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Search Results (204)

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Keywords = recurrent expansion

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14 pages, 9867 KiB  
Article
Recurrence Patterns After Resection of Sacral Chordoma: Toward an Optimized Postoperative Target Volume Definition
by Hanna Waldsperger, Burkhard Lehner, Andreas Geisbuesch, Felix Jotzo, Eva Meixner, Laila König, Sebastian Regnery, Katharina Kozyra, Lars Wessel, Sandro Krieg, Klaus Herfarth, Jürgen Debus and Katharina Seidensaal
Cancers 2025, 17(15), 2521; https://doi.org/10.3390/cancers17152521 - 30 Jul 2025
Abstract
Background: Postoperative recurrence of sacrococcygeal chordomas presents significant clinical challenges due to unusual recurrence patterns. This study aimed to characterize these patterns of recurrence to inform improved adjuvant radiotherapy planning. Methods: We retrospectively analyzed 31 patients with recurrent sacrococcygeal chordoma following surgery, assessing [...] Read more.
Background: Postoperative recurrence of sacrococcygeal chordomas presents significant clinical challenges due to unusual recurrence patterns. This study aimed to characterize these patterns of recurrence to inform improved adjuvant radiotherapy planning. Methods: We retrospectively analyzed 31 patients with recurrent sacrococcygeal chordoma following surgery, assessing recurrence locations considering initial tumor extent, resection levels, and postoperative anatomical changes on MRI. In 18 patients, pre- and postoperative imaging enabled the spatial mapping of early recurrence origins relative to the initial tumor volume using isotropic expansions. The median initial gross tumor volume was 113 mL. Results: Recurrences were mostly multifocal and predominantly involved soft tissues (e.g., mesorectal/perirectal space (80.6%), piriformis and gluteal muscles (80.6% and 67.7%, respectively) and osseous structures, particularly the sacrum (87.1%)). The median time to recurrence was 15 months. The initial surgery was R0 in 17 patients (55%). The highest infiltrated sacral vertebra was S1 in 3%, S2 in 10%, S3 in 35%, S4 in 23%, S5 in 10%, and coccygeal in 19%. Anatomical changes post-resection, including rectal herniation into gluteal and subcutaneous tissues, significantly affected radiotherapy planning. Expansion of the initial tumor volume by 2 cm failed to encompass all recurrence origins in 72% of cases. A 5 cm expansion was required to achieve full coverage in 56% of patients, though 22% of recurrences still lay beyond this margin and the remaining were covered only partially. Conclusions: Recurrent sacrococcygeal chordomas exhibit complex, soft-tissue-dominant patterns and are influenced by significant anatomical displacement post-surgery. Standard target volume expansions are often insufficient to cover the predominantly multifocal recurrences. Full article
(This article belongs to the Special Issue Advanced Research on Spine Tumor)
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16 pages, 2052 KiB  
Article
Prognostic Implications of T Cell Receptor Repertoire Diversity in Cervical Lymph Nodes of Oral Squamous Cell Carcinoma Patients
by Kenichi Kumagai, Yoshiki Hamada, Akihisa Horie, Yudai Shimizu, Yoshihiro Ohashi, Reo Aoki, Taiki Suzuki, Koji Kawaguchi, Akihiro Kuroda, Takahiro Tsujikawa, Kazuto Hoshi and Kazuhiro Kakimi
Int. J. Mol. Sci. 2025, 26(15), 7073; https://doi.org/10.3390/ijms26157073 - 23 Jul 2025
Viewed by 170
Abstract
The immune landscape of tumor-draining lymph nodes (TDLNs) plays a critical role in shaping antitumor responses and influencing prognosis in oral squamous cell carcinoma (OSCC). Among patients with lymph node (LN) metastasis, clinical outcomes vary widely, yet reliable biomarkers for prognostic stratification remain [...] Read more.
