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Published work

25 published item(s)

preprint2026arXiv

Autonomous Driving in Unstructured Environments: How Far Have We Come?

Research on autonomous driving in unstructured outdoor environments is less advanced than in structured urban settings due to challenges like environmental diversities and scene complexity. These environments-such as rural areas and rugged terrains-pose unique obstacles that are not common in structured urban areas. Despite these difficulties, autonomous driving in unstructured outdoor environments is crucial for applications in agriculture, mining, and military operations. Our survey reviews over 250 papers for autonomous driving in unstructured outdoor environments, covering offline mapping, pose estimation, environmental perception, path planning, end-to-end autonomous driving, datasets, and relevant challenges. We also discuss emerging trends and future research directions. This review aims to consolidate knowledge and encourage further research for autonomous driving in unstructured environments. To support ongoing work, we maintain an active repository with up-to-date literature and open-source projects at: https://github.com/chaytonmin/Survey-Autonomous-Driving-in-Unstructured-Environments.

preprint2026arXiv

SPAN: Benchmarking and Improving Cross-Calendar Temporal Reasoning of Large Language Models

We introduce SPAN, a cross-calendar temporal reasoning benchmark, which requires LLMs to perform intra-calendar temporal reasoning and inter-calendar temporal conversion. SPAN features ten cross-calendar temporal reasoning directions, two reasoning types, and two question formats across six calendars. To enable time-variant and contamination-free evaluation, we propose a template-driven protocol for dynamic instance generation that enables assessment on a user-specified Gregorian date. We conduct extensive experiments on both open- and closed-source state-of-the-art (SOTA) LLMs over a range of dates spanning 100 years from 1960 to 2060. Our evaluations show that these LLMs achieve an average accuracy of only 34.5%, with none exceeding 80%, indicating that this task remains challenging. Through in-depth analysis of reasoning types, question formats, and temporal reasoning directions, we identify two key obstacles for LLMs: Future-Date Degradation and Calendar Asymmetry Bias. To strengthen LLMs' cross-calendar temporal reasoning capability, we further develop an LLM-powered Time Agent that leverages tool-augmented code generation. Empirical results show that Time Agent achieves an average accuracy of 95.31%, outperforming several competitive baselines, highlighting the potential of tool-augmented code generation to advance cross-calendar temporal reasoning. We hope this work will inspire further efforts toward more temporally and culturally adaptive LLMs.

preprint2026arXiv

When Retrieval Hurts Code Completion: A Diagnostic Study of Stale Repository Context

Context: Retrieval-augmented code generation relies on cross-file repository context, but retrieved snippets may come from obsolete project states. Objectives: We study whether temporally stale repository snippets act as harmless noise or actively induce current-state-incompatible code. Methods: We conduct a controlled diagnostic study on a curated 17-sample set of production-helper signature changes from five Python repositories. For each sample, we compare current-only, stale-only, no-retrieval, and mixed current/stale retrieval conditions under prompts that hide commit freshness and expected current signatures. Results: Under neutralized prompts, stale-only retrieval induces stale helper references on 15/17 Qwen2.5-Coder-7B-Instruct samples and 13/17 gpt-4.1-mini samples, corresponding to 88.2 and 76.5 percentage-point increases over current-only retrieval. No retrieval produces zero stale references but only 1/17 passing completions. The two models share 75.0% Jaccard overlap among stale-triggering samples, and mixed conditions show that adding valid current evidence largely rescues stale-only failures. Conclusion: Temporal validity of retrieved repository context is a distinct diagnostic variable for Code RAG robustness: stale context can actively bias models toward obsolete repository state rather than merely removing useful evidence.

preprint2023arXiv

Level lowering for GU(1,2)

Mazur's principle gives a criterion under which an irreducible mod $\ell$ Galois representation arising from a modular form of level $Np$ (with $p$ prime to $N$) can also arise from a modular form of level $N.$ We prove an analogous result showing that a mod $\ell$ Galois representation arising from a stable cuspidal automorphic representation of the unitary similitude group $G=\mathrm{GU}(1,2)$ which is Steinberg at an inert prime $p$ can also arise from an automorphic representation of $G$ that is unramified at $p$.

preprint2022arXiv

Blockchain Meets COVID-19: A Framework for Contact Information Sharing and Risk Notification System

