Search Results (72)

With the increasing demands for autonomy and coverage efficiency in tasks such as security patrol and post-disaster exploration using mobile robots, achieving random, efficient, and complete coverage path planning has become a critical challenge. Traditional chaotic path planning methods, while capable of generating unpredictable trajectories, still have limitations in terms of randomness strength, traversal uniformity, and convergence coverage. To address this, this study proposes a complete-coverage random path planning method based on a novel four-dimensional fractal-fractional multi-scroll chaotic system. The main contributions of this research are as follows: First, by introducing additional state variables and fractal-fractional operators into the classical Chen system, a fractal-fractional chaotic system with a multi-scroll attractor structure is constructed. The output of this system is then mapped into robot angular velocity commands to achieve area coverage in unknown environments. Key findings include: the novel chaotic system possesses two positive Lyapunov exponents; Spectral Entropy (SE) and Complexity (CO) analyses indicate that when parameter B is fixed and the fractional order α increases, the dynamic complexity of the system significantly rises; in a 50 × 50 grid environment, the robot driven by this system achieved a coverage rate of 98.88% within 10,000 iterations, outperforming methods based on Lorenz, Chua systems, and random walks; ablation experiments further demonstrate that the combined effects of the fractal order β, fractional order α, and multi-scroll nonlinear terms are key to enhancing system complexity and coverage performance. The significance of this study lies in that it not only provides new ideas for constructing complex chaotic systems but also offers a reliable theoretical foundation and practical solution for mobile robots to perform efficient, random, and high-coverage autonomous inspection tasks in unknown regions. Full article

In multicellular organisms, the development of diverse cell types relies on stem cell differentiation through a hierarchy of fate decisions. Pluripotent stem cells first give rise to multipotent progenitors, which then undergo successive fate decisions to generate specialized cells within their respective lineages. Waddington used the metaphor of a marble rolling down a hill through hierarchically branching valleys that represent the various states of cell differentiation, with the final valleys at the bottom symbolizing the specialized cells. Mathematically, specialized cells are seen as stable attractors in a complex dynamical system that displays multistability. However, this framework does not necessarily describe the hierarchical branching of stem cell differentiation. In a recent study, we addressed this issue by assuming that each gene regulatory network (GRN) consists of hierarchically coupled gene subnetworks (modules) that are self-regulated due to epigenetic factors. Each module was modeled using the normal form of relevant bifurcations. Overall, this approach captures both multistability and hierarchical branching in differentiation. Here, the normal forms of bifurcations are replaced by realistic biochemical switches. Theoretical analysis and numerical simulations demonstrated that hierarchically coupled biochemical switches can depict the three fundamental aspects of Waddington’s epigenetic landscape: (a) differentiation trajectories exhibit hierarchical branching, (b) attractors are robust to perturbations (homeorhesis), and (c) the proportions of specialized cells are preserved. It was further shown that appropriate external interventions can induce either probabilistic cellular reprogramming or highly predictable reprogramming outcomes. The incorporation of biochemical switches, rather than purely abstract normal forms, can contribute to more biologically grounded mathematical models of stem cell differentiation. This work also highlights the importance of normal forms for qualitatively understanding cell state dynamics and for building realistic modular GRNs. Full article

The Hypernetic Law of Experience (HLE) generalizes Ashby’s neglected Law of Experience from determinate machines to stochastic, gradient-driven adaptive systems. The HLE characterizes a persistent tendency of adaptive systems exposed to sustained directional experience: internal variety is progressively consumed, and system trajectories converge toward increasingly narrow regions of state space, even when local transitions remain probabilistic. We formalize this contraction pressure using the Rebis equation, a discrete-time variance-contraction dynamic that relates optimization pressure and novelty injection to the evolution of internal diversity. Through cross-domain comparative analysis, we show that HLE-consistent geometry appears in biological evolution, recursive model collapse in machine learning, economic cycles, neural plasticity and habituation, linguistic convergence, and institutional lock-in. In these domains, excessive variety consumption is associated with brittle attractors and heightened vulnerability under distributional shift. We further show that biological systems employ countervailing mechanisms—such as sexual recombination, mutational plasticity, sleep-driven renormalization, and variance-preserving neuromodulation—that mitigate, but do not eliminate, the contraction pressure described by the HLE. We conclude that the HLE and the Rebis equation provide a systems-level diagnostic for identifying and explaining optimization-induced fragility and for informing the design of regulators, AI architectures, and institutions that remain viable under drift. Full article