The immune landscape of tumor-draining lymph nodes (TDLNs) plays a critical role in shaping antitumor responses and influencing prognosis in oral squamous cell carcinoma (OSCC). Among patients with lymph node (LN) metastasis, clinical outcomes vary widely, yet reliable biomarkers for prognostic stratification remain limited. This study aimed to identify immune features in tumors and LNs that differentiate between favorable and poor outcomes in OSCC patients with nodal metastasis. We analyzed T cell receptor (TCR) CDR3 repertoires and the expression of immune-related genes in primary tumors and paired sentinel LNs from OSCC patients who underwent tumor resection and lymphadenectomy. Patients were divided into three groups: Group A (no nodal metastasis), Group B1 (metastasis without recurrence), and Group B2 (metastasis with recurrence). TCR diversity was assessed using the Shannon index. The expression of immune-related genes (e.g., CD3E, CD4, CD8B, FOXP3, CTLA4, IL2, IL4) was measured by quantitative PCR and normalized to GAPDH. TCR diversity was lower in tumors than in non-metastatic LNs, reflecting clonal expansion. Metastatic LNs exhibited tumor-like diversity, suggesting infiltration by tumor-reactive clones. Tumor gene expression did not differ across groups, but LNs from metastatic cases showed the reduced expression of several immune genes. Notably, CD3E, CD8B, CTLA4, IL2, and IL4 distinguished B1 from B2. The immune profiling of LNs offers superior prognostic value over tumor analysis in OSCC patients with LN metastasis. LN-based evaluation may aid in postoperative risk stratification and personalized postoperative management and could inform decisions regarding adjuvant therapy and follow-up strategies. Full article
(This article belongs to the Section Molecular Biology)
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21 pages, 1759 KiB  
Review
Three Decades of Managing Pediatric Obstructive Sleep Apnea Syndrome: What’s Old, What’s New
by Beatrice Panetti, Claudia Federico, Giuseppe Francesco Sferrazza Papa, Paola Di Filippo, Armando Di Ludovico, Sabrina Di Pillo, Francesco Chiarelli, Alessandra Scaparrotta and Marina Attanasi
Children 2025, 12(7), 919; https://doi.org/10.3390/children12070919 - 11 Jul 2025
Viewed by 573
Abstract
Obstructive sleep apnea syndrome (OSAS) in children and adolescents is a prevalent and multifactorial disorder associated with significant short- and long-term health consequences. While adenotonsillectomy (AT) remains the first-line treatment, a substantial proportion of patients—especially those with obesity, craniofacial anomalies, or comorbid conditions—exhibit [...] Read more.
Obstructive sleep apnea syndrome (OSAS) in children and adolescents is a prevalent and multifactorial disorder associated with significant short- and long-term health consequences. While adenotonsillectomy (AT) remains the first-line treatment, a substantial proportion of patients—especially those with obesity, craniofacial anomalies, or comorbid conditions—exhibit persistent or recurrent symptoms, underscoring the need for individualized and multimodal approaches. This review provides an updated and comprehensive overview of current and emerging treatments for pediatric OSAS, with a focus on both surgical and non-surgical options, including pharmacological, orthodontic, and myofunctional therapies. A narrative synthesis of recent literature was conducted, including systematic reviews, randomized controlled trials, and large cohort studies published in the last 10 years. The review emphasizes evidence-based indications, mechanisms of action, efficacy outcomes, safety profiles, and limitations of each therapeutic modality. Adjunctive and alternative treatments such as rapid maxillary expansion, mandibular advancement devices, myofunctional therapy, intranasal corticosteroids, leukotriene receptor antagonists, and hypoglossal nerve stimulation show promising results in selected patient populations. Personalized treatment plans based on anatomical, functional, and developmental characteristics are essential to optimize outcomes. Combination therapies appear particularly effective in children with residual disease after AT or with specific phenotypes such as Down syndrome or maxillary constriction. Pediatric OSAS requires a tailored, multidisciplinary approach that evolves with the child’s growth and clinical profile. Understanding the full spectrum of available therapies allows clinicians to move beyond a one-size-fits-all model, offering more precise and durable treatment pathways. Emerging strategies may further redefine the therapeutic landscape in the coming years. Full article
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12 pages, 486 KiB  
Article
Five-Year Retrospective Analysis of Traumatic and Non-Traumatic Pneumothorax in 2797 Patients
by Ayhan Tabur and Alper Tabur
Healthcare 2025, 13(14), 1660; https://doi.org/10.3390/healthcare13141660 - 10 Jul 2025
Viewed by 308
Abstract
Objectives: Pneumothorax is a critical condition frequently encountered in emergency departments (EDs), with spontaneous pneumothorax (SP) and traumatic pneumothorax (TP) presenting distinct clinical challenges. This study aimed to evaluate the epidemiological characteristics, clinical outcomes, and treatment strategies for SP and TP across different [...] Read more.
