Search Results (127)

This study introduces a novel Fuzzy Piecewise Fractional Derivative (FPFD) framework to enhance epidemiological modeling, specifically for the multi-phasic co-infection dynamics of Omicron and malaria. We address the limitations of traditional models by incorporating two key realities. First, we use fuzzy set theory to manage the inherent uncertainty in biological parameters. Second, we employ piecewise fractional operators to capture the dynamic, phase-dependent nature of epidemics. The framework utilizes a fuzzy classical derivative for initial memoryless spread and transitions to a fuzzy Atangana–Baleanu–Caputo (ABC) fractional derivative to capture post-intervention memory effects. We establish the mathematical rigor of the FPFD model through proofs of positivity, boundedness, and stability of equilibrium points, including the basic reproductive number (R0). A hybrid numerical scheme, combining Fuzzy Runge–Kutta and Fuzzy Fractional Adams–Bashforth–Moulton algorithms, is developed for solving the system. Simulations show that the framework successfully models dynamic shifts while propagating uncertainty. This provides forecasts that are more robust and practical, directly informing public health interventions. Full article

Unmanned aerial vehicles (UAVs) often face significant challenges in trajectory tracking within complex dynamic environments, where uncertainties, external disturbances, and nonlinear dynamics hinder accurate and stable control. To address this issue, a bio-inspired deep reinforcement learning (DRL) algorithm is proposed, integrating behavior cloning (BC) and long short-term memory (LSTM) networks. This method can achieve autonomous learning of high-precision control policy without establishing an accurate system dynamics model. Motivated by the memory and prediction functions of biological neural systems, an LSTM module is embedded into the policy network of the Twin Delayed Deep Deterministic Policy Gradient (TD3) algorithm. This structure captures temporal state patterns more effectively, enhancing adaptability to trajectory variations and resilience to delays or disturbances. Compared to memoryless networks, the LSTM-based design better replicates biological time-series processing, improving tracking stability and accuracy. In addition, behavior cloning is employed to pre-train the DRL policy using expert demonstrations, mimicking the way animals learn from observation. This biomimetic plausible initialization accelerates convergence by reducing inefficient early-stage exploration. By combining offline imitation with online learning, the TD3-LSTM-BC framework balances expert guidance and adaptive optimization, analogous to innate and experience-based learning in nature. Simulation experimental results confirm the superior robustness and tracking accuracy of the proposed method, demonstrating its potential as a control solution for autonomous UAVs. Full article

The zero-error capacity of discrete memoryless channels (DMCs), introduced by Shannon, is a fundamental concept in information theory with significant operational relevance, particularly in settings where even a single transmission error is unacceptable. Despite its importance, no general closed-form expression or algorithm is known for computing this capacity. In this work, we investigate the computability-theoretic boundaries of the zero-error capacity and establish several fundamental limitations. Our main result shows that the zero-error capacity of noisy channels is not Banach–Mazur-computable and therefore is also not Borel–Turing-computable. This provides a strong form of non-computability that goes beyond classical undecidability, capturing the inherent discontinuity of the capacity function. As a further contribution, we analyze the deep connections between (i) the zero-error capacity of DMCs, (ii) the Shannon capacity of graphs, and (iii) Ahlswede’s operational characterization via the maximum-error capacity of 0–1 arbitrarily varying channels (AVCs). We prove that key semi-decidability questions are equivalent for all three capacities, thus unifying these problems into a common algorithmic framework. While the computability status of the Shannon capacity of graphs remains unresolved, our equivalence result clarifies what makes this problem so challenging and identifies the logical barriers that must be overcome to resolve it. Together, these results chart the computational landscape of zero-error information theory and provide a foundation for further investigations into the algorithmic intractability of exact capacity computations. Full article

