Search Results (77)

Background/Objectives: Systemic sclerosis-associated interstitial lung disease (SSc-ILD) and chronic obstructive pulmonary disease (COPD) are linked to multi-organ vulnerability involving the lungs, heart, and kidneys. This study aimed to compare the annual changes in pulmonary, cardiac, and renal parameters in patients with SSc-ILD and COPD across three consecutive years, using both individual biomarkers and integrated composite profiles. Methods: This observational longitudinal study included repeated assessments in 2023, 2024, and 2025. Functional, laboratory, and imaging parameters were collected: 6-min walk test (6MWT), SpO₂ (pre-/post-exercise), spirometry/CT lung volumes, gas exchange (pO₂/pCO₂/lactate), echocardiography [left ventricular ejection fraction (LVEF), estimated systolic pulmonary artery pressure (sPAP)], cardiac biomarkers (NT-proBNP, MR-proANP, hsTnT), renal markers [eGFR, creatinine, albuminuria, albumin-to-creatinine ratio (ACR)], heart rate variability (HRV), and renal CT densitometry. All markers were standardized (z-scores, higher values = worse). Subprofiles were generated and aggregated into three integrated profiles (cardiac, renal, pulmonary). Within-group dynamics were analyzed using the Wilcoxon signed-rank test (year-to-year deltas), between-group comparisons with the Mann–Whitney U test, effect sizes via Cliff’s delta, and multiple testing correction with the Benjamini–Hochberg false discovery rate (FDR). Results: Exercise tolerance declined in both groups: by 2025, 6MWT distance decreased by −10 m in SSc-ILD (p = 0.006; q = 0.010) and −20 m in COPD (p = 0.002; q = 0.004); post-exercise SpO₂ fell in both cohorts (both p < 0.001; q < 0.001). MR-proANP remained consistently higher in SSc-ILD across all years (p ≤ 0.005; q ≤ 0.028). sPAP increased in both groups, reaching higher values in COPD by 2025 (p = 0.007; q = 0.033). NT-proBNP and hsTnT increased over time, while eGFR declined, and ACR rose in both cohorts (both p < 0.001; q < 0.001). HRV (HF/total power) decreased by 2025. Composite profiles showed: in 2023, the cardiac profile was worse in SSc-ILD (δ ≈ 0.27; p = 0.011; q = 0.048), but differences diminished by 2025; the renal profile was initially worse in SSc-ILD but later shifted unfavorably in COPD; the pulmonary profile showed no consistent between-group differences. Conclusions: Over three years, patients with SSc-ILD and COPD exhibited concordant deterioration in pulmonary, cardiac, and renal function. Distinct leading markers emerged: desaturation during exercise and neurohormonal activation (MR-proANP) in SSc-ILD, versus reduced 6MWT and higher sPAP in COPD. These findings support the need for integrated monitoring of the cardio–pulmo–renal continuum. Limitations include the observational design, multiple comparisons, and absence of advanced repeated-measures modeling. Full article

We develop a convergence framework for Grünwald–Letnikov (GL) fractional and classical integer difference operators acting on sequences in fuzzy-paranormed (fp) spaces, motivated by data that are imprecise and contain sporadic outliers. Fuzzy paranorms provide a resolution-dependent notion of proximity, while statistical and lacunary statistical convergence downweight sparse deviations by natural density; together, they yield robust criteria for difference-filtered signals. Within this setting, we establish uniqueness of fp–${\mathsf{\Delta }}^m$ statistical limits; an equivalence between fp-statistical convergence of ${\mathsf{\Delta }}^m$ (and its GL extension ${\mathsf{\Delta }}^{\alpha }$) and fp-strong p-Cesàro summability; an equivalence between lacunary fp-${\mathsf{\Delta }}^m$ statistical convergence and blockwise strong p-Cesàro summability; and a density-based decomposition into a classically convergent part plus an fp-null remainder. We also show that GL binomial weights act as an ${\ell }^1$ convolution, ensuring continuity of ${\mathsf{\Delta }}^{\alpha }$ in the fp topology, and that nabla/delta forms are transferred by the discrete Q–operator. The usefulness of the criteria is illustrated on simple engineering-style examples (e.g., relaxation with memory, damped oscillations with bursts), where the fp-Cesàro decay of difference residuals serves as a practical diagnostic for Cesàro compliance. Beyond illustrative mathematics, we report engineering-style diagnostics where the fuzzy Cesàro residual index correlates with measurable quantities (e.g., vibration amplitude and energy surrogates) under impulsive disturbances and missing data. We also calibrate a global decision threshold ${\tau }_{\mathrm{glob}}$ via sensitivity analysis across $(\alpha ,p,m)$, where $m\in \mathbb{N}$ is the integer difference order, $\alpha >0$ is the fractional order, and $p\ge 1$ is the Cesàro exponent, and provide quantitative baselines (median/M-estimators, ${\ell }_1$ trend filtering, Gaussian Kalman filtering, and an $\alpha$-stable filtering structure) to show complementary gains under bursty regimes. The results are stated for integer m and lifted to fractional orders $\alpha >0$ through the same binomial structure and duality. Full article