Objectives: Pneumothorax is a critical condition frequently encountered in emergency departments (EDs), with spontaneous pneumothorax (SP) and traumatic pneumothorax (TP) presenting distinct clinical challenges. This study aimed to evaluate the epidemiological characteristics, clinical outcomes, and treatment strategies for SP and TP across different age groups and provide insights for optimizing emergency management protocols. Methods: This retrospective cohort study analyzed 2797 cases of pneumothorax over five years (2018–2023) at a tertiary care center. Patients were stratified by age (18–39, 40–64, and >65 years) and pneumothorax type (SP vs. TP). Data on demographics, clinical presentation, treatment, hospital stay, recurrence, and complications were extracted from medical records. Comparative statistical analyses were also conducted. Results: The mean age of patients with SP was 32.5 ± 14.7 years, whereas patients with TP were older (37.8 ± 16.2 years, p < 0.001). Male predominance was observed in both groups: 2085 (87.0%) in the SP group and 368 (92.0%) in the TP group (p = 0.01). The right lung was more frequently affected in the SP (64.2%) and TP (56.0%) groups (p < 0.001). Age-related differences were evident in both groups of patients. In the SP group, younger patients (18–39 years) represented the majority of cases, whereas older patients (≥65 years) were more likely to present with SSP and required more invasive management (p < 0.01). In the TP group, younger patients often had pneumothorax due to high-energy trauma, whereas older individuals developed pneumothorax due to falls or iatrogenic causes (p < 0.01). SP predominantly affected younger patients, with a history of smoking and male predominance associated with younger age (p < 0.01). TP is more frequent in older patients, often because of falls or iatrogenic injuries. Management strategies varied by age group; younger patients were often managed conservatively, whereas older patients underwent more invasive procedures (p < 0.01). Surgical intervention was more common in younger patients in the TP group, whereas conservative management was more frequent in elderly patients (p < 0.01). The clinical outcomes differed significantly, with older patients having longer hospital stays and higher rates of persistent air leaks (p < 0.01). Recurrence was more common in younger patients with SP, whereas TP recurrence rates were lower across all age groups (p < 0.01). No significant differences were observed in re-expansion pulmonary edema, empyema, or mortality rates between the age groups, suggesting that age alone was not an independent predictor of these complications when adjusted for pneumothorax severity and management strategy (p = 0.22). Conclusions: Age, pneumothorax subtype, and underlying pulmonary comorbidities were identified as key predictors of clinical outcomes. Advanced age, secondary spontaneous pneumothorax, and COPD were independently associated with recurrence, prolonged hospitalization, and in-hospital mortality, respectively. These findings highlight the need for risk-adapted management strategies to improve triaging and treatment decisions for spontaneous and traumatic pneumothorax. Full article
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21 pages, 4241 KiB  
Article
Federated Learning-Driven Cybersecurity Framework for IoT Networks with Privacy Preserving and Real-Time Threat Detection Capabilities
by Milad Rahmati and Antonino Pagano
Informatics 2025, 12(3), 62; https://doi.org/10.3390/informatics12030062 - 4 Jul 2025
Cited by 1 | Viewed by 705
Abstract
The rapid expansion of the Internet of Things (IoT) ecosystem has transformed industries but also exposed significant cybersecurity vulnerabilities. Traditional centralized methods for securing IoT networks struggle to balance privacy preservation with real-time threat detection. This study presents a Federated Learning-Driven Cybersecurity Framework [...] Read more.
