Search Results (2,488)

Herein, a highly selective and sensitive fluorescent sensing system is developed for the accurate quantitative determination of γ-Hexachlorocyclohexane (γ-HCH, Lindane). With carboxyl-functionalized CdSe/ZnS core–shell quantum dots (QDs) as the substrate, 3-Aminophenylboronic acid (3-APBA) is covalently conjugated onto the quantum dot surface via an amidation reaction. Systematic characterizations are used to confirm the successful fabrication of the CdSe/ZnS-COOH@3-APBA fluorescent probe, which exhibits excellent luminescence properties and superior colloidal dispersion stability. Under optimal experimental conditions, an increased γ-HCH concentration induces gradual attenuation of the probe fluorescence intensity. A favorable linear correlation is achieved within 10–140 nM, and the limit of detection is 2.62 nM. Mechanistic studies reveal that γ-HCH binds to 3-APBA on the probe surface via halogen bonding to form non-fluorescent ground-state association complexes, thereby triggering static quenching of the probe. This method can effectively distinguish α-, β-, and δ-hexachlorocyclohexane isomers. With the merits of simple operation, high sensitivity, excellent stability, and strong anti-interference capability, it provides a new strategy for the rapid screening and accurate quantification of γ-HCH residues in environmental and food matrices. Full article

Electric-field measurement in emerging power systems requires compatibility with multiple frequency bands, high field strengths, and complex electromagnetic environments. This study proposes a low-frequency AC electric-field amplitude reconstructed method based on the nitrogen-vacancy (NV) center in diamond. A Hahn–echo sequence converts the electric-field-induced quantum phase accumulation into NV fluorescence variations, and the field amplitude is retrieved through time-domain fitting and frequency-domain feature extraction. A parallel-plate electric-field generator was first calibrated using a standard electro-optic probe, followed by measurements at 2500 Hz. With the electro-optic probe result as the reference, the reconstructed electric-field amplitudes showed good quantitative agreement in the moderate-field range, with a best single-point absolute deviation of 0.0219 kV/m, while larger deviations were observed at the lower and higher ends of the tested amplitude range. By adjusting the Hahn–echo sequence to match different field periods, amplitudes at 1500 Hz and 2000 Hz were also successfully retrieved. The results demonstrate that the method is applicable to narrowband AC electric fields at known frequencies within a certain range, supporting an experimental basis for applying quantum sensing technology to power-equipment condition monitoring and measurements in complex electromagnetic environments. Full article

Entropy has evolved from a secondary thermodynamic property (Clausius, 1865) to a potentially fundamental organizing structure of physical reality, particularly through its gravitational manifestation in the Bekenstein–Hawking formula. This article systematically reviews four theoretical developments (2015–2024) that test this hypothesis using analytical methods from quantum information theory, holographic duality, and quantum gravity. First, we examine how the quantum island formula (Equation (¹)) resolves the black hole information paradox by demonstrating that fine-grained entropy depends on global causal structure rather than local degrees of freedom. Second, we analyze the Complexity = Volume and Complexity = Action conjectures, showing that computational complexity encodes post-thermalization dynamics on exponentially long timescales, with predicted maximum complexity $C_{max}\sim e^{S_{\mathrm{BH}}}$ testable in SYK simulations. Third, we examine the scope and limitations of three gravity frameworks (AdS/CFT holography, emergent gravity, loop quantum gravity) in addressing entropy’s role in initial conditions and extract their distinct observational signatures for 2025–2035 experiments. Fourth, we explore entropy–motion duality through mixed metric signatures; while the correspondence $\beta \leftrightarrow it$ is suggestive, its full physical interpretation remains conjectural outside semiclassical and toy-model contexts. We articulate quantum entropic relationalism as an epistemological framework wherein entropy constitutes an objective relational structural property encoding physical relations without substantial reducibility. This synthesis suggests spacetime emerges from quantum entanglement substrates, with testability prospects via gravitational interferometry (LISA, Einstein Telescope), quantum simulators, and cosmological observations (Cosmic Microwave Background (CMB)-S4, LiteBIRD) anticipated by 2035. Full article

