High-Density Lipoprotein: From Biological Functions to Clinical Perspectives

High-density lipoprotein (HDL) is a heterogeneous particle composed of apolipoproteins, enzymes, and lipids. Besides transporting cholesterol to the liver, HDL also exerts many protections on anti-oxidation, anti-inflammation, and anti-apoptosis. Initial understandings of HDL came from its protective roles against atherosclerosis and the observation that high plasma HDL cholesterol (HDL-C) levels seemed to decrease cardiovascular disease (CVD) attack. However, those patients either with cholesterol ester transfer protein (CETP) deficiency or taking CETP inhibitors substantially elevated HDL-C levels but did not necessarily decrease CVD risk. Thus, some researchers suggested that quantitative measurements of HDL particle (HDL-P) might be more valuable than traditional HDL-C measurements. What is more bewildering is that HDL from patients with systemic inflammation decreased its protective effects and even became a pro-inflammatory factor. Recently, synthesized HDL and apolipoprotein mimetic peptides showed biological functions similar to native ones. Expectedly, lots of novel measurement methods and therapeutic agents about HDL would be established soon

Norm and time optimal control problems of stochastic heat equations

This paper investigates the norm and time optimal control problems for stochastic heat equations. We begin by presenting a characterization of the norm optimal control, followed by a discussion of its properties. We then explore the equivalence between the norm optimal control and time optimal control, and subsequently establish the bang-bang property of the time optimal control. These problems, to the best of our knowledge, are among the first to discuss in the stochastic case

Optimal Actuator Location of the Norm Optimal Controls for Degenerate Parabolic Equations

This paper focuses on investigating the optimal actuator location for achieving minimum norm controls in the context of approximate controllability for degenerate parabolic equations. We propose a formulation of the optimization problem that encompasses both the actuator location and its associated minimum norm control. Specifically, we transform the problem into a two-person zero-sum game problem, resulting in the development of four equivalent formulations. Finally, we establish the crucial result that the solution to the relaxed optimization problem serves as an optimal actuator location for the classical problem

Null controllability of two kinds of coupled parabolic systems with switching control

The focus of this paper is on the null controllability of two kinds of coupled systems including both degenerate and non-degenerate equations with switching control. We first establish the observability inequality for measurable subsets in time for such coupled system, and then by the HUM method to obtain the null controllability. Next, we investigate the null controllability of such coupled system for segmented time intervals. Notably, these results are obtained through spectral inequalities rather than using the method of Carleman estimates. Such coupled systems with switching control, to the best of our knowledge, are among the first to discuss

Empirical likelihood-based portmanteau tests for autoregressive moving average models with possible infinite variance innovation

It is an important task in the literature to check whether a fitted autoregressive moving average (ARMA) model is adequate, while the currently used tests may suffer from the size distortion problem when the underlying autoregressive models have low persistence. To fill this gap, this paper proposes two empirical likelihood-based portmanteau tests. The first one is naive but can serve as a benchmark, and the second is for the case with infinite variance innovations. The asymptotic distributions under the null hypothesis are derived under mild moment conditions, and their usefulness is demonstrated by simulation experiments and two real data examples.Comment: 23 pages, 2 figure

Some controllability results of a class of N-dimensional parabolic equations with internal single-point degeneracy

This paper investigates the controllability of a class of $N$-dimensional degenerate parabolic equations with interior single-point degeneracy. We employ the Galerkin method to prove the existence of solutions for the equations. The analysis is then divided into two cases based on whether the degenerate point $x=0$ lies within the control region $\omega_0$ or not. For each case, we establish specific Carleman estimates. As a result, we achieve null controllability in the first case $0\in\omega_0$ and unique continuation and approximate controllability in the second case $0\notin\omega_0$

Observability inequalities for the backward stochastic evolution equations and their applications

The present article delves into the investigation of observability inequalities pertaining to backward stochastic evolution equations. We employ a combination of spectral inequalities, interpolation inequalities, and the telegraph series method as our primary tools to directly establish observability inequalities. Furthermore, we explore three specific equations as application examples: a stochastic degenerate equation, a stochastic fourth order parabolic equation and a stochastic heat equation. It is noteworthy that these equations can be rendered null controllability with only one control in the drift term to each system

Quantitative uniqueness estimates for stochastic parabolic equations on the whole Euclidean space

In this paper, a quantitative estimate of unique continuation for the stochastic heat equation with bounded potentials on the whole Euclidean space is established. This paper generalizes the earlier results in [29] and [17] from a bounded domain to an unbounded one. The proof is based on the locally parabolic-type frequency function method. An observability estimate from measurable sets in time for the same equation is also derived.Comment: 26 page

Layer-refined Graph Convolutional Networks for Recommendation

Recommendation models utilizing Graph Convolutional Networks (GCNs) have achieved state-of-the-art performance, as they can integrate both the node information and the topological structure of the user-item interaction graph. However, these GCN-based recommendation models not only suffer from over-smoothing when stacking too many layers but also bear performance degeneration resulting from the existence of noise in user-item interactions. In this paper, we first identify a recommendation dilemma of over-smoothing and solution collapsing in current GCN-based models. Specifically, these models usually aggregate all layer embeddings for node updating and achieve their best recommendation performance within a few layers because of over-smoothing. Conversely, if we place learnable weights on layer embeddings for node updating, the weight space will always collapse to a fixed point, at which the weighting of the ego layer almost holds all. We propose a layer-refined GCN model, dubbed LayerGCN, that refines layer representations during information propagation and node updating of GCN. Moreover, previous GCN-based recommendation models aggregate all incoming information from neighbors without distinguishing the noise nodes, which deteriorates the recommendation performance. Our model further prunes the edges of the user-item interaction graph following a degree-sensitive probability instead of the uniform distribution. Experimental results show that the proposed model outperforms the state-of-the-art models significantly on four public datasets with fast training convergence. The implementation code of the proposed method is available at https://github.com/enoche/ImRec.Comment: 12 pages, 5 figure

Very high cycle fatigue behavior of bridge steel welded joint

AbstractVery high cycle fatigue (VHCF) behaviors of bridge steel (Q345) welded joints were investigated using an ultrasonic fatigue test system at room temperature with a stress ratio R = −1. The results show that the fatigue strength of welded joints is dropped by an average of 60% comparing to the base metal and the fatigue failure still occurred beyond 107 cycles. The fatigue fracture of welded joints in the low cycle regime generally occurred at the solder while at the heat-affected zone (HAZ) in the very high cycle regime. The fatigue fracture surface was analyzed with scanning electron microscopy (SEM), showing welding defects such as pore, micro-crack and inclusion were the main factors on decreasing the fatigue properties of welded joints. The effect of welding defects on the fatigue behaviors of welded joints was discussed in terms of experimental results and finite element simulations