This is an evaluation and benchmarking study of an artificial neural network (ANN) surrogate for an existing stochastic model of cancer dynamics under oncolytic virotherapy; it does not propose a new stochastic cancer model or a clinical decision tool. The model considers the interactions between uninfected tumor cells, infected tumor cells, free virus particles and immune cells, with the random fluctuations in the system modeled via stochastic perturbation. Trajectories simulated with the Euler–Maruyama method are used to train and test a feed-forward ANN that predicts a tumor-burden proxy. In the original single-trajectory experiment, the ANN achieves an RMSE of 0.000547675 and an R2 of 1.000000 on the training subset, while validation yields an RMSE of 0.000827163 and an R2 of 0.995484. The test set, which is the chronologically later segment of the same trajectory and not an independent realization, however, has an R2 of −2.089698, indicating poor ability to generalize to the held-out segment of the simulated trajectory. We show that this failure is caused by extrapolation in time on a monotonically decaying trajectory and that, in this one-step design, a simple persistence predictor is more accurate than the ANN. In a revised benchmark with 70 independent stochastic realizations split by trajectory, a prediction horizon of 0.1 and increment targets, the ANN achieves a test RMSE of 0.0442±0.0008 (mean ± 95% CI over ten training runs, i.e., weight-initialization uncertainty) and outperforms persistence, autoregressive and Gaussian-process predictors and, modestly, linear regression (paired Wilcoxon signed-rank test over 20 test trajectories, p=0.0017; p<0.05 in all 10 individual training runs). This is a predictive skill on model-generated data, not a clinical predictive skill. Monte Carlo ensembles quantify the response of the tumor burden to the noise intensity, and control scenarios show that, within the assumed parameterized system, virotherapy accelerates the decline of the burden (area under the curve 32% smaller than in a no-virus control and 28% smaller than in an infection-disabled control with the same initial state) but does not change its equilibrium level. The importance of independent testing and of simple baselines is also highlighted. Clinical effectiveness cannot be inferred from the analysis as it is based on simulated data. Future research should involve experimental or clinical observations for the model calibration and external validation.
Pakistan is one of the last two countries where wild poliovirus type 1 (WPV1) remains endemic. We correct structural and parametric problems in the vaccination–sanitation poliomyelitis model of Bornaa, Seidu and Makinde and extend it to a Caputo fractional stochastic model with a delay representing the environmental persistence of shed virus. For the deterministic fractional delay model we prove well-posedness, positivity and boundedness, derive the basic reproduction number R0, show that the disease-free equilibrium is locally asymptotically stable if R0<1 for every fractional order and delay, and establish existence of endemic equilibria. In the Itô case (α=1) we prove global positivity and almost-sure extinction under a threshold condition that is uniform in the noise intensities. A drift-implicit product-integration midpoint scheme attains an observed order close to 1+α and remains stable where explicit fractional methods diverge. Calibrated by maximum likelihood to annual WPV1 cases in Pakistan for 2010–2025, the fractional model (α^=0.95) places the turning points of the series better than the integer-order model, but the evidence for memory is weak (borderline likelihood-ratio p≈0.017, a wide profile interval for α, and an AICc favouring α=1), so α remains partly a modelling assumption. Conditional on the fractional fit, restoring 2015–2018 campaign intensity and reducing transmission by 20% through sanitation would cut the projected 2027–2035 burden by about 74%.
Microscopic diagnosis of acute lymphoblastic leukemia (ALL) and multiple myeloma (MM) depends on expert review, and the public datasets available for automated analysis are small and imbalanced. This study presents a four-stage pipeline for nucleus segmentation and cell classification on the SN-AM and SegPC-2021 datasets. Images were enhanced with contrast-limited adaptive histogram equalization (CLAHE); a conditional generative adversarial network (pix2pix) generated 2500 synthetic image–mask pairs per dataset from new nucleus layouts; nuclei were segmented with UNet using five pre-trained CNN encoders and compared with YOLO26; and single cells were classified with XGBoost on fused, PCA-reduced deep features. Models were trained with and without synthetic data and evaluated on real test images only. The synthetic pairs improved UNet on SN-AM (Dice 0.934 to 0.951 for EfficientNetB7, six test images), whereas on SegPC-2021 their effect was within ±0.01 Dice; YOLO26 gave the best SegPC-2021 result (Dice 0.799). Fused features classified ALL and MM cells with a balanced accuracy of 0.978–0.984. However, background patches without leukocytes also identified the source dataset (ROC-AUC ≥ 0.996); in a same-source experiment, three fused feature sets still reached 0.993–0.996. Synthetic data helped most where annotations were scarce; larger same-source datasets are needed for confirmation.
Angiographically equivalent coronary lesions may not produce equivalent local biomechanical environments. This study tested whether a standardized stenosis generates different wall shear stress (WSS) distributions across geometries under matched pressure conditions. Steady-state computational fluid dynamics simulations used idealized left anterior descending (LAD), left circumflex (LCX), and right coronary artery (RCA) models derived from human morphometric parameters. Each contained a 50% diameter-reduction stenosis, 18 mm long and 35% eccentric. Diastolic pressures of 70, 90, and 130 mmHg and hematocrit levels of 25%, 45%, and 65% were evaluated using hematocrit-dependent effective Newtonian properties and a distal-to-proximal pressure ratio of 0.86. Blood flow was modeled under steady-state conditions with rigid arterial walls. A patient-derived LAD was included as a secondary analysis. At 130 mmHg and 65% hematocrit, WSS at the corresponding principal stenotic point reached 88.79 Pa in the RCA, 52.21 Pa in the LAD, and 32.18 Pa in the LCX. Changes in the prescribed hematocrit-dependent effective blood properties produced different WSS responses across the geometries. The patient-derived LAD showed comparable relative WSS responses. Thus, in these simulations, equivalent stenosis and pressure ratios did not produce biomechanically equivalent WSS environments. These findings indicate that artery-specific geometry contributes to local wall-shear exposure. Its potential relevance to plaque vulnerability and coronary risk should be assessed in future patient-specific studies incorporating plaque characteristics and clinical outcomes.
We establish explicitly conditioned multivariate Hermite–Hadamard–Fejér (HH–F) upper certificates for modified (h,m)–convexity on origin-anchored boxes and simplices, together with operator and matrix counterparts that yield trace- and eigenvalue-level certificates. To keep the theory mathematically consistent, the scalar and box analyses are organized into three rigorous regimes: the identity-generator case, the affine-generator case, and a genuinely nonlinear weighted case treated through w-adapted convexity along the pullback path induced by the kernel generator. The simplex analysis is presented in two layers, namely a standard radial theorem and a weighted radial extension. Within this structure, we introduce tensorized kernel-weighted integral operators generated by coordinate-wise maps wi and Fejér-symmetric kernels, recover classical rectangle bounds as limiting cases, and obtain dimension-explicit vertex certificates on boxes together with mixed facet and vertex certificates on simplices. In the operator setting, the commuting regime is fully rigorous by simultaneous diagonalization and functional calculus, whereas the noncommuting regime is stated only under explicit operator-compatibility hypotheses. Verified nonlinear pullback and simplex examples, an explicit certificate-screening step, and dimension-dependent cost calculations demonstrate the reach and limitations of the bounds. Engineering illustrations are analytic proof-of-concept calculations; previously reported empirical data-set tables lacking the requisite scripts and split indices have been withdrawn from the main text.
