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As a branch of advanced artificial intelligence, dialogue systems are prospering. Multi-turn response selection is a general research problem in dialogue systems. With the assistance of background information and pre-trained language models, the performance of state-of-the-art methods on this problem gains impressive improvement. However, existing studies neglect the importance of external commonsense knowledge. Hence, we design a Siamese network where a pre-trained Language model merges with a Graph neural network (SinLG). SinLG takes advantage of Pre-trained Language Models (PLMs) to catch the word correlations in the context and response candidates and utilizes a Graph Neural Network (GNN) to reason helpful common sense from an external knowledge graph. The GNN aims to assist the PLM in fine-tuning, and arousing its related memories to attain better performance. Specifically, we first extract related concepts as nodes from an external knowledge graph to construct a subgraph with the context response pair as a super node for each sample. Next, we learn two representations for the context response pair via both the PLM and GNN. A similarity loss between the two representations is utilized to transfer the commonsense knowledge from the GNN to the PLM. Then only the PLM is used to infer online so that efficiency can be guaranteed. Finally, we conduct extensive experiments on two variants of the PERSONA-CHAT dataset, which proves that our solution can not only improve the performance of the PLM but also achieve an efficient inference.

We employ the multipole expansion within the unified electroweak theory to develop a complete calculation method of the electron scattering cross section for light nuclei. The specific calculations for 6,7Li and 7Be nuclei indicate that the conventional impulse approximation can be applied to the electron-nucleus scattering only when the incident electron energy does not exceed twice the nucleon mass. In addition, the quasi-elastic scattering cross section of 7Li in the excitation from its ground state to the nearest excited state and that of elastic scattering in the ground state are independently treated, whereas they have not been separately measured in experiments. The obtained scattering cross sections corresponding to an appropriate adjustment of the harmonic oscillator parameter along with the V-A structure interpret reasonably well the available experimental data at MeV energies and provide predictive information at GeV energies. This gives new perspectives in studying the structure of nuclei and the weak interactions via electron or lepton scattering at high (GeV) energies, considering nuclei rather than quarks., Comment: 13 pages, 3 figures, 2 tables

Billions of organic molecules are known, but only a tiny fraction of the functional inorganic materials have been discovered, a particularly relevant problem to the community searching for new quantum materials. Recent advancements in machine-learning-based generative models, particularly diffusion models, show great promise for generating new, stable materials. However, integrating geometric patterns into materials generation remains a challenge. Here, we introduce Structural Constraint Integration in the GENerative model (SCIGEN). Our approach can modify any trained generative diffusion model by strategic masking of the denoised structure with a diffused constrained structure prior to each diffusion step to steer the generation toward constrained outputs. Furthermore, we mathematically prove that SCIGEN effectively performs conditional sampling from the original distribution, which is crucial for generating stable constrained materials. We generate eight million compounds using Archimedean lattices as prototype constraints, with over 10% surviving a multi-staged stability pre-screening. High-throughput density functional theory (DFT) on 26,000 survived compounds shows that over 50% passed structural optimization at the DFT level. Since the properties of quantum materials are closely related to geometric patterns, our results indicate that SCIGEN provides a general framework for generating quantum materials candidates., Comment: 512 pages total, 4 main figures + 218 supplementary figures

Optical properties in solids, such as refractive index and absorption, hold vast applications ranging from solar panels to sensors, photodetectors, and transparent displays. However, first-principles computation of optical properties from crystal structures is a complex task due to the high convergence criteria and computational cost. Recent progress in machine learning shows promise in predicting material properties, yet predicting optical properties from crystal structures remains challenging due to the lack of efficient atomic embeddings. Here, we introduce GNNOpt, an equivariance graph-neural-network architecture featuring automatic embedding optimization. This enables high-quality optical predictions with a dataset of only 944 materials. GNNOpt predicts all optical properties based on the Kramers-Kr{\"o}nig relations, including absorption coefficient, complex dielectric function, complex refractive index, and reflectance. We apply the trained model to screen photovoltaic materials based on spectroscopic limited maximum efficiency and search for quantum materials based on quantum weight. First-principles calculations validate the efficacy of the GNNOpt model, demonstrating excellent agreement in predicting the optical spectra of unseen materials. The discovery of new quantum materials with high predicted quantum weight, such as SiOs which hosts exotic quasiparticles, demonstrates GNNOpt's potential in predicting optical properties across a broad range of materials and applications., Comment: (i) Completely Rewritten Manuscript, including 5 main figures and 1 table. (ii) Supplementary Information, including 15 supplementary figures and 2 tables

