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27 pages, 2652 KB  
Article
SEER-PM: A Secure and Energy-Efficient Routing Protocol for Pipeline Monitoring Wireless Sensor Networks
by Rasha Hasan, Rafe Alasem, Ahmed Akl Mahmoud, Yazeed Alsarhan and Mahmud Mansour
Algorithms 2026, 19(6), 493; https://doi.org/10.3390/a19060493 (registering DOI) - 19 Jun 2026
Viewed by 448
Abstract
Oil and gas pipelines are critical infrastructures that require continuous and reliable monitoring to detect leaks, pressure anomalies, corrosion, and unauthorized activities. Wireless sensor networks (WSNs) have emerged as an effective solution for large-scale pipeline monitoring due to their low deployment cost and [...] Read more.
Oil and gas pipelines are critical infrastructures that require continuous and reliable monitoring to detect leaks, pressure anomalies, corrosion, and unauthorized activities. Wireless sensor networks (WSNs) have emerged as an effective solution for large-scale pipeline monitoring due to their low deployment cost and real-time sensing capabilities. However, the resource-constrained nature of sensor nodes and the open wireless communication environment expose pipeline monitoring systems to various routing attacks, for example, blackhole, sinkhole, selective forwarding, and false data injection attacks, while simultaneously demanding strict energy efficiency to prolong network lifetime. In this paper, we propose SEER-PM (Secure and Energy-Efficient Routing for Pipeline Monitoring): a novel protocol that integrates an Artificial neural network (ANN)-based trust mechanism with energy-aware routing metrics. SEER-PM dynamically evaluates node trustworthiness based on packet forwarding behavior, residual energy, and signal consistency. By training the ANN on historical behavioral data, the system accurately detects malicious nodes with high precision. Simulation results demonstrate that SEER-PM outperforms existing secure routing protocols (Sec-AODV and T-LEACH) in terms of packet delivery ratio (PDR) by 14%, detection rate by 9.5%, and network lifetime by 12% under heavy attack scenarios. The proposed protocol enhances the reliability, security, and sustainability of pipeline monitoring WSNs operating in harsh and remote environments. Full article
(This article belongs to the Section Combinatorial Optimization, Graph, and Network Algorithms)
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20 pages, 564 KB  
Article
A Line-Integral Representation of Gravitational Lensing by Black Holes
by İzzet Sakallı
Universe 2026, 12(6), 180; https://doi.org/10.3390/universe12060180 - 16 Jun 2026
Viewed by 99
Abstract
We present a path-based curvature representation of the gravitational bending of light in black-hole (BH) spacetimes. The bending angle is written as a one-dimensional line integral of the optical Gaussian curvature Kopt along the photon trajectory, weighted by a geometric kernel [...] Read more.
We present a path-based curvature representation of the gravitational bending of light in black-hole (BH) spacetimes. The bending angle is written as a one-dimensional line integral of the optical Gaussian curvature Kopt along the photon trajectory, weighted by a geometric kernel W(r,b). This representation sits within the Gibbons–Werner Gauss–Bonnet (GB) optical-geometry family rather than alongside it: the kernel is fixed by a co-area reduction of the GB surface integral along an undeflected reference path, and the single new computational object is the resulting radial integral together with its cumulative, directly plottable reading of how the deflection builds up along the ray. With the lever-arm choice W=r2b2, the integral reproduces α^=4M/b for every static, asymptotically flat metric (Theorem 1) and evaluates in closed form for Schwarzschild, Reissner–Nordström (RN), and equatorial Kerr. The representation becomes reliable at a large impact parameter; at the small impact parameters relevant to horizon-scale imaging, it is not numerically competitive with the standard expansions, a limitation we quantify. Beyond leading order the kernel must import information from the bent geodesic, after which the scheme reconstructs the known perturbative series; the second-order mismatch in the lever-arm result therefore measures, rather than hides, the deformation of the photon path away from the straight-line reference. Finite source–observer distances enter through the Ono–Ishihara–Asada (OIA) construction, and a winding-sum continuation outlines the route toward the strong-deflection regime, whose closed-form reduction is left to future work. Full article
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35 pages, 513 KB  
Article
Entropy Bounds and Capacity-Limited Information Flow in Black-Hole Evaporation
by Arkady Bolotin
Entropy 2026, 28(6), 671; https://doi.org/10.3390/e28060671 - 11 Jun 2026
Viewed by 251
Abstract
Black-hole evaporation exhibits a range of characteristic entropic phenomena, including Hawking thermality, monotonically increasing radiation entropy in semiclassical treatments, and the Page-curve behavior required by unitarity. These features are accompanied by long-standing puzzles concerning information loss, entanglement growth, and the transfer of correlations [...] Read more.
