Search Results (1,878)

Alzheimer’s disease (AD) develops as a progressive dementia condition through the step-by-step breakdown of nerve cells. Neurodegeneration in this context primarily results from metal ions, including copper, iron, zinc, and aluminum, building up in the system. The aggregation of amyloid-beta (Aβ) peptides and oxidative stress generation stem from metal ion involvement acting as defining characteristics of Alzheimer’s disease pathology. We developed a comprehensive mathematical model based on 24 coupled ordinary differential equations (ODEs) to represent the interactions between metal ions, Aβ peptides, reactive oxygen species (ROS), antioxidant defenses, and tau protein phosphorylation. The mathematical model monitors how metal ion concentrations change over time and examines their competitive binding effects, which trigger a series of reactions, resulting in oxidative stress and subsequent tau protein damage. The model uses analytical and numerical mathematical methods to expose nonlinear behaviors and threshold effects while offering mechanistic insights into the course of disease development. This model functions as a quantitative framework for assessing how therapeutic interventions that target metal dyshomeostasis and oxidative stress can potentially affect outcomes. Full article

This paper presents a real-time digital twin (DT) of the power conversion system used in offshore wind applications. The proposed DT is exploited to identify key electrical parameters of both the permanent magnet synchronous generator (PMSG) and the three-phase boost rectifier and has been developed with a Condition Monitoring (CM)-oriented approach. A Gated Recurrent Unit (GRU) neural network is adopted as a real-time digital model (RTDM) to estimate online the PMSG phase resistance and synchronous inductance, as well as the DC-link capacitance at the rectifier output. The network is trained in MATLAB using data generated by a Typhoon HIL 606 emulator, covering both balanced and unbalanced operating conditions and a wide range of parameter variations. The trained GRU is then deployed on the control board and implemented in LabVIEW Real-Time for embedded execution. Experimental tests on a PMSG-based generating unit confirm the effectiveness of the proposed RTDM, achieving low root-mean-square and mean percentage errors in parameter estimation. The results demonstrate that the enhanced neural real-time DT is a promising tool for condition monitoring and predictive maintenance of power conversion systems in offshore wind applications. Full article

A rapid quasi-one-dimensional (quasi-1D) reacting-flow analysis code was developed for the preliminary assessment of rocket-based combined cycle engines over a broad flight envelope. The internal flow was modeled as steady and quasi-1D in a variable-area duct by solving the coupled conservation equations together with species transport, and finite-rate chemical kinetics were included to represent combustion-induced heat release and composition change. To incorporate configuration-dependent mixing effects that affect RBCC heat release evolution and thermal choking tendencies, a streamwise mixing efficiency distribution was extracted from non-reacting 3D CFD and prescribed as an input to the quasi-1D formulation to represent the progressive availability of reactable fuel along the flowpath. A mode-dependent solution strategy was established by separating the computation into scramjet mode and ramjet mode procedures with a switching criterion based on whether a sonic condition occurs within the combustor, allowing thermal choking and mode transition behavior to be addressed within a single framework. The numerical solver was implemented in Python 3.12.2 and integrated using a stiff ordinary differential equation (ODE) scheme to ensure robust convergence in the presence of reaction-induced stiffness. Verification against previously published hydrogen-fueled scramjet results reproduced the overall streamwise trends of key quantities including Mach number, pressure, temperature, and density. The developed code was then applied to an RBCC configuration under operating conditions representative of ERJ and ESJ regimes, and the quasi-1D predictions were compared with cross-section-averaged 3D RANS CFD results, showing consistent mode identification and comparable axial behavior at a level suitable for preliminary analysis with substantially reduced computational cost. Full article

DBSCAN is widely used to identify structured regions in unlabeled data, but its performance depends critically on the selection of the neighborhood parameter $\epsilon$. Traditional heuristics for estimating $\epsilon$ often become unreliable in high-dimensional or varying-density settings because they rely heavily on local geometric criteria and may fail under smooth transitions or topological ambiguity. This work presents a three-level perspective on DBSCAN hyperparameter selection. At the algorithmic level, $\epsilon$ controls neighborhood connectivity and structural transitions in clustering. At the modeling level, the ordered k-distance signal is approximated through a surrogate dynamical estimation framework inspired by a mass–spring–damper system. At the causal level, the resulting estimator is interpreted through interventions on its internal threshold-selection mechanism. The proposed method models the variation of $\epsilon$ using ordinary differential equations defined on the ordered k-distance signal, enabling analysis of structural transitions in density organization via a surrogate dynamical representation. System identification is performed using L-BFGS-B optimization on the smoothed k-distance curve, while the system dynamics are solved with the fourth-order Runge–Kutta method. The resulting estimator identifies transition regions that are structurally informative for $\epsilon$ selection in DBSCAN. To analyze the estimator at the intervention level, Pearl’s do-calculus is used to compute the Average Causal Effect (ACE). The method was evaluated on synthetic benchmarks and on the Covtype dataset, including scenarios with multi-density overlap and dimensionality up to ${\mathbb{R}}^{10}$. The resulting ACE values, $+0.9352$, $+0.5148$, and $+0.9246$, indicate that the proposed estimator improves intervention-based $\epsilon$ selection relative to the geometric baseline across the evaluated datasets. Its practical computational cost is dominated by nearest-neighbor search, behaving approximately as $O(NlogN)$ under favorable indexing conditions and degrading toward $O\left(N^2\right)$ in high-dimensional or weak-pruning regimes. Full article