Computer viruses continue to threaten the security of digital networks, and their complex propagation dynamics require refined modelling tools. Most existing models rely on integer-order dynamics or assume uniform memory effects, which limit their ability to capture heterogeneous behaviours observed in practice. To address this gap, we propose a discrete incommensurate fractional-order virus model based on Caputo-like delta differences, where each compartment is assigned a distinct fractional order to represent mismatched time scales. The model’s dynamics are analysed in terms of stability, bifurcation, and chaos. Numerical results reveal the emergence of rich chaotic attractors, emphasizing the impact of fractional memory on system evolution. To quantify complexity, we employ Approximate Entropy and Spectral Entropy and relate these indicators to the maximum Lyapunov exponent, confirming the system’s sensitivity and unpredictability. All numerical simulations and visualizations were performed using MATLAB (R2015a). The findings highlight the importance of heterogeneous memory in computer-virus modeling and offer new insights for developing theoretical foundations of robust cybersecurity strategies. Full article

We present a unified framework for fuzzy statistical convergence of Grünwald–Letnikov (GL) fractional differences in Bag–Samanta fuzzy normed linear spaces, addressing memory effects and nonlocality inherent to fractional-order models. Theoretically, we establish the uniqueness, linearity, and invariance of fuzzy statistical limits and prove a Cauchy characterization: fuzzy statistical convergence implies fuzzy statistical Cauchyness, while the converse holds in fuzzy-complete spaces (and in the completion, otherwise). We further develop an inclusion theory linking fuzzy strong Cesàro summability—including weighted means—to fuzzy statistical convergence. Via the discrete Q-operator, all statements transfer verbatim between nabla-left and delta-right GL forms, clarifying the binomial GL↔discrete Riemann–Liouville correspondence. Beyond structure, we propose density-based residual diagnostics for GL discretizations of fractional initial-value problems: when GL residuals are fuzzy statistically negligible, trajectories exhibit Ulam–Hyers-type robustness in the fuzzy topology. We also formulate a fuzzy Korovkin-type approximation principle under GL smoothing: Cesàro control on the test set $\{1,x,x^2\}$ propagates to arbitrary targets, yielding fuzzy statistical convergence for positive-operator sequences. Worked examples and an engineering-style case study (thermal balance with memory and bursty disturbances) illustrate how the diagnostics certify robustness of GL numerical schemes under sparse spikes and imprecise data. Full article

Background: Ephedra przewalskii Stapf stems are a traditional Mongolian medicine commonly used to treat infectious diseases. Previous in vitro experiments have shown that the extract powder derived from its stems possesses antiviral activity. However, the active compounds responsible for this activity in E. przewalskii Stapf have not yet been identified or evaluated. This study aimed to identify the active components in E. przewalskii that exhibit antiviral effects against SARS-CoV-2 in vitro and validate their antiviral activity. Methods: E. przewalskii stem extracts were subjected to high-performance liquid chromatography with varying methanol ratios in the mobile phase to obtain fractions with different polarities. Antiviral activity was assessed by infecting VeroE6/TMPRSS2 cells with the SARS-CoV-2 Delta strain and treating them with the obtained fractions. Infectious titers were measured using the 50% tissue culture infective dose (TCID₅₀) method, and half-maximal inhibitory concentration (IC₅₀) values were calculated for each fraction. The active components in the two fractions with the highest antiviral activity were identified and structurally characterized by nuclear magnetic resonance analysis. The antiviral activity of these compounds was confirmed by adding them to SARS-CoV-2-infected cells and measuring their infectious titers using the TCID₅₀ method. The IC₅₀ values were also calculated. Viral-particle inactivation assays were conducted by mixing the extracts with SARS-CoV-2 and measuring infectious titers. Results: (−)-Catechin, (+)-epigallocatechin-(2α→O→7,4α→8)-(−)-epicatechin, and ent-epicatechin-(4α→8;2α→O→7)-catechin were isolated from E. przewalskii. These compounds exhibited significant antiviral activity against SARS-CoV-2 but demonstrated minimal direct virucidal effects. Conclusion: (−)-Catechin, (+)-epigallocatechin-(2α→O→7,4α→8)-(−)-epicatechin, and ent-epicatechin-(4α→8;2α→O→7)-catechin exhibit antiviral activity against SARS-CoV-2 in infected cells. Full article

