Application of Time-Fractional Order Bloch Equation in Magnetic Resonance Fingerprinting

Magnetic resonance fingerprinting (MRF) is one novel fast quantitative imaging framework for simultaneous quantification of multiple parameters with pseudo-randomized acquisition patterns. The accuracy of the resulting multi-parameters is very important for clinical applications. In this paper, we derived signal evolutions from the anomalous relaxation using a fractional calculus. More specifically, we utilized time-fractional order extension of the Bloch equations to generate dictionary to provide more complex system descriptions for MRF applications. The representative results of phantom experiments demonstrated the good accuracy performance when applying the time-fractional order Bloch equations to generate dictionary entries in the MRF framework. The utility of the proposed method is also validated by in-vivo study.Comment: Accepted at 2019 IEEE 16th International Symposium on Biomedical Imaging (ISBI 2019

Neural network encoded variational quantum algorithms

We introduce a general framework called neural network (NN) encoded variational quantum algorithms (VQAs), or NN-VQA for short, to address the challenges of implementing VQAs on noisy intermediate-scale quantum (NISQ) computers. Specifically, NN-VQA feeds input (such as parameters of a Hamiltonian) from a given problem to a neural network and uses its outputs to parameterize an ansatz circuit for the standard VQA. Combining the strengths of NN and parameterized quantum circuits, NN-VQA can dramatically accelerate the training process of VQAs and handle a broad family of related problems with varying input parameters with the pre-trained NN. To concretely illustrate the merits of NN-VQA, we present results on NN-variational quantum eigensolver (VQE) for solving the ground state of parameterized XXZ spin models. Our results demonstrate that NN-VQE is able to estimate the ground-state energies of parameterized Hamiltonians with high precision without fine-tuning, and significantly reduce the overall training cost to estimate ground-state properties across the phases of XXZ Hamiltonian. We also employ an active-learning strategy to further increase the training efficiency while maintaining prediction accuracy. These encouraging results demonstrate that NN-VQAs offer a new hybrid quantum-classical paradigm to utilize NISQ resources for solving more realistic and challenging computational problems.Comment: 4.4 pages, 5 figures, with supplemental material

Theory of polygonal phases self-assembled from T-shaped liquid crystalline polymers

Extensive experimental studies have shown that numerous ordered phases can be formed via the self-assembly of T-shaped liquid crystalline polymers (TLCPs) composed of a rigid backbone, two flexible end chains and a flexible side chain. However, a comprehensive understanding of the stability and formation mechanisms of these intricately nano-structured phases remains incomplete. Here we fill this gap by carrying out a theoretical study of the phase behaviour of TLCPs. Specifically, we construct phase diagrams of TLCPs by computing the free energy of different ordered phases of the system. Our results reveal that the number of polygonal edges increases as the length of side chain or interaction strength increases, consistent with experimental observations. The theoretical study not only reproduces the experimentally observed phases and phase transition sequences, but also systematically analyzes the stability mechanism of the polygonal phases

Differentiable Quantum Architecture Search

Quantum architecture search (QAS) is the process of automating architecture engineering of quantum circuits. It has been desired to construct a powerful and general QAS platform which can significantly accelerate current efforts to identify quantum advantages of error-prone and depth-limited quantum circuits in the NISQ era. Hereby, we propose a general framework of differentiable quantum architecture search (DQAS), which enables automated designs of quantum circuits in an end-to-end differentiable fashion. We present several examples of circuit design problems to demonstrate the power of DQAS. For instance, unitary operations are decomposed into quantum gates, noisy circuits are re-designed to improve accuracy, and circuit layouts for quantum approximation optimization algorithm are automatically discovered and upgraded for combinatorial optimization problems. These results not only manifest the vast potential of DQAS being an essential tool for the NISQ application developments, but also present an interesting research topic from the theoretical perspective as it draws inspirations from the newly emerging interdisciplinary paradigms of differentiable programming, probabilistic programming, and quantum programming.Comment: 9.1 pages + Appendix, 5 figure

New Method for Numerically Solving the Chemical Potential Dependence of the Dressed Quark Propagator

Based on the rainbow approximation of Dyson-Schwinger equation and the assumption that the inverse dressed quark propagator at finite chemical potential is analytic in the neighborhood of $\mu=0$, a new method for obtaining the dressed quark propagator at finite chemical potential $\mu$ from the one at zero chemical potential is developed. Using this method the dressed quark propagator at finite chemical potential can be obtained directly from the one at zero chemical potential without the necessity of numerically solving the corresponding coupled integral equations by iteration methods. A comparison with previous results is given.Comment: Revtex, 14 pages, 5 figure

Comparative Analysis of Y Chromosome Data from Xinjiang and Ningxia Hui Populations with Hui Population Nationwide

The Hui population, one of China’s ethnic minorities, is dispersed throughout the country and has a history of assimilation with indigenous East Asians. Previous studies have primarily focused on Hui populations in specific regions, lacking comprehensive comparative analyses. In this study, we analyzed 338 unrelated male individuals from Hui populations in Altay, Xinjiang, and Haiyuan or Tongxin, Ningxia, using 108 Y-chromosomal single nucleotide polymorphisms (Y-SNPs) and 24 Y-chromosomal short tandem repeats (Y-STRs). We compared our findings with data from 749 published individuals from Hui populations in 11 provinces and 997 published Eurasian populations. Our analysis revealed that the national Hui population can be categorized into three groups: Hui_Northwestern, Hui_Northern, and Hui_Southern, supported by AMOVA and Principal Component Analysis (PCA). In Altay, Xinjiang, and Haiyuan or Tongxin, Ningxia, the most prevalent Y-haplogroups in East Asian populations accounted for 53.8% and 59.1%, respectively, while common haplogroups in West Eurasian populations accounted for 46.2% and 40.9%, respectively. This suggests a mixed paternal origin from both East Asian and Eurasian populations in both study regions. High frequencies of haplogroups R1a1a1b2-Z93 and J-M304 were observed in the Hui populations studied, with the network of Haplogroup J-M304 indicating a unique cluster within the western Asian sub-haplogroup J2a-M410. The most recent common ancestor for this cluster was estimated to be approximately 1341.9 years ago. Additionally, the network of haplogroup R1a1a1b2-Z93 revealed similarities between northwestern Hui populations and Iranian/Turkic-speaking populations. Our study provides insight into the complexity of Hui populations on a national scale and sheds light on potential events and ancestral origins related to the formation of the Hui population

The dilemma of public information disclosures

In this paper, we document a novel fact that disclosures of public information reshape social dynamics in China. Using the staggered roll-out of a quasi-natural experiment of air pollution information disclosure and a novel high-frequency data set of social and public events, we find socioeconomic cooperation and protests both significantly decrease after disclosure. The negative effects are larger when the disclosed pollution level is higher and when residents have higher environmental awareness and lower trust in local governments. Our results are rationalized in a theoretical model and suggest that information disclosure involves a tradeoff between economic efficiency and political stability and leads to a dilemma for policymakers

Extreme high temperatures and adaptation by social dynamics: Theory and Evidence from China

Using a novel city-level high-frequency panel data set of social and public events in Chinese cities, we document that extreme high temperatures significantly reshape social dynamics. Extreme high temperatures lead to an increase in social cooperation, and the effects are more salient when productivity is lower and labor is more intensively used. This implies extreme high temperatures boost the relative returns of cooperation given lowered productivity. Our estimates and quantitative model suggest that the human race adapts to global warming by reshaping its social dynamics: adaptation via social dynamics offsets about one-third of the negative impacts of extreme high temperatures on the economy