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Keywords = quantum information geometry

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61 pages, 13225 KB  
Review
A Comprehensive Review of Optical Metrology and Perception Technologies
by Shuonan Shan, Fangyuan Zhao, Zinan Li, Linbin Luo and Xinghui Li
Sensors 2025, 25(22), 6811; https://doi.org/10.3390/s25226811 - 7 Nov 2025
Viewed by 701
Abstract
Optical metrology and perception technologies employ light as an information carrier to enable non-contact, high-precision measurement of geometry, dynamics, and material properties. They are widely deployed in industrial and consumer domains, from nanoscale defect inspection in semiconductor manufacturing to environmental perception in autonomous [...] Read more.
Optical metrology and perception technologies employ light as an information carrier to enable non-contact, high-precision measurement of geometry, dynamics, and material properties. They are widely deployed in industrial and consumer domains, from nanoscale defect inspection in semiconductor manufacturing to environmental perception in autonomous driving and spatial tracking in AR/VR. However, existing reviews often treat individual modalities—such as interferometry, imaging, or spectroscopy—in isolation, overlooking the increasing cross-domain integration in emerging systems. This review proposes a hierarchical taxonomy encompassing four core systems: interferometry, imaging, spectroscopy, and hybrid/advanced methods. It introduces a “theory–application–innovation” framework to unify fundamental principles, application scenarios, and evolutionary trends, revealing synergies across modalities. By mapping technological progress to industrial and societal needs, including AI-driven optimization and quantum-enhanced sensing, this work provides a structured, evolving knowledge base. The framework supports both cross-disciplinary understanding and strategic decision-making, offering researchers and engineers a consolidated reference for navigating the rapidly expanding frontiers of optical metrology and perception. Full article
(This article belongs to the Section Optical Sensors)
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10 pages, 332 KB  
Article
Epistemic Signatures of Fisher Information in Finite Fermions Systems
by Angelo Plastino and Victoria Vampa
Quantum Rep. 2025, 7(4), 48; https://doi.org/10.3390/quantum7040048 - 14 Oct 2025
Viewed by 326
Abstract
Beginning with Mandelbrot’s insight that Fisher information may admit a thermodynamic interpretation, a growing body of work has connected this information-theoretic measure to fluctuation–dissipation relations, thermodynamic geometry, and phase transitions. Yet, these connections have largely remained at the level of formal analogies. In [...] Read more.
Beginning with Mandelbrot’s insight that Fisher information may admit a thermodynamic interpretation, a growing body of work has connected this information-theoretic measure to fluctuation–dissipation relations, thermodynamic geometry, and phase transitions. Yet, these connections have largely remained at the level of formal analogies. In this work, we provide what is, to our knowledge, the first explicit realization of the epistemic-to-physical transition of Fisher information within a finite interacting quantum system. Specifically, we analyze a model of N fermions occupying two degenerate levels and coupled by a spin-flip interaction of strength V, treated in the grand canonical ensemble at inverse temperature β. We compute the Fisher information FN(V) associated with the sensitivity of the thermal state to changes in V, and show that it becomes an observer-independent, experimentally meaningful quantity: it encodes fluctuations, tracks entropy variations, and reveals structural transitions induced by interactions. Our findings thus demonstrate that Fisher information, originally conceived as an inferential and epistemic measure, can operate as a bona fide thermodynamic observable in quantum many-body physics, bridging the gap between information-theoretic foundations and measurable physical law. Full article
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28 pages, 1237 KB  
Article
Counting Cosmic Cycles: Past Big Crunches, Future Recurrence Limits, and the Age of the Quantum Memory Matrix Universe
by Florian Neukart, Eike Marx and Valerii Vinokur
Entropy 2025, 27(10), 1043; https://doi.org/10.3390/e27101043 - 7 Oct 2025
Viewed by 740
Abstract
We present a quantitative theory of contraction and expansion cycles within the Quantum Memory Matrix (QMM) cosmology. In this framework, spacetime consists of finite-capacity Hilbert cells that store quantum information. Each non-singular bounce adds a fixed increment of imprint entropy, defined as the [...] Read more.
