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Keywords = causal dynamical triangulations

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56 pages, 660 KB  
Review
Accelerated Expansion of the Universe as a Quantum Gravity Phenomenon
by Jan Novák and Oem Trivedi
Physics 2026, 8(3), 55; https://doi.org/10.3390/physics8030055 - 1 Jul 2026
Viewed by 678
Abstract
It has been known for about hundred years that the universe is expanding, but an impressive discovery came at the end of 20th century, when it was found that the universe is expanding with acceleration. Since then, many models have been developed in [...] Read more.
It has been known for about hundred years that the universe is expanding, but an impressive discovery came at the end of 20th century, when it was found that the universe is expanding with acceleration. Since then, many models have been developed in cosmology to explain this phenomenon. One of the possible elucidations is that the theory of gravity must be modified at the classical level. However, many such models have already been excluded by gravitational wave experiments. Therefore, one must put a more critical question: could accelerated expansion of the universe be a phenomenon of quantum gravity? Here, we review the basic models of how one explains the origin of dark energy or the cosmological constant in metastring theory, discrete approaches to quantum gravity, group field theory, non-commutative geometry, causal dynamical triangulation, asymptotic safety, and models based on holography and entropic gravity. At the end of a newly formed approach to the quantization of gravity, we mention the ring paradigm, which may, after application to cosmology, naturally model the late-time accelerated expansion epoch in the universe. What is most remarkable, though, is that the final formulation of this theory may ultimately solve the old problem of the cosmological constant. Full article
(This article belongs to the Special Issue Beyond the Standard Models of Physics and Cosmology: 2nd Edition)
34 pages, 39528 KB  
Article
Geospatial–Temporal Quantification of Tectonically Constrained Marble Resources Within the Wadi El Shati Extensional Regime via Multi-Sensor Sentinel and DEM Data Fusion
by Mahmood Salem Dhabaa, Ahmed Gaber and Adel Kamel Mohammed
Geosciences 2026, 16(2), 81; https://doi.org/10.3390/geosciences16020081 - 14 Feb 2026
Viewed by 672
Abstract
This study addresses a critical knowledge gap in quantifying strategic mineral resources within hyper-arid, tectonically complex terrains by establishing a recursive framework that reconciles deterministic resource estimation with the nonlinear dynamics of tectonically mediated metamorphic systems. Using Libya’s Wadi El Shati as a [...] Read more.
This study addresses a critical knowledge gap in quantifying strategic mineral resources within hyper-arid, tectonically complex terrains by establishing a recursive framework that reconciles deterministic resource estimation with the nonlinear dynamics of tectonically mediated metamorphic systems. Using Libya’s Wadi El Shati as a case study, legacy lithological misclassifications are rectified through the fusion of Sentinel-1 Synthetic Aperture Radar, Sentinel-2 multispectral imagery, and Digital Elevation Model analytics within a unified geospatial workflow. The methodology synergizes atmospherically corrected optical data, processed via supervised Maximum Likelihood Classification, with calibrated radar-derived structural lineaments. Classified marble-bearing zones within the Al Mahruqah Formation are integrated with DEM data and field-validated thickness measurements using Triangulated Irregular Network models to resolve surface–subsurface dependencies and compute volumes. The results demonstrate a 91% lithological classification accuracy, rectifying a 22% error in legacy maps. Structural analysis of 1213 lineaments confirms a dominant NE–SW extensional regime (σ3) that facilitated fluid conduits. The quantified marble-bearing horizon spans ~334 km2 with a volume of 6.0 km3 (±9%). Spatial analysis reveals a causal link between high-grade marble clusters, basaltic intrusions, and NE–SW fault systems, refining models of contact metamorphism in rift-related settings. Full article
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27 pages, 696 KB  
Article
The Impact of Economic Freedom on Economic Growth in Western Balkan Countries
by Roberta Bajrami, Kaltrina Bajraktari and Adelina Gashi
J. Risk Financ. Manag. 2025, 18(8), 461; https://doi.org/10.3390/jrfm18080461 - 19 Aug 2025
Cited by 1 | Viewed by 2771
Abstract
Although it is generally accepted that economic freedom stimulates economic growth, its effects in transitional economies are still up for debate. More empirical research is needed to examine the long-term effects of economic freedom on growth in the Western Balkans, a region characterised [...] Read more.
