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Tensors (hypermatrices) are multidimensional analogs of matrices. The tensor complementarity problem is a class of nonlinear complementarity problems with the involved function being defined by a tensor, which is also a direct and natural extension of the linear complementarity problem. In the last few years, the tensor complementarity problem has attracted a lot of attention, and has been studied extensively, from theory to solution methods and applications. This work, with its three parts, aims at contributing to review the state-of-the-art of studies for the tensor complementarity problem and related models. In this part, we describe the theoretical developments for the tensor complementarity problem and related models, including the nonemptiness and compactness of the solution set, global uniqueness and solvability, error bound theory, stability and continuity analysis, and so on. The developments of solution methods and applications for the tensor complementarity problem are given in the second part and the third part, respectively. Some further issues are proposed in all the parts.

We have reviewed some theoretical and algorithmic developments for tensor complementarity problems and related models in the first part and the second part of this paper, respectively. In this part, we present a survey for some applications of tensor complementarity problems and polynomial complementarity problems. We first describe some equivalent classes of tensor complementarity problems and polynomial complementarity problems, since many practical problems can be modeled as forms of those equivalent problems; and then, we review three practical applications of tensor complementarity problems and polynomial complementarity problems. The first practical application is about a class of multi-person noncooperative games, which is modeled as a tensor complementarity problem, and particularly, an explicit relationship between the solutions to these two classes of problems is presented. The second practical problem is about the hypergraph clustering problem, which can be solved by a tensor complementarity problem. The third practical problem is about a class of traffic equilibrium problems, which is modeled as a polynomial complementarity problem. Some further issues are given.

Summary Ligand‐receptor pairs play important roles in cell–cell communication for multicellular organisms in response to environmental cues. Recently, the emergence of single‐cell RNA‐sequencing (scRNA‐seq) provides unprecedented opportunities to investigate cellular communication based on ligand‐receptor expression. However, so far, no reliable ligand‐receptor interaction database is available for plant species. In this study, we developed PlantPhoneDB (https://jasonxu.shinyapps.io/PlantPhoneDB/), a pan‐plant database comprising a large number of high‐confidence ligand‐receptor pairs manually curated from seven resources. Also, we developed a PlantPhoneDB R package, which not only provided optional four scoring approaches that calculate interaction scores of ligand‐receptor pairs between cell types but also provided visualization functions to present analysis results. At the PlantPhoneDB web interface, the processed datasets and results can be searched, browsed, and downloaded. To uncover novel cell–cell communication events in plants, we applied the PlantPhoneDB R package on GSE121619 dataset to infer significant cell–cell interactions of heat‐shocked root cells in Arabidopsis thaliana. As a result, the PlantPhoneDB predicted the actively communicating AT1G28290‐AT2G14890 ligand‐receptor pair in atrichoblast–cortex cell pair in Arabidopsis thaliana. Importantly, the downstream target genes of this ligand‐receptor pair were significantly enriched in the ribosome pathway, which facilitated plants adapting to environmental changes. In conclusion, PlantPhoneDB provided researchers with integrated resources to infer cell–cell communication from scRNA‐seq datasets.

This work, with its three parts, reviews the state-of-the-art of studies for the tensor complementarity problem and some related models. In the first part of this paper, we have reviewed the theoretical developments of the tensor complementarity problem and related models. In this second part, we review the developments of solution methods for the tensor complementarity problem. It has been shown that the tensor complementarity problem is equivalent to some known optimization problems, or related problems such as systems of tensor equations, systems of nonlinear equations, and nonlinear programming problems, under suitable assumptions. By solving these reformulated problems with the help of structures of the involved tensors, several numerical methods have been proposed so that a solution of the tensor complementarity problem can be found. Moreover, based on a polynomial optimization model, a semidefinite relaxation method is presented so that all solutions of the tensor complementarity problem can be found under the assumption that the solution set of the problem is finite. Further applications of the tensor complementarity problem will be given and discussed in the third part of this paper.

ASFV is a large DNA virus that is highly pathogenic in domestic pigs. How this virus is sensed by the innate immune system as well as why it is so virulent remains enigmatic. In this study, we show that the ASFV genome contains AT-rich regions that are recognized by the DNA-directed RNA polymerase III (Pol-III), leading to viral RNA sensor RIG-I-mediated innate immune responses. We further show that ASFV protein I267L inhibits RNA Pol-III-RIG-I-mediated innate antiviral responses. I267L interacts with the E3 ubiquitin ligase Riplet, disrupts Riplet-RIG-I interaction and impairs Riplet-mediated K63-polyubiquitination and activation of RIG-I. I267L-deficient ASFV induces higher levels of interferon-β, and displays compromised replication both in primary macrophages and pigs compared with wild-type ASFV. Furthermore, I267L-deficiency attenuates the virulence and pathogenesis of ASFV in pigs. These findings suggest that ASFV I267L is an important virulence factor by impairing innate immune responses mediated by the RNA Pol-III-RIG-I axis.

In this paper, we consider a class of n -person noncooperative games, where the utility function of every player is given by a homogeneous polynomial defined by the payoff tensor of that player, which is a natural extension of the bimatrix game where the utility function of every player is given by a quadratic form defined by the payoff matrix of that player. We will call such a problem the multilinear game. We reformulate the multilinear game as a tensor complementarity problem, a generalization of the linear complementarity problem; and show that finding a Nash equilibrium point of the multilinear game is equivalent to finding a solution of the resulted tensor complementarity problem. Especially, we present an explicit relationship between the solutions of the multilinear game and the tensor complementarity problem, which builds a bridge between these two classes of problems. We also apply a smoothing-type algorithm to solve the resulted tensor complementarity problem and give some preliminary numerical results for solving the multilinear games.