To explore the emerging role of natural ligands, specifically coumarin and curcumin, and their coordination with the transition metals ruthenium (Ru) and iridium (Ir) as photosensitizers (PSs) in photodynamic therapy (PDT) for cancer. This highlights the integration of natural compounds and transition metals to overcome limitations in photophysical properties, hypoxia tolerance, and clinical translation. Regarding PDT oncology, this examines an immunological effect on Ru/Ir complexes and natural ligand–metal hybrids. They induce immunogenic cell death (ICD) through reactive oxygen species (ROS) generation, calreticulin exposure, extracellular ATP release, and HMGB1 secretion. These damage-associated molecular patterns act as “danger signals” to recruit dendritic cells, prime CD8⁺ cytotoxic T-cells, and establish systemic antitumor immunity. This study compares natural ligand–metal complexes with conventional Ru(II)/Ir(III) complexes and clinical PSs to assess their translational potential as immune-activating agents in PDT oncology, as well as focusing on the integration of nanotechnology with natural ligand–metal complexes to enhance delivery, biocompatibility, and clinical translation. A narrative review was conducted of the literature published between 2010 and 2025 across multiple electronic databases, including WanFang Data, PubMed, ScienceDirect, Scopus, Web of Science, Springer Link, SciFinder, and CNKI, without language restrictions. Studies focusing on coumarin, curcumin, Ru(II), Ir(III), and PDT were analyzed. Extracted data included chemical structures, absorption and emission spectra, singlet oxygen yields, biological activities, and therapeutic outcomes. Comparative evaluation was performed between free natural ligands, their Ru(II)/Ir(III) complexes, and nanodelivery systems to assess efficacy, biocompatibility, and translational potential. Coumarin and curcumin exhibited intrinsic antioxidant, anti-inflammatory, and anticancer properties but were limited by short absorption/emission ranges, poor photostability, and low singlet oxygen yields, restricting preclinical application. Coordination with Ru(II) and Ir(III) significantly enhanced intersystem crossing, extended absorption into the near-infrared region, and improved singlet oxygen quantum yields (Φ_Δ up to ~0.78). These complexes demonstrated potent photocytotoxicity under normoxia and hypoxia, achieving IC₅₀ values in the nanomolar range, which indicated organelle-specific targeting (mitochondria, lysosomes, ER), induced ICD, and synergized with checkpoint blockade. Nanocarrier encapsulation further improved solubility and tumor selectivity, and reduced systemic toxicity. Coumarin- and curcumin-based Ru/Ir complexes represent promising next-generation or immune-activating PDT agents by combining natural pharmacological activity with superior photophysical performance. The ability to generate reactive oxygen species under hypoxia and achieve multimodal therapeutic effects positions them as strong candidates for clinical translation. Clinical approval of natural ligand–Ru/Ir complexes depends on rigorous safety, pharmacokinetic, and nanodelivery validation, but these complexes clearly extend PDT beyond local cytotoxicity toward durable immune protection. Future research should prioritize ligand engineering, nanotechnology integration, and translational models to bridge preclinical promise with safe and effective clinical applications. Full article

The universal operator-growth hypothesis (OGH) states that, in a closed chaotic system, the Lanczos coefficients grow linearly, $b_n\simeq \alpha n$. We ask how this structure is modified when the system is coupled to a Markovian environment, so that the generator becomes non-Hermitian. Applying the Arnoldi recursion to the vectorized Lindbladian in the infinite-temperature Wightman inner product, we organize the resulting pair of growth rates ${\alpha }_{\mathbb{C}}\equiv {\alpha }_R+i{\alpha }_I$—defined as effective slopes of the sub-diagonal and diagonal Arnoldi coefficients over a pre-registered fit window—around two statements whose logical status we delimit precisely. First, whenever the dissipator acts as $\mathcal{D}=-2\gamma \widehat{G}$ with $\widehat{G}$, a Hermitian grading (all dephasing-type baths), the diagonal obeys the identity $\mathrm{Re}{a}_n=-2\gamma {⟨\widehat{G}⟩}_n$: the imaginary rate measures how fast the growing operator accumulates weight in the dissipation channels. Second, we prove a conditional parity theorem: if the Hamiltonian, jump operators, and seeds can be made simultaneously real in some basis (an antiunitary condition), then $b_n$ is even, and $\mathrm{Re}{a}_n$ is odd in $\gamma$ exactly, so ${\alpha }_R$ is renormalized only at $O\left({\gamma }^2\right)$, and ${\alpha }_I=2{\kappa }_0\gamma$ follows from closed-system data alone. We exhibit a one-qubit Lindbladian that satisfies the often-assumed generator symmetry ${\mathcal{G}}^{†}\left(\gamma \right)=-\mathcal{G}(-\gamma )$ yet violates parity ($b_1=|1-\gamma |$), showing that the extra condition is essential; all models studied here satisfy it bit-exactly. For large-q SYK, these ingredients predict ${\alpha }_{\mathbb{C}}=\mathcal{J}-2i(q-2)\gamma$, whose imaginary part is fixed solely by the interaction range; the first ladder step is exact, and the multi-step increments approach $q-2$ with system size ($1.92\pm 0.04$ at $N=12$, $q=4$). Under a common fit protocol, the closed-system rates saturate by $N=10$ (${\alpha }_R\left(0\right)\to 0.437$, $2{\kappa }_0\to 0.224$). The imaginary rate is not an independent observable at leading order—its content is its sign, which resolves how the growing operator meets its environment (opposite for spin chains and SYK). Full article

