Path integration refers to the process by which animals continuously update spatial position during movement by integrating locomotor stimuli such as speed and head direction, thereby enabling real-time localization in continuous space. This process relies on the cooperation of spatial neurons, including grid cells and place cells. In recent years, continuous attractor networks and recurrent neural networks have provided useful insights into the mechanisms of path integration; however, they often rely on fixed-weight connections or exhibit a lack of biological plausibility. To explore more biologically plausible mechanisms, we propose a path integrator based on the recurrent spiking neural network (RSNN). Employing recurrently connected leaky integrate and fire (LIF) neurons, the RSNN encodes spatial positions as spike sequences via membrane potential reset mechanisms, enabling robust long-term path integration. Analysis reveals the spontaneous emergence of spatial and locomotor units, with some units exhibiting spatial-locomotor conjunctive properties, indicating synergistic computations underlying path integration. Ablation experiments confirm that stripe and border units have a larger effect on performance than other unit types under our experimental conditions. Under sparse spiking conditions, the network naturally develops diverse biologically inspired representations. The RSNN’s performance provides novel insights into neuronal synergistic mechanisms in biological navigation, offering a biologically grounded framework for path integration modeling and contributing to the development of brain-inspired navigation algorithms.

Red blood cells (RBCs) are classically modeled as thin elastic surfaces governed by the Helfrich–Canham energy. Within the widely used axisymmetric framework, we provide what appears to be the first complete mathematical proof that Cassini ovals, except for the limiting round sphere, do not satisfy the Helfrich shape equation, even though they can approximate biconcave profiles over experimentally relevant parameter ranges. The argument proceeds by direct substitution of the Cassini meridian into the third-order reduced shape equation and yields an overdetermined algebraic system with no consistent solution for any nonzero Cassini eccentricity. Beyond this structural result, we place the analysis in a broader biophysical and geometric context. We review typical bending and shear moduli, reduced-volume constraints, and the role of area and volume conservation; we explain the geometric meaning of the Helfrich parameters and their relation to the Willmore functional; we connect our formulation to bilayer-couple and area-difference-elasticity (ADE) models; and we outline practical routes to parameter inference from micropipette aspiration, flicker spectroscopy, and optical tweezers. We also discuss why the specific curvature structure of Cassini ovals is conceptually incompatible with Helfrich equilibria, indicate regimes in which Cassini profiles remain useful surrogates for geometric descriptors and for initializing PDE-based solvers, and summarize recent models based on constant bending-energy density. Finally, we identify extensions with spatially varying spontaneous curvature that may accommodate membrane heterogeneity and more complex RBC morphologies.

We study the following semilinear system:

and we prove the existence of bounded weak solutions in W1,2 0 (Ω). Even if the system is nonlinear, we use a duality method. We dedicate this paper to Patrizia Pucci certain that she will help us for the study of (*) with nonlinear principal part.

This study investigates how to control chaos in discrete-time systems that have variable fractional orders. We examine a general type of discrete fractional-order equations where the order changes with time, and we show that these systems can become chaotic when certain parameters are chosen. To address this, we develop and apply tailored control techniques to suppress chaos and achieve system stabilization. Using detailed numerical simulations, we confirm that the suggested control method works effectively in two example cases. Our findings underscore that chaos control in variable fractional-order systems provides significant flexibility in modulating dynamic behavior, offering valuable insights into the broader applicability of these methods in discrete fractional- order systems.

Epigenetics refers to genetic modifications that cause changes in gene expression and are not encoded in DNA. These modifications, including histone, DNA, and RNA, as well as miRNA, are closely related to oncology research and have the potential to influence the treatment of metabolic, neurological, inflammatory, and cardiovascular diseases. In cancer treatment, targeting abnormal epigenetic regulation can be achieved through inhibition of abnormal DNA methylation and histone methylation and acetylation. However, the discovery of efficient epigenetic drugs often requires substantial time and resources. To aid in drug research, we propose an extraction method of molecule features based on a gated graph neural network (GGNN) and integrate four supervised classifiers to predict epigenetic targets in screened chemogenomic datasets. Our GGNN+XGBoost integrated model achieves an overall accuracy of 0.8158, with accuracy increasing to 0.981 in certain target datasets. This approach offers a promising solution for predicting epigenetic targets, with implications for cancer treatment and other diseases. Furthermore, our method showcases the potential of utilizing big datasets and predictive models to expedite epigenetic drug discovery.

