Search Results (25)

A Cournot triopoly is a type of oligopoly market involving three firms that produce and sell homogeneous or similar products without cooperating with one another. In Cournot models, firms’ decisions about production levels play a crucial role in determining overall market output. Compared to duopoly models, oligopolies with more than two firms have received relatively less attention in the literature. Nevertheless, triopoly models are more reflective of real-world market conditions, even though analyzing their dynamics remains a complex challenge. A reaction–diffusion system of PDEs generalizing a nonlinear triopoly model describing a master–slave Cournot game is introduced. The effect of diffusion on the stability of Nash equilibrium is investigated. Self-diffusion alone cannot induce Turing pattern formation. In fact, linear stability analysis shows that cross-diffusion is the key mechanism for the formation of spatial patterns. The conditions for the onset of cross-diffusion-driven instability are obtained via linear stability analysis, and the formation of several Turing patterns is investigated through numerical simulations. Full article

PDE11A is a little-studied phosphodiesterase sub-family that breaks down cAMP/cGMP, with the PDE11A4 isoform enriched in the memory-related hippocampal formation. Age-related increases in PDE11A expression occur in human and rodent hippocampus and cause age-related cognitive decline of social memories. Interestingly, age-related increases in PDE11A4 protein ectopically accumulate in spherical clusters that group together in the brain to form linear filamentous patterns termed “PDE11A4 ghost axons”. The biophysical/physiochemical mechanisms underlying this age-related clustering are not known. Here, we determine if age-related clustering of PDE11A4 reflects liquid–liquid phase separation (LLPS; biomolecular condensation), and if PDE11A inhibitors can reverse this LLPS. We show human and mouse PDE11A4 exhibit several LLPS-promoting sequence features, including intrinsically disordered regions, non-covalent pi–pi interactions, and prion-like domains that were particularly enriched in the N-terminal regulatory region. Further, multiple bioinformatic tools predict PDE11A4 undergoes LLPS. Consistent with these predictions, aging-like PDE11A4 clusters in HT22 hippocampal neuronal cells were membraneless spherical droplets that progressively fuse over time in a concentration-dependent manner. Deletion of the N-terminal intrinsically disordered region prevented PDE11A4 LLPS despite equal protein expression between WT and mutant constructs. 1,6-hexanediol, along with tadalafil and BC11-38 that inhibit PDE11A4, reversed PDE11A4 LLPS in HT22 hippocampal neuronal cells. Interestingly, PDE11A4 inhibitors reverse PDE11A4 LLPS independently of increasing cAMP/cGMP levels via catalytic inhibition. Importantly, orally dosed tadalafil reduced PDE11A4 ghost axons in old mouse ventral hippocampus by 50%. Thus, PDE11A4 exhibits the four defining criteria of LLPS, and PDE11A inhibitors reverse this age-related phenotype both in vitro and in vivo. Full article

Pulse detonation engines (PDEs) have become a transformative technology in the field of aerospace propulsion due to the high thermal efficiency of detonation combustion. However, initiating detonation waves within a limited space and time is key to their engineering application. Direct initiation, though theoretically feasible, requires very high critical energy, making it almost impossible to achieve in engineering applications. Therefore, indirect initiation methods are more practical for triggering detonation waves that produce a deflagration wave through a low-energy ignition source and realizing deflagration to detonation transition (DDT) through flame acceleration and the interaction between flames and shock waves. This review systematically summarizes recent advancements in DDT methods in pulse detonation engines, focusing on the basic principles, influencing factors, technical bottlenecks, and optimization paths of the following: hot jet ignition initiation, obstacle-induced detonation, shock wave focusing initiation, and plasma ignition initiation. The results indicate that hot jet ignition enhances turbulent mixing and energy deposition by injecting energy through high-energy jets using high temperature and high pressure; this can reduce the DDT distance of hydrocarbon fuels by 30–50%. However, this approach faces challenges such as significant jet energy dissipation, flow field instability, and the complexity of the energy supply system. Solid obstacle-induced detonation passively generates turbulence and shock wave reflection through geometric structures to accelerate flame propagation, which has the advantages of having a simple structure and high reliability. However, the problem of large pressure loss and thermal fatigue restricts its long-term application. Fluidic obstacle-induced detonation enhances mixing uniformity through dynamic disturbance to reduce pressure loss. However, its engineering application is constrained by high energy consumption requirements and jet–mainstream coupling instability. Shock wave focusing utilizes concave cavities or annular structures to concentrate shock wave energy, which directly triggers detonation under high ignition efficiency and controllability. However, it is extremely sensitive to geometric parameters and incident shock wave conditions, and the structural thermal load issue is prominent. Plasma ignition generates active particles and instantaneous high temperatures through high-energy discharge, which chemically activates fuel and precisely controls the initiation sequence, especially for low-reactivity fuels. However, critical challenges, such as high energy consumption, electrode ablation, and decreased discharge efficiency under high-pressure environments, need to be addressed urgently. In order to overcome the bottlenecks in energy efficiency, thermal management, and dynamic stability, future research should focus on multi-modal synergistic initiation strategies, the development of high-temperature-resistant materials, and intelligent dynamic control technologies. Additionally, establishing a standardized testing system to quantify DDT distance, energy thresholds, and dynamic stability indicators is essential to promote its transition to engineering applications. Furthermore, exploring the DDT mechanisms of low-carbon fuels is imperative to advance carbon neutrality goals. By summarizing the existing DDT methods and technical bottlenecks, this paper provides theoretical support for the engineering design and application of PDEs, contributing to breakthroughs in the fields of hypersonic propulsion, airspace shuttle systems, and other fields. Full article

