Search Results (72)

Blasting-induced seismic waves are typically nonlinear and non-stationary signals. The EMD-Hilbert transform is commonly used for time–frequency analysis of such signals. However, during the empirical mode decomposition (EMD) processing of blasting-induced seismic waves, endpoint effects occur, resulting in varying degrees of divergence in the obtained intrinsic mode function (IMF) components at both ends. The further application of the Hilbert transform to these endpoint-divergent IMFs yield artificial time–frequency analysis results, adversely impacting the assessment of blasting-induced seismic wave hazards. This paper proposes an improved EMD endpoint effect suppression algorithm that considers local endpoint development trends, global time distribution, energy matching, and waveform matching. The method first analyzes global temporal characteristics and endpoint amplitude variations to obtain left and right endpoint extension signal fragment S(t)_L and S(t)_R. Using these as references, the original signal is divided into “b” equal segments S(t)₁, S(t)₂ … S(t)_b. Energy matching and waveform matching functions are then established to identify signal fragments S(t)_i and S(t)_j that match both the energy and waveform characteristics of S(t)_L and S(t)_R. Replacing S(t)_L and S(t)_R with S(t)_i and S(t)_j effectively suppresses the EMD endpoint effects. To verify the algorithm’s effectiveness in suppressing EMD endpoint effects, comparative studies were conducted using simulated signals to compare the proposed method with mirror extension, polynomial fitting, and extreme value extension methods. Three evaluation metrics were utilized: error standard deviation, correlation coefficient, and computation time. The results demonstrate that the proposed algorithm effectively reduces the divergence at the endpoints of the IMFs and yields physically meaningful IMF components. Finally, the method was applied to the analysis of actual blasting seismic signals. It successfully suppressed the endpoint effects of EMD and improved the extraction of time–frequency characteristics from blasting-induced seismic waves. This has significant practical implications for safety assessments of existing structures in areas affected by blasting. Full article

Graph autoencoders’ inherent capability to capture node feature correlations poses significant privacy risks through attackers inference. Previous feature decoupling approaches predominantly apply uniform privacy protection across nodes, disregarding the varying sensitivity levels inherent in graph structures. To solve the above problems, we propose a novel dual-path graph autoencoder incorporating attention-aware privacy adaptation. Firstly, we design an attention-driven metric learning framework to quantify node-specific privacy importance through attention weights and select important nodes to construct the privacy distribution, so that realizing the dynamically privacy decoupling and reducing utility loss. Then, we introduce Hilbert-Schmidt Independence Criterion (HSIC) to measure the dependence between privacy and non-privacy information, which avoids the deviations that occur when using approximate methods such as variational inference. Finally, we use the method of alternating training to comprehensively evaluate the privacy importance of nodes. Experimental results on three real-world datasets—Yale, Rochester, and Credit Defaulter—demonstrate that our proposed method significantly outperforms existing approaches like PVGAE, GAE-MI, and APGE, where the inference accuracy regarding privacy decreased by 25.5%, but the accuracy rate of link prediction achieved the highest 84.7% compared to other methods. Full article

Wave Energy Converters (WECs) rely on effective Power Take-Off (PTO) control strategies to maximize energy absorption under dynamic sea conditions. Traditional hydrodynamic modeling techniques may require computationally intensive convolution calculations, making real-time control implementation challenging. This paper presents an alternative approach by leveraging instantaneous frequency estimation to dynamically adjust PTO damping in response to varying wave frequencies. Two real-time frequency estimation methods are explored: the Hilbert Transform (HT) and Phase-Locked Loop (PLL). The Hilbert Transform method provides accurate frequency tracking but introduces a delayed response due to its dependence on causal data. Conversely, the PLL approach demonstrates strong potential in frequency tracking but requires careful gain tuning, particularly in complex sea states. Comparative evaluations across multiple test cases—including sinusoidal variations, amplitude steps, frequency step changes, and real-world JONSWAP spectrum waves—highlight the strengths and limitations of each method. The two different PTO control techniques across the various frequency estimation methods were tested under real-sea states using a state-space model of a point-absorbing Wave Energy Converter. The Capture Width Ratio (CWR) is used as a performance metric, with results showing that the HT achieves a 10.6% improvement, while the PLL estimation yields a 0.9% improvement relative to the fixed parameter control baseline. These results highlight the effectiveness of real-time frequency estimation in improving energy absorption compared to static control parameters. Full article

