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Source author record

Ting Zhang

Ting Zhang appears in the imported research catalog. Authorship, coauthor and topic links are available while profile ownership is still unclaimed.

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math.APComputer VisionSoftware Engineeringcond-mat.mes-hallmath.STquant-phStatistics TheoryInformation RetrievalComputation and LanguageFormal Languages and Automata TheoryLogic in Computer ScienceArtificial IntelligenceMachine Learningmath.COmath.SPcond-mat.mtrl-scicond-mat.othercond-mat.quant-gascond-mat.supr-conCryptography and Securityeess.IVHuman-Computer InteractionMethodologyphysics.app-phphysics.ins-detphysics.med-phq-fin.ST

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Published work

58 published item(s)

preprint2026arXiv

An Execution-Verified Multi-Language Benchmark for Code Semantic Reasoning

Evaluating whether large language models (LLMs) can recover execution-relevant program structure, rather than only produce code that passes tests, remains an open problem. Existing code benchmarks emphasize test-passing outputs, from standalone programming tasks (HumanEval, MBPP, LiveCodeBench) to repository repair (SWE-Bench); this is useful, but offers limited diagnostic signal about which program semantics a model can recover from source. We introduce TraceEval, to our knowledge the first execution-verified, multi-language benchmark for code semantic reasoning: recovering a program's runtime call structure from source code. Unlike prior call-graph benchmarks that rely on static-tool output or hand-annotated ground truth, every positive edge in TraceEval is mechanically witnessed by validation execution, eliminating annotator disagreement and label noise for observed behavior. TraceEval consists of (i) 10,583 real-world programs (2,129 test, 8,454 train) extracted from 1,600+ open-source repositories across Python, JavaScript, and Java via an LLM-assisted harness-generation pipeline with tracer validation; and (ii) a reproducible pipeline that converts any open-source repository into new verified benchmark instances. We evaluate 10 LLMs at zero-shot on the held-out test split. The strongest model, Claude-Opus-4.6, reaches an average F1 of 72.9% across the three languages. To demonstrate the train split's utility as a supervision substrate, we fine-tune the Qwen2.5-Coder family on it: lifts of up to +55.6 F1 bring tuned Qwen2.5-Coder-32B to 71.2%, within 1.7 F1 of zero-shot Claude-Opus-4.6. We release the benchmark, pipeline, baselines, and a datasheet at https://github.com/yikun-li/TraceEva

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

FollowTable: A Benchmark for Instruction-Following Table Retrieval

Table Retrieval (TR) has traditionally been formulated as an ad-hoc retrieval problem, where relevance is primarily determined by topical semantic similarity. With the growing adoption of LLM-based agentic systems, access to structured data is increasingly instruction-driven, where relevance is conditional on explicit content and schema constraints rather than topical similarity alone. We therefore formalize Instruction-Following Table Retrieval (IFTR), a new task that requires models to jointly satisfy topical relevance and fine-grained instruction constraints. We identify two core challenges in IFTR: (i) sensitivity to content scope, such as inclusion and exclusion constraints, and (ii) awareness of schema-grounded requirements, including column semantics and representation granularity--capabilities largely absent in existing retrievers. To support systematic evaluation, we introduce FollowTable, the first large-scale benchmark for IFTR, constructed via a taxonomy-driven annotation pipeline. We further propose a new metric, termed the Instruction Responsiveness Score, to evaluate whether retrieval rankings consistently adapt to user instructions relative to a topic-only baseline. Our results indicate that existing retrieval models struggle to follow fine-grained instructions over tabular data. In particular, they exhibit systematic biases toward surface-level semantic cues and remain limited in handling schema-grounded constraints, highlighting substantial room for future improvements.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

LIDL: LLM Integration Defect Localization via Knowledge Graph-Enhanced Multi-Agent Analysis

LLM-integrated software, which embeds or interacts with large language models (LLMs) as functional components, exhibits probabilistic and context-dependent behaviors that fundamentally differ from those of traditional software. This shift introduces a new category of integration defects that arise not only from code errors but also from misaligned interactions among LLM-specific artifacts, including prompts, API calls, configurations, and model outputs. However, existing defect localization techniques are ineffective at identifying these LLM-specific integration defects because they fail to capture cross-layer dependencies across heterogeneous artifacts, cannot exploit incomplete or misleading error traces, and lack semantic reasoning capabilities for identifying root causes. To address these challenges, we propose LIDL, a multi-agent framework for defect localization in LLM-integrated software. LIDL (1) constructs a code knowledge graph enriched with LLM-aware annotations that represent interaction boundaries across source code, prompts, and configuration files, (2) fuses three complementary sources of error evidence inferred by LLMs to surface candidate defect locations, and (3) applies context-aware validation that uses counterfactual reasoning to distinguish true root causes from propagated symptoms. We evaluate LIDL on 146 real-world defect instances collected from 105 GitHub repositories and 16 agent-based systems. The results show that LIDL significantly outperforms five state-of-the-art baselines across all metrics, achieving a Top-3 accuracy of 0.64 and a MAP of 0.48, which represents a 64.1% improvement over the best-performing baseline. Notably, LIDL achieves these gains while reducing cost by 92.5%, demonstrating both high accuracy and cost efficiency.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

Out of Distribution, Out of Luck: How Well Can LLMs Trained on Vulnerability Datasets Detect Top 25 CWE Weaknesses?

Automated vulnerability detection research has made substantial progress, yet its real-world impact remains limited. Prior work found that current vulnerability datasets suffer from issues including label inaccuracy rates of 20%-71%, extensive duplication, and poor coverage of critical Common Weakness Enumeration (CWE). These issues create a significant generalization gap where models achieve misleading In-Distribution (ID) accuracies (testing on splits from the same dataset) by exploiting spurious correlations rather than learning true vulnerability patterns. To address these limitations, we present a three-part solution. First, we introduce BenchVul, which is a manually curated and balanced test dataset covering the MITRE Top 25 Most Dangerous CWEs, to enable fair model evaluation. Second, we construct a high-quality training dataset, TitanVul, comprising 38,548 functions by aggregating seven public sources and applying deduplication and validation using a novel multi-agent LLM pipeline. Third, we propose a Realistic Vulnerability Generation (RVG) pipeline, which synthesizes context-aware vulnerability examples for underrepresented but critical CWE types through simulated development workflows. Our evaluation reveals that In-Distribution (ID) performance does not reliably predict Out-of-Distribution (OOD) performance on BenchVul. For example, a model trained on BigVul achieves the highest 0.703 ID accuracy but fails on BenchVul's real-world samples (0.493 OOD accuracy). Conversely, a model trained on our TitanVul achieves the highest OOD performance on both the real-world (0.881) and synthesized (0.785) portions of BenchVul, improving upon the next-best performing dataset by 5.3% and 11.8% respectively, despite a modest ID score (0.590). Augmenting TitanVul with our RVG further boosts this leading OOD performance, improving accuracy on real-world data by 5.8% (to 0.932).