The T-product for third-order tensors has been used extensively in the literature. In this paper, we first introduce first-order and second-order T-derivatives for the multi-variable real-valued function with the tensor T-product. Inspired by an equivalent characterization of a twice continuously T-differentiable multi-variable real-valued function being convex, we present a definition of the T-positive semidefiniteness of third-order symmetric tensors. After that, we extend many properties of positive semidefinite matrices to the case of third-order symmetric tensors. In particular, analogue to the widely used semidefinite programming (SDP for short), we introduce the semidefinite programming over the space of third-order symmetric tensors (T-semidefinite programming or TSDP for short), and provide a way to solve the TSDP problem by converting it into an SDP problem in the complex domain. Furthermore, we give several TSDP examples and especially some preliminary numerical results for two unconstrained polynomial optimization problems. Experiments show that finding the global minimums of polynomials via the TSDP relaxation outperforms the traditional SDP relaxation for the test examples.

With the prevalence of pre-trained language models (PLMs) and the pre-training–fine-tuning paradigm, it has been continuously shown that larger models tend to yield better performance. However, as PLMs scale up, fine-tuning and storing all the parameters is prohibitively costly and eventually becomes practically infeasible. This necessitates a new branch of research focusing on the parameter-efficient adaptation of PLMs, which optimizes a small portion of the model parameters while keeping the rest fixed, drastically cutting down computation and storage costs. In general, it demonstrates that large-scale models could be effectively stimulated by the optimization of a few parameters. Despite the various designs, here we discuss and analyse the approaches under a more consistent and accessible term ‘delta-tuning’, where ‘delta’ a mathematical notation often used to denote changes, is borrowed to refer to the portion of parameters that are ‘changed’ during training. We formally describe the problem and propose a unified categorization criterion for existing delta-tuning methods to explore their correlations and differences. We also discuss the theoretical principles underlying the effectiveness of delta-tuning and interpret them from the perspectives of optimization and optimal control. Furthermore, we provide a holistic empirical study on over 100 natural language processing tasks and investigate various aspects of delta-tuning. With comprehensive study and analysis, our research demonstrates the theoretical and practical properties of delta-tuning in the adaptation of PLMs. Training a deep neural network can be costly but training time is reduced when a pre-trained network can be adapted to different use cases. Ideally, only a small number of parameters needs to be changed in this process of fine-tuning, which can then be more easily distributed. In this Analysis, different methods of fine-tuning with only a small number of parameters are compared on a large set of natural language processing tasks.

AHNAK nucleoprotein 2 (AHNAK2) has been emerged as a crucial protein for neuroblast differentiation and cell migration, thereby involving in the development of various cancers. However, the specific molecular mechanism of AHNAK2 in lung adenocarcinoma is inconclusive. By accessing to the Oncomine dataset and GEPIA website, a higher expression level of AHNAK2 was observed in lung adenocarcinoma tissue samples. Overall survival (OS) curve plotted by Kaplan-Meier method showed that up-regulation of AHNAK2 was related with poor prognosis of lung adenocarcinoma patients. Quantitative reverse transcription polymerase chain reaction (qRT-PCR) analysis and western blot were conducted to examine the expression level of genes in lung adenocarcinoma cells. Through functional in vitro experiments, cell proliferation, migration and invasion were all suppressed after AHNAK2 knockdown using Cell counting kit-8 (CCK-8) assay, wound-healing and transwell analysis. Reduction of AHNAK2 decreased the apoptosis rate using flow cytometry analysis. Moreover, the key markers of MAPK pathway, p-MEK, p-ERK and p-P90RSK were decreased due to the transfection of si-AHNAK2 in A549 cells. U0126, a MEK inhibitor, showed the similar effects on MAPK-related protein levels with si-AHNAK2. To sum up, AHNAK2 is significantly increased in lung adenocarcinoma and plays a carcinogenic role by activating the MAPK signaling pathway, providing a novel insight and raising possibility for lung adenocarcinoma treatment.

Background The co-culture strategy which mimics natural ecology by constructing an artificial microbial community is a useful tool to activate the biosynthetic gene clusters to generate new metabolites. However, the conventional method to study the co-culture is to isolate and purify compounds separated by HPLC, which is inefficient and time-consuming. Furthermore, the overall changes in the metabolite profile cannot be well characterized. Results A new approach which integrates computational programs, MS-DIAL, MS-FINDER and web-based tools including GNPS and MetaboAnalyst, was developed to analyze and identify the metabolites of the co-culture of Aspergillus sydowii and Bacillus subtilis . A total of 25 newly biosynthesized metabolites were detected only in co-culture. The structures of the newly synthesized metabolites were elucidated, four of which were identified as novel compounds by the new approach. The accuracy of the new approach was confirmed by purification and NMR data analysis of 7 newly biosynthesized metabolites. The bioassay of newly synthesized metabolites showed that four of the compounds exhibited different degrees of PTP1b inhibitory activity, and compound N2 had the strongest inhibition activity with an IC 50 value of 7.967 μM. Conclusions Co-culture led to global changes of the metabolite profile and is an effective way to induce the biosynthesis of novel natural products. The new approach in this study is one of the effective and relatively accurate methods to characterize the changes of metabolite profiles and to identify novel compounds in co-culture systems.