Latent variables play a crucial role in psychometric research, yet traditional models often struggle to address context-dependent effects, ambivalent states, and non-commutative measurement processes. This study proposes a quantum-inspired framework for latent variable modeling that employs Hilbert space representations, allowing questionnaire items to be treated as pure or mixed quantum states. By integrating concepts such as superposition, interference, and non-commutative probabilities, the framework captures cognitive and behavioral phenomena that extend beyond the capabilities of classical methods. To illustrate its potential, we introduce quantum-specific metrics—fidelity, overlap, and von Neumann entropy—as complements to correlation-based measures. We also outline a machine-learning pipeline using complex and real-valued neural networks to handle amplitude and phase information. Results highlight the capacity of quantum-inspired models to reveal order effects, ambivalent responses, and multimodal distributions that remain elusive in standard psychometric approaches. This framework broadens the multivariate analysis theoretical and methodological toolkit, offering a dynamic and context-sensitive perspective on latent constructs while inviting further empirical validation in diverse research settings. Full article

Quantum-inspired algorithms represent an important direction in modern software information technologies that use heuristic methods and approaches of quantum science. This work presents a quantum approach for document search, retrieval, and ranking based on the Bell-like test, which is well-known in quantum physics. We propose quantum probability theory in the hyperspace analog to language (HAL) framework exploiting a Hilbert space for word and document vector specification. The quantum approach allows for accounting for specific user preferences in different contexts. To verify the algorithm proposed, we use a dataset of synthetic advertising text documents from travel agencies generated by the OpenAI GPT-4 model. We show that the “entanglement” in two-word document search and retrieval can be recognized as the frequent occurrence of two words in incompatible query contexts. We have found that the user preferences and word ordering in the query play a significant role in relatively small sizes of the HAL window. The comparison with the cosine similarity metrics demonstrates the key advantages of our approach based on the user-enforced contextual and semantic relationships between words and not just their superficial occurrence in texts. Our approach to retrieving and ranking documents allows for the creation of new information search engines that require no resource-intensive deep machine learning algorithms. Full article

Semantic segmentation-based Complex Waterway Scene Understanding has shown great promise in the environmental perception of Unmanned Surface Vehicles. Existing methods struggle with estimating the edges of obstacles under conditions of blurred water surfaces. To address this, we propose the Lightweight Dual-branch Mamba Network (LDMNet), which includes a CNN-based Deep Dual-branch Network for extracting image features and a Mamba-based fusion module for aggregating and integrating global information. Specifically, we improve the Deep Dual-branch Network structure by incorporating multiple Atrous branches for local fusion; we design a Convolution-based Recombine Attention Module, which serves as the gate activation condition for Mamba-2 to enhance feature interaction and global information fusion from both spatial and channel dimensions. Moreover, to tackle the directional sensitivity of image serialization and the impact of the State Space Model’s forgetting strategy on non-causal data modeling, we introduce a Hilbert curve scanning mechanism to achieve multi-scale feature serialization. By stacking feature sequences, we alleviate the local bias of Mamba-2 towards image sequence data. LDMNet integrates the Deep Dual-branch Network, Recombine Attention, and Mamba-2 blocks, effectively capturing the long-range dependencies and multi-scale global context information of Complex Waterway Scene images. The experimental results on four benchmarks show that the proposed LDMNet significantly improves obstacle edge segmentation performance and outperforms existing methods across various performance metrics. Full article

The detection of limit cycles of differential equations poses a challenge due to the type of the nonlinear system, the regime of interest, and the broader context of applicable models. Consequently, attempts to solve Hilbert’s sixteenth problem on the maximum number of limit cycles of polynomial differential equations have been uniformly unsuccessful due to failing results and their lack of consistency. Here, the answer to this problem is finally obtained through information geometry, in which the Riemannian metrical structure of the parameter space of differential equations is investigated with the aid of the Fisher information metric and its scalar curvature R. We find that the total number of divergences of $\left|\mathrm{R}\right|$ to infinity provides the maximum number of limit cycles of differential equations. Additionally, we demonstrate that real polynomial systems of degree $n\ge 2$ have the maximum number of $2(n-1)\left(4\right(n-1)-2)$ limit cycles. The research findings highlight the effectiveness of geometric methods in analyzing complex systems and offer valuable insights across information theory, applied mathematics, and nonlinear dynamics. These insights may pave the way for advancements in differential equations, presenting exciting opportunities for future developments. Full article

