Search Results (23)

This paper proposes a novel fractional-order asset flow model based on the Atangana–Baleanu–Caputo (ABC) derivative to analyze asset price dynamics in financial markets. Compared to classical models, the proposed model incorporates a nonlocal and non-singular fractional operator, allowing for a more accurate representation of investor behavior and market adjustment processes. The model captures both short-term trend-driven responses and long-term valuation-based decisions. We establish key theoretical properties of the system, including the existence and uniqueness of solutions, positivity, boundedness, and both local and global stability using Lyapunov functions. Numerical simulations under varying fractional orders demonstrate how the ABC derivative governs the convergence speed and equilibrium behavior of the system. Compared to classical integer-order models, the ABC-based approach provides smoother dynamics, greater flexibility in modeling behavioral heterogeneity, and better alignment with observed long-term financial phenomena. Full article

Neural networks, mimicking the structural and functional aspects of the human brain, have found widespread applications in diverse fields such as pattern recognition, control systems, and information processing. A critical phenomenon in these systems is synchronization, where multiple neurons or neural networks harmonize their dynamic behaviors to a common rhythm, contributing significantly to their efficient operation. However, the inherent complexity and nonlinearity of neural networks pose significant challenges in understanding and controlling this synchronization process. In this paper, we focus on the synchronization of a class of fractional-order, delayed, and non-autonomous neural networks. Fractional-order dynamics, characterized by their ability to capture memory effects and non-local interactions, introduce additional layers of complexity to the synchronization problem. Time delays, which are ubiquitous in real-world systems, further complicate the analysis by introducing temporal asynchrony among the neurons. To address these challenges, we propose a straightforward yet powerful global synchronization framework. Our approach leverages novel state feedback control to derive an analytical formula for the synchronization controller. This controller is designed to adjust the states of the neural networks in such a way that they converge to a common trajectory, achieving synchronization. To establish the asymptotic stability of the error system, which measures the deviation between the states of the neural networks, we construct a Lyapunov function. This function provides a scalar measure of the system’s energy, and by showing that this measure decreases over time, we demonstrate the stability of the synchronized state. Our analysis yields sufficient conditions that guarantee global synchronization in fractional-order neural networks with time delays and Caputo derivatives. These conditions provide a clear roadmap for designing neural networks that exhibit robust and stable synchronization properties. To validate our theoretical findings, we present numerical simulations that demonstrate the effectiveness of our proposed approach. The simulations show that, under the derived conditions, the neural networks successfully synchronize, confirming the practical applicability of our framework. Full article

In recent years, numerous advanced lightweight models have been proposed for salient object detection (SOD) in optical remote sensing images (ORSI). However, most methods still face challenges such as performance limitations and imbalances between accuracy and computational cost. To address these issues, we propose SggNet, a novel semantic- and graph-guided lightweight network for ORSI-SOD. The SggNet adopts a classical encoder-decoder structure with MobileNet-V2 as the backbone, ensuring optimal parameter utilization. Furthermore, we design an Efficient Global Perception Module (EGPM) to capture global feature relationships and semantic cues through limited computational costs, enhancing the model’s ability to perceive salient objects in complex scenarios, and a Semantic-Guided Edge Awareness Module (SEAM) that leverages the semantic consistency of deep features to suppress background noise in shallow features, accurately predict object boundaries, and preserve the detailed shapes of salient objects. To further efficiently aggregate multi-level features and preserve the integrity and complexity of overall object shape, we introduce a Graph-Based Region Awareness Module (GRAM). This module incorporates non-local operations under graph convolution domain to deeply explore high-order relationships between adjacent layers, while utilizing depth-wise separable convolution blocks to significantly reduce computational cost. Extensive quantitative and qualitative experiments demonstrate that the proposed model achieves excellent performance with only 2.70 M parameters and 1.38 G FLOPs, while delivering an impressive inference speed of 108 FPS, striking a balance between efficiency and accuracy to meet practical application needs. Full article

