Search Results (147)

This study introduces an efficient and accurate two-stage explicit computational scheme for solving partial differential equations (PDEs) containing first-order time derivatives. The suggested method is a modification of the classical Runge–Kutta scheme that introduces a new first-stage formulation. This minimizes numerical error with moderate step sizes while preserving the stability region of the classical method. Spatial discretization is performed using a sixth-order compact finite-difference scheme to obtain high-resolution solutions. The analysis of stability and convergence is strictly determined for both scalar and system forms of convection–diffusion-type equations. To illustrate the suitability of the method, a dimensionless mathematical model of the unsteady, incompressible, laminar flow of a Prandtl-type non-Newtonian nanofluid over a Riga plate is considered, accounting for viscous dissipation, thermophoresis, Brownian motion, and a magnetic field. Here, the Prandtl ternary nanofluid is defined as a non-Newtonian nanofluid that follows the Prandtl rheological model, and it exhibits three critical transport phenomena: heat conduction, viscous dissipation, and nanoparticle diffusion. Representative values of the Prandtl number $P_r=3$ and Reynolds number $R_e=5$ are used to perform the simulation, and other parameters, including but not limited to the Hartmann number $H_a$, Williamson number $W_e$, thermophoresis $N_t$ and Brownian motion $N_b$, are varied to evaluate the flow behavior. Moreover, an artificial neural network (ANN)-developed surrogate model is used to calculate the skin friction coefficient and the local Sherwood number, using five input parameters: the Reynolds number, Prandtl number, Schmidt number, Brownian motion parameter, and thermophoresis parameter. The governing partial differential equations yield high-fidelity numerical data used to train the surrogate model. The data is split into 80% for training, 10% for validation, and 10% for testing. The ANN is tested using regression analysis and error histograms, which demonstrate high accuracy and generalization capacity. Numerical simulation combined with AI-based prediction is a cost-efficient method for real-time estimation of complex non-Newtonian nanofluid systems. Full article

Paeoniae Radix Alba Carbonisata (PRAC), carbonized decoction pieces of the traditional Chinese medicine Paeoniae Radix Alba, has been used in clinical practice for hepatoprotective purposes. Hepatic amyloidosis (HA), a severe complication of systemic AA amyloidosis, is characterized by the deposition of fibrillar amyloid proteins leading to progressive hepatic dysfunction. However, its role in HA remains unclear. Amyloid lysozyme (LYSO-6) was used to induce the NCTC1469 cell injury model and the HA mouse model. The effects of PRAC extract (PRAC-E) on liver injury were then evaluated using biochemical assays, enzyme-linked immunosorbent assay (ELISA), Congo red (CR) staining, Hematoxylin and Eosin (H&E) staining, and immunohistochemical staining. Liver transcriptomics combined with Western blotting was used to analyze the expression levels of key proteins in the cGMP/PKG/ATP2A1 signaling axis. UHPLC-Q-Exactive Orbitrap MS combined with network pharmacology was used to characterize the chemical components of PRAC-E and identify its core active constituents against HA. Quantitative analysis of core components was performed by UHPLC-QTRAP-MS/MS. Molecular docking predicted the binding stability of core components and key targets. The results showed that PRAC-E significantly alleviated HA. Collectively, PRAC-E restored calcium pump activity, corrected calcium homeostasis imbalance, reduced inflammatory factor levels, regulated Phosphodiesterase 5A (PDE5A), and activated the cGMP/PKG/ATP2A1 signaling axis. The main components of PRAC-E were phenolic acids, terpenoids, and flavonoids. Among these, six core components (SCCs) related to HA were Gallate (16.96 mg/g), Paeoniflorin (14.27 mg/g), Albiflorin (7.20 mg/g), Benzoyl paeoniflorin (5.33 mg/g), Methyl gallate (0.78 mg/g), and Catechin (0.09 mg/g). Molecular docking analysis demonstrated that SCCs formed stable complexes (∆G ≤ −6.2 kcal/mol) with ATP2A1. Full article

