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19 pages, 1384 KB  
Article
Scaling of Gas–Melt Decoupling in Silicic Eruptions: Magma Ascent, Connected Permeability, and Atmospheric Confinement
by Antonio F. Miguel, Vinicius R. Pepe and Luiz A. O. Rocha
Appl. Sci. 2026, 16(17), 8893; https://doi.org/10.3390/app16178893 - 7 Sep 2026
Abstract
Gas escape relative to magma ascent is a primary control on degassing, yet its governing parameters are difficult to compare across eruptions and planetary environments. This study develops a reduced-order dimensionless framework for diagnosing local gas–melt separation in connected, pre-fragmentation magma. The formulation [...] Read more.
Gas escape relative to magma ascent is a primary control on degassing, yet its governing parameters are difficult to compare across eruptions and planetary environments. This study develops a reduced-order dimensionless framework for diagnosing local gas–melt separation in connected, pre-fragmentation magma. The formulation combines phase mass conservation, porous gas transport, bubble-matrix permeability, independently constrained connected pathways, and inertial resistance. The resulting regime map separates the competition between magma advection and matrix gas segregation from changes caused by sealing, crystallization, fractures, and tuffisite pathways. It shows that crystallization has no unique effect. Matrix obstruction reduces gas escape, whereas brittle pathway formation can enhance it. Global sensitivity analysis indicates that ascent rate and bubble number density account for 98.4% of the variance in the matrix-controlled transport competition over the investigated ranges. When connected permeability is independently specified over the same logarithmic range as ascent rate, both contribute equally to the calculated variance. A literature-constrained calculation for the climactic Chaitén eruption places the bubble-matrix endmember in the advection-dominated regime without adjusting permeability to reproduce the observed outcome. Atmospheric scaling indicates strong near-surface suppression of bubble expansion on Venus, but its magnitude remains highly sensitive to the assumed mechanical overpressure scale. The framework provides a physically testable basis for comparing local degassing states without imposing an arbitrary eruption classifier. It does not predict eruption onset or fragmentation. These require time-dependent dynamics, mechanical failure criteria, and independent validation data. Full article
(This article belongs to the Special Issue Novel Developments in Fluid Flow and Energy Transfer)
45 pages, 1357 KB  
Article
Coupled-Channel Spectral Theory for a Non-Separable Geometry: Normal Modes and Two-Boundary Response in the Rotating AdS-Teo Wormhole
by Ramesh Radhakrishnan, William Julius and Gerald Cleaver
Symmetry 2026, 18(9), 1497; https://doi.org/10.3390/sym18091497 - 7 Sep 2026
Abstract
We investigate scalar perturbations of a rotating asymptotically anti-de Sitter (AdS)-Teo traversable wormhole with a controlled non-separable angular deformation. The geometry retains a regular wormhole throat and the required AdS asymptotics, while an explicit quadrupolar deformation generates angular-channel coupling in the intermediate region. [...] Read more.