In this paper we review the concepts of the Gibbs and conditional entropies and examine their dynamic behaviour when the underlying dynamics are described by ordinary differential equations or stochastic differential equations. We then go on to introduce techniques for the analogous examination when the dynamics involve delays and noise. It is found that the effects of stochastic perturbations and/or delayed dynamics may be such that the approach of the entropies to equilibrium are not necessarily monotone and are dependent on system parameters. Full article

Glucocorticoid-induced hypertension affects over 30% of treated patients, yet its underlying mechanisms remain unclear, particularly how glucocorticoids regulate renin within the renin-angiotensin-aldosterone system (RAAS). Modeling these dynamics is difficult because only four dose-response measurements are available at a single 24-h timepoint (36 observations total), while the system depends on roughly eleven biochemical parameters spanning minutes-long receptor interactions to days-long protein secretion. Classical parameter estimation becomes unreliable in this extremely underdetermined setting, and purely data-driven methods offer limited biological interpretability. In this paper, we introduce a physics-informed neural network (PINN) framework that integrates ELISA measurements from As4.1 juxtaglomerular cells, ordinary differential equations describing glucocorticoid receptor signaling and renin transcription, and automatic differentiation to enforce mechanistic constraints. By systematically tuning synthetic-data weights (SW in {0.2, 0.3, 0.5}), we identify an intermediate value of SW = 0.3 that provides the best overall balance between predictive accuracy, accepted ensemble size, and biologically plausible parameter estimates among the tested configurations. The framework uses adaptive constraint scheduling with a plateau ramp to reduce premature convergence and introduces calibrated plausibility thresholds reflecting experimental noise. The accepted PINN ensemble (n = 5, 50% success rate) achieved R² = 0.803, compared with 0.759 for the SW = 0.5 baseline and −0.220 for the ODE-only baseline, with RMSE = 0.024. Key learned parameters (IC₅₀ = 2.925 ± 0.012 mg/dL, Hill = 1.950 ± 0.009) are biologically plausible within the model assumptions, and the best single accepted model attained R² = 0.891. Information criteria favored the PINN over the ODE model, with improvements of approximately 77× (AIC) and 5.9× (BIC). Despite training on a single timepoint, the PINN also infers full 48-h trajectories and reproduces non-monotonic dose-response behavior. This work presents, to our knowledge, the first PINN framework for glucocorticoid-mediated renin regulation and should be interpreted as a proof-of-concept approach for integrating sparse biomedical data with mechanistic constraints. The inferred parameters and temporal dynamics are best viewed as model-dependent, hypothesis-generating estimates rather than validated biological quantities. Full article

The proper-time method for constructing perturbative dynamical gravitational fields is presented. Using the proper-time method, a perturbative analytical model of gravitational waves against the backdrop of an exact wave solution of Einstein’s equations in a Bianchi IV universe is constructed. To construct the perturbative analytical wave model a privileged wave coordinate system and a synchronous time function associated with the proper time of an observer freely moving in a gravitational wave are used. Reduction of the field equations, taking into account compatibility conditions, reduces the mathematical model of gravitational waves to a system of coupled ordinary differential equations for functions of the wave variable. Analytical solutions for the components of the gravitational wave metric have been found. The stability of the resulting perturbative solutions for the continuum domain of parameters is proven. The linear stability of the exact solution for a gravitational wave in the anisotropic Bianchi IV universe for the continuum domain of parameters is demonstrated. Full article

