Self-adjoint extensions for linear Hamiltonian systems with two singular endpoints

AbstractThis paper is concerned with self-adjoint extensions for a linear Hamiltonian system with two singular endpoints. The domain of the closure of the corresponding minimal Hamiltonian operator H0 is described by properties of its elements at the endpoints of the discussed interval, decompositions of the domains of the corresponding left and right maximal Hamiltonian operators are provided, and expressions of the defect indices of H0 in terms of those of the left and right minimal operators are given. Based on them, characterizations of all the self-adjoint extensions for a Hamiltonian system are obtained in terms of square integrable solutions. As a consequence, the characterizations of all the self-adjoint extensions are given for systems in several special cases

Configurable and Scalable Turbo Decoder for 4G Wireless Receivers

The increasing requirements of high data rates and quality of service (QoS) in fourth-generation (4G) wireless communication require the implementation of practical capacity approaching codes. In this chapter, the application of Turbo coding schemes that have recently been adopted in the IEEE 802.16e WiMax standard and 3GPP Long Term Evolution (LTE) standard are reviewed. In order to process several 4G wireless standards with a common hardware module, a reconfigurable and scalable Turbo decoder architecture is presented. A parallel Turbo decoding scheme with scalable parallelism tailored to the target throughput is applied to support high data rates in 4G applications. High-level decoding parallelism is achieved by employing contention-free interleavers. A multi-banked memory structure and routing network among memories and MAP decoders are designed to operate at full speed with parallel interleavers. A new on-line address generation technique is introduced to support multiple Turbo interleaving patterns, which avoids the interleaver address memory that is typically necessary in the traditional designs. Design trade-offs in terms of area and power efficiency are analyzed for different parallelism and clock frequency goals

Configurable and Scalable High Throughput Turbo Decoder Architecture for Multiple 4GWireless Standards

In this paper, we propose a novel multi-code turbo decoder architecture for 4G wireless systems. To support various 4G standards, a configurable multi-mode MAP (maximum a posteriori) decoder is designed for both binary and duo-binary turbo codes with small resource overhead (less than 10%) compared to the single-mode architecture. To achieve high data rates in 4G, we present a parallel turbo decoder architecture with scalable parallelism tailored to the given throughput requirements. High-level parallelism is achieved by employing contention-free interleavers. Multi-banked memory structure and routing network among memories and MAP decoders are designed to operate at full speed with parallel interleavers. We designed a very low-complexity recursive on-line address generator supporting multiple interleaving patterns, which avoids the interleaver address memory. Design trade-offs in terms of area and power efficiency are explored to find the optimal architectures. A 711 Mbps data rate is feasible with 32 Radix-4 MAP decoders running at 200 MHz clock rate.Texas Instruments Incorporate

Immunophenotyping characteristics and outcome of COVID‐19 patients: peripheral blood CD8+T cell as a prognostic biomarker for patients with Nirmatrelvir

BackgroundNirmatrelvir has been authorized for the treatment of both hospitalized and non-hospitalized COVID-19 patients. However, the association between T lymphocyte subsets and the outcome of hospitalized COVID-19 patients treated with oral Nirmatrelvir has not been investigated. The objective of this study was to examine whether lymphocyte subsets could serve as biomarkers to assess the risk of mortality in COVID-19 patients undergoing Nirmatrelvir treatment, with the aim of enhancing medication management for COVID-19 patients.MethodsWe conducted a retrospective cohort study at the Xiangya Hospital of Central South University in China between December 5, 2022 and January 31, 2023. The study reported demographic, clinical, T lymphocyte subsets, and inflammatory cytokine data of COVID-19 patients. We evaluated the associations of T lymphocyte subsets on admission with the composite outcome or death of patients using univariate and multivariable Cox regression analyses with hazards ratios (HRs) and 95% confidence intervals (CIs).ResultsWe identified 2118 hospitalized COVID-19 patients during the study period, and conducted a follow-up of up to 38 days. Of these, 131 patients received Nirmatrelvir, with 56 (42.7%) in the composite outcome group, and 75 (57.3%) in the non-composite outcome group. Additionally, 101 (77.1%) patients were discharged, while 30 (22.9%) died. Our results showed a significant decrease in the CD3+, CD4+, and CD8+ T cell counts of patients in the composite outcome group and mortality group compared to the non-composite outcome group and discharged group, respectively. Multivariate Cox regression analysis showed that the significant decrease in CD8+ T cell count in peripheral blood was independently associated with the composite outcome in COVID-19 patients treated with Nirmatrelvir, with an HR of 1.96 (95%CI: 1.01-3.80). The significant decrease in CD4+ and CD8+ T cell counts in peripheral blood increased the hazard of developing mortality, with HRs of 6.48 (95%CI: 1.47-28.63) and 3.75 (95%CI: 1.27-11.11), respectively.ConclusionOur study revealed a significant positive correlation between a decrease in CD8+ T cell counts and progression and mortality of hospitalized COVID-19 patients treated with Nirmatrelvir. Lower counts (/μL) of CD8+ T cell (<201) were associated with a higher risk of in-hospital severity and death. Our findings may provide valuable references for physicians in optimizing the use of Nirmatrelvir

Structure of shock compressed model basaltic glass: Insights from O K-edge X-ray Raman scattering and high-resolution ^(27)Al NMR spectroscopy

The detailed atomic structures of shock compressed basaltic glasses are not well understood. Here, we explore the structures of shock compressed silicate glass with a diopside–anorthite eutectic composition (Di_(64)An_(36)), a common Fe-free model basaltic composition, using oxygen K-edge X-ray Raman scattering and high- resolution ^(27)Al solid-state NMR spectroscopy and report previously unknown details of shock-induced changes in the atomic configurations. A topologically driven densification of the Di_(64)An_(36) glass is indicated by the increase in oxygen K-edge energy for the glass upon shock compression. The first experimental evidence of the increase in the fraction of highly coordinated Al in shock compressed glass is found in the ^(27)Al NMR spectra. This unambiguous evidence of shock-induced changes in Al coordination environments provides atomistic insights into shock compression in basaltic glasses and allows us to microscopically constrain the magnitude of impact events or relevant processes involving natural basalts on Earth and planetary surfaces