Search Results (70)

This paper presents a novel four-dimensional autonomous conservative model characterized by an infinite set of equilibrium points and an unusual algebraic structure in which all eigenvalues of the Jacobian matrix are zero. The linearization of the proposed model implies that classical stability analysis is inadequate, as only the center manifolds are obtained. Consequently, the stability of the system is investigated through both analytical and numerical methods using Lyapunov functions and numerical simulations. The proposed model exhibits rich dynamics, including hyperchaotic behavior, which is characterized using the Lyapunov exponents, bifurcation diagrams, sensitivity analysis, attractor projections, and Poincaré map. Moreover, in this paper, we explore the model with fractional-order derivatives, demonstrating that the fractional dynamics fundamentally change the geometrical structure of the attractors and significantly change the system stability. The Grünwald–Letnikov formulation is used for modeling, while numerical integration is performed using the Caputo operator to capture the memory effects inherent in fractional models. Finally, an analog electronic circuit realization is provided to experimentally validate the theoretical and numerical findings. Full article

The stability of hybrid stochastic differential equations (SDEs in short) depends on multiple factors, such as the structures and parameters of subsystems, switching rules, delay, etc. Regarding stability analysis for hybrid stochastic systems incorporating subsystems with diverse structures, existing research results require the system to possess either Markovian properties or finite memory characteristics. However, the stability problem remains unresolved for hybrid stochastic differential equations with infinite memory (hybrid IMSDEs in short), as no systematic theoretical framework currently exists for such systems. To bridge this gap, this paper develops a rigorous stability analysis for a class of hybrid IMSDEs by introducing a suitably chosen phase space and leveraging the theory of fading memory spaces. We establish sufficient conditions for exponential stability, extending the existing results to systems with unbounded memory effects. Finally, a numerical example is provided to illustrate the effectiveness of the proposed criteria. Full article

The Segment Anything Model 2 (SAM2) has achieved state-of-the-art performance in pixel-level object segmentation for both static and dynamic visual content. Its streaming memory architecture maintains spatial context across video sequences, yet struggles with long-term tracking due to its static inference framework. SAM 2’s fixed temporal window approach indiscriminately retains historical frames, failing to account for frame quality or dynamic motion patterns. This leads to error propagation and tracking instability in challenging scenarios involving fast-moving objects, partial occlusions, or crowded environments. To overcome these limitations, this paper proposes SAM2Plus, a zero-shot enhancement framework that integrates Kalman filter prediction, dynamic quality thresholds, and adaptive memory management. The Kalman filter models object motion using physical constraints to predict trajectories and dynamically refine segmentation states, mitigating positional drift during occlusions or velocity changes. Dynamic thresholds, combined with multi-criteria evaluation metrics (e.g., motion coherence, appearance consistency), prioritize high-quality frames while adaptively balancing confidence scores and temporal smoothness. This reduces ambiguities among similar objects in complex scenes. SAM2Plus further employs an optimized memory system that prunes outdated or low-confidence entries and retains temporally coherent context, ensuring constant computational resources even for infinitely long videos. Extensive experiments on two video object segmentation (VOS) benchmarks demonstrate SAM2Plus’s superiority over SAM 2. It achieves an average improvement of 1.0 in J&F metrics across all 24 direct comparisons, with gains exceeding 2.3 points on SA-V and LVOS datasets for long-term tracking. The method delivers real-time performance and strong generalization without fine-tuning or additional parameters, effectively addressing occlusion recovery and viewpoint changes. By unifying motion-aware physics-based prediction with spatial segmentation, SAM2Plus bridges the gap between static and dynamic reasoning, offering a scalable solution for real-world applications such as autonomous driving and surveillance systems. Full article

Many natural phenomena, such as physical, chemical, and biological processes, can be described using n-coupled nonlinearity anomalous subdiffusion systems. Furthermore, fractional differential equations are a useful tool for modeling practical problems in science because they allow for the incorporation of infinite memory through the consideration of previous states. This paper proposes numerical and analytical techniques for studying n-coupled fractional-order nonlinearity anomalous subdiffusion systems, including the construction of improved implicit difference methods and the discussion of stability and convergence using energy methods. The stability and convergence conditions are determined based on different implicit methods. The obtained conditions are related to the system dimension n. The effectiveness of the theoretical results is demonstrated using two numerical examples. Full article

