Well-posedness for the stochastic electrokinetic flow

We consider the stochastic electrokinetic flow in a smooth bounded domain $mathcal{D}$, modelled by a Nernst-Planck-Navier-Stokes system with a blocking boundary conditions for ionic species concentrations, perturbed by multiplicative noise. Several results are established in this paper. In both $2d$ and $3d$ cases, we establish the global existence of weak martingale solution which is weak in both PDEs and probability sense, and also the existence and uniqueness of the maximal strong pathwise solution which is strong in PDEs and probability sense. Particularly, we show that the maximal pathwise solution is global one in $2d$ case without the restriction of smallness of initial data.

Alternating Direction Method of Multiplier-Based Distributed Planning Model for Natural Gas, Electricity Network, and Regional Integrated Energy Systems

Regional integrated energy system coupling with multienergy devices, energy storage devices, and renewable energy devices has been regarded as one of the most promising solutions for future energy systems. Planning for existing natural gas and electricity network expansion, regional integrated energy system locations, or system equipment types and capacities are urgent problems in infrastructure development. This article employs a joint planning model to address these; however, the joint planning model ignores the potential ownerships by three agents, for which investment decisions are generally made by different investors. In this work, the joint planning model is decomposed into three distributed planning subproblems related to the corresponding stakeholders, and the alternating direction method of multipliers is adopted to solve the tripartite distributed planning problem. The effectiveness of the planning model is verified on an updated version of the Institute of Electrical and Electronics Engineers (IEEE) 24-bus electric system, the Belgian 20-node natural gas system, and three assumed integrated energy systems. Simulation results illustrate that a distributed planning model is more sensitive to individual load differences, which is precisely the defect of the joint planning model. Moreover, the algorithm performance considering rates of convergence and the impacts of penalty parameters is further analyzed

From Torus Bundles to Particle-Hole Equivariantization

We continue the program of constructing (pre)modular tensor categories from 3-manifolds first initiated by Cho-Gang-Kim using $M$ theory in physics and then mathematically studied by Cui-Qiu-Wang. An important structure involved is a collection of certain $text{SL}(2, mathbb{C})$ characters on a given manifold which serve as the simple object types in the corresponding category. Chern-Simons invariants and adjoint Reidemeister torsions play a key role in the construction, and they are related to topological twists and quantum dimensions, respectively, of simple objects. The modular $S$-matrix is computed from local operators and follows a trial-and-error procedure. It is currently unknown how to produce data beyond the modular $S$- and $T$-matrices. There are also a number of subtleties in the construction which remain to be solved. In this paper, we consider an infinite family of 3-manifolds, that is, torus bundles over the circle. We show that the modular data produced by such manifolds are realized by the $mathbb{Z}_2$-equivariantization of certain pointed premodular categories. Here the equivariantization is performed for the $mathbb{Z}_2$-action sending a simple (invertible) object to its inverse, also called the particle-hole symmetry. It is our hope that this extensive class of examples will shed light on how to improve the program to recover the full data of a premodular category.

AutoDebias: Learning to Debias for Recommendation

Recommender systems rely on user behavior data like ratings and clicks to build personalization model. However, the collected data is observational rather than experimental, causing various biases in the data which significantly affect the learned model. Most existing work for recommendation debiasing, such as the inverse propensity scoring and imputation approaches, focuses on one or two specific biases, lacking the universal capacity that can account for mixed or even unknown biases in the data. Towards this research gap, we first analyze the origin of biases from the perspective of textit{risk discrepancy} that represents the difference between the expectation empirical risk and the true risk. Remarkably, we derive a general learning framework that well summarizes most existing debiasing strategies by specifying some parameters of the general framework. This provides a valuable opportunity to develop a universal solution for debiasing, e.g., by learning the debiasing parameters from data. However, the training data lacks important signal of how the data is biased and what the unbiased data looks like. To move this idea forward, we propose textit{AotoDebias} that leverages another (small) set of uniform data to optimize the debiasing parameters by solving the bi-level optimization problem with meta-learning. Through theoretical analyses, we derive the generalization bound for AutoDebias and prove its ability to acquire the appropriate debiasing strategy. Extensive experiments on two real datasets and a simulated dataset demonstrated effectiveness of AutoDebias. The code is available at url{https://github.com/DongHande/AutoDebias}.