Peripheral arterial disease is a leading cause of amputation and/or death worldwide. Phosphodiesterase 4 (PDE 4) inhibitors demonstrated beneficial effects in ischemia–reperfusion (IR) settings, but whether PDE 4 inhibition protects skeletal muscle against IR deleterious effects is unknown. We therefore performed limb IR (two hours each) in twenty-one male Swiss mice (12–16-week-old) treated or not with Rolipram (1 mg/kg i.p. 30 min before ischemia and 5 min before reperfusion). The muscles were analyzed 4 h after the onset of ischemia. IR significantly increased leucocyte infiltration (93.13 ± 6.886 vs. 150.1 ± 18.38 cells/mg of muscle, p < 0.05) and apoptosis (Bax/Bcl2 ratio, +239%, p < 0.05), together with enhanced mitochondrial fission transcripts (+224% for Drp1, p < 0.01 and +368%, p < 0.0001 for Fis1), and decreased mitochondrial respiration and antioxidant defense. PDE 4 inhibition reduced leucocyte infiltration (150.1 ± 18.38 vs. 55.58 ± 13.83; p < 0.01) and apoptosis (+67%, NS) in association with reduced fission markers (+91% for Drp 1 and +111%, p < 0.05, for Fis 1). Muscle mitochondrial respiration did not improve. In conclusion, PDE 4 inhibition using Rolipram partly protected skeletal muscles against IR-induced deleterious effects. These data support further studies investigating the usefulness of leucocytes modulation in lower-limb IR and a potential beneficial effect of PDE 4 inhibition in peripheral arterial disease. Full article

Phospodiesterase 4 (PDE4) has long been an attractive target not only for the anti-inflammatory therapy in respiratory diseases, but also for other pathologies such as psoriatic arthritis and atopic dermatitis. In this study, we report the synthesis of 5-acetyl-2-ethyl-6-phenyl-3(2H)-pyridazinones differently substituted at position 4 with a variety of aryl/alkylamines, which act as potent PDE4B1 inhibitors in the low nanomolar range. The selectivity toward PDE4A4, PDE4D3 and HARBS, as well as the ability to inhibit TNFα production in human whole blood (hWB), was also evaluated for the most potent products, resulting in a small cluster of compounds with an interesting profile and two selected products (3a and 3k) have been in depth investigated with additional in vitro tests on metabolism and in vivo studies. Finally, molecular docking and minimization of the ligand-enzyme complexes were carried out. Full article

We develop a PDE and boundary integral framework for quaternion-valued fields on product domains $\Omega \subset \mathbb{H}\times \mathbb{H}$ governed by the mixed left/right Cauchy–Fueter system We identify the natural compatibility condition and prove local solvability with quantitative $H^1$ estimates, as well as global weak solvability on admissible products $U_x\times U_y$. Motivated by these estimates, we introduce domains of hyperholomorphy and hyper-conjugates for data that are harmonic in each factor (${\Delta }_{x}u={\Delta }_{y}u=0$), and we establish Carleman-type quantitative unique continuation tools (boundary blow-up, three-balls, and doubling), including a propagation-of-smallness principle across the two factors. On the potential-theoretic side, we construct a double boundary integral representation for biregular fields with kernel $K(\xi ,\eta ;x,y)=E(\xi -x)E(y-\eta )$, establish mapping and jump relations for the associated layer potentials on Lipschitz boundaries, and obtain a Fredholm boundary integral equation for the boundary density in the smooth admissible regime. Finally, we prove a constructive Runge approximation theorem on admissible products and outline a practical discretization workflow consistent with the analysis. Full article

