Counting Real Connected Components of Trinomial Curve Intersections and m-nomial Hypersurfaces

We prove that any pair of bivariate trinomials has at most 5 isolated roots in the positive quadrant. The best previous upper bounds independent of the polynomial degrees were much larger, e.g., 248832 (for just the non-degenerate roots) via a famous general result of Khovanski. Our bound is sharp, allows real exponents, allows degeneracies, and extends to certain systems of n-variate fewnomials, giving improvements over earlier bounds by a factor exponential in the number of monomials. We also derive analogous sharpened bounds on the number of connected components of the real zero set of a single n-variate m-nomial.Comment: 27 pages, 2 figures. Extensive revision of math.CO/0008069. To appear in Discrete and Computational Geometry. Technique from main theorem (Theorem 1) now pushed as far as it will go. In particular, Theorem 1 now covers certain fewnomial systems of type (n+1,...,n+1,m) and certain non-sparse fewnomial systems. Also, a new result on counting non-compact connected components of fewnomial hypersurfaces (Theorem 3) has been adde

Evaluation of Channel Coding Methods for Next Generation Mobile Communication Standards

La codificación de canales es crucial para los sistemas de comunicación móvil, y los sistemas de comunicación inalámbrica 5G han decidido utilizar los códigos LDPC como esquema de codificación para sus canales de datos y los códigos Polares como esquema de codificación para sus canales de control. Este estudio se centra en los fundamentos de los códigos LDPC y los códigos Polares, especialmente los nuevos códigos polares, explicando en detalle sus características de polarización y las técnicas de decodificación recursiva. También se estudia las especificaciones de diseño relacionadas con estos dos esquemas de codificación de canales en 5G. Mediante simulaciones, se compara el rendimiento del nuevo esquema de codificación de canales inalámbricos 5G con el de los códigos Turbo a diferentes longitudes de bloque y tasas de código, y se extraen conclusiones relevantes para demostrar la aplicabilidad del esquema de codificación de canales 5G NR.Channel coding is essential for mobile communication systems, and the 5G wireless standardization committees decided to use LDPC codes as the coding scheme of its data channel and Polar codes as the coding scheme of its control channel. This study focuses on the fundamentals of LDPC codes and Polar codes, especially the emerging Polar codes, with detailed explanations of their polarization characteristics and recursive decoding techniques. It is also focused on the design specification related to these two channel coding schemes in 5G. The performance of the 5G New Radio channel coding scheme is compared with that of LTE Turbo codes at different block lengths and code rates through simulations, and relevant conclusions are drawn to demonstrate the suitability of the 5G NR channel coding scheme.Grado en Ingeniería en Sistemas de Telecomunicació

Application of generalized equivalent uniform dose optimization in the treatment of nasopharyngeal carcinoma with intensity-modulated radiotherapy

Background and purpose: In the design of intensity-modulated radiotherapy (IMRT) for nasopharyngeal carcinoma, the traditional dose-volume (DV) physical optimization method is compared with the combined use of the DV physical optimization method and the generalized equivalent uniform dose (gEUD) optimization. This study aimed to investigate dosimetry differences in radiotherapy planning for nasopharyngeal carcinoma using gEUD method, to explore the effect of different optimization methods on the protection of organ at risk (OAR) in IMRT planning. Methods: Fifty patients with nasopharyngeal carcinoma in Eye & ENT Hospital of Fudan University from 2019 to 2021 were randomly selected, and two optimization plans were used for each case at the same time for optimization calculation. Group A used the traditional DV physical optimization method, while group B combined DV optimization and gEUD optimization methods adopted, in which gEUD was selected as a=1, 2, 5, 10 and 20. We evaluated the results of OAR dose data obtained by using different optimization schemes and different a values. Results: The planned data of the two plans were compared and analyzed, and there was no statistically significant difference in the dosimetry index of the target area between groups (P>0.05). However, in terms of the protection of the parotid gland and oral cavity, the results of the optimization plan of group B were significantly better compared with group A. The a value of gEUD had more obvious influence on the average dose of the parotid gland and the oral cavity. Conclusion: In the radiotherapy plan for nasopharyngeal carcinoma, the combined use of physical optimization and biological optimization can not only meet the target dose requirements but also better protect the parotid gland, oral cavity and other endangered OAR

Recent advances and prospect in immune microenvironment and its mechanisms of function in head and neck squamous cell carcinoma

Head and neck cancer (HNC) remains a significant cause of morbidity and mortality. The most prevalent pathology among HNC is head and neck squamous cell carcinoma (HNSCC). The tumor microenvironment (TME) encompasses the components surrounding tumor cells, including immune cells, stromal cells, extracellular matrix (ECM), blood and lymph vessels. Strategies targeting the TME have yielded significant outcomes. Thus, further exploration of the interactions between TME components is crucial. This review discussed recent advances in cytotoxic T lymphocytes (CTL), CD4+ T lymphocytes, regulatory T cells (Treg), myeloid-derived suppressor cells (MDSC), natural killer (NK) cells and tumor-associated macrophages (TAM) in HNSCC TME. The article summarized herein primarily focused on restoring the activity of anti-tumor cells and eliminating the immunosuppressive effects of Treg and so on, to provide new insights for more effective HNSCC therapy

Dose fall-off during the treatment of thoracic spine metastasis with CyberKnife stereotactic body radiation therapy (SBRT)

CyberKnife stereotactic body radiation therapy (SBRT) is becoming increasingly used for cancer treatment and, to maximize its clinical application, it is important to define the dosimetric characteristics, optimal dose and fractionation regimens. The aim of this study was to evaluate the dose fall-off in two fractionated regimens of CyberKnife SBRT during the treatment of thoracic spinal metastasis. Patients with spinal metastasis involving a vertebra and pedicle were treated with 40 Gy in 5 fractions (n = 4), and patients with spinal metastasis involving only a vertebra received 33 Gy in 3 fractions (n = 4). A new approach was used to measure absolute dose fall-off distance, relative dose fall-off distance, and the dose fall-off per unit distance along four reference directions in the axial plane. Patients treated with 33 Gy/3 fractions had a greater absolute dose fall-off distance in direction 1 (from the point with maximum dose [Dmax] towards the spinal cord) and direction 3 (the opposite of the direction 1), a greater relative dose fall-off distance in direction 3, and a lower dose fall-off per unit distance in direction 1 and 3 compared to patients treated with 40 Gy/5 fractions (all p < 0.05). Overall, the dose fall-off towards the spinal cord is rapid during the treatment of thoracic spinal metastasis with CyberKnife SBRT, which allows a higher dose of radiation to be delivered to the tumor and, at the same time, better protection of the spinal cord

Hyperbolic method to analyze the electrical resistivity curve of Portland cements with superplasticizer

Electrical measurement was employed to investigate the early hydration characteristics of cement pastes with different dosages of superplasticizer in the same W/C ratio. The hyperbolic method was applied to analyze the electrical resistivity development. The peak point (P-h) on the hyperbolic curve could be easily read. The time (t(h)) to reach the point Ph had strong relations with the setting time. th was delayed with the increment of the dosage of superplasticizer. The time th was used to plot the relationship between the initial setting time and final setting time. The hyperbolic equation was established to predict the ultimate resistivity. The retardation effect of the superplasticizer was confirmed in the same W/C ratio by setting time and isothermal heat evolution