Porcine latissimus dorsi muscle (LDM) is a crucial source of pork products. Meat quality indicators, such as the proportion of muscle fibers and intramuscular fat (IMF) deposition, vary during the growth and development of pigs. Numerous studies have highlighted the heterogeneous nature of skeletal muscle, with phenotypic differences reflecting variations in cellular composition and transcriptional profiles. This study investigates the cellular-level transcriptional characteristics of LDM in large white pigs at two growth stages (170 days vs. 245 days) using single-nucleus RNA sequencing (snRNA-seq). We identified 56,072 cells across 12 clusters, including myofibers, fibro/adipogenic progenitor (FAP) cells, muscle satellite cells (MUSCs), and other resident cell types. The same cell types were present in the LDM at both growth stages, but their proportions and states differed. A higher proportion of FAPs was observed in the skeletal muscle of 245-day-old pigs. Additionally, these cells exhibited more active communication with other cell types compared to 170-day-old pigs. For instance, more interactions were found between FAPs and pericytes or endothelial cells in 245-day-old pigs, including collagen and integrin family signaling. Three subclasses of FAPs was identified, comprising FAPs_COL3A1⁺, FAPs_PDE4D⁺, and FAPs_EBF1⁺, while adipocytes were categorized into Ad_PDE4D⁺ and Ad_DGAT2⁺ subclasses. The proportions of these subclasses differed between the two age groups. We also constructed differentiation trajectories for FAPs and adipocytes, revealing that FAPs in 245-day-old pigs differentiated more toward fibrosis, a characteristic reminiscent of the high prevalence of skeletal muscle fibrosis in aging humans. Furthermore, the Ad_PDE4D⁺ adipocyte subclass, predominant in 245-day-old pigs, originated from FAPs_PDE4D⁺ expressing the same gene, while the Ad_DGAT2⁺ subclass stemmed from FAPs_EBF1⁺. In conclusion, our study elucidates transcriptional differences in skeletal muscle between two growth stages of pigs and provides insights into mechanisms relevant to pork meat quality and skeletal muscle diseases. Full article

Solving partial differential equations (PDEs) on complex domains with hybrid boundary conditions presents significant challenges in numerical analysis. In this paper, we introduce a solution-structure-based framework that transforms non-homogeneous hybrid boundary problems into homogeneous ones, allowing exact conformity to the boundary conditions. By leveraging B-splines within the R-function method structure and adopting the stability principles of the WEB method, we construct a well-conditioned basis for numerical analysis. The framework is validated through a number of numerical examples of Poisson equations with hybrid boundary conditions on different implicit domains in two and three dimensions. The results reflect that the approach can achieve the optimal approximation order in solving hybrid problems. Full article