We present a quantitative theory of contraction and expansion cycles within the Quantum Memory Matrix (QMM) cosmology. In this framework, spacetime consists of finite-capacity Hilbert cells that store quantum information. Each non-singular bounce adds a fixed increment of imprint entropy, defined as the cumulative quantum information written irreversibly into the matrix and distinct from coarse-grained thermodynamic entropy, thereby providing an intrinsic, monotonic cycle counter. By calibrating the geometry–information duality, inferring today’s cumulative imprint from CMB, BAO, chronometer, and large-scale-structure constraints, and integrating the modified Friedmann equations with imprint back-reaction, we find that the Universe has already completed Npast=3.6±0.4 cycles. The finite Hilbert capacity enforces an absolute ceiling: propagating the holographic write rate and accounting for instability channels implies only Nfuture=7.8±1.6 additional cycles before saturation halts further bounces. Integrating Kodama-vector proper time across all completed cycles yields a total cumulative age tQMM=62.0±2.5Gyr, compared to the 13.8±0.2Gyr of the current expansion usually described by ΛCDM. The framework makes concrete, testable predictions: an enhanced faint-end UV luminosity function at z12 observable with JWST, a stochastic gravitational-wave background with f2/3 scaling in the LISA band from primordial black-hole mergers, and a nanohertz background with slope α2/3 accessible to pulsar-timing arrays. These signatures provide near-term opportunities to confirm, refine, or falsify the cyclical QMM chronology. Full article
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31 pages, 5301 KB  
Article
Comprehensive Computational Study of a Novel Chromene-Trione Derivative Bioagent: Integrated Molecular Docking, Dynamics, Topology, and Quantum Chemical Analysis
by P. Sivaprakash, A. Viji, S. Krishnaveni, K. M. Kavya, Deokwoo Lee and Ikhyun Kim
Int. J. Mol. Sci. 2025, 26(19), 9661; https://doi.org/10.3390/ijms26199661 - 3 Oct 2025
Viewed by 554
Abstract
This work thoroughly investigated the compound 4-(2,5-Dimethoxyphenyl)-3,4-dihydrobenzo[g]chromene-2,5,10-trione (DMDCT) using molecular docking, quantum chemical analysis, and vibrational spectroscopy methodology. The medicinal chemistry group has been particularly interested in chromene and benzochromene derivatives due to their wide range of pharmacological actions, including anticancer, antibacterial, anti-inflammatory, [...] Read more.
This work thoroughly investigated the compound 4-(2,5-Dimethoxyphenyl)-3,4-dihydrobenzo[g]chromene-2,5,10-trione (DMDCT) using molecular docking, quantum chemical analysis, and vibrational spectroscopy methodology. The medicinal chemistry group has been particularly interested in chromene and benzochromene derivatives due to their wide range of pharmacological actions, including anticancer, antibacterial, anti-inflammatory, antioxidant, antiviral, and neuroprotective capabilities. In this connection, DMDCT has been explored to evaluate its biological, electrical, and structural properties. DFT using the B3LYP functional and 6–31G basis was established to conduct theoretical computations with the Gaussian 09 program. The findings from these computations provide insight into the following topics: NBO interactions, optimal molecular geometry, Mulliken charge distribution, frontier molecular orbitals, and MEP. Second-order perturbation theory has been used to assess stabilization energies arising from donor–acceptor interactions. Furthermore, general features such as chemical hardness, softness, and electronegativity were studied. The results suggest that DMDCT has stable electronic configurations and biologically relevant active sites. This integrated experimental and theoretical study supports the potential of DMDCT as a practical scaffold for future therapeutic applications and contributes valuable information regarding its vibrational and electronic behavior. Full article
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19 pages, 1300 KB  
Article
Structured Emission and Entanglement Dynamics of a Giant Atom in a Photonic Creutz Ladder
by Vassilios Yannopapas
Photonics 2025, 12(8), 827; https://doi.org/10.3390/photonics12080827 - 20 Aug 2025
Viewed by 1405
Abstract
We explore the spontaneous emission dynamics of a giant atom coupled to a photonic Creutz ladder, focusing on how flat-band frustration and synthetic gauge fields shape atom–photon interactions. The Creutz ladder exhibits perfectly flat bands, Aharonov–Bohm caging, and topological features arising from its [...] Read more.