COVID-19 is a severe global epidemic in human history. Even though there are particular medications and vaccines to curb the epidemic, tracing and isolating the infection source is the best option to slow the virus spread and reduce infection and death rates. There are three disadvantages to the existing contact tracing system: 1. User data is stored in a centralized database that could be stolen and tampered with, 2. User's confidential personal identity may be revealed to a third party or organization, 3. Existing contact tracing systems only focus on information sharing from one dimension, such as location-based tracing, which significantly limits the effectiveness of such systems. We propose a global COVID-19 information sharing and risk notification system that utilizes the Blockchain, Smart Contract, and Bluetooth. To protect user privacy, we design a novel Blockchain-based platform that can share consistent and non-tampered contact tracing information from multiple dimensions, such as location-based for indirect contact and Bluetooth-based for direct contact. Hierarchical smart contract architecture is also designed to achieve global agreements from users about how to process and utilize user data, thereby enhancing the data usage transparency. Furthermore, we propose a mechanism to protect user identity privacy from multiple aspects. More importantly, our system can notify the users about the exposure risk via smart contracts. We implement a prototype system to conduct extensive measurements to demonstrate the feasibility and effectiveness of our system.

preprint2022arXiv

HMRNet: High and Multi-Resolution Network with Bidirectional Feature Calibration for Brain Structure Segmentation in Radiotherapy

Accurate segmentation of Anatomical brain Barriers to Cancer spread (ABCs) plays an important role for automatic delineation of Clinical Target Volume (CTV) of brain tumors in radiotherapy. Despite that variants of U-Net are state-of-the-art segmentation models, they have limited performance when dealing with ABCs structures with various shapes and sizes, especially thin structures (e.g., the falx cerebri) that span only few slices. To deal with this problem, we propose a High and Multi-Resolution Network (HMRNet) that consists of a multi-scale feature learning branch and a high-resolution branch, which can maintain the high-resolution contextual information and extract more robust representations of anatomical structures with various scales. We further design a Bidirectional Feature Calibration (BFC) block to enable the two branches to generate spatial attention maps for mutual feature calibration. Considering the different sizes and positions of ABCs structures, our network was applied after a rough localization of each structure to obtain fine segmentation results. Experiments on the MICCAI 2020 ABCs challenge dataset showed that: 1) Our proposed two-stage segmentation strategy largely outperformed methods segmenting all the structures in just one stage; 2) The proposed HMRNet with two branches can maintain high-resolution representations and is effective to improve the performance on thin structures; 3) The proposed BFC block outperformed existing attention methods using monodirectional feature calibration. Our method won the second place of ABCs 2020 challenge and has a potential for more accurate and reasonable delineation of CTV of brain tumors.

preprint2022arXiv

Iota: A Framework for Analyzing System-Level Security of IoTs

Most IoT systems involve IoT devices, communication protocols, remote cloud, IoT applications, mobile apps, and the physical environment. However, existing IoT security analyses only focus on a subset of all the essential components, such as device firmware, and ignore IoT systems' interactive nature, resulting in limited attack detection capabilities. In this work, we propose Iota, a logic programming-based framework to perform system-level security analysis for IoT systems. Iota generates attack graphs for IoT systems, showing all of the system resources that can be compromised and enumerating potential attack traces. In building Iota, we design novel techniques to scan IoT systems for individual vulnerabilities and further create generic exploit models for IoT vulnerabilities. We also identify and model physical dependencies between different devices as they are unique to IoT systems and are employed by adversaries to launch complicated attacks. In addition, we utilize NLP techniques to extract IoT app semantics based on app descriptions. To evaluate vulnerabilities' system-wide impact, we propose two metrics based on the attack graph, which provide guidance on fortifying IoT systems. Evaluation on 127 IoT CVEs (Common Vulnerabilities and Exposures) shows that Iota's exploit modeling module achieves over 80% accuracy in predicting vulnerabilities' preconditions and effects. We apply Iota to 37 synthetic smart home IoT systems based on real-world IoT apps and devices. Experimental results show that our framework is effective and highly efficient. Among 27 shortest attack traces revealed by the attack graphs, 62.8% are not anticipated by the system administrator. It only takes 1.2 seconds to generate and analyze the attack graph for an IoT system consisting of 50 devices.

preprint2022arXiv

Long Short-Term Preference Modeling for Continuous-Time Sequential Recommendation