Let $H$ be a nonabelian finite simple group. Huppert's conjecture asserts that if $G$ is a finite group with the same set of complex character degrees as $H$, then $G\cong H\times A$ for some abelian group $A$. Over the past two decades, several specific cases of this conjecture have been addressed. Recently, attention has shifted to the analogous conjecture for character codegrees: if $G$ has the same set of character codegrees as $H$, then $G\cong H$. Unfortunately, both problems have primarily been examined on a case-by-case basis. In this paper and the companion [HM22], we present a more unified approach to the codegree conjecture and confirm it for several families of simple groups.

This study focuses on developing an experimental system for estimating communication channels in a multi-robot mobile system using software-defined radio (SDR) devices. The system consists of two mobile robots programmed for two scenarios: one where the robot remains stationary and another where it follows a predefined trajectory. Communication within the system is conducted through orthogonal frequency-division multiplexing (OFDM) to mitigate the effects of multipath propagation in indoor environments. The system's performance is evaluated using the bit error rate (BER). Connections related to robot motion and communication are implemented using Raspberry Pi 3 and BladeRF x115, respectively. The least squares (LS) technique is employed to estimate the channel with a bit error rate of approximately 10^(-2)., Comment: in Vietnamese language

Cross-domain Recommendation (CDR) as one of the effective techniques in alleviating the data sparsity issues has been widely studied in recent years. However, previous works may cause domain privacy leakage since they necessitate the aggregation of diverse domain data into a centralized server during the training process. Though several studies have conducted privacy preserving CDR via Federated Learning (FL), they still have the following limitations: 1) They need to upload users' personal information to the central server, posing the risk of leaking user privacy. 2) Existing federated methods mainly rely on atomic item IDs to represent items, which prevents them from modeling items in a unified feature space, increasing the challenge of knowledge transfer among domains. 3) They are all based on the premise of knowing overlapped users between domains, which proves impractical in real-world applications. To address the above limitations, we focus on Privacy-preserving Cross-domain Recommendation (PCDR) and propose PFCR as our solution. For Limitation 1, we develop a FL schema by exclusively utilizing users' interactions with local clients and devising an encryption method for gradient encryption. For Limitation 2, we model items in a universal feature space by their description texts. For Limitation 3, we initially learn federated content representations, harnessing the generality of natural language to establish bridges between domains. Subsequently, we craft two prompt fine-tuning strategies to tailor the pre-trained model to the target domain. Extensive experiments on two real-world datasets demonstrate the superiority of our PFCR method compared to the SOTA approaches., Comment: 11 pages, 3 figures, accepted by WWW 2024

As an indispensable personalized service within Location-Based Social Networks (LBSNs), the Point-of-Interest (POI) recommendation aims to assist individuals in discovering attractive and engaging places. However, the accurate recommendation capability relies on the powerful server collecting a vast amount of users' historical check-in data, posing significant risks of privacy breaches. Although several collaborative learning (CL) frameworks for POI recommendation enhance recommendation resilience and allow users to keep personal data on-device, they still share personal knowledge to improve recommendation performance, thus leaving vulnerabilities for potential attackers. Given this, we design a new Physical Trajectory Inference Attack (PTIA) to expose users' historical trajectories. Specifically, for each user, we identify the set of interacted POIs by analyzing the aggregated information from the target POIs and their correlated POIs. We evaluate the effectiveness of PTIA on two real-world datasets across two types of decentralized CL frameworks for POI recommendation. Empirical results demonstrate that PTIA poses a significant threat to users' historical trajectories. Furthermore, Local Differential Privacy (LDP), the traditional privacy-preserving method for CL frameworks, has also been proven ineffective against PTIA. In light of this, we propose a novel defense mechanism (AGD) against PTIA based on an adversarial game to eliminate sensitive POIs and their information in correlated POIs. After conducting intensive experiments, AGD has been proven precise and practical, with minimal impact on recommendation performance.