Black-hole evaporation exhibits a range of characteristic entropic phenomena, including Hawking thermality, monotonically increasing radiation entropy in semiclassical treatments, and the Page-curve behavior required by unitarity. These features are accompanied by long-standing puzzles concerning information loss, entanglement growth, and the transfer of correlations between a black hole and its radiation. In this work we present an information-theoretic analysis of these phenomena based on a discrete causal model in which entropy evolution is governed by a competition between the growth of accessible degrees of freedom and a finite capacity for transmitting correlations across a boundary. Radiation is generated through stochastic sampling of interior degrees of freedom, while entanglement between interior and radiation subsystems is constrained by a boundary defined purely at the level of causal connectivity. Within this setting, radiation entropy increases at early times, reaches a maximum when boundary capacity becomes saturated, and decreases thereafter as additional emissions fail to carry independent correlations, yielding Page-curve behavior consistent with unitary evaporation. This capacity-limited mechanism does not rely on semiclassical spacetime geometry or quantum extremal surface constructions and instead follows directly from entropy bounds and information-flow constraints. By isolating the role of finite correlation capacity, the analysis provides a unified entropy-based perspective on black-hole evaporation, complementing semiclassical approaches while remaining applicable in discrete or non-geometric settings. Full article
(This article belongs to the Section Astrophysics, Cosmology, and Black Holes)
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9 pages, 263 KB  
Communication
A Single-Scale Regular Black-Hole Background for Black-Hole Quantum Information
by Lorenzo Albanese
Quantum Rep. 2026, 8(2), 53; https://doi.org/10.3390/quantum8020053 - 11 Jun 2026
Viewed by 145
Abstract
Regular black-hole models replace the Schwarzschild singularity with a finite inner core, thereby removing the geometric endpoint at which the classical spacetime description breaks down. This issue is relevant to black-hole quantum information, since a singular interior prevents a regular effective description of [...] Read more.
Regular black-hole models replace the Schwarzschild singularity with a finite inner core, thereby removing the geometric endpoint at which the classical spacetime description breaks down. This issue is relevant to black-hole quantum information, since a singular interior prevents a regular effective description of interior degrees of freedom and horizon correlations. In this work, the regular black-hole geometry introduced by Dymnikova is used as a compact, single-scale effective background for black-hole quantum information considerations. The aim is not to propose a new regular metric but to clarify how an established finite-core geometry can support a nonsingular description of the Schwarzschild interior at the effective level. The geometry preserves the Schwarzschild asymptotic limit while replacing the divergent central region with a finite de Sitter-like core. The curvature invariants remain finite, and the effective source admits an anisotropic-fluid interpretation whose central limit is isotropic and vacuum-like. This use therefore provides a minimal geometric setting, rather than a newly proposed metric solution, for discussing nonsingular black-hole interiors. It does not establish unitary evaporation, information recovery, dynamical stability, or a microscopic quantum-gravity mechanism. Instead, it identifies a finite-curvature spacetime framework in which questions concerning interior quantum degrees of freedom and horizon entanglement can be formulated without encountering a curvature singularity. Full article
(This article belongs to the Special Issue Exclusive Quantum Reports Feature Papers for 2026–2027)
28 pages, 2770 KB  
Article
Schwarzschild–Letelier Spacetime Surrounded by a King Dark Matter Halo: Geodesic, Shadow, and Thermodynamics
by Faizuddin Ahmed and Edilberto O. Silva
Universe 2026, 12(6), 174; https://doi.org/10.3390/universe12060174 - 11 Jun 2026
Viewed by 149
Abstract
We investigate a static and spherically symmetric Schwarzschild–Letelier Black Hole immersed in a King Dark Matter Halo and analyze how the combined effects of the cloud of strings and the dark-matter environment modify the spacetime geometry, particle dynamics, and thermodynamic behavior of the [...] Read more.