Modeling the evolution of user preference is essential in recommender systems. Recently, dynamic graph-based methods have been studied and achieved SOTA for recommendation, majority of which focus on user's stable long-term preference. However, in real-world scenario, user's short-term preference evolves over time dynamically. Although there exists sequential methods that attempt to capture it, how to model the evolution of short-term preference with dynamic graph-based methods has not been well-addressed yet. In particular: 1) existing methods do not explicitly encode and capture the evolution of short-term preference as sequential methods do; 2) simply using last few interactions is not enough for modeling the changing trend. In this paper, we propose Long Short-Term Preference Modeling for Continuous-Time Sequential Recommendation (LSTSR) to capture the evolution of short-term preference under dynamic graph. Specifically, we explicitly encode short-term preference and optimize it via memory mechanism, which has three key operations: Message, Aggregate and Update. Our memory mechanism can not only store one-hop information, but also trigger with new interactions online. Extensive experiments conducted on five public datasets show that LSTSR consistently outperforms many state-of-the-art recommendation methods across various lines.

preprint2022arXiv

Unlocking the synergy between CMB spectral distortions and anisotropies

Measurements of the cosmic microwave background (CMB) spectral distortions (SDs) will open a new window on the very early universe, providing new information complementary to that gathered from CMB temperature and polarization anisotropies. In this paper, we study their synergy as a function of the characteristics of the considered experiments. In particular, we examine a wide range of sensitivities for possible SD measurements, spanning from FIRAS up to noise levels 1000 times better than PIXIE, and study their constraining power when combined with current or future CMB anisotropy experiments such as Planck or LiteBIRD plus CMB-S4. We consider a number of different cosmological models such as the $Λ$CDM, as well as its extensions with the running of the scalar spectral index, the decay or the annihilation of dark matter (DM) particles. While upcoming CMB anisotropy experiments will be able to decrease the uncertainties on inflationary parameters such as $A_s$ and $n_s$ by about a factor 2 in the $Λ$CDM case, we find that an SD experiment 100 times more sensitive than PIXIE (comparable to the proposed Super-PIXIE satellite) could potentially further contribute to constrain these parameters. This is even more significant in the case of the running of the scalar spectral index. Furthermore, as expected, constraints on DM particles decaying at redshifts probed by SDs will improve by orders of magnitude even with an experiment 10 times worse than PIXIE as compared to CMB anisotropies or Big Bang Nucleosynthesis bounds. On the contrary, DM annihilation constraints will not significantly improve over CMB anisotropy measurements. Finally, we forecast the constraints obtainable with sensitivities achievable either from the ground or from a balloon.

preprint2021arXiv

The weak dependence of velocity dispersion on disk fractions, mass-to-light ratio and redshift: Implications for galaxy and black hole evolution

Velocity dispersion ($σ$) is a key driver for galaxy structure and evolution. We here present a comprehensive semi-empirical approach to compute $σ$ via detailed Jeans modelling assuming both a constant and scale-dependent mass-to-light ratio $M^*/L$. We compare with a large sample of local galaxies from MaNGA and find that both models can reproduce the Faber-Jackson (FJ) relation and the weak dependence of $σ$ on bulge-to-total ratio $B/T$ (for $B/T\gtrsim 0.25$). The dynamical-to-stellar mass ratio within $R\lesssim R_e$ can be fully accounted for by a gradient in $M^*/L$. We then build velocity dispersion evolutionary tracks $σ_{ap}[M^*,z]$ (within an aperture) along the main progenitor dark matter haloes assigning stellar masses, effective radii and Sersic indices via a variety of abundance matching and empirically motivated relations. We find: 1) clear evidence for downsizing in $σ_{ap}[M^*,z]$ along the progenitor tracks; 2) at fixed stellar mass $σ\propto(1+z)^{0.2-0.3}$ depending on the presence or not of a gradient in $M^*/L$. We extract $σ_{ap}[M^*,z]$ from the TNG50 hydrodynamic simulation and find very similar results to our models with constant $M^*/L$. The increasing dark matter fraction within $R_e$ tends to flatten the $σ_{ap}[M^*,z]$ along the progenitors at $z \gtrsim 1$ in constant $M^*/L$ models, while $σ_{ap}[M^*,z]$ have a steeper evolution in the presence of a stellar gradient. We then show that a combination of mergers and gas accretion are likely responsible for the constant or increasing $σ_{ap}[M^*,z]$ with time. Finally, our $σ_{ap}[M^*,z]$ are consistent with a nearly constant and steep $M_{bh}-σ$ relation at $z\lesssim 2$, with black hole masses derived from the $L_X-M^*$ relation.