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

PenForge: On-the-Fly Expert Agent Construction for Automated Penetration Testing

Penetration testing is essential for identifying vulnerabilities in web applications before real adversaries can exploit them. Recent work has explored automating this process with Large Language Model (LLM)-powered agents, but existing approaches either rely on a single generic agent that struggles in complex scenarios or narrowly specialized agents that cannot adapt to diverse vulnerability types. We therefore introduce PenForge, a framework that dynamically constructs expert agents during testing rather than relying on those prepared beforehand. By integrating automated reconnaissance of potential attack surfaces with agents instantiated on the fly for context-aware exploitation, PenForge achieves a 30.0% exploit success rate (12/40) on CVE-Bench in the particularly challenging zero-day setting, which is a 3 times improvement over the state-of-the-art. Our analysis also identifies three opportunities for future work: (1) supplying richer tool-usage knowledge to improve exploitation effectiveness; (2) extending benchmarks to include more vulnerabilities and attack types; and (3) fostering developer trust by incorporating explainable mechanisms and human review. As an emerging result with substantial potential impact, PenForge embodies the early-stage yet paradigm-shifting idea of on-the-fly agent construction, marking its promise as a step toward scalable and effective LLM-driven penetration testing.

0 citations0 reviewsNo code linkedOpen access
preprint2025arXiv

From Events to Trending: A Multi-Stage Hotspots Detection Method Based on Generative Query Indexing

LLM-based conversational systems have become a popular gateway for information access, yet most existing chatbots struggle to handle news-related trending queries effectively. To improve user experience, an effective trending query detection method is urgently needed to enable differentiated processing of such target traffic. However, current research on trending detection tailored to the dialogue system scenario remains largely unexplored, and methods designed for traditional search engines often underperform in conversational contexts due to radically distinct query distributions and expression patterns. To fill this gap, we propose a multi-stage framework for trending detection, which achieves systematic optimization from both offline generation and online identification perspectives. Specifically, our framework first exploits selected hot events to generate index queries, establishing a key bridge between static events and dynamic user queries. It then employs a retrieval matching mechanism for real-time online detection of trending queries, where we introduce a cascaded recall and ranking architecture to balance detection efficiency and accuracy. Furthermore, to better adapt to the practical application scenario, our framework adopts a single-recall module as a cold-start strategy to collect online data for fine-tuning the reranker. Extensive experiments demonstrate that our framework significantly outperforms baseline methods in both offline evaluations and online A/B tests, and user satisfaction is relatively improved by 27\% in terms of positive-negative feedback ratio.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Automatic Pull Request Title Generation

Pull Requests (PRs) are a mechanism on modern collaborative coding platforms, such as GitHub. PRs allow developers to tell others that their code changes are available for merging into another branch in a repository. A PR needs to be reviewed and approved by the core team of the repository before the changes are merged into the branch. Usually, reviewers need to identify a PR that is in line with their interests before providing a review. By default, PRs are arranged in a list view that shows the titles of PRs. Therefore, it is desirable to have a precise and concise title, which is beneficial for both reviewers and other developers. However, it is often the case that developers do not provide good titles; we find that many existing PR titles are either inappropriate in length (i.e., too short or too long) or fail to convey useful information, which may result in PR being ignored or rejected. Therefore, there is a need for automatic techniques to help developers draft high-quality titles. In this paper, we introduce the task of automatic generation of PR titles. We formulate the task as a one-sentence summarization task. To facilitate the research on this task, we construct a dataset that consists of 43,816 PRs from 495 GitHub repositories. We evaluated the state-of-the-art summarization approaches for the automatic PR title generation task. We leverage ROUGE metrics to automatically evaluate the summarization approaches and conduct a manual evaluation. The experimental results indicate that BART is the best technique for generating satisfactory PR titles with ROUGE-1, ROUGE-2, and ROUGE-L F1-scores of 47.22, 25.27, and 43.12, respectively. The manual evaluation also shows that the titles generated by BART are preferred.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Automatically Generating Counterfactuals for Relation Classification

The goal of relation classification (RC) is to extract the semantic relations between/among entities in the text. As a fundamental task in natural language processing, it is crucial to ensure the robustness of RC models. Despite the high accuracy current deep neural models have achieved in RC tasks, they are easily affected by spurious correlations. One solution to this problem is to train the model with counterfactually augmented data (CAD) such that it can learn the causation rather than the confounding. However, no attempt has been made on generating counterfactuals for RC tasks. In this paper, we formulate the problem of automatically generating CAD for RC tasks from an entity-centric viewpoint, and develop a novel approach to derive contextual counterfactuals for entities. Specifically, we exploit two elementary topological properties, i.e., the centrality and the shortest path, in syntactic and semantic dependency graphs, to first identify and then intervene on the contextual causal features for entities. We conduct a comprehensive evaluation on four RC datasets by combining our proposed approach with a variety of backbone RC models. The results demonstrate that our approach not only improves the performance of the backbones, but also makes them more robust in the out-of-domain test.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

AutoPRTitle: A Tool for Automatic Pull Request Title Generation

With the rise of the pull request mechanism in software development, the quality of pull requests has gained more attention. Prior works focus on improving the quality of pull request descriptions and several approaches have been proposed to automatically generate pull request descriptions. As an essential component of a pull request, pull request titles have not received a similar level of attention. To further facilitate automation in software development and to help developers in drafting high-quality pull request titles, we introduce AutoPRTitle. AutoPRTitle is specifically designed to automatically generate pull request titles. AutoPRTitle can generate a precise and succinct pull request title based on the pull request description, commit messages, and the associated issue titles. AutoPRTitle is built upon a state-of-the-art text summarization model, BART, which has been pre-trained on large-scale English corpora. We further fine-tuned BART in a pull request dataset containing high-quality pull request titles. We implemented AutoPRTitle as a stand-alone web application. We conducted two sets of evaluations: one concerning the model accuracy and the other concerning the tool usability. For model accuracy, BART outperforms the best baseline by 24.6%, 40.5%, and 23.3%, respectively. For tool usability, the evaluators consider our tool as easy-to-use and useful when creating a pull request title of good quality. Source code: https://github.com/soarsmu/Auto-PR-Title Video demo: https://tinyurl.com/AutoPRTitle

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Bootstrapped Masked Autoencoders for Vision BERT Pretraining