The quantum Mpemba effect refers to the counterintuitive phenomenon in which a system initially farther from equilibrium relaxes faster than one prepared closer to it. Several mechanisms have been identified in open quantum systems to explain this behavior, including the strong Mpemba effect, non-Markovian memory, and initial system–reservoir entanglement. Here, we unveil a distinct mechanism rooted in the non-normal nature of the Liouvillian superoperator in Markovian dynamics. When the Liouvillian’s eigenmodes are non-orthogonal, transient interference between decaying modes can induce anomalous early-time behavior—such as delayed thermalization or transient freezing—even though asymptotic decay rates remain unchanged. This differs fundamentally from strong Mpemba effects, which hinge on suppressed overlap with slow-decaying modes. We demonstrate this mechanism using a waveguide quantum electrodynamics model, where quantum emitters interact with the photonic modes of a one-dimensional waveguide. The directional and radiative nature of these couplings naturally introduces non-normality into the system’s dynamics. As a result, certain initial states—despite being closer to equilibrium—can exhibit slower relaxation at short times. This work reveals a previously unexplored and universal source of Mpemba-like behavior in memoryless quantum systems, expanding the theoretical framework for anomalous relaxation and opening new avenues for control in engineered quantum platforms. Full article

This study introduces a novel approach for analyzing the dynamic interplay among key economic indicators by employing a Caputo Fractional Fisher Information framework combined with partial information decomposition. By integrating fractional derivatives into traditional Fisher Information metrics, our methodology captures long-range memory effects that govern the evolution of monetary policy, credit risk, market volatility, and inflation, represented by INTEREST, CDS, VIX, CPI, and PPI, respectively. We perform a comprehensive comparative analysis using rolling-window estimates to generate Caputo Fractional Fisher Information values at different fractional orders alongside the memoryless Ordinary Fisher Information. Subsequent correlation, cross-correlation, and transfer entropy analyses reveal how historical dependencies influence both unique and synergistic information flows between indices. Notably, our partial information decomposition results demonstrate that deep historical interactions significantly amplify the informational contribution of each indicator, particularly under long-memory conditions, while the Ordinary Fisher Information framework tends to underestimate these synergistic effects. The findings underscore the importance of incorporating memory effects into information-theoretic models to better understand the intricate, time-dependent relationships among financial indicators, with significant implications for forecasting and policy analysis. Full article

The magnetic field of the Sun is formed by the mechanism of hydromagnetic dynamo. In this mechanism, the flow of the conducting medium (plasma) of the convective zone generates a magnetic field, and this field corrects the flow using the Lorentz force, creating feedback. An important role in dynamo is played by memory (hereditary), when a change in the current state of a physical system depends on its states in the past. Taking these effects into account may provide a more accurate description of the generation of the Sun’s magnetic field. This paper generalizes classical dynamo models by including hereditary feedback effects. The feedback parameters such as the presence or absence of delay, delay duration, and memory duration are additional degrees of freedom. This can provide more diverse dynamic modes compared to classical memoryless models. The proposed model is based on the kinematic dynamo problem, where the large-scale velocity field is predetermined. The field in the model is represented as a linear combination of two stationary predetermined modes with time-dependent amplitudes. For these amplitudes, equations are obtained based on the kinematic dynamo equations. The model includes two generators of a large-scale magnetic field. In the first, the field is generated due to large-scale flow of the medium. The second generator has a turbulent nature; in it, generation occurs due to the nonlinear interaction of small-scale pulsations of the magnetic field and velocity. Memory in the system under study is implemented in the form of feedback distributed over all past states of the system. The feedback is represented by an integral term of the type of convolution of a quadratic form of phase variables with a kernel of a fairly general form. The quadratic form models the influence of the Lorentz force. This integral term describes the turbulent generator quenching. Mathematically, this model is written with a system of integro-differential equations for amplitudes of modes. The model was applied to a real space object, namely, the solar dynamo. The model representation of the Sun’s velocity field was constructed based on helioseismological data. Free field decay modes were chosen as components of the magnetic field. The work considered cases when hereditary feedback with the system arose instantly or with a delay. The simulation results showed that the model under study reproduces dynamic modes characteristic of the solar dynamo, if there is a delay in the feedback. Full article

