arXiv subjects
Publications and source records attributed to Jin Cao.
We show that the Friedlander-Mazur conjecture holds for the product of an elliptic curve with some smooth projective variety of dimension 3. Moreover, we show that the Friedlander-Mazur conjecture is stable under a surjective map. As applications, we show that the Friedlander-Mazur conjecture holds uniruled threefolds and unirational varieties up to certain range.
We show that the Friedlander-Mazur conjecture holds for a complex smooth projective variety X of dimension three implies the standard conjectures hold for X. This together with a result of Friedlander yields the equivalence of the two conjectures in dimension three. From this we provide some new examples whose standard conjectures hold.
We consider the moduli space of abelian varieties with two marked points and a frame of the relative de Rham cohomolgy with boundary at these points compatible with its mixed Hodge structure. Such a moduli space gives a natural algebro-geometric framework for higher genus quasi Jacobi forms of index zero and their differential equations which are given as vector fields. In the case of elliptic curves we compute explicitly the Gauss-Manin connection and such vector fields.
The recurrent network architecture is a widely used model in sequence modeling, but its serial dependency hinders the computation parallelization, which makes the operation inefficient. The same problem was encountered in serial adder at the early stage of digital electronics. In this paper, we discuss the similarities between recurrent neural network (RNN) and serial adder. Inspired by carry-lookahead adder, we introduce carry-lookahead module to RNN, which makes it possible for RNN to run in parallel. Then, we design the method of parallel RNN computation, and finally Carry-lookahead RNN (CL-RNN) is proposed. CL-RNN takes advantages in parallelism and flexible receptive field. Through a comprehensive set of tests, we verify that CL-RNN can perform better than existing typical RNNs in sequence modeling tasks which are specially designed for RNNs.
The surface Fermi arc, as a hallmark of Weyl semimetals (WSMs), has been well known in current research, but it remains a challenge to unveil novel phenomena associated with the Fermi arc. Here, we predict a heretofore unrecognized process in WSMs, namely, the photoinduced transition between the bulk states and the Fermi arc. We find this process is significant and can lead to a large effective three-dimensional shift current on the boundaries with the Fermi arc in wide terahertz range. Moreover, due to the low symmetry of the boundaries, the surface photogalvanic effect predicted here can appear in a large class of WSMs that do not have bulk shift current. Hence, our work not only unveils a hidden photogalvanic effect in WSMs but also suggests that all the WSMs are promising material candidates for developing efficient terahertz photodetectors.
Ultracold assembly of diatomic molecules has enabled great advances in controlled chemistry, ultracold chemical physics, and quantum simulation with molecules. Extending the ultracold association to triatomic molecules will offer many new research opportunities and challenges in these fields. A possible approach is to form triatomic molecules in the ultracold atom and diatomic molecule mixture by employing the Feshbach resonance between them. Although the ultracold atom-diatomic-molecule Feshbach resonances have been observed recently, utilizing these resonances to form triatomic molecules remains challenging. Here we report on the evidence of the association of triatomic molecules near the Feshbach resonances between $^{23}$Na$^{40}$K molecules in the rovibrational ground state and $^{40}$K atoms. We apply a radio-frequency pulse to drive the free-bound transition and monitor the loss of $^{23}$Na$^{40}$K molecules. The association of triatomic molecules manifests itself as an additional loss feature in the radio-frequency spectra, which can be distinguished from the atomic loss feature.The binding energy of triatomic molecule is estimated from the measurement. Our work is helpful to understand the complex ultracold atom-molecule Feshbach resonance and may open up an avenue towards the preparation and control of ultracold triatomic molecules.
Dialog State Tracking (DST), an integral part of modern dialog systems, aims to track user preferences and constraints (slots) in task-oriented dialogs. In real-world settings with constantly changing services, DST systems must generalize to new domains and unseen slot types. Existing methods for DST do not generalize well to new slot names and many require known ontologies of slot types and values for inference. We introduce a novel ontology-free framework that supports natural language queries for unseen constraints and slots in multi-domain task-oriented dialogs. Our approach is based on generative question-answering using a conditional language model pre-trained on substantive English sentences. Our model improves joint goal accuracy in zero-shot domain adaptation settings by up to 9% (absolute) over the previous state-of-the-art on the MultiWOZ 2.1 dataset.
