Existing equivariant neural networks for continuous groups require discretization or group representations. All these approaches require detailed knowledge of the group parametrization and cannot learn entirely new symmetries. We propose to work with
the Lie algebra (infinitesimal generators) instead of the Lie group.Our model, the Lie algebra convolutional network (L-conv) can learn potential symmetries and does not require discretization of the group. We show that L-conv can serve as a building block to construct any group equivariant architecture. We discuss how CNNs and Graph Convolutional Networks are related to and can be expressed as L-conv with appropriate groups. We also derive the MSE loss for a single L-conv layer and find a deep relation with Lagrangians used in physics, with some of the physics aiding in defining generalization and symmetries in the loss landscape. Conversely, L-conv could be used to propose more general equivariant ansatze for scientific machine learning.
We investigate the role of disorder in the edge transport of axion insulator films. We predict by first-principles calculations that even-number-layer MnBi$_2$Te$_4$ have gapped helical edge states. The random potential will dramatically modify the e
dge spectral function to become gapless. However, such gapless helical state here is fundamentally different from that in quantum spin Hall insulator or topological Anderson insulator. We further study the edge transport in this system by Landauer-B{u}ttiker formalism, and find such gapless edge state is dissipative and not immune to backscattering, which would explain the dissipative nonlocal transport in the axion insulator state observed in six septuple layer MnBi$_2$Te$_4$ experimentally. Several transport experiments are proposed to verify our theory on the dissipative helical edge channels. In particular, the longitudinal resistance can be greatly reduced by adding an extra floating probe even if it is not used. These results will facilitate the observsation of long-sought topological magnetoelectric effect in axion insulators.
Early and accurate severity assessment of Coronavirus disease 2019 (COVID-19) based on computed tomography (CT) images offers a great help to the estimation of intensive care unit event and the clinical decision of treatment planning. To augment the
labeled data and improve the generalization ability of the classification model, it is necessary to aggregate data from multiple sites. This task faces several challenges including class imbalance between mild and severe infections, domain distribution discrepancy between sites, and presence of heterogeneous features. In this paper, we propose a novel domain adaptation (DA) method with two components to address these problems. The first component is a stochastic class-balanced boosting sampling strategy that overcomes the imbalanced learning problem and improves the classification performance on poorly-predicted classes. The second component is a representation learning that guarantees three properties: 1) domain-transferability by prototype triplet loss, 2) discriminant by conditional maximum mean discrepancy loss, and 3) completeness by multi-view reconstruction loss. Particularly, we propose a domain translator and align the heterogeneous data to the estimated class prototypes (i.e., class centers) in a hyper-sphere manifold. Experiments on cross-site severity assessment of COVID-19 from CT images show that the proposed method can effectively tackle the imbalanced learning problem and outperform recent DA approaches.
In this paper we systematically study a model of spherically symmetric polymer black holes recently proposed by Gambini, Olmedo, and Pullin (GOP). Within the framework of loop quantum gravity, the quantum parameters in the GOP model depend on the min
imal area gap and the size of the discretization of the physical states. In this model, a spacelike transition surface takes place of the classical singularity. By means of coordinate transformations, we first extend the metric to the white hole region, and find that the geometric structure of the quantum black hole is similar to the wormhole structure, and the radius of the most quantum region is equal to the wormhole radius. In addition, we show that the energy conditions are violated not only at throat, but also at horizons and the spatial infinities. In order to show how the quantum effects affect the spacetimes, we calculate the Ricci and Kretschmann scalars at different places. It turns out that, as expected, the most quantum region is at the throat. Finally, we consider the quasinormal modes (QNMs) of massless scalar field perturbations, electromagnetic field perturbations, and axial gravitational perturbations. QNMs in the Eikonal limits are also considered. As anticipated, the spectrum of QNMs deviates from that of the classical case due to quantum effects. Interestingly, our results show that the quasinormal frequencies of the perturbations share the same qualitative tendency while setting quantum parameters with various values in this effective model, even if the potential deviations are different with different spins.