We investigate a static and spherically symmetric Schwarzschild–Letelier Black Hole immersed in a King Dark Matter Halo and analyze how the combined effects of the cloud of strings and the dark-matter environment modify the spacetime geometry, particle dynamics, and thermodynamic behavior of the black hole. Particular attention is devoted to the motion of both massless photons and massive test particles in this black hole background. In the geodesic analysis, we derive the effective potential and study the properties of circular photon orbits, the associated black-hole shadow radius, and the innermost stable circular orbit (ISCO), highlighting the role played by the cloud of strings parameter and the King dark-matter halo parameters in shifting the orbital structure relative to the standard Schwarzschild case. To further characterize the spacetime from a topological perspective, we investigate the unstable circular null orbit using a normalized vector field constructed within the framework of Duan’s ϕ-Mapping Topological Current Theory. Through this method, we identify the corresponding topological charge and examine the relation between the photon sphere and the underlying topological structure of the black-hole configuration. In addition, we explore the thermodynamic properties of the system by computing the Hawking temperature, entropy, Helmholtz free energy, and heat capacity, thereby analyzing the black hole’s local and global thermodynamic stability. The influence of the surrounding dark-matter halo and cloud of strings on the phase structure and thermal behavior is discussed in detail. We further study the thermodynamic topology of the system via the off-shell free-energy formalism, which provides insight into possible thermodynamic phase transitions and the topological classification of black-hole states. Our analysis demonstrates that the combined effects of the cloud of strings and the King dark-matter halo significantly modify the horizon structure, geodesic dynamics, shadow characteristics, and thermodynamic properties of the black hole when compared with the standard Schwarzschild solution. Full article
(This article belongs to the Special Issue 10th Anniversary of Universe: Galaxies and Their Black Holes)
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31 pages, 3305 KB  
Article
A Synchronized Spin Model for Black-Hole Accretion Systems
by Masahiro Morikawa and Akika Nakamichi
Entropy 2026, 28(6), 663; https://doi.org/10.3390/e28060663 - 10 Jun 2026
Viewed by 191
Abstract
Black-hole accretion systems exhibit a characteristic coexistence of activities: broad-band X-ray variability, hot coronae, wide-angle winds, and both steady and discrete jets. This coexistence suggests a persistently time-dependent magnetic background in which noisy fluctuations and explosive release are both essential. In this paper, [...] Read more.
Black-hole accretion systems exhibit a characteristic coexistence of activities: broad-band X-ray variability, hot coronae, wide-angle winds, and both steady and discrete jets. This coexistence suggests a persistently time-dependent magnetic background in which noisy fluctuations and explosive release are both essential. In this paper, we connect them all to the storage, organization, and intermittent reconnection-mediated release of magnetic energy, and we propose a Synchronized Spin Model (SSM) in which multiple local dynamos in a rotating accretion flow are represented as interacting macro-spins. Their synchronization, partial synchronization, excursion, and reversal define a compact set of collective variables that organize both timing statistics and large-scale morphology. In this picture, multiscale magnetic reconnection converts stored magnetic energy into coronal heating, flares, intermittent outflows, and discrete jet activity, while the same synchronization dynamics produce amplitude modulation and demodulation, providing a route to 1/f-like variability, rms–flux/Taylor-like scaling, and approximately log-normal statistics of the demodulated envelope. We further argue that, although the continuous flux distribution in black-hole systems is more naturally discussed in multiplicative or log-normal terms, broader event-catalog statistics remain useful for describing suitably defined burst hierarchies, particularly by analogy with solar and stellar flare systems. The hard/soft cycle of X-ray binaries is then interpreted as motion through magnetic state space. Full article
(This article belongs to the Section Astrophysics, Cosmology, and Black Holes)
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13 pages, 578 KB  
Article
Hawking Atmosphere of Anti-de Sitter Black Holes
by A. F. Cardona and C. Molina
Universe 2026, 12(5), 141; https://doi.org/10.3390/universe12050141 - 9 May 2026
Viewed by 257
Abstract
This work investigates the semiclassical evolution of the Hawking atmosphere surrounding evaporating, spherically symmetric anti-de Sitter (adS) black holes. We model the evaporation process within a dynamical framework, treating the emission of Hawking radiation as a quantum tunneling process through the black-hole horizon. [...] Read more.