High-precision autonomous localization remains a critical challenge for intelligent mining vehicles in GNSS-denied and unstructured coal mine roadways, where traditional odometry-based methods suffer from severe cumulative drift and perceptual aliasing. Inspired by the synergy between mammalian visual cues and cognitive neural mechanisms, this paper proposes a robust biomimetic localization framework that integrates multi-source perception with a prior cognitive map. The core contributions are three-fold: First, a semantic-enhanced biomimetic localization method is developed, leveraging roadway sign data as absolute spatial anchors to suppress long-distance cumulative errors. Second, an optimized head direction (HD) cell model is formulated by incorporating a speed balance factor, kinematic constraints, and a drift correction influence factor, significantly improving the precision of angular perception. Third, boundary-adaptive and sign-based semantic constraint terms are integrated into a continuous attractor network (CAN)-based path integration model, effectively preventing trajectory deviation into non-navigable regions. Comprehensive evaluations conducted in large-scale underground scenarios demonstrate that the proposed framework consistently outperforms conventional IMU-odometry fusion, representative 3D SLAM solutions, and baseline biomimetic algorithms. By effectively integrating semantic landmarks as spatial anchors, the system exhibits superior resilience against cumulative drift, maintaining high localization precision where standard methods typically diverge. The results confirm that our approach significantly enhances both trajectory consistency and heading stability across extensive distances, validating its robustness and scalability in handling the inherent complexities of unstructured coal mine environments for enhanced intrinsic safety. Full article

Research shows that neurodegenerative processes do not develop from a single “broken” biochemistry process; rather, they develop when a complex multi-physics environment gradually loses its ability to stabilize the neuron via a collective action between the protein, ion, field and fluid dynamics of the neuron. The use of new technologies such as quantum-informed molecular simulation (QIMS), dielectric nanoscale mapping, fluid dynamics of the cell, and imaging of perivascular flow are allowing researchers to understand how the collective interactions among proteins, membranes and their electrical properties, along with fluid dynamics within the cell, form a highly interconnected dynamic system. These systems require fine control over the energetic, mechanical and electrical interactions that maintain their coherence. When there is even a small change in the protein conformations, the electric properties of the membrane, or the viscosity of the cell’s interior, it can cause changes in the high dimensional space in which the system operates to lose some of its stabilizing curvature and become prone to instability well before structural pathologies become apparent. AI has allowed researchers to create digital twin models using combined physical data from multiple scales and to predict the trajectory of the neural system toward instability by identifying signs of early deformation. Preliminary studies suggest that deviations in the ergodicity of metabolic–mechanical systems, contraction of dissipative bandwidth, and fragmentation of attractor basins could be indicators of vulnerability. This study will attempt to combine all of the current research into a cohesive view of the role of progressive loss of multi-physics coherence in neurodegenerative disease. Through integration of protein energetics, electrodynamic drift, and hydrodynamic irregularities, as well as predictive modeling utilizing AI, the authors will provide mechanistic insights and discuss potential approaches to early detection, targeted stabilization, and precision-guided interventions based on neurophysics. Full article