The rapid expansion of the Internet of Things (IoT) ecosystem has transformed industries but also exposed significant cybersecurity vulnerabilities. Traditional centralized methods for securing IoT networks struggle to balance privacy preservation with real-time threat detection. This study presents a Federated Learning-Driven Cybersecurity Framework designed for IoT environments, enabling decentralized data processing through local model training on edge devices to ensure data privacy. Secure aggregation using homomorphic encryption supports collaborative learning without exposing sensitive information. The framework employs GRU-based recurrent neural networks (RNNs) for anomaly detection, optimized for resource-constrained IoT networks. Experimental results demonstrate over 98% accuracy in detecting threats such as distributed denial-of-service (DDoS) attacks, with a 20% reduction in energy consumption and a 30% reduction in communication overhead, showcasing the framework’s efficiency over traditional centralized approaches. This work addresses critical gaps in IoT cybersecurity by integrating federated learning with advanced threat detection techniques. It offers a scalable, privacy-preserving solution for diverse IoT applications, with future directions including blockchain integration for model aggregation traceability and quantum-resistant cryptography to enhance security. Full article
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18 pages, 6896 KiB  
Article
Relationship Between Recurrent Magnetic Flux Rope and Moving Magnetic Features
by Yin Zhang, Jihong Liu, Quan Wang, Suo Liu, Jing Huang, Jie Chen and Baolin Tan
Universe 2025, 11(7), 222; https://doi.org/10.3390/universe11070222 - 3 Jul 2025
Viewed by 249
Abstract
Large-scale magnetic flux ropes (MFRs) usually become visible during an eruption and are the core structures of coronal mass ejections, but the nature of MFRs is still a mystery. Here, we identify a large transequatorial MFR that spans across NOAA 13373 (in the [...] Read more.
Large-scale magnetic flux ropes (MFRs) usually become visible during an eruption and are the core structures of coronal mass ejections, but the nature of MFRs is still a mystery. Here, we identify a large transequatorial MFR that spans across NOAA 13373 (in the Northern Hemisphere) and NOAA 13374 (in the Southern Hemisphere). Here, NOAA 13373 is a growing, newly emerging active region with a leading sunspot moving rapidly to the southwest, and it is surrounded by a highly dynamic moving magnetic feature (MMF), while NOAA 13374 is a decaying active region with a tiny leading negative sunspot and a large fading area. Recurrent reconnection, which occurs under the MFRs around the leading sunspot of NOAA 13373, results in local energy release, appearing as local EUV brightening, and it is related to the appearance of a transequatorial MFR. The appearance of this MFR involves several stages: EUV brightening, the slow rising and expansion of the MFR and its hosted filament, and, eventually, fading and shrinking. These observations demonstrate that a large-scale MFR can exist for a long-term period and that MMFs play a key role in building up free energy and triggering small-scale reconnections in the lower atmosphere. The energy released by these reconnection events is insufficient for triggering the eruption of an MFR but results in local disturbances. Full article
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15 pages, 946 KiB  
Review
Focal and Segmental Glomerulosclerosis: A Comprehensive State-of-the-Art Review
by Dearbhail Ni Cathain, Donnchadh Reidy, Serena Bagnasco and Sam Kant
Sclerosis 2025, 3(3), 24; https://doi.org/10.3390/sclerosis3030024 - 1 Jul 2025
Viewed by 425
Abstract
Focal and segmental glomerulosclerosis (FSGS) describes a histological pattern of injury seen by light microscopy in kidney biopsy specimens and is the end result of various injuries to the podocyte. Our understanding of this disease entity has evolved greatly since it was first [...] Read more.
Focal and segmental glomerulosclerosis (FSGS) describes a histological pattern of injury seen by light microscopy in kidney biopsy specimens and is the end result of various injuries to the podocyte. Our understanding of this disease entity has evolved greatly since it was first described, with particular focus on changes in the classification of FSGS as a disease entity and expansion in our understanding of the underlying pathophysiology. The incidence and prevalence of FSGS and FSGS-associated end-stage kidney disease (ESKD) have increased globally, particularly in the United States; it is now the most common primary glomerular disorder in those with ESKD. APOL-1 is likely responsible for this epidemiological trend in kidney disease in the US and is an important focus of clinical trials and potential targeted therapies. Currently, the goal of treatment in FSGS is to achieve remission of proteinuria and to prevent progression to ESKD. Remission is achieved by using immunosuppressive therapies in primary FSGS, but treatment in secondary and genetic FSGS is largely supportive. Recurrent FSGS (rFSGS) post-transplantation remains a significant clinical challenge to nephrologists; current monitoring and treatment strategies are based on retrospective meta-analysis and observational studies with no clear consensus as to the optimum approach. Emerging therapies are focused on developing more targeted interventions in genetic and secondary FSGS. This review article aims to comprehensively explore this multifaceted disease entity. Full article
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14 pages, 1555 KiB  
Review
Epigallocatechin Gallate as a Potential Therapeutic Agent in Endometriosis: A Narrative Review
by Anna Markowska, Zbigniew Kojs, Michał Antoszczak, Janina Markowska and Adam Huczyński
Nutrients 2025, 17(13), 2068; https://doi.org/10.3390/nu17132068 - 21 Jun 2025
Viewed by 669
Abstract
Endometriosis is a chronic, hormone-dependent disease that affects women of reproductive age. It leads to numerous adverse clinical symptoms, which significantly impact women’s quality of life. The chronic nature of the disease and its recurrence are the main reasons for the search for [...] Read more.