The newly realized twisted graphene systems such as twisted bilayer graphene (TBG), twisted double bilayer graphene (TDBG), and twisted trilayer graphene (TTG) have attracted widespread theoretical attention. Therefore, a simple and accurate model of the systems is of vital importance for the further study. Here, we construct the symmetry-adapted localized Wannier functions and the corresponding $\textit{ab initio}$ minimal two-valley four-band effective tight-binding models for generic twisted graphene systems with small twist angle. Such two-valley model evades the Wannier obstruction caused by the fragile topology in one-valley model. The real space valley operator is introduced to explicitly describe the valley $U_{v}\left(1\right)$ symmetry. Each symmetry-adapted Wannier orbital shows a peculiar three-peak form with its maximum at AA spots and its center at AB or BA spots. An extended Hubbard model is also given and the related parameters are presented explicitly. We provide an approach to systematically build the Wannier tight-binding model for generic twisted graphene systems. Our model provides a firm basis for further study of the many-body effects in these systems.
Much recent work on Spoken Language Understanding (SLU) falls short in at least one of three ways: models were trained on oracle text input and neglected the Automatics Speech Recognition (ASR) outputs, models were trained to predict only intents without the slot values, or models were trained on a large amount of in-house data. We proposed a clean and general framework to learn semantics directly from speech with semi-supervision from transcribed speech to address these. Our framework is built upon pretrained end-to-end (E2E) ASR and self-supervised language models, such as BERT, and fine-tuned on a limited amount of target SLU corpus. In parallel, we identified two inadequate settings under which SLU models have been tested: noise-robustness and E2E semantics evaluation. We tested the proposed framework under realistic environmental noises and with a new metric, the slots edit F1 score, on two public SLU corpora. Experiments show that our SLU framework with speech as input can perform on par with those with oracle text as input in semantics understanding, while environmental noises are present, and a limited amount of labeled semantics data is available.
Generating schema labels automatically for column values of data tables has many data science applications such as schema matching, and data discovery and linking. For example, automatically extracted tables with missing headers can be filled by the predicted schema labels which significantly minimizes human effort. Furthermore, the predicted labels can reduce the impact of inconsistent names across multiple data tables. Understanding the connection between column values and contextual information is an important yet neglected aspect as previously proposed methods treat each column independently. In this paper, we propose a context-aware semantic labeling method using both the column values and context. Our new method is based on a new setting for semantic labeling, where we sequentially predict labels for an input table with missing headers. We incorporate both the values and context of each data column using the pre-trained contextualized language model, BERT, that has achieved significant improvements in multiple natural language processing tasks. To our knowledge, we are the first to successfully apply BERT to solve the semantic labeling task. We evaluate our approach using two real-world datasets from different domains, and we demonstrate substantial improvements in terms of evaluation metrics over state-of-the-art feature-based methods.
Neural models have yielded state-of-the-art results in deciphering spoken language understanding (SLU) problems; however, these models require a significant amount of domain-specific labeled examples for training, which is prohibitively expensive. While pre-trained language models like BERT have been shown to capture a massive amount of knowledge by learning from unlabeled corpora and solve SLU using fewer labeled examples for adaption, the encoding of knowledge is implicit and agnostic to downstream tasks. Such encoding results in model inefficiencies in parameter usage: an entirely new model is required for every domain. To address these challenges, we introduce a novel SLU framework, comprising a conversational language modeling (CLM) pre-training task and a light encoder architecture. The CLM pre-training enables networks to capture the representation of the language in conversation style with the presence of ASR errors. The light encoder architecture separates the shared pre-trained networks from the mappings of generally encoded knowledge to specific domains of SLU, allowing for the domain adaptation to be performed solely at the light encoder and thus increasing efficiency. With the framework, we match the performance of state-of-the-art SLU results on Alexa internal datasets and on two public ones (ATIS, SNIPS), adding only 4.4% parameters per task.
Finding the common subsequences of $L$ multiple strings has many applications in the area of bioinformatics, computational linguistics, and information retrieval. A well-known result states that finding a Longest Common Subsequence (LCS) for $L$ strings is NP-hard, e.g., the computational complexity is exponential in $L$. In this paper, we develop a randomized algorithm, referred to as {\em Random-MCS}, for finding a random instance of Maximal Common Subsequence ($MCS$) of multiple strings. A common subsequence is {\em maximal} if inserting any character into the subsequence no longer yields a common subsequence. A special case of MCS is LCS where the length is the longest. We show the complexity of our algorithm is linear in $L$, and therefore is suitable for large $L$. Furthermore, we study the occurrence probability for a single instance of MCS and demonstrate via both theoretical and experimental studies that the longest subsequence from multiple runs of {\em Random-MCS} often yields a solution to $LCS$.