Physics-informed neural networks (PINNs) have recently emerged as a promising alternative to traditional numerical methods for solving partial differential equations (PDEs) in fluid dynamics. By using PDE-derived loss functions and auto-differentiation, PINNs can recover solutions without requiring costly simulation data, spatial gridding, or time discretization. However, PINNs often exhibit slow or incomplete convergence, depending on the architecture, optimization algorithms, and complexity of the PDEs. To address these difficulties, a variety of novel and repurposed techniques have been introduced to improve convergence. Despite these efforts, their effectiveness is difficult to assess due to the wide range of problems and network architectures. As a novel test case for PINNs, we propose one-dimensional shallow water equations with closed boundaries, where the solutions exhibit repeated boundary wave reflections. After carefully constructing a reference solution, we evaluate the performance of PINNs across different architectures, optimizers, and special training techniques. Despite the simplicity of the problem for classical methods, PINNs only achieve accurate results after prohibitively long training times. While some techniques provide modest improvements in stability and accuracy, this problem remains an open challenge for PINNs, suggesting that it could serve as a valuable testbed for future research on PINN training techniques and optimization strategies. Full article

In this article, an extension of a conventional partial discharge (PD) approach called partial discharge echo (PDE), which is applied to different classes of electrical insulation systems of power devices, is presented. Currently, high-voltage (HV) electrical insulation is attributed not only to transmission and distribution grids but also to the industrial environment and emerging segments such as transportation electrification, i.e., electric vehicles, more-electric aircraft, and propulsion in maritime vehicles. This novel PDE methodology extends the conventional and established PD-based assessment, which is perceived to be one of the crucial indicators of HV electrical insulation integrity. PD echo may provide additional insight into the surface conditions and charge transport phenomena in a non-invasive way. It offers new diagnostic attributes that expand the evaluation of insulation conditions that are not possible by conventional PD measurements. The effects of partial discharge echo in various segments of insulation systems (such as cross-linked polyethylene [XLPE] power cable sections that contain defects and a twisted-pair helical coil that represents motor-winding insulation) are shown in this paper. The aim is to demonstrate the echo response on representative electrical insulating materials; for example, polyethylene, insulating paper, and Nomex. Comparisons of the PD echo decay times among various insulation systems are depicted, reflecting dielectric surface phenomena. The presented approach offers extended quantitative assessments of the conditions of HV electrical insulation, including its detection, measurement methodology, and interpretation. Full article

The problem that the conventional double-exponential transient current model (DE model) can overdrive the circuit, which leads to the overestimation of the soft error rate of the logic cell, is solved. Our work uses a new and accurate model for predicting the soft error rate that brings the soft error rate closer to the actual. The piecewise double-exponential transient current model (PDE model) is chosen, and the accuracy of the model is reflected using the Layout Awareness Single Event Multi Transients Soft Error Rate Calculation tool (LA-SEMT-SER tool). The model can characterize transient current pulses piecewise and limit the peak current magnitude to not exceed the conduction current. TCAD models are constructed from 28 nm process library and cell layouts. The transfer characteristic curves of devices are calibrated, and functional timing verification is performed to ensure the accuracy of the TCAD model. The experimental results show that the PDE model is not only more consistent with TCAD simulation than the DE model in modeling the single event transient currents of the device, but also that the SER calculated by the LA-SEMT-SER tool based on the PDE model has a smaller error than the SER calculated by the LA-SEMT-SER tool based on the DE model. Full article

Recently, a Y727C variant in the dual-specific 3′,5′-cyclic nucleotide phosphodiesterase 11A (PDE11A-Y727C) was linked to increased sleep quality and reduced myopia risk in humans. Given the well-established role that the PDE11 substrates cAMP and cGMP play in eye physiology and sleep, we determined if (1) PDE11A protein is expressed in the retina or other eye segments in mice, (2) PDE11A-Y7272C affects catalytic activity and/or subcellular compartmentalization more so than the nearby suicide-associated PDE11A-M878V variant, and (3) Pde11a deletion alters eye growth or sleep quality in male and female mice. Western blots show distinct protein expression of PDE11A4, but not PDE11A1-3, in eyes of Pde11a WT, but not KO mice, that vary by eye segment and age. In HT22 and COS-1 cells, PDE11A4-Y727C reduces PDE11A4 catalytic activity far more than PDE11A4-M878V, with both variants reducing PDE11A4-cAMP more so than PDE11A4-cGMP activity. Despite this, Pde11a deletion does not alter age-related changes in retinal or lens thickness or axial length, nor vitreous or anterior chamber depth. Further, Pde11a deletion only minimally changes refractive error and sleep quality. That said, both variants also dramatically alter the subcellular compartmentalization of human and mouse PDE11A4, an effect occurring independently of dephosphorylating PDE11A4-S117/S124 or phosphorylating PDE11A4-S162. Rather, re-compartmentalization of PDE11A4-Y727C is due to the loss of the tyrosine changing how PDE11A4 is packaged/repackaged via the trans-Golgi network. Therefore, the protective impact of the Y727C variant may reflect a gain-of-function (e.g., PDE11A4 displacing another PDE) that warrants further investigation in the context of reversing/preventing sleep disturbances or myopia. Full article