preprint2020arXiv

"Love is as Complex as Math": Metaphor Generation System for Social Chatbot

As the wide adoption of intelligent chatbot in human daily life, user demands for such systems evolve from basic task-solving conversations to more casual and friend-like communication. To meet the user needs and build emotional bond with users, it is essential for social chatbots to incorporate more human-like and advanced linguistic features. In this paper, we investigate the usage of a commonly used rhetorical device by human -- metaphor for social chatbot. Our work first designs a metaphor generation framework, which generates topic-aware and novel figurative sentences. By embedding the framework into a chatbot system, we then enables the chatbot to communicate with users using figurative language. Human annotators validate the novelty and properness of the generated metaphors. More importantly, we evaluate the effects of employing metaphors in human-chatbot conversations. Experiments indicate that our system effectively arouses user interests in communicating with our chatbot, resulting in significantly longer human-chatbot conversations.

preprint2020arXiv

Drosophila-Inspired 3D Moving Object Detection Based on Point Clouds

3D moving object detection is one of the most critical tasks in dynamic scene analysis. In this paper, we propose a novel Drosophila-inspired 3D moving object detection method using Lidar sensors. According to the theory of elementary motion detector, we have developed a motion detector based on the shallow visual neural pathway of Drosophila. This detector is sensitive to the movement of objects and can well suppress background noise. Designing neural circuits with different connection modes, the approach searches for motion areas in a coarse-to-fine fashion and extracts point clouds of each motion area to form moving object proposals. An improved 3D object detection network is then used to estimate the point clouds of each proposal and efficiently generates the 3D bounding boxes and the object categories. We evaluate the proposed approach on the widely-used KITTI benchmark, and state-of-the-art performance was obtained by using the proposed approach on the task of motion detection.

preprint2020arXiv

IoTGaze: IoT Security Enforcement via Wireless Context Analysis

Internet of Things (IoT) has become the most promising technology for service automation, monitoring, and interconnection, etc. However, the security and privacy issues caused by IoT arouse concerns. Recent research focuses on addressing security issues by looking inside platform and apps. In this work, we creatively change the angle to consider security problems from a wireless context perspective. We propose a novel framework called IoTGaze, which can discover potential anomalies and vulnerabilities in the IoT system via wireless traffic analysis. By sniffing the encrypted wireless traffic, IoTGaze can automatically identify the sequential interaction of events between apps and devices. We discover the temporal event dependencies and generate the Wireless Context for the IoT system. Meanwhile, we extract the IoT Context, which reflects user's expectation, from IoT apps' descriptions and user interfaces. If the wireless context does not match the expected IoT context, IoTGaze reports an anomaly. Furthermore, IoTGaze can discover the vulnerabilities caused by the inter-app interaction via hidden channels, such as temperature and illuminance. We provide a proof-of-concept implementation and evaluation of our framework on the Samsung SmartThings platform. The evaluation shows that IoTGaze can effectively discover anomalies and vulnerabilities, thereby greatly enhancing the security of IoT systems.

preprint2020arXiv

Towards Learning-automation IoT Attack Detection through Reinforcement Learning

As a massive number of the Internet of Things (IoT) devices are deployed, the security and privacy issues in IoT arouse more and more attention. The IoT attacks are causing tremendous loss to the IoT networks and even threatening human safety. Compared to traditional networks, IoT networks have unique characteristics, which make the attack detection more challenging. First, the heterogeneity of platforms, protocols, software, and hardware exposes various vulnerabilities. Second, in addition to the traditional high-rate attacks, the low-rate attacks are also extensively used by IoT attackers to obfuscate the legitimate and malicious traffic. These low-rate attacks are challenging to detect and can persist in the networks. Last, the attackers are evolving to be more intelligent and can dynamically change their attack strategies based on the environment feedback to avoid being detected, making it more challenging for the defender to discover a consistent pattern to identify the attack. In order to adapt to the new characteristics in IoT attacks, we propose a reinforcement learning-based attack detection model that can automatically learn and recognize the transformation of the attack pattern. Therefore, we can continuously detect IoT attacks with less human intervention. In this paper, we explore the crucial features of IoT traffics and utilize the entropy-based metrics to detect both the high-rate and low-rate IoT attacks. Afterward, we leverage the reinforcement learning technique to continuously adjust the attack detection threshold based on the detection feedback, which optimizes the detection and the false alarm rate. We conduct extensive experiments over a real IoT attack dataset and demonstrate the effectiveness of our IoT attack detection framework.