We investigate scalar perturbations of a rotating asymptotically anti-de Sitter (AdS)-Teo traversable wormhole with a controlled non-separable angular deformation. The geometry retains a regular wormhole throat and the required AdS asymptotics, while an explicit quadrupolar deformation generates angular-channel coupling in the intermediate region. A sufficient condition is derived for an ergoregion-free parameter regime in which the spectral analysis is performed. Projecting the geometry-derived Klein–Gordon equation onto spherical harmonics yields a matrix-valued Sturm–Liouville system and an associated quadratic operator pencil. Throat regularity together with normalizable AdS boundary conditions leads to a determinant quantization condition for the discrete normal-mode spectrum. Two-, four-, and six-channel calculations demonstrate systematic numerical convergence of the retained low-lying normal-mode frequencies under enlargement of the angular basis. The complete finite generalized eigenspectrum is also examined without imposing a near-reality selection criterion, and no growing scalar mode is found within the ergoregion-free parameter range and numerical resolutions studied. The six-channel rotation continuation exhibits a finite interior level-repulsion feature accompanied by collective redistribution of the multichannel eigenvectors. The same coupled spectral framework formally defines a matrix-valued two-boundary response whose poles are selected by the normal-mode matching condition; the response plots presented here illustrate this structure using the reduced two-channel effective model rather than a numerical reconstruction of the full six-channel response. We further derive the geometry-dependent short-distance Hadamard subtraction and identify the finite inter-channel structure entering a truncated local quantum mode sum, without claiming a complete numerical evaluation of Φ2ren. Together, these results establish a geometry-to-spectrum framework in which the spacetime geometry determines the coupled operator, the global boundary conditions determine its normal-mode spectrum, and the same coupled spectral framework organizes the associated asymptotic response and local quantum mode-sum structure. Full article
19 pages, 3389 KB  
Article
Agronomic Response of Silage Maize to Varying Irrigation Water and Nitrogen Levels Under Subsurface Drip Irrigation: Implications for Yield and Water Use Productivity
by Filiz Akin, Köksal Aydinşakir, Ömer Özbek, Şekip Erdal, Gökhan Uçar, Mehmet Pamukçu, Mehmet Kocatürk, Cihan Karaca, Şerife Gülden Yilmaz, Dursun Büyüktaş and Bilal Cemek
Plants 2026, 15(17), 2734; https://doi.org/10.3390/plants15172734 - 7 Sep 2026
Abstract
Excessive or poorly timed nitrogen (N) fertilization can increase nitrate leaching and associated environmental risks. This two-year field study evaluated the combined effects of three irrigation regimes and four N rates on the biomass yield, water productivity, and economic performance of silage maize [...] Read more.
Excessive or poorly timed nitrogen (N) fertilization can increase nitrate leaching and associated environmental risks. This two-year field study evaluated the combined effects of three irrigation regimes and four N rates on the biomass yield, water productivity, and economic performance of silage maize under subsurface drip irrigation (SDI). The irrigation treatments were full irrigation (I1), 50% of I1 (deficit irrigation, I2), and 120% of I1 (excess irrigation, I3); the N treatments were 0 (N0), 140 (N1), 210 (N2), and 280 kg N ha−1 (N3). The experiment was established in a randomized complete block split-plot design with three replications during the 2022 and 2023 growing seasons. Seasonal irrigation ranged from 198 to 471 mm in 2022 and from 214 to 470 mm in 2023. The N1I2 treatment consistently produced the highest green forage yield (109,520 and 112,330 kg ha−1 in 2022 and 2023, respectively) while using approximately half the irrigation water applied to I1. It also produced the highest reported water productivity and irrigation water productivity, with values of 42.4 and 55.3 kg m−3 in 2022 and 44.4 and 52.5 kg m−3 in 2023, respectively. According to the partial-budget analysis, N1I2 generated the highest net profit (USD 31,941.83 ha−1 in 2022 and USD 28,500.08 ha−1 in 2023) and relative profit ratios of 4.17 and 11.48, respectively. Under the soil, climate, and price conditions of this study, applying 140 kg N ha−1 with deficit irrigation at 50% of the full-irrigation amount provided the best balance among biomass production, irrigation water use, and economic return. Full article
(This article belongs to the Special Issue Irrigation Management for Sustainable Soil and Plant Health)
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47 pages, 11264 KB  
Review
Natural Products and Neuroregeneration: Rethinking Discovery Beyond Bioavailability Through Pseudo-Natural Product Design
by Solomon Habtemariam
Biomedicines 2026, 14(9), 2009; https://doi.org/10.3390/biomedicines14092009 - 7 Sep 2026
Abstract
Natural product (NP)-based neuroregeneration research has generated extensive preclinical evidence over the past five decades. Pharmacological activity across core processes of central nervous system (CNS) repair including neurogenesis, axonal regeneration, and neuroplasticity have been documented. Despite consistent observations of neurite outgrowth, neuroprotection, and [...] Read more.
