Search Results (748)

Creative insight is a core phenomenon of human cognition, often characterized by the sudden emergence of novel and contextually appropriate ideas. Classical models based on symbolic search or associative networks struggle to capture the non-linear, context-sensitive, and interference-driven aspects of insight. In this work, we propose a computational model of insight generation grounded in continuous-time quantum walks over weighted semantic graphs, where nodes represent conceptual units and edges encode associative relationships. By exploiting the principles of quantum superposition and interference, the model enables the probabilistic amplification of semantically distant but contextually relevant concepts, providing a plausible account of non-local transitions in thought. The model is implemented using standard Python 3.10 libraries and is available both as an interactive fully reproducible Google Colab notebook and a public repository with code and derived datasets. Comparative experiments on ConceptNet-derived subgraphs, including the Candle Problem, 20 Remote Associates Test triads, and Alternative Uses, show that, relative to classical diffusion, quantum walks concentrate more probability on correct targets (higher AUC and peaks reached earlier) and, in open-ended settings, explore more broadly and deeply (higher entropy and coverage, larger expected radius, and faster access to distant regions). These findings are robust under normalized generators and a common time normalization, align with our formal conditions for transient interference-driven amplification, and support quantum-like dynamics as a principled process model for key features of insight. Full article

Bayesian analysis is particularly useful for inferring models and their parameters given data. This is a common task in metabolic modeling, where models of varying complexity are used to interpret data. Nested sampling is a class of probabilistic inference algorithms that are particularly effective for estimating evidence and sampling the parameter posterior probability distributions. However, the practicality of nested sampling for metabolic network inference has yet to be studied. In this technical report, we explore the amalgamation of nested sampling, specifically diffusive nested sampling, with reversible jump Markov chain Monte Carlo. We apply the algorithm to two synthetic problems from the field of metabolic flux analysis. We present run times and share insights into hyperparameter choices, providing a useful point of reference for future applications of nested sampling to metabolic flux problems. Full article

A class of initial boundary value problems is here considered for a one-dimensional diffusion equation with a general time-fractional derivative with the Sonin kernel. One of the boundary conditions is in a general non-classical form, which includes no-nlocal cases of integral or multi-point boundary conditions. The problem is studied here by applying spectral projection operators to convert it to a system of relaxation equations in generalized eigenspaces. The uniqueness of the solution is established based on the uniqueness property of the spectral expansion. An algorithm is given for constructing the solution in the form of spectral expansion in terms of the generalized eigenfunctions. Estimates for the time-dependent components in this expansion are established and applied to prove the existence of a solution in the classical sense. The obtained results are applied to a particular case in which the specified boundary conditions lead to two sequences of eigenvalues, one of which consists of triple eigenvalues. Full article

We present a hybrid parallel scheme for efficiently solving Caputo time-fractional partial differential equations (CTFPDEs) with integer-order spatial derivatives on multicore CPU and GPU platforms. The approach combines a second-order spatial discretization with the $L1$ time-stepping scheme and employs MATLAB parfor parallelization to achieve significant reductions in runtime and memory usage. A theoretical third-order convergence rate is established under smooth-solution assumptions, and the analysis also accounts for the loss of accuracy near the initial time $t=t_0$ caused by weak singularities inherent in time-fractional models. Unlike many existing approaches that rely on locally convergent strategies, the proposed method ensures global convergence even for distant or randomly chosen initial guesses. Benchmark problems from fractional biological models—including glucose–insulin regulation, tumor growth under chemotherapy, and drug diffusion in tissue—are used to validate the robustness and reliability of the scheme. Numerical experiments confirm near-linear speedup on up to four CPU cores and show that the method outperforms conventional techniques in terms of convergence rate, residual error, iteration count, and efficiency. These results demonstrate the method’s suitability for large-scale CTFPDE simulations in scientific and engineering applications. Full article

