Mathematics

We present a quantum-enhanced version of the classic k-Nearest Neighbors (kNN) classification algorithm, applied to the prediction of arterial hypertension. The traditional Euclidean distance metric of the kNN algorithm is replaced with a Fidelity-derived quantum dissimilarity measure to evaluate the similarity between data samples. We map classical real-world clinical and ECG-derived data features into quantum states via the Dense-Angle Encoding, which efficiently utilizes parameterized rotation gates to pack multiple features into minimal qubits while maintaining pure states. We evaluate the performance of the dissimilarity measure using both the noiseless state vector Simulator and the IBM Qiskit Estimator primitives. The quantum circuit demonstrates robust predictive capabilities comparable to the classical model. While it does not claim computational supremacy over the classical baseline, the framework proves that fidelity-based similarity is a physically meaningful and efficient approach for hybrid quantum classical classification.

Parameter estimation in nonlinear biological dynamical systems is a difficult inverse problem because the governing equations are often stiff or oscillatory, the data are sparse and noisy, and the objective landscape is non-convex. Physics-informed neural networks (PINNs) offer an alternative to purely simulation-based calibration by representing state trajectories with neural networks while penalizing violations of the governing equations. This paper studies the empirical reliability of PINNs for recovering the parameters of the repressilator, a synthetic genetic oscillator formed by three cyclically repressive genes. We use synthetic time-series generated from the standard ordinary differential equation model and train inverse PINNs to estimate the production parameter {beta} and the Hill coefficient n. The study varies observation noise, partial observation of repressors, sampling density, sensitivity to initial parameter guesses, and the difference between stable and oscillatory regimes. The results show that PINNs can reconstruct trajectories accurately when the model structure is correct and the three repressors are observed, but parameter recovery is more fragile than trajectory fitting. Noise, sparse sampling, unobserved variables, and unfavorable initial guesses increase the risk of biased estimates. The stable regime is easier to reconstruct, whereas the oscillatory regime provides richer information but also exposes optimization sensitivity. These findings support PINNs as a useful reverse-engineering tool for small gene-regulatory ODE models, while highlighting the need for repeated runs, uncertainty reporting, and experimental designs that improve identifiability.

Mechanisms that lead to viral chronicity are poorly understood, but cell-to-cell spread has been implicated in the establishment of chronic infections. We previously developed mathematical models to explore the nature of hepatitis C virus (HCV) cell-to-cell spread in vitro and quantified the effect of inhibiting individual host factors involved. However, the previous models were not designed to (i) address cell proliferation, (ii) account for differences in cell size, and (iii) did not include possible foci merging. Herein we have developed an agent-based model (ABM) to simulate HCV cell-to-cell spread in vitro by modeling individual cell behaviors. This model recapitulates the natural increase of cell confluence that occurs in vitro accompanied by a concomitant decrease in cell size by allowing for independent proliferation cycles of individual cells within a restricted space. The model fits the experimental foci expansion data well and allows assessment of foci merging while reproducing the irregular HCV foci shape observed in cell culture. Altogether, the new more inclusive model has the potential to help elucidate the dynamics of HCV cell-to-cell spread and provide accurate predictions regarding the efficacy of antiviral drugs. Author SummaryDespite remarkable progress in treatments for hepatitis C virus (HCV), HCV infection remains a global public health burden with over 50 million chronic HCV infections and about 1 million new infections occurring annually. Once infection occurs, HCV can spread in the liver multiple ways. One mechanism is cell-to-cell (CTC) spread where the virus moves directly from one infected cell to an adjacent cell without moving through the extracellular space. Previous mathematical models of HCV CTC spread were not designed to incorporate cell proliferation, cell size, or foci merging. Therefore, to better mimic cells in culture, we developed a novel agent-based model (ABM) that allows the simulated cells to proliferate resulting in an increased number of cells with concomitant decrease in cell/agent size analogous to what happens as cells become tightly packed in culture. This new ABM not only can be used to estimate efficacy values of HCV cell-to-cell spread inhibitors (e.g., when different factors involved in cell-to-cell spread are blocked), but also should enable modeling of HCV CTC spread under a wider variety of cell culture conditions and thus help elucidate the impact of different viral-host dynamics on HCV CTC spread.