Although it is generally accepted that economic freedom stimulates economic growth, its effects in transitional economies are still up for debate. More empirical research is needed to examine the long-term effects of economic freedom on growth in the Western Balkans, a region characterised by uneven reform trajectories, fiscal pressures, and institutional fragility. This study examines the effects of seven fundamental factors on real GDP per capita growth (annual percentage change) in six Western Balkan nations between 2013 and 2023. These factors include property rights, government spending, government integrity, business freedom, monetary freedom, trade openness, and education spending. Importantly, in order to better capture macroeconomic constraints, it takes into account two fiscal burden indicators: the public debt and the government budget deficit. A triangulated analytical framework is used: Random Forest regression identifies non-linear patterns and ranks the importance of variables; Bayesian Vector Autoregression (VAR) models dynamic interactions and inertia; and the Generalised Method of Moments (GMM) handles endogeneity and reveals causal relationships. The GMM results show that while government integrity (β = −0.0820, p = 0.0206), government spending (β = −0.0066, p = 0.0312), and public debt (β = −0.0172, p = 0.0456) have negative effects on growth, property rights (β = 0.0367, p = 0.0208), monetary freedom (β = 0.0413, p = 0.0221), and the government budget deficit (β = 0.0498, p = 0.0371) have positive and significant effects on growth. Although the majority of economic freedom indicators are statistically insignificant, Bayesian VAR confirms strong growth persistence (GDP(−1) = 0.7169, SE = 0.0373). On the other hand, the Random Forest model identifies the most significant variables as property rights (3.72), public debt (5.88), business freedom (4.65), and government spending (IncNodePurity = 9.80). These results show that the growth effects of economic freedom depend on the context and are mediated by the state of the economy. Market liberalisation and legal certainty promote growth, but their advantages could be offset by inadequate budgetary restraint and difficulties with transitional governance. A hybrid policy approach, one that blends strategic market reforms with improved institutional quality, prudent debt management, and efficient public spending, is necessary for the region to achieve sustainable development. Full article
(This article belongs to the Section Economics and Finance)
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18 pages, 4489 KB  
Article
Influence of Regional PM2.5 Sources on Air Quality: A Network-Based Spatiotemporal Analysis in Northern Thailand
by Khuanchanok Chaichana, Supanut Chaidee, Sayan Panma, Nattakorn Sukantamala, Neda Peyrone and Anchalee Khemphet
Mathematics 2025, 13(15), 2468; https://doi.org/10.3390/math13152468 - 31 Jul 2025
Cited by 3 | Viewed by 4008
Abstract
Northern Thailand frequently suffers from severe PM2.5 air pollution, especially during the dry season, due to agricultural burning, local emissions, and transboundary haze. Understanding how pollution moves across regions and identifying source–receptor relationships are critical for effective air quality management. This study investigated [...] Read more.