Natural product (NP)-based neuroregeneration research has generated extensive preclinical evidence over the past five decades. Pharmacological activity across core processes of central nervous system (CNS) repair including neurogenesis, axonal regeneration, and neuroplasticity have been documented. Despite consistent observations of neurite outgrowth, neuroprotection, and partial functional recovery in cellular and animal models, translation into durable clinical therapies has remained limited. Neurotrophins such as nerve growth factor (NGF) and brain-derived neurotrophic factor (BDNF) similarly exhibit strong regenerative effects in experimental systems, but even direct central administration has failed to produce sustained long-distance axonal regeneration or stable circuit reconstruction. This suggests that delivery constraints alone do not explain the failure to achieve clinically-relevant functional repair. It is proposed herein that this limitation reflects intrinsic constraints in how regenerative signalling is organised across multiple biological scales. Integrating evidence from in vitro and in vivo injury models, we can introduce a Target–Mechanism–Network (T-M-N) approach that systematically maps NPs activity onto a hierarchical regulatory architecture. Across diverse NPs classes, ~55 recurrent molecular targets cluster into 10 functional mechanisms, which converge into four higher-order network control regimes governing energetic competence, regenerative signalling capacity, redox-immune balance, and structural plasticity. This analysis reveals that NPs converge on shared regenerative networks but rarely coordinate all required domains within a unified pharmacological programme. They can thus be seen to represent a pre-organised source of evolutionarily selected pharmacophores encoding discrete elements of neuroregenerative network control. On this basis, pseudo-natural product (PNP) design enabled by computational chemistry and phenotypic screening may provide a strategy to recombine these fragments into engineered scaffolds with improved functional selectivity and regenerative coherence. The need to shift drug discovery from optimisation of individual NPs toward architecture-driven design of multi-functional molecules that address the integrated demands of neuroregeneration is discussed. Full article
(This article belongs to the Section Drug Discovery, Development and Delivery)
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26 pages, 15558 KB  
Article
Testing a Novel Multi-Temporal Multidimensional Assessment of Cooling Performance for Blue, Green, and Grey Parks: A Case Study in Wuhan, China
by Yuxin You, Yi Huang, Houbin Ma and Qin Wang
Sustainability 2026, 18(17), 9180; https://doi.org/10.3390/su18179180 - 7 Sep 2026
Abstract
Urban parks are “cool islands” for mitigating urban heat, yet most snapshot-based assessments overlook intraday cooling dynamics and divergent mechanisms across park typologies. This study examines 52 parks in Wuhan, a humid city with routine park irrigation, using thermal data from Landsat 9 [...] Read more.
Urban parks are “cool islands” for mitigating urban heat, yet most snapshot-based assessments overlook intraday cooling dynamics and divergent mechanisms across park typologies. This study examines 52 parks in Wuhan, a humid city with routine park irrigation, using thermal data from Landsat 9 and ECOSTRESS across morning, noon, and nightfall. Through stepwise analysis and blue–green classification, we quantify diurnal cooling dynamics and their drivers. While previous studies have examined diurnal (within-day) cooling, multidimensional indicators, or scale effects separately, our contribution lies in establishing a multi-temporal assessment framework that integrates temporal dynamics with blue, green, and grey park typologies to reveal how cooling patterns diverge across blue, green, and grey parks throughout the day. Results show park cooling intensity (PCI) and gradient (PCG) peak at noon, while cooling area (PCA) remains stable. Elevated cooling efficiency (PCE) at nightfall is driven not by ecological cooling, but by the rapid thermal response of impervious surfaces with low thermal inertia. Area, greenspace proportion, and building height are primary drivers, shifting from scale dominance in the morning to vegetation and building at noon, with a preliminary transition range of approximately 14–16 hm2 identified for this regime shift, though this finding warrants further validation with larger samples. Based on blue–green composition, parks are categorised as blue, green, or grey, with divergent cooling dynamics due to thermophysical properties. Blue parks cool steadily all day, green parks peak at noon, while grey parks’ elevated PCE at nightfall is an apparent thermal response, not ecological cooling. Typological heterogeneity weakens models that pool all parks together, as water storage, vegetation evapotranspiration, and impervious thermal response vary across types and cancel out when pooled. Findings show that single-time-phase or full averaging insufficiently captures park cooling dynamics, underscoring the value of considering both diurnal and typological variations in climate-adaptive planning for dense cities. Full article
(This article belongs to the Section Sustainable Urban and Rural Development)
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32 pages, 1948 KB  
Article
Textual Sentiment and Financial Market Dynamics: Econometric Evidence from Eastern Europe’s Green and Digital Transition
by Cristian-Valentin Hapenciuc, Daniela Mihaela Neamțu, Teodora Cajvan, Camelia Băeșu and Otilia-Maria Bordeianu
Sustainability 2026, 18(17), 9177; https://doi.org/10.3390/su18179177 - 7 Sep 2026
Abstract
Conventional macroeconomic indicators are released with a time lag and may therefore provide limited information about rapidly changing market expectations, creating a need for complementary high-frequency indicators capable of capturing the informational content of financial narratives. This study examines whether sentiment extracted from [...] Read more.
