Criticality in Translation-Invariant Parafermion Chains

In this work we numerically study critical phases in translation-invariant $\mathbb{Z}_N$ parafermion chains with both nearest- and next-nearest-neighbor hopping terms. The model can be mapped to a $\mathbb{Z}_N$ spin model with nearest-neighbor couplings via a generalized Jordan-Wigner transformation and translation invariance ensures that the spin model is always self-dual. We first study the low-energy spectrum of chains with only nearest-neighbor coupling, which are mapped onto standard self-dual $\mathbb{Z}_N$ clock models. For $3\leq N\leq 6$ we match the numerical results to the known conformal field theory(CFT) identification. We then analyze in detail the phase diagram of a $N=3$ chain with both nearest and next-nearest neighbor hopping and six critical phases with central charges being $4/5$, 1 or 2 are found. We find continuous phase transitions between $c=1$ and $c=2$ phases, while the phase transition between $c=4/5$ and $c=1$ is conjectured to be of Kosterlitz-Thouless type.Comment: published versio

Topology and Criticality in Resonating Affleck-Kennedy-Lieb-Tasaki loop Spin Liquid States

We exploit a natural Projected Entangled-Pair State (PEPS) representation for the resonating Affleck-Kennedy-Lieb-Tasaki loop (RAL) state. By taking advantage of PEPS-based analytical and numerical methods, we characterize the RAL states on various two-dimensional lattices. On square and honeycomb lattices, these states are critical since the dimer-dimer correlations decay as a power law. On kagome lattice, the RAL state has exponentially decaying correlation functions, supporting the scenario of a gapped spin liquid. We provide further evidence that the RAL state on the kagome lattice is a $\mathbb{Z}_2$ spin liquid, by identifying the four topological sectors and computing the topological entropy. Furthermore, we construct a one-parameter family of PEPS states interpolating between the RAL state and a short-range Resonating Valence Bond state and find a critical point, consistent with the fact that the two states belong to two different phases. We also perform a variational study of the spin-1 kagome Heisenberg model using this one-parameter PEPS.Comment: 10 pages, 14 figures, published versio

Minimizing Age of Information for Mobile Edge Computing Systems: A Nested Index Approach

Exploiting the computational heterogeneity of mobile devices and edge nodes, mobile edge computation (MEC) provides an efficient approach to achieving real-time applications that are sensitive to information freshness, by offloading tasks from mobile devices to edge nodes. We use the metric Age-of-Information (AoI) to evaluate information freshness. An efficient solution to minimize the AoI for the MEC system with multiple users is non-trivial to obtain due to the random computing time. In this paper, we consider multiple users offloading tasks to heterogeneous edge servers in a MEC system. We first reformulate the problem as a Restless Multi-Arm-Bandit (RMAB) problem and establish a hierarchical Markov Decision Process (MDP) to characterize the updating of AoI for the MEC system. Based on the hierarchical MDP, we propose a nested index framework and design a nested index policy with provably asymptotic optimality. Finally, the closed form of the nested index is obtained, which enables the performance tradeoffs between computation complexity and accuracy. Our algorithm leads to an optimality gap reduction of up to 40%, compared to benchmarks. Our algorithm asymptotically approximates the lower bound as the system scalar gets large enough

PM2.5-GNN: A Domain Knowledge Enhanced Graph Neural Network For PM2.5 Forecasting

When predicting PM2.5 concentrations, it is necessary to consider complex information sources since the concentrations are influenced by various factors within a long period. In this paper, we identify a set of critical domain knowledge for PM2.5 forecasting and develop a novel graph based model, PM2.5-GNN, being capable of capturing long-term dependencies. On a real-world dataset, we validate the effectiveness of the proposed model and examine its abilities of capturing both fine-grained and long-term influences in PM2.5 process. The proposed PM2.5-GNN has also been deployed online to provide free forecasting service.Comment: Pre-print version of a ACM SIGSPATIAL 2020 poster [paper](https://dl.acm.org/doi/10.1145/3397536.3422208). The code is available at [Github](https://github.com/shawnwang-tech/PM2.5-GNN), and the talk is available at [YouTube](https://www.youtube.com/watch?v=VX93vMthkGM

Development and application of an advection-dispersion model for data analysis of electromigration experiments with intact rock cores

An advection-dispersion model was developed for interpreting the experimental results of electromigration in granitic rock cores. The most important mechanisms governing the movement of the tracer ions, i.e. electromigration, electroosmosis and dispersion were taken into account by the advection-dispersion model, but the influence of aqueous chemistry was ignored. An analytical solution in the Laplace domain was derived and then applied to analyze the measured results of a series of experiments, performed in an updated device with different applied voltages. The modelling results suggested that both studied tracers, i.e. iodide and selenite, are effectively non-sorbing in the intact rock investigated. The effective diffusivities and formation factors evaluated from the model were also found to be in good agreement with data reported in literature and the associated uncertainties are much smaller than those obtained from the classical ideal plug-flow model, which accounts only for the dominant effect of electromigration on ionic transport. To explore further how the quality of parameter identifications would be influenced by neglect of aqueous chemistry, a reactive transport model was also implemented, which may be regarded as a multi-component version of the advection-dispersion model. The analysis showed that the advection-dispersion model works equally well as the reactive transport model but requires much less computational demanding. It can, therefore, be used with great confidence to interpret the experimental results of electromigration for studies of diffusion and sorption behavior of radionuclides in intact rock cores.Peer reviewe

Deep learning forecasts of cosmic acceleration parameters from DECi-hertz Interferometer Gravitational-wave Observatory

Validating the accelerating expansion of the universe is an important issue for understanding the evolution of the universe. By constraining the cosmic acceleration parameter $X_H$, we can discriminate between the $\Lambda \mathrm{CDM}$ (cosmological constant plus cold dark matter) model and LTB (the Lema\^itre-Tolman-Bondi) model. In this paper, we explore the possibility of constraining the cosmic acceleration parameter with the inspiral gravitational waveform of neutron star binaries (NSBs) in the frequency range of 0.1Hz-10Hz, which can be detected by the second-generation space-based gravitational wave detector DECIGO. We use a convolutional neural network (CNN), a long short-term memory (LSTM) network combined with a gated recurrent unit (GRU), and Fisher information matrix to derive constraints on the cosmic acceleration parameter $X_H$. Based on the simulated gravitational wave data with a time duration of 1 month, we conclude that CNN can limit the relative error to 14.09%, while LSTM network combined with GRU can limit the relative error to 13.53%. Additionally, using Fisher information matrix for gravitational wave data with a 5-year observation can limit the relative error to 32.94%. Compared with the Fisher information matrix method, deep learning techniques will significantly improve the constraints on the cosmic acceleration parameters at different redshifts. Therefore, DECIGO is expected to provide direct measurements of the acceleration of the universe, by observing the chirp signals of coalescing binary neutron stars