Stochastic pole expansion method

In this paper, we propose a new analytic continuation method to extract real frequency spectral functions from imaginary frequency Green's functions of quantum many-body systems. This method is based on the pole representation of Matsubara Green's function and a stochastic sampling procedure is utilized to optimize the amplitudes and locations of poles. In order to capture narrow peaks and sharp band edges in the spectral functions, a constrained sampling algorithm and a self-adaptive sampling algorithm are developed. To demonstrate the usefulness and performance of the new method, we at first apply it to study the spectral functions of representative fermionic and bosonic correlators. Then we employ this method to tackle the analytic continuation problems of matrix-valued Green's functions. The synthetic Green's functions, as well as realistic correlation functions from finite temperature quantum many-body calculations, are used as input. The benchmark results demonstrate that this method is capable of reproducing most of the key characteristics in the spectral functions. The sharp, smooth, and multi-peak features in both low-frequency and high-frequency regions of spectral functions could be accurately resolved, which overcomes one of the main limitations of the traditional maximum entropy method. More importantly, it exhibits excellent robustness with respect to noisy and incomplete input data. The causality of spectral function is always satisfied even in the presence of sizable noises. As a byproduct, this method could derive a fitting formula for the Matsubara data, which provides a compact approximation to the many-body Green's functions. Hence, we expect that this new method could become a pivotal workhorse for numerically analytic continuation and be broadly useful in many applications.Comment: 26 pages, 20 figure

Reconstructing lattice QCD spectral functions with stochastic pole expansion and Nevanlinna analytic continuation

The reconstruction of spectral functions from Euclidean correlation functions is a well-known, yet ill-posed inverse problem in the fields of many-body and high-energy physics. In this paper, we present a comprehensive investigation of two recently developed analytic continuation methods, namely stochastic pole expansion and Nevanlinna analytic continuation, for extracting spectral functions from mock lattice QCD data. We examine a range of Euclidean correlation functions generated by representative models, including the Breit-Wigner model, the Gaussian mixture model, the resonance-continuum model, and the bottomonium model. Our findings demonstrate that the stochastic pole expansion method, when combined with the constrained sampling algorithm and the self-adaptive sampling algorithm, successfully recovers the essential features of the spectral functions and exhibits excellent resilience to noise of input data. In contrast, the Nevanlinna analytic continuation method suffers from numerical instability, often resulting in the emergence of spurious peaks and significant oscillations in the high-energy regions of the spectral functions, even with the application of the Hardy basis function optimization algorithm.Comment: 14 pages, 8 figure

Multifunctional Bracts in the Dove Tree Davidia involucrata (Nyssaceae:Cornales)

Although there has been much experimental work on floral traits that are under selection from mutualists and antagonists, selection by abiotic environmental factors on flowers has been largely ignored. Here we test whether pollen susceptibility to rain damage could have played a role in the evolution of the reproductive architecture of Davidia involucrata, an endemic in the mountains of western China. Flowers in this tree species lack a perianth and are arranged in capitula surrounded by large (up to 10 cm#5 cm) bracts that at anthesis turn from green to white, losing their photosynthetic capability. Flowers are nectarless, and pollen grains are presented on the recurved anther walls for 5–7 days. Flower visitors, and likely pollinators, were mainly pollen-collecting bees from the genera Apis, Xylocopa, Halictus, and Lasioglossum. Capitula with natural or white paper bracts attracted significantly more bees per hour than capitula that had their bracts removed or replaced by green paper. Experimental immersion of pollen grains in water resulted in rapid loss of viability, and capitula with bracts lost less pollen to rain than did capitula that had their bracts removed, suggesting that the bracts protect the pollen from rain damage as well as attracting pollinators

Distributed Contingency Analysis over Wide Area Network among Dispatch Centers

Traditionally, a regional dispatch center uses the equivalent method to deal with external grids, which fails to reflect the interactions among regions. This paper proposes a distributed N-1 contingency analysis (DCA) solution, where dispatch centers join a coordinated computation using their private data and computing resources. A distributed screening method is presented to determine the Critical Contingency Set (DCCS) in DCA. Then, the distributed power flow is formulated as a set of boundary equations, which is solved by a Jacobi-Free Newton-GMRES (JFNG) method. During solving the distributed power flow, only boundary conditions are exchanged. Acceleration techniques are also introduced, including reusing preconditioners and optimal resource scheduling during parallel processing of multiple contingencies. The proposed method is implemented on a real EMS platform, where tests using the Southwest Regional Grid of China are carried out to validate its feasibility.Comment: 5 pages, 6 figures, 2017 IEEE PES General Meetin

Dark Energy and Fate of the Universe

We explore the ultimate fate of the Universe by using a divergence-free parametrization for dark energy $w(z)=w_0+w_a({\ln (2+z)\over 1+z}-\ln2)$. Unlike the CPL parametrization, this parametrization has well behaved, bounded behavior for both high redshifts and negative redshifts, and thus can genuinely cover many theoretical dark energy models. After constraining the parameter space of this parametrization by using the current cosmological observations, we find that, at the 95.4% confidence level, our Universe can still exist at least 16.7 Gyr before it ends in a big rip. Moreover, for the phantom energy dominated Universe, we find that a gravitationally bound system will be destroyed at a time $t \simeq P\sqrt{2|1+3w(-1)|}/[6\pi |1+w(-1)|]$, where $P$ is the period of a circular orbit around this system, before the big rip.Comment: 5 pages, 3 figures; typos corrected, publication version, Sci China-Phys Mech Astron, doi: 10.1007/s11433-012-4748-

Family Foundation Development in China: Two Case Studies

Amid the accumulation of private wealth in China, family foundations have begun to emerge in recent decades. Little research, however, has explored this nascent phenomenon. This article examines the development of two Chinese family foundations — the Lao Niu Foundation and the Lu Jiaxiang Foundation — using document analyses and semi-structured interviews with foundation leaders. While detailed data on program effectiveness and efficiency is lacking because of underdeveloped methods of evaluation, it is evident that both foundations have generated positive impacts on social development despite an overall lack of support for the foundation sector from Chinese government policy. The case studies indicate that Chinese family foundations are exploring new paths in an increasingly mature philanthropic environment, and suggest several development approaches for family foundations in China and other emerging philanthropic sectors