The unoccupied part of the band structure in the magnetic topological insulator MnBi$_2$Te$_4$ is studied by first-principles calculations. We find a second, unoccupied topological surface state with similar electronic structure to the celebrated occ
upied topological surface state. This state is energetically located approximate $1.6$ eV above the occupied Dirac surface state around $Gamma$ point, which permit it to be directly observed by the two-photon angle-resolved photoemission spectroscopy. We propose a unified effective model for the occupied and unoccupied surface states. Due to the direct optical coupling between these two surface states, we further propose two optical effects to detect the unoccupied surface state. One is the polar Kerr effect in odd layer from nonvanishing ac Hall conductance $sigma_{xy}(omega)$, and the other is higher-order terahertz-sideband generation in even layer, where the non-vanishining Berry curvature of the unoccupied surface state is directly observed from the giant Faraday rotation of optical emission.
Item response theory (IRT) has become one of the most popular statistical models for psychometrics, a field of study concerned with the theory and techniques of psychological measurement. The IRT models are latent factor models tailored to the analys
is, interpretation, and prediction of individuals behaviors in answering a set of measurement items that typically involve categorical response data. Many important questions of measurement are directly or indirectly answered through the use of IRT models, including scoring individuals test performances, validating a test scale, linking two tests, among others. This paper provides a review of item response theory, including its statistical framework and psychometric applications. We establish connections between item response theory and related topics in statistics, including empirical Bayes, nonparametric methods, matrix completion, regularized estimation, and sequential analysis. Possible future directions of IRT are discussed from the perspective of statistical learning.
We show that the K-moduli spaces of log Fano pairs $(mathbb{P}^3, cS)$ where $S$ is a quartic surface interpolate between the GIT moduli space of quartic surfaces and the Baily-Borel compactification of moduli of quartic K3 surfaces as $c$ varies in
the interval $(0,1)$. We completely describe the wall crossings of these K-moduli spaces. As the main application, we verify Laza-OGradys prediction on the Hassett-Keel-Looijenga program for quartic K3 surfaces. We also obtain the K-moduli compactification of quartic double solids, and classify all Gorenstein canonical Fano degenerations of $mathbb{P}^3$.
The increased uptake of electric vehicles (EVs) leads to increased demand for electricity, and sometime pressure to power grids. Uncoordinated charging of EVs may result in putting pressure on distribution networks, and often some form of optimisatio
n is required in the charging process. Optimal coordinated charging is a multi-objective optimisation problem in nature, with objective functions such as minimum price charging and minimum disruptions to the grid. In this manuscript, we propose a general multi-objective EV charging/discharging schedule (MOEVCS) framework, where the time of use (TOU) tariff is designed according to the load request at each time stamp. To obtain the optimal scheduling scheme and balance the competing benefits from different stakeholders, such as EV owners, EV charging stations (EVCS), and the grid operator, we design three conflicting objective functions including EV owner cost, EVCS profit, and the network impact. Moreover, we create four application scenarios with different charging request distributions over the investigated periods. We use a constraint multi-objective evolutionary algorithm (MOEA) to solve the problem. Our results demonstrate the effectiveness of MOEVCS in making a balance between three conflicting objectives.
We consider a two-color formaldehyde PLIF thermometry scheme using a wavelength-switching injection seeding Nd:YAG laser at 355 nm. The 28183.5 cm-1 and 28184.5 cm-1 peaks of formaldehyde are used to measure low temperature combustion zone. Using a b
urst mode amplifier and a high speed camera, high-repetition rate (20 kHz) temperature field measurement is validated on a laminar coflow diffusion flame and demonstrated on a turbulent confined jet in hot crossflow flame.
In this work, we analytically derive the exact closed dynamical equations for a liquid with short-ranged interactions in large spatial dimensions using the same statistical mechanics tools employed to analyze Brownian motion. Our derivation greatly s
implifies the original path-integral-based route to these equations and provides new insight into the physical features associated with high-dimensional liquids and glass formation. Most importantly, our construction provides a facile route to the exact dynamical analysis of important related dynamical problems, as well as a means to devise cluster generalizations of the exact solution in infinite dimensions. This latter fact opens the door to the construction of increasingly accurate theories of vitrification in three-dimensional liquids.
