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In this paper, we propose a deep learning framework for solving high-dimensional partial integro-differential equations (PIDEs) based on the temporal difference learning. We introduce a set of Levy processes and construct a corresponding reinforcement learning model. To simulate the entire process, we use deep neural networks to represent the solutions and non-local terms of the equations. Subsequently, we train the networks using the temporal difference error, termination condition, and properties of the non-local terms as the loss function. The relative error of the method reaches O(10^{-3}) in 100-dimensional experiments and O(10^{-4}) in one-dimensional pure jump problems. Additionally, our method demonstrates the advantages of low computational cost and robustness, making it well-suited for addressing problems with different forms and intensities of jumps.

Revealing hidden dynamics from the stochastic data is a challenging problem as randomness takes part in the evolution of the data. The problem becomes exceedingly complex when the trajectories of the stochastic data are absent in many scenarios. Here we present an approach to effectively modeling the dynamics of the stochastic data without trajectories based on the weak form of the Fokker-Planck (FP) equation, which governs the evolution of the density function in the Brownian process. Taking the collocations of Gaussian functions as the test functions in the weak form of the FP equation, we transfer the derivatives to the Gaussian functions and thus approximate the weak form by the expectational sum of the data. With a dictionary representation of the unknown terms, a linear system is built and then solved by the regression, revealing the unknown dynamics of the data. Hence, we name the method with the Weak Collocation Regression (WCR) method for its three key components: weak form, collocation of Gaussian kernels, and regression. The numerical experiments show that our method is flexible and fast, which reveals the dynamics within seconds in multi-dimensional problems and can be easily extended to high-dimensional data such as 20 dimensions. WCR can also correctly identify the hidden dynamics of the complex tasks with variable-dependent diffusion and coupled drift, and the performance is robust, achieving high accuracy in the case with noise added.

Rheumatoid arthritis (RA) is an autoimmune inflammatory disease. It is a systemic inflammatory disease, characterized by chronic, symmetrical, multi-articular synovial arthritis. IL-25 (IL-17E) is a member of the recently emerged cytokine family (IL-17s), which is expressed in Th2 cells and bone marrow-derived mast cells. Unlike the other members of this family, IL-25 is capable of inducing Th2-associated cytokines (IL-4, IL-5, and IL-13) and also promotes the release of some pro-immune factors (IL-6 and IL-8). IL-25 is also a pleiotropic factor, which constitutes a tissue-specific pathological injury and chronic inflammation. In this study, we used chicken collagen II-induced experimental arthritis (CIA) model in DBA/1 mice to investigate the relationship between IL-25 and other inflammatory factors, revealing the possible mechanism in CIA. Our results showed that the expression level of IL-25 was enhanced in the late stage of CIA, and IL-17 was increased in the early stage of the disease. It is well known that IL-17 has a crucial role in the development of RA pathogenesis, and IL-25 plays a significant role in humoral immune. For reasons given above, we suggested that the IL-25 inhibited IL-17 expression to some extent, while enhancing the production of IL-4. It was confirmed that IL-25 not only regulated the cellular immune, but also involved the humoral immune in rheumatoid arthritis.

The development of new digital terrestrial TV broadcasting services led to scarcity of useable frequencies, it is necessary to assign each transmitter a suitable frequency to guarantee well function of transmitters with minimum frequency span. Frequency assignment problem is a combinatorial optimization problem, in this paper introduced a simple frequency assignment model which only took distance constraint into consider, and generated the distance constraint graph, both local search algorithm and simulated annealing algorithm were used to solve the problem, the comparison of the two algorithms was given, as well as some suggestions on accelerating simulated annealing algorithm for its time-consuming disadvantage in solving frequency assignment problem.