To address the problems of enhanced non-stationarity, significant feature distribution shift, and insufficient cross-condition generalization capability of traditional fault diagnosis methods under variable operating conditions such as varying speed and load, a rolling bearing fault diagnosis method integrating group sparse reconstruction and a multi-strategy improved quantum particle swarm optimization-based relevance vector machine (RVM) is proposed. First, group sparse representation learning is employed to reconstruct the original vibration signals, thereby suppressing background noise and enhancing fault-related impulsive components to improve signal separability and stability. Subsequently, a modal component selection criterion combining kurtosis and correlation coefficients is introduced to optimize and reconstruct the decomposed modal components, enabling the reconstructed signals to retain more fault-sensitive information. On this basis, multiple information entropy features are extracted from the reconstructed signals to construct high-dimensional state feature vectors for comprehensively characterizing the dynamic operating states of rolling bearings. To further enhance the parameter optimization capability, Chebyshev chaotic mapping is incorporated into the quantum particle swarm optimization (QPSO) algorithm to improve the uniformity of population initialization. Meanwhile, a Cauchy mutation strategy is introduced to strengthen the global search capability and avoid premature convergence, thereby forming a multi-strategy improved QPSO algorithm. Finally, the improved optimization algorithm is utilized to adaptively optimize the key hyperparameters of the RVM, resulting in a fault diagnosis model with high accuracy, strong generalization capability, and sparse characteristics. Experimental validation on the HUST and XJTU-SY bearing datasets demonstrates that the proposed MIQPSO-RVM framework achieves diagnostic accuracies of 96.70% and 94.83%, respectively. Compared with several representative intelligent diagnosis methods and deep learning models, the proposed method exhibits superior diagnostic performance, robustness, and generalization capability under complex operating conditions. Full article

Clustering may uncover latent behavioral structure in Autism Spectrum Disorder (ASD) screening data without using outcome labels, but the resulting partitions depend strongly on data geometry and the adopted similarity measure. Quantum-hybrid clustering offers alternative distance and similarity estimators, yet whether these subroutines improve on classical methods under controlled conditions remains unclear. We conduct a benchmark of k-means, DBSCAN, agglomerative clustering, and spectral clustering against their quantum-hybrid counterparts. All methods are evaluated in a common 13-dimensional representation, with hyperparameters selected exclusively through internal validation indices. The evaluation covers four synthetic geometries and a 13-dimensional PCA representation of an ASD screening dataset, each containing 300 samples and evaluated over 10 seed-defined stochastic runs. Clustering quality is measured using the Silhouette Index (SI), Davies–Bouldin Index (DBI), Calinski–Harabasz Index (CHI), Adjusted Mutual Information (AMI), and Adjusted Rand Index (ARI). Under this validation protocol, Q-means exactly recovers the Gaussian clusters and improves label agreement on anisotropic data, but it does not outperform classical k-means on the ASD screening data. Q-spectral significantly reduces DBI on Two Moons, Concentric Rings, and ASD screening data, although these reductions do not consistently translate into higher AMI or ARI. Q-DBSCAN and Q-agglomerative exhibit greater sensitivity to distance distortions and finite-shot noise. Overall, the results reveal geometry-dependent trade-offs rather than uniform quantum-hybrid superiority. We relate these findings to theoretical complexity, measurement noise, state-preparation costs, and eigensolver bottlenecks in near-term implementations. Full article