We explore the spontaneous emission dynamics of a giant atom coupled to a photonic Creutz ladder, focusing on how flat-band frustration and synthetic gauge fields shape atom–photon interactions. The Creutz ladder exhibits perfectly flat bands, Aharonov–Bohm caging, and topological features arising from its nontrivial hopping structure. By embedding the giant atom at multiple spatially separated sites, we reveal interference-driven emission control and the formation of nonradiative bound states. Using both spectral and time-domain analyses, we uncover strong non-Markovian dynamics characterized by persistent oscillations, long-lived entanglement, and recoherence cycles. The emergence of bound-state poles in the spectral function is accompanied by spatially localized photonic profiles and directionally asymmetric emission, even in the absence of band dispersion. Calculations of von Neumann entropy and atomic purity confirm the formation of coherence-preserving dressed states in the flat-band regime. Furthermore, the spacetime structure of the emitted field displays robust zig-zag interference patterns and synthetic chirality, underscoring the role of geometry and topology in photon transport. Our results demonstrate how flat-band photonic lattices can be leveraged to engineer tunable atom–photon entanglement, suppress radiative losses, and create structured decoherence-free subspaces for quantum information applications. Full article
(This article belongs to the Special Issue Recent Progress in Optical Quantum Information and Communication)
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28 pages, 9730 KB  
Article
Interplay of Connectivity and Unwanted Physical Interactions Within the Architecture of the D-Wave 2000Q Chimera Processor
by Jessica Park, Susan Stepney and Irene D’Amico
Technologies 2025, 13(8), 355; https://doi.org/10.3390/technologies13080355 - 12 Aug 2025
Viewed by 439
Abstract
We consider dynamics relevant to annealing in qubit networks modelled on the architecture of the D-Wave 2000Q quantum processor (known as the Chimera topology). Our results report on the effects of the qubits’ connectivity and variable coupling strengths (based on physical interactions) on [...] Read more.
We consider dynamics relevant to annealing in qubit networks modelled on the architecture of the D-Wave 2000Q quantum processor (known as the Chimera topology). Our results report on the effects of the qubits’ connectivity and variable coupling strengths (based on physical interactions) on the dynamics of network. The networks we examine are up to 32 qubits in size and include coupling lengths varying by almost an order of magnitude. We show that while information transfer within the network can be strongly affected by the different interactions, the system maintains similar clusters of qubits with comparable fidelities even in the presence of some of the physical interactions. This suggests an intrinsic robustness of the Chimera topology to these perturbations, even if it includes such a variety of coupling lengths. Moreover, a similar clustering geometry was observed for other qubit properties in previous analysis of actual data from D-Wave 2000Q. This comparable behaviour suggests that the real quantum annealing chip is subject to little or no unwanted effects due to interactions that scale with the coupling lengths. This could be due to absence of the most damaging type of physical interactions and/or to D-Wave calibration methods tuning the control lines such that the couplings perform as if there is no effect due to their physical length. Our results are also relevant to the use of chaining for the creation of logical qubits. They show that even with very strong interactions between the chain, significant unwanted perturbations may occur due to the inhomogeneous fidelities of the overall dynamics and inhomogeneous dynamics should be expected for any given algorithm. Full article
(This article belongs to the Section Quantum Technologies)
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18 pages, 305 KB  
Article
Entropic Dynamics Approach to Relational Quantum Mechanics
by Ariel Caticha and Hassaan Saleem
Entropy 2025, 27(8), 797; https://doi.org/10.3390/e27080797 - 26 Jul 2025
Cited by 2 | Viewed by 893
Abstract
The general framework of Entropic Dynamics (ED) is used to construct non-relativistic models of relational Quantum Mechanics from well-known inference principles—probability, entropy and information geometry. Although only partially relational—the absolute structures of simultaneity and Euclidean geometry are still retained—these models provide a useful [...] Read more.
The general framework of Entropic Dynamics (ED) is used to construct non-relativistic models of relational Quantum Mechanics from well-known inference principles—probability, entropy and information geometry. Although only partially relational—the absolute structures of simultaneity and Euclidean geometry are still retained—these models provide a useful testing ground for ideas that will prove useful in the context of more realistic relativistic theories. The fact that in ED the positions of particles have definite values, just as in classical mechanics, has allowed us to adapt to the quantum case some intuitions from Barbour and Bertotti’s classical framework. Here, however, we propose a new measure of the mismatch between successive states that is adapted to the information metric and the symplectic structures of the quantum phase space. We make explicit that ED is temporally relational and we construct non-relativistic quantum models that are spatially relational with respect to rigid translations and rotations. The ED approach settles the longstanding question of what form the constraints of a classical theory should take after quantization: the quantum constraints that express relationality are to be imposed on expectation values. To highlight the potential impact of these developments, the non-relativistic quantum model is parametrized into a generally covariant form and we show that the ED approach evades the analogue of what in quantum gravity has been called the problem of time. Full article
(This article belongs to the Section Quantum Information)
13 pages, 1550 KB  
Article
The Effect of Trap Design on the Scalability of Trapped-Ion Quantum Technologies
by Le Minh Anh Nguyen, Brant Bowers and Sara Mouradian
Entropy 2025, 27(6), 576; https://doi.org/10.3390/e27060576 - 29 May 2025
Cited by 2 | Viewed by 2401
Abstract
To increase the power of a trapped-ion quantum information processor, the qubit number, gate speed, and gate fidelity must all increase. All three of these parameters are influenced by the trapping field, which, in turn, depends on the electrode geometry. Here, we consider [...] Read more.
