Gellan gum based thiol-ene hydrogels with tunable properties for use as tissue engineering scaffolds

Gellan gum is a naturally occurring polymer that can crosslink in the presence of divalent cations to form biocompatible hydrogels. However, physically crosslinked gellan gum hydrogels lose stability under physiological conditions, which substantially limits the applications of these hydrogels in vivo. In order to improve the mechanical strength, we incorporated methacrylate into gellan gum and chemically crosslinked the hydrogel through three polymerization methods: step growth through thiol-ene photoclick chemistry, chain growth via photopolymerization, and mixed model in which both mechanisms were employed. Methacrylation was confirmed and quantified by proton nuclear magnetic resonance (1H NMR) and Fourier transform infrared spectroscopy (FTIR). The mechanical property and chemistry of the crosslinked gels were systematically explored by varying the reaction conditions. The swelling ratios of the hydrogels were correlated with the compression moduli and affected by the addition of calcium. In vitro enzymatic degradation rate was found dependent on the degree of methacrylation. NIH/3T3 fibroblast cell proliferation and morphology were related to substrate stiffness with high stiffness leading generally to higher proliferation. The proliferation is further affected by the thiol-ene ratios. We then further modified methacrylate Gellan gum with alkane bromide to increase hydrophobicity. Cell attachment on resultant hydrogels were assessed and imaged. Cytokine release was also measured with comparison to pristine methacrylated Gellan gum based hydrogels. The results suggest that a hydrogel platform based on gellan gum can offer versatile chemical modifications and tunable mechanical properties for a variety of biomaterials applications, such as the wound healing scaffold

Mean reflected BSDE driven by a marked point process and application in insurance risk management

This paper aims to solve a super-hedging problem along with insurance re-payment under running risk management constraints. The initial endowment for the super-heding problem is characterized by a class of mean reflected backward stochastic differential equation driven by a marked point process (MPP) and a Brownian motion. By Lipschitz assumptions on the generators and proper integrability on the terminal value, we give the well-posedness of this kind of BSDEs by combining a representation theorem with the fixed point argument.Comment: arXiv admin note: text overlap with arXiv:2310.1472

Reflected BSDE driven by a marked point process with a convex/concave generator

In this paper, a class of reflected backward stochastic differential equations (RBSDE) driven by a marked point process (MPP) with a convex/concave generator is studied. Based on fixed point argument, $\theta$-method and truncation technique, the well-posedness of this kind of RBSDE with unbounded terminal condition and obstacle is investigated. Besides, we present an application on the pricing of American options via utility maximization, which is solved by constructing an RBSDE with a convex generator.Comment: arXiv admin note: substantial text overlap with arXiv:2310.1472

Quadratic exponential BSDEs driven by a marked point process

In this paper, the well-posedness of quadratic exponential backward stochastic differential equations driven by marked point process (MPP) under unbounded terminal condition is studied based on a fixed point argument, $\theta$-method and an approximation procedure. We also prove the solvability of the mean reflected quadratic exponential backward stochastic differential equations driven by marked point process via $\theta$-method

A two-stage framework for optical coherence tomography angiography image quality improvement

IntroductionOptical Coherence Tomography Angiography (OCTA) is a new non-invasive imaging modality that gains increasing popularity for the observation of the microvasculatures in the retina and the conjunctiva, assisting clinical diagnosis and treatment planning. However, poor imaging quality, such as stripe artifacts and low contrast, is common in the acquired OCTA and in particular Anterior Segment OCTA (AS-OCTA) due to eye microtremor and poor illumination conditions. These issues lead to incomplete vasculature maps that in turn makes it hard to make accurate interpretation and subsequent diagnosis.MethodsIn this work, we propose a two-stage framework that comprises a de-striping stage and a re-enhancing stage, with aims to remove stripe noise and to enhance blood vessel structure from the background. We introduce a new de-striping objective function in a Stripe Removal Net (SR-Net) to suppress the stripe noise in the original image. The vasculatures in acquired AS-OCTA images usually exhibit poor contrast, so we use a Perceptual Structure Generative Adversarial Network (PS-GAN) to enhance the de-striped AS-OCTA image in the re-enhancing stage, which combined cyclic perceptual loss with structure loss to achieve further image quality improvement.Results and discussionTo evaluate the effectiveness of the proposed method, we apply the proposed framework to two synthetic OCTA datasets and a real AS-OCTA dataset. Our results show that the proposed framework yields a promising enhancement performance, which enables both conventional and deep learning-based vessel segmentation methods to produce improved results after enhancement of both retina and AS-OCTA modalities

It Ain't That Bad: Understanding the Mysterious Performance Drop in OOD Generalization for Generative Transformer Models

Generative Transformer-based models have achieved remarkable proficiency on solving diverse problems. However, their generalization ability is not fully understood and not always satisfying. Researchers take basic mathematical tasks like n-digit addition or multiplication as important perspectives for investigating their generalization behaviors. Curiously, it is observed that when training on n-digit operations (e.g., additions) in which both input operands are n-digit in length, models generalize successfully on unseen n-digit inputs (in-distribution (ID) generalization), but fail miserably and mysteriously on longer, unseen cases (out-of-distribution (OOD) generalization). Studies try to bridge this gap with workarounds such as modifying position embedding, fine-tuning, and priming with more extensive or instructive data. However, without addressing the essential mechanism, there is hardly any guarantee regarding the robustness of these solutions. We bring this unexplained performance drop into attention and ask whether it is purely from random errors. Here we turn to the mechanistic line of research which has notable successes in model interpretability. We discover that the strong ID generalization stems from structured representations, while behind the unsatisfying OOD performance, the models still exhibit clear learned algebraic structures. Specifically, these models map unseen OOD inputs to outputs with equivalence relations in the ID domain. These highlight the potential of the models to carry useful information for improved generalization