This paper proposes a quantum algorithm, named Dicke state quantum search (DSQS), to set qubits in the Dicke state $|D_k^n⟩$ of D states in superposition to locate the target inputs or solutions of specific patterns among $2^n$ unstructured input instances, where n is the number of input qubits and $D=\left({\displaystyle \genfrac{}{}{0pt}{}{n}{k}}\right)=\mathrm{O}\left(n^k\right)$ for $min(k,n-k)\ll n/2$. Compared to Grover’s algorithm, a famous quantum search algorithm that calls an oracle and a diffuser O($\sqrt{2^n}$) times, DSQS requires no diffuser and calls an oracle only once. Furthermore, DSQS does not need to know the number of solutions in advance. We prove the correctness of DSQS with unitary transformations, and show that each solution can be found by DSQS with an error probability less than 1/3 through O($n^k$) repetitions, as long as $min(k,n-k)\ll n/2$. Additionally, this paper proposes a classical algorithm, named DSQS-VCP, to generate quantum circuits based on DSQS for solving the k-vertex cover problem (k-VCP), a well-known NP-complete (NPC) problem. Complexity analysis demonstrates that DSQS-VCP operates in polynomial time and that the quantum circuit generated by DSQS-VCP has a polynomial qubit count, gate count, and circuit depth as long as $min(k,n-k)\ll n/2$. We thus conclude that the k-VCP can be solved by the DSQS-VCP quantum circuit in polynomial time with an error probability less than 1/3 under the condition of $min(k,n-k)\ll n/2$. Since the k-VCP is NP-complete, NP and NPC problems can be polynomially reduced to the k-VCP. If the reduced k-VCP instance satisfies $min(k,n-k)\ll n/2$, then both the instance and the original NP/NPC problem instance to which it corresponds can be solved by the DSQS-VCP quantum circuit in polynomial time with an error probability less than 1/3. All statements of polynomial algorithm execution time in this paper apply only to VCP instances and similar instances of other problems, where $min(k,n-k)\ll n/2$. Thus, they imply neither NP ⊆ BQP nor P = NP. In this restricted regime of $min(k,n-k)\ll n/2$, the Dicke state subspace has a polynomial size of $D=\left({\displaystyle \genfrac{}{}{0pt}{}{n}{k}}\right)=\mathrm{O}\left(n^k\right)$, and our DSQS algorithm samples from it without asymptotic superiority over exhaustive enumeration. Nevertheless, DSQS may be combined with other quantum algorithms to better exploit the strengths of quantum computation in practice. Experimental results using IBM Qiskit packages show that the DSQS-VCP quantum circuit can solve the k-VCP successfully. Full article

Imaging through dynamic scattering media remains a fundamental challenge because of severe information loss and the ill-posed nature of the inversion problem. Conventional methods often struggle to strike a balance between reconstruction fidelity and efficiency in evolving environments. In this study, we present DynaFlowNet, a framework that leverages conditional flow matching theory to establish a continuous, invertible mapping from speckle patterns to target images via deterministic ordinary differential equation (ODE) integration. Central to this is the novel temporal–conditional residual attention block (TCResAttnBlock), which is designed to model spatiotemporal scattering dynamics. DynaFlowNet achieves real-time performance at 134.77 frames per second (FPS), which is 117 times faster than diffusion-based models, while maintaining state-of-the-art reconstruction quality (28.46 dB peak signal-to-noise ratio (PSNR), 0.9112 structural similarity index (SSIM), and 0.8832 Pearson correlation coefficient (PCC)). In addition, the proposed framework demonstrates exceptional geometric generalization, with only a 1.05 dB PSNR degradation across unseen geometries, significantly outperforming existing methods. This study establishes a new paradigm for real-time high-fidelity imaging using dynamic scattering media, with direct implications for biomedical imaging, remote sensing, and underwater exploration. Full article

This study presents the Fourier–Gegenbauer integral Galerkin (FGIG) method, a new numerical framework that uniquely integrates Fourier series and Gegenbauer polynomials to solve the one-dimensional advection–diffusion (AD) equation with spatially symmetric periodic boundary conditions, achieving exponential convergence and reduced computational cost compared to traditional methods. The FGIG method uniquely combines Fourier series for spatial periodicity and Gegenbauer polynomials for temporal integration within a Galerkin framework, resulting in highly accurate numerical and semi-analytical solutions. Unlike traditional approaches, this method eliminates the need for time-stepping procedures by reformulating the problem as a system of integral equations, reducing error accumulation over long-time simulations and improving computational efficiency. Key contributions include exponential convergence rates for smooth solutions, robustness under oscillatory conditions, and an inherently parallelizable structure, enabling scalable computation for large-scale problems. Additionally, the method introduces a barycentric formulation of the shifted Gegenbauer–Gauss (SGG) quadrature to ensure high accuracy and stability for relatively low Péclet numbers. This approach simplifies calculations of integrals, making the method faster and more reliable for diverse problems. Numerical experiments presented validate the method’s superior performance over traditional techniques, such as finite difference, finite element, and spline-based methods, achieving near-machine precision with significantly fewer mesh points. These results demonstrate its potential for extending to higher-dimensional problems and diverse applications in computational mathematics and engineering. The method’s fusion of spectral precision and integral reformulation marks a significant advancement in numerical PDE solvers, offering a scalable, high-fidelity alternative to conventional time-stepping techniques. Full article