In this study, we introduced and investigated new classes of k-Mittag-Leffler-Konhauser polynomials and bivariate k-Mittag-Leffler functions, which encompass several well-known 2D polynomials and Mittag-Leffler functions as special cases. We explored their key properties, including double k-Riemann-Liouville fractional calculus, double Laplace transforms, and k-fractional calculus operators. To further support the theoretical results, a new section presents numerical validation through simulation examples, illustrating the accuracy and practical applicability of the proposed formulas. We conclude by proposing several open questions to inspire further research and continued exploration in this area.

For partial differential equations, traditional methods are characterized by high accuracy, yet they face difficulties in handling complex high-dimensional. Although physics-informed neural networks (PINNs) can effectively solve high-dimensional problems, their accuracy still needs to be improved. The Fourier neural operator (FNO) has an advantage in capturing the global characteristics of physical systems, but it relies on a large amount of training data. To address these limitations, this paper proposes a hybrid method, FNO-PINN, which integrates the FNO with a PINN. This method devises a hybrid architecture consisting of an enhanced FNO, high precision difference calculation, multi-objective physical constraints, and post processing mechanisms. Meanwhile, a dynamic weight adjustment strategy and an iterative auxiliary data loss for different time-scale variables are proposed to effectively alleviate the imbalance problem during the training process. The numerical experimental results of three examples show that compared with the traditional PINNs method, the proposed FNO-PINN method has a faster convergence speed and smaller error, and it demonstrates superior performance in handling coupled systems with multiple time scales.

In this paper, we investigate the finite-time blowup phenomenon in the fractional Klein-Gordon-Schrödinger (FKGS) system featuring nongauge-invariant power-type nonlinearities on Rⁿ. The system models interactions between nucleon and meson fields, augmented by fractional Laplacian operators and nonlinear terms that disrupt conservation laws. By introducing a novel test function tailored to address the difficulties posed by mixed fractional operators and the absence of energy conservation, we established sufficient conditions for finite-time blowup under specific initial data constraints. Our analysis revealed that solutions fail to exist globally when the nonlinear exponents and initial energy satisfy critical inequalities, with the lifespan bounded by a power-law dependence on the problem parameters.

DNS-over-HTTPS (DoH) effectively improves domain name system (DNS) security by encapsulating DNS query and response content in HTTPS packets, and also provides an opportunity for DoH-based covert tunneling attacks. Aiming at the problems of poor feature representation ability and low classification accuracy in the classification research of existing DoH tunneling tools, a multi-modal fusion deep learning classification model of DoH tunneling tools based on transformer-gated unit recurrent (GRU)-multilayer perceptron (MLP) (TGM) is proposed to help security personnel accurately locate specific threat types and take corresponding defensive measures. The model combines the spatial sequence feature extraction ability of the transformer encoder and the time sequence feature learning advantage of GRU to capture deep-level features between traffic generated by different DoH tunneling tools, and uses MLP to learn statistical features. Finally, we fuse the output embeddings of the three branches and learn the weights of different branch features through an attention mechanism. The experimental results show that our method achieves classification accuracy of 98.87% and F1-score of 98.02%, which are all better than the existing state-of-the-art methods.

This paper investigates the existence and uniqueness of solutions for fractional differential equations with nonlocal conditions. The results are derived using measure theory, Monch’s fixed point theorem, and semigroup theory. An illustrative example is also presented, involving a nonlocal fractional evolution problem in $L^{2}((0, \pi), \mathbb{R})$. This example demonstrates the effect of the ψ-Caputo derivative on the mild solution in comparison with the standard Caputo derivative, highlighting the influence of non-uniform time scaling and memory effects.

