Mathematics, Volume 12, Issue 3 (February-1 2024) – 143 articles

This research introduces the Multi-Depot Waste Collection Vehicle Routing Problem with Time Windows and Self-Delivery Option (MDWCVRPTW-SDO). The problem comes from the waste bank operation implemented in Yogyakarta City, Indonesia. A set of vehicles is dispatched from the waste banks to pick up waste from residents’ locations within the time windows specified by the residents. Residents may be compensated for delivering their waste to a waste bank by themselves. The objective of MDWCVRPTW-SDO is minimizing the sum of investment costs, routing costs, and total compensation paid to the residents. We model this problem as a mixed integer linear programming model and propose Simulated Annealing (SA) as an effective solution approach. Extensive computational experiments confirm that SA is effective to solve MDWCVRPTW-SDO. Moreover, the number of waste banks, compensation paid to residents, and the distribution of residents of each type are crucial for the success of the implementation. Full article

In this study, Ostrowski-type inequalities in fuzzy settings were investigated. A detailed theory of fuzzy analysis is provided and utilized to establish the Ostrowski-type inequality in the fuzzy number-valued space. The results obtained in this research not only provide a generalization of the results of Dragomir but also give an extended version of the Ostrowski-type inequalities obtained by Anastassiou. Full article

In this paper, we present a three-step sixth-order class of iterative schemes to estimate the solutions of a nonlinear system of equations. This procedure is designed by means of a weight function technique. We apply this procedure for predicting the shear strength of a reinforced concrete beam. The values for the parameters of the nonlinear system describing this problem were randomly selected inside the prescribed ranges by technical standards for structural concrete. Moreover, some of these parameters were fixed taking into consideration the solvability region of the adopted steel constitutive model. The effectiveness of the new class is also compared with other current schemes in terms of the computational efficiency and numerical performance, with very good results. The advantages of this new class come from the low computational cost, due to the existence of an only inverse operator. Full article

Flag codes are a recent network coding strategy based on linear algebra. Fuzzy vector subspaces extend the notions of classical linear algebra. They can be seen as abstractions of flags to the point that several fuzzy vector subspaces can be identified to the same flag, which naturally induces an equivalence relation on the set of fuzzy vector subspaces. The main contributions of this work are the methodological abstraction of flags and flag codes in terms of fuzzy vector subspaces, as well as the generalisation of three distinct equivalence relations that originated from the fuzzy subgroup theory and study of their connection with flag codes, computing the number of equivalence classes in the discrete case, which represent the number of essentially distinct flags, and a comprehensive analysis of such relations and the properties of the corresponding quotient sets. Full article

This study adopts a data-driven methodology to address the challenge of garment fitting for individuals with diverse body shapes. Focusing on young Chinese women aged 18–25 from Central China, we utilized the German VITUS SMART LC3 3D body scanning technology to measure 62 body parts pertinent to fashion design on a sample of 220 individuals. We then employed a hybrid approach, integrating the circumference difference classification method with the characteristic value classification method, and applied the K-means clustering algorithm to categorize these individuals into four distinct body shape groups based on cluster center analysis. Building upon these findings, we formulated specific linear regression models for key body parts associated with each body shape category. This led to the development of an intelligent software capable of automatically calculating the dimensions of 28 body parts and accurately determining the body shape type for young Central Chinese women. Our research underscores the significant role of intelligent predictive systems in the realm of fashion design, particularly within a data-driven framework. The system we have developed offers precise body measurements and classification outcomes, empowering businesses to create garments that more accurately conform to the wearer’s body, thus enhancing both the fit and aesthetic value of the clothing. Full article

Mobile Edge Computing (MEC) is a new distributed computing method based on the mobile communication network. It can provide cloud services and an IT service environment for application developers and service providers at the edge of the network. Computation offloading is a crucial technology of edge computing. However, computation offloading will consume the resources of the edge devices, and therefore the edge devices will not offload computation unconditionally. In addition, the service quality of edge computing applications is related to the cooperation rate of edge devices. Therefore, it is essential to design an appropriate incentive mechanism to motivate edge devices to execute computation offloading. However, the current existing incentive mechanisms have two problems: Firstly, existing mechanisms do not account for probability distortions under uncertainty in collaborator utility valuation models. Secondly, the platform ignores the risk preferences of collaborators in multiple rounds of decision-making. To address these issues, we propose an incentive mechanism based on risk preference, IMRP. The IMRP considers the collaborator’s probability distortion, introduces an uncertain utility bonus scheme, and builds a probability distortion model to influence the collaborator’s willingness to offload tasks. The IMRP also considers the collaborator’s risk preference and builds the collaborator’s risk preference model to influence the collaborator’s bidding decision. Simulation results show that our mechanism effectively improves the cooperation rate of edge devices and the utility of the requester. Full article