Endometriosis is a chronic, hormone-dependent disease that affects women of reproductive age. It leads to numerous adverse clinical symptoms, which significantly impact women’s quality of life. The chronic nature of the disease and its recurrence are the main reasons for the search for new, non-hormonal drugs and drug candidates, either as adjunct treatment options or alternative therapies. The catechin found in green tea, epigallocatechin gallate (EGCG), has been shown to exhibit a wide array of biological activities, which may also contribute to its potential effectiveness in treating endometriosis. The poor physicochemical stability and relatively low bioavailability of EGCG have stimulated the development of a peracetylated prodrug (pro-EGCG) and other solutions, based on nanotechnology, that would eliminate the problems with EGCG. In this review article, we summarize the studies on the effects of EGCG, pro-EGCG, and EGCG-based nanoparticles on the course of endometriosis published in the GoogleScholar and PubMed databases. Of note is the fact that the results of in vitro and animal model studies have suggested that EGCG and pro-EGCG can reduce the number of endometriosis foci and their size and volume, and they can prevent fibrosis by affecting multiple molecular factors and signaling pathways. The promising results provide a basis for using green herbal extracts for endometriosis treatment in a clinical trial. Nevertheless, it should be emphasized that the number of studies on the topic is currently very limited; further expansion in the coming years is necessary. Broad, well-designed clinical trials are also essential to validate the true potential of EGCG and related compounds in the fight against endometriosis. Full article
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14 pages, 5444 KiB  
Case Report
Radiographic and Histopathological Characteristics of Chronic Nonbacterial Osteomyelitis of the Mandible in Pediatric Patients: Case Series
by Mohammed Barayan, Nagla’a Abdel Wahed, Narmin Helal, Hisham Abbas Komo, Durer Iskanderani, Raghd Alansari, Nada A. Alhindi, Azza F. Alhelo, Hanadi Khalifa and Hanadi Sabban
Diagnostics 2025, 15(12), 1549; https://doi.org/10.3390/diagnostics15121549 - 18 Jun 2025
Viewed by 451
Abstract
Background and Clinical Significance: Chronic nonbacterial osteomyelitis (CNO) of the jaw is a rare autoinflammatory bone disorder that primarily affects children and adolescents. Diagnosing CNO of the mandible can be challenging due to its rarity, and the clinical and radiographic findings overlap with [...] Read more.
Background and Clinical Significance: Chronic nonbacterial osteomyelitis (CNO) of the jaw is a rare autoinflammatory bone disorder that primarily affects children and adolescents. Diagnosing CNO of the mandible can be challenging due to its rarity, and the clinical and radiographic findings overlap with those of other bone disorders. Case Presentation: This case series retrospectively presents four female pediatric patients (9–12 years old) diagnosed with mandibular CNO. The patients were treated at King Abdulaziz University Dental Hospital, Jeddah, Saudi Arabia, between 2018 and 2024. Clinical features and radiographic and histopathological findings were evaluated. All cases had mandibular swelling and pain. Radiographic features consistently revealed mixed sclerotic and radiolucent lesions with bone expansion and periosteal reactions. Histopathological findings revealed viable bone interspersed with varying degrees of fibrous tissue. No evidence of bacterial colonies or inflammation was observed. This case series highlights the radiographic and histopathological features of CNO in the mandible of pediatric patients. The mixed radiographic features and variability of histopathological findings combined with the refractory nature of the lesions contribute to diagnostic complexity. Diagnostic challenges include differentiating CNO from other inflammatory and fibro-osseous conditions. The presence of recurrent episodes of pain, the formation of subperiosteal bone, periostitis, lysis of the cortical layer, expansion of the mandibular canal, and sterile bone biopsies with nonspecific inflammatory changes were related mainly to CNO. Conclusions: These findings underscore the need for increased awareness and a multidisciplinary approach for accurate diagnosis and management of CNO. Conservative management, particularly in dental cases, avoids prolonged unnecessary use of antibiotics, and the prescription of nonsteroidal anti-inflammatory drugs should be followed. Full article
(This article belongs to the Special Issue Computed Tomography Imaging in Medical Diagnosis, 2nd Edition)
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10 pages, 2778 KiB  
Case Report
Protracted Tonsillitis as an Atypical Initial Manifestation of Methotrexate-Induced EBV-Positive Lymphoproliferative Disorder in Rheumatoid Arthritis: A Case Report and Literature Review
by Ting-Shen Lin, Tang-Yi Tsao, Shih-Wei Chen, Min-Cheng Ko and Stella Chin-Shaw Tsai
Diagnostics 2025, 15(12), 1517; https://doi.org/10.3390/diagnostics15121517 - 14 Jun 2025
Cited by 1 | Viewed by 500
Abstract
Background and Clinical Significance: Methotrexate is widely used as a disease-modifying antirheumatic drug for rheumatoid arthritis (RA), yet prolonged immunosuppression may lead to rare complications, including Epstein–Barr virus (EBV)-positive lymphoproliferative disorders (LPDs). Case Presentation: We present the case of a 70-year-old woman with [...] Read more.