We systematically present experimental and theoretical results for the dual-wavelength switching of 1560 nm, 75 fs signal pulses (SPs) driven by 1030 nm, 270 fs control pulses (CPs) in a dual-core fiber (DCF). We demonstrate a switching contrast of 31.9 dB, corresponding to a propagation distance of 14 mm, achieved by launching temporally synchronized SP-CP pairs into the fast core of the DCF with moderate inter-core asymmetry. Our analysis employs a system of three coupled propagation equations to identify the compensation of the asymmetry by nonlinearity as the physical mechanism behind the efficient switching performance., Comment: 4 figures, 5 pages, to be published in Optics Letters

Three-dimensional layered Mg$_3$Bi$_2$ has emerged as thermoelectric material due to its high cooling performance at ambient temperature, which benefits from its low lattice thermal conductivity and semimetal character. However, the semimetal character of Mg$_3$Bi$_2$ is sensitive to spin-orbit coupling (SOC). Thus, the underlying origin of low lattice thermal conductivity needs to be clarified in the presence of the SOC. In this work, the first-principles calculations within the two-channel model are employed to investigate the effects of the SOC on the phonon-phonon scattering on the phonon transport of Mg$_3$Bi$_2$. Our results show that the SOC strongly reduces the lattice thermal conductivity (up to $\sim 35$ %). This reduction originates from the influence of the SOC on the transverse acoustic modes involving interlayer shearing, leading to weak interlayer bonding and enhancement anharmonicity around 50 cm$^{-1}$. Our results clarify the mechanism of low thermal conductivity in Mg$_3$Bi$_2$ and support the design of Mg$_3$Bi$_2$-based materials for thermoelectric applications., Comment: 4 pages, 3 figures, 1 table

We present an open-source program QERaman that computes first-order resonance Raman spectroscopy of materials using the output data from Quantum ESPRESSO. Complex values of Raman tensors are calculated based on the quantum description of the Raman scattering from calculations of electron-photon and electron-phonon matrix elements, which are obtained by using the modified Quantum ESPRESSO. Our program also calculates the resonant Raman spectra as a function of incident laser energy for linearly- or circularly-polarized light. Hands-on tutorials for graphene and MoS$_2$ are given to show how to run QERaman. All codes, examples, and scripts are available on the GitHub repository., Comment: 10 pages, 6 figures, 2 tables

This paper introduces a new class of iterated function systems (IFSs) called R-IFSs, which include both rotation/reflection maps and contraction maps. The study of R-IFSs is motivated by the recent research direction on enriching IFSs by adding other types of mappings. The paper investigates the existence and properties of the semi-attractor and compact invariant sets of R-IFSs, as well as the class of minimal invariant sets of R-IFSs. The paper also provides a familiar setting that is an invariant set of R-IFS but not an invariant set of any IFS., Comment: 11 pages, 4 figures