Employing variational methods in conjunction with the technique of invariant sets of descending flow, we study the existence and multiplicity of solutions for a second-order difference equation subject to a three-point boundary condition. By imposing suitable growth and sign conditions on the nonlinearity, we establish sufficient criteria for the existence of at least three nontrivial solutions. These solutions are characterized by their nodal properties: one positive, one negative, and one sign- changing solution, in addition to the trivial solution. Our results generalize and extend previous work on discrete boundary value problems (BVPs), notably encompassing and broadening known results for Robin boundary conditions. Furthermore, two demonstrative examples are provided not only to validate the theoretical results but also to illustrate the applicability of the problem in modeling phenomenological processes.

Rumors circulating on social media can have significant adverse impacts on society, high- lighting the urgent need for effective rumor detection. However, most existing methods predominantly focus on rumor identification only after widespread dissemination has occurred, when substantial harm has been inflicted. Early-stage rumor detection is a major challenge due to limited reach and small sample sizes, which restrict the use of large datasets and traditional propagation models. To overcome these challenges, a cross-modal deep fusion method based on small samples for early rumor detection is proposed, which includes a multimodal feature extraction network and a cross-modal deep fusion network. The multimodal feature extraction network captures features from multiple modalities, while the multimodal deep information extraction network derives deep representations from these modalities. The cross-modal deep fusion network integrates textual and visual features for rumor classification. Furthermore, an enhanced meta-learning training approach based on model-agnostic meta-learning is proposed to improve the efficiency of rumor detection by employing distinct learning rates both within and between tasks. Experimental results on two publicly available datasets demonstrate that the proposed cross-modal deep fusion method outperforms baseline methods and exhibits promising performance.

We studied an intraguild–predation system where an intermediate consumer and a top consumer exploit a shared basal resource. A compact nondimensionalization yielded five interpretable parameters-relative predator growth α, crowding β, enrichment γ, and depletion couplings δ, ε. We presented closed-form thresholds that organize the dynamics: the coexistence equilibrium exists exactly when a quadratic in the resource steady state has a root in (0, β); as γ varies, a two- equilibria window appears and terminates at an explicit saddle–node value γ⁺ 1, with transversality confirmed and transcritical/pitchfork alternatives excluded. A Hopf onset criterion was given via the characteristic polynomial coefficients along the interior branch. For the forward-Euler discretization we established positivity, an absorbing set under an explicit stepsize bound, and stability tests that reduce to |1 + ∆τλ| = 1. Extensions to diffusion and stochastic forcing suggest the incorporation of more realistic spatial and stochastic factors. The thresholds were directly calibratable, enabling reproducible, mechanistic predictions for applied systems.

In this paper, we investigated the coefficient-based regularized distribution regression for data generated by unbounded sampling processes. The algorithm adopts a two-stage sampling framework: the first-stage sample consists of probability distributions, from which the second-stage sample is drawn. A rigorous capacity-dependent convergence analysis was conducted under more general conditions, and its performance was comparable to that of one-stage sampling learning. Regularization was imposed on the coefficients and the kernel K was permitted to be indefinite. The important feature of this algorithm is that it can improve the saturation effect suffered by classical kernel ridge regression (KRR). Notably, the output sample values were assumed to satisfy a moment condition (rather than the stricter uniform boundedness constraint common in related works). We derived the convergence error bounds via the novel integral operator techniques, and further established the minimax optimal learning rates of the algorithm, which were comparable to those achieved under bounded sampling settings.

This study investigated the spatial behavior and structural stability of solutions for a higher-order heat conduction model within the second gradient theory of type III. By constructing a tailored energy functional and employing integral-differential inequality techniques, we derived a continuous dependence estimate for the solution with respect to the elastic coefficient µ. Our results demonstrate that the energy not only decays exponentially with respect to the spatial variable z, but also diminishes as the parameter µ tends to zero. This work extends the understanding of structural stability in unbounded domains and underscores the robustness of the model under perturbations of material parameters.