In this paper, a large class of contractions is studied that contains Banach and Matkowski maps as particular cases. Sufficient conditions for the existence of fixed points are proposed in the framework of b-metric spaces. The convergence and stability of the Picard iterations are analyzed, giving error estimates for the fixed-point approximation. Afterwards, the iteration proposed by Kirk in 1971 is considered, studying its convergence, stability, and error estimates in the context of a quasi-normed space. The properties proved can be applied to other types of contractions, since the self-maps defined contain many others as particular cases. For instance, if the underlying set is a metric space, the contractions of type Kannan, Chatterjea, Zamfirescu, Ćirić, and Reich are included in the class of contractivities studied in this paper. These findings are applied to the construction of fractal surfaces on Banach algebras, and the definition of two-variable frames composed of fractal mappings with values in abstract Hilbert spaces. Full article

Picard iteration is on the basis of a great number of numerical methods and applications of mathematics. However, it has been known since the 1950s that this method of fixed-point approximation may not converge in the case of nonexpansive mappings. In this paper, an extension of the concept of nonexpansiveness is presented in the first place. Unlike the classical case, the new maps may be discontinuous, adding an element of generality to the model. Some properties of the set of fixed points of the new maps are studied. Afterwards, two iterative methods of fixed-point approximation are analyzed, in the frameworks of b-metric and Hilbert spaces. In the latter case, it is proved that the symmetrically averaged iterative procedures perform well in the sense of convergence with the least number of operations at each step. As an application, the second part of the article is devoted to the study of fractal mappings on Hilbert spaces defined by means of nonexpansive operators. The paper considers fractal mappings coming from $\phi$-contractions as well. In particular, the new operators are useful for the definition of an extension of the concept of $\alpha$-fractal function, enlarging its scope to more abstract spaces and procedures. The fractal maps studied here have quasi-symmetry, in the sense that their graphs are composed of transformed copies of itself. Full article

The common geometrical (symplectic) structures of classical mechanics, quantum mechanics, and classical thermodynamics are unveiled with three pictures. These cardinal theories, mainly at the non-relativistic approximation, are the cornerstones for studying chemical dynamics and chemical kinetics. Working in extended phase spaces, we show that the physical states of integrable dynamical systems are depicted by Lagrangian submanifolds embedded in phase space. Observable quantities are calculated by properly transforming the extended phase space onto a reduced space, and trajectories are integrated by solving Hamilton’s equations of motion. After defining a Riemannian metric, we can also estimate the length between two states. Local constants of motion are investigated by integrating Jacobi fields and solving the variational linear equations. Diagonalizing the symplectic fundamental matrix, eigenvalues equal to one reveal the number of constants of motion. For conservative systems, geometrical quantum mechanics has proved that solving the Schrödinger equation in extended Hilbert space, which incorporates the quantum phase, is equivalent to solving Hamilton’s equations in the projective Hilbert space. In classical thermodynamics, we take entropy and energy as canonical variables to construct the extended phase space and to represent the Lagrangian submanifold. Hamilton’s and variational equations are written and solved in the same fashion as in classical mechanics. Solvers based on high-order finite differences for numerically solving Hamilton’s, variational, and Schrödinger equations are described. Employing the Hénon–Heiles two-dimensional nonlinear model, representative results for time-dependent, quantum, and dissipative macroscopic systems are shown to illustrate concepts and methods. High-order finite-difference algorithms, despite their accuracy in low-dimensional systems, require substantial computer resources when they are applied to systems with many degrees of freedom, such as polyatomic molecules. We discuss recent research progress in employing Hamiltonian neural networks for solving Hamilton’s equations. It turns out that Hamiltonian geometry, shared with all physical theories, yields the necessary and sufficient conditions for the mutual assistance of humans and machines in deep-learning processes. Full article

We evaluate here the quantum gravity partition function that counts the dimension of the Hilbert space of a simply connected spatial region of a fixed proper volume in the context of Lovelock gravity, generalizing the results for Einstein gravity. It is found that there are sphere saddle metrics for a partition function at a fixed spatial volume in Lovelock theory. Those stationary points take exactly the same forms as in Einstein gravity. The logarithm of Z corresponding to a zero effective cosmological constant indicates that the Bekenstein–Hawking entropy of the boundary area and that corresponding to a positive effective cosmological constant points to the Wald entropy of the boundary area. We also show the existence of zeroth-order phase transitions between different vacua, a phenomenon distinct from Einstein gravity. Full article