Imbalanced node classification widely exists in real-world networks where graph neural networks (GNNs) are usually highly inclined to majority classes and suffer from severe performance degradation on classifying minority class nodes. Various imbalanced node classification methods have been proposed recently which construct synthetic nodes and edges w.r.t. minority classes to balance the label and topology distribution. However, they are all based on the homophilic assumption that nodes of the same label tend to connect despite the wide existence of heterophilic edges in real-world graphs. Thus, they uniformly aggregate features from both homophilic and heterophilic neighbors and rely on feature similarity to generate synthetic edges, which cannot be applied to imbalanced graphs in high heterophily. To address this problem, we propose a novel GraphSANN for imbalanced node classification on both homophilic and heterophilic graphs. Firstly, we propose a unified feature mixer to generate synthetic nodes with both homophilic and heterophilic interpolation in a unified way. Next, by randomly sampling edges between synthetic nodes and existing nodes as candidate edges, we design an adaptive subgraph extractor to adaptively extract the contextual subgraphs of candidate edges with flexible ranges. Finally, we develop a multi-filter subgraph encoder that constructs different filter channels to discriminatively aggregate neighbor's information along the homophilic and heterophilic edges. Extensive experiments on eight datasets demonstrate the superiority of our model for imbalanced node classification on both homophilic and heterophilic graphs.

We study the zero-sharing behavior among irreducible characters of a finite group. For symmetric groups $S_n$, it is proved that, with one exception, any two irreducible characters have at least one common zero. To further explore this phenomenon, we introduce the common-zero graph of a finite group $G$, with non-linear irreducible characters of $G$ as vertices, and edges connecting characters that vanish on some common group element. We show that for solvable and simple groups, the number of connected components of this graph is bounded above by 3. Lastly, the result for $S_n$ is applied to prove the non-equivalence of the metrics on permutations induced from faithful irreducible characters of the group.

As an indispensable personalized service in Location-based Social Networks (LBSNs), the next Point-of-Interest (POI) recommendation aims to help people discover attractive and interesting places. Currently, most POI recommenders are based on the conventional centralized paradigm that heavily relies on the cloud to train the recommendation models with large volumes of collected users' sensitive check-in data. Although a few recent works have explored on-device frameworks for resilient and privacy-preserving POI recommendations, they invariably hold the assumption of model homogeneity for parameters/gradients aggregation and collaboration. However, users' mobile devices in the real world have various hardware configurations (e.g., compute resources), leading to heterogeneous on-device models with different architectures and sizes. In light of this, We propose a novel on-device POI recommendation framework, namely Model-Agnostic Collaborative learning for on-device POI recommendation (MAC), allowing users to customize their own model structures (e.g., dimension \& number of hidden layers). To counteract the sparsity of on-device user data, we propose to pre-select neighbors for collaboration based on physical distances, category-level preferences, and social networks. To assimilate knowledge from the above-selected neighbors in an efficient and secure way, we adopt the knowledge distillation framework with mutual information maximization. Instead of sharing sensitive models/gradients, clients in MAC only share their soft decisions on a preloaded reference dataset. To filter out low-quality neighbors, we propose two sampling strategies, performance-triggered sampling and similarity-based sampling, to speed up the training process and obtain optimal recommenders. In addition, we design two novel approaches to generate more effective reference datasets while protecting users' privacy.

We classify Sylow $p$-subgroups of finite groups whose principal $p$-blocks have precisely six ordinary irreducible characters., Comment: 18 pages, 1 table. The second version includes comments from Gunter Malle

We study the codegree isomorphism problem for finite simple groups. In particular, we show that such a group is determined by the codegrees (counting multiplicity) of its irreducible characters. The proof is uniform for all simple groups and only depends on the classification by means of Artin-Tits' simple order theorem., Comment: 24 pages, 2 tables

This paper deals with Pareto solutions of a nonsmooth fractional interval-valued multiobjective optimization. We first introduce four types of Pareto solutions of the considered problem by considering the lower-upper interval order relation and then apply some advanced tools of variational analysis and generalized differentiation to establish necessary optimality conditions for these solutions. Sufficient conditions for Pareto solutions of such a problem are also provided by means of introducing the concepts of (strictly) generalized convex functions defined in terms of the limiting/Mordukhovich subdifferential of locally Lipschitzian functions. Finally, a Mond--Weir type dual model is formulated, and weak, strong and converse-like duality relations are examined., Comment: 17 pages. arXiv admin note: text overlap with arXiv:2201.09000