Global Positioning System (GPS) positioning accuracy is strongly affected by inaccurate noise modeling and non-Gaussian pseudorange measurement errors, including heavy-tailed disturbances and abnormal outliers caused by multipath propagation and signal degradation. Conventional extended Kalman filters (EKFs) generally assume Gaussian measurement noise with fixed covariance matrices, which limits their robustness under degraded measurement conditions. This study proposes a Student-t robust quantum-behaved particle swarm optimization-based extended Kalman filter (ST-QPSO-EKF) for adaptive GPS state estimation. The proposed framework combines quantum-behaved particle swarm optimization (QPSO) with a Student-t-based robust measurement update, where the process-noise scaling factor, measurement-noise scaling factor, and Student-t degrees-of-freedom parameter are jointly optimized. The optimized parameters are obtained through an offline calibration stage and subsequently applied in the recursive GPS filtering process. A nonlinear GPS navigation simulation was conducted using Gaussian, Student-t heavy-tailed, and outlier-contaminated pseudorange measurement scenarios. The proposed method was compared with conventional EKF, QPSO-EKF, and Student-t EKF using 20 independent Monte Carlo realizations. The results demonstrate that QPSO-EKF provides improved accuracy under nominal Gaussian conditions, whereas ST-QPSO-EKF achieves superior performance under non-Gaussian measurement environments. Under Student-t heavy-tailed noise, ST-QPSO-EKF reduced the position RMSE to 3.814 m, while under outlier-contaminated noise it achieved a position RMSE of 3.952 m, outperforming the other compared methods. In addition, the proposed method maintained comparable online computational cost because the QPSO optimization was performed offline. The results indicate that jointly optimizing covariance parameters and Student-t robustness provides an effective strategy for improving GPS positioning reliability under complex pseudorange measurement conditions. Full article

A new class of Ln(III) Schiff base (SB) complexes has been synthesized with the general formula [LnL(hfac)₃], where Ln = Tb (TbL), Eu (EuL), Sm (SmL) or Gd (GdL). The molecular structure of the complex was determined using the X-ray diffraction method. The IR spectra show that the C=O stretching is shifted from 1695 cm⁻¹ in pure PMMA to 1719–1724 cm⁻¹ in LnL-PMMA hybrid materials. This means that LnL materials are successfully embedded into the PMMA backbone in the polymeric films. However, the Ln(III) SB complexes exhibit emission spectra that cover the visible region. The TbL complex displays an intense green emission combined with a large emission lifetime of 0.505 ms. However, the incorporation of Ln-SB complexes into PMMA (polymethylmethacrylate) polymeric films was investigated. The thermal stabilities of the LnL-PMMA hybrid materials increased from 140 to 250 °C when compared with the LnL-SB complexes. Furthermore, their luminescence intensity and lifetimes were also enhanced due to their induced structural rigidity. The molecular interactions of the LnL complexes with the PMMA matrix were monitored by investigating the luminescence properties of EuL-PMMA. Detailed photoluminescence studies showed insights into the non-radiative rates and improved quantum yields (Q_Eu = 23%) from Eu(III). Furthermore, the higher values of Judd–Ofelt parameters Ω₂ and Ω₄ indicate strong hydrogen bonding interactions between L and PMMA. Nevertheless, these significant optical properties enable LnL-PMMA polymeric materials as colored phosphors for the design of opto-electronic devices. Full article

Biorthogonal quantum geometry is often read through scalar tensor components. In non-Hermitian bands, however, the biorthogonal contraction can lose the ordering of the left-right interband matrix elements from which a scalar component is formed. We study this information loss for spectrally separated, diagonalizable two-band Bloch Hamiltonians. For a specified control parameter, the Hamiltonian variation defines a local response vertex. In the instantaneous biorthogonal eigenbasis, the interband part of this vertex is completely specified by two ordered matrix elements, whereas the corresponding equal-parameter scalar QGT component retains only their product. This separation leads to a local classification of interband vertices into no-interband, Hermitian-locked, generic complex-transverse, and complex-null cases. On a complex-null branch, the scalar component can vanish even though one ordered interband matrix element remains nonzero. We identify this as a local chiral-vertex mechanism in a vertex-resolved geometric response kernel, distinct from generic non-Hermiticity or exceptional-point proximity. Nonreciprocal SSH, a two-dimensional complex-spin–orbit lattice, and a $k_z$-only chiral ladder stack realize the same mechanism in one, two, and three dimensions, while diagonal and gain–loss-like vertices provide nonselective comparisons. Full article

