Bent functions have a wide range of applications in combinatorial designs, error-correcting codes, sequences, and other domains. The class of 2 n -variable bent functions D , defined by functions of the form f ( x , y ) = x ⋅ π ( y ) + 1 E 1 ( x ) 1 E 2 ( y ) , was initially proposed by Carlet (1994) three decades ago as a construction based on the permutation π , but only one explicit subclass D 0 was presented. To date, only three explicit constructions of D class bent functions have been identified. Moreover, for any bent function f in D (excluding D 0 ), the problem of whether f is equivalent to a function in one of the known primary classes of bent functions (such as PS , M ) remains mainly open. In this paper, we investigate the algebraic structure of bent functions in the D class and their relationship to the completed Maiorana–McFarland class M # . Our primary contribution is to establish a complete characterization of D ∩ M # using the algebraic properties of the permutation π and the subspace E 1 under the condition that dim ( E 1 ) < n − 3 . Specifically, we prove that f belongs to M # if the permutation π is affine, thereby resolving an open problem posed in Zhang et al. (2020). In addition, we show that f is outside M # if π is not affine on any ( n − k − 1 ) -dimensional subspace of E 2 , which generalizes a prior result from Kudin et al. (2022). Furthermore, we demonstrate that the probability of a 2 n -variable bent function of the PS a p class also being in D 1 approaches zero as n increases by comparing their algebraic ranks. Finally, as an application, we construct two new infinite families of bent functions in the D 1 class that lie outside M # .

Threshold private set intersection is a basic primitive of secure multiparty computation, which has many important applications in the field of privacy preservation and information security, especially in a ride sharing system, one of the most transforming and innovative technologies enabled by the Internet of Things. In this paper, we propose a new proposal for threshold private set intersection based on quantum homomorphic encryption, in which both the number of users and the designated trusted party are flexible. Furthermore, the complicated computing task can be delegated to a server for processing contributing to the speciality of quantum homomorphic encryption. More importantly, the users’ privacy is perfectly guaranteed because all the calculations are performed on the quantum encrypted data. Therefore, this proposal is more practical compared with the prior work.

The task offloading and resource allocation strategies aim to provide efficient edge computing services for ground mobile devices in mobile edge computing (MEC) environments. In this paper, we propose a UAV-assisted dynamic deployment and decision-making framework (dDDM) to address the issue of insufficient base station coverage in remote areas or emergency scenarios, which leverages the flexibility and computational capabilities of unmanned aerial vehicle (UAV) to supplement terrestrial cellular networks. We focus on optimizing the UAV trajectory to support and enhance the effectiveness of task offloading and resource allocation strategies under conditions of user mobility and stochastic task arrivals. Therefore, a joint optimization problem is formulated with the objective of minimizing the weighted sum of the total latency of ground mobile devices and the overall energy consumption of UAV. To solve this problem, the original optimization problem is decomposed into two subproblems: UAV trajectory planning, and decision-making for task offloading & computing resource allocation. For the UAV trajectory planning subproblem, we propose an improved particle swarm optimization(PSO) algorithm integrated withK-means clustering, i.e., KMPSO algorithm, enabling dynamic UAV deployment in response to user mobility. For the task offloading and resource allocation decision-making, an improved black-winged kite algorithm (IBKA) is developed to determine optimal offloading and allocation strategies. Simulation results demonstrate that the proposed approach outperforms existing benchmark algorithms in terms of both latency and energy consumption.

In Vehicle Edge Computing Network (VECN), task offloading is a key technique to provide the satisfactory quality of service (QoS) for latency-sensitive tasks. However, the diversity of computational resources in edge nodes (i.e., RSU and idle vehicles) and the mobility of vehicles present significant challenges to task offloading. Hence, to address these challenges, we propose an offloading scheme that jointly allocates RSU nodes (including MEC servers) and idle service vehicle resources in this paper. We first prioritize these tasks based on their maximum tolerable latency and design a utility function to capture the executing cost for latency-sensitive tasks. Then, we propose a joint optimization algorithm of task offloading location and proportion based on Multi-agent Deep Reinforcement Learning (jTOLP-MADRL algorithm) for latency-sensitive tasks in VECN, which consists of two sub-algorithms: the Offloading Location Selection (OLS) algorithm and the Offloading Proportion Allocation (OPA) algorithm. Additionally, we design a Convolutional Recurrent Actor-Critic Network (CRACN) to enhance the learning efficiency of the OLS algorithm. Finally, we indicate our algorithm is effective based on simulation results. Compared with the other benchmark algorithms, jTOLP-MADRL can significantly reduce latency and enhance system utility.