This paper focused on the control design problem regarding the hydraulic support pushing system, with full consideration of the saturation structure of the control input. With the help of the backstepping technique, some sufficient conditions were established to ensure local exponential stability of the error system between the hydraulic support pushing system and the reference system, simultaneously providing an estimation of the attractive domain. In addition, a potential relationship between the saturation structure and attractive domain was established, which was crucial for achieving local exponential stability in the framework of saturation limitations. It showed that the size of the attractive domain was not only determined by the structure of control input but was also affected by the saturation structure. Finally, some simulations were presented to illustrate the effectiveness of the proposed results.

This study centers on infectious disease models that feature a delayed mortality rate and the Holling II type functional response function. Through a theoretical analysis, it is confirmed that the solutions of the model possess positivity and boundedness, and the equilibrium points are obtained with their local and global stability conditions ascertained. The research indicates that, in the absence of time delay, transcritical and Hopf bifurcations emerge in the model under specific parameter conditions, thus furnishing a foundation to understand the dynamics of disease transmission. Subsequently, a time delay is incorporated into the system, and its impact on the Hopf bifurcation is analyzed. Numerical simulations depict the dynamic behaviors of the model at different delay times. For instance, the system can swiftly reach a stable state without delay, and periodic oscillations occur when the delay surpasses the critical value, thus validating the theory and suggesting that the delayed death factor has a significant influence. By comparing with actual data, the model effectively depicts the spread and lethality of the disease in infected ash trees across different regions, and uncovers the population differences and dynamic change patterns. Thus, it offers targeted strategies for disease prevention and control, as well as the ecological management of ash trees, which is relevant to the study on the impacts of delayed mortality and the Holling-II functional response function on the population dynamics of infected ash trees.

Most prior couple dynamics research has focused on either high-conflict, low-stability relationships or low-conflict, high-stability relationships, relying predominantly on deterministic models. We investigate the stability of the far-less-studied dynamically balanced regime characterized by recurrent small conflicts, occasional large conflicts, and spontaneous repair processes in an intrinsically stochastic environment. An intimacy–conflict model couples dual stochasticity: event timing follows independent Poisson processes, and impact magnitudes follow uniform distributions. Formal proofs establish the existence and uniqueness of solutions, bounded states within [0, 1], stochastic stability of intimacy around its baseline, and convergence to a unique stationary distribution. Simulations show that intimacy drifts back to its usual level, that the impact of each event depends on the couple’s current state, and that built-in repair keeps the system steady while mirroring real-life ups and downs. The study extends theory on conflict–intimacy coevolution and provides a framework for marital research and intervention.

A novel metric, called partial martingale difference-angle divergence, is proposed to test and measure partial conditional mean (in)dependence for Hilbert elements. The partial martingale difference-angle divergence has some appealing properties. It is nonnegative and equals zero if and only if the partial conditional mean independence holds; it has a simple expectation form; it does not require the moment condition for the predictor variable. We construct an estimator for partial martingale difference-angle divergence and derive its asymptotic properties. Finite sample simulations show that the proposed test performs well and has strong testing power for nonlinear relationships. Two real data examples are introduced to illustrate the application of the proposed test.

The source number so(X) of a Tychonoff space X denotes the minimal cardinal τ such that X has an open source S in some compactification bX for which |$\mathcal{S}$| ≤ τ. In this paper some properties of source numbers are studied. Among other things, we showed that the equalities w(X) = nw(X)so(X) and w(X) = so(X)Nag(X)iw(X) hold for every Tychonoff space X, where w(X), nw(X), iw(X), Nag(X) denote the weight, network weight, i-weight, and Nagami number of a space X, respectively. Some corollaries about the two statements were obtained.

This study investigated the problem of model order reduction by employing the ν-gap metric and introduced a metaheuristic optimization framework to address its inherent nonconvexity. The ν-gap metric quantifies the closed-loop distance between two systems, making it useful for generating low-order models that preserve closed-loop stability characteristics. However, minimizing the conventional ν-gap alone may result in poor dynamic fidelity. To address this limitation, a modified ν-gap metric based on frequency response matching was developed to explicitly capture frequency-wise discrepancies associated with time-domain behavior. By jointly considering the conventional and modified ν-gap metrics, a dual ν-gap–based multi-objective model reduction framework was formulated, in which stability-related and time-domain fidelity objectives are treated in a complementary manner. The resulting optimization problem is highly nonconvex and constrained due to the winding number condition. A multi-objective particle swarm optimization framework was therefore employed as a numerical tool to generate Pareto-optimal reduced-order models. Benchmark studies on large-scale systems demonstrated that the proposed framework enables a systematic exploration of trade-offs between stability preservation and time-domain fidelity, yielding practically meaningful reduced-order models with tunable performance characteristics.

