Topolgical Charged Black Holes in Generalized Horava-Lifshitz Gravity

As a candidate of quantum gravity in ultrahigh energy, the $(3+1)$-dimensional Ho\v{r}ava-Lifshitz (HL) gravity with critical exponent $z\ne 1$, indicates anisotropy between time and space at short distance. In the paper, we investigate the most general $z=d$ Ho\v{r}ava-Lifshitz gravity in arbitrary spatial dimension $d$, with a generic dynamical Ricci flow parameter $\lambda$ and a detailed balance violation parameter $\epsilon$. In arbitrary dimensional generalized HL$_{d+1}$ gravity with $z\ge d$ at long distance, we study the topological neutral black hole solutions with general $\lambda$ in $z=d$ HL$_{d+1}$, as well as the topological charged black holes with $\lambda=1$ in $z=d$ HL$_{d+1}$. The HL gravity in the Lagrangian formulation is adopted, while in the Hamiltonian formulation, it reduces to Dirac$-$De Witt's canonical gravity with $\lambda=1$. In particular, the topological charged black holes in $z=5$ HL$_6$, $z=4$ HL$_5$, $z=3,4$ HL$_4$ and $z=2$ HL$_3$ with $\lambda=1$ are solved. Their asymptotical behaviors near the infinite boundary and near the horizon are explored respectively. We also study the behavior of the topological black holes in the $(d+1)$-dimensional HL gravity with $U(1)$ gauge field in the zero temperature limit and finite temperature limit, respectively. Thermodynamics of the topological charged black holes with $\lambda=1$, including temperature, entropy, heat capacity, and free energy are evaluated.Comment: 51 pages, published version. The theoretical framework of z=d HL gravity is set up, and higher curvature terms in spatial dimension become relevant at UV fixed point. Lovelock term, conformal term, new massive term, and Chern-Simons term with different critical exponent z are studie

An Exploration Study of Mixed-initiative Query Reformulation in Conversational Passage Retrieval

In this paper, we report our methods and experiments for the TREC Conversational Assistance Track (CAsT) 2022. In this work, we aim to reproduce multi-stage retrieval pipelines and explore one of the potential benefits of involving mixed-initiative interaction in conversational passage retrieval scenarios: reformulating raw queries. Before the first ranking stage of a multi-stage retrieval pipeline, we propose a mixed-initiative query reformulation module, which achieves query reformulation based on the mixed-initiative interaction between the users and the system, as the replacement for the neural reformulation method. Specifically, we design an algorithm to generate appropriate questions related to the ambiguities in raw queries, and another algorithm to reformulate raw queries by parsing users' feedback and incorporating it into the raw query. For the first ranking stage of our multi-stage pipelines, we adopt a sparse ranking function: BM25, and a dense retrieval method: TCT-ColBERT. For the second-ranking step, we adopt a pointwise reranker: MonoT5, and a pairwise reranker: DuoT5. Experiments on both TREC CAsT 2021 and TREC CAsT 2022 datasets show the effectiveness of our mixed-initiative-based query reformulation method on improving retrieval performance compared with two popular reformulators: a neural reformulator: CANARD-T5 and a rule-based reformulator: historical query reformulator(HQE).Comment: The Thirty-First Text REtrieval Conference (TREC 2022) Proceeding

Zero-shot Query Reformulation for Conversational Search

As the popularity of voice assistants continues to surge, conversational search has gained increased attention in Information Retrieval. However, data sparsity issues in conversational search significantly hinder the progress of supervised conversational search methods. Consequently, researchers are focusing more on zero-shot conversational search approaches. Nevertheless, existing zero-shot methods face three primary limitations: they are not universally applicable to all retrievers, their effectiveness lacks sufficient explainability, and they struggle to resolve common conversational ambiguities caused by omission. To address these limitations, we introduce a novel Zero-shot Query Reformulation (ZeQR) framework that reformulates queries based on previous dialogue contexts without requiring supervision from conversational search data. Specifically, our framework utilizes language models designed for machine reading comprehension tasks to explicitly resolve two common ambiguities: coreference and omission, in raw queries. In comparison to existing zero-shot methods, our approach is universally applicable to any retriever without additional adaptation or indexing. It also provides greater explainability and effectively enhances query intent understanding because ambiguities are explicitly and proactively resolved. Through extensive experiments on four TREC conversational datasets, we demonstrate the effectiveness of our method, which consistently outperforms state-of-the-art baselines.Comment: Accepted by the 9th ACM SIGIR International Conference on the Theory of Information Retrieva

Auslander-Reiten translations in monomorphism categories

We generalize Ringel and Schmidmeier's theory on the Auslander-Reiten translation of the submodule category $\mathcal S_2(A)$ to the monomorphism category $\mathcal S_n(A)$. As in the case of $n=2$, $\mathcal S_n(A)$ has Auslander-Reiten sequences, and the Auslander-Reiten translation $\tau_{\mathcal{S}}$ of $\mathcal S_n(A)$ can be explicitly formulated via $\tau$ of $A$-mod. Furthermore, if $A$ is a selfinjective algebra, we study the periodicity of $\tau_{\mathcal{S}}$ on the objects of $\mathcal S_n(A)$, and of the Serre functor $F_{\mathcal S}$ on the objects of the stable monomorphism category $\underline{\mathcal{S}_n(A)}$. In particular, $\tau_{\mathcal S}^{2m(n+1)}X\cong X$ for X\in\mathcal{S}_n(\A(m, t)); and $F_{\mathcal S}^{m(n+1)}X\cong X$ for X\in\underline{\mathcal{S}_n(\A(m, t))}, where \A(m, t), \ m\ge1, \ t\ge2, are the selfinjective Nakayama algebras.Comment: 33 pages, 1 figure