In unveiling the non-parametric estimation of the conditional hazard function through the local linear method, our study yields key insights into the method’s behavior. We present rigorous analyses demonstrating the mean square convergence of the estimator, subject to specific conditions, within the realm of independent observations with missing data. Furthermore, our contributions extend to the derivation of expressions detailing both bias and variance of the estimator. Emphasizing the practical implications, we underscore the applicability of two distinct models discussed in this paper for single index estimation scenarios. These findings not only enhance our understanding of survival analysis methodologies but also provide practitioners with valuable tools for navigating the complexities of missing data in the estimation of conditional hazard functions. Ultimately, our results affirm the robustness of the local linear method in non-parametrically estimating the conditional hazard function, offering a nuanced perspective on its performance in the challenging context of independent observations with missing data. Full article

Over the last two decades, meshfree Galerkin methods have become increasingly popular in solid and fluid mechanics applications. A variety of these methods have been developed, each incorporating unique meshfree approximation schemes to enhance their performance. In this study, we examine the application of the Moving Least Squares and Local Maximum-Entropy (LME) approximations within the framework of Optimal Transportation Meshfree for solving Galerkin boundary-value problems. We focus on how the choice of basis order and the non-negativity, as well as the weak Kronecker-delta properties of shape functions, influence the performance of numerical solutions. Through comparative numerical experiments, we evaluate the efficiency, accuracy, and capabilities of these two approximation schemes. The decision to use one method over the other often hinges on factors like computational efficiency and resource management, underscoring the importance of carefully considering the specific attributes of the data and the intrinsic nature of the problem being addressed. Full article

Due to the non-linear and non-stationary nature of daily new 2019 coronavirus disease (COVID-19) case time series, existing prediction methods struggle to accurately forecast the number of daily new cases. To address this problem, a hybrid prediction framework is proposed in this study, which combines ensemble empirical mode decomposition (EEMD), fuzzy entropy (FE) reconstruction, and a CNN-LSTM-ATT hybrid network model. This new framework, named EEMD-FE-CNN-LSTM-ATT, is applied to predict the number of daily new COVID-19 cases. This study focuses on the daily new case dataset from the United States as the research subject to validate the feasibility of the proposed prediction framework. The results show that EEMD-FE-CNN-LSTM-ATT outperforms other baseline models in all evaluation metrics, demonstrating its efficacy in handling the non-linear and non-stationary epidemic time series. Furthermore, the generalizability of the proposed hybrid framework is validated on datasets from France and Russia. The proposed hybrid framework offers a new approach for predicting the COVID-19 pandemic, providing important technical support for future infectious disease forecasting. Full article

The utilization of seismic barriers for protection against the hazardous impact of natural or technogenic waves is an extremely promising emerging technology to secure buildings, structures and entire areas against earthquake-generated seismic waves, high-speed-transport-induced vibrations, etc. The current research is targeted at studying the effect of seismic-barrier shape on the reduction of seismic-wave magnitudes within the protected region. The analytical solution of Lamb’s problem was used to verify the adopted numerical approach. It was demonstrated that the addition of complementary geometric features to a simple barrier shape provides the possibility of significantly increasing the resulting seismic protection. A simple genetic algorithm was employed to evaluate the nontrivial but extremely effective geometry of the seismic barrier. The developed approach can be used in various problems requiring optimization of non-parameterizable geometric shapes. The applicability of genetic algorithms and other generative algorithms to discover optimal (or close to optimal) geometric configurations for the essentially multiscale problems of the interaction of mechanical waves with inclusions is discussed. Full article

The linkable ring signature supporting stealth addresses (SALRS) is a recently proposed cryptographic primitive, which is designed to comprehensively address the soundness and privacy requirements associated with concealing the identities of both the payer and payee in cryptocurrency transactions. However, concerns regarding the scalability of SALRS have been underexplored. This becomes notably pertinent in intricate blockchain systems where multiple cryptographic primitives operate concurrently. To bridge this gap, our work revisited and formalized the ideal functionality of SALRS within the universal composability (UC) model. This encapsulates all correctness, soundness, and privacy considerations. Moreover, we established that the newly proposed UC-security property for SALRS is equivalent to the concurrent satisfaction of signer-unlinkability, signer-non-slanderability, signer-anonymity, and master-public-key-unlinkability. These properties represent the four crucial game-based security aspects of SALRS. This result ensures the ongoing security of previously presented SALRS constructions within the UC framework. It also underscores their adaptability for seamless integration with other UC-secure primitives in complex blockchain systems. Full article

