Cross Section Evaluation by Spinor Integration II: The massive case in 4D

In this paper, we continue our study of calculating the cross section by the spinor method, i.e., performing the phase space integration using the spinor method. We have focused on the case where the physical momenta are massive and in pure 4D. We established the framework of such a new method and presented several examples, including two real progresses: $Z^0\to l^+ l^- H$ and $\bar{qq} \to \bar{ff} H^0$.Comment: 23 pages, 1 figure;further comments and references adde

A multidimensional decision with nested probabilistic linguistic term sets and its application in corporate investment

With the rapid development of information, decision making problems in various fields have presented multidimensional, complex and uncertain characteristics. Nested probabilistic-numerical linguistic term set (NPNLTS) is an effective tool to describe complex information due to the nested structure and diverse variables. This paper extends the concept of NPNLTS, and defines an improved form, i.e., nested probabilistic linguistic term set (NPLTS), and then proposes a novel VIKOR method with nested probabilistic linguistic information to solve the model. Within the context of empirical corporate finance, a case study related to corporate investment decision is presented and handled by the novel VIKOR method. After that, comparative analysis is carried out considering other decision-making methods, decision coefficient in VIKOR, and weights of attributes. As a result, the proposed method not only provides a rational and effective solution, but also reveals the rule in the case when decision coefficient and weights of attributes change, respectively. Finally, we discuss the proposed method from the theoretical and application aspects with a view to guiding future research. To a certain extent, this study provides a new decision environment to deal with multidimensional problems

Learning Specialized Activation Functions for Physics-informed Neural Networks

Physics-informed neural networks (PINNs) are known to suffer from optimization difficulty. In this work, we reveal the connection between the optimization difficulty of PINNs and activation functions. Specifically, we show that PINNs exhibit high sensitivity to activation functions when solving PDEs with distinct properties. Existing works usually choose activation functions by inefficient trial-and-error. To avoid the inefficient manual selection and to alleviate the optimization difficulty of PINNs, we introduce adaptive activation functions to search for the optimal function when solving different problems. We compare different adaptive activation functions and discuss their limitations in the context of PINNs. Furthermore, we propose to tailor the idea of learning combinations of candidate activation functions to the PINNs optimization, which has a higher requirement for the smoothness and diversity on learned functions. This is achieved by removing activation functions which cannot provide higher-order derivatives from the candidate set and incorporating elementary functions with different properties according to our prior knowledge about the PDE at hand. We further enhance the search space with adaptive slopes. The proposed adaptive activation function can be used to solve different PDE systems in an interpretable way. Its effectiveness is demonstrated on a series of benchmarks. Code is available at https://github.com/LeapLabTHU/AdaAFforPINNs

Focal adhesions are foci for tyrosine-based signal transduction via GIV/Girdin and G proteins.

GIV/Girdin is a multimodular signal transducer and a bona fide metastasis-related protein. As a guanidine exchange factor (GEF), GIV modulates signals initiated by growth factors (chemical signals) by activating the G protein Gαi. Here we report that mechanical signals triggered by the extracellular matrix (ECM) also converge on GIV-GEF via β1 integrins and that focal adhesions (FAs) serve as the major hubs for mechanochemical signaling via GIV. GIV interacts with focal adhesion kinase (FAK) and ligand-activated β1 integrins. Phosphorylation of GIV by FAK enhances PI3K-Akt signaling, the integrity of FAs, increases cell-ECM adhesion, and triggers ECM-induced cell motility. Activation of Gαi by GIV-GEF further potentiates FAK-GIV-PI3K-Akt signaling at the FAs. Spatially restricted signaling via tyrosine phosphorylated GIV at the FAs is enhanced during cancer metastasis. Thus GIV-GEF serves as a unifying platform for integration and amplification of adhesion (mechanical) and growth factor (chemical) signals during cancer progression

Pedestrian Trajectory Prediction Using Dynamics-based Deep Learning

Pedestrian trajectory prediction plays an important role in autonomous driving systems and robotics. Recent work utilising prominent deep learning models for pedestrian motion prediction makes limited a priori assumptions about human movements, resulting in a lack of explainability and explicit constraints enforced on predicted trajectories. This paper presents a dynamics-based deep learning framework where a novel asymptotically stable dynamical system is integrated into a deep learning model. Our novel asymptotically stable dynamical system is used to model human goal-targeted motion by enforcing the human walking trajectory converges to a predicted goal position and provides a deep learning model with prior knowledge and explainability. Our deep learning model utilises recent innovations from transformer networks and is used to learn some features of human motion, such as collision avoidance, for our proposed dynamical system. The experimental results show that our framework outperforms recent prominent models in pedestrian trajectory prediction on five benchmark human motion datasets.Comment: 8 pages (including references), 5 figures, submitted to ICRA2024 for revie