This work investigates the semiclassical evolution of the Hawking atmosphere surrounding evaporating, spherically symmetric anti-de Sitter (adS) black holes. We model the evaporation process within a dynamical framework, treating the emission of Hawking radiation as a quantum tunneling process through the black-hole horizon. Using the Parikh–Wilczek tunneling method, we incorporate backreaction effects, with the emission probability being linked to the resulting change in the Bekenstein–Hawking entropy of the black hole. This probability is then used to compute the time-dependent luminosity of the system, revealing significant deviations from ideal blackbody behavior, particularly for small adS black holes. For these objects, the luminosity does not increase with temperature due to strong mass variations during evaporation. To complement this microscopic approach, we compute the renormalized energy–momentum tensor for a quantum field propagating in the Vaidya-adS geometry modelling the evaporation process. Together, these approaches clarify the interplay between geometry, quantum fields, and thermodynamics in shaping the Hawking atmosphere and the evaporation dynamics of black holes in asymptotically adS spacetimes. Full article
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17 pages, 6467 KB  
Article
The No-Hair Theorems at Work in the Tidal Disruption Event AT2020afhd
by Lorenzo Iorio
Universe 2026, 12(5), 120; https://doi.org/10.3390/universe12050120 - 23 Apr 2026
Viewed by 918
Abstract
Recently, the coprecession of both the accretion disk and the jet formed following the tidal disruption event associated with the optical transient AT2020afhd, driven by a supermassive black hole of almost ten million solar masses, were independently measured in both the X and [...] Read more.
Recently, the coprecession of both the accretion disk and the jet formed following the tidal disruption event associated with the optical transient AT2020afhd, driven by a supermassive black hole of almost ten million solar masses, were independently measured in both the X and radio bands, respectively, showing a periodicity of nearly 20 days over about 300 days. An analytical model of the general relativistic gravitomagnetic Lense-Thirring precession of the effective orbit of a fictitious test particle revolving about a spinning primary can explain the observed precessional features. It yields allowed regions in the system’s parameter space which, as far as the hole’s dimensionless spin parameter is concerned, are essentially in agreement with those obtained in the literature with general relativistic magnetohydrodynamic simulations. The present analytical approach can be extended to include the precession due to the hole’s quadrupole mass moment as well. It breaks the degeneracy in the allowed regions occurring for negative and positive values of the spin parameter when only the Lense-Thirring effect is considered. The best estimate for the hole’s mass yields the range 0.185–0.215 for the dimensionless spin parameter. Using the same strategy with the gravitomagnetic frequency for an extended disk of finite size with a parameterized power-law mass density yields to distinct, generally non-overlapping allowed regions for each value of the power-law index adopted. Some of the assumptions on which this work is based are critically examined. Full article
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16 pages, 311 KB  
Article
Volume-Law Entropy as a Mesoscopic Anomaly
by Lamine Bougueroua
Entropy 2026, 28(4), 444; https://doi.org/10.3390/e28040444 - 14 Apr 2026
Viewed by 437
Abstract
Area-law entropy appears in local quantum ground states, low-temperature Gibbs states, and gravitational physics, whereas classical thermodynamics is formulated with volume-extensive entropy. We propose a coarse-grained information-theoretic framework, based on an effective free-energy functional combining Fisher information, a potential term, and Shannon entropy, [...] Read more.
