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

Chiral susceptibility and the scalar Ward identity

The chiral susceptibility is given by the scalar vacuum polarisation at zero total momentum. This follows directly from the expression for the vacuum quark condensate so long as a nonperturbative symmetry preserving truncation scheme is employed. For QCD in-vacuum the susceptibility can rigorously be defined via a Pauli-Villars regularisation procedure. Owing to the scalar Ward identity, irrespective of the form or Ansatz for the kernel of the gap equation, the consistent scalar vertex at zero total momentum can automatically be obtained and hence the consistent susceptibility. This enables calculation of the chiral susceptibility for markedly different vertex Ansaetze. For the two cases considered, the results were consistent and the minor quantitative differences easily understood. The susceptibility can be used to demarcate the domain of coupling strength within a theory upon which chiral symmetry is dynamically broken. Degenerate massless scalar and pseudoscalar bound-states appear at the critical coupling for dynamical chiral symmetry breaking.Comment: 9 pages, 5 figures, 1 tabl

cis-Tetra­aqua­bis­{5-[4-(1H-imidazol-1-yl-κN 3)phen­yl]tetra­zolido}manganese(II) dihydrate

In the title compound, [Mn(C10H7N6)2(H2O)4]·2H2O, the complex unit comprises an Mn2+ ion, coordinated by two imidazole N atoms from cis-related monodentate 5-[4-(imidazol-1-yl)phen­yl]tetra­zolide ligands and four water mol­ecules, together with two water mol­ecules of solvation. The Mn2+ ion lies on a twofold rotation axis and has a slightly distorted octa­hedral geometry. The mol­ecules are connected by O—H⋯N and O—H⋯O hydrogen bonds involving both coordinated and solvent water mol­ecules, generating a three-dimensional structure. Two C atoms of the imidazole ring of the ligand are each disordered over two sites with occupancy factors of 0.75 and 0.25

Anatomical study of simple landmarks for guiding the quick access to humeral circumflex arteries

BACKGROUND: The posterior and anterior circumflex humeral artery (PCHA and ACHA) are crucial for the blood supply of humeral head. We aimed to identify simple landmarks for guiding the quick access to PCHA and ACHA, which might help to protect the arteries during the surgical management of proximal humeral fractures. METHODS: Twenty fresh cadavers were dissected to measure the distances from the origins of PCHA and ACHA to the landmarks (the acromion, the coracoid, the infraglenoid tubercle, the midclavicular line) using Vernier calipers. RESULTS: The mean distances from the origin of PCHA to the infraglenoid tubercle, the coracoid, the acromion and the midclavicular line were 27.7 mm, 50.2 mm, 68.4 mm and 75.8 mm. The mean distances from the origin of ACHA to the above landmarks were 26.9 mm, 49.2 mm, 67.0 mm and 74.9 mm. CONCLUSION: Our study provided a practical method for the intraoperative identification as well as quick access of PCHA and ACHA based on a series of anatomical measurements