Conventional macroeconomic indicators are released with a time lag and may therefore provide limited information about rapidly changing market expectations, creating a need for complementary high-frequency indicators capable of capturing the informational content of financial narratives. This study examines whether sentiment extracted from unstructured financial text contains incremental predictive information for short-horizon market dynamics in the context of Eastern Europe’s green and digital transition. Using financial news and discourse collected between May 2025 and May 2026, a FinBERT-based Daily Sentiment Index (DSI) is constructed for selected technology, energy, and sustainability-related narratives and linked to market indicators and representative assets, including the DAX, UiPath, and OMV Petrom. The empirical strategy combines Granger predictability tests, vector autoregression (VAR), GARCH(1,1) models with sentiment effects, lead–lag analysis, Bai–Perron structural-break tests, and Markov-switching specifications to assess predictive temporal relationships, volatility dynamics, and time variation in sentiment–market interactions. Forecasting utility is further evaluated through an expanding-window out-of-sample exercise in which a sentiment-augmented VAR is compared with a benchmark autoregressive specification using one-day-ahead DAX returns, with relative predictive accuracy evaluated via the Diebold–Mariano test. The results indicate that lagged sentiment contains statistically significant predictive information for subsequent market returns and that incorporating the DSI significantly improves out-of-sample forecast accuracy relative to the benchmark specification. The evidence also reveals heterogeneous and time-varying responses across the selected cases: technology-related assets exhibit comparatively differentiated sensitivity to macro-sentiment conditions, whereas the energy case displays stronger exposure to transition-related narratives. Structural-break and regime-dependent estimates further suggest instability in the relationship between ESG sentiment and market performance over the sample period, but do not establish a permanent structural transformation in investor preferences. The study contributes to the narrative-economics and computational-finance literature by providing applied evidence that domain-specific textual sentiment contains incremental short-horizon information beyond conventional market dynamics and can complement lagged macroeconomic indicators in financial forecasting and risk-monitoring applications. Full article
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12 pages, 8713 KB  
Article
Flame Front Stratification During Quasi-Flame Flashback
by Vladimir Lukashov, Andrey Tupikin, Vladimir Labusov and Igor Zarubin
Processes 2026, 14(17), 2857; https://doi.org/10.3390/pr14172857 - 7 Sep 2026
Abstract
During the study of premixed NH3/CH4 fuel mixtures, flame separation into two reaction zones was observed upon flashback into a Bunsen burner. Stable combustion regimes were obtained, with a gap between the burner rim and the upper luminous region, the [...] Read more.