A unitary-evolution process leading to an ultimate collapse and to a complete loss of observability alias quantum phase transition is studied. A specific solvable $N\mathrm{-}$state model is considered, characterized by a non-stationary non-Hermitian Hamiltonian. Our analysis uses quantum mechanics formulated in Schrödinger picture in which, in principle, only the knowledge of a complete set of observables (i.e., operators ${\mathrm{\Lambda }}_j$) enables one to guarantee the uniqueness of the related physical Hilbert space (i.e., of its inner-product metric $\mathrm{\Theta }$). Nevertheless, for the sake of simplicity, we only assume the knowledge of just a single input observable (viz., of the energy-representing Hamiltonian $H\equiv {\mathrm{\Lambda }}_1$). Then, out of all of the eligible and Hamiltonian-dependent “Hermitizing” inner-product metrics $\mathrm{\Theta }=\mathrm{\Theta }\left(H\right)$, we pick up just the simplest possible candidate. Naturally, this slightly restricts the scope of the theory, but in our present model, such a restriction is more than compensated for by the possibility of an alternative, phenomenologically better motivated constraint by which the time-dependence of the metric is required to be smooth. This opens a new model-building freedom which, in fact, enables us to force the system to reach the collapse, i.e., a genuine quantum catastrophe as a result of the mere conventional, strictly unitary evolution. Full article

The role of transformers in power distribution is crucial, as their reliable operation is essential for maintaining the electrical grid’s stability. Single-phase transformers are highly versatile, making them suitable for various applications requiring precise voltage control and isolation. In this study, we investigated the fault diagnosis of a 1 kVA single-phase transformer core subjected to induced faults. Our diagnostic approach involved using a combination of advanced signal processing techniques, such as the fast Fourier transform (FFT) and Hilbert transform (HT), to analyze the current signals. Our analysis aimed to differentiate and characterize the unique signatures associated with each fault type, utilizing statistical feature selection based on the Pearson correlation and a machine learning classifier. Our results showed significant improvements in all metrics for the classifier models, particularly the k-nearest neighbor (KNN) algorithm, with 83.89% accuracy and a computational cost of 0.2963 s. For future studies, our focus will be on using deep learning models to improve the effectiveness of the proposed method. Full article

We solve the particle-antiparticle and cosmological constant problems proceeding from quantum theory, which postulates that: various states of the system under consideration are elements of a Hilbert space $\mathcal{H}$ with a positive definite metric; each physical quantity is defined by a self-adjoint operator in $\mathcal{H}$; symmetry at the quantum level is defined by a representation of a real Lie algebra A in $\mathcal{H}$ such that the representation operator of any basis element of A is self-adjoint. These conditions guarantee the probabilistic interpretation of quantum theory. We explain that in the approaches to solving these problems that are described in the literature, not all of these conditions have been met. We argue that fundamental objects in particle theory are not elementary particles and antiparticles but objects described by irreducible representations (IRs) of the de Sitter (dS) algebra. One might ask why, then, experimental data give the impression that particles and antiparticles are fundamental and there are conserved additive quantum numbers (electric charge, baryon quantum number and others). The reason is that, at the present stage of the universe, the contraction parameter R from the dS to the Poincare algebra is very large and, in the formal limit $R\to \infty$, one IR of the dS algebra splits into two IRs of the Poincare algebra corresponding to a particle and its antiparticle with the same masses. The problem of why the quantities $(c,\hslash ,R)$ are as are does not arise because they are contraction parameters for transitions from more general Lie algebras to less general ones. Then the baryon asymmetry of the universe problem does not arise. At the present stage of the universe, the phenomenon of cosmological acceleration (PCA) is described without uncertainties as an inevitable kinematical consequence of quantum theory in semiclassical approximation. In particular, it is not necessary to involve dark energy the physical meaning of which is a mystery. In our approach, background space and its geometry are not used and R has nothing to do with the radius of dS space. In semiclassical approximation, the results for the PCA are the same as in General Relativity if $\mathsf{\Lambda }=3/R^2$, i.e., $\mathsf{\Lambda }>0$ and there is no freedom for choosing the value of $\mathsf{\Lambda }$. Full article

To estimate the degree of quantum entanglement of random pure states, it is crucial to understand the statistical behavior of entanglement indicators such as the von Neumann entropy, quantum purity, and entanglement capacity. These entanglement metrics are functions of the spectrum of density matrices, and their statistical behavior over different generic state ensembles have been intensively studied in the literature. As an alternative metric, in this work, we study the sum of the square root spectrum of density matrices, which is relevant to negativity and fidelity in quantum information processing. In particular, we derive the finite-size mean and variance formulas of the sum of the square root spectrum over the Bures–Hall ensemble, extending known results obtained recently over the Hilbert–Schmidt ensemble. Full article