We propose bootstrapped masked autoencoders (BootMAE), a new approach for vision BERT pretraining. BootMAE improves the original masked autoencoders (MAE) with two core designs: 1) momentum encoder that provides online feature as extra BERT prediction targets; 2) target-aware decoder that tries to reduce the pressure on the encoder to memorize target-specific information in BERT pretraining. The first design is motivated by the observation that using a pretrained MAE to extract the features as the BERT prediction target for masked tokens can achieve better pretraining performance. Therefore, we add a momentum encoder in parallel with the original MAE encoder, which bootstraps the pretraining performance by using its own representation as the BERT prediction target. In the second design, we introduce target-specific information (e.g., pixel values of unmasked patches) from the encoder directly to the decoder to reduce the pressure on the encoder of memorizing the target-specific information. Thus, the encoder focuses on semantic modeling, which is the goal of BERT pretraining, and does not need to waste its capacity in memorizing the information of unmasked tokens related to the prediction target. Through extensive experiments, our BootMAE achieves $84.2\%$ Top-1 accuracy on ImageNet-1K with ViT-B backbone, outperforming MAE by $+0.8\%$ under the same pre-training epochs. BootMAE also gets $+1.0$ mIoU improvements on semantic segmentation on ADE20K and $+1.3$ box AP, $+1.4$ mask AP improvement on object detection and segmentation on COCO dataset. Code is released at https://github.com/LightDXY/BootMAE.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Experimental investigation of quantum uncertainty relations with classical shadows

The quantum component in uncertainty relation can be naturally characterized by the quantum coherence of a quantum state, which is of paramount importance in quantum information science. Here, we experimentally investigate quantum uncertainty relations construed with relative entropy of coherence, $l_1$ norm of coherence and coherence of formation. In stead of quantum state tomographic technology, we employ the classical shadow algorithm for the detection of lower bounds in quantum uncertainty relations. With an all optical setup, we prepare a family of quantum states whose purity can be fully controlled. We experimentally explore the tightness of various lower bounds in different reference bases on the prepared states. Our results indicate the tightness of quantum coherence lower bounds dependents on the reference bases as well as the purity of quantum state.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Gate-Tunable Spin-Orbit Coupling in a Germanium Hole Double Quantum Dot

Hole spins confined in semiconductor quantum dot systems have gained considerable interest for their strong spin-orbit interactions (SOIs) and relatively weak hyperfine interactions. Here we experimentally demonstrate a tunable SOI in a double quantum dot in a Germanium (Ge) hut wire (HW), which could help enable fast all-electric spin manipulations while suppressing unwanted decoherence. Specifically, we measure the transport spectra in the Pauli spin blockade regime in the double quantum dot device.By adjusting the interdot tunnel coupling, we obtain an electric field tuned spin-orbit length lso = 2.0 - 48.9 nm. This tunability of the SOI could pave the way toward the realization of high-fidelity qubits in Ge HW systems.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

General Facial Representation Learning in a Visual-Linguistic Manner

How to learn a universal facial representation that boosts all face analysis tasks? This paper takes one step toward this goal. In this paper, we study the transfer performance of pre-trained models on face analysis tasks and introduce a framework, called FaRL, for general Facial Representation Learning in a visual-linguistic manner. On one hand, the framework involves a contrastive loss to learn high-level semantic meaning from image-text pairs. On the other hand, we propose exploring low-level information simultaneously to further enhance the face representation, by adding a masked image modeling. We perform pre-training on LAION-FACE, a dataset containing large amount of face image-text pairs, and evaluate the representation capability on multiple downstream tasks. We show that FaRL achieves better transfer performance compared with previous pre-trained models. We also verify its superiority in the low-data regime. More importantly, our model surpasses the state-of-the-art methods on face analysis tasks including face parsing and face alignment.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

iTiger: An Automatic Issue Title Generation Tool

In both commercial and open-source software, bug reports or issues are used to track bugs or feature requests. However, the quality of issues can differ a lot. Prior research has found that bug reports with good quality tend to gain more attention than the ones with poor quality. As an essential component of an issue, title quality is an important aspect of issue quality. Moreover, issues are usually presented in a list view, where only the issue title and some metadata are present. In this case, a concise and accurate title is crucial for readers to grasp the general concept of the issue and facilitate the issue triaging. Previous work formulated the issue title generation task as a one-sentence summarization task. A sequence-to-sequence model was employed to solve this task. However, it requires a large amount of domain-specific training data to attain good performance in issue title generation. Recently, pre-trained models, which learned knowledge from large-scale general corpora, have shown much success in software engineering tasks. In this work, we make the first attempt to fine-tune BART, which has been pre-trained using English corpora, to generate issue titles. We implemented the fine-tuned BART as a web tool named iTiger, which can suggest an issue title based on the issue description. iTiger is fine-tuned on 267,094 GitHub issues. We compared iTiger with the state-of-the-art method, i.e., iTAPE, on 33,438 issues. The automatic evaluation shows that iTiger outperforms iTAPE by 29.7%, 50.8%, and 34.1%, in terms of ROUGE-1, ROUGE-2, ROUGE-L F1-scores. The manual evaluation also demonstrates the titles generated by BART are preferred by evaluators over the titles generated by iTAPE in 72.7% of cases. Besides, the evaluators deem our tool as useful and easy-to-use. They are also interested to use our tool in the future.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Layer-Polarized Anomalous Hall Effect in Valleytronic van der Waals Bilayers

Layer-polarized anomalous Hall effect (LP-AHE), derived from the coupling between Berry curvature and layer degree of freedom, is of importance for both fundamental physics and device applications. Nonetheless, the current research paradigm is rooted in topological systems, rendering such phenomenon rather scarce. Here, through model analysis, we propose an alternative, but general mechanism to realize the LP-AHE in valleytronic van der Waals bilayers by interlayer sliding. The interaction between the out-of-plane ferroelectricity and A-type antiferromagnetism gives rise to the layer-locked Berry curvature and thus the long-sought LP-AHE in the bilayer systems. The LP-AHE can be strongly coupled with sliding ferroelectricity, to enable ferroelectrically controllable and reversible. The mechanism is demonstrated in a series of real valleytronic materials, including bilayer VSi2P4, VSi2N4, FeCl2, RuBr2 and VClBr. The new mechanism and phenomena provide a significant new direction to realize LP-AHE and explore its application in electronics.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

MC-UNet Multi-module Concatenation based on U-shape Network for Retinal Blood Vessels Segmentation