Geomagnetic field measurements indicate that at present we may be on the brink of the Earth’s magnetic field reversal, potentially resulting in all the accompanying negative consequences for the mankind. Mathematical modelling is necessary in order to find precursors for reversals and excursions of the magnetic field. With this purpose in mind, following the Podvigina scenario for the emergence of the reversals, we have studied convective flows not far (in the parameter space) from their onset and the onset of magnetic field generation, and found a flow demonstrating reversals of polarity of some harmonics comprising the magnetic field. We discuss a simulated regime featuring patterns of behaviour that apparently indicate future reversals of certain harmonics of the magnetic field. It remains to be seen whether reversal precursors similar to the observed ones exist and might be applicable for the much more complex geomagnetic dynamo. Full article

In a public health emergency, residents urgently require a large number of rescue materials for treatment or protection. These rescue materials are usually located far from the emergency area. The government must organize rescue materials transportation by selecting suitable transport modes. Thus, we propose a material allocation model for public health emergencies under a multimodal transportation network to determine the best rescue material supply route. In this model, we set the demand priorities according to the emergency degrees to decide the transportation sequence. Meanwhile, we introduce the psychological pain cost brought by the rescue material shortage into the proposed model to trade off the priority and fairness of demand. Having compared it to the research literature, this is the first study that considers multiple categories of materials, absolute pain costs, relative pain costs and demand priority under multimodal transportation. The research problem is formulated into an integer programming model, and we develop a modified genetic algorithm to solve it. A set of numerical examples are conducted to test the performance of the proposed algorithm, and to investigate features and applications of the proposed model. The results indicate that the modified genetic algorithm performs better in the calculation examples at different scales. For small-scale instances, the algorithm produces consistent results with Gurobi. As the instance size increases, Gurobi fails to find the optimal solution within 1800 s, while this algorithm is able to find the optimal solution within an acceptable time frame. Additionally, when dealing with large-scale instances, the algorithm exhibits a significant advantage in terms of runtime. Sensitivity analysis of key factors indicate that (1) Adjusting the relative pain cost coefficient can make the best trade-off between fairness, economy and timeliness; (2) Compared with a single mode of transport, multimodal transport can reduce the psychological pain cost and the logistics cost; (3) Improving the loading and unloading capacity of nodes can reduce the delivery time of materials and the psychological pain cost of residents, but the influence of other factors and cost-effectiveness need to be considered. Full article

The prediction of future disease development based on past diagnosis records has gained significant attention due to the growing health awareness among individuals. Recent deep learning-based methods have successfully predicted disease development by establishing relationships for each diagnosis record and extracting features from a patient’s past diagnoses in chronological order. However, most of these models have ignored the connections between identified diseases and low-risk diseases, leading to bottlenecks and limitations. In addition, the extraction of temporal characteristics is also hindered by the problem of global feature forgetting. To address these issues, we propose a global context-aware net using disease relationship reasoning and attention-based feature fusion, abbreviated as DRR. Our model incorporates a disease relationship reasoning module that enhances the model’s attention to the relationship between confirmed diseases and low-risk diseases, thereby alleviating the current model’s bottlenecks. Moreover, we have established a global graph-based feature fusion module that integrates global graph-based features with temporal features, mitigating the issue of global feature forgetting. Extensive experiments were conducted on two publicly available datasets, and the experiments show that our method achieves advanced performance. Full article

We study the solvability of the Ionkin problem for some differential equations with one space variable. These equations include parabolic and quasiparabolic, hyperbolic and quasihyperbolic, pseudoparabolic and pseudohyperbolic, elliptic and quasielliptic equations and equations of many other types. For the above equations, the following theorems are proved with the use of the splitting method: the existence of regular solutions—solutions that all have weak derivatives in the sense of S. L. Sobolev and occur in the corresponding equation. Full article