This work focuses on the global and partial identification problem for fractional differential equations. We provide a general numerical procedure based on global and local optimization algorithms with two refinements for biological systems that ensure solution positivity and homogeneous parameter units. The method is applied to a new fractional model of Dengue outbreak called the Fractional Homogeneous Nishiura (FHN) model, calibrated using data of newly infected people in Cape Verde. We show that our identification method yields a better fit between data and model solutions than previous approaches and that our FHN model captures the dynamics of Dengue more closely than existing systems.

Length and time constants are foundational to the study of conduction in neurons and other biological cables but are exactly defined only for passive membranes. Here we define and derive exact length and time constants for propagating action potentials in unmyelinated axons. This derivation exploits specific instants during action potential conduction when the net transmembrane ionic current is zero, but axial current remains non-zero. At these instants, we define a curvature parameter,{kappa} , explore its determinants using computer modelling, demonstrate that it is the local real Laplace exponent of the action potential upstroke, and suggest practical approaches for its experimental measurement. From{kappa} , we define action potential length and time constants, {lambda}AP = 1/{surd}({kappa}racm) and {tau}AP = 1/{kappa}, and show that action potential propagation velocity is exactly {lambda}AP/{tau}AP.

We examine the long-range temporal structure of forecasts produced by Time-Series Foundation Models (TSFMs) on heartbeat dynamics using the MIT-BIH Normal Sinus Rhythm Database (NSRDB). Our findings indicate that these models do not adequately capture long-range dependencies, as reflected in growing errors in RR-interval predictions over longer forecast horizons. Code is available at https://github.com/SubramanianLab/ecg-tsfm-benchmark.

Mental health challenges among university students have increased due to academic pressure, lifestyle changes, and continuous digital engagement. Existing approaches for mental health assessment often rely either on self-reported psychological scales or isolated behavioral indicators, limiting their ability to capture complex temporal and contextual patterns. This study proposes an interpretable multimodal framework for student mental health risk assessment using behavioral sensing, academic information, ecological momentary assessments (EMA), and psychometric survey data. A bidirectional Long Short-Term Memory autoencoder is employed to learn latent temporal representations from day-level behavioral sequences, while graph embeddings capture structural relationships among students using similarity-based neighborhood graphs. These representations are fused with academic and survey-derived features and reduced using Principal Component Analysis and Uniform Manifold Approximation and Projection. K-means clustering is then applied to identify behaviorally distinct student groups. Experimental analysis on the StudentLife dataset demonstrates meaningful clustering performance with a Silhouette Score of 0.4209 and Adjusted Rand Index stability of 0.6869. The identified clusters correspond to low-risk, moderate-risk, and high-risk behavioral profiles. To improve interpretability and practical usability, a fuzzy inference system is introduced to compute mental risk, academic risk, and wellbeing indices using psychometric indicators including PHQ-9, PSS, PANAS, VR-12, and Big Five personality traits. The results demonstrate the potential of combining multimodal behavioral modeling with interpretable fuzzy reasoning to support early mental health risk assessment in educational settings.

Cardiovascular diseases, such as stroke and heart attacks, are the leading cause of death worldwide. Computational models like cardiovascular digital twins (CVDTs) offer a promising path for research and intervention but are challenged by the complexity of simulating the full human vasculature. This study evaluates the feasibility of simulating blood flow through a vascular network containing 34 billion vessels (the estimated number in the human body) using first-principles physics and simplified geometry which is a first step towards CVDT. We synthesized 3D vasculature using a fractal model and computed blood flow rates via Poiseuille equation and steady-state fluid dynamics, implemented with high-performance computing. Simulations were conducted for networks ranging from 6 vessels to 34 billion vessels. The results demonstrated high accuracy (within 1% of bench-marks), reproducibility across platforms, and strong scalability. Simulating the full vasculature required 156 node-hours on the second-fastest supercomputer in the world, using 29 TB of memory and 84 TFLOPS. Maximum speedup factor was 80, with parallel efficiency no lower than 0.48. These findings show it is computationally feasible to simulate blood flow through a full-body vascular network at scale. The approach is well suited to parallel computing, suggesting that with continued development, CVDTs could enable whole-organism modeling for applications such as stroke, trauma, radiation injury, and cancer metastasis.