Area-law entropy appears in local quantum ground states, low-temperature Gibbs states, and gravitational physics, whereas classical thermodynamics is formulated with volume-extensive entropy. We propose a coarse-grained information-theoretic framework, based on an effective free-energy functional combining Fisher information, a potential term, and Shannon entropy, that organises these different scalings within a single thermodynamic picture. Comparing localisation costs, external stabilisation, and gravitational self-interaction at the level of scaling reveals three regimes. At microscopic scales, locality and low-temperature coherence enforce area-type entropy scaling. At intermediate scales, volume-law entropy emerges as an effective regime sustained by non-gravitational confinement or external support; in the absence of such support, volume-extensive entropy does not by itself define an intrinsically stable equilibrium. At large scales dominated by gravitational self-interaction, a reduced scaling analysis identifies area-type behaviour as the distinguished infrared scaling, consistent with black-hole thermodynamics and with macroscopic universality requirements. The framework clarifies the limited domain of classical extensivity and offers a unified coarse-grained perspective on the recurrence of area-law scaling across quantum and gravitational settings. Full article
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28 pages, 2765 KB  
Article
Machine Learning-Based Approach for Malicious Node Security and Trust Provision in 5G-Enabled VANET
by Samuel Kofi Erskine
AI 2026, 7(4), 136; https://doi.org/10.3390/ai7040136 - 9 Apr 2026
Viewed by 646
Abstract
This research utilizes machine learning (ML)-based malicious node detection techniques to effectively incorporate security and trustworthiness into fifth-generation (5G) and Vehicular Ad hoc Network (VANET) systems, in contrast to traditional methods that do not employ modern techniques. VANET may be vulnerable due to [...] Read more.
This research utilizes machine learning (ML)-based malicious node detection techniques to effectively incorporate security and trustworthiness into fifth-generation (5G) and Vehicular Ad hoc Network (VANET) systems, in contrast to traditional methods that do not employ modern techniques. VANET may be vulnerable due to vehicle mobility, network openness, and the conventional network architecture. Therefore, security and trust management using modern methodologies, such as ML approaches, is essential for 5G-enabled VANET integration, which has become a paramount concern. And due to limitations imposed by traditional security methods, which are unable to identify malicious nodes in VANET completely, processing delays are longer. Therefore, this research utilizes the VANET malicious-node dataset designed for real-time malicious node/attack detection in VANET. The proposed ML methodology uses a Random Forest (RF) and an optimized ensemble ML classifier, such as XGBoost and LightGBM, which require a security and trustworthiness solution provided by the RF Trust Extended Authentication (TEA). We simulate vehicle-to-vehicle (V2V) and vehicle-to-infrastructure (V2I) mobility, communication behaviors, and trust metrics to assess the accuracy of malicious-vehicular-node features for the identification and detection of attacks, including False Injection, Sybil, blackhole, and Denial-of-Service (DoS). The proposed ML methodology also identifies these attack patterns, providing a realistic dataset for Intelligent Transportation System (ITS) research. In contrast, traditional VANET methods do not. We compared the performance of the proposed ML method with other literature-standard ML and RF methods using metrics such as accuracy, confusion matrices, and precision, Recall, and F1-score to measure effectiveness. In our proposed machine learning (ML) method, we achieve 99% accuracy in classifying MVN and predicting both attack, including False Injection, Sybil, blackhole, and Denial-of-Service (DoS), and benign classes, with precision, recall, and F1-score of 100% each, and establish a trustworthiness score of 100%, Whilst the standard models, such as other VANET methods achieved an accuracy of only 95%, with precision, recall, and F1-score of 98%, without a confusion matrix to confirm the model’s performance. Full article
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15 pages, 377 KB  
Article
Planar Black Holes and Entanglement Entropy in Analog Gravity Models
by Neven Bilic and Tobias Zingg
Entropy 2026, 28(3), 345; https://doi.org/10.3390/e28030345 - 19 Mar 2026
Viewed by 598
Abstract
Via constructing an explicit Lagrangian for which the perturbation equations are analogs of a scalar field propagating in a planar black-hole space–time, it is found that all planar black holes conformal to a Painlevé–Gullstrand-type line element can be realized as analog metrics. We [...] Read more.
