only to stratify forecast errors. Forecast ranking is strongly horizon-dependent. In the full-sample benchmark, drift performs best at the 1-, 7-, and 14-day horizons, while seasonal naive performs best at 3 days. Among the transformed statistical models, ARIMA(log1p) is competitive at short horizons, whereas ETS(log1p) becomes stronger at 7 and 14 days. Diebold-Mariano tests confirm that several of these differences are statistically meaningful, particularly in favor of drift at short and long horizons and in favor of ETS(log1p) over ARIMA(log1p) at longer horizons. Prophet(log1p) is not competitive in point forecasting and achieves high nominal interval coverage mainly through very wide prediction intervals. Robustness analyses show that the main ranking patterns are broadly stable to alternative segmentation settings, training-window policies, coverage-stabilized subsamples, and alternative target construction based on cumulative confirmed counts. Overall, the results show that simple baselines remain difficult to outperform in epidemic surveillance data and that horizon-specific rolling evaluation is essential for credible forecast comparison under structural change. Author summaryForecasting infectious disease incidence is difficult when case data change rapidly over time and when reporting systems are still evolving. In this study, I examined how several common statistical forecasting models perform on global daily COVID-19 incidence during the early pandemic. Rather than asking which model is best overall, I focused on whether model ranking changes across forecast horizons and whether those conclusions remain stable under different evaluation choices. I compared simple baselines, including naive, seasonal naive, and drift forecasts, with ARIMA, exponential smoothing, and Prophet models using a rolling-origin benchmark that mimics real-time forecasting. I found that forecast ranking depends strongly on the horizon: drift performed best at 1, 7, and 14 days, while seasonal naive performed best at 3 days. Among the transformed statistical models, ARIMA was more competitive at shorter horizons, whereas exponential smoothing was stronger at longer horizons. I also found that these conclusions remained broadly stable under alternative segmentation settings, training windows, coverage-stabilized subsamples, and target definitions. These results show that simple baselines can remain highly competitive in epidemic surveillance data and that horizon-specific evaluation is essential for fair forecast comparison under structural change.

Synchrony is a key mechanism that builds up the foundations of human interactions. Quantifying the level of physiological synchronization that occurs during dyadic exchanges is essential to fully comprehend social phenomena. We present a new index to characterize the coupling of complex physiological dynamics: the optimized Multichannel Complexity Index (opMCI). We validated this approach using synthetic time series of two coupled Henon Maps, with four different coupling levels in unidirectional and bidirectional manners. We demonstrated that the opMCI method allows to effectively discern between all coupling levels. Then, we applied the opMCI metric on heart rate variability data collected from 37 parent-infant dyads, during shared reading and playing activities, in the framework of the Shared Emotional Reading (SHER) project, with the aim of assessing the effects of early intervention in preterm babies. Two groups presented preterm infants: an intervention group, who participated in a two-month shared reading program, and a control group, who practiced shared play activities. A full-term group provided additional control data. The opMCI values were significantly higher for the intervention dyads with respect to the other groups during the shared reading task, showing that an early reading intervention program could increase parent-infant synchrony in preterm babies.

Airway epithelium plays a major role as the primary interface between human body and the external environment, acting both as a physical and functional barrier. In vitro airway models that reproduce the epithelium architecture are therefore a valuable tool for studying infection, inflammation, and transport processes. In this work, we present a label-free, non-invasive method to visualize and measure mucociliary transport in air-liquid human models using third-harmonic generation (THG) microscopy with an optical parametric amplifier laser source at 1300 nm. By exploiting the intrinsic nonlinear contrast at optical heterogeneities, THG provides high-resolution images of both epithelial structures and of the overlying mucus layer without the need for fluorescence staining or sample processing. Time-lapse THG imaging reveals depth-dependent transport dynamics within the mucus, offering new insights into mucociliary transport mechanism. Our approach offers a physiologically relevant way to assess mucociliary function in vitro and could support studies on respiratory diseases, drug delivery and efficacy, and epithelial remodeling. O_FIG O_LINKSMALLFIG WIDTH=200 HEIGHT=117 SRC="FIGDIR/small/717621v1_ufig1.gif" ALT="Figure 1"> View larger version (52K): org.highwire.dtl.DTLVardef@62e8acorg.highwire.dtl.DTLVardef@199a8b7org.highwire.dtl.DTLVardef@113bb84org.highwire.dtl.DTLVardef@7be3f8_HPS_FORMAT_FIGEXP M_FIG For Table of Contents Only C_FIG

AO_SCPLOWBSTRACTC_SCPLOWSerological surveys measure the presence of antibodies in a population to infer past exposure to an infectious pathogen. If study participants ages are known, serocatalytic models can be used to retrace the historical transmission strength of a pathogen within that population, quantified by the force of infection (FOI). These models rely on age information as a key variable since infection risks are interpreted in relation to how long individuals have been at risk. However, due to data constraints, participants ages may be provided only within "age bins". A common approach is then to assign individuals ages to be midpoints of their respective age bins, ignoring uncertainty in this quantity. In this study, we quantify the bias introduced by this midpoint approach and develop a Bayesian framework that explicitly accounts for uncertainty in age. By comparing inference under constant, age-dependent, and time-dependent FOI scenarios, we show that incorporating uncertainty in age in serocatalytic models yields more reliable FOI estimates without sacrificing computational complexity. These improvements support the interpretation of serological data and inform public health decisions, such as estimating disease burden and identifying targeted vaccination groups.