The emergence of a hantavirus variant aboard a commercial cruise ship presents a significant public health concern. This study develops a discrete-time stochastic Susceptible-Exposed-Infectious-Recovered-Dead model to estimate transmission dynamics, hidden exposed infections, and outbreak risk among passengers and crew. Epidemiological parameters and latent disease states were inferred using an Ensemble Adjustment Kalman Filter calibrated to reported case data from WHO and ECDC situation reports. The estimated basic reproduction number was 2.76, with a 95% confidence interval of 2.52-2.99, indicating substantial potential for sustained onboard transmission before strict quarantine measures. Simulations further suggest that several exposed individuals may remain unidentified during the early outbreak phase, creating a hidden reservoir that symptom-based surveillance alone may fail to detect. These findings highlight the importance of rapid surveillance, widespread testing, targeted quarantine, and active monitoring of exposed individuals in confined travel settings. The proposed modeling framework can support timely outbreak assessment and intervention planning for infectious-disease events in similarly dense and spatially constrained populations.

Infectious disease transmission evolves as a dynamic process shaped by biological mechanisms, population behavior, and intervention policies, yet public health responses are often driven by lagging indicators. Accurate short- and long-term disease forecasting is essential for the timely deployment of intervention strategies, healthcare capacity planning, and uncertainty-aware, risk-informed decision-making. To address this challenge, three broad classes of forecasting models have traditionally been used: statistical, machine learning, and mechanistic approaches. However, each of these modeling paradigms faces fundamental limitations. In particular, traditional statistical models often lack the flexibility needed to capture complex disease dynamics, machine learning approaches require large, high-quality data streams, and mechanistic models are notoriously difficult to calibrate. To overcome these challenges, we propose a novel physics-informed machine learning (PIML) framework for forecasting infectious disease dynamics. Our approach simultaneously forecasts new case and hospitalization counts, along with other key epidemiological quantities such as the time-varying reproduction number. This is achieved through the design of a machine learning model and estimation strategy regularized by a system of differential equations that encode disease dynamics of the SIHR model, thereby bridging the gap between purely data-driven and mechanistic models. We demonstrate the proposed methodology through in-depth numerical studies and an application to COVID-19 data collected in the state of South Carolina.

Calibration of closed-loop lumped-parameter cardiovascular models remains a major bottleneck for scalable digital-twin generation because inverse estimation is ill-conditioned and typically requires computationally expensive iterative forward simulation. This study investigates whether a supervised neural network (NN) can provide a fast inverse estimator for a paediatric sepsis cardiovascular ODE model by learning a direct mapping from prescribed haemodynamic target vectors to calibrated parameter sets. Training data are generated by sampling model parameters at random, forward-simulating the closed-loop system to steady state, and pairing the resulting target summaries with the corresponding parameters; the same target definitions and evaluation populations are used throughout for consistency. We evaluate NN inference by forward re-simulation to steady state and benchmark performance against a simulator-constrained calibration reference (Embedded Gradient Descent, EGD) using relative-error statistics, distributional similarity of achieved outputs and inferred parameters (median shift, IQR ratio, Wasserstein distance, KS statistic), and target-space localisation of parameter-space disparity (cosine distance). The NN reproduces the prescribed targets with predominantly small errors for most samples, while the largest discrepancies are confined to a well defined set of target configurations that also yield high residuals under the reference method, indicating feasibility limits of the target/model combination. Overall, NN-guided calibration provides a computationally efficient accelerator for virtual-twin generation and target-space screening, with simulator-based refinement and forward re-simulation retained to handle infeasible regimes and enforce mechanistic plausibility.

Patients suffering from sepsis need to be treated with an effective antibiotic therapy within the first hour after sepsis onset to decrease their risk of death. Microbiological data that provide information about the suitability of antibiotic therapies, however, is usually available only after 72 hours. Consequently, the treating physicians need to judge a therapy's effectiveness based on the patients' measured health records and their general health condition. This medical assessment is complex and requires years of experience. In our study, we investigate how statistical modeling can contribute to assessing the effectiveness of antibiotic therapies. To that purpose, we describe the effectiveness of antibiotic therapies by modeling sepsis patients' health conditions using a three-state continuous-time hidden Markov model (ctHMM). In literature, procalcitonin (PCT) and lactate have proven to be helpful for deriving the health condition in this context. The state probabilities obtained by the ctHMM are subsequently used to quantify the effectiveness of antibiotic therapies. To this end, we apply two different approaches, namely (i) averaging of the state probabilities and (ii) a logistic regression model. For (i), we calculate the average of the state probabilities for the state indicating a sepsis-free condition over an antibiotic administration period of 48 hours. For (ii), we use the information about antibiotic susceptibility testings as dependent variable in the logistic regression model; as independent variables, we calculate the difference between state probabilities at the start of antibiotic administration and 48 hours later. With this work, we are able to better understand the relationship between laboratory values, in particular PCT and lactate, and the patients' health condition. We further provide approaches for quantifying the effectiveness. Therefore, our work contributes to developing a clinical decision support system which helps physicians assess the effectiveness of antibiotic therapies in patients with sepsis. Supported by such a system, a physician is able to quickly adjust an ineffective therapy which avoids antibiotic resistances and increases a patient's chance to survive a sepsis.