Contrastive learning (CL) has recently been demonstrated critical in improving recommendation performance. The underlying principle of CL-based recommendation models is to ensure the consistency between representations derived from different graph augmentations of the user-item bipartite graph. This self-supervised approach allows for the extraction of general features from raw data, thereby mitigating the issue of data sparsity. Despite the effectiveness of this paradigm, the factors contributing to its performance gains have yet to be fully understood. This paper provides novel insights into the impact of CL on recommendation. Our findings indicate that CL enables the model to learn more evenly distributed user and item representations, which alleviates the prevalent popularity bias and promoting long-tail items. Our analysis also suggests that the graph augmentations, previously considered essential, are relatively unreliable and of limited significance in CL-based recommendation. Based on these findings, we put forward an eXtremely Simple Graph Contrastive Learning method (XSimGCL) for recommendation, which discards the ineffective graph augmentations and instead employs a simple yet effective noise-based embedding augmentation to generate views for CL. A comprehensive experimental study on four large and highly sparse benchmark datasets demonstrates that, though the proposed method is extremely simple, it can smoothly adjust the uniformity of learned representations and outperforms its graph augmentation-based counterparts by a large margin in both recommendation accuracy and training efficiency. The code and used datasets are released at https://github.com/Coder-Yu/SELFRec., Comment: Extension of our SIGIR'22 paper "Are Graph Augmentations Necessary? Simple Graph Contrastive Learning for Recommendation", Accepted by TKDE

Owing to its nature of scalability and privacy by design, federated learning (FL) has received increasing interest in decentralized deep learning. FL has also facilitated recent research on upscaling and privatizing personalized recommendation services, using on-device data to learn recommender models locally. These models are then aggregated globally to obtain a more performant model, while maintaining data privacy. Typically, federated recommender systems (FRSs) do not consider the lack of resources and data availability at the end-devices. In addition, they assume that the interaction data between users and items is i.i.d. and stationary across end-devices, and that all local recommender models can be directly averaged without considering the user's behavioral diversity. However, in real scenarios, recommendations have to be made on end-devices with sparse interaction data and limited resources. Furthermore, users' preferences are heterogeneous and they frequently visit new items. This makes their personal preferences highly skewed, and the straightforwardly aggregated model is thus ill-posed for such non-i.i.d. data. In this paper, we propose Resource Efficient Federated Recommender System (ReFRS) to enable decentralized recommendation with dynamic and diversified user preferences. On the device side, ReFRS consists of a lightweight self-supervised local model built upon the variational autoencoder for learning a user's temporal preference from a sequence of interacted items. On the server side, ReFRS utilizes a semantic sampler to adaptively perform model aggregation within each identified user cluster. The clustering module operates in an asynchronous and dynamic manner to support efficient global model update and cope with shifting user interests. As a result, ReFRS achieves superior performance in terms of both accuracy and scalability, as demonstrated by comparative experiments.

We investigate dissipationless magneto-Seebeck effect in three-dimensional Dirac/Weyl semimetal. The Hall resistivity $\rho_{yx}$ and thermoelectric Hall coefficient $\alpha_{xy}$ exhibit plateaus at the quantum limit, where electrons occupy only the zeroth Landau level. In this condition, quantum oscillation in the Seebeck coefficient $S_{xx}\approx \rho_{yx}\alpha_{xy} $ is suppressed, and the massless fermions are transformed into a Fermi liquid system. We show that the Seebeck coefficient at the quantum limit is expressed by the harmonic sum of Fermi wavelength and thermal de Broglie wavelength scaled by magnetic length., Comment: 5 pages, 3 figures