To increase the power of a trapped-ion quantum information processor, the qubit number, gate speed, and gate fidelity must all increase. All three of these parameters are influenced by the trapping field, which, in turn, depends on the electrode geometry. Here, we consider how the electrode geometry affects the following radial trapping parameters: trap height, harmonicity, depth, and trap frequency. We introduce a simple multi-wafer geometry comprising a ground plane above a surface trap and compare the performance of this trap to a surface trap and a multi-wafer trap that is a miniaturized version of a linear Paul trap. We compare the voltage and frequency requirements needed to reach a desired radial trap frequency and find that the two multi-wafer trap designs provide significant improvements in expected power dissipation over the surface trap design in large part due to increased harmonicity. Finally, we consider the fabrication requirements and the path towards the integration of the necessary optical control. This work provides a basis to optimize future trap designs with scalability in mind. Full article
(This article belongs to the Special Issue Quantum Computing with Trapped Ions)
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39 pages, 401 KB  
Article
Computational Holography
by Logan Nye
Int. J. Topol. 2025, 2(2), 5; https://doi.org/10.3390/ijt2020005 - 15 Apr 2025
Viewed by 1386
Abstract
We establish a comprehensive framework demonstrating that physical reality can be understood as a holographic encoding of underlying computational structures. Our central thesis is that different geometric realizations of the same physical system represent equivalent holographic encodings of a unique computational structure. We [...] Read more.
We establish a comprehensive framework demonstrating that physical reality can be understood as a holographic encoding of underlying computational structures. Our central thesis is that different geometric realizations of the same physical system represent equivalent holographic encodings of a unique computational structure. We formalize quantum complexity as a physical observable, establish its mathematical properties, and demonstrate its correspondence with geometric descriptions. This framework naturally generalizes holographic principles beyond AdS/CFT correspondence, with direct applications to black hole physics and quantum information theory. We derive specific, quantifiable predictions with numerical estimates for experimental verification. Our results suggest that computational structure, rather than geometry, may be the more fundamental concept in physics. Full article
(This article belongs to the Special Issue Feature Papers in Topology and Its Applications)
17 pages, 283 KB  
Article
What Is Ontic and What Is Epistemic in the Quantum Mechanics of Spin?
by Ariel Caticha
Entropy 2025, 27(3), 315; https://doi.org/10.3390/e27030315 - 18 Mar 2025
Viewed by 738
Abstract
Entropic Dynamics (ED) provides a framework that allows the reconstruction of the formalism of quantum mechanics by insisting on ontological and epistemic clarity and adopting entropic methods and information geometry. Our present goal is to extend the ED framework to account for spin. [...] Read more.
Entropic Dynamics (ED) provides a framework that allows the reconstruction of the formalism of quantum mechanics by insisting on ontological and epistemic clarity and adopting entropic methods and information geometry. Our present goal is to extend the ED framework to account for spin. The result is a realist ψ-epistemic model in which the ontology consists of a particle described by a definite position plus a discrete variable that describes Pauli’s peculiar two-valuedness. The resulting dynamics of probabilities is, as might be expected, described by the Pauli equation. What may be unexpected is that the generators of transformations—Hamiltonians and angular momenta, including spin, are all granted clear epistemic status. To the old question, ‘what is spinning?’ ED provides a crisp answer: nothing is spinning. Full article
(This article belongs to the Special Issue Maximum Entropy Principle and Applications)
48 pages, 1898 KB  
Essay
The Code Underneath
by Julio Rives
Axioms 2025, 14(2), 106; https://doi.org/10.3390/axioms14020106 - 30 Jan 2025
Viewed by 1125
Abstract
An inverse-square probability mass function (PMF) is at the Newcomb–Benford law (NBL)’s root and ultimately at the origin of positional notation and conformality. PrZ=2Z2, where ZZ+. Under its tail, we find information [...] Read more.