Northern Thailand frequently suffers from severe PM2.5 air pollution, especially during the dry season, due to agricultural burning, local emissions, and transboundary haze. Understanding how pollution moves across regions and identifying source–receptor relationships are critical for effective air quality management. This study investigated the spatial and temporal dynamics of PM2.5 in northern Thailand. Specifically, it explored how pollution at one monitoring station influenced concentrations at others and revealed the seasonal structure of PM2.5 transmission using network-based analysis. We developed a Python-based framework to analyze daily PM2.5 data from 2022 to 2023, selecting nine representative stations across eight provinces based on spatial clustering and shape-based criteria. Delaunay triangulation was used to define spatial connections among stations, capturing the region’s irregular geography. Cross-correlation and Granger causality were applied to identify time-lagged relationships between stations for each season. Trophic coherence analysis was used to evaluate the hierarchical structure and seasonal stability of the resulting networks. The analysis revealed seasonal patterns of PM2.5 transmission, with certain stations, particularly in Chiang Mai and Lampang, consistently acting as source nodes. Provinces such as Phayao and Phrae were frequently identified as receptors, especially during the winter and rainy seasons. Trophic coherence varied by season, with the winter network showing the highest coherence, indicating a more hierarchical but less stable structure. The rainy season exhibited the lowest coherence, reflecting greater structural stability. PM2.5 spreads through structured, seasonal pathways in northern Thailand. Network patterns vary significantly across seasons, highlighting the need for adaptive air quality strategies. This framework can help identify influential monitoring stations for early warning and support more targeted, season-specific air quality management strategies in northern Thailand. Full article
(This article belongs to the Special Issue Application of Mathematical Theory in Data Science)
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35 pages, 7938 KB  
Article
Network Geometry of Borsa Istanbul: Analyzing Sectoral Dynamics with Forman–Ricci Curvature
by Ömer Akgüller, Mehmet Ali Balcı, Larissa Margareta Batrancea and Lucian Gaban
Entropy 2025, 27(3), 271; https://doi.org/10.3390/e27030271 - 5 Mar 2025
Cited by 2 | Viewed by 5814
Abstract
This study investigates the dynamic interdependencies among key sectors of Borsa Istanbul—industrial, services, technology, banking, and electricity—using a novel network-geometric framework. Daily closure prices from 2022 to 2024 are transformed into logarithmic returns and analyzed via a sliding window approach. In each window, [...] Read more.
This study investigates the dynamic interdependencies among key sectors of Borsa Istanbul—industrial, services, technology, banking, and electricity—using a novel network-geometric framework. Daily closure prices from 2022 to 2024 are transformed into logarithmic returns and analyzed via a sliding window approach. In each window, mutual information is computed to construct weighted networks that are filtered using Triangulated Maximally Filtered Graphs (TMFG) to isolate the most significant links. Forman–Ricci curvature is then calculated at the node level, and entropy measures over k-neighborhoods (k=1,2,3) capture the complexity of both local and global network structures. Cross-correlation, Granger causality, and transfer entropy analyses reveal that sector responses to macroeconomic shocks—such as inflation surges, interest rate hikes, and currency depreciation—vary considerably. The services sector emerges as a critical intermediary, transmitting shocks between the banking and both the industrial and technology sectors, while the electricity sector displays robust, stable interconnections. These findings demonstrate that curvature-based metrics capture nuanced network characteristics beyond traditional measures. Future work could incorporate high-frequency data to capture finer interactions and empirically compare curvature metrics with conventional indicators. Full article
(This article belongs to the Special Issue Entropy-Based Applications in Sociophysics II)
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28 pages, 761 KB  
Article
Counterintuitive Scenarios in Discrete Gravity Without Quantum Effects or Causality Violations
by Benjamin F. Dribus, Jesiah T. Darnell and Neil Goldsmith
Symmetry 2024, 16(12), 1609; https://doi.org/10.3390/sym16121609 - 4 Dec 2024
Cited by 1 | Viewed by 2545
Abstract
In certain established approaches to quantum gravity, such as causal set theory and causal dynamical triangulations, discrete spacetime structure is taken to be a primary feature, not a secondary effect of “quantizing” a pre-existing classical continuum-based theory, as is done in approaches such [...] Read more.
In certain established approaches to quantum gravity, such as causal set theory and causal dynamical triangulations, discrete spacetime structure is taken to be a primary feature, not a secondary effect of “quantizing” a pre-existing classical continuum-based theory, as is done in approaches such as string theory and loop quantum gravity. For a priori discrete models, the full quantum theory is often obtained via some version of Feynman’s sum-over-histories approach, in which each “history” is a discrete object viewed as a classical spacetime. Counterintuitive physical scenarios such as Schrödinger’s cat or the grandfather paradox are typically associated with either quantum effects or causality violations, but we demonstrate that equally bizarre scenarios can arise at a purely classical level in the discrete causal context due to symmetry considerations. In particular, the graph-theoretic phenomenon of pseudosimilarity leads to situations in which alternative events occurring at physically distinguishable locations in the universe can cause different parts of the universe to “swap identities” in a fugue-like manner alien to continuum-based theories. This phenomenon is perhaps best understood as an extension of the relativity principle, which we call relativity of identity. Full article
(This article belongs to the Special Issue Symmetries in Gravity Research: Classical and Quantum)
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45 pages, 697 KB  
Article
The Computational Universe: Quantum Quirks and Everyday Reality, Actual Time, Free Will, the Classical Limit Problem in Quantum Loop Gravity and Causal Dynamical Triangulation
by Piero Chiarelli and Simone Chiarelli
Quantum Rep. 2024, 6(2), 278-322; https://doi.org/10.3390/quantum6020020 - 20 Jun 2024
Cited by 1 | Viewed by 4200
Abstract
The simulation analogy presented in this work enhances the accessibility of abstract quantum theories, specifically the stochastic hydrodynamic model (SQHM), by relating them to our daily experiences. The SQHM incorporates the influence of fluctuating gravitational background, a form of dark energy, into quantum [...] Read more.