Let $p$ be a prime and $G$ a finite group. We propose a strong bound for the number of $p'$-degree irreducible characters of $G$ in terms of the commutator factor group of a Sylow $p$-subgroup of $G$. The bound arises from a recent conjecture of Navarro and Tiep [NT21] on fields of character values and a phenomenon called the continuity of $p$-rationality level of $p'$-degree characters. This continuity property in turn is predicted by the celebrated McKay-Navarro conjecture [Nav04]. We achieve both the bound and the continuity property for $p=2$., Comment: 22 pages. To appear in TAMS

Automatic Program Repair (APR) aims at fixing buggy source code with less manual debugging efforts, which plays a vital role in improving software reliability and development productivity. Recent APR works have achieved remarkable progress via applying deep learning (DL), particularly neural machine translation (NMT) techniques. However, we observe that existing DL-based APR models suffer from at least two severe drawbacks: (1) Most of them can only generate patches for a single programming language, as a result, to repair multiple languages, we have to build and train many repairing models. (2) Most of them are developed in an offline manner. Therefore, they won't function when there are new-coming requirements. To address the above problems, a T5-based APR framework equipped with continual learning ability across multiple programming languages is proposed, namely \emph{C}ont\emph{I}nual \emph{R}epair a\emph{C}ross Programming \emph{L}anguag\emph{E}s (\emph{CIRCLE}). Specifically, (1) CIRCLE utilizes a prompting function to narrow the gap between natural language processing (NLP) pre-trained tasks and APR. (2) CIRCLE adopts a difficulty-based rehearsal strategy to achieve lifelong learning for APR without access to the full historical data. (3) An elastic regularization method is employed to strengthen CIRCLE's continual learning ability further, preventing it from catastrophic forgetting. (4) CIRCLE applies a simple but effective re-repairing method to revise generated errors caused by crossing multiple programming languages. We train CIRCLE for four languages (i.e., C, JAVA, JavaScript, and Python) and evaluate it on five commonly used benchmarks. The experimental results demonstrate that CIRCLE not only effectively and efficiently repairs multiple programming languages in continual learning settings, but also achieves state-of-the-art performance with a single repair model., Comment: This paper was accepted by ISSTA2022

Modern recommender systems operate in a fully server-based fashion. To cater to millions of users, the frequent model maintaining and the high-speed processing for concurrent user requests are required, which comes at the cost of a huge carbon footprint. Meanwhile, users need to upload their behavior data even including the immediate environmental context to the server, raising the public concern about privacy. On-device recommender systems circumvent these two issues with cost-conscious settings and local inference. However, due to the limited memory and computing resources, on-device recommender systems are confronted with two fundamental challenges: (1) how to reduce the size of regular models to fit edge devices? (2) how to retain the original capacity? Previous research mostly adopts tensor decomposition techniques to compress the regular recommendation model with limited compression ratio so as to avoid drastic performance degradation. In this paper, we explore ultra-compact models for next-item recommendation, by loosing the constraint of dimensionality consistency in tensor decomposition. Meanwhile, to compensate for the capacity loss caused by compression, we develop a self-supervised knowledge distillation framework which enables the compressed model (student) to distill the essential information lying in the raw data, and improves the long-tail item recommendation through an embedding-recombination strategy with the original model (teacher). The extensive experiments on two benchmarks demonstrate that, with 30x model size reduction, the compressed model almost comes with no accuracy loss, and even outperforms its uncompressed counterpart in most cases., Comment: To Appear in SIGIR'22

This article presents an in-depth review of the topic of path following for autonomous robotic vehicles, with a specific focus on vehicle motion in two dimensional space (2D). From a control system standpoint, path following can be formulated as the problem of stabilizing a path following error system that describes the dynamics of position and possibly orientation errors of a vehicle with respect to a path, with the errors defined in an appropriate reference frame. In spite of the large variety of path following methods described in the literature we show that, in principle, most of them can be categorized in two groups: stabilization of the path following error system expressed either in the vehicle's body frame or in a frame attached to a "reference point" moving along the path, such as a Frenet-Serret (F-S) frame or a Parallel Transport (P-T) frame. With this observation, we provide a unified formulation that is simple but general enough to cover many methods available in the literature. We then discuss the advantages and disadvantages of each method, comparing them from the design and implementation standpoint. We further show experimental results of the path following methods obtained from field trials testing with under-actuated and fully-actuated autonomous marine vehicles. In addition, we introduce open-source Matlab and Gazebo/ROS simulation toolboxes that are helpful in testing path following methods prior to their integration in the combined guidance, navigation, and control systems of autonomous vehicles.