Accurate segmentation of the blood vessels of the retina is an important step in clinical diagnosis of ophthalmic diseases. Many deep learning frameworks have come up for retinal blood vessels segmentation tasks. However, the complex vascular structure and uncertain pathological features make the blood vessel segmentation still very challenging. A novel U-shaped network named Multi-module Concatenation which is based on Atrous convolution and multi-kernel pooling is put forward to retinal vessels segmentation in this paper. The proposed network structure retains three layers the essential structure of U-Net, in which the atrous convolution combining the multi-kernel pooling blocks are designed to obtain more contextual information. The spatial attention module is concatenated with dense atrous convolution module and multi-kernel pooling module to form a multi-module concatenation. And different dilation rates are selected by cascading to acquire a larger receptive field in atrous convolution. Adequate comparative experiments are conducted on these public retinal datasets: DRIVE, STARE and CHASE_DB1. The results show that the proposed method is effective, especially for microvessels. The code will be put out at https://github.com/Rebeccala/MC-UNet

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Mixed-signal data acquisition system for optically detected magnetic resonance of solid-state spins

We report a mixed-signal data acquisition (DAQ) system for optically detected magnetic resonance (ODMR) of solid-state spins. This system is designed and implemented based on a Field-Programmable-Gate-Array (FPGA) chip assisted with high-speed peripherals. The ODMR experiments often require high-speed mixed-signal data acquisition and processing for general and specific tasks. To this end, we realized a mixed-signal DAQ system which can acquire both analog and digital signals with precise hardware synchronization. The system consist of 4 analog channels (2 inputs and 2 outputs) and 16 optional digital channels works at up to 125 MHz clock rate. With this system, we performed general-purpose ODMR and advanced Lock-in detection experiments of nitrogen-vacancy (NV) centers, and the reported DAQ system shows excellent performance in both single and ensemble spin cases. This work provides a uniform DAQ solution for NV center quantum control system and could be easily extended to other spin-based systems.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Modified scattering for the one-dimensional Schrödinger equation with a subcritical dissipative nonlinearity

We study the asymptotic behavior in time of solutions to the one dimensional nonlinear Schrödinger equation with a subcritical dissipative nonlinearity $λ|u|^αu$, where $0<α<2$, and $λ$ is a complex constant satisfying $\text{Im} λ>\frac{α|\text{Re} λ|}{2\sqrt{ α+1}}$. For arbitrary large initial data, we present the uniform time decay estimates when $4/3<α<2$, and the large time asymptotics of the solution when $\frac{7+\sqrt{145}}{12}<α<2$. The proof is based on the vector fields method and a semiclassical analysis method.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Pretraining is All You Need for Image-to-Image Translation

We propose to use pretraining to boost general image-to-image translation. Prior image-to-image translation methods usually need dedicated architectural design and train individual translation models from scratch, struggling for high-quality generation of complex scenes, especially when paired training data are not abundant. In this paper, we regard each image-to-image translation problem as a downstream task and introduce a simple and generic framework that adapts a pretrained diffusion model to accommodate various kinds of image-to-image translation. We also propose adversarial training to enhance the texture synthesis in the diffusion model training, in conjunction with normalized guidance sampling to improve the generation quality. We present extensive empirical comparison across various tasks on challenging benchmarks such as ADE20K, COCO-Stuff, and DIODE, showing the proposed pretraining-based image-to-image translation (PITI) is capable of synthesizing images of unprecedented realism and faithfulness.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Protecting Celebrities from DeepFake with Identity Consistency Transformer

In this work we propose Identity Consistency Transformer, a novel face forgery detection method that focuses on high-level semantics, specifically identity information, and detecting a suspect face by finding identity inconsistency in inner and outer face regions. The Identity Consistency Transformer incorporates a consistency loss for identity consistency determination. We show that Identity Consistency Transformer exhibits superior generalization ability not only across different datasets but also across various types of image degradation forms found in real-world applications including deepfake videos. The Identity Consistency Transformer can be easily enhanced with additional identity information when such information is available, and for this reason it is especially well-suited for detecting face forgeries involving celebrities. Code will be released at \url{https://github.com/LightDXY/ICT_DeepFake}

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Semi-Supervised Image-to-Image Translation using Latent Space Mapping

Recent image-to-image translation works have been transferred from supervised to unsupervised settings due to the expensive cost of capturing or labeling large amounts of paired data. However, current unsupervised methods using the cycle-consistency constraint may not find the desired mapping, especially for difficult translation tasks. On the other hand, a small number of paired data are usually accessible. We therefore introduce a general framework for semi-supervised image translation. Unlike previous works, our main idea is to learn the translation over the latent feature space instead of the image space. Thanks to the low dimensional feature space, it is easier to find the desired mapping function, resulting in improved quality of translation results as well as the stability of the translation model. Empirically we show that using feature translation generates better results, even using a few bits of paired data. Experimental comparisons with state-of-the-art approaches demonstrate the effectiveness of the proposed framework on a variety of challenging image-to-image translation tasks

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preprint2022arXiv

The (degree)-Kirchhoff index of linear crossed octagonal-quadrilateral networks

The Kirchhoff index and degree-Kirchhoff index have attracted extensive attentions due to its practical applications in complex networks, physics, and chemistry. In 2019, Liu et al. [Int. J. Quantum Chem. 119 (2019) e25971] derived the formula of the degree-Kirchhoff index of linear octagonal-quadrilateral networks. In the present paper, we consider linear crossed octagonal-quadrilateral networks $Q_n$. Explicit closed-form formulas of the Kirchhoff index, the degree-Kirchhoff index, and the number of spanning trees of $Q_n$ are obtained. Moreover, the Kirchhoff index (resp. degree-Kirchhoff index) of $Q_n$ is shown to be almost 1/4 of its Wiener index (resp. Gutman index).

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

The Normalized Laplacian Spectrum Analysis of Fractal Mobius Octagonal Networks and its Applications

The study and calculation of spectrum of networks can be used to describe networks structure and quantify analysis of networks performance. The fractal Möbius octagonal networks, denoted by $Q_n$, is derived from the inverse identification of the opposite lateral edges of fractal linear octagonal networks. In this paper, the normalized Laplacian spectrum of $Q_n$ is determined by two matrices $\mathcal {L}_A$ and $\mathcal {L}_S$. As an important application of our results, some topological indices (multiplicative degree-Kirchhoff index, the number of spanning trees) formulas of $Q_n$ are obtained.

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preprint2021arXiv

Field-effect chirality devices with Dirac semimetal

Charge-based field-effect transistors (FETs) greatly suffer from unavoidable carrier scattering and heat dissipation. In analogy to valley degree of freedom in semiconductors, chiral anomaly current in Weyl/Dirac semimetals is theoretically predicted to be nearly non-dissipative over long distances, but still lacks experimental ways to efficiently control its transport. Here we demonstrate field-effect chirality devices with Dirac semimetal PtSe2, in which its Fermi level is close to the Dirac point in conduction band owing to intrinsic defects. The chiral anomaly is further corroborated with nonlocal valley transport measurement, which can also be effectively modulated by external fields, showing robust nonlocal valley transport with micrometer diffusion length. Similar to charge-based FETs, the chiral conductivity in PtSe2 devices can be modulated by electrostatic gating with an ON/OFF ratio more than 103. We also demonstrate basic logic functions in the devices with electric and magnetic fields as input signals.