Image super-resolution (SR) algorithms based on deep learning yield good visual performances on visible images. Due to the blurred edges and low contrast of infrared (IR) images, methods transferred directly from visible images to IR images have a poor performance and ignore the demands of downstream detection tasks. Therefore, an Inception Dilated Super-Resolution (IDSR) network with multiple branches is proposed. A dilated convolutional branch captures high-frequency information to reconstruct edge details, while a non-local operation branch captures long-range dependencies between any two positions to maintain the global structure. Furthermore, deformable convolution is utilized to fuse features extracted from different branches, enabling adaptation to targets of various shapes. To enhance the detection performance of low-resolution (LR) images, we crop the images into patches based on target labels before feeding them to the network. This allows the network to focus on learning the reconstruction of the target areas only, reducing the interference of background areas in the target areas’ reconstruction. Additionally, a feature-driven module is cascaded at the end of the IDSR network to guide the high-resolution (HR) image reconstruction with feature prior information from a detection backbone. This method has been tested on the FLIR Thermal Dataset and the M3FD Dataset and compared with five mainstream SR algorithms. The final results demonstrate that our method effectively maintains image texture details. More importantly, our method achieves 80.55% mAP, outperforming other methods on FLIR Dataset detection accuracy, and with 74.7% mAP outperforms other methods on M3FD Dataset detection accuracy. Full article

Infrared detection, known for its robust anti-interference capabilities, performs well in all weather conditions and various environments. Its applications include precision guidance, surveillance, and early warning systems. However, detecting infrared dim and small targets presents challenges, such as weak target features, blurred targets with small area percentages, missed detections, and false alarms. To address the issue of insufficient target feature information, this paper proposes a high-precision method for detecting dim and small infrared targets based on the YOLOv7 network model, which integrates both local and non-local bidirectional features. Additionally, a local feature extraction branch is introduced to enhance target information by applying local magnification at the feature extraction layer allowing for the capture of more detailed features. To address the challenge of target and background blending, we propose a strategy involving multi-scale fusion of the local branch and global feature extraction. Additionally, the use of a 1 × 1 convolution structure and concat operation reduces model computation. Compared to the baseline, our method shows a 2.9% improvement in mAP₅₀ on a real infrared dataset, with the detection rate reaching 93.84%. These experimental results underscore the effectiveness of our method in extracting relevant features while suppressing background interference in infrared dim and small target detection (IDSTD), making it more robust. Full article

Fractional differential operators are inherently non-local, so global methods, such as spectral methods, are well suited for handling these non-local operators. Long-time integration of differential models such as chaotic dynamical systems poses specific challenges and considerations that make multi-domain numerical methods advantageous when dealing with such problems. This study proposes a novel multi-domain pseudospectral method based on the first kind of Chebyshev polynomials and the Gauss–Lobatto quadrature for fractional initial value problems.The proposed technique involves partitioning the problem’s domain into non-overlapping sub-domains, calculating the fractional differential operator in each sub-domain as the sum of the ‘local’ and ‘memory’ parts and deriving the corresponding differentiation matrices to develop the numerical schemes. The linear stability analysis indicates that the numerical scheme is absolutely stable for certain values of arbitrary non-integer order and conditionally stable for others. Numerical examples, ranging from single linear equations to systems of non-linear equations, demonstrate that the multi-domain approach is more appropriate, efficient and accurate than the single-domain scheme, particularly for problems with long-term dynamics. Full article

In the case of one spatial independent variable, we study hyperbolic differential-difference equations with potentials represented as linear combinations of translations of the desired function along the spatial variable. The qualitative novelty of this investigation is that, unlike previous research, it is not assumed that the real part of the symbol of the differential-difference operator contained in the equation has a constant sign. Previously, it was possible to remove that substantial restriction (i.e., the specified sign constancy) only for the case where the nonlocal term (i.e., the translated potential) is unique. In the present paper, we consider the case of the general-kind one-variable nonlocal potential, i.e., equations with an arbitrary amount of translated terms. No commensurability assumptions are imposed on the translation lengths. The following results are presented: We find a condition relating the coefficients at the nonlocal terms of the investigated equation and the length of the translations, providing the global solvability of the investigated equation. Under this condition, we explicitly construct a three-parametric family of smooth global solutions of the investigated equation. Full article

