A Theoretical View of Linear Backpropagation and its Convergence.

Backpropagation (BP) is widely used for calculating gradients in deep neural networks (DNNs). Applied often along with stochastic gradient descent (SGD) or its variants, BP is considered as a de-facto choice in a variety of machine learning tasks including DNN training and adversarial attack/defense. Recently, a linear variant of BP named LinBP was introduced for generating more transferable adversarial examples for performing black-box attacks, by (Guo et al. 2020). Although it has been shown empirically effective in black-box attacks, theoretical studies and convergence analyses of such a method is lacking. This paper serves as a complement and somewhat an extension to Guo et al. (2020) paper, by providing theoretical analyses on LinBP in neural-network-involved learning tasks, including adversarial attack and model training. We demonstrate that, somewhat surprisingly, LinBP can lead to faster convergence in these tasks in the same hyper-parameter settings, compared to BP. We confirm our theoretical results with extensive experiments.

Fe-MOF-based fluorescent sensor with on/off capabilities for the highly sensitive detection of tert-butylhydroquinone in edible oils.

In this work, a "turn off-on" fluorescent sensor was developed for highly sensitive determination of tert-butylhydroquinone (TBHQ) based on an Fe(III)-based metal-organic framework (Fe-MOF). An Fe-MOF with an octahedral structure was synthesized via a simple hydrothermal method using ferric chloride hexahydrate and 2-aminoterephthalic acid (NH2-BDC) as raw materials. The fluorescence of Fe-MOF is extremely weak owing to ligand-to-metal charge transfer (LMCT) and internal filtration effect (IFE). When the system contained TBHQ, the binding of TBHQ to Fe(III) inhibited the LMCT of the fluorescent ligand NH2-BDC to Fe(III), releasing the fluorescence of NH2-BDC and thus restoring the fluorescence. With this as the basis, a rapid, sensitive, and selective fluorescence sensor is developed for the detection of TBHQ. Under the optimal conditions, TBHQ showed good linearity with fluorescence intensity in the range of 0-1.5 × 102 µmol L-1 and a detection limit of 0.0030 µmol L-1 (S/N = 3). The selectivity, reproducibility, and stability of the developed Fe-MOF-based sensors are comprehensively studied. Finally, the practicality of the method is verified by examining the detection of TBHQ in soybean oil; the results are consistent with those obtained using conventional high-performance liquid chromatography.

The non-Hermitian geometrical property of 1D Lieb lattice under Majorana's stellar representation.

The topological properties of non-Hermitian Hamiltonian is a hot topic, and the theoretical studies along this research line are usually based on the two-level non-Hermitian Hamiltonian (or, equivalently, a spin-1/2 non-Hermitian Hamiltonian). We are motivated to study the geometrical phases of a three-level Lieb lattice model (or, equivalently, a spin-1 non-Hermitian Hamiltonian) with the flat band in the context of a polariton condensate. The topological invariants are calculated by both winding numbers in the Brillouin zone and the geometrical phase of Majorana stars on the Bloch sphere. Besides, we provide an intuitive way to study the topological phase transformation with the higher spin, and the flat band offers a platform to define the topological phase transition on the Bloch sphere. According to the trajectories of the Majorana stars, we calculate the geometrical phases of the Majorana stars. We study the Lieb lattice with a complex hopping and find their phases have a jump when the parameters change from the trivial phase to the topological phase. The correlation phase of Majorana stars will rise along with the increase of the imaginary parts of the hopping energy. Besides, we also study the Lieb lattice with different intracell hopping and calculate the geometrical phases of the model using non-Bloch factor under the Majorana's stellar representation. In this case, the correlation phases will always be zero because of the normalized coefficient is always a purely real number and the phase transition is vividly shown with the geometrical phases of the Majorana stars calculated by the mean values of the total phases of both right and the joint left eigenstates.

Quantum synchronization of two mechanical oscillators in coupled optomechanical systems with Kerr nonlinearity.

We investigate the quantum synchronization phenomena of two mechanical oscillators of different frequencies in two optomechanical systems under periodically modulating cavity detunings or driving amplitudes, which can interact mutually through an optical fiber or a phonon tunneling. The cavities are filled with Kerr-type nonlinear medium. It is found that, no matter which the coupling and periodically modulation we choose, both of the quantum synchronization of nonlinear optomechanical system are more appealing than the linear optomechanical system. It is easier to observe greatly enhanced quantum synchronization with Kerr nonlinearity. In addition, the different influences on the quantum synchronization between the two coupling ways and the two modulating ways are compared and discussed.

The Exact Curve Equation for Majorana Stars.

Majorana stars are visual representation for a quantum pure state. For some states, the corresponding majorana stars are located on one curve on the Block sphere. However, it is lack of exact curve equations for them. To find the exact equations, we consider a superposition of two bosonic coherent states with an arbitrary relative phase. We analytically give the curve equation and find that the curve always goes through the North pole on the Block sphere. Furthermore, for the superpositions of SU(1,1) coherent states, we find the same curve equation.

Correlation of iron deposition and change of gliocyte metabolism in the basal ganglia region evaluated using magnetic resonance imaging techniques: an in vivo study.

INTRODUCTION: We assessed the correlation between iron deposition and the change of gliocyte metabolism in healthy subjects' basal ganglia region, by using 3D-enhanced susceptibility weighted angiography (ESWAN) and proton magnetic resonance spectroscopy ((1)H-MRS). MATERIAL AND METHODS: Seventy-seven healthy volunteers (39 female and 38 male subjects; age range: 24-82 years old) were enrolled in the experiment including ESWAN and proton MRS sequences, consent for which was provided by themselves or their guardians. For each subject, the mean phase value gained by ESWAN was used to evaluate the iron deposition; choline/creatine (Cho/Cr) and mI/Cr ratios gained by (1)H-MRS were used to evaluate gliocyte metabolism in the basal ganglia region of both sides. The paired t test was used to test the difference between the two sides of the basal ganglia region. Linear regression was performed to evaluate the relation between mean phase value and age. Pearson's correlation coefficient was calculated to analyze the relationship between the result of ESWAN and (1)H-MRS. RESULTS: There was no difference between the two sides of the basal ganglia region in the mean phase value and Cho/Cr. But in mI/Cr the mean phase value of each nucleus in bilateral basal ganglia decreased with increasing age. There are 16 r-values between the mean phase value and Cho/Cr and mI/Cr in bilateral basal ganglia region. And each of all p-values is less than 0.001 (p < 0.001). CONCLUSIONS: Iron deposition in the bilateral basal ganglia is associated with the change of gliocyte metabolism with increasing age. Iron deposition in each nucleus of the basal ganglia region changes with age.

Non-adiabatic holonomic quantum computation in linear system-bath coupling.

Non-adiabatic holonomic quantum computation in decoherence-free subspaces protects quantum information from control imprecisions and decoherence. For the non-collective decoherence that each qubit has its own bath, we show the implementations of two non-commutable holonomic single-qubit gates and one holonomic nontrivial two-qubit gate that compose a universal set of non-adiabatic holonomic quantum gates in decoherence-free-subspaces of the decoupling group, with an encoding rate of (N - 2)/N. The proposed scheme is robust against control imprecisions and the non-collective decoherence, and its non-adiabatic property ensures less operation time. We demonstrate that our proposed scheme can be realized by utilizing only two-qubit interactions rather than many-qubit interactions. Our results reduce the complexity of practical implementation of holonomic quantum computation in experiments. We also discuss the physical implementation of our scheme in coupled microcavities.