Abstract Network function virtualization (NFV) has been proposed to enable flexible management and deployment of the network service in cloud. In NFV architecture, a network service needs to invoke several service functions (SFs) in a particular order following the service chain function. The placement of SFs has significant impact on the performance of network services. However, stochastic nature of the network service arrivals and departures as well as meeting the end-to-end Quality of Service(QoS) makes the SFs placement problem even more challenging. In this paper, we firstly provide a system architecture for the SFs placement of cloud service with end-to-end QoS deadline. We then formulate the end-to-end service placement as a Markov decision process (MDP) which aims to minimize the placement cost and the end-to-end delay. In our MDP, the end-to-end delay of active services in the network is considered to be the state of the system, and the placement (nonplacement or placement) of SF is considered as the action. Also, we discuss the rationality of our analytical model by analyzing the Markov stochastic property of the end-to-end service placement. To obtain the optimal placement policy, we then propose an algorithm (Algorithm 1) for dynamic SFs placement based on our model and use successive approximations, i.e. $\epsilon $-iteration algorithm (Algorithm 2) to obtain action distribution. Finally, we evaluate the proposed MDP by comparing our optimal method with DDQP, DRL-QOR, MinPath and MinDelay for QoS optimization, including acceptance probability, average delay, resource utilization, load-balancing and reliability.

Abstract Linear discriminant analysis is a classical method for solving problems of dimensional reduction and pattern classification. Although it has been extensively developed, however, it still suffers from various common problems, such as the Small Sample Size (SSS) and the multimodal problem. Neighbourhood linear discriminant analysis (nLDA) was recently proposed to solve the problem of multimodal class caused by the contravention of independently and identically distributed samples. However, due to the existence of many small‐scale practical applications, nLDA still has to face the SSS problem, which leads to instability and poor generalisation caused by the singularity of the within‐neighbourhood scatter matrix. The authors exploit the eigenspectrum regularisation techniques to circumvent the singularity of the within‐neighbourhood scatter matrix of nLDA, which is called Eigenspectrum Regularisation Reverse Neighbourhood Discriminative Learning (ERRNDL). The algorithm of nLDA is reformulated as a framework by searching two projection matrices. Three eigenspectrum regularisation models are introduced to our framework to evaluate the performance. Experiments are conducted on the University of California, Irvine machine learning repository and six image classification datasets. The proposed ERRNDL‐based methods achieve considerable performance.

Multimodal image fusion plays an essential role in medical image analysis and application, where computed tomography (CT), magnetic resonance (MR), single-photon emission computed tomography (SPECT), and positron emission tomography (PET) are commonly-used modalities, especially for brain disease diagnoses. Most existing fusion methods do not consider the characteristics of medical images, and they adopt similar strategies and assessment standards to natural image fusion. While distinctive medical semantic information (MS-Info) is hidden in different modalities, the ultimate clinical assessment of the fusion results is ignored. Our MsgFusion first builds a relationship between the key MS-Info of the MR/CT/PET/SPECT images and image features to guide the CNN feature extractions using two branches and the design of the image fusion framework. For MR images, we combine the spatial domain feature and frequency domain feature (SF) to develop one branch. For PET/SPECT/CT images, we integrate the gray color space feature and adapt the HSV color space feature (GV) to develop another branch. A classification-based hierarchical fusion strategy is also proposed to reconstruct the fusion images to persist and enhance the salient MS-Info reflecting anatomical structure and functional metabolism. Fusion experiments are carried out on many pairs of MR-PET/SPECT and MR-CT images. According to seven classical objective quality assessments and one new subjective clinical quality assessment from 30 clinical doctors, the fusion results of the proposed MsgFusion are superior to those of the existing representative methods.

Tradeoffs between the spatial and temporal resolutions of current satellite instruments limit our ability to conduct high-quality and continuous monitoring of the earth’s surface dynamics. Spatiotemporal image fusion has become increasingly necessary to obtain remote sensing images with high spatiotemporal resolution. However, current learning-based methods concentrate on predicting images only from spatial similarity and neglect spectral correlations of remote sensing images, leading to significant spectral information loss. In this article, we develop a novel nonlocal tensor sparse representation-based semicoupled dictionary learning approach (SCDNTSR) for spatiotemporal fusion. In the SCDNTSR method, the spectral correlation and the spatial similarity of the nonlocal similar cubes are simultaneously exploited through the tensor–tensor product-based tensor sparse representation. Furthermore, the semicoupled mapping prior knowledge of sparse coefficients across the high- and low-spatial resolution (HSR\LSR) image spaces is exploited with the coupled dictionary to constrain the similarity of sparse coefficients to improve the prediction performance. In addition, to capture additional prior spatial information, the SCDNTSR provides a new method to determine the degradation relationship between the target HSR and LSR difference images with the help of the known HSR and LSR difference images. The proposed SCDNTSR method was tested on real datasets at both the Coleambally Irrigation Area study site and the Lower Gwydir Catchment study site. Results show that the proposed method outperforms five state-of-the-art methods, especially in maintaining the spectral information, proving the feasibility of integrating the degradation relationship, spatio-spectral-nonlocal correlation, and semicoupled mapping priors of the multisource data into the proposed model.