The article presents a mathematical description of the thermal phenomena occurring both inside and on the surfaces of a homogeneous plate subjected to an external heat flux on one side. Analytical formulae for thermal excitation, with a given duration and constant power, are derived, enabling the determination of temperature increases on both the heated and unheated surfaces of the plate under specific heat transfer conditions to the surroundings. Convective heat transfer, with individual heat transfer coefficients on both sides of the slab, is considered; however, radiative heat loss can also be included. The solution of the problem obtained using two methods is presented: the method of separation of variables (MSV) and the Laplace transform (LT). The advantages and disadvantages of both analytical formulae, as well as the impact of various factors on the accuracy of the solution, are discussed. Among others, the MSV solution works well for a sufficiently long time, whereas the LT solution is better for a sufficiently short time. The theoretical considerations are illustrated with diagrams for several configurations, each representing various heat transfer conditions on both sides of the plate. The presented solution can serve as a starting point for further analysis of more complex geometries or multilayered structures, e.g., in non-destructive testing using active thermography. The developed theoretical model is verified for a determination of the thermal diffusivity of a reference material. The model can be useful for analyzing the method’s sensitivity to various factors occurring during the measurement process, or the method can be adapted to a pulse of known duration and constant power, which is much easier to implement technically than a very short impulse (Dirac) with high energy. Full article

Aiming at the core problem of high false and missed alarm rate and insufficient interference resistance of existing smoke and fire detection algorithms in complex scenes, this paper proposes a target detection network based on improved feature pyramid structure. By constructing a Context Guided Convolutional Block instead of the traditional convolutional operation, the detected target and the surrounding environment information are fused with secondary features while reconfiguring the feature dimensions, which effectively solves the problem of edge feature loss in the down-sampling process. The Poly Kernel Inception Block is designed, and a multi-branch parallel network structure is adopted to realize multi-scale feature extraction of the detected target, and the collaborative characterization of the flame profile and smoke diffusion pattern is realized. In order to further enhance the logical location sensing ability of the target, a Manhattan Attention Mechanism Unit is introduced to accurately capture the spatial and temporal correlation characteristics of the flame and smoke by establishing a pixel-level long-range dependency model. Experimental tests are conducted using a self-constructed high-quality smoke and fire image dataset, and the results show that, compared with the existing typical lightweight smoke and fire detection models, the present algorithm has a significant advantage in detection accuracy, and it can satisfy the demand for real-time detection. Full article

Modern network intrusion detection systems (NIDSs) rely on complex deep learning models. However, the “black-box” nature of deep learning methods hinders transparency and trust in predictions, preventing the timely implementation of countermeasures against intrusion attacks. Although explainable AI (XAI) methods provide a solution to this problem by providing insights into the reasons behind the predictions, the explanations provided by the majority of them cannot be trivially converted into actionable countermeasures. In this work, we propose a novel tabular diffusion-based counterfactual explanation framework that can provide actionable explanations for network intrusion attacks. We evaluated our proposed algorithm against several other publicly available counterfactual explanation algorithms on three modern network intrusion datasets. To the best of our knowledge, this work also presents the first comparative analysis of the existing counterfactual explanation algorithms within the context of NIDSs. Our proposed method provides plausible and diverse counterfactual explanations more efficiently than the tested counterfactual algorithms, reducing the time required to generate explanations. We also demonstrate how the proposed method can provide actionable explanations for NIDSs by summarizing them into a set of actionable global counterfactual rules, which effectively filter out incoming attack queries. This ability of the rules is crucial for efficient intrusion detection and defense mechanisms. We have made our implementation publicly available on GitHub. Full article