An inverse-square probability mass function (PMF) is at the Newcomb–Benford law (NBL)’s root and ultimately at the origin of positional notation and conformality. PrZ=2Z2, where ZZ+. Under its tail, we find information as harmonic likelihood Ls,t=Ht1Hs1, where Hn is the nth harmonic number. The global Q-NBL is Prb,q=Lq,q+1L1,b=qHb11, where b is the base and q is a quantum (1q<b). Under its tail, we find information as logarithmic likelihood i,j=lnji. The fiducial R-NBL is Prr,d=d,d+11,r=logr1+1d, where rb is the radix of a local complex system. The global Bayesian rule multiplies the correlation between two numbers, s and t, by a likelihood ratio that is the NBL probability of bucket s,t relative to b’s support. To encode the odds of quantum j against i locally, we multiply the prior odds Prb,jPrb,i by a likelihood ratio, which is the NBL probability of bin i,j relative to r’s support; the local Bayesian coding rule is o˜j:i|r=ijlogrji. The Bayesian rule to recode local data is o˜j:i|r=o˜j:i|rlnrlnr. Global and local Bayesian data are elements of the algebraic field of “gap ratios”, ABCD. The cross-ratio, the central tool in conformal geometry, is a subclass of gap ratio. A one-dimensional coding source reflects the global Bayesian data of the harmonic external world, the annulus xQ|1x<b, into the local Bayesian data of its logarithmic coding space, the ball xQ|x<11b. The source’s conformal encoding function is y=logr2x1, where x is the observed Euclidean distance to an object’s position. The conformal decoding function is x=121+ry. Both functions, unique under basic requirements, enable information- and granularity-invariant recursion to model the multiscale reality. Full article
(This article belongs to the Special Issue Mathematical Modelling of Complex Systems)
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14 pages, 315 KB  
Article
Variational Information Principles to Unveil Physical Laws
by D. Bernal-Casas and J. M. Oller
Mathematics 2024, 12(24), 3941; https://doi.org/10.3390/math12243941 - 14 Dec 2024
Cited by 3 | Viewed by 1298
Abstract
This article demonstrates that the application of the variation method to purely information-theoretic models can lead to the discovery of fundamental equations in physics, such as Schrödinger’s equation. Our solution, expressed in terms of information parameters rather than physical quantities, suggests a profound [...] Read more.
This article demonstrates that the application of the variation method to purely information-theoretic models can lead to the discovery of fundamental equations in physics, such as Schrödinger’s equation. Our solution, expressed in terms of information parameters rather than physical quantities, suggests a profound implication—Schrödinger’s equation can be viewed as a unique physical expression of a more profound informational formalism, inspiring new avenues of research. Full article
13 pages, 3601 KB  
Article
Texture-Induced Strain in a WS2 Single Layer to Monitor Spin–Valley Polarization
by George Kourmoulakis, Antonios Michail, Dimitris Anestopoulos, Joseph A. Christodoulides, Manoj Tripathi, Alan Β. Dalton, John Parthenios, Konstantinos Papagelis, Emmanuel Stratakis and George Kioseoglou
Nanomaterials 2024, 14(17), 1437; https://doi.org/10.3390/nano14171437 - 3 Sep 2024
Cited by 1 | Viewed by 2482
Abstract
Nanoscale-engineered surfaces induce regulated strain in atomic layers of 2D materials that could be useful for unprecedented photonics applications and for storing and processing quantum information. Nevertheless, these strained structures need to be investigated extensively. Here, we present texture-induced strain distribution in single-layer [...] Read more.