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preprint2021arXiv

Local well-posedness and finite time blowup for fourth-order Schrödinger equation with complex coefficient

We consider the fourth-order Schrödinger equation $$ i\partial_tu+Δ^2 u+μΔu+λ|u|^αu=0, $$ where $α>0,μ=\pm1$ or $0$ and $λ\in\mathbb{C}$. Firstly, we prove local well-posedness in $H^4\left(\R^N\right)$ in both $H^4$ subcritical and critical case: $α>0$, $(N-8)α\leq8$. Then, for any given compact set $K\subset\mathbb{R}^N$, we construct $H^4(\R^N)$ solutions that are defined on $(-T, 0)$ for some $T>0$, and blow up exactly on $K$ at $t=0$.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Prototypical Pseudo Label Denoising and Target Structure Learning for Domain Adaptive Semantic Segmentation

Self-training is a competitive approach in domain adaptive segmentation, which trains the network with the pseudo labels on the target domain. However inevitably, the pseudo labels are noisy and the target features are dispersed due to the discrepancy between source and target domains. In this paper, we rely on representative prototypes, the feature centroids of classes, to address the two issues for unsupervised domain adaptation. In particular, we take one step further and exploit the feature distances from prototypes that provide richer information than mere prototypes. Specifically, we use it to estimate the likelihood of pseudo labels to facilitate online correction in the course of training. Meanwhile, we align the prototypical assignments based on relative feature distances for two different views of the same target, producing a more compact target feature space. Moreover, we find that distilling the already learned knowledge to a self-supervised pretrained model further boosts the performance. Our method shows tremendous performance advantage over state-of-the-art methods. We will make the code publicly available.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Simulation of an imaging system for internal contamination of lungs using MPA-MURA coded aperture collimator

The nuclides inhaled during nuclear accidents usually cause internal contamination of the lungs with low activity. Although a parallel-hole imaging system, which is widely used in medical gamma cameras, has a high resolution and good image quality, owing to its extremely low detection efficiency, it remains difficult to obtain images of inhaled lung contamination. In this study, the Monte Carlo method was used to study the internal lung contamination imaging using the MPA-MURA coded-aperture collimator. The imaging system consisted of an adult male lung model, with a mosaicked, pattern-centered, and anti-symmetric MURA coded-aperture collimator model and a CsI(Tl) detector model. The MLEM decoding algorithm was used to reconstruct the internal contamination image, and the complementary imaging method was used to reduce the number of artifacts. The full width at half maximum of the I-131 point source image reconstructed by the mosaicked, pattern-centered, and anti-symmetric Modified uniformly redundant array (MPA-MURA) coded-aperture imaging reached 2.51 mm, and the signal-to-noise ratio of the simplified respiratory tract source (I-131) image reconstructed through MPA-MURA coded-aperture imaging was 3.98 dB. Although the spatial resolution of MPA-MURA coded aperture imaging is not as good as that of parallel-hole imaging, the detection efficiency of PMA-MURA coded-aperture imaging is two orders of magnitude higher than that of parallel hole collimator imaging. Considering the low activity level of internal lung contamination caused by nuclear accidents, PMA-MURA coded-aperture imaging has significant potential for the development of lung contamination imaging.

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preprint2020arXiv

Critical regularity criteria for Navier-Stokes equations in terms of one directional derivative of the velocity

In this paper, we consider the 3D Navier-Stokes equations in the whole space. We investigate some new inequalities and \textit{a priori} estimates to provide the critical regularity criteria in terms of one directional derivative of the velocity field, namely $\partial_3 \mathbf{u} \in L^p((0,T); L^q(\mathbb{R}^3)), ~\frac{2}{p} + \frac{3}{q} = 2, ~\frac{3}{2}<q\leq 6$. Moreover, we extend the range of $q$ while the solution is axisymmetric, i.e. the axisymmetric solution $\mathbf{m}{u}$ is regular in $(0,T]$, if $ \partial_3 u^3 \in L^p((0,T); L^q(\mathbb{R}^3)), ~\frac{2}{p} + \frac{3}{q} = 2, ~\frac{3}{2}<q< \infty$.

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preprint2020arXiv

Face X-ray for More General Face Forgery Detection

In this paper we propose a novel image representation called face X-ray for detecting forgery in face images. The face X-ray of an input face image is a greyscale image that reveals whether the input image can be decomposed into the blending of two images from different sources. It does so by showing the blending boundary for a forged image and the absence of blending for a real image. We observe that most existing face manipulation methods share a common step: blending the altered face into an existing background image. For this reason, face X-ray provides an effective way for detecting forgery generated by most existing face manipulation algorithms. Face X-ray is general in the sense that it only assumes the existence of a blending step and does not rely on any knowledge of the artifacts associated with a specific face manipulation technique. Indeed, the algorithm for computing face X-ray can be trained without fake images generated by any of the state-of-the-art face manipulation methods. Extensive experiments show that face X-ray remains effective when applied to forgery generated by unseen face manipulation techniques, while most existing face forgery detection or deepfake detection algorithms experience a significant performance drop.

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preprint2020arXiv

Hole spin in tunable Ge hut wire double quantum dot

Holes in germanium (Ge) exhibit strong spin-orbit interaction, which can be exploited for fast and all-electrical manipulation of spin states. Here, we report transport experiments in a tunable Ge hut wire hole double quantum dot. We observe the signatures of Pauli spin blockade (PSB) with a large singlet-triplet energy splitting of ~1.1 meV and extract the g factor. By analyzing the the PSB leakage current, we obtain a spin-orbit length l_so of ~ 40-100 nm. Furthermore, we demonstrate the electric dipole spin resonance. These results lay a solid foundation for implementing high quality tunable hole spin-orbit qubits.

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preprint2020arXiv

Peierls-type metal-insulator transition in carbon nanostructures

We report the observation of Peierls-type metal-insulator transition in carbon nanostructures formed by chemical vapor deposition inside the pore network of the ZSM-5 zeolite. The Raman spectrum of this nanocarbon@ZSM-5 indicates a clear signature of the radial breathing mode (RBM) for (3,0) carbon nanotubes that can constitute the carbon network segments. Electrical transport measurements on multiple few-micron-sized nanocarbon@ZSM-5 crystals showed metallic temperature of resistance dependence down to 30 K, at which point the resistance exhibited a sharp upturn that is accompanied by the opening of a quasigap at the Fermi level as indicated by the differential resistance measurements. Further Hall measurements have yielded both the sign of the charge carrier and its density. The latter demonstrated excellent consistency with the quasigap data. We employed first-principles calculations to verify that there can indeed be softening of the phonon modes in the (3,0) carbon nanotubes.