Fibrous Monolith Composites (FMCs) have emerged as an exciting new class of structural ceramics in recent years primarily due to their advantageous characteristics, such as enhanced damage tolerance, high fracture energy, high toughness and R-curve behavior, improved thermal and chemical stability, while fabricated at relatively low cost. FMC material systems have been used in wear and high temperature applications and most recently in energetic reactive structures. Understanding the mechanical characteristics of FMCs is critical for their safe and reliable use. However, critical tools for stress and failure analysis for FMC based structures have not yet been developed. Therefore, the objective of the present research is to establish effective tools for the analysis of this new generation of FMC material systems. In this study, we develop suitable numerical and analytical tools to characterize the performance of FMC material systems, including their linear elastic and non-linear mechanical response, their proportional limit, their fracture characteristics through near-tip stress field studies and macroscopic mechanical response through modeling of tensile experiments. The elastic response of FMCs is investigated using the finite element method (FEM). In this study, we assume material, geometric and loading uniformity in the z direction which allows us to reduce the problem to a two-dimensional (2-D) problem. A representative unit-cell is extracted from micro-structure of FMCs for FEM studies. Robust 2-D FEM meshes are developed capable of modeling a wide range of FMC micro-structures. Three in-plane Boundary Value Problems (BVPs) are established for estimating the in-plane effective properties of FMCs. Parametric studies are employed on predicting elastic properties for a broad range of FMC micro-structures. Out of plane properties are obtained through complementary 3-D finite element studies. A failure model is utilized for predicting the initiation of cracking in FMCs subjected to general in-plane loading. The non-linear response of FMCs is investigated by employing a discrete microcracking model as part of an incremental and iterative modeling scheme. The model is represented by a microcracking law which relates the current state of stress to the current state of microcracking damage. It is expected that the FMC material systems behave non-linearity due to the degradation of micro-constituent stiffness. Non-linear stress-strain curves are also obtained through parametric studies. Degradation of the in-plane effective properties of FMC unit-cell and evolution of damage within FMC unit-cell are monitored throughout the simulations. Also in this study a computationally efficient semi-analytical method is developed for calculating the elastic micro-stress fields of FMCs. Analytical displacement estimates are derived using the Rayleigh-Ritz method for a FMC composite plate, the approximation solutions are derived with the aid of Kirchhoff-Love deformation hypothesis. The elastic micro-fields under remote in-plane loading are obtained by solving requisite BVPs. The semi-analytical results are compared with respective finite element results. It is evident that the finite element approximations are in an overall sense in good agreement with the semi-analytical model predictions. A specialized finite element is developed utilizing an asymptotic displacement expansion comprised of the homogenized displacements and the local micro-displacements which are based on Rayleigh-Ritz method. The element performance is demonstrated via near-tip studies for a crack under mode-I and mode-II fracture conditions. As the final task of this research, the tensile stress-strain response of fiber reinforced FMCs is analyzed using a crack propagation model. The crack growth in the composite specimens is evaluated using a stress intensity approach. The influences of the fibers that bridge the matrix cracking are represented by closure tractions at the crack surface. The calculated stress-strain curves are compared with experiments which are used for the mechanical characterization of a special class of reactive FMC systems. Importantly, the latter systems contain a polymer binder phase used in forming the fabrication slurry and left in the system for their safe production. Useful insights are gained regarding the effects of the composite microstructure and processing conditions on the mechanical response of the composite system. The models developed in this research aim at assisting the material design community in developing novel composite micro-structures associated with superior macro-mechanical performance.

Follicular helper T (TFH) cells control antibody responses by supporting antibody affinity maturation and memory formation. Inadequate TFH function has been found in individuals with ineffective responses to vaccines, but the mechanism underlying TFH regulation in vaccination is not understood. Here, we report that lower serum levels of the metabolic hormone leptin associate with reduced vaccine responses to influenza or hepatitis B virus vaccines in healthy populations. Leptin promotes mouse and human TFH differentiation and IL-21 production via STAT3 and mTOR pathways. Leptin receptor deficiency impairs TFH generation and antibody responses in immunisation and infection. Similarly, leptin deficiency induced by fasting reduces influenza vaccination-mediated protection for the subsequent infection challenge, which is mostly rescued by leptin replacement. Our results identify leptin as a regulator of TFH cell differentiation and function and indicate low levels of leptin as a risk factor for vaccine failure., T follicular helper (TFH) cell numbers are increased after vaccination and fewer of these cells might result in reduced vaccine responses. Here the authors show in mice and humans that leptin promotes TFH differentiation and that low leptin levels can impair TFH response to vaccines and virus protection in mice.