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Multiscale is a hallmark feature of complex systems, presenting challenges for traditional numerical methods due to their reliance on local Taylor series constraints. Further, multiscale techniques often face limitations in identifying appropriate heuristic closures used to handle unresolved scales or processes within the system being modeled. In this study, we develop an efficient time-stepping strategy for multiscale problems. The proposed method's novelty lies in synergizing the hierarchical deep learning formalism with an adaptive step-size estimation process to approximate dynamical system flow maps across timescales efficiently. The model is purely data-driven and provides improved forecasting accuracy compared to fixed-step neural network time steppers. To demonstrate the effectiveness of the proposed scheme, we provide numerical simulations for several canonical nonlinear systems and source codes for their implementation. We believe the method has the potential to benefit multiscale analysis of complex systems and encourage further investigation in this area. • Identifies potential drawbacks in the current multiscale methods. • Introduces efficient time-stepping algorithm for multiscale problems using hierarchical deep learning. • Demonstrates the application of adaptive time-stepping on canonical ODEs and PDEs with noisy measurements. [ABSTRACT FROM AUTHOR]

Multiscale is a hallmark feature of complex systems, presenting challenges for traditional numerical methods due to their reliance on local Taylor series constraints. Further, multiscale techniques often face limitations in identifying appropriate heuristic closures used to handle unresolved scales or processes within the system being modeled. In this study, we develop an efficient time-stepping strategy for multiscale problems. The proposed method's novelty lies in synergizing the hierarchical deep learning formalism with an adaptive step-size estimation process to approximate dynamical system flow maps across timescales efficiently. The model is purely data-driven and provides improved forecasting accuracy compared to fixed-step neural network time steppers. To demonstrate the effectiveness of the proposed scheme, we provide numerical simulations for several canonical nonlinear systems and source codes for their implementation. We believe the method has the potential to benefit multiscale analysis of complex systems and encourage further investigation in this area. • Identifies potential drawbacks in the current multiscale methods. • Introduces efficient time-stepping algorithm for multiscale problems using hierarchical deep learning. • Demonstrates the application of adaptive time-stepping on canonical ODEs and PDEs with noisy measurements. [ABSTRACT FROM AUTHOR]

This manuscript combines the recently developed nonlinear moment-matching (NLMM) technique with dynamic mode decomposition (DMD) to obtain a simulation-free reduction framework for power systems. Unlike the conventional model reduction methods for power systems, where the external area is linearized, we consider the nonlinear effective network (EN) and the synchronous motor (SM) power grid models. First, the reduced system is constructed from the solution of the underlying approximate Sylvester equation by exciting the system with user-defined inputs from a representative exogenous system. Then, a non-intrusive reduction is performed using DMD to approximate the nonlinear function via Koopman modes in an equation-free manner. The advantage is that a "simulation-free" nonlinear model order reduction framework is obtained to approximate the response of the large-scale power grid models. Finally, we substantiate our observations using numerical simulations of reduced EN and SM models of the IEEE 118 and IEEE 300 bus systems for realistic fault scenarios. Results show that the overall CPU times of the reduced-order models are lowered to half as compared to the original models while maintaining the fidelity. The results are also compared with POD-DEIM for reference. • The study presents the dimensionality reduction of large-scale power system models. • The intrusive MOR is achieved using approximated nonlinear moment-matching technique. • DMD is used to obtain a low-rank approximation of the underlying nonlinear function. • The overall combination yields an efficient reduction framework for power grids. • Results show considerable savings in the CPU times of the ROMs thus obtained. [ABSTRACT FROM AUTHOR]

In this manuscript, we propose a novel reduction framework for obtaining Reduced Order Models (ROMs) of large-scale, nonlinear dynamical systems. We advocate the use of Nonlinear Moment Matching (NLMM) with the Dynamic Mode Decomposition (DMD) to get a much efficient dimensionality reduction scheme. While NLMM does not require the expensive computation of the time-displaced snapshot ensemble of the Full Order Model (FOM) in the offline stage, DMD avoids the evaluation of the nonlinear term in the online stage. Thus, significant savings in terms of the overall CPU-time is achieved. To substantiate our observations, we test the proposed scheme on a variety of benchmark models and compare the results with POD–DEIM for reference. • A simulation-free scheme based on NLMM and DMD is presented. • The offline collection of time-snapshots for the FOM is avoided in NLMM. • The underlying nonlinearity is further approximated via DMD modes. • Results show a considerable saving in terms of overall CPU times. [ABSTRACT FROM AUTHOR]

