Single-Valued Hamiltonian via Legendre-Fenchel Transformation and Time Translation Symmetry

Under conventional Legendre transformation, systems with a non-convex Lagrangian will result in a multi-valued Hamiltonian as a function of conjugate momentum. This causes problems such as non-unitary time evolution of quantum state and non-determined motion of classical particles, and is physically unacceptable. In this work, we propose a new construction of single-valued Hamiltonian by applying Legendre-Fenchel transformation, which is a mathematically rigorous generalization of conventional Legendre transformation, valid for non-convex Lagrangian systems, but not yet widely known to the physics community. With the new single-valued Hamiltonian, we study spontaneous breaking of time translation symmetry and derive its vacuum state. Applications to theories of cosmology and gravitation are discussed.Comment: Journal Version, 16pp. All results + conclusions un-changed, only minor refinements to clarify the importance of our new LFT method and its physics applications; references adde

Generalizations of the Double-Copy: the KLT Bootstrap

We formulate a new program to generalize the double-copy of tree amplitudes. The approach exploits the link between the identity element of the KLT algebra and the KLT kernel, and we demonstrate how this leads to a set of KLT bootstrap equations that the double-copy kernel has to satisfy (in addition to locality constraints). We solve the KLT bootstrap equations perturbatively to find the most general higher-derivative corrections to the 4- and 5-point field theory KLT kernel. The new kernel generalizes the string KLT kernel and its associated monodromy relations. It admits new color-structures in the effective theories it double-copies. It provides distinct generalized KK and BCJ relations for the left and right single-color theories and is in that sense a heterotic-type double-copy. We illustrate the generalized double-copy in detail for 4d Yang-Mills theory with higher-derivative corrections that produce dilaton-axion-gravity with local operators up order $\nabla^{10} R^4$. Finally, we initiate a search for new double-copy kernels.Comment: 56 page

The burden of cardiovascular disease in Asia from 2025 to 2050: a forecast analysis for East Asia, South Asia, South-East Asia, Central Asia, and high-income Asia Pacific regions.

Summary Background Given the rapidly growing burden of cardiovascular disease (CVD) in Asia, this study forecasts the CVD burden and associated risk factors in Asia from 2025 to 2050. Methods Data from the Global Burden of Disease 2019 study was used to construct regression models predicting prevalence, mortality, and disability-adjusted life years (DALYs) attributed to CVD and risk factors in Asia in the coming decades. Findings Between 2025 and 2050, crude cardiovascular mortality is expected to rise 91.2% despite a 23.0% decrease in the age-standardised cardiovascular mortality rate (ASMR). Ischaemic heart disease (115 deaths per 100,000 population) and stroke (63 deaths per 100,000 population) will remain leading drivers of ASMR in 2050. Central Asia will have the highest ASMR (676 deaths per 100,000 population), more than three-fold that of Asia overall (186 deaths per 100,000 population), while high-income Asia sub-regions will incur an ASMR of 22 deaths per 100,000 in 2050. High systolic blood pressure will contribute the highest ASMR throughout Asia (105 deaths per 100,000 population), except in Central Asia where high fasting plasma glucose will dominate (546 deaths per 100,000 population). Interpretation This forecast forewarns an almost doubling in crude cardiovascular mortality by 2050 in Asia, with marked heterogeneity across sub-regions. Atherosclerotic diseases will continue to dominate, while high systolic blood pressure will be the leading risk factor. Funding This was supported by the NUHS Seed Fund (NUHSRO/2022/058/RO5+6/Seed-Mar/03), National Medical Research Council Research Training Fellowship (MH 095:003/008-303), National University of Singapore Yong Loo Lin School of Medicine's Junior Academic Fellowship Scheme, NUHS Clinician Scientist Program (NCSP2.0/2024/NUHS/NCWS) and the CArdiovascular DiseasE National Collaborative Enterprise (CADENCE) National Clinical Translational Program (MOH-001277-01)

The burden of cardiovascular disease in Asia from 2025 to 2050: a forecast analysis for East Asia, South Asia, South-East Asia, Central Asia, and high-income Asia Pacific regions