Background/Objectives: Glioblastoma (GBM) exhibits heterogeneous, nonlinear invasion patterns that challenge conventional modeling and radiomic prediction. Most deep learning approaches describe the morphology but rarely capture the dynamical stability of tumor evolution. We propose an AI framework that approximates a latent attractor landscape of GBM morphodynamics—stable basins in a continuous manifold that are consistent with reproducible morphologic regimes. Methods: Multimodal MRI scans from BraTS 2020 (n = 494) were standardized and embedded with a 3D autoencoder to obtain 128-D latent representations. Unsupervised clustering identified latent basins (“attractors”). A neural ordinary differential equation (neural-ODE) approximated latent dynamics. All dynamics were inferred from cross-sectional population variability rather than longitudinal follow-up, serving as a proof-of-concept approximation of morphologic continuity. Voxel-level perturbation quantified local morphodynamic sensitivity, and proof-of-concept control was explored by adding small inputs to the neural-ODE using both a deterministic controller and a reinforcement learning agent based on soft actor–critic (SAC). Survival analyses (Kaplan–Meier, log-rank, ridge-regularized Cox) assessed associations with outcomes. Results: The learned latent manifold was smooth and clinically organized. Three dominant attractor basins were identified with significant survival stratification (χ² = 31.8, p = 1.3 × 10⁻⁷) in the static model. Dynamic attractor basins derived from neural-ODE endpoints showed modest and non-significant survival differences, confirming that these dynamic labels primarily encode the morphodynamic structure rather than fixed prognostic strata. Dynamic basins inferred from neural-ODE flows were not independently prognostic, indicating that the inferred morphodynamic field captures geometric organization rather than additional clinical risk information. The latent stability index showed a weak but borderline significant negative association with survival (ρ = −0.13 [−0.26, −0.01]; p = 0.0499). In multivariable Cox models, age remained the dominant covariate (HR = 1.30 [1.16–1.45]; p = 5 × 10⁻⁶), with overall C-indices of 0.61–0.64. Voxel-level sensitivity maps highlighted enhancing rims and peri-necrotic interfaces as influential regions. In simulation, deterministic control redirected trajectories toward lower-risk basins (≈57% success; ≈96% terminal distance reduction), while a soft actor–critic (SAC) agent produced smoother trajectories and modest additional reductions in terminal distance, albeit without matching the deterministic controller’s success rate. The learned attractor classes were internally consistent and clinically distinct. Conclusions: Learning a latent attractor landscape links generative AI, dynamical systems theory, and clinical outcomes in GBM. Although limited by the cross-sectional nature of BraTS and modest prognostic gains beyond age, these results provide a mechanistic, controllable framework for tumor morphology in which inferred dynamic attractor-like flows describe latent organization rather than a clinically predictive temporal model, motivating prospective radiogenomic validation and adaptive therapy studies. Full article

Background: Glioblastoma (GBM) is among the most aggressive and morphologically heterogeneous brain tumors. Beyond static imaging biomarkers, its structural organization can be viewed as a nonlinear dynamical system. Characterizing morphodynamic attractors within such a system may reveal latent stability patterns of morphological change and potential indicators of morphodynamic organization. Methods: We analyzed 494 subjects from the multi-institutional BraTS 2020 dataset using a fully automated computational pipeline. Each multimodal MRI volume was encoded into a 16-dimensional latent space using a 3D convolutional autoencoder. Synthetic morphological trajectories, generated through bidirectional growth–shrinkage transformations of tumor masks, enabled training of a contraction-regularized Neural Ordinary Differential Equation (Neural ODE) to model continuous-time latent morphodynamics. Morphological complexity was quantified using fractal dimension (DF), and local dynamical stability was measured via a Lyapunov-like exponent (λ). Robustness analyses assessed the stability of DF–λ regimes under multi-scale perturbations, synthetic-order reversal (directionality; sign-aware comparison) and stochastic noise, including cross-generator generalization against a time-shuffled negative control. Results: The DF–λ morphodynamic phase map revealed three characteristic regimes: (1) stable morphodynamics (λ < 0), associated with compact, smoother boundaries; (2) metastable dynamics (λ ≈ 0), reflecting weakly stable or transitional behavior; and (3) unstable or chaotic dynamics (λ > 0), associated with divergent latent trajectories. Latent-space flow fields exhibited contraction-induced attractor-like basins and smoothly diverging directions. Kernel-density estimation of DF–λ distributions revealed a prominent population cluster within the metastable regime, characterized by moderate-to-high geometric irregularity (DF ≈ 1.85–2.00) and near-neutral dynamical stability (λ ≈ −0.02 to +0.01). Exploratory clinical overlays showed that fractal dimension exhibited a modest negative association with survival, whereas λ did not correlate with clinical outcome, suggesting that the two descriptors capture complementary and clinically distinct aspects of tumor morphology. Conclusions: Glioblastoma morphology can be represented as a continuous dynamical process within a learned latent manifold. Combining Neural ODE–based dynamics, fractal morphometry, and Lyapunov stability provides a principled framework for dynamic radiomics, offering interpretable morphodynamic descriptors that bridge fractal geometry, nonlinear dynamics, and deep learning. Because BraTS is cross-sectional and the synthetic step index does not represent biological time, any clinical interpretation is hypothesis-generating; validation in longitudinal and covariate-rich cohorts is required before prognostic or treatment-monitoring use. The resulting DF–λ morphodynamic map provides a hypothesis-generating morphodynamic representation that should be evaluated in covariate-rich and longitudinal cohorts before any prognostic or treatment-monitoring use. Full article

