Search Results (71)

We investigate the dynamics of vector solitons in a two-component Bose–Einstein condensates governed by the system of Gross–Pitaevskii equations. Using a gauge-transformation approach, we construct a four-soliton solution and analyze their interactions, including superposition states, fission, and shape-preserving collisions. We explore the ability of time-dependent parameters, such as the intra- and intercomponent interaction coefficients and trapping potential, to control the soliton properties. In particular, we demonstrate controlled four-soliton fission, highlighting its potential applications to quantum data processing and coherent matter-wave transport. The results suggest experimental realization in BEC systems and provide insights into nonlinear wave interactions in multicomponent quantum fluids. Full article

This paper develops a novel modeling framework that integrates time-varying quantile-based spillover effects into a regime-switching realized volatility model. A dynamic spillover factor is constructed by identifying the most influential contributors to Bitcoin’s realized volatility across different quantile levels. This quantile-layered structure enables the model to capture heterogeneous spillover paths under varying market conditions at a macro level while also enhancing the sensitivity of volatility regime identification via its incorporation into a time-varying transition probability (TVTP) Markov-switching mechanism at a micro level. Empirical results based on the cryptocurrency market demonstrate the superior forecasting performance of the proposed TVTP-MS-HAR model relative to standard benchmark models. The model exhibits strong capability in identifying state-dependent spillovers and capturing nonlinear market dynamics. The findings further reveal an asymmetric dual-tail amplification and time-varying interconnectedness in the spillover effects, along with a pronounced asymmetry between market capitalization and systemic importance. Compared to decomposition-based approaches, the X-RV type of models—especially when combined with the proposed quantile-driven factor—offers improved robustness and predictive accuracy in the presence of extreme market behavior. This paper offers a coherent approach that bridges phenomenon identification, source localization, and predictive mechanism construction, contributing to both the academic understanding and practical risk assessment of cryptocurrency markets. Full article

Analyzing and measuring the similarity between two signals is a common task in many vibration-based structural health monitoring applications. Coherence between input and response signals serves as a convenient indicator of damage, based on the premise that nonlinearity due to damage in a linear system manifests as a loss of coherence in specific frequency bands. Because input excitations in civil structures are difficult to measure, damage indicators based on the coherence between two response signals have been developed. These indicators have shown promise in detecting nonlinear behavior in structures that were initially linear. This paper proposes a new damage indicator based on Mutual Information, a nonlinear extension of the squared correlation coefficient, to quantify the similarity between two signals without making assumptions about the nature of their interactions or the underlying dynamics of the system. Mutual Information is distinguished from other nonlinear similarity metrics due to its ability to capture all types of nonlinear dependencies, its high computational efficiency, and its invariance to invertible transformations, such as scaling. The proposed approach is demonstrated using a standard dataset containing experimental data from a three-story aluminum frame structure under 17 different damage states. The results show that the proposed metric can detect deviations from the baseline state due to changes in mass, stiffness, or newly induced nonlinear behavior, suggesting its potential for monitoring changes in the structural system. Full article

Hyperspectral sparse unmixing (SU) networks have recently received considerable attention due to their model hyperspectral images (HSIs) with a priori spectral libraries and to capture nonlinear features through deep networks. This method effectively avoids errors associated with endmember extraction, and enhances the unmixing performance via nonlinear modeling. However, two major challenges remain: the use of large spectral libraries with high coherence leads to computational redundancy and performance degradation; moreover, certain feature extraction models, such as Transformer, while exhibiting strong representational capabilities, suffer from high computational complexity. To address these limitations, this paper proposes a hyperspectral unmixing dual-branch network integrating an adaptive hop-aware GCN and neighborhood offset Mamba that is termed DGMNet. Specifically, DGMNet consists of two parallel branches. The first branch employs the adaptive hop-neighborhood-aware GCN (AHNAGC) module to model global spatial features. The second branch utilizes the neighborhood spatial offset Mamba (NSOM) module to capture fine-grained local spatial structures. Subsequently, the designed Mamba-enhanced dual-stream feature fusion (MEDFF) module fuses the global and local spatial features extracted from the two branches and performs spectral feature learning through a spectral attention mechanism. Moreover, DGMNet innovatively incorporates a spectral-library-pruning mechanism into the SU network and designs a new pruning strategy that accounts for the contribution of small-target endmembers, thereby enabling the dynamic selection of valid endmembers and reducing the computational redundancy. Finally, an improved ESS-Loss is proposed, which combines an enhanced total variation (ETV) with an $l_{1/2}$ sparsity constraint to effectively refine the model performance. The experimental results on two synthetic and five real datasets demonstrate the effectiveness and superiority of the proposed method compared with the state-of-the-art methods. Notably, experiments on the Shahu dataset from the Gaofen-5 satellite further demonstrated DGMNet’s robustness and generalization. Full article