Background and Clinical Significance: Methotrexate is widely used as a disease-modifying antirheumatic drug for rheumatoid arthritis (RA), yet prolonged immunosuppression may lead to rare complications, including Epstein–Barr virus (EBV)-positive lymphoproliferative disorders (LPDs). Case Presentation: We present the case of a 70-year-old woman with RA on chronic immunosuppressive therapy who developed symptoms resembling recurrent tonsillitis. CT imaging revealed bilateral necrotic palatine tonsils and extensive necrotic lymphadenopathy involving the cervical, mediastinal, and axillary regions. Bilateral tonsillectomy was performed due to concerns about malignancy or infection, and histopathology confirmed a polymorphic EBV-positive LPD with Hodgkin-like features, consistent with iatrogenic immunodeficiency-associated LPD. Methotrexate was subsequently discontinued, and the patient was managed conservatively without systemic chemotherapy. Clinical recovery was observed during follow-up. Conclusions: This case highlights the importance of considering methotrexate-associated LPDs in the differential diagnosis of atypical tonsillar infections in immunosuppressed patients, particularly when necrotic features or systemic lymphadenopathy are present. The pathogenesis may involve EBV reactivation under impaired immune surveillance due to methotrexate, leading to abnormal B-cell proliferation and clonal expansion. This case is contextualized through a comparative analysis of published reports, highlighting clinical features and treatment responses of methotrexate-associated EBV-positive LPDs in the form of a focused literature review. Full article
(This article belongs to the Special Issue Diagnosis and Management in Otolaryngology 2025)
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21 pages, 330 KiB  
Review
Schrödinger Potentials with Polynomial Solutions of Heun-Type Equations
by Géza Lévai and Tibor Soltész
Mathematics 2025, 13(12), 1963; https://doi.org/10.3390/math13121963 - 14 Jun 2025
Viewed by 289
Abstract
The present review discusses the solution of the Heun, confluent, biconfluent, double confluent, and triconfluent equations in terms of polynomial expansions, and applies the results to generate exactly solvable Schrödinger potentials. Although there are more general approaches to solve these differential equations in [...] Read more.