Understanding how past factors influence ion channel kinetics is essential for understanding complex phenomena in cardiac electrophysiology, such as early afterdepolarizations (EADs), which are abnormal depolarizations during the action potential plateau associated with life-threatening arrhythmias. We developed a mathematical framework that extends Hodgkin-Huxley type equations with gamma Mittag-Leffler distributed delays, using tools from Fractional Calculus. Traditional memoryless two-variable models fail to reproduce EADs. Our approach modifies FitzHugh-Nagumo, Mitchell-Schaeffer, and Karma cardiac models, enabling the generation of EADs in each of them. We analyze the emergence of these oscillations by discussing the fractional parameters and the mean and variance of the memory kernels. Stability observations are also presented. Full article

The notion of $\delta$-mutual information between non-stochastic uncertain variables is introduced as a generalization of Nair’s non-stochastic information functional. Several properties of this new quantity are illustrated and used in a communication setting to show that the largest $\delta$-mutual information between received and transmitted codewords over $ϵ$-noise channels equals the $(ϵ,\delta )$-capacity. This notion of capacity generalizes the Kolmogorov $ϵ$-capacity to packing sets of overlap at most $\delta$ and is a variation of a previous definition proposed by one of the authors. Results are then extended to more general noise models, including non-stochastic, memoryless, and stationary channels. The presented theory admits the possibility of decoding errors, as in classical information theory, while retaining the worst-case, non-stochastic character of Kolmogorov’s approach. Full article

This study proposes a hybrid PSO-EDO algorithm, integrating Particle Swarm Optimization (PSO) and the Exponential Distribution Optimizer (EDO) for efficient and accurate estimation of soil property parameters. The proposed algorithm combines the strengths of Standard PSO (SPSO) and the Exponential Distribution Optimizer (EDO). Three key innovations are introduced: (1) SPM chaotic mapping enhances initial population diversity; (2) dynamic inertia weight balances global exploration and local exploitation; (3) the memoryless property of EDO improves escape capability from local optima. Benchmark tests demonstrate that PSO-EDO achieves near-theoretical optimal convergence errors (mean error ≤ 10⁻¹⁶ for unimodal functions such as F1 and F2) and reduces the computation time by 14.5% compared to EDO. For multimodal functions (e.g., F3), PSO-EDO significantly outperforms PSO-WOA (Particle Swarm Optimization-Whale Optimization Algorithm) with a 22.3% reduction in error. Simulation experiments further validate its engineering practicality: in soil parameter estimation, PSO-EDO completes 1000 iterations in just 1.95 s, with key parameters (e.g., sinkage coefficient n) controlled within a 7.32% error margin. This provides an efficient solution for real-time traversability assessment of autonomous vehicles on soft terrains. Full article

We consider the problem of successive-refinement coding for lossy compression of individual sequences, namely, compression in two stages, where in the first stage, a coarse description at a relatively low rate is sent from the encoder to the decoder, and in the second stage, an additional coding rate is allocated in order to refine the description and thereby improve the reproduction. Our main result is in establishing outer bounds (converse theorems) for the rate region where we limit the encoders to be finite-state machines in the spirit of Ziv and Lempel’s 1978 model. The matching achievability scheme is conceptually straightforward. We also consider the more general multiple description coding problem on a similar footing and propose achievability schemes that are analogous to the well-known El Gamal–Cover and the Zhang–Berger achievability schemes of memoryless sources and additive distortion measures. Full article

One of the fundamental problems of information theory, since its foundation by C. Shannon, has been the computation of the capacity of a discrete memoryless channel, a quantity expressing the maximum rate at which information can travel through the channel. In this paper, we investigate the properties of a novel approach to computing the capacity, based on a continuous-time dynamical system. Interestingly, the proposed dynamical system can be regarded as a continuous-time version of the classical Blahut–Arimoto algorithm, and we can prove that the former shares with the latter an exponential rate of convergence if certain conditions are met. Moreover, a circuit design is presented to implement the dynamics, hence enabling analog computation to estimate the capacity. Full article