An involution refers to a function that acts as its own inverse. In this paper, our focus lies on exploring two-dimensional involutive maps defined by rational functions. These functions have denominators represented by polynomials of degree one and numerators by polynomials of a degree of, at most, two, depending on parameters. We identify the sets in the parameter space of the maps that correspond to involutions. The investigation relies on leveraging algorithms from computational commutative algebra based on the Groebner basis theory. To expedite the computations, we employ modular arithmetic. Furthermore, we showcase how involution can serve as a valuable tool for identifying reversible and integrable systems within families of planar polynomial ordinary differential equations. Full article

This paper tests using two-regime Markov-switching models with asymmetric, time-varying exponential generalized autoregressive conditional heteroskedasticity (MS-EGARCH) variances in random-length lumber futures trading. By assuming a two-regime context (a low $s=1$ and high $s=2$ volatility), a trading algorithm was simulated with the following trading rule: invest in lumber futures if the probability of being in the high-volatility regime $s=2$ is lower or equal to 50%, or invest in the 3-month U.S. Treasury bills (TBills) otherwise. The rationale tested in this paper was that using a two-regime Markov-switching (MS) algorithm leads to an overperformance against a buy-and-hold strategy in lumber futures. To extend the current literature in MS trading algorithms, two location parameter scenarios were simulated. The first uses an unconditional mean or expected value (no factors), and the second incorporates market and behavioral factors. With weekly simulations form 2 January 1994 to 28 July 2023, the results suggest that using MS-EGARCH models in a no-factors scenario is appropriate for active lumber futures trading with an accumulated return of 158.33%. Also, the results suggest that it is not useful to add market and behavioral factors in the MS-GARCH estimation because it leads to a lower performance. Full article

This article describes the solution of two problems. First, based on the fractional diffusion equation, a boundary problem with arbitrary values of derivative indicators was formulated and solved, describing more general cases than existing solutions. Secondly, from the consideration of the probability schemes of transitions between states of the process, which can be observed in complex systems, a fractional-differential equation of the telegraph type with multiples is obtained (in time: β, 2β, 3β, … and state: α, 2α, 3α, …) using orders of fractional derivatives and its analytical solution for one particular boundary problem is considered. In solving edge problems, the Fourier method was used. This makes it possible to represent the solution in the form of a nested time series (one in time t, the second in state x), each of which is a function of the Mittag-Leffler type. The eigenvalues of the Mittag-Leffler function for describing states can be found using boundary conditions and the Fourier coefficient based on the initial condition and orthogonality conditions of the eigenfunctions. An analysis of the characteristics of time series of changes in the emotional color of users’ comments on published news in online mass media and the electoral campaigns of the US presidential elections showed that for the mathematical expectation of amplitudes of deviations of series levels from the size of the amplitude calculation interval (“sliding window”), a root dependence of fractional degree was observed; for dispersion, a power law with a fractional index greater than 1.5 was observed; and the behavior of the excess showed the presence of so-called “heavy tails”. The obtained results indicate that time series have unsteady non-locality, both in time and state. This provides the rationale for using differential equations with partial fractional derivatives to describe time series dynamics. Full article

Industry is the primary application for induction machines. As such, it is essential to calculate the induction devices’ electrical properties accurately. With DC testing, no-load rotor tests, and locked rotor tests, one may empirically evaluate the electrical variables of induction motors. These tests are expensive and difficult to conduct, however. The information supplied by machine makers can also be used to accurately approximate the equivalent variables of the circuits in induction machines. This article has successfully predicted motor reactance (Xm) for both double- and single-cage models using artificial neural networks (ANN). Although ANNs have been investigated in the literature, the ANN structures were trained to use unmemorized training. Besides ANN, six other approaches have been suggested to address this issue: heap-based optimization (HBO), leagues championship algorithm (LCA), multi-verse optimization (MVO), osprey optimization algorithm (OOA), cuckoo optimization algorithm (COA), and sooty tern optimization algorithm (STOA). The efficaciousness of the suggested approaches was compared with each another. Regarding the obtained outcomes, the suggested MVO- multi-layer perceptron (MLP) technique performed better than the other five methods regarding reactance prediction, with R² of 0.99598 and 0.9962, and RMSE of 20.31492 and 20.80626 in the testing and training phases, respectively. For the projected model, the suggested ANNs have produced great results. The novelty lies in the mentioned methods’ ability to tackle the complexities and challenges associated with induction motor reactance optimization, providing innovative approaches to finding optimal or near-optimal solutions. As researchers continue to explore and refine these techniques, their impact on motor design and efficiency will likely grow, driving advancements in electrical engineering. Full article

