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To study discontinuous precipitation, which is an important method for strengthening materials, we observed the nucleation and growth of discontinuous precipitates in Cu–Ag alloys using electron backscatter diffraction and scanning transmission electron microscopy. We found that discontinuous precipitation always started with Ag precipitates, which nucleated on Cu grain boundaries. These precipitates then each took the shape of a large, abutted cone that shared a semi-coherent interface with one of the Cu grains, topped by a small spherical cap that shared an incoherent interface with the Cu grain on the opposite side of the boundary. This formation created a difference between the levels of interface energy on each side of boundary. We assume that this difference and boundary curvature together generates the driving force necessary to push grain boundary migration, thus triggering discontinuous precipitation. Because of grain boundary migration, Ag solute was consumed at one side of the grain, which causes a solute difference. The difference produces mainly driving force, pushing the boundaries to migrate forward.

 

Protein fold recognition is a critical step toward protein structure and function prediction, aiming at providing the most likely fold type of the query protein. In recent years, the development of deep learning (DL) technique has led to massive advances in this important field, and accordingly, the sensitivity of protein fold recognition has been dramatically improved. Most DL-based methods take an intermediate bottleneck layer as the feature representation of proteins with new fold types. However, this strategy is indirect, inefficient and conditional on the hypothesis that the bottleneck layer’s representation is assumed as a good representation of proteins with new fold types. To address the above problem, in this work, we develop a new computational framework by combining triplet network and ensemble DL. We first train a DL-based model, termed FoldNet, which employs triplet loss to train the deep convolutional network. FoldNet directly optimizes the protein fold embedding itself, making the proteins with the same fold types be closer to each other than those with different fold types in the new protein embedding space. Subsequently, using the trained FoldNet, we implement a new residue–residue contact-assisted predictor, termed FoldTR, which improves protein fold recognition. Furthermore, we propose a new ensemble DL method, termed FSD_XGBoost, which combines protein fold embedding with the other two discriminative fold-specific features extracted by two DL-based methods SSAfold and DeepFR. The Top 1 sensitivity of FSD_XGBoost increases to 74.8% at the fold level, which is ~9% higher than that of the state-of-the-art method. Together, the results suggest that fold-specific features extracted by different DL methods complement with each other, and their combination can further improve fold recognition at the fold level. The implemented web server of FoldTR and benchmark datasets are publicly available at http://csbio.njust.edu.cn/bioinf/foldtr/.

 

This paper is pedagogic in nature, meant to provide researchers a single reference for learning how to apply the emerging literature on differential variational inequalities to the study of dynamic traffic assignment problems that are Cournot-like noncooperative games. The paper is presented in a style that makes it accessible to the widest possible audience. In particular, we apply the theory of differential variational inequalities (DVIs) to the dy- namic user equilibrium (DUE) problem. We first show that there is a variational inequality whose necessary conditions describe a DUE. We restate the flow conservation constraint associated with each origin-destination pair as a first-order two-point boundary value problem, thereby leading to a DVI representation of DUE; then we employ Pontryagin-type necessary conditions to show that any DVI solution is a DUE. We also show that the DVI formulation leads directly to a fixed-point algorithm. We explain the fixed-point algorithm by showing the calculations intrinsic to each of its steps when applied to simple examples. 

Dynamic user equilibrium (DUE) is the most widely studied form of dynamic traffic assignment (DTA), in which road travelers engage in a non-cooperative Nash-like game with departure time and route choices. DUE models describe and predict the time-varying traffic flows on a network consistent with traffic flow theory and travel behavior. This paper documents theoretical and numerical advances in synthesizing traffic flow theory and DUE modeling, by presenting a holistic computational theory of DUE, which is numerically implemented in a MATLAB package. In particular, the dynamic network loading (DNL) sub-problem is formulated as a system of differential algebraic equations based on the Lighthill-Whitham-Richards fluid dynamic model, which captures the formation, propagation and dissipation of physical queues as well as vehicle spillback on networks. Then, the fixed-point algorithm is employed to solve the DUE problems with simultaneous route and departure time choices on several large-scale networks. We make openly available the MATLAB package, which can be used to solve DUE problems on user-defined networks, aiming to not only facilitate benchmarking a wide range of DUE algorithms and solutions, but also offer researchers a platform to further develop their own models and applications. The MATLAB package and computational examples are available online. 

Dynamic traffic assignment models rely on a network performance module known as dynamic network loading (DNL), which expresses flow propagation, flow conservation, and travel delay at a network level. The DNL defines the so-called network delay operator , which maps a set of path departure rates to a set of path travel times (or costs). It is widely known that the delay operator is not available in closed form, and has undesirable properties that severely complicate DTA analysis and computation, such as discontinuity, nondifferentiability, nonmonotonicity, and computational inefficiency. This paper proposes a fresh take on this important and difficult issue, by providing a class of surrogate DNL models based on a statistical learning method known as Kriging . We present a metamodeling framework that systematically approximates DNL models and is flexible in the sense of allowing the modeler to make trade-offs among model granularity, complexity, and accuracy. It is shown that such surrogate DNL models yield highly accurate approximations (with errors below 8%) and superior computational efficiency (9 to 455 times faster than conventional DNL procedures such as those based on the link transmission model). Moreover, these approximate DNL models admit closed-form and analytical delay operators, which are Lipschitz continuous and infinitely differentiable, with closed-form Jacobians. We provide in-depth discussions on the implications of these properties to DTA research and model applications.