Melanocytes become cancerous, forming tumors that may invade and destroy the surrounding tissues. When melanocytes acquire invasive characteristics, the anchored melanoma begins to damage the normal cells. Therefore, early intervention and diagnosis are essential to avoid high morbidity and mortality in malignant melanoma. However, It is challenging to distinguish the difference between malignant melanoma and benign clump of melanocytes. Based on a data set of 10,000 melanocyte tumors, this paper develops a new model system to improve the accuracy of distinguishing between benign and malignant melanocytes. In the first stage, the original CNN architectures are used, such as ResNet18, ResNet50, VGG11, and VGG16. Synthetic medical images, generated via a Diffusion Model to extract informative features from the original dataset, are used to train the CNN architectures. This approach improves classification accuracy from 91.1% to 92.9%. In the second stage, the fully connected layer of each neural network is replaced with a high-level classifier, XGBoost, to perform secondary classification. This hybrid strategy further enhances performance, achieving up to 93.3% accuracy by using the synthetic images.

Cervical cancer represents a pressing global health challenge, emphasizing the critical need for accurate and timely diagnostic methods to facilitate effective treatment and improve survival rates. In response to this challenge, the study presents CerViX-Net, an innovative classification framework designed to advance cervical cancer detection through enhanced computational efficiency and diagnostic accuracy. The development of CerViX-Net is motivated by the limitations of traditional diagnostic models, particularly in handling the computational and memory demands of large-scale data, while ensuring precise feature extraction and classification. CerViX-Net employs a hybrid deep learning architecture that combines the capabilities of ResNet50, EfficientNet-B0, and a Modified Vision Transformer (ViT) module. The ResNet50 branch extracts hierarchical features through stacked convolutional and identity blocks. In another path, the modified ViT module transforms image patches via linear projection, augments them with positional and class embeddings, and processes them using Parallel Transformer Encoder layers to model contextual relationships. Concurrently, EfficientNet-B0 utilizes MBConv blocks to extract multi-scale representations. The feature outputs from all three branches are integrated and passed through a classification head consisting of dropout layers and dense layers to ensure robust and accurate predictions. The proposed framework is rigorously evaluated on the Mendeley LBC dataset, achieving exceptional performance metrics with an accuracy of 99.69%, precision of 99.28%, recall of 99.48%, and an F1-score of 99.52%. The robustness of CerViX-Net is further validated on the SIPaKMeD and Herlev Pap Smear datasets, where it demonstrates comparable excellence, underscoring its efficacy and adaptability across diverse cytology datasets. Statistical validation using Friedman's test further reinforces its superiority over competing methods.

Parkinsons Disease (PD) Motor Scores (MDS-UPDRS Part III) are quite noisy. This paper proposes a new methodology for processing these scores by first denoising the scores to enhance the underlying progression signal, and then conducting a high-dimensional analysis which does not sum the scores into a total movement score. The analysis gives novel insights into PD progression heterogeneity: it reveals that the heterogeneity is continuously variable rather than clustered into "subtypes" and that the variability is along two easily understood axes. This analysis also resolves some of the discrepancies in previously reported progression subtypes. Finally, the analysis reveals that patient-specific progression cannot be predicted from baseline using only MDS-UPDRS Part III scores.

Genome-scale metabolic network reconstructions contain extremely detailed and valuable information regarding cellular metabolism. For many applications such as finding genetic engineering targets and reduced kinetic model construction, metabolic network analysis techniques exist. Yield spaces based on the extreme rays of solution cones related to the metabolic network are frequently constructed for these types of analyses. However, for genome-scale networks, full enumeration of these extreme rays is not computationally feasible. In this work, a novel direct generation method for yield spaces is presented. This allows the application of many metabolic network analysis techniques to even the most recent genome-scale metabolic networks. Inspired by principles from multi-objective optimization algorithms, the proposed method performs highly efficient recursive exploration but specifically adapted to the mathematical properties of yield spaces. Two case studies showcase both the efficiency of the method and its applicability for analysis of genome-scale metabolic networks.