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preprint2016arXiv

A unified approach to self-normalized block sampling

The inference procedure for the mean of a stationary time series is usually quite different under various model assumptions because the partial sum process behaves differently depending on whether the time series is short or long-range dependent, or whether it has a light or heavy-tailed marginal distribution. In the current paper, we develop an asymptotic theory for the self-normalized block sampling, and prove that the corresponding block sampling method can provide a unified inference approach for the aforementioned different situations in the sense that it does not require the {\em a priori} estimation of auxiliary parameters. Monte Carlo simulations are presented to illustrate its finite-sample performance. The R function implementing the method is available from the authors.

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preprint2016arXiv

Charge Density Wave Phase Transition on the Surface of Electrostatically Doped Multilayer Graphene

We demonstrate that charge density wave (CDW) phase transition occurs on the surface of electronically doped multilayer graphene when the Fermi level approaches the M points (also known as van Hove singularities where the density of states diverge) in the Brillouin zone of graphene band structure. The occurrence of such CDW phase transitions are supported by both the electrical transport measurement and optical measurements in electrostatically doped multilayer graphene. The CDW transition is accompanied with the sudden change of graphene channel resistance at T$_m$= 100K, as well as the splitting of Raman G peak (1580 cm$^{-1}$). The splitting of Raman G peak indicats the lifting of in-plane optical phonon branch degeneracy and the non-degenerate phonon branches are correlated to the lattice reconstructions of graphene -- the CDW phase transition.

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preprint2016arXiv

Deeply-Fused Nets

In this paper, we present a novel deep learning approach, deeply-fused nets. The central idea of our approach is deep fusion, i.e., combine the intermediate representations of base networks, where the fused output serves as the input of the remaining part of each base network, and perform such combinations deeply over several intermediate representations. The resulting deeply fused net enjoys several benefits. First, it is able to learn multi-scale representations as it enjoys the benefits of more base networks, which could form the same fused network, other than the initial group of base networks. Second, in our suggested fused net formed by one deep and one shallow base networks, the flows of the information from the earlier intermediate layer of the deep base network to the output and from the input to the later intermediate layer of the deep base network are both improved. Last, the deep and shallow base networks are jointly learnt and can benefit from each other. More interestingly, the essential depth of a fused net composed from a deep base network and a shallow base network is reduced because the fused net could be composed from a less deep base network, and thus training the fused net is less difficult than training the initial deep base network. Empirical results demonstrate that our approach achieves superior performance over two closely-related methods, ResNet and Highway, and competitive performance compared to the state-of-the-arts.

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preprint2016arXiv

Global solutions to the isentropic compressible Navier-Stokes equations with a class of large initial data

In this paper, we consider the global well-posedness problem of the isentropic compressible Navier-Stokes equations in the whole space $\R^N$ with $N\ge2$. In order to better reflect the characteristics of the dispersion equation, we make full use of the role of the frequency on the integrability and regularity of the solution, and prove that the isentropic compressible Navier-Stokes equations admit global solutions when the initial data are close to a stable equilibrium in the sense of suitable hybrid Besov norm. As a consequence, the initial velocity with arbitrary $\dot{B}^{\fr{N}{2}-1}_{2,1}$ norm of potential part $\Pe^\bot u_0$ and large highly oscillating are allowed in our results. The proof relies heavily on the dispersive estimates for the system of acoustics, and a careful study of the nonlinear terms.

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preprint2015arXiv

Global axisymmetric solutions of 3D inhomogeneous incompressible Navier-Stokes Systems with nonzero swirl

In this paper, we investigate the global well-posedness for the 3-D inhomogeneous incompressible Navier-Stokes system with the axisymmetric initial data. We prove the global well-posedness provided that $$\|\frac{a_{0}}{r}\|_{\infty} \textrm{ and } \|u_{0}^θ\|_{3} \textrm{ are sufficiently small}. $$ Furthermore, if $\mathbf{u}_0\in L^1$ and $ru^θ_0\in L^1\cap L^2$, we have \begin{equation*} \|u^θ(t)\|_{2}^{2}+\langle t\rangle \|\nabla (u^θ\mathbf{e}_θ)(t)\|_{2}^{2}+t\langle t\rangle(\|u_{t}^θ(t)\|_{2}^{2}+\|Δ(u^θ\mathbf{e}_θ)(t)\|_{2}^{2}) \leq C \langle t\rangle^{-\frac{5}{2}},\ \forall\ t>0. \end{equation*}

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preprint2015arXiv

One-dimensional sawtooth and zigzag lattices for ultracold atoms

We describe tunable optical sawtooth and zigzag lattices for ultracold atoms. Making use of the superlattice generated by commensurate wavelengths of light beams, tunable geometries including zigzag and sawtooth configurations can be realised. We provide an experimentally feasible method to fully control inter- ($t$) and intra- ($t'$) unit-cell tunnelling in zigzag and sawtooth lattices. We analyse the conversion of the lattice geometry from zigzag to sawtooth, and show that a nearly flat band is attainable in the sawtooth configuration by means of tuning the lattice parameters. The bandwidth of the first excited band can be reduced up to 2$\%$ of the ground bandwidth for a wide range of lattice setting. A nearly flat band available in a tunable sawtooth lattice would offer a versatile platform for the study of interaction-driven quantum many-body states with ultracold atoms.

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preprint2015arXiv

Regularity of 3D axisymmetric Navier-Stokes equations

In this paper, we study the three-dimensional axisymmetric Navier-Stokes system with nonzero swirl. By establishing a new key inequality for the pair $(\frac{ω^{r}}{r},\frac{ω^θ}{r})$, we get several Prodi-Serrin type regularity criteria based on the angular velocity, $u^θ$. Moreover, we obtain the global well-posedness result if the initial angular velocity $u_{0}^θ$ is appropriate small in the critical space $L^{3}(\R^{3})$. Furthermore, we also get several Prodi-Serrin type regularity criteria based on one component of the solutions, say $ω^3$ or $u^3$.

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preprint2015arXiv

Time-varying nonlinear regression models: Nonparametric estimation and model selection

This paper considers a general class of nonparametric time series regression models where the regression function can be time-dependent. We establish an asymptotic theory for estimates of the time-varying regression functions. For this general class of models, an important issue in practice is to address the necessity of modeling the regression function as nonlinear and time-varying. To tackle this, we propose an information criterion and prove its selection consistency property. The results are applied to the U.S. Treasury interest rate data.