Next Point-of-Interest (POI) recommendation has become an indispensable functionality in Location-based Social Networks (LBSNs) due to its effectiveness in helping people decide the next POI to visit. However, accurate recommendation requires a vast amount of historical check-in data, thus threatening user privacy as the location-sensitive data needs to be handled by cloud servers. Although there have been several on-device frameworks for privacy-preserving POI recommendations, they are still resource-intensive when it comes to storage and computation, and show limited robustness to the high sparsity of user-POI interactions. On this basis, we propose a novel decentralized collaborative learning framework for POI recommendation (DCLR), which allows users to train their personalized models locally in a collaborative manner. DCLR significantly reduces the local models' dependence on the cloud for training, and can be used to expand arbitrary centralized recommendation models. To counteract the sparsity of on-device user data when learning each local model, we design two self-supervision signals to pretrain the POI representations on the server with geographical and categorical correlations of POIs. To facilitate collaborative learning, we innovatively propose to incorporate knowledge from either geographically or semantically similar users into each local model with attentive aggregation and mutual information maximization. The collaborative learning process makes use of communications between devices while requiring only minor engagement from the central server for identifying user groups, and is compatible with common privacy preservation mechanisms like differential privacy. We evaluate DCLR with two real-world datasets, where the results show that DCLR outperforms state-of-the-art on-device frameworks and yields competitive results compared with centralized counterparts., Comment: 21 Pages, 3 figures, 4 tables

This paper deals with approximate solutions of a nonsmooth semi-infinite programming with multiple interval-valued objective functions. We first introduce four types of approximate quasi Pareto solutions of the considered problem by considering the lower-upper interval order relation and then apply some advanced tools of variational analysis and generalized differentiation to establish necessary optimality conditions for these approximate solutions. Sufficient conditions for approximate quasi Pareto solutions of such a problem are also provided by means of introducing the concepts of approximate (strictly) pseudo-quasi generalized convex functions defined in terms of the limiting subdifferential of locally Lipschitz functions. Finally, a Mond--Weir type dual model in approximate form is formulated, and weak, strong and converse-like duality relations are proposed.

The effects of the unique density of states (DOS) of a topological type-II nodal-line semimetal (NLS) on its thermoelectric (TE) transport properties are investigated through a combination of semi-analytical and first-principles methods with "spinless Mg$_3$Bi$_2$" as artificial material. The DOS in such a type-II NLS possesses two van Hove singularities near the energy of the nodal line that leads to a large $S$ value compared to the normal metals. Combined with the linear band at the nodal line that gives high electrical conductivity $\sigma$, the type-II NLS can exhibit a relatively high TE power factor ($\text{PF}=S^2\sigma$) at the nodal line. In particular, we find $\text{PF} \sim 60$ $\mu$W/cmK$^2$ at 300 K for the n-type Mg$_3$Bi$_2$ by considering the electron-phonon scattering, in which the relaxation time $\tau$ of carriers can be expressed as $\tau\propto\text{DOS}^{-1}$ for the type-II NLS. Furthermore, we optimize parameters for the TE power factor of type-II NLSs in general by adopting the two-band model with the DOS-dependent relaxation time approximation. Our results suggest the type-II NLSs as a potential class of high-performance TE materials among metals and semimetals, which are traditionally considered not good TE materials compared to semiconductors., Comment: 5 pages, 3 figures