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Subsampling or subdata selection is a useful approach in large-scale statistical learning. Most existing studies focus on model-based subsampling methods which significantly depend on the model assumption. In this paper, we consider the model-free subsampling strategy for generating subdata from the original full data. In order to measure the goodness of representation of a subdata with respect to the original data, we propose a criterion, generalized empirical F-discrepancy (GEFD), and study its theoretical properties in connection with the classical generalized L2-discrepancy in the theory of uniform designs. These properties allow us to develop a kind of low-GEFD data-driven subsampling method based on the existing uniform designs. By simulation examples and a real case study, we show that the proposed subsampling method is superior to the random sampling method. Moreover, our method keeps robust under diverse model specifications while other popular subsampling methods are under-performing. In practice, such a model-free property is more appealing than the model-based subsampling methods, where the latter may have poor performance when the model is misspecified, as demonstrated in our simulation studies.

Using Machine Learning and Deep Learning to predict cognitive tasks from electroencephalography (EEG) signals has been a fast-developing area in Brain-Computer Interfaces (BCI). However, during the COVID-19 pandemic, data collection and analysis could be more challenging. The remote experiment during the pandemic yields several challenges, and we discuss the possible solutions. This paper explores machine learning algorithms that can run efficiently on personal computers for BCI classification tasks. The results show that Random Forest and RBF SVM perform well for EEG classification tasks. Furthermore, we investigate how to conduct such BCI experiments using affordable consumer-grade devices to collect EEG-based BCI data. In addition, we have developed the data collection protocol, EEG4Students, that grants non-experts who are interested in a guideline for such data collection. Our code and data can be found at https://github.com/GuangyaoDou/EEG4Students.

We first compare the geometric frameworks behind the Uhlmann and Berry phases in a fiber-bundle language and then evaluate the Uhlmann phases of bosonic and fermionic coherent states. The Uhlmann phases of both coherent states are shown to carry geometric information and decrease smoothly with temperature. Importantly, the Uhlmann phases approach the corresponding Berry phases as temperature decreases. Together with previous examples in the literature, we propose a correspondence between the Uhlmann and Berry phases in the zero-temperature limit as a general property except some special cases and present a conditional proof of the correspondence., Comment: 23 pages, no figure

Using Machine Learning and Deep Learning to predict cognitive tasks from electroencephalography (EEG) signals is a rapidly advancing field in Brain-Computer Interfaces (BCI). In contrast to the fields of computer vision and natural language processing, the data amount of these trials is still rather tiny. Developing a PC-based machine learning technique to increase the participation of non-expert end-users could help solve this data collection issue. We created a novel algorithm for machine learning called Time Majority Voting (TMV). In our experiment, TMV performed better than cutting-edge algorithms. It can operate efficiently on personal computers for classification tasks involving the BCI. These interpretable data also assisted end-users and researchers in comprehending EEG tests better.

Using Machine Learning and Deep Learning to predict cognitive tasks from electroencephalography (EEG) signals has been a fast-developing area in Brain-Computer Interfaces (BCI). However, during the COVID-19 pandemic, data collection and analysis could be more challenging than before. This paper explored machine learning algorithms that can run efficiently on personal computers for BCI classification tasks. Also, we investigated a way to conduct such BCI experiments remotely via Zoom. The results showed that Random Forest and RBF SVM performed well for EEG classification tasks. The remote experiment during the pandemic yielded several challenges, and we discussed the possible solutions; nevertheless, we developed a protocol that grants non-experts who are interested a guideline for such data collection., Comment: 6 pages, 6 figures, HCII2022

Two representations of mixed states by state-vectors, known as purified state and thermal vacuum, have been realized on quantum computers. While the two representations look similar, they differ by a partial transposition in the ancilla space. While ordinary observables cannot discern the two representations, we generalize the Berry phase of pure quantum states to mixed states and construct two geometric phases that can reflect the partial transposition. By generalizing the adiabatic condition, we construct the thermal Berry phase, whose values from the two representations can be different, However, the thermal Berry phase may contain non-geometrical contributions. Alternatively, we generalize the parallel-transport condition to include the system and ancilla and show the dynamical phase is excluded under parallel transport. The geometrical phase accumulated in parallel transport is the generalized Berry phase, which may or may not differentiate a purified state from a thermal vacuum depending on the protocol. The generalizations of the Berry phase to mixed states may be realized and measured on quantum computers via the two representations to reveal the rich physics of finite-temperature quantum systems., Comment: 15 pages, 1 figure