In this paper, the upper bound of the dimension of the global attractor associated with the four-dimensional cubic complex Ginzburg-Landau system is derived using the Lyapunov exponent method. First, by employing the Faedo-Galerkin method and energy estimation, the existence and uniqueness of solutions under the variational form of the system are established. Subsequently, a specific quantity is constructed and transformed into an inequality, from which the upper bound of the fractal dimension corresponding to the global attractor of the dynamical system is obtained.

Tensor ring (TR) decomposition has demonstrated remarkable capability in capturing low- rank tensor structures, achieving significant success in color image completion tasks. However, relying solely on the tensor low-rank prior cannot fully capture the details of a color image. Thus, traditional model-driven TR decomposition models often fail to recover satisfactory local detail. A natural idea is to introduce a deep neural network with end-to-end training to improve the detail quality of image reconstruction. Thus, we proposed a novel hybrid model that integrates model-driven TR decomposition with data-driven deep learning regularization. The proposed framework introduces an energy functional regularization term based on the FFDNET architecture, which enhances the robustness of rank selection while preserving global low-rank and local details. In particular, we assumed that the unfolding matrices of the TR factors exhibited low-rank properties. Thus, nuclear- norm regularization constraints were incorporated on the TR factors to enhance their global low-rank characteristics. Additionally, a deep prior regularization term derived from the FFDNET network was introduced to preserve the local details of the target tensor. We further developed an efficient alternating direction method for the multiplier algorithm to address the associated optimization problem. Extensive experiments on color images have demonstrated that the proposed method outperforms denoising approaches, yielding satisfactory results. The code for implementing the proposed method is available at https://github.com/110500617/TRDD.

This study explores a system of singular nonlinear higher-order katugampola fractional differential equations (KFDEs) with nonlocal coupled Riemann-Stieltjes integral boundary conditions. First, the addressed KFDEs are reformulated as the equivalent integral equations through explicit construction of some appropriate Green’s functions. Second, through synergistic application of Schauder’s and Guo-Krasnoselskii’s fixed-point theorems, some explicit parameter interval-dependent existence criteria are established for at least one or two positive solutions to the considered KFDEs with the help of the properties of Green’s functions. Finally, some concrete examples are provided to validate the effectiveness of the main theoretical results.

Maritime transportation underpins global trade and supply chains, with bunker fuel comprising a major share of voyage operating costs. Optimizing ship refueling is thus critical for improving energy efficiency and reducing expenses. A common sequential (two-stage) framework first derives a cost-minimal bunkering plan and then maximizes profit from cargo flows under that plan. Yet, this decoupled approach often yields suboptimal solutions, as refueling and container decisions are optimized separately. We develop an integrated one-stage model that simultaneously optimizes refueling and container flows on fixed liner services, comparing it to the two-stage model on stylized, industry-calibrated networks of 3, 8, and 15 ports. Results reveal consistent profit superiority for the integrated model, with gaps expanding alongside network scale and complexity (1.02% for 3 ports to 12.99% for 15 ports). Sensitivity tests on fuel-tank capacity, revenue levels, and local fuel price shocks affirm robustness, with gains amplifying under high demand or capacity constraints. Although the two-stage model provides modular transparency, the integrated formulation better balances fuel costs and cargo revenues, delivering substantial economic benefits in complex, constrained settings. Both models solve to optimality in seconds to minutes on standard hardware for tested instances, underscoring the integrated model’s viability as a tactical decision tool. Overall, findings illuminate refueling optimization dynamics, quantify the inefficiency of bunker-first sequencing, and advise adopting integrated methods for larger networks.