Classical approaches often treat interaction as engineered product terms or as emergent patterns in flexible models, offering little control over how synergy or antagonism arises. We take a quantum-inspired view: following the Born rule (probability as squared amplitude), coherent aggregation sums complex amplitudes before squaring, creating an interference cross-term, whereas an incoherent proxy sums squared magnitudes and removes it. Representing input contributions as complex amplitudes, the relative phase between amplitudes modulates the sign and magnitude of this cross-term, providing a mechanism-level account of synergy versus antagonism. In a minimal amplitude-linear model over a $2\times 2$ design—the simplest setting for feature interaction—this cross-term equals the standard interaction contrast ${\Delta }_{\mathrm{INT}}$, which can be interpreted as the potential-outcome interaction measure under randomized assignment. We instantiate this idea in a lightweight Interference Kernel Classifier (IKC) and introduce two diagnostics: Coherent Gain (log-likelihood gain of coherent aggregation over the incoherent proxy) and Interference Information (the induced Kullback–Leibler gap). A controlled phase sweep recovers this identity. On a high-interaction synthetic task (XOR), IKC attains predictive performance closely matching that of the evaluated classical baselines under paired, budget-matched comparisons; on real tabular data, its competitiveness is dataset-dependent, trailing the best evaluated baseline on Adult while outperforming it on Bank Marketing. In coherent–incoherent ablations with learned parameters held fixed, removing the coherent cross-terms degrades negative log-likelihood, Brier score, and expected calibration error on both datasets, with positive Coherent Gain. This quantum-inspired approach offers an interpretable mechanism for modeling and diagnosing feature interactions in probabilistic classification. Full article

Purpose: Marking the one hundredth anniversary of quantum mechanics in 2025, quantum science has become foundational for the development of contemporary technologies, enabling advances in sensing, imaging, computing, and materials engineering. Cancer radiotherapy, although traditionally developed within the scope of classical dosimetric models and phenomenological biological frameworks, is fundamentally initiated by quantum-mechanical radiation-matter interactions. Radiation-induced DNA damage, which ultimately determines therapeutic effectiveness, originates from primary quantum-mechanical processes involving particle transport, electronic excitation and ionisation, followed by successive physicochemical and chemical stages including water radiolysis and radical formation. As scientific disciplines undergo a rapid “quantum transition,” radiation cancer treatment is increasingly positioned to benefit from deeper integration of quantum principles and emerging quantum technologies. Methods: This review examines how quantum mechanics governs the primary radiation-matter interactions that initiate the physical, physicochemical, chemical, and ultimately biological stages of radiation action at the (sub)cellular level, with particular emphasis on track structure, water radiolysis, DNA damage induction, and multiscale biological response. Contemporary approaches to DNA damage modeling are discussed, including track-structure Monte Carlo methods, nanodosimetric frameworks, and multi-scale simulation approaches that connect microscopic interaction events with biological outcomes. Key quantum concepts relevant to radiation therapy are outlined, together with emerging quantum technologies such as nanoscale quantum sensing, quantum lasers, quantum dots, and quantum computing, which are evaluated for their potential roles in dosimetry, imaging, treatment planning, and radiation transport simulations. In this context, artificial intelligence (AI) is considered a complementary tool to accelerate computation and integrate quantum-informed data across multiple scales. Results: The review highlights that quantum-informed modeling enables a more consistent description of radiation-induced processes across spatial and temporal scales, linking microscopic interaction mechanisms to DNA damage formation and macroscopic biological outcomes. Recent advances in track-structure and radiobiological modeling provide new opportunities for improving predictions of radiation effects and treatment response. Emerging quantum technologies show potential to enhance measurement sensitivity, improve simulation efficiency, and enable more precise control of radiation delivery. Furthermore, AI-assisted approaches facilitate the extraction of predictive patterns from complex datasets, supporting faster and more accurate estimation of biological endpoints such as DNA damage and cell survival. Conclusions: The quantum aspects of advanced treatment modalities, including proton and heavy-ion therapy, ultrafast radiation delivery, and the FLASH effect, as well as future concepts such as laser-plasma-driven and coherence-informed radiotherapy systems, indicate a promising direction for next-generation cancer treatment. By critically assessing both opportunities and limitations, this work provides a coherent framework for integrating DNA damage modeling, quantum principles, quantum-inspired techniques, emerging quantum technologies, and advanced computational tools to guide future developments in radiation oncology. Full article