Differential operators often admit multiple algebraically equivalent symbolic formulations, yet those formulations can differ in the organization of their internal structure prior to solution analysis. A reproducible symbolic framework is introduced to compare such formulations at the level of operator expressions. Within a declared symbolic specification consisting of a fixed grammar, an admissible weight class, canonical compression rules, and an admissible family of reformulations, we define four encoding-relative structural descriptors: structural strain $\tau$, structural curvature $\kappa$, compressibility $\sigma$, and the balance ratio $\Gamma =\kappa /\tau$. Structural strain compares an encoding to a designated reference representation, while compressibility measures reduction under canonical symbolic compression. These quantities are deterministic descriptors within the declared encoding class rather than coordinate-free invariants of the underlying operator. The structural length functional underlying these descriptors is developed, canonical compression is formalized, and finite symbolic comparison is distinguished from pathwise symbolic deformation. A robustness theorem shows that, away from the threshold surface $\Gamma =\sigma$, sufficiently small admissible perturbations preserve the induced diagnostic label. A supporting weight-robustness result further shows that qualitative labels persist across a local admissible family of weight choices under corresponding nondegeneracy conditions. The framework serves as a reproducible diagnostic for operator representations alongside Lyapunov, spectral, pseudospectral, and energy-based stability theories. Examples of representative ordinary and partial differential operators illustrate how the descriptors are computed and how they behave under admissible re-expression, while the appendices provide the technical backbone of the paper: formal definitions, reproducibility protocol, extended perturbation arguments, and explicit failure-mode analysis. Additional sensitivity checks regarding encoding, weights, and threshold variation clarify the method’s scope, and explicit failure modes delineate the boundary cases in which the descriptors cease to apply. The main contribution of this study is a formally delimited and reproducible symbolic framework for comparing differential operators under a fixed, declared specification, together with robustness results and worked examples that clarify the method’s scope. Full article

The paper proposes a new mathematical framework in explaining the effect of periodic electric fields on the nonlinear interfacial instability emerging between two Walters’ B/Rivlin–Ericksen of non-Newtonian fluids. The suggested approach is designed to increase the prediction and control of electrically induced instability phenomena observed in advanced Electrohydrodynamics. Accordingly, under the impact of periodic EFs, the instability properties between the two superposed, electrically conducting viscoelastic fluids passing through a porous medium are examined. Furthermore, the fluids differ in their densities, electrical conductivities, permeabilities, and viscoelastic characteristics, surface tension and are supposed to performance at the disturbed interface. To decrease the mathematical complexity, viscous potential theory is adopted. By combining the pertinent nonlinear boundary conditions with the governing linearized equations of motion, more simplifications are made. The methodology leads to a nonlinear Mathieu oscillator characterizing the interfacial displacement. Within the scope of the non-perturbative approach, the resulting nonlinear ordinary differential equation is converted into an equivalent linear representation. A non-dimensional analysis yields a set of typical dimensionless parameters, significantly reducing the number of governing variables and facilitating physical interpretation. The stability criteria are numerically studied under complex conditions, indicating that the fundamental stability mechanism stays unchanged for both real and imaginary coefficients of the nonlinear characteristic equation regulating the interfacial motion. Full article

We investigate the asymptotic behavior of a proposed ordinary differential equation (ODE) model for Genetic Toggle switches from Gardner et. al. and I. Rajapakse and S. Smale: ${\displaystyle \frac{dx}{dt}}={\displaystyle \frac{a}{1+y^m}}-x$ and ${\displaystyle \frac{dy}{dt}}={\displaystyle \frac{b}{1+x^n}}-y$ where $a,b,m,n>0$ and $x\left(t\right),y\left(t\right)\ge 0$. We also investigate the asymptotic behavior of the Euler discretization of this system: $x_{n+1}=a_1{x}_n+{\displaystyle \frac{b_1}{1+y_n^m}}=f(x_n,y_n)$ and $y_{n+1}=a_2{y}_n+{\displaystyle \frac{b_2}{1+x_n^n}}=g(x_n,y_n),$ where $1-h=a_1$, $1-k=a_2$, $ah=b_1$ and $bk=b_2$, $a_1,a_2\in (0,1)$ and $h,k>0$ are steps of discretizations. Here, x and y represent protein concentrations at a particular time in both genes and $a,b,m,n>0$, respectively, above. We will apply the theory of competitive maps to find the basins of attractions of different equilibrium points and period-two solutions of systems of difference equations. Full article

In the present work a new regime of periodical energy exchange between pump, signal and idler waves, under the influence of the process of four-wave mixing (FWM), with additional consideration of the effects of self-phase modulation (SPM) and cross-phase modulation (XPM), is presented. In our previous papers a theoretical model which successfully describes the amplification and periodic energy exchange between the three optical waves in CW regime of laser source propagation (short-cut equations) was developed. Exact analytical solutions, describing the periodic changes in the intensities of pump, signal and idler waves, were found and expressed by the Jacobi elliptic functions. The period of the energy exchange between the waves can be presented by elliptic integral of the first kind. In the current research, the periods of energy exchange between the pump, signal and idler waves in the process of FWM, additionally taking into account the effects of SPM and XPM, are investigated. A comparison between the obtained results has been made. It is shown that the effects of self-phase modulation and cross-phase modulation increase the period of energy exchange. Full article

