Existence of solutions for fourth order elliptic equations of Kirchhoff type on RN

In this paper, we study the positive solutions to a class of fourth order elliptic equations of Kirchhoff type on $R^N$ by using variational methods and the truncation method

Periodic solutions of a nonlinear suspension bridge equation with damping and nonconstant load

AbstractThe paper is concerned with the existence of periodic solutions for the Lazer–McKenna suspension bridge equation with damping and nonconstant load. By using the Lyapunov–Schmidt reduction methods, the author discuss the relationship between the sign-changing solutions and the source terms. The result answers partly the open problem in Lazer and McKenna (SIAM Rev. 32 (1990) 537–578)

Recursive Multi-Time-Step Coupling of Multiple Subdomains

The need for efficient computation methods for modeling of large-scale structures has become critically important over the past few years. Efficient means of analysis often involve coupling in space through domain decomposition and multi scale methods in time. The multi-time-step coupling method is a coupling method in time which allows for efficient analysis of large-scale problems for structural dynamics where a large structural model is decomposed into smaller subdomains that are solved independently and then coupled back together to obtain the global solution. For coupling of more than two subdomains that are solved at different timesteps, we employ recursive methods. Currently a constraint on this recursive coupling is that subdomains with the same time step must be coupled first before coupling with other subdomains of different time steps. In this research, we develop a computational algorithm to overcome this constraint and allow the user to specify general coupling orders for the different subdomains. Our efforts till now have been directed towards coding the recursive coupling of multi-subdomain models and we have verified that the equations that will allow us to overcome coupling constraint are correct. We are in the process of implementing these equations into our codes. Once in place, these sets of codes will allow users to conduct simulation of structural dynamics in a very efficient manner

Positive Solutions for Singular Complementary Lidstone Boundary Value Problems

By using fixed-point theorems of a cone, we investigate the existence and multiplicity of positive solutions for complementary Lidstone boundary value problems: (−1)(2+1)()=ℎ()(()), in 0<<1, (0)=0, (2+1)(0)=(2+1)(1)=0, 0≤≤−1, where ∈

AutoMorph: Automated Retinal Vascular Morphology Quantification Via a Deep Learning Pipeline

Purpose: To externally validate a deep learning pipeline (AutoMorph) for automated analysis of retinal vascular morphology on fundus photographs. AutoMorph has been made publicly available, facilitating widespread research in ophthalmic and systemic diseases. Methods: AutoMorph consists of four functional modules: image preprocessing, image quality grading, anatomical segmentation (including binary vessel, artery/vein, and optic disc/cup segmentation), and vascular morphology feature measurement. Image quality grading and anatomical segmentation use the most recent deep learning techniques. We employ a model ensemble strategy to achieve robust results and analyze the prediction confidence to rectify false gradable cases in image quality grading. We externally validate the performance of each module on several independent publicly available datasets. Results: The EfficientNet-b4 architecture used in the image grading module achieves performance comparable to that of the state of the art for EyePACS-Q, with an F1-score of 0.86. The confidence analysis reduces the number of images incorrectly assessed as gradable by 76%. Binary vessel segmentation achieves an F1-score of 0.73 on AV-WIDE and 0.78 on DR HAGIS. Artery/vein scores are 0.66 on IOSTAR-AV, and disc segmentation achieves 0.94 in IDRID. Vascular morphology features measured from the AutoMorph segmentation map and expert annotation show good to excellent agreement. Conclusions: AutoMorph modules perform well even when external validation data show domain differences from training data (e.g., with different imaging devices). This fully automated pipeline can thus allow detailed, efficient, and comprehensive analysis of retinal vascular morphology on color fundus photographs. Translational Relevance: By making AutoMorph publicly available and open source, we hope to facilitate ophthalmic and systemic disease research, particularly in the emerging field of oculomics