During the study of premixed NH3/CH4 fuel mixtures, flame separation into two reaction zones was observed upon flashback into a Bunsen burner. Stable combustion regimes were obtained, with a gap between the burner rim and the upper luminous region, the size of which depended on the mixture composition and the position of the combustion zone inside the burner. The work examines combustion regimes of NH3/CH4 mixtures with an ammonia content of 10–60% in the fuel blend. The equivalence ratio was varied in the range of 0.95–1.1. The Reynolds number was maintained in the range of 270–300, ensuring laminar flow conditions. At the burner exit, temperature and gas composition profiles were measured. Flame emission was recorded at the chemiluminescence bands of OH* (308 nm) and CH* (431 nm), and emission spectra were acquired both inside and outside the burner. Spectra in the range of 190–1080 nm were recorded. Spectral analysis revealed a band corresponding to NO2 emission in the upper part of the luminous region. It is most likely that nitrogen dioxide is formed through low-temperature reactions occurring when the combustion products mix with atmospheric air. Full article
(This article belongs to the Section Energy Systems)
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7 pages, 343 KB  
Proceeding Paper
Impact of the Primary Zone Excess Air Ratio in Gas Turbine Engine Combustors on Pollutant Emissions
by Abay Dostiyarov, Iliya Iliev, Yerdaulet Baigozha, Madina Kumargazina, Nurasyl Tolembay, Hristo Beloev and Ivan Beloev
Eng. Proc. 2026, 154(1), 53; https://doi.org/10.3390/engproc2026154053 - 7 Sep 2026
Abstract
The transition to a low-carbon energy paradigm requires reducing nitrogen oxide NOx and carbon monoxide CO emissions to 5–9 ppm. This study investigates the impact of the primary zone excess air ratio α and mixing quality on pollutant yields, addressing the “seesaw” [...] Read more.
The transition to a low-carbon energy paradigm requires reducing nitrogen oxide NOx and carbon monoxide CO emissions to 5–9 ppm. This study investigates the impact of the primary zone excess air ratio α and mixing quality on pollutant yields, addressing the “seesaw” trade-off mechanism between NOx and products of incomplete combustion. Analysis of Lean Premixed and Micromix technologies demonstrates that achieving NOx levels below 5 ppm requires local α fluctuations to remain within a root-mean-square deviation of 3–4%. An original burner design with an intelligent emission control system is presented, enabling dynamic adjustment of local αin to maintain combustion within a narrow stability window. Experimental results confirm that minimum toxicity, with NOx concentrations below 20 ppm, is achieved at αin = 1.7–1.8. The implementation of this technology ensures stable operation across transient and part-load regimes while mitigating thermal NOx formation and thermoacoustic instabilities. Full article
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21 pages, 966 KB  
Article
Digital Financial Inclusion and Agricultural New Quality Productive Forces: Evidence from China
by Songqi Liu, Yuwen Qiu, Zanliang Meng, Zibin Dai and Lingui Qin
Sustainability 2026, 18(17), 9149; https://doi.org/10.3390/su18179149 - 7 Sep 2026
Abstract
Agricultural new quality productive forces (ANQP) provide an important foundation for high-quality agricultural development and sustainable rural transformation. Using panel data for 30 Chinese provinces from 2011 to 2022, this study examines the effect of digital financial inclusion (DFI) on ANQP and the [...] Read more.
Agricultural new quality productive forces (ANQP) provide an important foundation for high-quality agricultural development and sustainable rural transformation. Using panel data for 30 Chinese provinces from 2011 to 2022, this study examines the effect of digital financial inclusion (DFI) on ANQP and the channels through which that effect operates. The results show that DFI is significantly and positively associated with ANQP. A one-standard-deviation increase in DFI is associated with an increase in ANQP equivalent to approximately 64.35% of its sample mean. Green technological innovation serves as a statistically significant transmission channel, although its indirect effect accounts for only 3.31% of the total effect. The relationship between DFI and ANQP exhibits a double-threshold pattern with respect to the level of DFI and a single-threshold pattern with respect to regional economic development, with the estimated coefficients increasing gradually across regimes. Decomposing DFI shows that coverage breadth, usage depth, and digitization all contribute positively to ANQP. Further analysis of the outcome dimensions indicates that DFI is positively associated with agricultural laborers, agricultural labor objects, and agricultural labor resources. The estimated association is also larger in regions with more developed traditional financial systems. These results provide a multidimensional and stage-based understanding of the relationship between digital finance and agricultural productive-capability upgrading. Full article
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25 pages, 5957 KB  
Article
A Multi-Scale Fractal Feature Extraction Method for CNN-Based Plant Disease Classification
by Egor Savchenko and Anna Maslovskaya
Mach. Learn. Knowl. Extr. 2026, 8(9), 273; https://doi.org/10.3390/make8090273 - 7 Sep 2026
Abstract
Plant diseases, being a subject of interdisciplinary research, significantly reduce crop yield, quality, and economic returns, while the misidentification of pathogens often leads to ineffective treatments and may harm beneficial organisms and ecosystems. This work develops an approach for robust visual classification of [...] Read more.