Castrate-resistant prostate cancer (PCa) is a critical situation in which many patients will relapse. Hormonal androgen deprivation therapy (HADT) is the gold standard of care when a patient relapses, following primary surgical or radiation therapy. Usually, the benefits from HADT are poor and recurrent disease after HADT treatment is termed castrate-resistant prostate cancer (CRPC), which is in most cases fatal. The therapeutic regimens for CRPC include chemotherapy with docetaxel, immunotherapy agent sipuleucel-T, the taxane cabazitaxel, the CYP17 inhibitor abiraterone acetate and the androgen receptor (AR) antagonist enzalutamide. Thus, it is imperative to study the inherent property of prostate cancer cells, to resist therapy and reconsider the therapeutic protocols (continuous v’s intermittent). We make use of a hybrid mathematical model which consists of an extension of a very potent ordinary differential equation (ODE) Baez–Kuang model, combined with two Game Theory components: the Minority Game for adaptive behavior and the Axelrod model for heterogeneity behavior. Our study suggests that increasing tumor adaptability, through Minority Game dynamics, improves short-term prostatic-specific antigen (PSA) control and stabilizes therapy cycles. However, this comes at the cost of driving the tumor to a homogeneous, androgen-independent (AI) state, which is therapy-resistant. Conversely, maintaining heterogeneity, via Axelrod dynamics, sustains a mixed population, with androgen-dependent (AD) cells persisting longer and potentially delaying resistance emergence. Full article

Currently, epidemiological models can not only be found in epidemiology but also in other research disciplines. However, an interdisciplinary perspective that highlights the commonalities of epidemiological models across disciplines is missing. The goal of the current study is to foster such a perspective. To this end, a methodology is used that sets the current study apart from traditional review studies. Two benchmark epidemiological models formulated in terms of coupled ordinary differential equations, the susceptible–infected–recovered model and the susceptible–exposed–infected–recovered model, are followed through eight disciplines: epidemiology, virus dynamics within humans, computer viruses, drug addiction, voter dynamics, rumor spreading, sales dynamics, and viral marketing. Structural similarities and structural differences across these disciplines within the context of these two models are worked out. It is shown how the exact same mathematical structure can be applied for quite different interpretations across the selected disciplines. It is also shown that more complex model variants exhibit structural differences across research disciplines. In this way, this study helps researchers compare their own works on a structural level with related works in other disciplines. The particular importance of the current study is that it can boost progress in epidemiological modeling by making researchers aware of an interdisciplinary perspective. Full article

This paper presents a physics-based hazard model for catastrophe (CAT) modelling of urban flood risk—a first step toward a complete CAT modelling framework. We introduce a linear second-order ordinary differential equation (ODE) system to simulate the underlying mechanisms of water accumulation, absorption, routing, and drainage across interconnected surfaces in densely built urban areas. The model treats an urban zone as a multivariate network of surfaces, each with unique hydrological properties, linked by directed water flows. For risk analysis, the external meteorological forcing (representing the precipitation input) is randomised. Our risk-analysis protocol relies on a Monte Carlo simulation of stochastic forcing. Its reliability is founded on rigorous mathematical properties proven for the ODE system (existence, uniqueness, positivity, monotonicity, and a priori bounds), ensuring that the probabilistic outputs are well-defined and physically plausible. A three-surface example illustrates the framework and a complete risk analysis is performed, yielding concrete risk metrics that inform mitigation strategies. Computational efficiency is shown to be optimal for linear ODE systems, outperforming generic methods. This work provides a foundational, physics-informed hazard model for next-generation CAT models, directly supporting the insurance industry’s adaptation to climate change. Full article

Accurate and long-horizon forecasting is essential for reliable planning of solar and wind power generation. Most existing models rely on high-resolution meteorological data, which are often unavailable in practical microgrid environments. This study proposes SNORF, a solar–wind neural ordinary differential equation model that uses only basic meteorological variables such as solar radiation, cloud cover, and wind speed together with lagged generation values. However, reliance on lagged generation inherently limits the effective forecasting horizon of conventional models. To address this limitation, SNORF extends the forecasting horizon while maintaining accuracy and stability through a rolling forecasting framework with a bounded input-dependent drift function and repeated Euler integration that promotes smooth hidden-state dynamics. SNORF supports both deterministic point forecasting and probabilistic forecasting through quantile-based loss functions. Experiments on solar and wind power datasets show that SNORF consistently outperforms representative time-series forecasting models. For solar forecasting, SNORF reduces RMSE and MAE by 15.35% and 16.93% on average compared with baseline models. For wind forecasting, the improvements reach 44.77% in RMSE and 52.85% in MAE on average. Furthermore, when evaluated under the official protocol of the 2024 IEEE Hybrid Energy Forecasting and Trading Competition, SNORF achieves a top 4% ranking using only the officially provided basic weather dataset, demonstrating its practical applicability to renewable energy forecasting in microgrids and virtual power plants. Full article