The aim of this study was to describe changes in estimated glomerular filtration rate (eGFR), left ventricular ejection fraction (LVEF) and clinical outcomes in a real-world cohort of patients with heart failure with reduced ejection fraction (HFrEF) and atrial fibrillation (AF). A total of 321 patients (67 [58–74] years old, 19.3% females) were included; 134 (41.7%) had AF. AF patients were less frequently prescribed angiotensin receptor–neprilysin inhibitor (ARNi), with no differences concerning sodium–glucose transport protein 2 inhibitors (SGLT2is) and had lower median baseline eGFR values. At 6- and 12-month follow-ups, renal function declined similarly in both groups, with no difference in the proportion of patients experiencing an eGFR decrease of ≥30% from baseline. Regarding cardiac remodeling, patients without AF showed a higher proportion of individuals with an LVEF improvement of ≥10% from baseline, however with no differences between groups in LVEF final recovery. During a median follow-up of 582 (339–1481) days, AF patients showed a higher risk of composite outcome (aHR, 95% CI: 2.12, 1.16–3.86) and of hospitalization for heart failure (hHF) (2.80, 1.44–5.46), without differences in all-cause death. Delta eGFR changes with at least a 30% decline in eGFR were associated with a higher risk of the primary endpoint. Despite lower baseline renal function, AF patients exhibited similar LVEF improvement and renal decline, which emphasizes the importance of guideline-directed medical therapy. AF was associated with a higher risk of adverse events, primarily driven by hHF. Full article

The asymptotic behavior of discrete Riemann–Liouville fractional difference equations is a fundamental problem with important mathematical and physical implications. In this paper, we investigate a particular case of such an equation of the order $0.5$ subject to a given initial condition. We establish the existence of a unique solution expressed via a Mittag-Leffler-type function. The delta-asymptotic behavior of the solution is examined, and its convergence properties are rigorously analyzed. Numerical experiments are conducted to illustrate the qualitative features of the solution. Furthermore, a neural network-based approximation is employed to validate and compare with the analytical results, confirming the accuracy, stability, and sensitivity of the proposed method. Full article

Despite the global imperative to enhance carbon sequestration in agricultural landscapes, saline–alkali soils present distinctive soil–microbe constraints that limit our understanding of optimal management strategies. This study addresses critical knowledge gaps regarding the mechanistic relationships between bacterial community structure and carbon stabilization processes in saline–alkali soil. A three-year field experiment was conducted in the Yellow River Delta, China, with two N levels (N1, 270 kg N ha⁻¹; N2, 210 kg N ha⁻¹) and three C treatments (S0, 0 kg C ha⁻¹; S1, 5000 kg C ha⁻¹; S2, 10,000 kg C ha⁻¹). SOC sequestration by straw incorporation increased by 16.34–22.86% and 8.18–11.91%, with no significant difference between the S1 and S2 treatments, because the specific C mineralization rate (SCMR) of the S2 treatment was 13.80–41.61% higher than the S1 treatment. The reduced nitrogen application (N2) enhanced SOC sequestration efficiency by 3.40–12.97% compared with conventional rates, particularly when combined with half straw incorporation. Furthermore, compared with the N1S1 treatment, the N2S1 treatment induced qualitative transformations in carbon chemistry, increasing aromatic carbon compounds (28.79%) while reducing carboxylic fractions (10.06%), resulting in enhanced structural stability of sequestered carbon. Bacterial community analysis revealed distinctive shifts in bacterial composition under different treatments. Half straw incorporation (S1) increased the abundance of oligotrophic strategists (Verrucomicrobiae and Acidimicrobiia) while decreasing copiotrophic bacteria (Bacteroidia), indicating a transition from r-strategy to k-strategy microbial communities that fundamentally altered carbon cycling. Half straw incorporation and reduced N application were beneficial to stabilize SOC composition, reduce mineralization rates, optimize bacterial survival strategy, and thus achieve SOC sequestration. Full article