Many data we collect today are in tabular form, with rows as records and columns as attributes associated with each record. Understanding the structural relationship in tabular data can greatly facilitate the data science process. Traditionally, much of this relational information is stored in table schema and maintained by its creators, usually domain experts. In this paper, we develop automated methods to uncover deep relationships in a single data table without expert or domain knowledge. Our method can decompose a data table into layers of smaller tables, revealing its deep structure. The key to our approach is a computationally lightweight forward addition algorithm that we developed to recursively extract the functional dependencies between table columns that are scalable to tables with many columns. With our solution, data scientists will be provided with automatically generated, data-driven insights when exploring new data sets.
Monolayer AlB$_2$ is composed of two atomic layers: honeycomb borophene and triangular aluminum. In contrast with the bulk phase, monolayer AlB$_2$ is predicted to be a superconductor with a high critical temperature. Here, we demonstrate that monolayer AlB$_2$ can be synthesized on Al(111) via molecular beam epitaxy. Our theoretical calculations revealed that the monolayer AlB$_2$ hosts several Dirac cones along the $Γ$--M and $Γ$--K directions; these Dirac cones are protected by crystal symmetries and are thus resistant to external perturbations. The extraordinary electronic structure of the monolayer AlB$_2$ was confirmed via angle-resolved photoemission spectroscopy measurements. These results are likely to stimulate further research interest to explore the exotic properties arising from the interplay of Dirac fermions and superconductivity in two-dimensional materials.
We describe an algebra of meromorphic functions on the Siegel domain of genus two which contains Siegel modular forms for an arithmetic index six subgroup of the symplectic group and it is closed under three canonical derivations of the Siegel domain. The main ingredients of our study are the moduli of enhanced genus two curves, Gauss-Manin connection and the modular vector fields living on such moduli spaces.
Photo sensing and energy harvesting based on exotic properties of quantum materials and new operation principles have great potentials to break the fundamental performance limit of conventional photodetectors and solar cells. As topological nontrivial materials, Weyl semimetals have demonstrated novel optoelectronic properties that promise potential applications in photo detection and energy harvesting arising from their gapless linear dispersion near Weyl nodes and Berry field enhanced nonlinear optical effect at the vicinity of Weyl nodes. In this work, we demonstrate robust photocurrent generation from charge separation of photoexctied electron-hole pairs at the edge of Td-WTe2, a type-II Weyl semimetal, due to crystalline-symmetry breaking along certain crystal fracture directions and possibly enhanced by robust fermi-arc type surface states. Using scanning photocurrent microscopy (SPCM) measurements, we further demonstrate that the edge current response is robust over a wide excitation photon energy. We find that this robust feature is highly generic, and shall arise universally in a wide class of quantum materials with similar crystal symmetries. In addition, possible connections between these edge photocurrents and topological properties of Weyl semimetals are explored. The robust and generic edge current response demonstrated in this work provides a new type of charge separation mechanism for photosensing and energy harvesting over broad wavelength range.
Conversion of raw data into insights and knowledge requires substantial amounts of effort from data scientists. Despite breathtaking advances in Machine Learning (ML) and Artificial Intelligence (AI), data scientists still spend the majority of their effort in understanding and then preparing the raw data for ML/AI. The effort is often manual and ad hoc, and requires some level of domain knowledge. The complexity of the effort increases dramatically when data diversity, both in form and context, increases. In this paper, we introduce our solution, Augmented Data Science (ADS), towards addressing this "human bottleneck" in creating value from diverse datasets. ADS is a data-driven approach and relies on statistics and ML to extract insights from any data set in a domain-agnostic way to facilitate the data science process. Key features of ADS are the replacement of rudimentary data exploration and processing steps with automation and the augmentation of data scientist judgment with automatically-generated insights. We present building blocks of our end-to-end solution and provide a case study to exemplify its capabilities.
In this paper we describe the category of motives for an elliptic curve in the sense of Voevodsky as a derived category of dg modules over a commutative differential graded algebra in the category of representations over some reductive group.