Via constructing an explicit Lagrangian for which the perturbation equations are analogs of a scalar field propagating in a planar black-hole space–time, it is found that all planar black holes conformal to a Painlevé–Gullstrand-type line element can be realized as analog metrics. We also introduce the concept of holographic entanglement entropy for planar black-hole space–times. This is valid for an arbitrary choice of conformal and blackening factor, thereby vastly extending the number of known examples of explicitly known analog metrics. Full article
(This article belongs to the Special Issue Coarse and Fine-Grained Aspects of Gravitational Entropy)
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25 pages, 3362 KB  
Article
Adaptive Clustering and Machine-Learning-Based DoS Intrusion Detection in MANETs
by Hwanseok Yang
Appl. Sci. 2026, 16(6), 2723; https://doi.org/10.3390/app16062723 - 12 Mar 2026
Viewed by 468
Abstract
Mobile ad hoc networks (MANETs) are highly vulnerable to denial-of-service (DoS) attacks because their decentralized operation, rapidly changing topology, and constrained node resources limit the use of heavyweight security mechanisms. This paper presents an Adaptive Clustering and Random-Forest-based Intrusion Detection System (ACRF-IDS), a [...] Read more.
Mobile ad hoc networks (MANETs) are highly vulnerable to denial-of-service (DoS) attacks because their decentralized operation, rapidly changing topology, and constrained node resources limit the use of heavyweight security mechanisms. This paper presents an Adaptive Clustering and Random-Forest-based Intrusion Detection System (ACRF-IDS), a lightweight intrusion detection framework that combines mobility-aware adaptive clustering with supervised learning to detect network-layer DoS behaviors. Cluster heads are elected using a multi-metric utility (residual energy, link stability, and mobility) to stabilize observations under node movement. Within fixed monitoring windows, cluster heads aggregate routing-, forwarding-, and energy-related features and classify nodes using a Random Forest model; a temporal voting scheme further suppresses transient mobility-induced alarms. Using ns-2.35 simulations with Ad hoc On-Demand Distance Vector (AODV) and both flooding and blackhole DoS scenarios, ACRF-IDS is compared with (i) a static clustering-based threshold IDS, (ii) a non-clustered Support Vector Machine (SVM)-based IDS, and (iii) AIFAODV, which specializes in flooding. Across the evaluated network sizes (4–50 nodes), the proposed method achieves a higher detection rate and F1-score while maintaining a lower false positive rate than the baseline techniques. We additionally quantify network-level impact using PDR, throughput, and routing overhead, showing that ACRF-IDS improves availability under DoS while adding bounded overhead. Future work will extend the evaluation to more diverse attack behaviors and validate the approach in real-world MANET testbeds. Full article
(This article belongs to the Section Computing and Artificial Intelligence)
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20 pages, 581 KB  
Article
Population–Coherence Routes to Purity in Page-Type Models of Black-Hole Evaporation
by José J. Gil
Entropy 2026, 28(3), 263; https://doi.org/10.3390/e28030263 - 27 Feb 2026
Viewed by 531
Abstract
We revisit the black-hole information problem from the viewpoint of a population–coherence decomposition of density-matrix purity. Building on a previously developed formalism for n-dimensional density matrices, we characterize each state by a normalized global purity index and two complementary indices, which quantify [...] Read more.