Introduction. Adrenalmyelolipoma is a rare tumor that is benign in nature, usually asymptomatic, unilateral, and nonsecreting. It is composed of variable mixture of mature adipose tissue and hematopoietic elements and develops within the adrenal gland. With the widespread use of cross-sectional imagingmodalities such as ultrasonography and computed tomography, the incidental detection of these tumors is increasing in frequency. Case Presentation. We report a case of adrenal myelolipoma in a 63-year-old Kashmiri male, who presented with pain in the right upper abdomen. Physical examination was unremarkable. Ultrasound abdomen showed the presence of a hyperechoic mass in the right suprarenal region with undefined margins. Contrast-enhanced computed tomography (CECT) scan of abdomen revealed a well-defined, round lesion in the right suprarenal region with heterogeneous attenuation suggesting the possibility of myelolipoma. The patient was subjected to right adrenalectomy and his postoperative course was uneventful. The histopathological evaluation of the mass confirmed the initial diagnosis of adrenal myelolipoma. Conclusion. Althoughmostly discovered as an "incidentaloma", the diagnosis of adrenalmyelolipoma warrants thorough diagnostic study. Imaging techniques such as ultrasonography and CT scans as well as biochemical studies are useful for indicating the best treatment taking into account the size of the mass and possible hormone production. Surgical resection is advocated through extraperitoneal approach as it minimizes postoperative complications and leads to quicker recovery. [ABSTRACT FROM AUTHOR]

Synovial sarcomas are rare tumors accounting for approximately 5-10% of soft tissue sarcomas. They occur predominantly in the extremities, followed by head and neck. Primary pulmonary sarcomas are very rare and comprise only 0.5% of all primary lung malignancies. The diagnosis is established only after sarcomas like primary lung malignancies, and metastatic sarcomas have been excluded. For synovial sarcomas that arise at unusual locations, a deinitive diagnosis is challenging and requires the use of ancillary diagnostic procedures such as immunohistochemistry (IHC) and molecular genetic techniques for conirmation of diagnosis. We report a case of 29-year-old male who had right lower lobe lung mass. He underwent right lower lobectomy. Intraoperative squash smears revealed spindle cell sarcoma. Subsequent histopathology and IHC conirmed the diagnosis as synovial sarcoma. We report this case on account of its rarity and to emphasize the utility of intraoperative squash smears in the diagnosis of such cases, which has been under-utilized in clinical practice. [ABSTRACT FROM AUTHOR]

Background: Meningiomas comprise 15%–20% of all primary intracranial tumors. They are generally benign tumors, and most patients are cured after surgery and remain free of recurrence. However, some tumors behave in an aggressive manner, and patients develop local recurrence or metastasis. Overall prognosis is good. Patients and Methods: This is an 11-year retrospective study conducted in the Departments of Pathology and Neurosurgery at Sheri-I-Kashmir Institute of Medical Sciences, Kashmir, India. Besides the demographic profile, the parameters analyzed were location of tumor on imaging, histopathological subtype, and grade of tumor according to the 2007 WHO classification and recurrence at follow-up. Results: A total of 254 patients were included in our study, of which 205 (80.7%) were brain meningiomas and 49 (19.3%) were spinal, with an overall female: male ratio of 2:1. Female: male ratio was more in spinal meningiomas, 15.3:1. Most of our patients were in the 4–6th decade of life with a mean age of 48 years (range: 5–73 years). Meningothelial meningioma was the most common histological type. Of ten patients who showed recurrence, seven cases showed only recurrence, but no progression to higher grade and three cases showed recurrence with progression by one WHO-grade. We also noticed that recurrence was higher in Simpson Grades II and III. Conclusion: Meningiomas are common in females and most of the meningiomas do well after surgery. The recurrence rate was 3.93% in our study and Simpson grade of tumor excision and histopathological grade contribute significantly to the recurrence of the tumor. [ABSTRACT FROM AUTHOR]