We systematically evaluate and compare the performance of classical statistical methods (ARIMA), mechanistic compartmental models (SEIR), modern deep learning architectures (LSTM, DLinear, Autoformer), and an emerging time-series foundation model (TabPFN-TS) to forecasts the incidence of Influenza-Like Illness (ILI) across nine European countries. The models are benchmarked against a naive baseline and a multi-model ensemble (RespiCast) created by an initiative of the ECDC. In line with the operational practice of existing forecasting hubs, our entire evaluation is explicitly optimized for short-term horizons (1 to 4 weeks ahead). Interestingly, we found that the foundation model TabPFN-TS allows for great zero-shot inference capabilities. Without any task-specific retraining, it successfully overcomes extreme data scarcity to consistently outperform all other individual architectures, frequently rivalling or surpassing the RespiCast ensemble. Our results highlight how deep learning architectures are severely constrained by extreme data scarcity, typical in epidemic forecasting, requiring targeted endogenous data augmentation to reduce predictive errors. Within the deep learning class of models, we observe that simpler architectures (such as DLinear and LSTM) frequently exhibit greater robustness and outperform complex, attention-based models (such as Autoformer) when data is constrained. Finally, our results show how a weighted ensemble, constructed by fusing all the models, delivers highly robust forecasts in all regions considered. Overall, our findings showcase the transformative potential of zero-shot foundation models in epidemic forecasting and confirm the importance of multi-model ensembles.

During the 2026 Bundibugyo virus disease outbreak in the Democratic Republic of the Congo and Uganda, we projected potential airline-mediated importation risk using contemporary airline network and an externally calibrated Ebola importation hazard. Effective-distance analyses identified major international hub countries, including Belgium, France, South Africa, Kenya, and the United Arab Emirates, as higher-probability gateways within 30 days. These early projections provide a reproducible framework for real-time international situational awareness, while emphasizing that importation risk does not imply local transmission risk.

The advancement in deep learning techniques has made Convolutional Neural Networks (CNNs) a powerful tool for the fully automated classification of zooplankton images. In this study, we systematically investigate how network selection, colour information and differences in imaging instruments affect the classification of zooplankton images by comparing multiple state-of-the-art CNNs on images of zooplankton and marine snow from the in situ Continuous Particle Imaging and Classification Sensor (CPICS), Video Plankton Recorder (VPR), In Situ Ichtyoplankton Imaging System (ISIIS), and the on-board Plankton Imager (Pi-10). With differences between models of 7.8 to 19% in F1-score, we find that model selection strongly affects the classification performance, with EfficientNetV2S showing the most reliable overall performance. Moreover, differences between model architectures are largest for the least abundant classes (<100 labeled images), which implies that when these are present, careful model selection is most beneficial. The high image quality of the Pi-10 strongly increases the performance for the least abundant classes compared to the other instruments. In addition, we find a significant correlation (r = 0.597) between ImageNet the performance and F1-score on zooplankton images, which implies that more generally, a model that performs well on ImageNet will perform well for zooplankton classification. Colour information increases the F1-score of the best performing classifier with 2.8%, but provides a stronger benefit (25% F1-score) for classes with <100 images. The overall performance increase of colour information is less than expected and questions the advantage of recording colour information for zooplankton.

Cervical spinal cord injuries (cSCI) induce profound denervation in respiratory muscles leading to hypoventilation that compromises quality of life. Respiratory neuromuscular electrical stimulation of extra-diaphragmatic muscles (rNMES) could be a non-invasive approach to improve respiratory function following cSCI. However, it is critical to first synchronize rNMES with spontaneous breathing. An Ordinary Differential Equation (ODE) was solved and fitted to experimental breathing signals obtained via plethysmography in ten mice. Optimal stimulation ODE-based parameters were identified for intercostal and abdominal muscle stimulation for breathing-synchronized rNMES training. Feasibility was tested on tolerance to repetitive anesthesia and stimulation for ten training sessions in six mice. The ODE-based breathing signals matched the experimental ones with an average coefficient of determination (R{superscript 2}) of 81%. The developed algorithm, Algostim, provided average theoretical optimal times of 0.12 s for intercostal and 0.32 s for abdominal muscles contraction. Feasibility and tolerance to rNMES were favorable after ten sessions. This innovative mathematical approach to rNMES allows optimal stimulation of respiratory muscles while accounting for spontaneous breathing rate. Algostim established a framework for personalized rNMES therapies, enabling the delivery of standardized stimulation parameters and allowing detailed investigation into the underlying mechanisms of rNMES.