Cognitive deterioration and the transition to neurodegenerative disease does not develop through simple, linear regression; it develops as rapid and global transitions from one state to another within the neural network. Developing understanding and control over these events is among the largest tasks facing contemporary neuroscience. This paper will discuss a conceptual reframing of cognitive decline as a transitional phase of the functional state of complex neural networks resulting from the intertwining of molecular degradation, vascular dysfunction and systemic disarray. The paper will integrate the latest findings that have demonstrated how the disruptive changes in glymphatic clearance mechanisms, aquaporin-4 polarity, venous output, and neuroimmune signaling increasingly correlate with the neurophysiologic homeostasis landscape, ultimately leading to the destabilization of the network attraction sites of memory, consciousness, and cognitive resilience. Furthermore, the destabilizing processes are exacerbated by epigenetic silencing; neurovascular decoupling; remodeling of the extracellular matrix; and metabolic collapse that result in accelerating the trajectory of neural circuits towards the pathological tipping point of various neurodegenerative diseases including Alzheimer’s disease; Parkinson’s disease; traumatic brain injury; and intracranial hypertension. New paradigms in systems neuroscience (connectomics; network neuroscience; and critical transition theory) provide an intellectual toolkit to describe and predict these state changes at the systems level. With artificial intelligence and machine learning combined with single cell multi-omics; radiogenomic profiling; and digital twin modeling, the predictive biomarkers and early warnings of impending collapse of the system are beginning to emerge. In terms of therapeutic intervention, the possibility of reprogramming the circuitry of the brain into stable attractor states using precision neurointervention (CRISPR-based neural circuit reprogramming; RNA guided modulation of transcription; lineage switching of glia to neurons; and adaptive neuromodulation) represents an opportunity to prevent further progression of neurodegenerative disease. The paper will address the ethical and regulatory implications of this revolutionary technology, e.g., algorithmic transparency; genomic and other structural safety; and equity of access to advanced neurointervention. We do not intend to present a list of the many vertices through which the mechanisms listed above instigate, exacerbate, or maintain the neurodegenerative disease state. Instead, we aim to present a unified model where the phenomena of molecular pathology; circuit behavior; and computational intelligence converge in describing cognitive decline as a translatable change of state, rather than an irreversible succumbing to degeneration. Thus, we provide a framework for precision neurointervention, regenerative brain medicine, and adaptive intervention, to modulate the trajectory of neurodegeneration. Full article