As a metastasis-prone malignancy, the metastatic form and location of melanoma seriously affect its prognosis. Although effective surgical methods and targeted drugs are available to enable the treatment of carcinoma in situ, for metastatic tumors, the diagnosis, prognosis assessment and development of immunotherapy are still pending. This study aims to integrate multiple bioinformatics approaches to identify immune-related molecular targets viable for the treatment and prognostic assessment of metastatic melanoma, thus providing new strategies for its use as an immunotherapy. Immunoinfiltration analysis revealed that M1-type macrophages have significant infiltration differences in melanoma development and metastasis. In total, 349 genes differentially expressed in M1-type macrophages and M2-type macrophages were extracted from the MSigDB database. Then we derived an intersection of these genes and 1111 melanoma metastasis-related genes from the GEO database, and 31 intersected genes identified as melanoma macrophage immunomarkers (MMIMs) were obtained. Based on MMIMs, a risk model was constructed using the Lasso algorithm and regression analysis, which contained 10 genes (NMI, SNTB2, SLC1A4, PDE4B, CLEC2B, IFI27, COL1A2, MAF, LAMP3 and CCDC69). Patients with high+ risk scores calculated via the model have low levels of infiltration by CD8⁺ T cells and macrophages, which implies a poor prognosis for patients with metastatic cancer. DCA decision and nomogram curves verify the high sensitivity and specificity of this model for metastatic cancer patients. In addition, 28 miRNAs, 90 transcription factors and 29 potential drugs were predicted by targeting the 10 MMIMs derived from this model. Overall, we developed and validated immune-related prognostic models, which accurately reflected the prognostic and immune infiltration characteristics of patients with melanoma metastasis. The 10 MMIMs may also be prospective targets for immunotherapy. Full article

Reflected partial differential equations (PDEs) have important applications in financial mathematics, stochastic control, physics, and engineering. This paper aims to present a numerical method for solving high-dimensional reflected PDEs. In fact, overcoming the “dimensional curse” and approximating the reflection term are challenges. Some numerical algorithms based on neural networks developed recently fail in solving high-dimensional reflected PDEs. To solve these problems, firstly, the reflected PDEs are transformed into reflected backward stochastic differential equations (BSDEs) using the reflected Feyman–Kac formula. Secondly, the reflection term of the reflected BSDEs is approximated using the penalization method. Next, the BSDEs are discretized using a strategy that combines Euler and Crank–Nicolson schemes. Finally, a deep neural network model is employed to simulate the solution of the BSDEs. The effectiveness of the proposed method is tested by two numerical experiments, and the model shows high stability and accuracy in solving reflected PDEs of up to 100 dimensions. Full article

This work presents the thermochemical analysis of a packed-bed reactor via multi-dimensional CFD modeling using FlexPDE and COMSOL Multiphysics. The temperature, concentration, and reaction rate profiles for methane production following the Fischer–Tropsch (F-T) synthesis were studied. To this end, stationary and dynamic differential equations for mass and heat transfer were solved via the finite element technique. The transport equations for 1-D and 2-D models using FlexPDE consider dispersion models, where the fluid and the catalyst can be treated as either homogeneous or heterogenous systems depending on the gradient extents. On the other hand, the 3-D model obtained in COMSOL deems the transport equations incorporated in the Porous Media module. The aim was to compare the FlexPDE and COMSOL models, and to validate them with experimental data from literature. As a result, all models were in good agreement with experimental data, especially for the 2-D and 3-D dynamic models. In terms of kinetics, the predicted reaction rate profiles from the COMSOL model and the 2-D dynamic model followed the temperature trend, thus reflecting the temperature dependence of the reaction. Based on these findings, it was demonstrated that applying different approaches for the CFD modeling of F-T processes conducts reliable results. Full article