River nodes play a crucial role in regulating water and sediment transport within river networks. The SiXianJiao (SXJ) node serves as a key exchange point between the West River (WR) and North River (NR) in the Pearl River Delta (PRD), South China. Understanding the differences in flood diversion dynamics between X-shaped and H-shaped configurations under varying geomorphic conditions is essential for flood management. This study employs the Delft3D-Flow model to investigate the flood diversion mechanisms of these composite river nodes. Results revealed distinct hydrodynamic behaviors: the X-shaped node facilitates greater water exchange due to a shared channel segment, whereas the H-shaped node experiences restricted exchange due to flow resistance in the connecting branch. Both configurations exhibit self-regulating flood diversion processes that significantly reduce flood risks. A critical flow fraction of approximately 75.9% [WR/(WR + NR)] is identified, at which water levels (WLs) at both ends of the SXJ node almost equalize. When the WR flow fraction exceeds this threshold, floodwaters are diverted toward the NR. Below it, the diversion direction reverses. Additionally, flood diversion synchronizes asynchronous flood waves, stabilizing the discharge fraction at Makou (Sanshui), which fluctuates around 75.8% (24.2%) for the X-shaped node and 76.6% (23.4%) for the H-shaped node. These findings enhance our understanding of flood diversion dynamics and provide valuable insights for optimizing flood mitigation strategies and hydraulic infrastructure planning in the PRD and comparable river systems worldwide. Full article

Background: The delta neutrophil index (DNI) represents the immature granulocyte fraction and is determined by subtracting the fraction of mature polymorphonuclear leucocytes from the sum of myeloperoxidase-reactive cells. The DNI has been proposed as a useful prognostic marker for sepsis. This study evaluated the clinical utility of DNI as a predictive marker in patients with pneumonia-induced sepsis in the intensive care unit (ICU). Methods: We conducted a retrospective study of pneumonia-induced sepsis in patients who were admitted to the Kangdong Sacred Heart Hospital’s medical ICUs from July 2022 to March 2024. The DNI was measured on three consecutive days after ICU admission. The primary outcome of this study was a 28-day mortality. Results: A total of 227 patients with pneumonia-induced sepsis were included in this study. A 28-day mortality occurred 20.3% of the time in our study. In a univariate analysis, age (p = 0.05), lymphocyte (p = 0.02), DNI 1 (p = 0.01), DNI 2 (p = 0.00), DNI 3 (p = 0.00), and lactic acid (p = 0.00) were significantly associated with 28-day mortality. In a multivariable analysis, lactate (adj. OR: 0.86, 95% CI: 0.78–0.95, p = 0.002), and DNI 3 (adj. OR: 0.94, 95% CI: 0.89–0.99, p = 0.048) were significantly associated with 28-day mortality. In our study, the most appropriate cut-off values were DNI 1 (7.15), DNI 2 (8.9), and DNI 3 (2.6). Patients with higher DNI 3 (≥2.6) showed higher 28-day mortality than patients with lower DNI 3 values of <2.6 (67.4% vs. 32.6%; p < 0.001). However, those aged ≥70 did not show statistically significantly different DNI 1 values between the survivor and non- survivor groups. Conclusions: The DNI at 72 h after ICU admission is a promising predictive prognostic marker of 28-day mortality in patients with pneumonia-induced sepsis in the ICU. However, the interpretation of the DNI in sepsis patients aged 70 and older on the first day of hospitalization should be approached with caution. Full article