Plant diseases, being a subject of interdisciplinary research, significantly reduce crop yield, quality, and economic returns, while the misidentification of pathogens often leads to ineffective treatments and may harm beneficial organisms and ecosystems. This work develops an approach for robust visual classification of plant diseases under limited and heterogeneous data based on multi-scale fractal texture descriptors integrated into a convolutional neural network. The proposed method employs wavelet transform modulus maxima to extract two complementary fractal characteristics, local fractal dimension and singularity spectrum width, from leaf images at several spatial scales. These descriptors form multi-channel fractal maps fed into a fractal attention module (FAM) inserted after the third stage of a ResNet-50 architecture. The FAM learns to emphasize spatial regions where fractal properties are most discriminative, while a parallel branch encodes global fractal statistics into an auxiliary vector combined with backbone features at the final classification layer. Experiments are conducted on a large heterogeneous collection of 11 public plant disease datasets under 5-shot, 50-shot, and full-scale training regimes. The fractal-augmented model raises classification accuracy from 57.06% to 67.73% on 5 shots and from 80.81% to 86.11% on 50 shots, red outperforming the plain ResNet-50 in these settings, converges within 1–2 epochs versus 25–40, and shows markedly better resilience to color distortions, random occlusions, and grayscale conversion in most cases. The generated attention maps provide spatially explicit explanations of the model’s decisions, increasing transparency for practical use. The proposed approach demonstrates that fractal analysis, embedded as a modulating signal inside a deep network, can serve as an efficient and interpretable inductive bias, which is particularly valuable under data scarcity and noisy agricultural imagery. Full article
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37 pages, 434 KB  
Article
A Trace-Based Structural Observability Framework for Network-on-Chip Routing Evaluation
by Ahmed Mesellem and Mohammed Mana
Algorithms 2026, 19(9), 765; https://doi.org/10.3390/a19090765 - 6 Sep 2026
Abstract
Traditional evaluation of Networks-on-Chip is based on aggregate metrics. Most of these metrics (latency, throughput, hop count, packet loss, energy consumption, buffer occupancy, thermal or reliability summaries) compress detailed execution traces into a few scalar values. This dimensionality reduction hides spatial, temporal, and [...] Read more.
Traditional evaluation of Networks-on-Chip is based on aggregate metrics. Most of these metrics (latency, throughput, hop count, packet loss, energy consumption, buffer occupancy, thermal or reliability summaries) compress detailed execution traces into a few scalar values. This dimensionality reduction hides spatial, temporal, and resource-level differences between simulations. This paper introduces an Entropic Structural Observability framework for routing-independent post-simulation analysis of NoC traces. The main idea of the framework is to convert typed packet-level events into probability distributions over used resources, including routers, directed links, time windows, and critical resources. As a final report, the method builds a structural signature. This signature includes normalized entropy, effective support, concentration, spatiotemporal mutual information, distribution drift, topology-aware spatial statistics, buffer-pressure measures, and classical imbalance indicators. The analysis does not modify simulation traces; it operates as a diagnostic layer. It reveals activity distribution, temporal dependence, spatial evolution, resource pressure, and structural imbalance. The framework is evaluated on 256-router 2D and 3D mesh topologies using deterministic and adaptive routing policies under diverse traffic patterns and injection rates, enabling its structural signatures to be examined across different network dimensionalities. The results reveal distinct structural regimes: deterministic dimension-order routing shows broad spatial and temporal dispersion, DyAD exhibits stronger time-space coupling and drift, and Fully-Adaptive presents an intermediate profile with high dispersion but moderate temporal variation. Full article
(This article belongs to the Collection Feature Papers in Algorithms for Multidisciplinary Applications)
34 pages, 2449 KB  
Article
Modeling Financial Stability Under Economic and Financial Downturns: A PDE-Constrained Optimization Approach with Regime-Switching Stochastic Volatility and Jumps
by Desmond Marozva, Selah Tanaka Marozva and Ştefan Cristian Gherghina
Mathematics 2026, 14(17), 3217; https://doi.org/10.3390/math14173217 - 5 Sep 2026
Abstract
We develop a PDE-constrained optimization framework for calibrating a regime-switching Heston–Merton model to S&P 500 index option prices. The model features two latent Markov regimes modulating stochastic volatility parameters and compound Poisson jumps, capturing the stylized fact that market volatility clusters differently during [...] Read more.