We study the slightly broken higher-spin currents in various CFTs with $\mathrm{U}(1)$ gauge field, including the tricritical QED, scalar QED, fermionic QED and QED-Gross-Neveu-Yukawa theory. We calculate their anomalous dimension by making use of the classical non-conservation equation and the equations of motion. We find a logarithmic asymptotic behaviour ($\gamma_s\sim 16/(N\pi^2) \log s $) of the anomalous dimension at large spin $s$, which is different from other interacting CFTs without gauge fields and may indicate certain unique features of gauge theories. We also study slightly broken higher-spin currents of the $\mathrm{SU}(N)_1$ WZW model at $d=2+\epsilon$ dimensions by formulating them as the QED theory, and we again find its anomalous dimension has a logarithmic asymptotic behaviour with respect to spin. This result resolves the mystery regarding the mechanism of breaking higher spin currents of Virasoro symmetry at $d=2+\epsilon$ dimensions, and may be applicable to other interesting problems such as the $2+\epsilon$ expansion of Ising CFT., Comment: 25 pages

A generalized inhomogeneous higher-order nonlinear Schrodinger (GIHNLS) equation for the Heisenberg ferromagnetic spin chain system in (1+1)-dimensions under zero boundary condition at infinity is taken into account. The spectral analysis is first performed to generate a related matrix Riemann-Hilbert problem on the real axis. Then, through solving the resulting matrix Riemann-Hilbert problem by taking the jump matrix to be the identity matrix, the general bright multi-soliton solutions to the GIHNLS equation are attained. Furthermore, the one- and two-soliton solutions are written out and analyzed by figures.

This paper concentrates on the Heisenberg ferromagnetic spin chain (HFSC) equation in (2+1)-dimensions modelling nonlinear wave propagation in ferromagnetic spin chain. A variable transformation is first employed to reduce the studied equation. And then an associated matrix Riemann-Hilbert problem is built on the real line through analyzing spectral problem of the reduced equation. As a consequence, solving the obtained matrix Riemann-Hilbert problem with the identity jump matrix, corresponding to the reflectionless, the general multi-soliton solutions to the HFSC equation in (2+1)-dimensions are acquired. Specially, the one- and two-soliton solutions are worked out and analyzed graphically.

The emerging neural topic models make topic modeling more easily adaptable and extendable in unsupervised text mining. However, the existing neural topic models is difficult to retain representative information of the documents within the learnt topic representation. In this paper, we propose a neural topic model which incorporates deep mutual information estimation, i.e., Neural Topic Modeling with Deep Mutual Information Estimation(NTM-DMIE). NTM-DMIE is a neural network method for topic learning which maximizes the mutual information between the input documents and their latent topic representation. To learn robust topic representation, we incorporate the discriminator to discriminate negative examples and positive examples via adversarial learning. Moreover, we use both global and local mutual information to preserve the rich information of the input documents in the topic representation. We evaluate NTM-DMIE on several metrics, including accuracy of text clustering, with topic representation, topic uniqueness and topic coherence. Compared to the existing methods, the experimental results show that NTM-DMIE can outperform in all the metrics on the four datasets., Comment: 24 page, 10 Figures and 7 Tables

Synthetic dimensions based on particles' internal degrees of freedom, such as frequency, spatial modes and arrival time, have attracted significant attention. They offer ideal large-scale lattices to simulate nontrivial topological phenomena. Exploring more synthetic dimensions is one of the paths toward higher dimensional physics. In this work, we design and experimentally control the coupling among synthetic dimensions consisting of the intrinsic photonic orbital angular momentum and spin angular momentum degrees of freedom in a degenerate optical resonant cavity, which generates a periodically driven spin-orbital coupling system. We directly characterize the system's properties, including the density of states, energy band structures and topological windings, through the transmission intensity measurements. Our work demonstrates a novel mechanism for exploring the spatial modes of twisted photons as the synthetic dimension, which paves the way to design rich topological physics in a highly compact platform.

Cat states, which were initially proposed to manifest macroscopic superpositions, play an outstanding role in fundamental aspects of quantum dynamics. In addition, they have potential applications in quantum computation and quantum sensing. However, cat states are vulnerable to dissipation, which puts the focus of cat-state generation on higher speed and increased robustness. Dissipative cat-state generation is a common approach based on the nonlinear coupling between a lossy pump field and a half-frequency signal field. In such an approach, the pump field is usually kept in equilibrium, which limits the cat-state generation. We show that the equilibrium requirement can be removed by leveraging a synchronous pump method. In this nonequilibrium regime, the speed of the cat-state generation can be increased by one order of magnitude, and the robustness to single-photon loss can be enhanced. The realization of synchronous pumps is discussed for both time-multiplexed systems and standing modes.