Background: Given the rapidly growing burden of cardiovascular disease (CVD) in Asia, this study forecasts the CVD burden and associated risk factors in Asia from 2025 to 2050. Methods: Data from the Global Burden of Disease 2019 study was used to construct regression models predicting prevalence, mortality, and disability-adjusted life years (DALYs) attributed to CVD and risk factors in Asia in the coming decades. Findings: Between 2025 and 2050, crude cardiovascular mortality is expected to rise 91.2% despite a 23.0% decrease in the age-standardised cardiovascular mortality rate (ASMR). Ischaemic heart disease (115 deaths per 100,000 population) and stroke (63 deaths per 100,000 population) will remain leading drivers of ASMR in 2050. Central Asia will have the highest ASMR (676 deaths per 100,000 population), more than three-fold that of Asia overall (186 deaths per 100,000 population), while high-income Asia sub-regions will incur an ASMR of 22 deaths per 100,000 in 2050. High systolic blood pressure will contribute the highest ASMR throughout Asia (105 deaths per 100,000 population), except in Central Asia where high fasting plasma glucose will dominate (546 deaths per 100,000 population). Interpretation:This forecast forewarns an almost doubling in crude cardiovascular mortality by 2050 in Asia, with marked heterogeneity across sub-regions. Atherosclerotic diseases will continue to dominate, while high systolic blood pressure will be the leading risk factor

Evanescent Effects Can Alter Ultraviolet Divergences in Quantum Gravity without Physical Consequences

Evanescent operators such as the Gauss-Bonnet term have vanishing perturbative matrix elements in exactly D=4 dimensions. Similarly, evanescent fields do not propagate in D=4; a three-form field is in this class, since it is dual to a cosmological-constant contribution. In this Letter, we show that evanescent operators and fields modify the leading ultraviolet divergence in pure gravity. To analyze the divergence, we compute the two-loop identical-helicity four-graviton amplitude and determine the coefficient of the associated (non-evanescent) R^3 counterterm studied long ago by Goroff and Sagnotti. We compare two pairs of theories that are dual in D=4: gravity coupled to nothing or to three-form matter, and gravity coupled to zero-form or to two-form matter. Duff and van Nieuwenhuizen showed that, curiously, the one-loop conformal anomaly --- the coefficient of the Gauss-Bonnet operator --- changes under p-form duality transformations. We concur, and also find that the leading R^3 divergence changes under duality transformations. Nevertheless, in both cases the physical renormalized two-loop identical-helicity four-graviton amplitude can be chosen to respect duality. In particular, its renormalization-scale dependence is unaltered

Single-cell and spatial transcriptomics reveal 5-methylcytosine RNA methylation regulators immunologically reprograms tumor microenvironment characterizations, immunotherapy response and precision treatment of clear cell renal cell carcinoma

Clear cell Renal Cell Carcinoma (ccRCC) is a highly heterogeneous disease, making it challenging to predict prognosis and therapy efficacy. In this study, we aimed to explore the role of 5-methylcytosine (m5C) RNA modification in ccRCC and its potential as a predictor for therapy response and overall survival (OS). We established a novel 5-methylcytosine RNA modification-related gene index (M5CRMRGI) and studied its effect on the tumor microenvironment (TME) using single-cell sequencing data for in-depth analysis, and verified it using spatial sequencing data. Our results showed that M5CRMRGI is an independent predictor of OS in multiple datasets and exhibited outstanding performance in predicting the OS of ccRCC. Distinct mutation profiles, hallmark pathways, and infiltration of immune cells in TME were observed between high- and low-M5CRMRGI groups. Single-cell/spatial transcriptomics revealed that M5CRMRGI could reprogram the distribution of tumor-infiltrating immune cells. Moreover, significant differences in tumor immunogenicity and tumor immune dysfunction and exclusion (TIDE) were observed between the two risk groups, suggesting a better response to immune checkpoint blockade therapy of the high-risk group. We also predicted six potential drugs binding to the core target of the M5CRMRGI signature via molecular docking. Real-world treatment cohort data proved once again that high-risk patients were appropriate for immune checkpoint blockade therapy, while low-risk patients were appropriate for Everolimus. Our study shows that the m5C modification landscape plays a role in TME distribution. The proposed M5CRMRGI-guided strategy for predicting survival and immunotherapy efficacy, we reported here, might also be applied to more cancers other than ccRCC