From Three Dimensional Manifolds to Modular Tensor Categories

Using M-theory in physics, Cho, Gang, and Kim (JHEP 2020, 115 (2020) ) recently outlined a program that connects two parallel subjects of three dimensional manifolds, namely, geometric topology and quantum topology. They suggest that classical topological invariants such as Chern-Simons invariants of $text{SL}(2,mathbb{C})$-flat connections and adjoint Reidemeister torsions of a three manifold can be packaged together to produce a $(2+1)$-topological quantum field theory, which is essentially equivalent to a modular tensor category. It is further conjectured that every modular tensor category can be obtained from a three manifold and a semi-simple Lie group. In this paper, we study this program mathematically, and provide strong support for the feasibility of such a program. The program produces an algorithm to generate the potential modular $T$-matrix and the quantum dimensions of a candidate modular data. The modular $S$-matrix follows from essentially a trial-and-error procedure. We find modular tensor categories that realize candidate modular data constructed from Seifert fibered spaces and torus bundles over the circle that reveal many subtleties in the program. We make a number of improvements to the program based on our computations. Our main result is a mathematical construction of a premodular category from each Seifert fibered space with three singular fibers and a family of torus bundles over the circle with Thurston SOL geometry. The premodular categories from Seifert fibered spaces are related to Temperley-Lieb-Jones categories and the ones from torus bundles over the circle are related to metaplectic categories. We conjecture that a resulting premodular category is modular if and only if the three manifold is a $mathbb{Z}_2$-homology sphere and condensation of bosons in premodular categories leads to either modular or super-modular categories.

Scene Text Detection with Scribble Lines

Scene text detection, which is one of the most popular topics in both academia and industry, can achieve remarkable performance with sufficient training data. However, the annotation costs of scene text detection are huge with traditional labeling methods due to the various shapes of texts. Thus, it is practical and insightful to study simpler labeling methods without harming the detection performance. In this paper, we propose to annotate the texts by scribble lines instead of polygons for text detection. It is a general labeling method for texts with various shapes and requires low labeling costs. Furthermore, a weakly-supervised scene text detection framework is proposed to use the scribble lines for text detection. The experiments on several benchmarks show that the proposed method bridges the performance gap between the weakly labeling method and the original polygon-based labeling methods, with even better performance. We will release the weak annotations of the benchmarks in our experiments and hope it will benefit the field of scene text detection to achieve better performance with simpler annotations.

Invariant measure for 2D stochastic Cahn-Hilliard-Navier-Stokes equations

Using the Maslowski and Seidler method, the existence of invariant measure for 2-dimensional stochastic Cahn-Hilliard-Navier-Stokes equations with multiplicative noise is proved in state space $L_x^2times H^1$, working with the weak topology. Also, the existence of global pathwise solution is investigated using the stochastic compactness argument.

Ground Subspaces of Topological Phases of Matter as Error Correcting Codes

Topological quantum computing is believed to be inherently fault-tolerant. One mathematical justification would be to prove that ground subspaces or ground state manifolds of topological phases of matter behave as error correction codes with macroscopic distance. While this is widely assumed and used as a definition of topological phases of matter in the physics literature, besides the doubled abelian anyon models in Kitaevs seminal paper, no non-abelian models are proven to be so mathematically until recently. Cui et al extended the theorem from doubled abelian anyon models to all Kitaev models based on any finite group. Those proofs are very explicit using detailed knowledge of the Hamiltonians, so it seems to be hard to further extend the proof to cover other models such as the Levin-Wen. We pursue a totally different approach based on topological quantum field theories (TQFTs), and prove that a lattice implementation of the disk axiom and annulus axiom in TQFTs as essentially the equivalence of TQO1 and TQO2 conditions. We confirm the error correcting properties of ground subspaces for topological lattice Hamiltonian schemas of the Levin-Wen model and Dijkgraaf-Witten TQFTs by providing a lattice version of the disk axiom and annulus of the underlying TQFTs. The error correcting property of ground subspaces is also shared by gapped fracton models such as the Haah codes. We propose to characterize topological phases of matter via error correcting properties, and refer to gapped fracton models as lax-topological.

Can High-Temperature Reactions Be Described by a Minimum Energy Path Model? Steric Hindrance Matters

High-temperature reactions widely exist in nature. However, they are difficult to be characterized either experimentally or computationally. The routinely used minimum energy path (MEP) model in computational modeling of chemical reactions is not justified to describe high-temperature reactions since high-energy structures are actively involved there. In this study, using CH4 decomposition on the Cu(111) surface as an example, we systematically compare MEP results with those obtained by explicitly sampling all relevant structures via ab initio molecular dynamics (AIMD) simulations at different temperatures. Interestingly, we find that, for reactions protected by a strong steric hindrance effect, the MEP is still effectively followed even at a temperature close to the Cu melting point. In contrast, without such a protection, the flexibility of surface Cu atoms can lead to a significant free energy barrier reduction at a high temperature. Accordingly, some conclusions about graphene growth mechanisms based on MEP calculations should be revisited. Physical insights provided by this study can deepen our understanding on high-temperature surface reactions.