Nanoscale-engineered surfaces induce regulated strain in atomic layers of 2D materials that could be useful for unprecedented photonics applications and for storing and processing quantum information. Nevertheless, these strained structures need to be investigated extensively. Here, we present texture-induced strain distribution in single-layer WS2 (1L-WS2) transferred over Si/SiO2 (285 nm) substrate. The detailed nanoscale landscapes and their optical detection are carried out through Atomic Force Microscopy, Scanning Electron Microscopy, and optical spectroscopy. Remarkable differences have been observed in the WS2 sheet localized in the confined well and at the periphery of the cylindrical geometry of the capped engineered surface. Raman spectroscopy independently maps the whole landscape of the samples, and temperature-dependent helicity-resolved photoluminescence (PL) experiments (off-resonance excitation) show that suspended areas sustain circular polarization from 150 K up to 300 K, in contrast to supported (on un-patterned area of Si/SiO2) and strained 1L-WS2. Our study highlights the impact of the dielectric environment on the optical properties of two-dimensional (2D) materials, providing valuable insights into the selection of appropriate substrates for implementing atomically thin materials in advanced optoelectronic devices. Full article
(This article belongs to the Special Issue Recent Advances in Optical Spectroscopy of Layered Materials)
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20 pages, 4951 KB  
Article
Spectral Characteristics, In Silico Perspectives, Density Functional Theory (DFT), and Therapeutic Potential of Green-Extracted Phycocyanin from Spirulina
by Velichka Andonova, Krastena Nikolova, Ivelin Iliev, Svetlana Georgieva, Nadezhda Petkova, Mehran Feizi-Dehnayebi, Stoyanka Nikolova and Anelia Gerasimova
Int. J. Mol. Sci. 2024, 25(17), 9170; https://doi.org/10.3390/ijms25179170 - 23 Aug 2024
Cited by 18 | Viewed by 2169
Abstract
Phycocyanin (PC) is a naturally occurring green pigment in Spirulina. It was extracted by ultrasonic extraction using green technology, and its structure was studied using IR- and NMR-spectroscopy. Spectral data confirmed the PC structure. This study also involves an in silico assessment of [...] Read more.
Phycocyanin (PC) is a naturally occurring green pigment in Spirulina. It was extracted by ultrasonic extraction using green technology, and its structure was studied using IR- and NMR-spectroscopy. Spectral data confirmed the PC structure. This study also involves an in silico assessment of the diverse applications of green pigment PC. Utilizing QSAR, PreADME/T, SwissADME, and Pro-Tox, this study explores the safety profile, pharmacokinetics, and potential targets of PC. QSAR analysis reveals a favorable safety profile, with the parent structure and most metabolites showing no binding to DNA or proteins. PreADME/T indicates low skin permeability, excellent intestinal absorption, and medium permeability, supporting oral administration. Distribution analysis suggests moderate plasma protein binding and cautious blood–brain barrier permeability, guiding formulation strategies. Metabolism assessments highlight interactions with key cytochrome P450 enzymes, influencing drug interactions. Target prediction analysis unveils potential targets, suggesting diverse therapeutic effects, including cardiovascular benefits, anti-inflammatory activities, neuroprotection, and immune modulation. Based on the in silico analysis, PC holds promise for various applications due to its safety, bioavailability, and potential therapeutic benefits. Experimental validation is crucial to elucidate precise molecular mechanisms, ensuring safe and effective utilization in therapeutic and dietary contexts. DFT calculations, including geometry optimization, MEP analysis, HOMO-LUMO energy surface, and quantum reactivity parameters of the PC compound, were obtained using the B3LYP/6–311G(d,p) level. This integrated approach contributes to a comprehensive understanding of PC’s pharmacological profile and informs future research directions. Full article
(This article belongs to the Special Issue Computational, Structural and Spectroscopic Studies of Macromolecules)
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14 pages, 4026 KB  
Article
Augmentation of Soft Partition with a Granular Prototype Based Fuzzy C-Means
by Ruixin Wang, Kaijie Xu and Yixi Wang
Mathematics 2024, 12(11), 1639; https://doi.org/10.3390/math12111639 - 23 May 2024
Viewed by 1158
Abstract
Clustering is a fundamental cornerstone in unsupervised learning, playing a pivotal role in various data mining techniques. The precise and efficient classification of data stands as a central focus for numerous researchers and practitioners alike. In this study, we design an effective soft [...] Read more.
Clustering is a fundamental cornerstone in unsupervised learning, playing a pivotal role in various data mining techniques. The precise and efficient classification of data stands as a central focus for numerous researchers and practitioners alike. In this study, we design an effective soft partition classification method which refines and extends the prototype of the well-known Fuzzy C-Means clustering algorithm. Specifically, the developed scheme employs membership function to extend the prototypes into a series of granular prototypes, thus achieving a deeper revelation of the structure of the data. This process softly divides the data into core and extended parts. The core part can be succinctly encapsulated through several information granules, whereas the extended part lacks discernible geometry and requires formal descriptors (such as membership formulas). Our objective is to develop information granules that shape the core structure within the dataset, delineate their characteristics, and explore the interaction among these granules that result in their deformation. The granular prototypes become the main component of the information granules and provide an optimization space for traditional prototypes. Subsequently, we apply quantum-behaved particle swarm optimization to identify the optimal partition matrix for the data. This optimized matrix significantly enhances the partition performance of the data. Experimental results provide substantial evidence of the effectiveness of the proposed approach. Full article
(This article belongs to the Special Issue New Advances in Data Analytics and Mining)
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