Medical image fusion technology integrates the contents of medical images of different modalities, thereby assisting users of medical images to better understand their meaning. However, the fusion of medical images corrupted by noise remains a challenge. To solve the existing problems in medical image fusion and denoising algorithms related to excessive blur, unclean denoising, gradient information loss, and color distortion, a novel medical image fusion and denoising algorithm is proposed. First, a new image layer decomposition model based on hybrid variation-sparse representation and weighted Schatten p-norm is proposed. The alternating direction method of multipliers is used to update the structure, detail layer dictionary, and detail layer coefficient map of the input image while denoising. Subsequently, appropriate fusion rules are employed for the structure layers and detail layer coefficient maps. Finally, the fused image is restored using the fused structure layer, detail layer dictionary, and detail layer coefficient maps. A large number of experiments confirm the superiority of the proposed algorithm over other algorithms. The proposed medical image fusion and denoising algorithm can effectively remove noise while retaining the gradient information without color distortion.

The recently developed multiscale-based fusion methods can be improved with two approaches: an advanced image decomposition scheme and an advanced fusion rule. In this paper, three-layer image decomposition, enhanced illumination fusion rule-based method is proposed. The proposed method includes three steps. First, each input image is decomposed into its corresponding smooth, texture, and edge layers using defined local extrema and low-pass filters in the spatial domain. Second, three different strategies are applied as fusion rules for the three-layer representation. To preserve the illumination closely related to tumors, the illumination is corrected by applying a higher contrast to the decomposed image details, including the texture and edge inputs, such as those found in grayscale CT and MRI images. The final fused image is created by the addition of the normalized smooth, texture, and edge image layers. The experiments demonstrate that the proposed method performs better than the existing state-of-the-art fusion methods.

A novel method for performing anatomical (MRI)-functional (PET or SPECT) image fusion is presented. The method merges specific feature information from input image signals of a single or multiple medical imaging modalities into a single fused image while preserving more information and generating less distortion. The proposed method uses a local Laplacian filtering based technique realized through a novel multi-scale system architecture. Firstly, the input images are generated in a multi-scale image representation and are processed using local Laplacian filtering. Secondly, at each scale, the decomposed images are combined to produce fused approximate images using a local energy maximum scheme and produce the fused residual images using an information of interest-based scheme. Finally, a fused image is obtained using a reconstruction process that is analogous to that of conventional Laplacian pyramid transform. Experimental results computed using individual multi-scale analysis-based decomposition schemes or fusion rules clearly demonstrate the superiority of the proposed method through subjective observation as well as objective metrics. Furthermore, the proposed method can obtain better performance, compared to the state-of-the-art fusion methods.

Abstract Rotation symmetric Boolean functions have been extensively studied in the recent years because of their applications in cryptography. In this study, a novel method to constructp‐variable 1‐resilient rotation symmetric functions overGF(p) is proposed based on a Latin square with maximum cycle structure, which is not required to solve any equation system. And a lower bound on the number ofp‐variable 1‐resilient rotation symmetric functions is given. At last, an equivalent characterization ofp‐variable 1‐resilient rotation symmetric functions overGF(p) is demonstrated, as a direct corollary, the number ofp‐variable 1‐resilient rotation symmetric functions is represented by all the solutions of the equation system. Copyright © 2017 John Wiley & Sons, Ltd.

In this study, the properties of the support tables of rotation symmetric Boolean functions (RSBFs for simplicity) are studied, and two sufficient and necessary conditions for RSBFs being 1‐ and 2‐resilient are obtained, respectively. Based on the relations between resilient functions and orthogonal arrays, with the help of the properties about the support tables of RSBFs, it is shown that the constructions of 1‐resilient RSBFs on given number of variables are equivalent to solving an equation system, and the number of functions is equal to the number of solutions of the equation system. Moreover, similar results are also obtained for 2‐resilient RSBFs. Lastly, a simple example is given to demonstrate our method. The results indicate that the constructions of n ‐variable 1‐resilient RSBFs are equivalent to studying the cyclotomic cosets C s modulo 2 n − 1 with respect to 2.