We revisit the black-hole information problem from the viewpoint of a population–coherence decomposition of density-matrix purity. Building on a previously developed formalism for n-dimensional density matrices, we characterize each state by a normalized global purity index and two complementary indices, which quantify the contributions of level populations and coherences. This yields a simple quadratic relation and a geometric representation in a “population–coherence plane”, where different routes to purity can be distinguished. In the two-level case, we construct explicit families of states with identical spectra and global purity but opposite internal structure, realizing population-dominated and coherence-dominated routes. We then apply this framework to a standard Page-type evaporation model without an explicit Hamiltonian, in which a black hole and its Hawking radiation form a bipartite pure state with varying Hilbert-space dimensions. Using known results for typical reduced states in large dimensions, we analyze the behavior of population and coherence components of purity along the evaporation process. Under the physically motivated requirement that, in this energy-free setting, the radiation populations remain nearly uniform in the chosen basis, we show that the late-time recovery of purity must be coherence-dominated: the global purity of the radiation approaches unity while the population index stays small and the coherence index carries essentially all the purity. Full article
(This article belongs to the Special Issue Coarse and Fine-Grained Aspects of Gravitational Entropy)
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17 pages, 662 KB  
Article
Attention-Based Transformer Encoder for Secure Wireless Sensor Operations
by Mohammad H. Baniata, Chayut Bunterngchit, Laith H. Baniata, Malek A. Almomani and Muhannad Tahboush
Future Internet 2026, 18(3), 119; https://doi.org/10.3390/fi18030119 - 27 Feb 2026
Viewed by 634
Abstract
Wireless sensor networks (WSNs) are integral components of smart environments. These allow monitoring and communication to take place autonomously across distributed sensor nodes. Nevertheless, they suffer from constrained resources that make them susceptible to routine-layer attacks. These specifically involve blackhole, flooding, selective forwarding [...] Read more.
Wireless sensor networks (WSNs) are integral components of smart environments. These allow monitoring and communication to take place autonomously across distributed sensor nodes. Nevertheless, they suffer from constrained resources that make them susceptible to routine-layer attacks. These specifically involve blackhole, flooding, selective forwarding attack traffic and normal traffic. The conventional machine learning and deep learning methods employed are effective in catering to these attacks, yet they have generalization issues when the network conditions are dynamic. The models are generally trained on the local features that make them more dependable and less interpretable. To overcome these issues, this paper proposes an attention-driven transformer encoder for tabular WSN traffic, designed for robust and interpretable intrusion detection in WSNs. The model represents the WSN features as sequential tokens and employs multi-head self-attention to capture global and local dependencies among sensor attributes and employs a multi-head self-attention for capturing the local and global dependencies among the sensor attributes. The framework integrated several components, including normalization, chi-square-based feature selection, and positional embedding. These are followed by multi-layer transformer encoding blocks for the feature fusion and subsequent classification. The framework has been evaluated on the publicly available WSN dataset. Results have been shown to attain an accuracy of 99.37%, which makes it outperform the traditional deep learning baseline models. The comparative analysis has shown the model to be superior in terms of generalization and reduced convergence time. It further offers enhanced interpretability that makes it a good fit to be deployed in real-world scenarios where resources can be constrained. Full article
(This article belongs to the Special Issue Anomaly and Intrusion Detection in Networks)
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18 pages, 2527 KB  
Article
Chaotic Motion of Strings in a Quantum-Corrected AdS Reissner–Nordström Black Hole
by Kai Li, Da-Zhu Ma and Zhen-Meng Xu
Universe 2026, 12(2), 57; https://doi.org/10.3390/universe12020057 - 20 Feb 2026
Viewed by 575
Abstract
It has been reported that quantum correction modifies the topological charges of Anti-de-Sitter Reissner–Nordström (AdS-RN) black holes in Kiselev spacetime, yielding new perspectives on topological classification. This leads us to focus on how quantum corrections and other parameters collectively influence the long-term dynamic [...] Read more.
It has been reported that quantum correction modifies the topological charges of Anti-de-Sitter Reissner–Nordström (AdS-RN) black holes in Kiselev spacetime, yielding new perspectives on topological classification. This leads us to focus on how quantum corrections and other parameters collectively influence the long-term dynamic evolution of strings. First, we analytically examine whether the strings’ motion violates the Maldacena–Shenker–Stanford (MSS) bound. Then, we employ numerical integration to study the influence of various parameters on string chaotic dynamics. Our results demonstrate that the quantum-correction parameter a, the normalization factor c, and black-hole charge Q significantly influence chaotic behavior and the violation of the MSS bound. In particular, as a increases, the system undergoes an order–chaos–order transition, whereas an increase in c or a decrease in Q drives the system from order to chaos. Full article
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