This study introduces a new methodology for an Inference Index (InI) called the Inference Index In Testing Model Effectiveness methodology (INFINITE), aiming to evaluate the performance of Large Language Models (LLMs) in code generation tasks. The InI index provides a comprehensive assessment focusing on three key components: efficiency, consistency, and accuracy. This approach encapsulates time-based efficiency, response quality, and the stability of model outputs, offering a thorough understanding of LLM performance beyond traditional accuracy metrics. We apply this methodology to compare OpenAI’s GPT-4o (GPT), OpenAI-o1 pro (OAI1), and OpenAI-o3 mini-high (OAI3) in generating Python code for two tasks: a data-cleaning and statistical computation task and a Long Short-Term Memory (LSTM) model generation task for forecasting meteorological variables such as temperature, relative humidity, and wind speed. Our findings demonstrate that GPT outperforms OAI1 and performs comparably to OAI3 regarding accuracy and workflow efficiency. The study reveals that LLM-assisted code generation can produce results similar to expert-designed models with effective prompting and refinement. GPT’s performance advantage highlights the benefits of widespread use and user feedback. These findings contribute to advancing AI-assisted software development, providing a structured approach for evaluating LLMs in coding tasks and setting the groundwork for future studies on broader model comparisons and expanded assessment frameworks. Full article

This paper presents Boundary-Aware Concurrent Queue (BACQ), a high-performance queue designed for modern GPUs, which focuses on high concurrency in massively parallel environments. BACQ operates at the warp level, leveraging intra-warp locality to improve throughput. A key to BACQ’s design is its ability to replace conflicting accesses to shared data with independent accesses to private data. It uses a ticket-based system to ensure fair ordering of operations and supports infinite growth of the head and tail across its ring buffer. The leader thread of each warp coordinates enqueue and dequeue operations, broadcasting offsets for intra-warp synchronization. BACQ dynamically adjusts operation priorities based on the queue’s state, especially as it approaches boundary conditions such as overfilling the buffer. It also uses a virtual caching layer for intra-warp communication, reducing memory latency. Rigorous benchmarking results show that BACQ outperforms the BWD (Broker Queue Work Distributor), the fastest known GPU queue, by more than 2× while preserving FIFO semantics. The paper demonstrates BACQ’s superior performance through real-world empirical evaluations. Full article

In this article, we consider the dynamics of a viscoelastic plate equation with internal fractional damping, a nonlinear logarithmic source, and infinite memory effects. The existence of a local weak solution is shown effectively through the framework of semigroup theory. Furthermore, we show that the blow-up in finite time of the local solution may occur under specific conditions and is demonstrated within the development of a suitable Lyapunov functional. Our result offers an insight into the challenges presented by this class of equations and their relevance to physical systems. Full article

Nanoporous membranes are heterogeneous structures, with heterogeneity manifesting at the microscale. In examining particle transport through such media, it has been observed that this transport deviates from classical diffusion, as described by Fick’s second law. Moreover, the classical model is physically unsustainable, as it is non-causal and predicts an infinite speed of concentration perturbation propagation through a substantial medium. In this work, we have derived two causal models as extensions of Fick’s second law, where causality is linked to the effects of inertial memory in the nanoporous membrane. The results of the derived models have been compared with each other and with those obtained from the classical model. It has been demonstrated that both causal models, one with exponentially fading inertial memory and the other with power-law fading memory, predict that the concentration perturbation propagates as a damped wave, leading to an increased time required for the cumulative amount of molecules passing through the membrane to reach a steady state compared to the classical model. The power-law fading memory model predicts a longer time required to achieve a stationary state. These findings have significant implications for understanding cell physiology, developing drug delivery systems, and designing nanoporous membranes for various applications. Full article

The continuous Hopfield network (CHN) is a common recurrent neural network. The CHN tool can be used to solve a number of ranking and optimization problems, where the equilibrium states of the ordinary differential equation (ODE) related to the CHN give the solution to any given problem. Because of the non-local characteristic of the “infinite memory” effect, fractional-order (FO) systems have been proved to describe more accurately the behavior of real dynamical systems, compared to the model’s ODE. In this paper, a fractional-order variant of a Hopfield neural network is introduced to solve a Quadratic Knap Sac Problem (QKSP), namely the fractional CHN (FRAC-CHN). Firstly, the system is integrated with the quadratic method for fractional-order equations whose trajectories have shown erratic paths and jumps to other basin attractions. To avoid these drawbacks, a new algorithm for obtaining an equilibrium point for a CHN is introduced in this paper, namely the optimal fractional CHN (OPT-FRAC-CHN). This is a variable time-step method that converges to a good local minima in just a few iterations. Compared with the non-variable time-stepping CHN method, the optimal time-stepping CHN method (OPT-CHN) and the FRAC-CHN method, the OPT-FRAC-CHN method, produce the best local minima for random CHN instances and for the optimal feeding problem. Full article