Prostate cancer is a complex and heterogeneous disease, but a small number of cell lines have dominated basic prostate cancer research, representing a major obstacle in the field of drug and biomarker discovery. A growing lack of confidence in cell lines has seen a shift toward more sophisticated pre-clinical cancer models that incorporate patient-derived tumors as xenografts or explants, to more accurately reflect clinical disease. Not only do these models retain critical features of the original tumor, and account for the molecular diversity and cellular heterogeneity of prostate cancer, but they provide a unique opportunity to conduct research in matched tumor samples. The challenge that accompanies these complex tissue models is increased complexity of analysis. With over 10 years of experience working with patient-derived explants (PDEs) of prostate cancer, this study provides guidance on the PDE method, its limitations, and considerations for addressing the heterogeneity of prostate cancer PDEs that are based on statistical modeling. Using inhibitors of the molecular chaperone heat shock protein 90 (Hsp90) as an example of a drug that induces robust proliferative response, we demonstrate how multi-omics analysis in prostate cancer PDEs is both feasible and essential for identification of key biological pathways, with significant potential for novel drug target and biomarker discovery. Full article

Apremilast (Otezla^®) is an oral small molecule phosphodiesterase 4 (PDE4) inhibitor approved for the treatment of psoriasis, psoriatic arthritis, and oral ulcers associated with Behçet’s disease. While PDE4 inhibition overall is mechanistically understood, the effect of apremilast on the innate immune response, particularly inflammasome activation, remains unknown. Here, we assessed the effect of apremilast in a psoriasis mouse model and primary human cells. Psoriatic lesion development in vivo was studied in K5.Stat3C transgenic mice treated with apremilast for 2 weeks, resulting in a moderate (2 mg/kg/day) to significant (6 mg/kg/day) resolution of inflamed plaques after 2-week treatment. Concomitantly, epidermal thickness dramatically decreased, the cutaneous immune cell infiltrate was reduced, and proinflammatory cytokines were significantly downregulated. Additionally, apremilast significantly inhibited lipopolysaccharide- or anti-CD3-induced expression of proinflammatory cytokines in peripheral mononuclear cells (PBMCs). Notably, inflammasome activation and secretion of IL-1β were not inhibited by apremilast in PBMCs and in human primary keratinocytes. Collectively, apremilast effectively alleviated the psoriatic phenotype of K5.Stat3 transgenic mice, further substantiating PDE4 inhibitor-efficiency in targeting key clinical, histopathological and inflammatory features of psoriasis. Despite lacking direct effect on inflammasome activation, reduced priming of inflammasome components upon apremilast treatment reflected the indirect benefit of PDE4 inhibition in reducing inflammation. Full article

The most common scoring system for critically ill patients is the Sequential Organ Failure Assessment (SOFA) score. Little is known about specific molecular signaling networks underlying the SOFA criteria. We characterized these networks and identified specific key regulatory molecules. We prospectively studied seven patients with sepsis and six controls with high-throughput RNA sequencing (RNAseq). Quantitative reverse transcription PCR (RT-qPCR) confirmation was performed in a second independent cohort. Differentially and significantly expressed miRNAs and their target mRNA transcripts were filtered for admission SOFA criteria and marker RNAs for the respective criteria identified. We bioinformatically constructed molecular signaling networks specifically reflecting these criteria followed by RT-qPCR confirmation of RNAs with important regulatory functions in the networks in the second cohort. RNAseq identified 82 miRNAs (45% upregulated) and 3254 mRNAs (50% upregulated) differentially expressed between sepsis patients and controls. Bioinformatic analysis characterized 6 miRNAs and 76 mRNA target transcripts specific for the SOFA criteria. RT-qPCR validated miRNA and mRNAs included IGFBP2 (respiratory system); MMP9 and PDE4B (nervous system); PPARG (cardiovascular system); AKR1B1, ANXA1, and LNC2/NGAL (acute kidney injury); GFER/ALR (liver); and miR-30c-3p (coagulopathy). There are specific canonical networks underlying the SOFA score. Key regulatory miRNA and mRNA transcripts support its biologic validity. Full article