We review some aspects of accretion disks physics, spacetime photon shell and photon orbits, related to retrograde (counter-rotating) motion in Kerr black hole (BH) spacetimes. In this brief review, we examine the counter-rotating components of the Kerr BH shadow boundary, under the influence of counter-rotating accretion tori, accreting flows and proto-jets (open critical funnels of matter, associated with the tori) orbiting around the central BH. We also analyze the redshifted emission arising from counter-rotating structures. Regions of the shadows and photon shell are constrained in their dependence of the BH spin and observational angle. The effects of the counter-rotating structures on these are proven to be typical of the fast-spinning BHs, and accordingly can be observed only in the restricted classes of the Kerr BH spacetimes. This review is intended as a concise guide to the main properties of counter-rotating fluxes and counter-rotating disks in relation to the photon shell and the BH shadow boundary. Our findings may serve as the basis for different theoretical frameworks describing counter-rotating accretion flows with observable imprints manifesting at the BH shadow boundary. The results can eventually enable the distinction of counter-rotating fluxes through their observable imprints, contributing to constraints on both the BH spin and the structure of counter-rotating accretion disks. In particular, photon trajectories and their impact parameters can manifest in the morphology of the BH shadow. Such features, when accessible through high-resolution imaging and spectral or polarization measurements, could provide a direct avenue for testing different theoretical models on accretion disk dynamics and their BH attractors. Full article

This study introduces a novel robotic control paradigm, “chaos redirection,” which utilizes a single chaotic Hopfield Neural Network (HNN). We introduce “false attractors” synthetic trajectories created by applying controlled temporal shifts to the HNN’s state variables. This method allows a single chaotic source to be sculpted into distinct, task-specific behaviors for autonomous robots. We apply this framework to three applications: area cleaning, systematic search, and security patrol. Quantitative, statistically validated analysis demonstrates the successful generation of functionally distinct behaviors, including high-frequency, confined re-visitation for security patrols; maximized exploratory efficiency for search tasks; and high-entropy, non-repetitive paths for thorough cleaning. Our findings establish this as a robust and computationally efficient framework for applications requiring unpredictable, yet structured, behavior. Full article

Chaotic systems, governed by deterministic nonlinear equations yet exhibiting highly complex and unpredictable behaviors, have emerged as valuable tools at the intersection of mathematics, engineering, and information security. This paper presents a comparative study of the Lorenz and Rössler systems, focusing on their dynamic complexity and statistical independence—two critical properties for applications in chaos-based cryptography. By integrating techniques from nonlinear dynamics (e.g., Lyapunov exponents, KS entropy, Kaplan–Yorke dimension) and statistical testing (e.g., chi-square and Gaussian transformation-based independence tests), we provide a quantitative framework to evaluate the pseudo-randomness potential of chaotic trajectories. Our results show that the Lorenz system offers faster convergence to chaos and superior statistical independence over time, making it more suitable for rapid encryption schemes. In contrast, the Rössler system provides complementary insights due to its simpler attractor and longer memory. These findings contribute to a multidisciplinary methodology for selecting and optimizing chaotic systems in secure communication and signal processing contexts. Full article