We carried out a comparative study of the phase space evolution of SU(2) and SU(1,1) coherent states generated by the same nonlinear two-mode Hamiltonian. We analyze the dynamics of the Wigner functions in the respective phase spaces and discuss the principal associated physical effects: the squeezing of the appropriate observables and the Schrödinger’s cat state generation characteristic of both the considered symmetry groups. Full article

Audio-driven emotional talking face generation aims to generate talking face videos with rich facial expressions and temporal coherence. Current diffusion model-based approaches predominantly depend on either single-label emotion annotations or external video references, which often struggle to capture the complex relationships between modalities, resulting in less natural emotional expressions. To address these issues, we propose MF-ETalk, a multimodal feature-guided method for emotional talking face generation. Specifically, we design an emotion-aware multimodal feature disentanglement and fusion framework that leverages Action Units (AUs) to disentangle facial expressions and models the nonlinear relationships among AU features using a residual encoder. Furthermore, we introduce a hierarchical multimodal feature fusion module that enables dynamic interactions among audio, visual cues, AUs, and motion dynamics. This module is optimized through global motion modeling, lip synchronization, and expression subspace learning, enabling full-face dynamic generation. Finally, an emotion-consistency constraint module is employed to refine the generated results and ensure the naturalness of expressions. Extensive experiments on the MEAD and HDTF datasets demonstrate that MF-ETalk outperforms state-of-the-art methods in both expression naturalness and lip-sync accuracy. For example, it achieves an FID of 43.052 and E-FID of 2.403 on MEAD, along with strong synchronization performance (LSE-C of 6.781, LSE-D of 7.962), confirming the effectiveness of our approach in producing realistic and emotionally expressive talking face videos. Full article

The fifth-order nonlinear polarizability has been extensively studied in the field of quantum communication due to its ease of manipulation. By adjusting the relative size of the Rabi frequency and dephasing rate of the dressing field, natural non-Hermitian exceptional points can be generated, and further evolution can be achieved by varying the types of dressing fields. However, as the demand for information capacity in quantum communication continues to increase, research on the higher-order seventh-order nonlinear polarizability, based on four-photon states, and the number of coherent channels and resonance positions has gradually come to the forefront. This paper focuses on the simultaneous generation of a seventh-order nonlinear polarizability through a spontaneous eight-wave mixing (SEWM) process in an atomic medium involving four photons. Compared to the fifth-order nonlinear polarizability, the seventh-order polarizability shows an exponential increase in coherent channels and resonance positions due to its strong dressing effect. Additionally, the interaction between the four photons is stronger than that between three photons, making it possible for even the difficult-to-dress eigenvalues to be influenced by the dressing field and dephasing rate, resulting in more complex coherent channels. These are manifested as more complex, damped Rabi oscillations, with periods that can be controlled by the dressing field. These findings may contribute to a promising new method for quantum communication. Full article

Hand displacements during task-directed movements are not random, but exhibit fractal behavior. Wearable sensing e.g., accelerometer-derived hand movement fluctuations, could add a significant contribution to cognitive and behavioral sciences, by accounting for fractal dynamics. In particular, multifractal testing of fluctuation time series has been shown to reflect the adaptive use of cognition, i.e., cognitive flexibility. This important property might be enhanced by an improved mental state. Here, an experimental group (16 participants, 3 females) practiced 5 min cardiac coherence (CC) prior to a cognitive flexibility task and was compared to a control group (13 participants, 4 females). Accelerometer-derived hand motion was analyzed using multifractal-multiscale detrended fluctuation analysis (MFMS-DFA) during a task involving cognitive flexibility, the Wisconsin Card Sorting Test (WCST). WCST included four phases alternating the use of cards with original shapes or animal pictures developed for children in previous research. Hand behavioral time series derived from the wearable accelerometer effectively exhibited nonlinear multifractality as shown using linearized surrogates testing. Multifractal-multiscale metrics revealed significant effects of pre-task CC practice, specifically during WCST shape condition where CC participants showed lower multifractal degree despite similar performances (perseverative errors). We conclude that multifractal-multiscale testing of accelerometer-derived hand motion could make a significant contribution to interpreting changes in cognitive flexibility. Full article