The simulation analogy presented in this work enhances the accessibility of abstract quantum theories, specifically the stochastic hydrodynamic model (SQHM), by relating them to our daily experiences. The SQHM incorporates the influence of fluctuating gravitational background, a form of dark energy, into quantum equations. This model successfully addresses key aspects of objective-collapse theories, including resolving the ‘tails’ problem through the definition of quantum potential length of interaction in addition to the De Broglie length, beyond which coherent Schrödinger quantum behavior and wavefunction tails cannot be maintained. The SQHM emphasizes that an external environment is unnecessary, asserting that the quantum stochastic behavior leading to wavefunction collapse can be an inherent property of physics in a spacetime with fluctuating metrics. Embedded in relativistic quantum mechanics, the theory establishes a coherent link between the uncertainty principle and the constancy of light speed, aligning seamlessly with finite information transmission speed. Within quantum mechanics submitted to fluctuations, the SQHM derives the indeterminacy relation between energy and time, offering insights into measurement processes impossible within a finite time interval in a truly quantum global system. Experimental validation is found in confirming the Lindemann constant for solid lattice melting points and the 4He transition from fluid to superfluid states. The SQHM’s self-consistency lies in its ability to describe the dynamics of wavefunction decay (collapse) and the measure process. Additionally, the theory resolves the pre-existing reality problem by showing that large-scale systems naturally decay into decoherent states stable in time. Continuing, the paper demonstrates that the physical dynamics of SQHM can be analogized to a computer simulation employing optimization procedures for realization. This perspective elucidates the concept of time in contemporary reality and enriches our comprehension of free will. The overall framework introduces an irreversible process impacting the manifestation of macroscopic reality at the present time, asserting that the multiverse exists solely in future states, with the past comprising the formed universe after the current moment. Locally uncorrelated projective decays of wavefunction, at the present time, function as a reduction of the multiverse to a single universe. Macroscopic reality, characterized by a foam-like consistency where microscopic domains with quantum properties coexist, offers insights into how our consciousness perceives dynamic reality. It also sheds light on the spontaneous emergence of gravity in discrete quantum spacetime evolution, and the achievement of the classical general relativity limit in quantum loop gravity and causal dynamical triangulation. The simulation analogy highlights a strategy focused on minimizing information processing, facilitating the universal simulation in solving its predetermined problem. From within, reality becomes the manifestation of specific physical laws emerging from the inherent structure of the simulation devised to address its particular issue. In this context, the reality simulation appears to employ an optimization strategy, minimizing information loss and data management in line with the simulation’s intended purpose. Full article
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17 pages, 10143 KB  
Article
Opportunities to Develop Lifelong Learning Tendencies in Practice-Based Teacher Education: Getting Ready for Education 4.0
by Kiomi Matsumoto-Royo, Maria Soledad Ramírez-Montoya and Paulette Conget
Future Internet 2021, 13(11), 292; https://doi.org/10.3390/fi13110292 - 19 Nov 2021
Cited by 35 | Viewed by 7307
Abstract
Education 4.0 prepares new generations to develop the skills required to perform in a technological, dynamic, and unpredictable world. The main barrier to implementing Education 4.0 in schools is that teachers have not been trained for it. Given the advances and new resources [...] Read more.