The present review discusses the solution of the Heun, confluent, biconfluent, double confluent, and triconfluent equations in terms of polynomial expansions, and applies the results to generate exactly solvable Schrödinger potentials. Although there are more general approaches to solve these differential equations in terms of the expansions of certain special functions, the importance of polynomial solutions is unquestionable, as most of the known potentials are solvable in terms of the hypergeometric and confluent hypergeometric functions; i.e., Natanzon-class potentials possess bound-state solutions in terms of classical orthogonal polynomials, to which the (confluent) hypergeometric functions can be reduced. Since some of the Heun-type equations contain the hypergeometric and/or confluent hypergeometric differential equations as special limits, the potentials generated from them may also contain Natanzon-class potentials as special cases. A power series expansion is assumed around one of the singular points of each differential equation, and recurrence relations are obtained for the expansion coefficients. With the exception of the triconfluent Heun equations, these are three-term recurrence relations, the termination of which is achieved by prescribing certain conditions. In the case of the biconfluent and double confluent Heun equations, the expansion coefficients can be obtained in the standard way, i.e., after finding the roots of an (N + 1)th-order polynomial in one of the parameters, which, in turn, follows from requiring the vanishing of an (N + 1) × (N + 1) determinant. However, in the case of the Heun and confluent Heun equations, the recurrence relation can be solved directly, and the solutions are obtained in terms of rationally extended X1-type Jacobi and Laguerre polynomials, respectively. Examples for solvable potentials are presented for the Heun, confluent, biconfluent, and double confluent Heun equations, and alternative methods for obtaining the same potentials are also discussed. These are the schemes based on the rational extension of Bochner-type differential equations (for the Heun and confluent Heun equation) and solutions based on quasi-exact solvability (QES) and on continued fractions (for the biconfluent and double confluent equation). Possible further lines of investigations are also outlined concerning physical problems that require the solution of second-order differential equations, i.e., the Schrödinger equation with position-dependent mass and relativistic wave equations. Full article
(This article belongs to the Section E4: Mathematical Physics)
17 pages, 698 KiB  
Article
Numerical Method for Band Gap Structure and Dirac Point of Photonic Crystals Based on Recurrent Neural Network
by Yakun Wang and Jianhua Yuan
Axioms 2025, 14(6), 445; https://doi.org/10.3390/axioms14060445 - 6 Jun 2025
Viewed by 433
Abstract
In this paper, we propose a recurrent neural network numerical method with the finite element method for partial differential equations to study the band gap structure and Dirac points in two-dimensional photonic crystals. Electromagnetic wave propagation is governed by Maxwell’s equations. We transform [...] Read more.
In this paper, we propose a recurrent neural network numerical method with the finite element method for partial differential equations to study the band gap structure and Dirac points in two-dimensional photonic crystals. Electromagnetic wave propagation is governed by Maxwell’s equations. We transform the partial differential equations into large-scale generalized eigenvalue problems by spatially discretising them using the finite element method. Compared with traditional numerical computation methods, neural networks can perform high-speed parallel computation. Existing neural network-based eigenvalue solvers are typically restricted to computing extremal eigenvalues of real symmetric matrix pairs. To overcome this limitation, we develop a novel RNN-based numerical scheme tailored for solving the band structure problem in photonic crystals. We validate our method by computing the dispersion relations of photonic crystals with periodic dielectric columns, achieving excellent agreement with the plane-wave expansion method. In addition, we calculate the Dirac points at the center of the Brillouin zone, which is crucial for understanding the unique optical properties of photonic crystals. We determine the precise filling ratios at which these Dirac points appear, thus providing insight into the relationship between geometrical and material parameters and the appearance of Dirac points. Full article
(This article belongs to the Topic Numerical Methods for Partial Differential Equations)
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19 pages, 1842 KiB  
Article
A.A.A. Good Wines WANTED: Blockchain, Non-Destructive Ultrasonic Techniques and Soil Health Assessment for Wine Traceability
by Diego Romano Perinelli, Martina Coletta, Beatrice Sabbatini, Aldo D’Alessandro, Fabio Fabiani, Andrea Passacantando, Giulia Bonacucina and Antonietta La Terza
Sensors 2025, 25(11), 3567; https://doi.org/10.3390/s25113567 - 5 Jun 2025
Viewed by 491
Abstract
The wine industry faces increasing challenges related to authenticity, safety, and sustainability due to recurrent fraud, shifting consumer preferences, and environmental concerns. In this study, as part of the B.I.O.C.E.R.T.O project, we integrated blockchain technology with ultrasonic spectroscopy and soil quality data by [...] Read more.