We present a novel formulation of structural design optimization problems specifically tailored to be solved by qa. Structural design optimization aims to find the best, i.e., material-efficient yet high-performance, configuration of a structure. To this end, computational optimization strategies can be employed, where a recently evolving strategy based on quantum mechanical effects is qa. This approach requires the optimization problem to be present, e.g., as a qubo model. Thus, we develop a novel formulation of the optimization problem. The latter typically involves an analysis model for the component. Here, we use energy minimization principles that govern the behavior of structures under applied loads. This allows us to state the optimization problem as one overall minimization problem. Next, we map this to a qubo problem that can be immediately solved by qa. We validate the proposed approach using a size optimization problem of a compound rod under self-weight loading. To this end, we develop strategies to account for the limitations of currently available hardware. Remarkably, for small-scale problems, our approach showcases functionality on today’s hardware such that this study can lay the groundwork for continued exploration of qa’s impact on engineering design optimization problems. Full article

Intelligent fault diagnosis encounters the challenges of varying working conditions and sample class imbalance individually, but very few approaches address both challenges simultaneously. This article proposes an improvement network model named ICDAN-F, which can deal with fault diagnosis scenarios with class imbalance and working condition variations in an integrated way. First, Focal Loss, which was originally designed for target detection, is introduced to alleviate the sample class imbalance problem of fault diagnosis and emphasize the key features. Second, the domain discriminator is improved by the default ReLU activation function being replaced with Tanh so that useful negative value information can help extract transferable fault features. Extensive transfer experiments dealing with varying working conditions are conducted on two bearing fault datasets with the effect of class imbalance. The results show that the fault diagnosis performance of ICDAN-F outperforms several other widely used domain adaptation methods, achieving 99.76% and 96.76% fault diagnosis accuracies in Case 1 and Case 2, respectively, which predicts that ICDAN-F can handle both challenges in a cohesive manner. Full article

In this paper, we investigate mathematical models of meteorological forecasting based on the work of neural networks, which allow us to calculate presumptive meteorological parameters of the desired location on the basis of previous meteorological data. A new method of grouping neural networks to obtain a more accurate output result is proposed. An algorithm is presented, based on which the most accurate meteorological forecast was obtained based on the results of the study. This algorithm can be used in a wide range of situations, such as obtaining data for the operation of equipment in a given location and studying meteorological parameters of the location. To build this model, we used data obtained from personal weather stations of the Weather Underground company and the US National Digital Forecast Database (NDFD). Also, a Google remote learning machine was used to compare the results with existing products on the market. The algorithm for building the forecast model covered several locations across the US in order to compare its performance in different weather zones. Different methods of training the machine to produce the most effective weather forecast result were also considered. Full article

This paper investigates the path planning problem of the coal mine solid-filling and pushing mechanism and proposes a hybrid improved adaptive genetic particle swarm algorithm (AGAPSO). To enhance the efficiency and accuracy of path planning, the algorithm combines a particle swarm optimization algorithm (PSO) and a genetic algorithm (GA), introducing the sharing mechanism and local search capability of the particle swarm optimization algorithm. The path planning of the pushing mechanism for the solid-filling scenario is optimized by dynamically adjusting the algorithm parameters to accommodate different search environments. Subsequently, the proposed algorithm’s effectiveness in the filling equipment path planning problem is experimentally verified using a simulation model of the established filling equipment path planning scenario. The experimental findings indicate that the improved hybrid algorithm converges three times faster than the original algorithm. Furthermore, it demonstrates approximately 92% and 94% better stability and average performance, respectively, than the original algorithm. Additionally, AGAPSO achieves a 27.59% and 19.16% improvement in path length and material usage optimization compared to the GA and GAPSO algorithms, showcasing superior efficiency and adaptability. Therefore, the AGAPSO method offers significant advantages in the path planning of the coal mine solid-filling and pushing mechanism, which is crucial for enhancing the filling effect and efficiency. Full article

Convexity plays a crucial role in the development of fractional integral inequalities. Many fractional integral inequalities are derived based on convexity properties and techniques. These inequalities have several applications in different fields such as optimization, mathematical modeling and signal processing. The main goal of this article is to establish a novel and generalized identity for the Caputo–Fabrizio fractional operator. With the help of this specific developed identity, we derive new fractional integral inequalities via exponential convex functions. Furthermore, we give an application to some special means. Full article