preprint2019arXiv

Non-imaging single-pixel sensing with optimized binary modulation

The conventional high-level sensing techniques require high-fidelity images as input to extract target features, which are produced by either complex imaging hardware or high-complexity reconstruction algorithms. In this letter, we propose single-pixel sensing (SPS) that performs high-level sensing directly from coupled measurements of a single-pixel detector, without the conventional image acquisition and reconstruction process. The technique consists of three steps including binary light modulation that can be physically implemented at $\sim$22kHz, single-pixel coupled detection owning wide working spectrum and high signal-to-noise ratio, and end-to-end deep-learning based sensing that reduces both hardware and software complexity. Besides, the binary modulation is trained and optimized together with the sensing network, which ensures least required measurements and optimal sensing accuracy. The effectiveness of SPS is demonstrated on the classification task of handwritten MNIST dataset, and 96.68% classification accuracy at $\sim$1kHz is achieved. The reported single-pixel sensing technique is a novel framework for highly efficient machine intelligence.

preprint2019arXiv

The effects of KSEA interaction on the ground-state properties of spin chains in a transverse field

The effects of symmetric helical interaction which is called the Kaplan, Shekhtman, Entin-Wohlman, and Aharony (KSEA) interaction on the ground-state properties of three kinds of spin chains in a transverse field have been studied by means of correlation functions and chiral order parameter. We find that the anisotropic transition of $XY$ chain in a transverse field ($XY$TF) disappears because of the KSEA interaction. For the other two chains, we find that the regions of gapless chiral phases in the parameter space induced by the DM or $XZY-YZX$ type of three-site interaction are decreased gradually with increase of the strength of KSEA interaction. When it is larger than the coefficient of DM or $XZY-YZX$ type of three-site interaction, the gapless chiral phases also disappear.

preprint2016arXiv

Classical analog of Stückelberg interferometry with two coupled mechanical resonators

Coupled nanomechanical resonators have recently attracted much attention for both fundamental studies in physics and broad applications in high-precession detection or sensing. By studying the Landau-Zener transitions and Rabi oscillation of two coupled resonators, it has been shown that such a two-mode system acts as a classical two-level system bearing the analog to a quantum mechanical two-level one. Here we construct a Stückelberg interferometer with two coupled cantilevers by driving the system through the avoided crossing twice. By measuring the non-adiabatic phase acquired at the Landau-Zener transition, we unveil an in-depth analog between the two-mode and quantum two-level systems. Our study opens up new opportunities for constructing interferometers with classical devices.

preprint2016arXiv

Computer assisted proof for Apwenian sequences related to Hankel determinants

An infinite $\pm 1$-sequence is called {\it Apwenian} if its Hankel determinant of order $n$ divided by $2^{n-1}$ is an odd number for every positive integer $n$. In 1998, Allouche, Peyrière, Wen and Wen discovered and proved that the Thue--Morse sequence is an Apwenian sequence by direct determinant manipulations. Recently, Bugeaud and Han re-proved the latter result by means of an appropriate combinatorial method. By significantly improving the combinatorial method, we prove that several other Apwenian sequences related to the Hankel determinants with Computer Assistance.

preprint2016arXiv

FlowIntent: Detecting Privacy Leakage from User Intention to Network Traffic Mapping

The exponential growth of mobile devices has raised concerns about sensitive data leakage. In this paper, we make the first attempt to identify suspicious location-related HTTP transmission flows from the user's perspective, by answering the question: Is the transmission user-intended? In contrast to previous network-level detection schemes that mainly rely on a given set of suspicious hostnames, our approach can better adapt to the fast growth of app market and the constantly evolving leakage patterns. On the other hand, compared to existing system-level detection schemes built upon program taint analysis, where all sensitive transmissions as treated as illegal, our approach better meets the user needs and is easier to deploy. In particular, our proof-of-concept implementation (FlowIntent) captures sensitive transmissions missed by TaintDroid, the state-of-the-art dynamic taint analysis system on Android platforms. Evaluation using 1002 location sharing instances collected from more than 20,000 apps shows that our approach achieves about 91% accuracy in detecting illegitimate location transmissions.

preprint2016arXiv

Joint remote preparation of an arbitrary four-qubit |\c{hi}>-type entangled state

We present two schemes for joint remote preparation of an arbitrary four-qubit j\c{hi}i -type entangled state via three three- and (N+1)-qubit GHZ states as the quantum channel, respectively. In these schemes, two senders (or N senders) share the original state which they wish to help the receiver to remotely prepare. To complete the JRSP schemes, several novel sets of mutually orthogonal basis vectors are introduced. It is shown that, only if two senders (or N senders) collaborate with each other, and perform projective measurements under suitable measuring basis on their own qubits respectively, the receiver can reconstruct the original state by means of some appropriate unitary operations and suitable C-NOT gates. Compared with the previous schemes for the JRSP of four-qubit |\c{hi}>-type state, the advantages of the present schemes are that the total successful probability of JRSP can reach 1 and the entanglement resource can be reduced

preprint2016arXiv

Predicting Social Status via Social Networks: A Case Study on University, Occupation, and Region