Neurodegeneration is increasingly recognized not as a linear trajectory of protein accumulation, but as a multidimensional collapse of biological organization—spanning intracellular signaling, transcriptional identity, proteostatic integrity, organelle communication, and network-level computation. This review intends to synthesize emerging frameworks that reposition neurodegenerative diseases (ND) as progressive breakdowns of interpretive cellular logic, rather than mere terminal consequences of protein aggregation or synaptic attrition. The discussion aims to provide a detailed mapping of how critical signaling pathways—including PI3K–AKT–mTOR, MAPK, Wnt/β-catenin, and integrated stress response cascades—undergo spatial and temporal disintegration. Special attention is directed toward the roles of RNA-binding proteins (e.g., TDP-43, FUS, ELAVL2), m6A epitranscriptomic modifiers (METTL3, YTHDF1, IGF2BP1), and non-canonical post-translational modifications (SUMOylation, crotonylation) in disrupting translation fidelity, proteostasis, and subcellular targeting. At the organelle level, the review seeks to highlight how the failure of ribosome-associated quality control (RQC), autophagosome–lysosome fusion machinery (STX17, SNAP29), and mitochondrial import/export systems (TIM/TOM complexes) generates cumulative stress and impairs neuronal triage. These dysfunctions are compounded by mitochondrial protease overload (LONP1, CLPP), UPR maladaptation, and phase-transitioned stress granules that sequester nucleocytoplasmic transport proteins and ribosomal subunits, especially in ALS and FTD contexts. Synaptic disassembly is treated not only as a downstream event, but as an early tipping point, driven by impaired PSD scaffolding, aberrant endosomal recycling (Rab5, Rab11), complement-mediated pruning (C1q/C3–CR3 axis), and excitatory–inhibitory imbalance linked to parvalbumin interneuron decay. Using insights from single-cell and spatial transcriptomics, the review illustrates how regional vulnerability to proteostatic and metabolic stress converges with signaling noise to produce entropic attractor collapse within core networks such as the DMN, SN, and FPCN. By framing neurodegeneration as an active loss of cellular and network “meaning-making”—a collapse of coordinated signal interpretation, triage prioritization, and adaptive response—the review aims to support a more integrative conceptual model. In this context, therapeutic direction may shift from damage containment toward restoring high-dimensional neuronal agency, via strategies that include the following elements: reprogrammable proteome-targeting agents (e.g., PROTACs), engineered autophagy adaptors, CRISPR-based BDNF enhancers, mitochondrial gatekeeping stabilizers, and glial-exosome neuroengineering. This synthesis intends to offer a translational scaffold for viewing neurodegeneration as not only a disorder of accumulation but as a systems-level failure of cellular reasoning—a perspective that may inform future efforts in resilience-based intervention and precision neurorestoration. Full article

This study introduces a memristive Hopfield neural network (M-HNN) model to investigate electromagnetic radiation impacts on neural dynamics in complex electromagnetic environments. The proposed framework integrates a magnetic flux-controlled memristor into a three-neuron Hopfield architecture, revealing significant alterations in network dynamics through comprehensive nonlinear analysis. Numerical investigations demonstrate that memristor-induced electromagnetic effects induce distinctive phenomena, including coexisting attractors, transient chaotic states, symmetric bifurcation diagrams and attractor structures, and constant chaos. The proposed system can generate more than 12 different attractors and extends the chaotic region. Compared with the chaotic range of the baseline Hopfield neural network (HNN), the expansion amplitude reaches 933%. Dynamic characteristics are systematically examined using phase trajectory analysis, bifurcation mapping, and Lyapunov exponent quantification. Experimental validation via a DSP-based hardware implementation confirms the model’s operational feasibility and consistency with numerical predictions, establishing a reliable platform for electromagnetic–neural interaction studies. Full article

In this study, we investigate the nonlinear dynamical behavior of a one-dimensional linear piecewise-smooth discontinuous (LPSD) map with a negative slope, motivated by its occurrence in systems exhibiting discontinuities, such as power electronic converters. The objective of the proposed research is to develop an analytical approach. Analytical conditions are derived for the existence of stable period-1 and period-2 orbits within the third quadrant of the parameter space defined by slope coefficients $a<0$ and $b<0$. The coexistence of multiple attractors is demonstrated. We also show that a novel class of orbits exists in which both points lie entirely in either the left or right domain. These orbits are shown to eventually exhibit periodic behavior, and a closed-form expression is derived to compute the number of iterations required for a trajectory to converge to such orbits. This method also enhances the ease of analyzing system stability by mapping the state–variable dynamics using a non-smooth discontinuous map. The analytical findings are validated using bifurcation diagrams, cobweb plots, and basin of attraction visualizations. Full article

In this article, fourth-order systems of ordinary differential equations are studied. These systems are of a special form, which is used in modeling gene regulatory networks. The nonlinear part depends on the regulatory matrix W, which describes the interrelation between network elements. The behavior of solutions heavily depends on this matrix and other parameters. We research the evolution of trajectories. Two approaches are employed for this. The first approach combines a fourth-order system of two two-dimensional systems and then introduces specific perturbations. This results in a system with periodic attractors that may exhibit sensitive dependence on initial conditions. The second approach involves extending a previously identified system with chaotic solution behavior to a fourth-order system. By skillfully scanning multiple parameters, this method can produce four-dimensional chaotic systems. Full article