Cap-and-trade models have been largely studied in the literature when it comes to reducing emissions in a supply chain. In this paper, further pursuing the goal of analyzing the effectiveness of cap-and-trade strategies in reducing emissions in supply chains, we propose a mathematical model for sustainable supply chain management. This optimization program aims at reducing emissions and supply chain costs in an unregulated scenario w.r.t. the cap definition, i.e., trading CO₂ is allowed but no formal limit on the CO₂ emissions is imposed. Also, we considered an initial budget for technological investments by the facilities in the considered supply chain, allowing plants to reduce their unit production emissions at a different unit production cost. For this model, differently from what exists in the literature, we derive some theoretical conditions guaranteeing that, if obeyed, the emissions over time have a non-increasing trend meaning that decreasing caps over time can be attained with a self-regulated scenario. Computational results show the effectiveness of our approach. Full article

Dynamical systems are ubiquitous in the physical world and are often well-described by partial differential equations (PDEs). Despite their formally infinite-dimensional solution space, a number of systems have long time dynamics that live on a low-dimensional manifold. However, current methods to probe the long time dynamics require prerequisite knowledge about the underlying dynamics of the system. In this study, we present a data-driven hybrid modeling approach to help tackle this problem by combining numerically derived representations and latent representations obtained from an autoencoder. We validate our latent representations and show they are dynamically interpretable, capturing the dynamical characteristics of qualitatively distinct solution types. Furthermore, we probe the topological preservation of the latent representation with respect to the raw dynamical data using methods from persistent homology. Finally, we show that our framework is generalizable, having been successfully applied to both integrable and non-integrable systems that capture a rich and diverse array of solution types. Our method does not require any prior dynamical knowledge of the system and can be used to discover the intrinsic dynamical behavior in a purely data-driven way. Full article

In this paper, two randomized block Kaczmarz methods to compute inner inverses of any rectangular matrix A are presented. These are iterative methods without matrix multiplications and their convergence is proved. The numerical results show that the proposed methods are more efficient than iterative methods involving matrix multiplications for the high-dimensional matrix. Full article

In this research, a novel approach is presented to enhance the precision of open-type optical linear encoders, focusing on reducing subdivisional errors (SDEs). Optical linear encoders are crucial in high-precision machinery. The overall error in optical linear encoders encompasses baseline error, SDE, and position noise. This study concentrates on mitigating SDEs, which are recurrent errors within each pitch period and arise from various contributing factors. A novel method is introduced to improve the quality of sinusoidal signals in open-type optical linear encoders by incorporating specially designed angle shift patterns on the main scale. The proposed method effectively suppresses the third order harmonics, resulting in enhanced accuracy without significant increases in production costs. Experimental results indicate a substantial reduction in SDEs compared to traditional methods, emphasizing the potential for cost-effective, high-precision optical linear encoders. This paper also discusses the correlation between harmonic suppression and SDE reduction, emphasizing the significance of this method in achieving higher resolutions in optical linear encoders. Full article

This article is devoted to the synthesis and analysis of the quality of the statistical estimate of parameters of a multidimensional linear system (MLS) with one input and m outputs. A nontrivial case is investigated when the one-dimensional input signal of MLS is a deterministic process, the values of which are unknown nuisance parameters. The estimate is based only on observations of MLS output signals distorted by random Gaussian stationary $m$-dimensional noise with a known spectrum. It is assumed that the likelihood function of observations of the output signals of MLS satisfies the conditions of local asymptotic normality. The $\sqrt{n}$-consistency of the estimate is established. Under the assumption of asymptotic normality of an objective function, the limiting covariance matrix of the estimate is calculated for case where the number of observations tends to infinity. Full article

Training large-scale models needs big data. However, the few-shot problem is difficult to resolve due to inadequate training data. It is valuable to use only a few training samples to perform the task, such as using big data for application scenarios due to cost and resource problems. So, to tackle this problem, we present a simple and efficient method, contrastive label generation with knowledge for few-shot learning (CLG). Specifically, we: (1) Propose contrastive label generation to align the label with data input and enhance feature representations; (2) Propose a label knowledge filter to avoid noise during injection of the explicit knowledge into the data and label; (3) Employ label logits mask to simplify the task; (4) Employ multi-task fusion loss to learn different perspectives from the training set. The experiments demonstrate that CLG achieves an accuracy of 59.237%, which is more than about 3% in comparison with the best baseline. It shows that CLG obtains better features and gives the model more information about the input sentences to improve the classification ability. Full article