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preprint2014arXiv

An elementary proof of the global existence and uniqueness theorem to 2-D incompressible non-resistive MHD system

In this paper, we provide a much simplified proof of the main result in [Lin, Xu, Zhang, arXiv:1302.5877] concerning the global existence and uniqueness of smooth solutions to the Cauchy problem for a 2D incompressible viscous and non-resistive MHD system under the assumption that the initial data are close to some equilibrium states. Beside the classical energy method, the interpolating inequalities and the algebraic structure of the equations coming from the incompressibility of the fluid are crucial in our arguments. We combine the energy estimates with the $L^\infty$ estimates for time slices to deduce the key $L^1$ in time estimates. The latter is responsible for the global in time existence.

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preprint2014arXiv

Global Small Solutions to a Complex Fluid Model in 3D

In this paper, we provide a much simplified proof of the main result in [Lin and Zhang, Comm. Pure Appl. Math.,67(2014), 531--580] concerning the global existence and uniqueness of smooth solutions to the Cauchy problem for a 3D incompressible complex fluid model under the assumption that the initial data are close to some equilibrium states. Beside the classical energy method, the interpolating inequalities and the algebraic structure of the equations coming from the incompressibility of the fluid are crucial in our arguments. We combine the energy estimates with the $L^\infty$ estimates for time slices to deduce the key $L^1$ in time estimates. The latter is responsible for the global in time existence.

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preprint2014arXiv

Global well-posedness to the 3-D incompressible inhomogeneous Navier-Stokes equations with a class of large velocity

In this article, we consider the global well-posedness to the 3-D incompressible inhomogeneous Navier-Stokes equations with a class of large velocity. More precisely, assuming $a_0 \in \dot{B}_{q,1}^{\frac{3}{q}}(\mathbb{R}^3)$ and $u_0=(u_0^h,u_0^3)\in \dot{B}_{p,1}^{-1+\frac{3}{p}}(\mathbb{R}^3)$ for $p,q \in (1,6)$ with $\sup(\frac{1}{p}, \frac{1}{q})\leq\frac{1}{3}+ \inf (\frac{1}{p}, \frac{1}{q})$, we prove that if $C\|a_0\|_{\dot{B}_{q,1}^{\frac{3}{q}}}^α(\|u_0^3\|_{\dot{B}_{p,1}^{-1+\frac{3}{p}}}/μ+1)\leq1$, $\frac{C}μ(\|u_0^h\|_{\dot{B}_{p,1}^{-1+\frac{3}{p}}}+\|u_0^3\|_{\dot{B}_{p,1}^{-1+\frac{3}{p}}}^{1-α}\|u_0^h\|_{\dot{B}_{p,1}^{-1+\frac{3}{p}}}^α)\leq 1$, then the system has a unique global solution $a\in\widetilde{\mathcal{C}}([0,\infty);\dot{B}_{q,1}^{\frac{3}{q}}(\mathbb{R}^3))$, $u\in\widetilde{\mathcal{C}}([0,\infty);\dot{B}_{p,1}^{-1+\frac{3}{p}}(\mathbb{R}^3))\cap L^1(\mathbb{R}^+;\dot{B}_{p,1}^{1+\frac{3}{p}}(\mathbb{R}^3))$. It improves the recent result of M. Paicu, P. Zhang (J. Funct. Anal. 262 (2012) 3556-3584), where the exponent form of the initial smallness condition is replaced by a polynomial form.

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preprint2014arXiv

Latent Feature Based FM Model For Rating Prediction

Rating Prediction is a basic problem in Recommender System, and one of the most widely used method is Factorization Machines(FM). However, traditional matrix factorization methods fail to utilize the benefit of implicit feedback, which has been proved to be important in Rating Prediction problem. In this work, we consider a specific situation, movie rating prediction, where we assume that watching history has a big influence on his/her rating behavior on an item. We introduce two models, Latent Dirichlet Allocation(LDA) and word2vec, both of which perform state-of-the-art results in training latent features. Based on that, we propose two feature based models. One is the Topic-based FM Model which provides the implicit feedback to the matrix factorization. The other is the Vector-based FM Model which expresses the order info of watching history. Empirical results on three datasets demonstrate that our method performs better than the baseline model and confirm that Vector-based FM Model usually works better as it contains the order info.

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preprint2013arXiv

Block Sampling under Strong Dependence

The paper considers the block sampling method for long-range dependent processes. Our theory generalizes earlier ones by Hall, Jing and Lahiri (1998) on functionals of Gaussian processes and Nordman and Lahiri (2005) on linear processes. In particular, we allow nonlinear transforms of linear processes. Under suitable conditions on physical dependence measures, we prove the validity of the block sampling method. The problem of estimating the self-similar index is also studied.

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preprint2012arXiv

Can Nondeterminism Help Complementation?

Complementation and determinization are two fundamental notions in automata theory. The close relationship between the two has been well observed in the literature. In the case of nondeterministic finite automata on finite words (NFA), complementation and determinization have the same state complexity, namely Theta(2^n) where n is the state size. The same similarity between determinization and complementation was found for Buchi automata, where both operations were shown to have 2^Θ(n lg n) state complexity. An intriguing question is whether there exists a type of omega-automata whose determinization is considerably harder than its complementation. In this paper, we show that for all common types of omega-automata, the determinization problem has the same state complexity as the corresponding complementation problem at the granularity of 2^Θ(.).

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preprint2012arXiv

Classification of entanglement and quantum phase transition in XX model

We study the relation between entanglement and quantum phase transition (QPT) from a new perspective. Motivated by one's intuition: QPT is characterized by the change of the ground-state structure, while entangled states belong to different classes have different structures, we conjecture that QPT occurs as the class of ground-state entanglement changes and prove it in XX model. Despite the classification of multipartite entanglement is yet unresolved, we proposed a new method to judge whether two many-body states belong to the same entanglement class.

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preprint2012arXiv

Global existence in critical spaces for density-dependent incompressible viscoelastic fluids

In this paper we consider the local and global well-posedness to the density-dependent incompressible viscoelastic fluids. We first study some linear models associated to the incompressible viscoelastic system. Then we approximate the system by a sequence of ordinary differential equations, by means of the Friedrichs method. Some uniform estimates for those solutions will be obtained. Using compactness arguments, we will get the local existence up to extracting a subsequence by means of Ascoli's lemma. With the help of small data conditions and hybird Besov spaces, we finally derive the global existence.

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preprint2012arXiv

Inference of time-varying regression models

We consider parameter estimation, hypothesis testing and variable selection for partially time-varying coefficient models. Our asymptotic theory has the useful feature that it can allow dependent, nonstationary error and covariate processes. With a two-stage method, the parametric component can be estimated with a $n^{1/2}$-convergence rate. A simulation-assisted hypothesis testing procedure is proposed for testing significance and parameter constancy. We further propose an information criterion that can consistently select the true set of significant predictors. Our method is applied to autoregressive models with time-varying coefficients. Simulation results and a real data application are provided.