Modeling the brain dependence network is central to understanding underlying neural mechanisms such as perception, action, and memory. In this study, we present a broad range of statistical methods for analyzing dependence in a brain network. Leveraging a combination of classical and cutting-edge approaches, we analyze multivariate hippocampal local field potential (LFP) time series data concentrating on the encoding of nonspatial olfactory information in rats. We present the strengths and limitations of each method in capturing neural dynamics and connectivity. Our analysis begins with exploratory techniques, including correlation, partial correlation, spectral matrices, and coherence, to establish foundational connectivity insights. We then investigate advanced methods such as Granger causality (GC), robust canonical coherence analysis, spectral transfer entropy (STE), and wavelet coherence to capture dynamic and nonlinear interactions. Additionally, we investigate the utility of topological data analysis (TDA) to extract multi-scale topological features and explore deep learning-based canonical correlation frameworks for connectivity modeling. This comprehensive approach offers an introduction to the state-of-the-art techniques for the analysis of dependence networks, emphasizing the unique strengths of various methodologies, addressing computational challenges, and paving the way for future research. Full article

Chimera states and bump states are collective synchronization phenomena observed independently (in different parameter regions) in networks of coupled nonlinear oscillators. And while chimera states are characterized by coexistence of coherent and incoherent domains, bump states consist of alternating active and inactive domains. The idea of multistable plasticity in the network connections originates from brain dynamics where the strength of the synapses (axons) connecting the network nodes (neurons) may change dynamically in time; when reaching the steady state the network connections may be found in one of many possible values depending on various factors, such as local connectivity, influence of neighboring cells etc. The sign of the link weights is also a significant factor in the network dynamics: positive weights are characterized as excitatory connections and negative ones as inhibitory. In the present study we consider the simplest case of bistable plasticity, where the link dynamics has only two fixed points. During the system/network integration, the link weights change and as a consequence the network organizes in excitatory or inhibitory domains characterized by different synaptic strengths. We specifically explore the influence of bistable plasticity on collective synchronization states and we numerically demonstrate that the dynamics of the linking may, under special conditions, give rise to co-existence of bump-like and chimera-like states simultaneously in the network. In the case of bump and chimera co-existence, confinement effects appear: the different domains stay localized and do not travel around the network. Memory effects are also reported in the sense that the final spatial arrangement of the coupling strengths reflects some of the local properties of the initial link distribution. For the quantification of the system’s spatial and temporal features, the global and local entropy functions are employed as measures of the network organization, while the average firing rates account for the network evolution and dynamics. In particular, the spatial minima of the local entropy designate the transition points between domains of different synaptic weights in the hybrid states, while the number of minima corresponds to the number of different domains. In addition, the entropy deviations signify the presence of chimera-like or bump-like states in the network. Full article

We introduce a novel class of coherent states, termed ${\mathcal{W}}_{\alpha ,\beta ,\nu }$-coherent states, constructed using a deformed boson algebra based on the generalised factorial ${\left[n\right]}_{\alpha ,\beta ,\nu }!$. This algebra extends conventional factorials, incorporating advanced special functions such as the Mittag-Leffler and Wright functions, enabling the exploration of a broader class of quantum states. The mathematical properties of these states, including their continuity, completeness, and quantum fluctuations, are analysed. A key aspect of this work is the resolution of the Stieltjes moment problem associated with these states, achieved through the inverse Mellin transformation method. The framework provides insights into the interplay between the classical and quantum regimes, with potential applications in quantum optics and fractional quantum mechanics. By extending the theoretical landscape of coherent states, this study opens avenues for further exploration in mathematical physics and quantum technologies. Full article