The wine industry faces increasing challenges related to authenticity, safety, and sustainability due to recurrent fraud, shifting consumer preferences, and environmental concerns. In this study, as part of the B.I.O.C.E.R.T.O project, we integrated blockchain technology with ultrasonic spectroscopy and soil quality data by using the arthropod-based Soil Biological Quality Index (QBS-ar) to enhance traceability, ensure wine quality, and certify sustainable vineyard practices. Four representative wines from the Marche region (Sangiovese, Maceratino, and two Verdicchio PDO varieties) were analyzed across two vintages (2021 and 2022). Ultrasound spectroscopy demonstrated high sensitivity in distinguishing wines based on ethanol and sugar content, comparably to conventional viscosity-based methods. The QBS-ar index was applied to investigate the soil biodiversity status according to the agricultural management practices applied in each vineyard, reinforcing consumer confidence in environmentally responsible viticulture. By recording these data on a public blockchain, we developed a secure, transparent, and immutable certification system to verify the geographical origin of wines along with their unique characteristics. This is the first study to integrate advanced analytical techniques with blockchain technology for wine traceability, simultaneously addressing counterfeiting, consumer demand for transparency, and biodiversity preservation. Our findings support the applicability of this model to other agri-food sectors, with potential for expansion through additional analytical techniques, such as isotopic analysis and further agroecosystem sustainability indicators. Full article
(This article belongs to the Section Chemical Sensors)
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22 pages, 612 KiB  
Article
Quantitative Recurrence Properties in Some Irregular Sets for Beta Dynamical Systems
by Yuanyang Chang and Wenna Liu
Mathematics 2025, 13(11), 1850; https://doi.org/10.3390/math13111850 - 2 Jun 2025
Viewed by 306
Abstract
Let β>1 be a real number and Tβx=βx(mod1). This paper is concerned with the quantitative recurrence properties of the system [...] Read more.
Let β>1 be a real number and Tβx=βx(mod1). This paper is concerned with the quantitative recurrence properties of the system ([0,1],Tβ) in some (refined) irregular sets. Specifically, let α1,α2>0 and ψ:N(0,1) be a positive function; we define the set Eα1,α2β=x[0,1):lim infn1nSn(x,β)=α1,lim supn1nSn(x,β)=α2, and calculate the Hausdorff dimension of the set Eα1,α2β(ψ):=xEα1,α2β:|Tβnxx|<ψ(n)i.m.nN, where i.m. stands for infinitely many. Consequently, the Hausdorff dimension of the set E^β(ψ)=x[0,1):limn1nSn(x,β)doesnotexist, |Tβnxx|<ψ(n)i.m.nN is also determined. Full article
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20 pages, 3652 KiB  
Article
Hydroclimatic and Land Use Drivers of Wildfire Risk in the Colombian Caribbean
by Yiniva Camargo Caicedo, Sindy Bolaño-Diaz, Geraldine M. Pomares-Meza, Manuel Pérez-Pérez, Tionhonkélé Drissa Soro, Tomás R. Bolaño-Ortiz and Andrés M. Vélez-Pereira
Fire 2025, 8(6), 221; https://doi.org/10.3390/fire8060221 - 31 May 2025
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Abstract
Fire-driven land cover change has generated a paradox: while habitat fragmentation from agriculture, livestock, and urban expansion has reduced natural fire occurrences, human-induced ignitions have increased wildfire frequency and intensity. In northern Colombia’s Magdalena Department, most of the territory faces moderate to high [...] Read more.
Fire-driven land cover change has generated a paradox: while habitat fragmentation from agriculture, livestock, and urban expansion has reduced natural fire occurrences, human-induced ignitions have increased wildfire frequency and intensity. In northern Colombia’s Magdalena Department, most of the territory faces moderate to high wildfire risk, especially during recurrent dry seasons and periods of below-average precipitation. However, knowledge of wildfire spatiotemporal occurrence and its drivers remains scarce. This work addresses this gap by identifying fire-prone zones and analyzing the influence of climate and vegetation in the Magdalena Department. Fire-prone zones were identified using the Getis–Ord Gi* method over fire density and burned area data from 2001 to 2023; then, they were analyzed with seasonally aggregated hydroclimatic indices via logistic regression to quantify their influence on wildfires. Vegetation susceptibility was assessed using geostatistics, obtaining land cover types most affected by fire and their degree of fragmentation. Fire-prone zones in the Magdalena Department covered ~744.35 km2 (3.21%), with a weak but significant (τ = 0.20, p < 0.01) degree of coincidence between classification based on fire density, as pre-fire variable, and burned area, as a post-fire variable. Temporally, fire probability increased during the dry season, driven by short-lagged precursors such as Dry Spell Length and precipitation from the preceding wet season. Fire-prone zones were dominated by pastures (62.39%), grasslands and shrublands (19.61%) and forests (15.74%), and exhibited larger, more complex high-risk patches, despite similar spatial connectedness with non-fire-prone zones. These findings enhance wildfire vulnerability understanding, contributing to risk-based territorial planning. Full article
(This article belongs to the Section Fire Science Models, Remote Sensing, and Data)
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