Artificial Intelligence-driven detection mechanisms present both opportunities and challenges in modern systems, particularly within smart cities that rely on complex operational technologies. In the context of Saudi urban infrastructure, rapidly evolving and multidimensional cyber threats require advanced, energy-efficient security solutions. This research proposes an Artificial Intelligence-based Threat Detection Mechanism designed to proactively identify and mitigate cyber threats while maximizing energy efficiency and minimizing cost and system complexity. Purpose: The proposed theoretical framework focuses on securing sustainable smart cities by integrating Artificial Intelligence-based anomaly detection with quantum-enhanced algorithms to address high-dimensional and emerging cyber threats across interconnected urban systems. The Artificial Intelligence-based Threat Detection Mechanism enables early and proactive threat detection across sustainable smart city networks, including connections to external and global infrastructures, ensuring continuous monitoring, resilience, and service continuity. Methods: The methodology emphasizes the development of energy-efficient Artificial Intelligence models and quantum protocols, incorporating intelligent risk assessment, adaptive calibration, and automated response mechanisms. In addition, the framework introduces distributed security hubs to enhance cybersecurity robustness and scalability. Anticipated Results and Conclusions: Anticipated outcomes include improved security management policies, automated threat detection and response, and adaptive protection against evolving cyber risks. The proposed framework provides a scalable and cost-effective solution aligned with sustainability objectives. Ultimately, this research contributes a proactive and intelligent framework for securing smart city ecosystems, supporting long-term development goals and aligning with Saudi Vision 2030. Full article

Quantum machine learning (QML) has emerged as a promising approach for analyzing the complex, high-dimensional data encountered in oncology, yet research in this area remains fragmented. This systematic literature review synthesizes current applications of QML in cancer care. Following PRISMA guidelines, six databases were searched for peer-reviewed English-language studies published between 2020 and 2026. Of the 212 records identified, 49 studies met the inclusion criteria after screening and quality assessment. The findings show that QML research is dominated by classification and detection tasks, while segmentation is beginning to emerge. Breast cancer and brain tumors are the most frequently investigated domains. Hybrid quantum-classical models, particularly quantum kernel methods, quantum neural networks, and quantum convolutional neural networks, are the predominant approaches. The main barriers to adoption are hardware limitations, including quantum noise, limited qubit availability, and reliance on simulators. Overall, QML in oncology remains in its early stages of development, with limited clinical validation, insufficient model interpretability, and little evidence of a clear quantum advantage. Future research should prioritize evaluation on real quantum hardware, larger and more diverse clinical datasets, standardized benchmarking against classical methods, and closer collaboration between computer scientists and oncology experts to facilitate clinical translation. Full article

Single-path transmission optimization is a core task for resource scheduling and operation of complex networks, which requires coordinated optimization of transmission cost and flow. Classical algorithms bear heavy computational loads in high-dimensional decision spaces as networks grow. This paper constructs a hybrid quantum model integrating quantum approximate optimization algorithm (QAOA) and cubic spline interpolation. Paths, discrete flows, and trade-off coefficients are unified within a quadratic unconstrained binary optimization (QUBO) model. Least-squares fitting converts native parameters into QUBO coefficients, whose fitting errors are measured to verify robustness and penalty sensitivity, and auxiliary variables eliminate high-order terms to exponentially cut qubit consumption. QAOA narrows the feasible range via global coarse search, and cubic spline interpolation further yields precise continuous flow values. Powered by quantum superposition for parallel full-space exploration, the framework avoids repeated modeling for separate bias coefficients. Mixed integer programming (MIP) and genetic algorithm (GA) are adopted as comparative benchmarks. For the small-scale network instance, the relative error between the proposed method and the global optimum solved by MIP is less than 1%. For the large-scale case, the overall error of our approach remains within an acceptable range even when discrepancies exist between results yielded by classical algorithms. Full article