The standard way to measure the performance of existing continuous variable quantum key distribution (CVQKD) protocols is by using the achievable secret key rate (SKR) with respect to one parameter while keeping all other parameters constant. However, this atomistic method requires many individual parameter analyses while overlooking the co-dependence of other parameters. In this work, a numerical tool is developed for comparing different CVQKD protocols while taking into account the simultaneous effects of multiple CVQKD parameters on the capability of protocols to produce positive SKRs. Using the transmittance, excess noise, and modulation amplitude parameter space, regions of positive SKR are identified to compare three discrete modulated (DM) CVQKD protocols. The results show that the M-QAM protocol outperforms the M-APSK and M-PSK protocols and that there is a non-linear increase in the capability to produce positive SKRs as the number of coherent states used for a protocol increases. The tool developed is beneficial for choosing the optimum protocol in unstable channels, such as free space, where the transmittance and excess noise fluctuate, providing a more holistic assessment of a protocol’s capability to produce positive SKRs. Full article

The cooling of a macroscopic mechanical oscillator to its quantum ground state is an important step for achieving coherent control over mechanical quantum states. Here, we theoretically study the cooling of a rotating mirror in a Laguerre–Gaussian (L-G) cavity optorotational system with a nonlinear cross-Kerr (CK) interaction. We discuss the effects of the nonlinear CK coupling strength, the cavity detuning, the power of the input Gaussian beam, the topological charge (TC) of the L-G cavity mode, the mass of the rotating mirror, and the cavity length on the cooling of the rotating mirror. We find that it is only possible to realize the improvement in the cooling of the rotating mirror by the nonlinear CK interaction when the cavity detuning is less than the mechanical frequency. Compared to the case without the nonlinear CK interaction, we find that the cooling of the rotating mirror can be improved by the nonlinear CK interaction at lower laser powers, smaller TCs of the L-G cavity mode, larger masses of a rotating mirror, and longer optorotational cavities. We show that the cooling of the rotating mirror can be enhanced by the nonlinear CK interaction by a factor of about 23.3 compared to that without the nonlinear CK interaction. Full article

We consider a two-group social conflict under the corporates’ research and development (R&D) business processes. Conflict participants are divided into two groups depending on their attitude to new ideas, technologies, and behavioral style for R&D creative problems—innovators and adapters. We reveal the contradiction that arises between the need to include both types of employees in one project team and their objectively antagonistic positions regarding the methods and approaches to R&D processes. The proposed research methodology is based on a modern post-non-classical paradigm formed on the principles of coherence, interdisciplinarity, openness, and nonlinearity, as well as a sociophysical approach to the social conflicts modeling. We use the general theories of magnetism, paramagnetism, and functions of P. Langevin and L. Brillouin to describe the dynamics of group participants’ preferences regarding the style of conflict behavior. The analogy of paramagnetism, consisting in the orienting effect of the magnetic field, is used to describe social groups interactions that have not only their own interests, but are also influenced by the opinions of opposite social groups. A two-dimensional, four-parameter map represents the dynamics of group conflict. Modeling results show that regardless of the initial states and with certain parameters of intra-group and intergroup interactions, the trajectories eventually converge to an attractor (limit cycle) in a two-dimensional space. No non-periodic or chaotic modes are identified in the two-group conflict, which determines the controllability of the described conflict. The results of the simulation experiments are used as decision support and contradictions resolution aimed at forming the required modes of the corporates’ research and development business processes and ensuring the group participants’ cohesion and depolarization. The results of testing the model at an industrial enterprise are presented. Full article

A coherent optical spectrum analyzer is integrated with a rotating quarter wave plate polarimeter. The combined polarimeter optical spectrum analyzer (POSA) allows the extraction of the state of polarization with high spectral resolution. The POSA is used in this work to study two optical systems. The first is an optical modulator based on a ferrimagnetic sphere resonator. The POSA is employed to explore the underlying magneto–optical mechanism responsible for modulation sideband asymmetry. The second system under study is a cryogenic fiber loop laser, which produces an unequally spaced optical comb. The polarization measurements provide insights into the nonlinear processes responsible for comb creation. Characterizations extracted from the POSA data provide guidelines for the performance optimization of applications based on the systems under study. Full article