With the rapid development of big data and artificial intelligence, the problem of image privacy leakage has become increasingly prominent, especially for images containing sensitive information such as faces, which poses a higher security risk. In order to improve the security and efficiency of image privacy protection, this paper proposes an image encryption scheme that integrates face detection and multi-level encryption technology. Specifically, a multi-task convolutional neural network (MTCNN) is used to accurately extract the face area to ensure accurate positioning and high processing efficiency. For the extracted face area, a hierarchical encryption framework is constructed using chaotic systems, lightweight block permutations, RNA cryptographic systems, and bit diffusion, which increases data complexity and unpredictability. In addition, a key update mechanism based on dynamic feedback is introduced to enable the key to change in real time during the encryption process, effectively resisting known plaintext and chosen plaintext attacks. Experimental results show that the scheme performs well in terms of encryption security, robustness, computational efficiency, and image reconstruction quality. This study provides a practical and effective solution for the secure storage and transmission of sensitive face images, and provides valuable support for image privacy protection in intelligent systems. Full article

This paper introduces an efficient numerical method based on applying the typical Petrov–Galerkin approach ($\mathrm{PGA}$) to solve the time fractional diffusion wave equation ($\mathcal{TFDWE}$). The method utilises asymmetric polynomials, namely, shifted second-kind Chebyshev polynomials ($\mathrm{SSKCPs}$). New derivative formulas are derived and used for these polynomials to establish the operational matrices of their derivatives. The paper presents rigorous error bounds for the proposed method in Chebyshev-weighted Sobolev space and demonstrates its accuracy and efficiency through several illustrative numerical examples. The results reveal that the method achieves high accuracy with relatively low polynomial degrees. Full article

The efficiency of various numerical methods for solving Huxley’s equation—which includes a diffusion term and a nonlinear reaction term—is investigated. Conventional explicit finite difference algorithms often suffer from severe stability limitations and can yield unphysical concentration values. In this study, we collect a range of stable, explicit time integration methods of first to fourth order, originally developed for the diffusion equation, and design treatments of the nonlinear term which ensure that the solution remains within the physically meaningful unit interval. This property, called dynamical consistency, is analytically proven and implies unconditional stability. In addition to this, the most effective ones are identified from the large number of constructed method combinations. We conduct systematic tests in one and two spatial dimensions, also evaluating computational efficiency in terms of CPU time. Our results show that higher-order schemes are not always the most efficient: in certain parameter regimes, second-order methods can outperform their higher-order counterparts. Full article

This paper introduces a lightweight cryptographic hash algorithm, LWH-128, developed using a sponge-based construction and specifically adapted for operation under constrained computational and energy conditions typical of embedded systems and Internet of Things devices. The algorithm employs a two-layer processing structure based on simple logical operations (XOR, cyclic shifts, and S-boxes) and incorporates a preliminary diffusion transformation function G, along with the Davis–Meyer compression scheme, to enhance irreversibility and improve cryptographic robustness. A comparative analysis of hardware implementation demonstrates that LWH-128 exhibits balanced characteristics in terms of circuit complexity, memory usage, and processing speed, making it competitive with existing lightweight hash algorithms. As part of the cryptanalytic evaluation, a Boolean SATisfiability (SAT) Problem-based model of the compression function is constructed in the form of a conjunctive normal form of Boolean variables. Experimental results using the Parkissat SAT solver show an exponential increase in computational time as the number of unknown input bits increased. These findings support the conclusion that the LWH-128 algorithm exhibits strong resistance to preimage attacks based on SAT-solving techniques. Full article

Background: Bulk RNA-seq is a cost-effective method for measuring average gene expression in tissue samples, but its lack of single-cell resolution limits the understanding of cellular heterogeneity. Computational deconvolution aims to infer cell-type proportions from bulk RNA-seq data; however, the accuracy of existing methods needs improvement, especially in complex tissues. Methods: In this study, we introduce DiffFormer, a novel deconvolution model that, for the first time, integrates a conditional diffusion model with a Transformer architecture. We systematically evaluated DiffFormer on four pseudo-bulk datasets and validated it on a gold-standard real-world dataset with FACS-based ground truth. Results: DiffFormer demonstrated consistent and strong performance across all test datasets, outperforming existing methods and a baseline MLP-based diffusion model (DiffMLP). For instance, on the pbmc3k dataset, DiffFormer reduced the Root Mean Square Error (RMSE) from 0.1060 to 0.0120 compared to DiffMLP. This advantage was further confirmed on the real-world dataset, where DiffFormer achieved the highest Pearson Correlation Coefficient (PCC). Conclusions: This work provides a high-precision, reproducible tool for cellular deconvolution. Crucially, the direct comparison with an MLP-based diffusion model provides definitive evidence that the Transformer architecture is key to its success, highlighting the potential of such models for solving complex bioinformatics problems. Full article