We develop a PDE-constrained optimization framework for calibrating a regime-switching Heston–Merton model to S&P 500 index option prices. The model features two latent Markov regimes modulating stochastic volatility parameters and compound Poisson jumps, capturing the stylized fact that market volatility clusters differently during normal and crisis periods. Using real data from the Federal Reserve Economic Data (FRED) database covering July 2016 to July 2026 (2609 business days), we identify crisis regimes via VIX thresholds and estimate transition probabilities. Our empirical analysis reveals that crisis regimes exhibit 3.78 times higher long-run variance, 1.60 times higher vol-of-vol, and 113 times higher jump intensity compared to normal regimes. We derive the full adjoint system for the forward PIDE, including the previously undocumented jump operator adjoint and Markov-switching generator adjoint, and demonstrate that the adjoint method reduces per-iteration PDE solves from order-P to 2 regardless of parameter dimensionality. A panel calibration exercise demonstrates superior in-sample fit (RMSEIV=1.24 vol points) versus the nested Heston (2.87), Bates (2.31), and Black–Scholes (19.46) models. Out-of-sample Diebold–Mariano tests confirm statistically significant forecasting gains at the 1% level. The Feller condition is satisfied in both regimes. Full article
(This article belongs to the Special Issue Applied Mathematics in Financial Markets and Risk Analysis)
28 pages, 698 KB  
Article
Volatility Specification and Deep Learning Anomaly Detection: Robustness of Transformer Architectures to GARCH Model Choice
by Sara Chegdal, Mustapha Kabil and Abdeljalil Settar
J. Risk Financ. Manag. 2026, 19(9), 690; https://doi.org/10.3390/jrfm19090690 - 5 Sep 2026
Abstract
Modern financial risk management increasingly relies on transformer-based anomaly detection, although the sensitivity of these methods to the underlying volatility model specifications remains unexplored. This study thoroughly compares four GARCH variants—symmetric GARCH and asymmetric specifications (EGARCH, GJR-GARCH, APARCH)—across two state-of-the-art transformer architectures (TranAD [...] Read more.
Modern financial risk management increasingly relies on transformer-based anomaly detection, although the sensitivity of these methods to the underlying volatility model specifications remains unexplored. This study thoroughly compares four GARCH variants—symmetric GARCH and asymmetric specifications (EGARCH, GJR-GARCH, APARCH)—across two state-of-the-art transformer architectures (TranAD for point anomalies, VTT for regime detection) using S&P 500 returns spanning 1980 to 2026. The investigation addresses a fundamental question for practitioners integrating econometric and deep learning methods: does the additional complexity of asymmetric volatility modeling yield meaningfully different anomaly detection when passed through transformer architectures? The analysis reveals that the GARCH specification affects anomaly severity rankings rather than detection consensus, with high cross-model agreement (minimum Jaccard of 0.88 for TranAD and 0.76 for VTT) despite statistically significant differences in score distributions. Asymmetric models exhibit extended post-crisis sensitivity, driven by their stronger response to negative shocks—the leverage effect captured by the GJR-GARCH threshold term—rather than by greater persistence; indeed, the symmetric GARCH exhibits the longest half-life. This enables specification selection based on risk philosophy: conservative monitoring via GJR-GARCH or efficient normalization via symmetric specifications. The choice of detection method—point versus regime identification—proves more consequential for anomaly detection performance than volatility model specification. Full article
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45 pages, 758 KB  
Review
Optimizing K-Means Clustering for Big Data: A Review
by Ravil Mussabayev and Rustam Mussabayev
Symmetry 2026, 18(9), 1489; https://doi.org/10.3390/sym18091489 - 5 Sep 2026
Abstract
This paper presents a comparative analysis of optimization techniques for the minimum sum-of-squares clustering (MSSC) problem—widely known in applied research as the K-means clustering problem—in the context of big data. K-means is the most widely used algorithmic framework for solving this problem, but [...] Read more.