Kolmogorov–Arnold Networks employ learnable univariate activation functions on edges rather than fixed node nonlinearities. Standard B-spline implementations require $O\left(3KW\right)$ parameters per layer (K basis functions, W connections). We introduce shared Gaussian radial basis functions with learnable centers ${\mu }_k^{\left(l\right)}$ and widths ${\sigma }_k^{\left(l\right)}$ maintained globally per layer, reducing parameter complexity to $O(KW+2LK)$ for L layers—a threefold reduction, while preserving Sobolev convergence rates $O\left(h^{s-\mathrm{\Omega }}\right)$. Width clamping at ${\sigma }_{min}={10}^{-6}$ and tripartite regularization ensure numerical stability. On MNIST with architecture $[784,128,10]$ and $K=5$, RBF-KAN achieves $87.8\%$ test accuracy versus $89.1\%$ for B-spline KAN with $1.4\times$ speedup and 33% memory reduction, though generalization gap increases from $1.1\%$ to $2.7\%$ due to global Gaussian support. Physics-informed neural networks demonstrate substantial improvements on partial differential equations: elliptic problems exhibit a $45\times$ reduction in PDE residual and maximum pointwise error, decreasing from $1.32$ to $0.18$; parabolic problems achieve a $2.1\times$ accuracy gain; hyperbolic wave equations show a $19.3\times$ improvement in maximum error and a $6.25\times$ reduction in $L^2$ norm. Superior hyperbolic performance derives from infinite differentiability of Gaussian bases, enabling accurate high-order derivatives without polynomial dissipation. Ablation studies confirm that coefficient regularization reduces mean error by 40%, while center diversity prevents basis collapse. Optimal basis count $K\in [3,5]$ balances expressiveness and overfitting. The architecture establishes Gaussian RBFs as efficient alternatives to B-splines for learnable activation networks with advantages in scientific computing. Full article

Tumor angiogenesis models based on coupled nonlinear parabolic partial differential equations require solving stiff systems where explicit time-stepping methods impose severe stability constraints on the time step size. Implicit–Explicit (IMEX) schemes relax this constraint by treating diffusion terms implicitly and reaction–chemotaxis terms explicitly, reducing each time step to a single linear system solution. However, standard Gaussian elimination with partial pivoting exhibits cubic complexity in the number of spatial grid points, dominating computational cost for realistic discretizations in the range of 400–800 grid points. This work presents a CUDA-based parallel algorithm that accelerates the IMEX scheme through GPU implementation of three core computational kernels: pivot finding via atomic operations on double-precision floating-point values, row swapping with coalesced memory access patterns, and elimination updates using optimized two-dimensional thread grids. Performance measurements on an NVIDIA H100 GPU demonstrate speedup factors, achieving speedup factors from 3.5× to 113× across spatial discretizations spanning $M\in [25,800]$ grid points relative to sequential CPU execution, approaching 94.2% of the theoretical maximum speedup predicted by Amdahl’s law. Numerical validation confirms that GPU and CPU solutions agree to within twelve digits of precision over extended time integration, with conservation properties preserved to machine precision. Performance analysis reveals that the elimination kernel accounts for nearly 90% of total execution time, justifying the focus on GPU parallelization of this component. The method enables parameter studies requiring $\sim {10}^4$ PDE solves, previously computationally prohibitive, facilitating model-driven investigation of anti-angiogenic therapy design. Full article

This study investigates the antioxidant properties of aucubin (AU), an iridoid compound, focusing on its ability to scavenge hydroxyl radicals (^•OH) through its hydroxyl functional groups. Gaussian software was employed to model and validate the underlying antioxidant reaction mechanisms. Three primary pathways were examined: hydrogen atom transfer (HAT), sequential electron transfer-proton transfer (SET-PT), and sequential proton loss–electron transfer (SPLET). All calculations were performed using the M06-2X functional within density functional theory (DFT) at the def2-TZVP level, incorporating Grimme’s D3 dispersion correction and the implicit solvation model based on solute electron density (SMD) for water. Various thermodynamic parameters were determined to analyze and compare the antioxidant reactions, including the O-H bond dissociation energy (BDE), ionization potential (IP), proton dissociation enthalpy (PDE), electron transfer enthalpy (ETE), and proton affinity (PA) of the hydroxy groups. The results indicated that the HAT mechanism is the dominant pathway in the scavenging of ^•OH radicals by AU. The key active sites were identified as the 6-OH group in the aglycone structure and the 6′-OH group in the sugar moiety. Moreover, the polar aqueous environment promoted O-H bond homolysis to enhance the antioxidant activity. Full article

We consider the fourth-order PDE $u_{xxxx}+2u_{xxyy}+u_{yyyy}-u_{tt}=h\left(u\right)$. The Lie and Noether symmetry generators are constructed, and we reduce the PDE to simpler ODEs. Furthermore, we use some well-known methods to compute the conserved vectors associated with the PDE. An analysis of reduced ordinary differential equations (ODEs), invariant solutions, and their physical interpretations is presented. Full article