Education 4.0 prepares new generations to develop the skills required to perform in a technological, dynamic, and unpredictable world. The main barrier to implementing Education 4.0 in schools is that teachers have not been trained for it. Given the advances and new resources of the technological field, teacher preparation will be insufficient if it focuses on technological skills but does not incorporate the necessary dispositions for lifelong learning. Universities have the ethical imperative to update teacher education so teachers can become lifelong learners. The objective of this study was to understand whether practice-based curricula offer opportunities to promote lifelong learning tendencies. We used a sequential explanatory method. Quantitative and qualitative instruments were applied to pre-service teachers (survey: n = 231, semi-structured interviews: n = 8), and causal and descriptive approaches were supported by a structural equation model and constant comparative method, respectively. Data triangulation confirmed and added depth to the relationship found. Practice opportunities provided by teacher educators in learning activities and assessment tasks promote curiosity, motivation, perseverance, and self-learning regulation, when they are (i) systematic; (ii) relevant to the classroom work; (iii) presented with clear instructions and effective rubrics; (iv) accompanied with feedback focused on the task, soliciting reflection, and performed by peers and teacher educators in a trustworthy environment. This research may be of value to universities looking to renew their Education 4.0 programs because it shows that practice-based curricula not only transform pre-service teachers into teaching experts but also into lifelong learners. Full article
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26 pages, 3165 KB  
Review
CDT Quantum Toroidal Spacetimes: An Overview
by Jan Ambjorn, Zbigniew Drogosz, Jakub Gizbert-Studnicki, Andrzej Görlich, Jerzy Jurkiewicz and Dániel Németh
Universe 2021, 7(4), 79; https://doi.org/10.3390/universe7040079 - 26 Mar 2021
Cited by 21 | Viewed by 4200
Abstract
Lattice formulations of gravity can be used to study non-perturbative aspects of quantum gravity. Causal Dynamical Triangulations (CDT) is a lattice model of gravity that has been used in this way. It has a built-in time foliation but is coordinate-independent in the spatial [...] Read more.
Lattice formulations of gravity can be used to study non-perturbative aspects of quantum gravity. Causal Dynamical Triangulations (CDT) is a lattice model of gravity that has been used in this way. It has a built-in time foliation but is coordinate-independent in the spatial directions. The higher-order phase transitions observed in the model may be used to define a continuum limit of the lattice theory. Some aspects of the transitions are better studied when the topology of space is toroidal rather than spherical. In addition, a toroidal spatial topology allows us to understand more easily the nature of typical quantum fluctuations of the geometry. In particular, this topology makes it possible to use massless scalar fields that are solutions to Laplace’s equation with special boundary conditions as coordinates that capture the fractal structure of the quantum geometry. When such scalar fields are included as dynamical fields in the path integral, they can have a dramatic effect on the geometry. Full article
(This article belongs to the Special Issue Gravitational Singularities and Their Quantum Fates)
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11 pages, 444 KB  
Review
Closed Timelike Curves, Singularities and Causality: A Survey from Gödel to Chronological Protection
by Jean-Pierre Luminet
Universe 2021, 7(1), 12; https://doi.org/10.3390/universe7010012 - 12 Jan 2021
Cited by 20 | Viewed by 12937
Abstract
I give a historical survey of the discussions about the existence of closed timelike curves in general relativistic models of the universe, opening the physical possibility of time travel in the past, as first recognized by K. Gödel in his rotating universe model [...] Read more.
I give a historical survey of the discussions about the existence of closed timelike curves in general relativistic models of the universe, opening the physical possibility of time travel in the past, as first recognized by K. Gödel in his rotating universe model of 1949. I emphasize that journeying into the past is intimately linked to spacetime models devoid of timelike singularities. Since such singularities arise as an inevitable consequence of the equations of general relativity given physically reasonable assumptions, time travel in the past becomes possible only when one or another of these assumptions is violated. It is the case with wormhole-type solutions. S. Hawking and other authors have tried to “save” the paradoxical consequences of time travel in the past by advocating physical mechanisms of chronological protection; however, such mechanisms remain presently unknown, even when quantum fluctuations near horizons are taken into account. I close the survey by a brief and pedestrian discussion of Causal Dynamical Triangulations, an approach to quantum gravity in which causality plays a seminal role. Full article
(This article belongs to the Special Issue Universe: 5th Anniversary)
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