Coastal saltmarsh wetlands are vital “blue carbon” ecosystems. Fractional vegetation cover (FVC) is a key indicator revealing the spatial distribution and growth status of vegetation. Remote sensing has proven a vital tool for FVC estimation at regional or landscape scales. Establishing a species-level FVC estimation model usually requires sufficient field measurements as training/validation samples. However, field-based sample collection in wetlands is challenging because of the harsh environment. In this study, we proposed a Fractional Vegetation Cover Wasserstein Generative Adversarial Network (FVC-WGAN) model for FVC sample expansion. We chose the Yellow River Delta as the study area and utilized the time series Sentinel-2 imagery and random forest regression model for species-level FVC estimation with the assistance of FVC-WGAN-generated samples. To assess the efficacy of FVC-WGAN, we designed 13 experimental schemes using different combinations of real and generated samples. Our results show that the FVC-WGAN-generated samples had similar feature values to the real samples. Supplementing 500 real samples with generated samples can achieve good accuracy with an average RMSE < 0.1. As the number of real samples increased, the accuracies of FVC estimation improved. When the number of the generated samples was balanced with the real samples, the accuracy improved in terms of both R², RMSE and the spatial consistency. Full article

Special functions have been widely used in fractional calculus, particularly for addressing the symmetric behavior of the function. This paper provides improved delta Mittag–Leffler and exponential functions to establish new types of fractional difference operators in the setting of Riemann–Liouville and Liouville–Caputo. We give some properties of these discrete functions and use them as the kernel of the new fractional operators. In detail, we propose the construction of the new fractional sums and differences. We also find the Laplace transform of them. Finally, the relationship between the Riemann–Liouville and Liouville–Caputo operators are examined to verify the feasibility and effectiveness of the new fractional operators. Full article

Alzheimer’s disease (AD) is the most widespread neurodegenerative disorder. Recently, it was found that mucus extract from Cornu aspersum has beneficial effects on memory and cognitive processes in a rat scopolamine model of AD. The present study elucidated the mechanisms of action of standardized mucus snail extract (SE) enriched with a fraction above 20 kDa on Alzheimer-type dementia in rats. Using proteomic analysis on two-dimensional polyacrylamide gel electrophoresis (2D–PAGE) on rat cortex extracts, we compared protein expression in both groups: the first group was treated intraperitoneally with scopolamine (Sco, 2 mg/kg, 11 days) and the second (Sco + SE) group was treated intraperitoneally with Sco (Sco, 2 mg/kg) and protected by SE (0.5 mL/100 g bw) applied daily orally for 11 days. Brain cortex was separated and the expressions of various proteins related to memory and cognitive functions were identified. We found that the expression of Ubiquitin carboxyl-terminal hydrolase isozyme L1, Calbindin, Vacuolar ATP synthase catalytic subunit A, Tropomyosin beta chain, 14-3-3 zeta/delta, Kinesin-1 heavy chain, and Stathmin-4 significantly differs in SE-protected rats as compared to dement animals treated only by Sco, and these brain proteins might be potential therapeutic targets for Alzheimer’s-type dementia treatment. Full article

(1) Background: Considering the increasing workload of pathologists, computer-assisted methods have the potential to come to their aid. Considering the prognostic role of myocardial fibrosis, its precise quantification is essential. Currently, the evaluation is performed semi-quantitatively by the pathologist, a method exposed to the issues of subjectivity. The present research proposes validating a semi-automatic algorithm that aims to quantify myocardial fibrosis on microscopic images. (2) Methods: Forty digital images were selected from the slide collection of The Iowa Virtual Slidebox, from which the collagen volume fraction (CVF) was calculated using two semi-automatic methods: CIELAB-MATLAB^® and CIELAB-Python. These involve the use of color difference analysis, using Delta E, in a rectangular region for CIELAB-Python and a region with a random geometric shape, determined by the user’s cursor movement, for CIELAB-MATLAB^®. The comparison was made between the stereological evaluation and ImageJ. (3) Results: A total of 36 images were included in the study (n = 36), demonstrating a high, statistically significant correlation between stereology and ImageJ on the one hand, and the proposed methods on the other (p < 0.001). The mean CVF determined by the two methods shows a mean bias of 1.5% compared with stereology and 0.9% compared with ImageJ. Conclusions: The combined algorithm has a superior performance compared to the proposed methods, considered individually. Despite the relatively small mean bias, the limits of agreement are quite wide, reflecting the variability of the images included in the study. Full article

The present paper is dedicated to the examination of maximum and minimum results based on Green’s functions via delta fractional differences for a class of fractional boundary problems. For such a purpose, we built the corresponding Green’s functions based on the falling factorial functions. In addition, using the constructed Green’s function, the positivity of the function and its corresponding delta function are presented. We also verified the occurrence of two distinct functions with the same Green’s function. The maximality and minimality of the Green’s function show a good qualitative agreement. Finally, we considered some special examples to explain the obtained results. Full article