This study investigates hydrogen storage enhancement through adsorption in porous materials by coupling the Dubinin–Astakhov (D-A) adsorption model with H₂ conservation equations (mass, momentum, and energy). The resulting system of partial differential equations (PDEs) was solved numerically using the finite element method (FEM). Experimental work using activated carbon as an adsorbent was carried out to validate the model. The comparison showed good agreement in terms of temperature distribution, average pressure of the system, and the amount of adsorbed hydrogen (H₂). Further simulations with different adsorbents indicated that compact metal–organic framework 5 (MOF-5) is the most effective material in terms of H₂ adsorption. Additionally, the pair (273 K, 800 s) remains the optimal combination of injection temperature and time. The findings underscore the prospective advantages of optimized MOF-5-based systems for enhanced hydrogen storage. These systems offer increased capacity and safety compared to traditional adsorbents. Subsequent research should investigate multi-objective optimization of material properties and system geometry, along with evaluating dynamic cycling performance in practical operating conditions. Additionally, experimental validation on MOF-5-based storage prototypes would further reinforce the model’s predictive capabilities for industrial applications. Full article

The freezing method is widely employed in the construction of a vertical shaft in soft soil and water-rich strata. As the construction depth increases, investigating the water–heat–force coupling effects induced by the hydration heat (internal heat source) of concrete is crucial for the safety of the lining structure and its resistance to cracking and seepage. A three-dimensional coupled thermal–hydraulic–mechanical analysis model was developed, incorporating temperature and soil relative saturation as unknown variables based on heat transfer in porous media, unsaturated soil seepage, and frost heave theory. The coefficient type PDE module in COMSOL was used for secondary development to solve the coupling equation, and the on-site temperature and pressure monitoring data of the frozen construction process were compared. This study obtained the model-related parameters and elucidated the evolution mechanism of freeze–thaw and freeze–swelling pressures of a frozen wall under the influence of hydration heat. The resulting model shows that the maximum thaw depth of the frozen wall reaches 0.3576 m after 160 h of pouring, with an error rate of 4.64% compared to actual measurements. The peak temperature of the shaft wall is 73.62 °C, with an error rate of 3.76%. The maximum influence range of hydration heat on the frozen temperature field is 1.763 m. The peak freezing pressure is 4.72 MPa, which exhibits a 5.03% deviation from the actual measurements, thereby confirming the reliability of the resulting model. According to the strength growth pattern of concrete and the freezing pressure bearing requirements, it can provide a theoretical basis for quality control of the lining structure and a safety assessment of the freezing wall. Full article

Inherited retinal dystrophies (IRDs) are a diverse group of monogenic disorders associated with dysfunction of the retina. High myopia, commonly defined as a spherical equivalent ≤ −6.00 D or axial length ≥ 26.5 mm, is a recurring clinical feature across several IRDs, and could serve as an early diagnostic clue. This review provides a summary of IRDs associated with high myopia to guide the clinician in establishing a molecular diagnosis for patients. We performed a comprehensive literature review of articles in PubMed, ScienceDirect, and JAMA Network to identify associations between monogenic IRDs and high myopia. Genes associated with IRDs and high myopia clustered into functional categories that included collagen/structural integrity (COL2A1, COL9A1, COL11A1, COL18A1, P3H2), phototransduction and visual cycle (PDE6C, PDE6H, GUCY2D, ARR3, RBP3), ciliary trafficking and microtubule-associated genes (RPGR, RP2, IFT140, CFAP418, FAM161A), synaptic ribbon and bipolar cell signaling (NYX, CACNA1F, TRPM1, GRM6, LRIT3, GPR179), opsin-related genes (OPN1LW, OPN1MW), and miscellaneous categories (VPS13B, ADAMTS18, LAMA1). Associations between IRDs and high myopia spanned stationary and progressive retinal disorders and included both cone-dominant and rod-dominant diseases. High myopia accompanied by other visual symptoms and signs such as nyctalopia, photophobia, or reduced best-corrected visual acuity should heighten suspicion for an underlying IRD. Earlier diagnosis of IRDs for patients could facilitate timely genetic counseling, participation in clinical trials, and interventions for patients to preserve vision.: Full article