This paper presents a comparative analysis of optimization techniques for the minimum sum-of-squares clustering (MSSC) problem—widely known in applied research as the K-means clustering problem—in the context of big data. K-means is the most widely used algorithmic framework for solving this problem, but MSSC methods can suffer from scalability issues when dealing with large datasets. The paper reviews approaches for overcoming these issues, including decomposition, sampling, initialization, preprocessing, parallel and distributed computation, data summarization, acceleration of distance computations, and hybridization with various metaheuristic frameworks. The experimental evaluation compares selected big data MSSC algorithms under a common benchmark protocol and assesses them according to the dominance criterion provided by the “less is more” approach (LIMA), i.e., simultaneously along the dimensions of clustering quality, speed, and simplicity. The results reveal distinct accuracy–time regimes and a multi-algorithm Pareto front under LIMA dominance, indicating that no method is universally preferable and that greater algorithmic complexity does not by itself ensure a better practical trade-off. Lightweight simplest methods generally favor speed but may sacrifice accuracy, while more complex hybrid methods reach stricter accuracy levels at substantially greater computational cost; competitive stochastic-sampling methods occupy intermediate accuracy–time–simplicity trade-offs. Full article
(This article belongs to the Section A: Computer Science)
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33 pages, 2276 KB  
Review
Laccase-Mediated Fabrication of Food Packaging Films: A Critical Review of Functional Performance, Safety, and Industrial Viability
by Alessandro D’Annibale and Rosita Marabottini
Biomolecules 2026, 16(9), 1285; https://doi.org/10.3390/biom16091285 - 5 Sep 2026
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Abstract
Although natural biopolymers represent promising sustainable packaging alternatives, their weak mechanical and barrier properties limit industrial use. While previous reviews focus on descriptive aspects of enzymatic modification, this review fills a critical literature gap by systematically bridging molecular-level laccase-driven reactions with quantitative techno-economic [...] Read more.
Although natural biopolymers represent promising sustainable packaging alternatives, their weak mechanical and barrier properties limit industrial use. While previous reviews focus on descriptive aspects of enzymatic modification, this review fills a critical literature gap by systematically bridging molecular-level laccase-driven reactions with quantitative techno-economic and safety and regulatory frameworks. We evaluate the kinetic and topological differences between direct tyrosyl-coupled protein homopolymerisation and mediator-assisted ‘graft-then-link’ polysaccharide strategies. Crucially, we analyse how entrapment versus surface-immobilised architectures dictate mass-transfer regimes, establishing their specific functional fitness for active oxygen scavenging or intelligent time-temperature monitoring. Beyond physical performance, we critically assess the translational bottlenecks currently hindering industrial scaling. For the first time, we integrate a quantitative techno-economic analysis using the Technology Readiness Level (TRL) framework, demonstrating that active film fabrication costs (EUR 0.01–0.10/m2) are heavily offset by high-protein food waste savings (>EUR 2.00/kg). Finally, we navigate European and US regulatory landscapes for enzymatically active materials and evaluate safety risks via the Threshold of Toxicological Concern (TTC) model and deterministic migration modelling. This comprehensive analysis establishes a ‘Safe-by-Design’ paradigm, guiding the scalable development of intrinsically safe, high-performance biocatalytic packaging. Full article
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