We study hyperbolic equations with positive coefficients at potentials undergoing translations with respect to the spatial independent variable. The qualitative novelty of the investigation is that the real part of the symbol of the differential-difference operator contained in the equation is allowed to change its sign. Earlier, only the case where the said sign is constant was investigated. We find a condition relating the coefficient at the nonlocal term of the investigated equation and the length of the translation, guaranteeing the global solvability of the investigated equation. Under this condition, we explicitly construct a three-parametric family of smooth global solutions of the investigated equation. Full article

We suggest a new formulation of the inverse spectral problem for second-order functional-differential operators on star-shaped graphs with global delay. The latter means that the delay, which is measured in the direction of a specific boundary vertex, called the root, propagates through the internal vertex to other edges. Now, we intend to recover the potentials from the spectra of two boundary value problems on the graph with a common set of boundary conditions at all boundary vertices except the root. For simplicity, we focus on star graphs with equal edges when the delay parameter is not less than their length. Under the assumption that the common boundary conditions are of the Robin type and they are known and pairwise linearly independent, the uniqueness theorem is proven and a constructive procedure for solving the proposed inverse problem is obtained. Full article

Quantum information applications emerged decades ago, initially introducing a parallel development that mimicked the approach and development of classical computer science. However, in the current decade, novel computer-science concepts were rapidly extended to the fields of quantum processing, computation, and communication. Thus, areas such as artificial intelligence, machine learning, and neural networks have their quantum versions; furthermore, the quantum brain properties of learning, analyzing, and gaining knowledge are discussed. Quantum properties of matter conglomerates have been superficially explored in such terrain; however, the settlement of organized quantum systems able to perform processing can open a new pathway in the aforementioned domains. In fact, quantum processing involves certain requisites as the settlement of copies of input information to perform differentiated processing developed far away or in situ to diversify the information stored there. Both tasks at the end provide a database of outcomes with which to perform either information matching or final global processing with at least a subset of those outcomes. When the number of processing operations and input information copies is large, parallel processing (a natural feature in quantum computation due to the superposition) becomes the most convenient approach to accelerate the database settlement of outcomes, thus affording a time advantage. In the current study, we explored certain quantum features to realize a speed-up model for the entire task of processing based on a common information input to be processed, diversified, and finally summarized to gain knowledge, either in pattern matching or global information availability. By using superposition and non-local properties, the most valuable features of quantum systems, we realized parallel local processing to set a large database of outcomes and subsequently used post-selection to perform an ending global processing or a matching of information incoming from outside. We finally analyzed the details of the entire procedure, including its affordability and performance. The quantum circuit implementation, along with tentative applications, were also discussed. Such a model could be operated between large processing technological systems using communication procedures and also on a moderately controlled quantum matter conglomerate. Certain interesting technical aspects involving the non-local control of processing via entanglement were also analyzed in detail as an associated but notable premise. Full article

This note studies the linearly damped generalized Hartree equation $i\dot{u}-{(-\mathsf{\Delta })}^{s}u+iau=\pm {\left|u\right|}^{p-2}(J_{\gamma }{\ast \left|u\right|}^p)u,0<s<1,a>0,p\ge 2.$ Indeed, one proves an exponential scattering of the energy global solutions, with spherically symmetric datum. This means that, for large time, the solution goes exponentially to the solution of the associated free problem $i\dot{u}-{(-\mathsf{\Delta })}^{s}u+iau=0$, in $H^s$ norm. The radial assumption avoids a loss of regularity in Strichartz estimates. The exponential scattering, which means that $v:=e^{at}u$ scatters in $H^s$, is proved in the energy sub-critical defocusing regime and in the mass-sub-critical focusing regime. This result is presented because of the gap due to the lack of scattering in the mass sub-critical regime, which seems not to be well understood. In this manuscript, one needs to overcome three technical difficulties which are mixed together: the first one is a fractional Laplace operator, the second one is a Choquard (non-local) source term, including the Hartree-type term when $p=2$ and the last one is a damping term $iau$. In a work in progress, the authors investigate the exponential scattering of global solutions to the above Schrödinger problem, with different kind of damping terms. Full article