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preprint2012arXiv

Zero-electron-mass limit of Euler-Poisson equations

This paper is concerned with multidimensional Euler-Poisson equations for plasmas. The equations take the form of Euler equations for the conservation laws of the mass density and current density for charge-carriers (electrons and ions), coupled to a Poisson equation for the electrostatic potential. We study the limit to zero of some physical parameters which arise in the scaled Euler-Poisson equations, more precisely, which is the limit of vanishing ratio of the electron mass to the ion mass. When the initial data are small in critical Besov spaces, by virtue of the ``Shizuta-Kawashima" skew-symmetry condition, we establish the uniform global existence and uniqueness of classical solutions. Then we develop new frequency-localization Strichartz-type estimates for the equation of acoustics (a modified wave equation) with the aid of the detailed analysis of the semigroup formulation generated by this modified wave operator. Finally, it is shown that the uniform classical solutions converge towards that of the incompressible Euler equations (for \textit{ill-prepared} initial data) in a refined way as the scaled electron-mass tends to zero.

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preprint2011arXiv

A Tight Lower Bound for Streett Complementation

Finite automata on infinite words ($ω$-automata) proved to be a powerful weapon for modeling and reasoning infinite behaviors of reactive systems. Complementation of $ω$-automata is crucial in many of these applications. But the problem is non-trivial; even after extensive study during the past four decades, we still have an important type of $ω$-automata, namely Streett automata, for which the gap between the current best lower bound $2^{Ω(n \lg nk)}$ and upper bound $2^{Ω(nk \lg nk)}$ is substantial, for the Streett index size $k$ can be exponential in the number of states $n$. In arXiv:1102.2960 we showed a construction for complementing Streett automata with the upper bound $2^{O(n \lg n+nk \lg k)}$ for $k = O(n)$ and $2^{O(n^{2} \lg n)}$ for $k=ω(n)$. In this paper we establish a matching lower bound $2^{Ω(n \lg n+nk \lg k)}$ for $k = O(n)$ and $2^{Ω(n^{2} \lg n)}$ for $k = ω(n)$, and therefore showing that the construction is asymptotically optimal with respect to the $2^{Θ(\cdot)}$ notation.

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preprint2011arXiv

Decay Estimates for Isentropic Compressible Navier-Stokes Equations in Bounded Domain

In this paper, under the hypothesis that $ρ$ is upper bounded, we construct a Lyapunov functional for the multidimensional isentropic compressible Navier-Stokes equations and show that the weak solutions decay exponentially to the equilibrium state in $L^2$ norm. This can be regarded as a generalization of Matsumura and Nishida's results in 1982, since our analysis is done in the framework of Lions 1998 and Feireisl et al. 2001, the higher regularity of $(ρ, u)$ and the uniformly positive lower bound of $ρ$ are not necessary in our analysis and vacuum may be admitted. Indeed, the upper bound of the density $ρ$ plays the essential role in our proof.

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preprint2011arXiv

Global existence in critical spaces for incompressible viscoelastic fluids

We investigate local and global strong solutions for the incompressible viscoelastic system of Oldroyd--B type. We obtain the existence and uniqueness of a solution in a functional setting invariant by the scaling of the associated equations. More precisely, the initial velocity has the same critical regularity index as for the incompressible Navier--Stokes equations, and one more derivative is needed for the deformation tensor. We point out a smoothing effect on the velocity and a $L^1-$decay on the difference between the deformation tensor and the identity matrix. Our result implies that the deformation tensor $F$ has the same regularity as the density of the compressible Navier--Stokes equations.

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preprint2011arXiv

Global well-posedness for the incompressible viscoelastic fluids in the critical $L^p$ framework

We investigate global strong solutions for the incompressible viscoelastic system of Oldroyd--B type with the initial data close to a stable equilibrium. We obtain the existence and uniqueness of the global solution in a functional setting invariant by the scaling of the associated equations, where the initial velocity has the same critical regularity index as for the incompressible Navier--Stokes equations, and one more derivative is needed for the deformation tensor. Like the classical incompressible Navier-Stokes, one may construct the unique global solution for a class of large highly oscillating initial velocity. Our result also implies that the deformation tensor $F$ has the same regularity as the density of the compressible Navier--Stokes equations.

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preprint2011arXiv

Testing for Parallelism Between Trends in Multiple Time Series

This paper considers the inference of trends in multiple, nonstationary time series. To test whether trends are parallel to each other, we use a parallelism index based on the L2-distances between nonparametric trend estimators and their average. A central limit theorem is obtained for the test statistic and the test's consistency is established. We propose a simulation-based approximation to the distribution of the test statistic, which significantly improves upon the normal approximation. The test is also applied to devise a clustering algorithm. Finally, the finite-sample properties of the test are assessed through simulations and the test methodology is illustrated with time series from Motorola cell phone activity in the United States.

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preprint2011arXiv

Tight Upper Bounds for Streett and Parity Complementation

Complementation of finite automata on infinite words is not only a fundamental problem in automata theory, but also serves as a cornerstone for solving numerous decision problems in mathematical logic, model-checking, program analysis and verification. For Streett complementation, a significant gap exists between the current lower bound $2^{Ω(n\lg nk)}$ and upper bound $2^{O(nk\lg nk)}$, where $n$ is the state size, $k$ is the number of Streett pairs, and $k$ can be as large as $2^{n}$. Determining the complexity of Streett complementation has been an open question since the late '80s. In this paper show a complementation construction with upper bound $2^{O(n \lg n+nk \lg k)}$ for $k = O(n)$ and $2^{O(n^{2} \lg n)}$ for $k = ω(n)$, which matches well the lower bound obtained in \cite{CZ11a}. We also obtain a tight upper bound $2^{O(n \lg n)}$ for parity complementation.

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preprint2009arXiv

1D goes 2D: A Kosterlitz Thouless transition in superconducting arrays of 4-Angstrom carbon nanotubes

We report superconducting resistive transition characteristics for array(s) of coupled 4-Angstrom single wall carbon nanotubes embedded in aluminophosphate-five (AFI) zeolite. The transition was observed to initiate at 15K with a slow resistance decrease switching to a sharp, order of magnitude drop between 7.5-6.0K. The transition has strong (anisotropic) magnetic field dependence. Differential resistance versus current (voltage) measurements indicate that the establishment of coherence proceeds in stages as the temperature is lowered below 15K. In particular, the sharp resistance drop and its attendant nonlinear IV characteristics are consistent with the manifestations of a Kosterlitz-Thouless (KT) transition that establishes quasi long range order in the plane transverse to the c-axis of the nanotubes, leading to an inhomogeneous system comprising 3D superconducting regions connected by weak links. Global coherence is established at below 5K with the appearance of a well-defined supercurrent gap at 2K.

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