Heated pipe flow is widely used in thermal engineering applications, but the presence of buoyancy force can cause intermittency, or multiple flow states at the same parameter values. Such changes in the flow lead to substantial changes in its heat transfer properties and thereby significant changes in the axial temperature gradient. We therefore introduce a model that features a time-dependent background axial temperature gradient, and consider two temperature boundary conditions—fixed temperature difference and fixed boundary heat flux. Direct numerical simulations (DNSs) are based on the pseudo-spectral framework, and good agreement is achieved between present numerical results and experimental results. The code extends Openpipeflow and is available at the website. The effect of the axially periodic domain on flow dynamics and heat transfer is examined, using pipes of length $L=5D$ and $L=25D$. Provided that the flow is fully turbulent, results show close agreement for the mean flow and temperature profiles, and only slight differences in root-mean-square fluctuations. When the flow shows spatial intermittency, heat transfer tends to be overestimated using a short pipe, as shear turbulence fills the domain. This is particularly important when shear turbulence starts to be suppressed at intermediate buoyancy numbers. Finally, at such intermediate buoyancy numbers, we confirm that the decay of localised shear turbulence in the heated pipe flow follows a memoryless process, similar to that in isothermal flow. While isothermal flow then laminarises, convective turbulence in the heated flow can intermittently trigger bursts of shear-like turbulence. Full article

In the identification (ID) scheme proposed by Ahlswede and Dueck, the receiver’s goal is simply to verify whether a specific message of interest was sent. Unlike Shannon’s transmission codes, which aim for message decoding, ID codes for a discrete memoryless channel (DMC) are far more efficient; their size grows doubly exponentially with the blocklength when randomized encoding is used. This indicates that when the receiver’s objective does not require decoding, the ID paradigm is significantly more efficient than traditional Shannon transmission in terms of both energy consumption and hardware complexity. Further benefits of ID schemes can be realized by leveraging additional resources such as feedback. In this work, we address the problem of joint ID and channel state estimation over a DMC with independent and identically distributed (i.i.d.) state sequences. State estimation functions as the sensing mechanism of the model. Specifically, the sender transmits an ID message over the DMC while simultaneously estimating the channel state through strictly causal observations of the channel output. Importantly, the random channel state is unknown to both the sender and the receiver. For this system model, we present a complete characterization of the ID capacity–distortion function. Full article

We consider a basic joint communication and sensing setup comprising a transmitter, a receiver and a sensor. The transmitter sends a codeword to the receiver through a discrete memoryless channel, and the receiver is interested in decoding the transmitted codeword. At the same time, the sensor picks up a noisy version of the transmitted codeword through one of two possible discrete memoryless channels. The sensor knows the codeword and wishes to discriminate between the two possible channels, i.e., to identify the channel that has generated the output given the input. We study the trade-off between communication and sensing in the asymptotic regime, captured in terms of the channel coding rate against the two types of discrimination error exponents. We characterize the optimal trade-off between the rate and the exponents for general discrete memoryless channels with an input cost constraint. Full article

Unsupervised anomaly detection is a challenging computer vision task, in which 2D-based anomaly detection methods have been extensively studied. However, multimodal anomaly detection based on RGB images and 3D point clouds requires further investigation. The existing methods are mainly inspired by memory bank-based methods commonly used in 2D-based anomaly detection, which may cost extra memory for storing multimodal features. In the present study, a novel memoryless method MDSS is proposed for multimodal anomaly detection, which employs a lightweight student–teacher network and a signed distance function to learn from RGB images and 3D point clouds, respectively, and complements the anomaly information from the two modalities. Specifically, a student–teacher network is trained with normal RGB images and masks generated from point clouds by a dynamic loss, and the anomaly score map could be obtained from the discrepancy between the output of student and teacher. Furthermore, the signed distance function learns from normal point clouds to predict the signed distances between points and surfaces, and the obtained signed distances are used to generate an anomaly score map. Subsequently, the anomaly score maps are aligned to generate the final anomaly score map for detection. The experimental results indicate that MDSS is comparable but more stable than SOTA methods and, furthermore, performs better than other baseline methods. Full article