Social status refers to the relative position within the society. It is an important notion in sociology and related research. The problem of measuring social status has been studied for many years. Various indicators are proposed to assess social status of individuals, including educational attainment, occupation, and income/wealth. However, these indicators are sometimes difficult to collect or measure. We investigate social networks for alternative measures of social status. Online activities expose certain traits of users in the real world. We are interested in how these activities are related to social status, and how social status can be predicted with social network data. To the best of our knowledge, this is the first study on connecting online activities with social status in reality. In particular, we focus on the network structure of microblogs in this study. A user following another implies some kind of status. We cast the predicted social status of users to the "status" of real-world entities, e.g., universities, occupations, and regions, so that we can compare and validate predicted results with facts in the real world. We propose an efficient algorithm for this task and evaluate it on a dataset consisting of 3.4 million users from Sina Weibo. The result shows that it is possible to predict social status with reasonable accuracy using social network data. We also point out challenges and limitations of this approach, e.g., inconsistence between online popularity and real-world status for certain users. Our findings provide insights on analyzing online social status and future designs of ranking schemes for social networks.

preprint2016arXiv

Trust Exploitation and Attention Competition: A Game Theoretical Model

The proliferation of Social Network Sites (SNSs) has greatly reformed the way of information dissemination, but also provided a new venue for hosts with impure motivations to disseminate malicious information. Social trust is the basis for information dissemination in SNSs. Malicious hosts judiciously and dynamically make the balance between maintaining its social trust and selfishly maximizing its malicious gain over a long time-span. Studying the optimal response strategies for each malicious host could assist to design the best system maneuver so as to achieve the targeted level of overall malicious activities. In this paper, we propose an interaction-based social trust model, and formulate the maximization of long-term malicious gains of multiple competing hosts as a non-cooperative differential game. Through rigorous analysis, optimal response strategies are identified and the best system maneuver mechanism is presented. Extensive numerical studies further verify the analytical results.

preprint2015arXiv

Joint Power Splitting and Secure Beamforming Design in the Wireless-powered Untrusted Relay Networks

In this work, we maximize the secrecy rate of the wireless-powered untrusted relay network by jointly designing power splitting (PS) ratio and relay beamforming with the proposed global optimal algorithm (GOA) and local optimal algorithm (LOA). Different from the literature, artificial noise (AN) sent by the destination not only degrades the channel condition of the eavesdropper to improve the secrecy rate, but also becomes a new source of energy powering the untrusted relay based on PS. Hence, it is of high economic benefits and efficiency to take advantage of AN compared with the literature. Simulation results show that LOA can achieve satisfactory secrecy rate performance compared with that of GOA, but with less computation time.

preprint2014arXiv

On $t$-extensions of the Hankel determinants of certain automatic sequences

In 1998, Allouche, Peyrière, Wen and Wen considered the Thue--Morse sequence, and proved that all the Hankel determinants of the period-doubling sequence are odd integral numbers. We speak of $t$-extension when the entries along the diagonal in the Hankel determinant are all multiplied by~$t$. Then we prove that the $t$-extension of each Hankel determinant of the period-doubling sequence is a polynomial in $t$, whose leading coefficient is the {\it only one} to be an odd integral number. Our proof makes use of the combinatorial set-up developed by Bugeaud and Han, which appears to be very suitable for this study, as the parameter $t$ counts the number of fixed points of a permutation. Finally, we prove that all the $t$-extensions of the Hankel determinants of the regular paperfolding sequence are polynomials in $t$ of degree less than or equal to $3$.

preprint2011arXiv

Laser spot position dependent photothermal mode cooling of a micro-cantilever

We explore the laser spot position (LSP) dependent photothermal mode cooling of a micro-cantilever in a Fabry-Pérot (FP) cavity. Depending on the LSP along the lever, photothermal coupling to the first two mechanical modes can be either parallel or anti-parallel. This LSP dependent behavior is analyzed theoretically by a simple model, which is in quantitatively agreement with our experimental observation. From simulation, the parallel and anti-parallel coupling region is identified along the lever. We conclude that a more efficient mode cooling may be achieved in the parallel coupling region.