We found that a second-order ideal memristor [whose state is the charge, i.e., $\mathit{x}=q$ in $\mathit{v}=\mathit{R}\left(\mathit{x},\mathit{i},\mathit{t}\right)\mathit{i}$] degenerates into a negative nonlinear resistor with an internal power source. After extending analytically and geographically the above local activity (experimentally verified by the two active higher-integral-order memristors extracted from the famous Hodgkin–Huxley circuit) to other higher-order circuit elements, we concluded that all higher-order passive memory circuit elements do not exist in nature and that the periodic table of the two-terminal passive ideal circuit elements can be dramatically reduced to a reduced table comprising only six passive elements: a resistor, inductor, capacitor, memristor, mem-inductor, and mem-capacitor. Such a bounded table answered an open question asked by Chua 40 years ago: Are there an infinite number of passive circuit elements in the world? Full article

Continual learning (CL) from infinite data streams has become a challenge for neural network models in real-world scenarios. Catastrophic forgetting of previous knowledge occurs in this learning setting, and existing supervised CL methods rely excessively on accurately labeled samples. However, the real-world data labels are usually misled by noise, which influences the CL agents and aggravates forgetting. To address this problem, we propose a method named noise-labeled online continual learning (NLOCL), which implements the online CL model with noise-labeled data streams. NLOCL uses an empirical replay strategy to retain crucial examples, separates data streams by small-loss criteria, and includes semi-supervised fine-tuning for labeled and unlabeled samples. Besides, NLOCL combines small loss with class diversity measures and eliminates online memory partitioning. Furthermore, we optimized the experience replay stage to enhance the model performance by retaining significant clean-labeled examples and carefully selecting suitable samples. In the experiment, we designed noise-labeled data streams by injecting noisy labels into multiple datasets and partitioning tasks to simulate infinite data streams realistically. The experimental results demonstrate the superior performance and robust learning capabilities of our proposed method. Full article

Glaucoma is a chronic eye condition that seriously impairs vision and requires early diagnosis and treatment. Automated detection techniques are essential for obtaining a timely diagnosis. In this paper, we propose a novel method for feature selection that integrates the cuckoo search algorithm with Caputo fractional order (CFO-CS) to enhance the performance of glaucoma classification. However, when using the infinite series, the Caputo definition has memory length truncation issues. Therefore, we suggest a fixed memory step and an adjustable term count for optimization. We conducted experiments integrating various feature extraction techniques, including histograms of oriented gradients (HOGs), local binary patterns (LBPs), and deep features from MobileNet and VGG19, to create a unified vector. We evaluate the informative features selected from the proposed method using the k-nearest neighbor. Furthermore, we use data augmentation to enhance the diversity and quantity of the training set. The proposed method enhances convergence speed and the attainment of optimal solutions during training. The results demonstrate superior performance on the test set, achieving 92.62% accuracy, 94.70% precision, 93.52% F1-Score, 92.98% specificity, 92.36% sensitivity, and 85.00% Matthew’s correlation coefficient. The results confirm the efficiency of the proposed method, rendering it a generalizable and applicable technique in ophthalmology. Full article

This research relies on several kinds of Volterra-type integral differential systems and their associated stability concerns under the impulsive effects of the Volterra integral terms at certain time instants. The dynamics are defined as delay-free dynamics contriobution together with the contributions of a finite set of constant point delay dynamics, plus a Volterra integral term of either a finite length or an infinite one with intrinsic memory. The global asymptotic stability is characterized via Krasovskii–Lyapuvov functionals by incorporating the impulsive effects of the Volterra-type terms together with the effects of the point delay dynamics. Full article

We consider a damped transmission problem in a bounded domain where the damping is effective in a neighborhood of a suitable subset of the boundary. Using the semigroup approach together with Hille–Yosida theorem, we prove the existence and uniqueness of global solution. Under suitable assumption on the geometrical conditions on the damping, we establish the exponential stability of the solution by introducing a suitable Lyapunov functional. Full article

To reduce computational load and memory consumption, multirate repetitive control (MRC) with downsampling rates provides a flexible and efficient design for proportional-integral multi-resonant repetitive control (PIMR-RC) systems for grid-tied inverters. However, in MRC systems, repetitive controllers with low sampling rates produce low delay periods, and integer-order phase lead compensation may cause undercompensation or overcompensation. These imprecise linear phase lead compensations may result in deteriorated control performance. To address these problems, based on an infinite impulse response (IIR) filter, a fractional-order phase lead proportional-integral multi-resonant multirate repetitive control (FPL-PIMR-MRC) is proposed for grid-tied inverters in this paper. The proposed method can provide a suitable fractional phase lead step to achieve a wide stability region, minor tracking errors, and low hardware costs. The IIR fractional-order lead filter design, stability analysis, and the step-by-step parameter tuning of the FPL-PIMR-MRC system are derived in detail. Finally, simulation performed confirms the feasibility and effectiveness of the proposed scheme. Full article