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Let $X$ be a complex smooth quasi-projective variety with a fixed epimorphism $\nu\colon\pi_1(X)\twoheadrightarrow H$, where $H$ is a finitely generated abelian group with $\mathrm{rank}H\geq 1$. In this paper, we study the asymptotic behaviour of Betti numbers with all possible field coefficients and the order of the torsion subgroup of singular homology associated to $\nu$, known as the $L^2$-type invariants. When $\nu$ is orbifold effective, we give explicit formulas of these invariants at degree 1. This generalizes the authors' previous work for $H\cong \Z$., Comment: 12 pages, to appear in Chinese Annals of Mathematics, series B. arXiv admin note: text overlap with arXiv:2110.03356

Machine learning is gaining growing momentum in various recent models for the dynamic analysis of information flows in data communications networks. These preliminary models often rely on off-the-shelf learning models to predict from historical statistics while disregarding the physics governing the generating behaviors of these flows. This paper instead introduces Flow Neural Network (FlowNN) to improve the feature representation with learned physical bias. This is implemented by an induction layer, working upon the embedding layer, to impose the physics connected data correlations, and a self-supervised learning strategy with stop-gradient to make the learned physics universal. For the short-timescale network prediction tasks, FlowNN achieves 17% - 71% of loss decrease than the state-of-the-art baselines on both synthetic and real-world networking datasets, which shows the strength of this new approach.

Let X be a complex smooth quasi-projective variety with a fixed epimorphism $\nu\colon\pi_1(X)\twoheadrightarrow \mathbb{Z}$. In this paper, we consider the asymptotic behaviour of invariants such as Betti numbers with all possible field coefficients and the order of the torsion part of singular integral homology associated to $\nu$, known as the $L^2$-type invariants. At homological degree one, we give concrete formulas for these limits by the geometric information of $X$ when $\nu$ is orbifold effective. The proof relies on a study about cohomological degree one jump loci of $X$. We extend part of Arapura's result for cohomological degree one jump loci of $X$ with complex field coefficients to the one with positive characteristic field coefficients. As an application, when $X$ is a hyperplane arrangement complement, a combinatoric upper bound is given for the number of parallel positive dimensional components in cohomological degree one jump loci with complex coefficients. Another application is that we give a positive answer to a question posed by Denham and Suciu for hyperplane arrangement., Comment: 35 pages.Section 4 are completely rewritten. We give new and shorter proofs for the main results using Hochschild-Serre spectral sequence

Different people have different habits of describing their intents in conversations. Some people tend to deliberate their intents in several successive utterances, i.e., they use several consistent messages for readability instead of a long sentence to express their question. This creates a predicament faced by the application of dialogue systems, especially in real-world industry scenarios, in which the dialogue system is unsure whether it should answer the query of user immediately or wait for further supplementary input. Motivated by such an interesting predicament, we define a novel Wait-or-Answer task for dialogue systems. We shed light on a new research topic about how the dialogue system can be more intelligent to behave in this Wait-or-Answer quandary. Further, we propose a predictive approach named Predict-then-Decide (PTD) to tackle this Wait-or-Answer task. More specifically, we take advantage of a decision model to help the dialogue system decide whether to wait or answer. The decision of decision model is made with the assistance of two ancillary prediction models: a user prediction and an agent prediction. The user prediction model tries to predict what the user would supplement and uses its prediction to persuade the decision model that the user has some information to add, so the dialogue system should wait. The agent prediction model tries to predict the answer of the dialogue system and convince the decision model that it is a superior choice to answer the query of user immediately since the input of user has come to an end. We conduct our experiments on two real-life scenarios and three public datasets. Experimental results on five datasets show our proposed PTD approach significantly outperforms the existing models in solving this Wait-or-Answer problem., Comment: The latest version has been accepted to IEEE/ACM Transactions on Audio, Speech, and Language Processing, doi: 10.1109/TASLP.2021.3110145

Producing natural and accurate responses like human beings is the ultimate goal of intelligent dialogue agents. So far, most of the past works concentrate on selecting or generating one pertinent and fluent response according to current query and its context. These models work on a one-to-one environment, making one response to one utterance each round. However, in real human-human conversations, human often sequentially sends several short messages for readability instead of a long message in one turn. Thus messages will not end with an explicit ending signal, which is crucial for agents to decide when to reply. So the first step for an intelligent dialogue agent is not replying but deciding if it should reply at the moment. To address this issue, in this paper, we propose a novel Imagine-then-Arbitrate (ITA) neural dialogue model to help the agent decide whether to wait or to make a response directly. Our method has two imaginator modules and an arbitrator module. The two imaginators will learn the agent's and user's speaking style respectively, generate possible utterances as the input of the arbitrator, combining with dialogue history. And the arbitrator decides whether to wait or to make a response to the user directly. To verify the performance and effectiveness of our method, we prepared two dialogue datasets and compared our approach with several popular models. Experimental results show that our model performs well on addressing ending prediction issue and outperforms baseline models., Comment: This is an outdated version of "Predict-then-Decide: A Predictive Approach for Wait or Answer Task in Dialogue Systems," in IEEE/ACM Transactions on Audio, Speech, and Language Processing, doi: 10.1109/TASLP.2021.3110145