Quantum kernel methods offer a potential advantage for classification tasks in high-dimensional feature spaces, yet their practical benefit critically depends on how input features are prepared. We compare five dimensionality reduction strategies--principal component analysis (PCA), Gaussian random projection (RP Gaussian), sparse random projection (RP Sparse), partial least squares (PLS), and uniform manifold approximation and projection (UMAP) -- as pre-processing steps for quantum kernel support vector machines (SVMs) applied to trabecular bone classification from synthetic micro-computed tomography (micro-CT) data. Using a custom procedural generator based on Gaussian random field zero-crossings, we produced 500 synthetic trabecular bone volumes with controlled morphometric properties such as bone volume fraction (BV/TV), trabecular thickness (Tb.Th), number (Tb.N) and spacing (Tb.Sp). Texture features extracted from grayscale slices are reduced to 8-dimensional quantum circuit inputs via each method, then classified using both classical radial basis function (RBF)-SVMs and quantum kernel SVMs with ZZ feature maps on a statevector simulator, both evaluated with 5 x 5 repeated stratified cross-validation (25 folds). Our results show that UMAP is the only reduction method where the quantum kernel remains competitive with the classical baseline. Under repeated cross-validation, UMAP showed a +0.032 accuracy gap favouring the quantum kernel (Dietterich 5 x 2 CV p = 0.177); however, validation on 10 fully independent datasets--each with independently generated samples, separate reduction fits, and separate kernel matrices -- reversed the sign to -0.030 (paired t-test p = 0.123; Wilcoxon p = 0.193; quantum wins 3/10 datasets), indicating that the apparent advantage was likely inflated by fold dependence. Nevertheless, UMAPs gap remains small and non-significant in both analyses, whereas all linear methods (PCA, RP Gaussian, PLS) show substantial quantum deficits of -0.090 to -0.116 across BV/TV classification, with PCA and PLS remaining significant under corrected tests (5 x 2 CV p = 0.004 and p = 0.007 respectively). We additionally evaluate quantum kernel ridge regression for continuous morphometric prediction, finding that ZZ quantum kernels fail uniformly at regression (negative R2 for all methods except PLS at 4 qubits), suggesting that the ZZ kernel captures decision boundaries but not smooth metric structure. These findings provide practical guidance for feature engineering in near-term quantum machine learning pipelines and demonstrate that the choice of dimensionality reduction can determine whether quantum kernels remain competitive with classical baselines.

The Poisson-Nernst-Planck (PNP) system is an accurate model of electrodiffusion of ionic species. It is commonly used in situations where nanoscale resolution is required, for instance close to ion channels in the membranes of biological cells. The inherent stiffness of the equations has made them challenging to solve and has limited the applicability of the system. In particular, the time step required for stable solutions has typically needed to be very short (nanoseconds), which makes simulations on the time scale of an action potential (milliseconds) difficult. Recently, it has been observed that avoiding operator splitting and instead solving the concentration equations and the electrostatic equation in a coupled manner relaxes the time-step limitation considerably. However, no theoretical explanation of this observation has been provided. Here, we aim to explain why the coupled scheme allows much larger time steps. We illustrate the mechanism by considering special cases that define necessary, but not sufficient, conditions for stability. We also show that these conditions remain relevant for the fully coupled PNP model in 3D.

A major challenge in neuroscience is to predict how currents in nanodomains affect voltage and ionic concentrations. Cable and Rall theory provide analytic current-voltage relations by neglecting concentration gradients, and the impact of concentration gradients is usually studied numerically with the Poisson-Nernst-Planck (PNP) model. A precise quantitative understanding of the combined dynamics remains limited because analytic current-voltage-concentration relations are missing. In this work we derive such relations using a novel approach based on cross-diffusion equations. For narrow cylindrical domains, we derive time-dependent and steady-state expressions that explicitly show how currents affect voltage and ionic concentrations. We find that the influx of only one ion can significantly change the concentrations of all the other ions even if no channels for these ions are present. After a current injection we compute a biphasic voltage transient where the small-time asymptotic corresponds to the steady-state solution of the cable equation. We show that the accuracy of cable theory prediction for the voltage depends on how the current is distributed among the various ions. Finally, we develop an iterative method to accurately compute steady-state profiles for voltage and concentrations using first-order results by subdividing a cylinder into small segments.