Considered herein is the initial-boundary value problem for a semilinear parabolic equation with a memory term and non-local source $w_t-{\mathrm{\Delta }}_{\mathbb{B}}w-{\mathrm{\Delta }}_{\mathbb{B}}{w}_t+{\int }_0^{t}g(t-\tau ){\mathrm{\Delta }}_{\mathbb{B}}w\left(\tau \right)d\tau ={|w|}^{p-1}w-\frac{1}{|\mathbb{B}|}{\int }_{\mathbb{B}}{|w|}^{p-1}w\frac{d{x}_1}{x_1}d{x}^{\prime }$ on a manifold with conical singularity, where the Fuchsian type Laplace operator ${\mathrm{\Delta }}_{\mathbb{B}}$ is an asymmetry elliptic operator with conical degeneration on the boundary $x_1=0$. Firstly, we discuss the symmetrical structure of invariant sets with the help of potential well theory. Then, the problem can be decomposed into two symmetric cases: if $w_0\in W$ and $\mathrm{\Pi }\left(w_0\right)>0$, the global existence for the weak solutions will be discussed by a series of energy estimates under some appropriate assumptions on the relaxation function, initial data and the symmetric structure of invariant sets. On the contrary, if $w_0\in V$ and $\mathrm{\Pi }\left(w_0\right)<0$, the nonexistence of global solutions, i.e., the solutions blow up in finite time, is obtained by using the convexity technique. Full article

Obtaining high-spatial–high-temporal (HTHS) resolution remote sensing images from a single sensor remains a great challenge due to the cost and technical limitations. Spatiotemporal fusion (STF) technology breaks through the technical limitations of existing sensors and provides a convenient and economical solution for obtaining HTHS resolution images. At present, most STF methods use stacked convolutional layers to extract image features and then obtain fusion images by using a summation strategy. However, these convolution operations may lead to the loss of feature information, and the summation strategy results in poorly fused images due to a lack of consideration of global spatial feature information. To address these issues, this article proposes a STF network architecture based on multiscale and attention mechanisms (MANet). The multiscale mechanism module composed of dilated convolutions is used to extract the detailed features of low-spatial resolution remote sensing images at multiple scales. The channel attention mechanism adaptively adjusts the weights of the feature map channels to retain more temporal and spatial information in the upsampling process, while the non-local attention mechanism adjusts the initial fusion images to obtain more accurate predicted images by calculating the correlation between pixels. We use two datasets with different characteristics to conduct the experiments, and the results prove that the proposed MANet method with fewer parameters obtains better fusion results than the existing machine learning-based and deep learning-based fusion methods. Full article

We examine a viscous Cahn–Hilliard phase-separation model with memory and where the chemical potential possesses a nonlocal fractional Laplacian operator. The existence of global weak solutions is proven using a Galerkin approximation scheme. A continuous dependence estimate provides uniqueness of the weak solutions and also serves to define a precompact pseudometric. This, in addition to the existence of a bounded absorbing set, shows that the associated semigroup of solution operators admits a compact connected global attractor in the weak energy phase space. The minimal assumptions on the nonlinear potential allow for arbitrary polynomial growth. Full article

Point clouds are widely used as representations of 3D objects and scenes in a number of applications, including virtual and mixed reality, autonomous driving, antiques reconstruction. To reduce the cost for transmitting and storing such data, this paper proposes an end-to-end learning-based point cloud attribute compression (PCAC) approach. The proposed network adopts a sparse convolution-based variational autoencoder (VAE) structure to compress the color attribute of point clouds. Considering the difficulty of stacked convolution operations in capturing long range dependencies, the attention mechanism is incorporated in which a non-local attention module is developed to capture the local and global correlations in both spatial and channel dimensions. Towards the practical application, an additional modulation network is offered to achieve the variable rate compression purpose in a single network, avoiding the memory cost of storing multiple networks for multiple bitrates. Our proposed method achieves state-of-the-art compression performance compared to other existing learning-based methods and further reduces the gap with the latest MPEG G-PCC reference software TMC13 version 14. Full article