This paper investigates the asymptotic behavior of solutions to the inflow problem for the one-dimensional bipolar compressible quantum Navier-Stokes-Poisson system, a model describing the motion of two-species charged particles, electrons and holes, in ultra-small sub-micron semiconductor devices where quantum effects are significant. First, with the aid of stable manifold theory and center manifold theory, we established the existence and spatial-decay properties of the boundary layer to the inflow problem for the transonic and subsonic cases. Next, under suitable assumptions on the boundary data and the space-asymptotic states, we proved the asymptotic stability of the boundary layer and the superposition of the boundary layer and the rarefaction wave in the case that the initial perturbation and the strength of the boundary layer are sufficiently small. The proof was completed by the L²-energy method with the help of the spatial-decay properties of the boundary layer and the time-decay properties of the smooth approximate rarefaction wave.

In this paper, we present a nonlinear correction finite volume scheme that preserves the discrete extremum principle for convection-diffusion equations on tetrahedral meshes. The approximation of the diffusive flux is based on a nonlinear correction of the second-order linear flux, while the convection flux is approximated by the upwind scheme with second-order accuracy given by a Taylor expansion. In the construction of the new scheme, the requirement to represent auxiliary unknowns as convex combinations of primary unknowns can be removed, which greatly reduces the restrictions on diffusion coefficients and mesh geometry. Moreover, the obtained new scheme is cell-centered and satisfies local conservation. In addition, we theoretically testify that the numerical solution of the new scheme keeps the discrete extremum principle and verify it numerically. Numerical results also show that our scheme has almost second-order accuracy.

We considered the following parabolic system:

subject to Dirichlet (or Neumann) boundary conditions. Here $\Omega \subset \mathbb{R}^{N}(N \geq 1)$ is a bounded smooth domain. In addition to some results on blowup and global existence of the solution, we found some more interesting results as follows: (1) There exists double thresholds for blowup and global existence of the solution. Under certain conditions, if $f(u, v)=f_{1}(v) g_{1}(u) \text { and } g(u, v)=f_{2}(v) g_{2}(u)$, then the first watershed is and the second watershed is Here $\tilde{f}, \tilde{g}, \tilde{F} \text { and } \tilde{G}$ will be defined in Section 2.2. (2) If there exist nonnegative smooth functions h(u), l(v) and H(s) such that then the watershed for blowup in finite time and global existence of the solution is

A Holling type IV predator-prey system with a rational nonlinear harvesting rate and gestation delay of prey species is studied, which is formulated by delayed differential-algebra equations. Its dynamical behaviors are investigated in terms of differential-algebra system theory, bifurcation theory, and center manifold theorem. By choosing the gestation delay as a bifurcation parameter, we first show that Hopf bifurcations can occur as the delay increases through a sequence of threshold values. Second, we derive an explicit algorithm for determining the stability and direction of the Hopf bifurcations. Last, some numerical simulations are performed to illustrate the analytical results, and their biological significances are explained.

Regularities of viscous fluid flow in the hydrodynamic entrance region of a round pipe under turbulent unsteady flow conditions were studied, taking into account the tangential stresses that develop between the fluid layers. What distinguishes the proposed research is the method for generating tangential tensions between fluid layers, which impacts the accurate monitoring of the current hydrodynamic events. The study was based on the system of differential equations of viscous fluid flow, where viscous forces in turbulent flows were calculated using the Prandtl calculation method for stationary turbulent flows. Nevertheless, this formula could also be used in the case of unstable turbulent flows. This theory about the appearance of viscous forces in turbulent flows led to the creation of a mathematical model of the issue and the development of a method for its integration. Integration throughout the length of the inlet transition section led to the derivation of calculation formulas for the hydrodynamic properties of the current. These calculations showed the ongoing phenomena. In order to accurately design the transition sections of automatic hydrocontrolled equipment, it was crucial to understand the inlet transition section. Conclusions were drawn from the analysis of the results of computerized experimental research using the obtained analytical solutions. Scientific research and engineering applications may benefit from the study’s findings.