In this paper, we develop a concise differential–potential framework for the functions of a generalized quaternionic variable in the two-parameter algebra ${\mathbb{H}}_{\alpha ,\beta }$, with $\alpha ,\beta \in \mathbb{R}\setminus \left\{0\right\}$. Starting from left/right difference quotients, we derive complete Cauchy–Riemann (CR) systems and prove that, away from the null cone where the reduced norm N vanishes, these first-order systems are necessary and, under ${\mathcal{C}}^1$ regularity, sufficient for left/right differentiability, thereby linking classical one-dimensional calculus to a genuinely four-dimensional setting. On the potential theoretic side, the Dirac factorization ${\Delta }_{\alpha ,\beta }=\overline{\mathcal{D}}\mathcal{D}=\mathcal{D}\overline{\mathcal{D}}$ shows that each real component of a differentiable mapping is ${\Delta }_{\alpha ,\beta }$-harmonic, yielding a clean second-order theory that separates the elliptic (Hamiltonian) and split (coquaternionic) regimes via the principal symbol. In the classical case $(\alpha ,\beta )=(-1,-1)$, we present a Poisson-type representation solving a model Dirichlet problem on the unit ball $B\subset {\mathbb{R}}^4$, recovering mean-value and maximum principles. For computation and symbolic verification, real $4\times 4$ matrix models for left/right multiplication linearize the CR systems. Examples (polynomials, affine CR families, and split-signature contrasts) illustrate the theory, and the outlook highlights boundary integral formulations, Green kernel constructions, and discretization strategies for quaternionic PDEs. Full article

Atopic dermatitis (AD) is a chronic, relapsing inflammatory skin disorder characterized by immune dysregulation and epidermal barrier dysfunction. Advances in understanding the interplay of genetic predisposition, cytokine signaling, and environmental triggers have led to the emergence of targeted therapies. Although biologic agents such as dupilumab, tralokinumab, and lebrikizumab have revolutionized AD management, their high costs, injectable administration, and limited global accessibility highlight the need for alternative options. Small molecule therapies are gaining momentum as they target intracellular pathways central to AD pathogenesis and offer oral or topical administration routes. This review provides a comprehensive analysis of key agents including Janus kinase (JAK) inhibitors (upadacitinib, abrocitinib, baricitinib, ruxolitinib, delgocitinib), phosphodiesterase 4 (PDE4) inhibitors (crisaborole, difamilast, roflumilast, apremilast), as well as STAT6 degraders (KT621, NX3911), aryl hydrocarbon receptor modulators, histamine H4 receptor antagonists (adriforant, izuforant), and sphingosine-1-phosphate receptor modulators (etrasimod, BMS-986166). We summarize their mechanisms of action, pharmacological profiles, and pivotal clinical trial data, emphasizing their potential to address unmet therapeutic needs. Finally, we discuss safety concerns, long-term tolerability, and future directions for integrating small molecule therapies into precision treatment strategies for moderate-to-severe AD. Full article

Dexamethasone, widely used as an exogenous glucocorticoid in clinical and animal practice, has recently been recognized as an environmental contaminant of concern. Existing evidence documents its ability to induce persistent dyslipidemia in adult offspring. In this study, plasma cholesterol levels in male rats exposed to dexamethasone prenatally (PDE) were increased. Meanwhile, developmental tracking revealed a reduction in hepatic low-density lipoprotein receptor (LDLR) promoter H3K27 acetylation (H3K27ac) and corresponding transcriptional activity across gestational-to-postnatal stages. Mechanistic investigations established glucocorticoid receptor/histone deacetylase2 (GR/HDAC2) axis-mediated epigenetic programming of LDLR through H3K27ac modulation in PDE offspring, potentiating susceptibility to hypercholesterolemia. Additionally, in peripheral blood mononuclear cells (PBMC) of PDE male adult offspring, LDLR H3K27ac level and expression were also decreased and positively correlated with those in the liver. Clinical studies further substantiated that male newborns prenatally treated with dexamethasone exhibited increased serum cholesterol levels and consistent reductions in LDLR H3K27ac levels and corresponding transcriptional activity in PBMC. This study establishes a complete evidence chain linking PDE with epigenetic programming and cholesterol metabolic dysfunction, proposing PBMC epigenetic biomarkers as a novel non-invasive monitoring tool for assessing the developmental toxicity of chemical exposures during pregnancy. This has significant implications for improving environmental health risk assessment systems. Full article